Molecular Modeling

计算化学基本概念分子模拟(Molecular Modeling)泛指用于模拟分子或分子体系性质的方法，定位于表述和处理基于三维结构的分子结构和性质。

Quantum Mechanics (QM) 量子力学Molecular Mechanics (MM) 分子力学Theoretical Chemistry 理论化学Computational Chemistry 计算化学Computer Chemistry 计算机化学Molecular Modeling 分子模拟量子化学简介量子化学的研究范围和内容9稳定和不稳定分子的结构、性能，及其结构与性能之间的关系9分子和分子之间的相互作用9分子和分子之间的相互碰撞和相互反应等问题计算与预测各种分子性质(如分子几何构型、偶极矩、分子内旋势能、NMR、振动频率与光谱强度)预测化学反应过程中的过渡态及中间体、研究反应机理理解分子间作用力及溶液、固体中的分子行为计算热力学性质(熵、Gibbs函数、热容等)量子力学与经典力学的差别首先表现在对粒子的状态和力学量的描述及其变化规律上。

在量子力学中，粒子的状态用波函数来描述，它是坐标和时间的复函数。

为了描述粒子状态变化的规律，就需要找出波函数所满足的运动方程。

这个方程是薛定谔在1926年首先提出的，被称为薛定谔方程。

求解薛定谔方程，即可从电子结构层面来阐明分子的能量、性质及分子间相互作用的本质。

Schrödinger 方程The ab initio Molecular Orbital TheoryThe Hartree-Fock EquationThe Self-Consistent Field TheoryLinear Combination of Atomic OrbitalsBasis Sets: Slater-Type Orbitals(STO) and Gaussian-Type Orbitals(GTO) 当我们决定由原子轨道线性组合成分子轨道时，就要考虑采取什么数学形式来表示原子轨道。

分子动力学软件选择There are widely used packages like AMBER, CHARMm and X-PLOR/amber/amber.html//CHARMm and X-PLOR both use the same forcefield. Amber's is different.If you're Wintel-bound, you could try Hyperchem, which has a free downloadable demo: /products/hc5_features.htmlIt has a nice structure build capability (the other packages havepowerful languages, but can be intimidating to new users).OpenSource adherents can find a wealth of free packages at SAL, anexcellent site:/Z/2/index.shtmlMy personal favourites are MMTK, EGO and VMD/NAMD.I compiled a list of free and commerical programs at/chemistry/soft_mod_en.htmlmodeling in solution is possible e.g. with these programs (to the best of my knowledge):commercial: AMSOL, GROMOS, Titanfree: GAMESOL, GROMACS, MOIL, OMNISOL, TinkerYou find links to all of these programs at/chemistry/soft_mod_en.htmlPAPA (计算粒状物料的三维并行分子动力学计算程序)【URL】http://www.ica1.uni-stuttgart.de/Research/Software_P3T/papa.html【作者】 ICA 1 Group, Institute of Computer Applications (ICA) of the University of Stuttgart【语言版本】 English【收费情况】免费【用途】 Characteristic:dissipative interaction for rotating, rough, spherical particlesgeometry elements: walls, cylinders, spheres, etc freely configurablematerial properties of walls and particles freely configurable for an arbitray number of materialsobject oriented, written in C++full checkpointing supportedseveral compilation options: support of X11 graphics, reduction to 2D, debugging aids, etc. Applications:simulation of granular media, silo filling and steady flow problems, sphere packings of mono- and polydisperse systemProtoMol (分子动力学并行计算软件)【URL】/~lcls/Protomol.html【作者】 LCLS Group at the University of Notre Dame【语言版本】 English【操作系统】 SunOS 5.8, IRIX 6.5, Linux 2.4, AIX 5.1【收费情况】免费【用途】 PROTOMOL is an object-oriented component based framework for molecular dynamics simulations. The framework supports the CHARMM 19 and 28a2 force fields and is able to process PDB, PSF, XYZ and DCD trajectory files. It is designed for high flexibility, easy extendibility and maintenance, and high performance demands, including parallelization. The technique of multiple time-stepping has been used to improvelong-term efficiency, and the use of fast electrostatic force evaluation algorithms like plain Ewald, Particle Mesh Ewald, and Multigrid summation further improves performance. Longer time steps are possible using MOLLY, Langevin Molly and Hybrid Monte Carlo, Nose-Hoover, and Langevin integrators. In addition, PROTOMOL has been designed to interact with VMD, a visualization engine developed by the University of Illinois that is used for displaying large biomolecular systems in three dimensions. PROTOMOL is free distributed software, and the source code is in cluded.【相关链接】VMD (分子可视化软件)美国圣母大学：计算生命科学实验室Claessen站点的分子模型化软件【URL】/chemistry/soft_mod_en.html【简介】Molecular ModelingCommercial Software3D Viewer: converts 2D structures into 3D with simple MM2Alchemy 2000: semi empirical, QSAR, Protein, Polymer, LogPAMPAC: semiempirical quantum mechanical programAMSOL: semi empirical, solvation models for free energies of solvation in aqueous solutions and in alkane solventsPersonal CAChe: visualize molecules in 3D, search for conformations, analyze chemical reactivity and predict properties of compoundsQuantum CAChe: Personal CaChe plus molecular dynamics and semi-empirical MOPAC and ZINDO quantum mechanicsChem3D: MOPAC and Gaussian integration, ChemProp, ...Gaussian 98W: MP2, MP3, MP4, MP5, HF, CASSCF, GVB, QCISD, BD, CCSD, G1, G2, ZINDO, ONIOM calculations, DFT excited states, VCD intensities, ...GROMOS: general-purpose molecular dynamics computer simulation package for the study of biomolecular systemsHyperchem Suite: semi empirical, RMS Fit, Molecule Presentations, Sequence Editor, Crystal Builder, Sugar Builder, Conformational Search, QSAR Properties, ScriptEditor ...(Hyperchem Pro, Hyperchem Std.)Jaguar: electronic structure calculationMacroModel: allows the graphical construction of complex chemical structures mechanics and dynamics techniques in vacuo or in solutionMOPAC 2000: the latest version of MOPACSpartan: MM, semiempirical, ab initio, DFT, ...Titan: TITAN is the union of Wavefunction's versatile, easy-to-use interface with fast, computational algorithms from Schr鰀inger's JaguarWinMOPAC: based on MOPACShareware/Freeware3D Viewer for ISIS Draw: converts 2D structures into 3D with simple MM2Biomer: online java applet, model builders for polynucleotides (DNA/RNA), polysaccharides and proteins, interactive molecule editor, AMBER force-field based geometry optimization, simulated annealing with molecular dynamics, and the ability to save gif, jpeg, and ppm imagesChem3D Net: demo version of Chem3DCOLUMBUS: high-level ab initio molecular electronic structure calculationsDalton: quantum chemistry programGAMESOL: calculate free energies of solvation based on fixed, gas-phase solute geometries interfacing GAMESSGAMESS: General Atomic and Molecular Electronic Structure System is a general ab initio quantum chemistry packageGaussian Basis Set: get any Gaussian basis set you can imagineGROMACS: fully automated topology builder for proteins, molecular dynamics, leap-frog integrator, position langevin dynamics, normal mode analysis, electrostatics,non-equilibrium MD, NMR refinement with NOE data, large number of powerful analysis tools, ...Hückel: constructs the Hückel matrix, the programs then calculate, displayMOIL: molecular modeling, energy minimization and molecular dynamics simulation for biomolecules like proteinsMoldy: molecular dynamics simulation program, liquids, solids, rigid surfacesMOPAC: general purpose semiempirical molecular orbital package for the study of chemical structures and reactionsMOPAC 5.08mn: modified version of MOPACNWChem: quantum package for supercomputers and Linux, SCF, RHF, UHF, DFT, CASSCF, interface to Python programming languageOMNISOL: calculating free energies of solvation for organic molecules containing H, C, N, O, F, S, Cl, Br, and I in water and organic solventsPC GAMESS: GAMESS for the Intel communityQ: molecular dynamics package designed for free energy calculations in biomolecular systemTinker: molecular modeling software is a complete and general package for molecular mechanics and dynamicsVMD (分子可视化软件)【URL】/Research/vmd/【作者】 Biophysics Group,University of Illinois at Urbana-Champaign (UIUC)【语言版本】 English【收费情况】免费【用途】 VMD is a molecular visualization program for displaying, animating, and analyzing large biomolecular systems using 3-D graphics and built-in scripting. VMD supports computers running MacOS-X, Unix, or Windows, is distributed free of charge, and includes source code.VMD is designed for the visualization and analysis of biological systems such as proteins, nucleic acids, lipid bilayer assemblies, etc. It may be used to view more general molecules, as VMD can read standard Protein Data Bank (PDB) files and display the contained structure. VMD provides a wide variety of methods for rendering and coloring a molecule: simple points and lines, CPK spheres and cylinders, licorice bonds, backbone tubes and ribbons, cartoon drawings, and others. VMD can be used to animate and analyze the trajectory of a molecular dynamics (MD) simulation. In particular, VMD can act as a graphical front end for an external MD program by displaying and animating a molecule undergoing simulation on a remote computer. VMD uses OpenGL to provide high performance 3-D molecular graphics【相关链接】RasMol:3D分子结构显示程序PDB文件显示程序KineMage美国伊利诺依大学：理论生物物理学研究组JMV (Java分子可视化工具)ProtoMol (分子动力学并行计算软件)ORAC (用于模拟溶剂化生物分子的分子动力学计算程序, 意大利佛罗伦萨大学)【URL】http://www.chim.unifi.it/orac/【作者】 Massimo Marchi and P. Procacci【语言版本】 English【操作系统】 UNIX【收费情况】免费【用途】 ORAC is a program for running classical simulations of biomolecules. Simulations can be carried out in the NVE, NPT, NHP, and NVT thermodynamic ensembles. The integration of the equations of motion in any ensemble can be carried out with the r-RESPA multiple time step integrator and electrostatic interactions can be handled with the Smooth Particle Mesh Ewald method.【备注】A parallel version of ORAC4.0 (MPI/T3E) is available upon request to:Massimo MarchiSection de Biophysique des Proteines et des Membranes,DBCM, DSV, CEA, Centre d'Etudes,Saclay, 91191 Gif-sur-Yvette Cedex, FRANCEVirtual Molecular Dynamics Laboratory (分子动力学软件)【URL】/vmdl/index.html【作者】 Amit Bansil, Lidia Braunstein【语言版本】 English【收费情况】免费【用途】 The Virtual Molecular Dynamics Laboratory enables the student to visualize atomic motion, manipulate atomic interactions, and quantitatively investigate the resulting macroscopic properties of biological, chemical, and physical systems.The Virtual Laboratory is a suite of research-based molecular dynamics software toolsand project-based curriculum guides. The software tools are: "Simple Molecular Dynamics (SMD)", "Universal Molecular Dynamics", and "Water".【相关链接】美国波士顿大学聚合物研究中心(可视化模拟)DL_POLY (分子动力学模拟软件)【URL】/msi/software/DL_POLY/【作者】 W. Smith and T.R. Forester【语言版本】 English【收费情况】免费DL_POLY is supplied to individuals under a licence and is free of cost to academic scientists pursuing scientific research of a non-commercial nature. A group licence is also available for academic research groups. All recipients of the code must first agree to the terms of the licence.Commercial organisations interested in acquiring the package should approach Dr. W. Smith at Daresbury Laboratory in the first instance. Daresbury Laboratory is the sole centre for distribution of the package.【用途】 DL_POLY is a general purpose serial and parallel molecular dynamics simulation package originally developed at Daresbury Laboratory by W. Smith and T.R. Forester under the auspices of the Engineering and Physical Sciences Research Council (EPSRC) for the EPSRC's Collaborative Computational Project for the Computer Simulation of Condensed Phases (CCP5) and the Molecular Simulation Group (MSG) at Daresbury Laboratory. The package is the property of the Central Laboratory of the Research Councils.Two versions of DL_POLY are currently available. DL_POLY_2 is the original version which has been parallelised using the Replicated Data strategy and is useful for simulations of up to 30,000 atoms on 100 processors. DL_POLY_3 is a version which uses Domain Decomposition to achieve parallelism and is suitable for simulations of order 1 million atoms on 8-1024 processors.DL_POLY (分子动力学模拟软件)【URL】/msi/software/DL_POLY/【作者】 W. Smith and T.R. Forester【语言版本】 English【收费情况】免费DL_POLY is supplied to individuals under a licence and is free of cost to academicscientists pursuing scientific research of a non-commercial nature. A group licence is also available for academic research groups. All recipients of the code must first agree to the terms of the licence.Commercial organisations interested in acquiring the package should approach Dr. W. Smith at Daresbury Laboratory in the first instance. Daresbury Laboratory is the sole centre for distribution of the package.【用途】 DL_POLY is a general purpose serial and parallel molecular dynamics simulation package originally developed at Daresbury Laboratory by W. Smith and T.R. Forester under the auspices of the Engineering and Physical Sciences Research Council (EPSRC) for the EPSRC's Collaborative Computational Project for the Computer Simulation of Condensed Phases (CCP5) and the Molecular Simulation Group (MSG) at Daresbury Laboratory. The package is the property of the Central Laboratory of the Research Councils.Two versions of DL_POLY are currently available. DL_POLY_2 is the original version which has been parallelised using the Replicated Data strategy and is useful for simulations of up to 30,000 atoms on 100 processors. DL_POLY_3 is a version which uses Domain Decomposition to achieve parallelism and is suitable for simulations of order 1 million atoms on 8-1024 processors.PMDS (并行分子动力学模板库)【URL】http://stencil.koma.jaeri.go.jp/【作者】 Japan Atomic Energy Research Institute【语言版本】 English【收费情况】免费【用途】 Parallel Molecular Dynamics Stencil (PMDS) is an assembly of subroutine programs for executing parallel short-range molecular-dynamics simulations of solids. PMDS is written in C language using MPI for parallelization, and is designed to separate and conceal parts of the programs for parallel algorithms such as inter-processor communications so that parallel programming for force calculation can be done in the same way as serial programming; it can be easily revised according to physical models.MDRANGE (分子动力学计算ion ranges)【URL】http://beam.helsinki.fi/~knordlun/mdh/mdh_program.html【作者】 Kai Nordlund【语言版本】 English【收费情况】免费【用途】 The official name of the program is MDRANGE. However, in the actual program files the shorter, more convenient name mdh (abbreviated from Molecular Dynamics High-energy) is used. Both names therefore (at least for now) mean exactly the same program. The program is a molecular dynamics (MD) simulation program tailored for effective calculation of ion ranges. The word effective used here must be understood in the context of high-energy molecular dynamics calculations.What it doesCalculates ion ranges in solidsCalculates deposited energiesCalculates the primary recoil spectrumObtaining stopping powers possible indirectlyIon and sample elements which can be used: anyEnergy range in which calculation can be done: roughly 1 eV/amu - 10 MeV/amuEnergy range in which use is justified: roughly 100 eV/amu - 100 keV/amuMDRANGE3.0: option for Puska-Echenique-Nieminen-Ritchie(PENR)-electronic stopping model [Sil00]. Needs charge density file from user.MDRANGE3.0: option for Brandt-Kitakawa(BK)-electronic stopping model. Needs charge density file from user.【备注】Kai NordlundAccelerator Laboratory, University of Helsinki, P.O. BOX 43, FIN-00014 Helsinki, Finland (email kai.nordlund@helsinki.fi)Car-Parrinello分子动力学(CPMD, ab-initio分子动力学计算软件)【URL】/【作者】 Jurg Hutter【语言版本】 English【操作系统】 Unix/Linux【下载】 /ftp.html【收费情况】免费【用途】泛函：LDA，LSD，GGA，自由能密度泛函。

Available online at Recent development of in silico molecular modeling for gas and liquid separations in metal–organic frameworksJianwen JiangAs a new family of nanoporous materials,metal–organic frameworks(MOFs)are considered versatile materials for widespread applications.Majority of current studies in MOFs have been experimentally based,thus little fundamental guidance exists for the judicious screening and design of task-specific MOFs.With synergistic advances in mathematical methods,computational hardware and software,in silico molecular modeling has become an indispensable tool to unravel microscopic properties in MOFs that are otherwise experimentally inaccessible or difficult to obtain.In this article,the recent development of molecular modeling is critically highlighted for gas and liquid separations in MOFs.Bottom-up strategies have been proposed for gas separation in MOFs,particularly CO2capture.Meanwhile, interest for liquid separation in MOFs is growing and modeling is expected to provide in-depth mechanistic understanding. Despite considerable achievements,substantial challenges and new opportunities are foreseeable in more practical modeling endeavors for economically viable separationsin MOFs.AddressDepartment of Chemical and Biomolecular Engineering,National University of Singapore,117576,SingaporeCorresponding author:Jiang,Jianwen(chejj@.sg)Current Opinion in Chemical Engineering2012,1:138–144This review comes from a themed issue onNanotechnologyEdited by Hua Chun ZengAvailable online23rd December20112211-3398/$–see front matter#2011Elsevier Ltd.All rights reserved.DOI10.1016/j.coche.2011.11.002IntroductionDuring the past decade,metal–organic frameworks (MOFs)have emerged as a new family of nanoporous materials[1,2].In remarkable contrast to traditional inor-ganic zeolites,MOFs can be synthesized from various inorganic clusters and organic linkers,thus possess a wide range of surface area and pore size.More fascinatingly, the judicious selection of building blocks allows the pore volume and functionality to be tailored in a rational manner.With such salient features,MOFs are considered versatile materials for widespread potential applications [3,4]as illustrated in Figure1.Indeed,MOFs have been identified as a topical area in materials science and technology because of their implications for global and national economies[5].To date,thousands of MOFs have been synthesized in this vibrantfield and several(Cu-BTC,ZIF-8,MIL-53,etc.) are commercially available under the trade name Basoli-te TM[6].However,massive research efforts on MOFs have been primarily based on experiments.It is impractical to search for task-specific MOFs by trial-and-error from infinitely large number of possible candidates.Therefore, quantitative guidelines are desired for the high-throughput screening of enormous MOFs and the rational design of new MOFs towards practical applications.In this context, clear and deep microscopic understanding from a molecu-lar level is indispensable.With synergistic advances in mathematical methods,computational hardware and soft-ware,in silico molecular modeling has played an increas-ingly important role in unraveling microscopic properties in MOFs[7 ,8 ,9 ].Sophisticated modeling and simu-lation provide molecular insights that are experimentally intractable,if not impossible,thus elucidate underlying physics from bottom-up.Among many potential appli-cations of MOFs,separations are of central importance in chemical industry and have been actively investigated [10].In this article,the recent development of molecular modeling is critically highlighted for both gas and liquid separations in MOFs,and the foreseeable challenges and opportunities are discussed.Gas separationThe overwhelming majority of studies for gas separation in MOFs have been focused on CO2capture.This is because the combustion of fossil fuels produces a huge quantity of CO2emissions into the atmosphere.Carbon capture and sequestration is crucial to environmental protection and sustainable economy.As an essential pre-requisite,CO2has to be captured fromflue gas/ shifted syngas in post-/pre-combustion processes. Another important gas separation involving CO2is puri-fication of natural gas,in which impurities such as CO2 need to be separated to enhance calorie content.MOF adsorbentsMost synthesized MOFs are crystallites and tested as adsorbents for gas separation.Several reviews have sum-marized numerous experimental studies for CO2capture in MOF adsorbents[11–13].Nevertheless,nearly all these experiments examined the adsorption of pure gases (e.g.CO2,N2,CH4,and H2)due to the formidable difficulty associated with mixtures.By contrast,simu-lation can be readily used for single or multi-componentsystems.Thus,quantitative understanding of mixture adsorption in MOFs has been obtained,to a large extent,from simulation studies.Several bottom-up strategies as illustrated in Figure 2have been proposed to tune CO 2capture performance,for example,using specific MOFs with small pores,catenation,functionalization,ionic fra-meworks,exposed metals or metal doping.Yang and Zhong [14]simulated the adsorption of CO 2/CH 4/H 2mixture in two MOFs (IRMOF-1and Cu-BTC)and found pore size strongly affects separation efficiency.However,IRMOF-1and Cu-BTC do not possess iden-tical topology,leading to ambiguous interplay with the effect of pore size.In this regard,Babarao et al.[15]examined the separation of CO 2/CH 4mixture in isostruc-tural MOFs (Cu-BTC and PCN-60)and observed that the selectivity in Cu-BTC with small pores is nearly twice of that in PCN-60.This strategy of small pores is also reflected in framework catenation that can induce con-stricted pores and greater potential overlaps.For example,catenated IRMOF-13and PCN-6exhibit a larger selectivity for CO 2/CH 4mixture than non-cate-nated counterparts [15].An appealing strategy is to use ionic MOFs as demonstrated by Jiang and co-workers [16,17 ,18]for the separation of CO 2-containing mixtures.Simulation reveals that CO 2molecules are strongly adsorbed onto the ionic frameworks and nonframeworkions,and the predicted selectivity is significantly higher than in neutral MOFs and many other nanoporous materials.On the other hand,Yazaydin et al.[19]screened a diverse set of 14MOFs for low-pressure CO 2capture from flue gas combining simulation and experiment.The results show that M/DOBDC (M =Zn,Mg,Co or Ni)with high density of exposed metals strongly interact with CO 2.By physical and chemical doping,Xu et al.[20 ]estimated the separation of CO 2/CH 4mixtures in Li-modified MOF-5.Owing to the enhancement of electro-static potentials,adsorption selectivity was predicted to be much higher than in MOF-5.In a separate study,Lan et al.[21 ]simulated CO 2capture in covalent-organic frameworks doped by alkali,alkaline-earth and transition metals,and concluded that Li is the best surface modifier for CO 2capture.The strategies outlined in Figure 2have been compre-hensively discussed [24 ,25 ].Two of them (ionic fra-meworks and metal doping)appear to be more efficient to enhance CO 2capture.It should be noted that these strategies also can tune the separation of other mixtures,for example,the selectivity of alkane isomers was found to be enhanced by framework catenation [26].In a recent perspective,Krishna and van Baten [27 ]highlighted the potency of simulation in screening of best MOFs for CO 2capture and hydrocarbon separation,and they furtherRecent development of in silico molecular modeling Jiang 139Figure 1Purification Toxics RemovalDrug DeliveryFuel Cell SystemsStorageStorage and SeparationCarbon SequestrationSensingMOPWidespread potential applications of MOFs (/ees6/clathrates/index.shtml ).compared MOFs against traditional zeolites with regard to separation characteristics.As an alternative to simulation,analytical theories have been developed for gas separation in MOFs.Liu et al.[28,29]proposed a density functional theory (DFT)in 3D-nanoconfined space.The theory was applied to adsorption and separation in 3D-MOFs with complex pore networks,whereas most DFT studies are limited in simple confined geometries (e.g.slit and cylindrical pores).Good agree-ment was obtained between theoretical predictions,simu-lation and experimental data.Coudert et al.[30]developed the osmotic framework adsorbed solution theory (OFAST)in terms of a competition between host’s free energy and adsorption energy.This theory is based exclusively on pure-component adsorption and has the superior capability to describe flexible MOFs.For illustration,the authors used the OFAST to examine the effect of breathing on separation of CO 2/CH 4mixtures in MIL-53.The modeling studies discussed above for gas separation in MOF adsorbents are primarily focused on adsorption selectivity.However,several other factors (e.g.working capacity,regenerability,etc.)should be included in prac-tice as discussed by Bae and Snurr [31 ].Another crucial issue is how moisture in gas mixtures would affect sep-aration performance?From systematical simulation stu-dies in various neutral and ionic MOFs,Jiang and coworkers observed four different intriguing effects ofH 2O on CO 2capture [25 ].It is also instructive to examine structural change in flexible MOFs that might occur upon adsorption [32].The incorporation of flexi-bility to simulate structural change would need a robust force field.However,a general force field is currently unavailable for MOFs and first-principles modeling is expected to play a pivotal role [33 ].In addition,the chemical and thermal stability of MOFs are important for separation [34].A large number of MOFs are unstable in atmosphere or under moisture,which impedes their util-ization.Therefore,it is indispensable to develop molecu-lar guidelines for the design of stable MOFs.Nevertheless,unraveling what govern the stability of MOFs at a microscopic level is a challenge.MOF membranesCompared with adsorptive separation,membrane-based separation is considered to be energetically more effi-cient,lower capital cost and larger separation capability.However,the fabrication of MOF membranes is a for-midable task [35].Only in recent years,have there been active experimental endeavors to explore MOF mem-branes for gas separation [36 ].Since both equilibrium and dynamic properties are required,simulation for gas separation in MOF mem-branes is more time-consuming than in MOF adsorbents.Nevertheless,a handful of simulation studies have been reported.Keskin and Sholl [37 ]examined the separation140NanotechnologyFigure 2functionalizationmetal dopingionic frameworksexposed metalssmall porescatenationBottom-up strategies to tune CO 2capture performance.The representative MOFs are from [15,17 ,20 ,22,23].performance of diverse MOFs for CO2/CH4and CO2/H2 mixtures.They found that all the MOFs examined exhi-bit unfavorably low CO2selectivities and mixture effects play a crucial role in determining the performance.By combining simulation and IR microscopy,Bux et al.[38] simulated ethene/ethane separation in ZIF-8membrane. They found that ethane adsorbs more strongly than ethene,but ethene diffuses faster;and the interplay results in a membrane permeation selectivity for ethene. Krishna and van Baten[27 ]underlined the advantages of using simulation tools in the screening of MOF mem-branes for CO2capture.Along with considerable interest in MOF membranes, MOF-based composite membranes have received increasing attention for gas separation.In this emerging area,a handful of experiments have been conducted[39], but modeling studies are ing atomistic simulation and continuum model,Keskin and Sholl[40]attempted to select MOF/polymer membranes for high-perform-ance gas separation.A highly selective MOF was ident-ified and predicted to enhance the performance of Matrimid and other polymers for CO2/CH4separation. Chen et al.[41]proposed a composite with ionic liquid (IL)supported on IRMOF-1.The simulation reveals that ions in the composite act as favorable sites for CO2adsorption,and the selectivity for CO2/N2mixture is higher than in neat IL,IRMOF-1and many other supported IL membranes.It is worthwhile to note that defects and inter-crystalline interstices usually exist in synthesized MOF membranes. Nevertheless,most simulation studies use perfect and rigid models for MOF membranes.How to incorporate defects and interstices into practical modeling is challenging.On the other hand,theflexibility of MOF structures may have a larger influence in membrane separation than adsorbent separation[36 ],and should be implemented as well into modeling.Another essential issue is the mech-anical properties of MOFs[42].The high pressure exerted for membrane separation may distort MOF structures and deteriorate performance.It is thus crucial to quantitatively understand how pressure affects pore geometries and framework dimensionalities.For MOF-based composite membranes,microscopic insights into the interactions between MOF and other species(e.g.polymer or ionic liquid)are strikingly important and fundamental studies at a molecular level are desired.Liquid separationWhile gas separation in MOFs has been extensively investigated,endeavors for liquid separation are lagged behind[43 ].A recent trend has been to explore the use of MOF adsorbents and membranes for liquid separation. By combining chromatographic and breakthrough exper-iments,Alaerts et al.determined the adsorption and separation of ortho-substituted alkylaromatics(xylenes, ethylbenzene,ethyltoluenes and cymenes)in a column packed with MIL-53crystallites[44].Jin and coworkers tested the separation of water/organics mixtures in MIL-53membrane and observed a high selectivity for water removal from ethyl acetate solution[45].Simulation for liquid separation in MOFs is scarce owing to the significant amount of computational time required to sample liquid phase.Consequently,the microscopic understanding of liquid separation in MOFs is far from complete.To the best of our knowledge,only two simu-lation studies have been reported in this area,one for water desalination and the other for biofuel purification. Recent development of in silico molecular modeling Jiang141Figure3Selectivities of biofuel in Na-rho-ZMOF and Zn4O(bdc)(bpz)2by pervaporation[47 ].Specifically,Hu et al.[46]performed simulation on the desalination of NaCl aqueous solution through a ZIF-8 membrane by reverse osmosis.Because of the sieving effect of small apertures in ZIF-8,Na+and ClÀions could not transport through ZIF-8membrane and water desa-lination was observed.Theflux of water permeating the membrane was found to scale linearly with external pressure.In a separate study,Nalaparaju et al.[47 ] examined hydrophilic Na-rho-ZMOF and hydrophobic Zn4O(bdc)(bpz)2for biofuel purification.The selectiv-ities between water and ethanol in the two MOFs are largely determined by adsorption behavior.As indicated in Figure3,Na-rho-ZMOF is preferable to remove water, whereas Zn4O(bdc)(bpz)2is promising to enrich ethanol. The simulation provides molecular guidelines for the selection of appropriate MOFs towards efficient biofuel purification.Currently,modeling for liquid separation in MOFs is very limited.With increasing demands for clean water,liquid fuels and other liquid-based applications,more efforts are expected in order to provide deep molecular insights.A pre-requisite for liquid separation is that the MOFs used should be stable in water or other liquids[48],it is crucial to understand what factors govern the stability of MOFs, which would allow to produce stable MOFs for liquid separation.ConclusionAs a burgeoningfield,research activities in MOFs are rather hectic.In addition to enormous experimental stu-dies,we have witnessed the recent development of in silico molecular modeling for MOFs.Microscopic under-standing has been achieved for gas separation particularly CO2capture in MOFs,and bottom-up strategies have been proposed to enhance separation efficiency.How-ever,liquid separation in MOFs remains largely unex-plored at a molecular level and more endeavors are desired towards this end.It is obvious that current molecular modeling for separ-ations using MOFs is still in an infant stage.As discussed above,substantial challenges are foreseen for more prac-tical modeling and precise description.A number of issues should be considered in future modeling,such as the stability and mechanical properties of MOFs, structuralflexibility,material regenerability,and effect of moisture(in gas separation).These challenges provide new opportunities for modeling studies to unravel in-depth microscopic insights and thus provide quantitative guidelines on the rational screening and design of novel MOFs.Furthermore,for energy-efficient and cost-effec-tive separations,process requirements are essential to be integrated with material properties at a system level.In this context,molecular modeling,process optimization, as well as material synthesis,should be synergized holi-stically towards 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An efficient approximate method is introduced to screen MOF mem-branes for gas separation with a connection between mixture adsorption and mixture self-diffusion properties.The method is applied to MOF membranes with chemical diversity for light gas separation.38.Bux H,Chmelik C,Krishna R,Caro J:Ethene/ethane separationby ZIF-8membrane:molecular correlation of permeation,adsorption,diffusion.J Membr Sci2011,369:284-289.39.Vinh-Thang H,Kaliaguine S:MOF-based mixed-matrix-membranes for industrial applications.In CoordinationPolymers and Metal Organic Frameworks.Edited by Ortiz OL,Ramı´rez LD.Nova Science Publishers;2011.40.Keskin S,Sholl DS:Selecting metal organic frameworks asenabling materials in mixed matrix membranes for highefficiency natural gas purification.Energy Environ Sci2010,3:343-351.41.Chen YF,Hu ZQ,Gupta KM,Jiang JW:Ionic liquid/metal–organicframework composite for CO2capture:a computationalinvestigation.J Phys Chem C2011,115:21736-21742.42.Tan JC,Cheetham AK:Mechanical properties of hybridinorganic-organic framework materials:establishingfundamental structure–property relationships.Chem Soc Rev 2011,40:1059-1080.43.Cychosz KA,Ahmad R,Matzger AJ:Liquid phase separation by crystalline microporous coordination polymers.Chem Sci2010,1:293-302.This perspective details the experimental studies reported on liquid-phase separation using microporous coordination polymers(MCPs).Guest mole-cules examined include those as small as water to large organic dyes.In many cases,MCPs outperform zeolites and activated carbons in both kinetics and efficiency.Recent development of in silico molecular modeling Jiang143。

How to predict diffusion of medium-sized molecules in polymer matrices. From atomistic to coarse grainsimulationsAbstract :The normal diffusion regime of many small and medium-sized molecules occurs on a time scale that is too long to be studied by atomistic simulations. Coarse-grained (CG) molecular simulations allow to investigate length and time scales that are orders of magnitude larger compared to classical molecular dynamics simulations, hence providing avaluable approach to span time and length scales where normal diffusion occurs. Here we develop a novel multi-scale method for the prediction of diffusivity in polymer matrices which combines classical and CG molecular simulations. We applied an atomistic-based method in order to parameterize the CG MARTINI force field, providing an extension for the study of diffusion behavior of penetrant molecules in polymer matrices. As a case study, we found the parameters for benzene (as medium sized penetrant molecule whose diffusivity cannot be determined through atomistic models) and Poly (vinyl alcohol) (PVA) as polymer matrix. We validated our extended MARTINI force field determining the self diffusion coefficient of benzene (2.27·10−9m2s−1) and the diffusion coefficient of benzene in PVA(0.263·10−12m2s−1). The obtained diffusion coefficients are in remarkable agreement with experimental data (2.20·10−9m2s−1 and 0.25·10−12m2s−1, respectively). We believe that this method can extend the application range of computational modeling, providing modeling tools to study the diffusion of larger molecules and complex polymeric materials.Keywords:Coarse grain . Diffusion .Molecular dynamics simulation . Multi scale models . Nanofiltration . Polymeric matricesIntroduction:Molecular dynamics (MD) simulations are a powerful tool in the material science field as they provide material’s structural and dynamics details that are difficult, cost- or time-consuming to be assessed with experimental techniques. In particular, MD simulations are a valid tool for the design of polymeric membranes with tuned permeability properties. Up to now, however, the design of barrier materials is based on trial and error experimental procedures, in which a large part of the effort is spent to synthesize and characterize materials and blends which finally turn out to be unsatisfactory.Atomistic simulation have been successfully applied in the past to obtain the diffusion coefficients of small molecules (like oxygen, carbon dioxide or water) inpolymeric membranes [1–7], polymeric blends [8, 9], biopolymers [10, 11] and organic-inorganic hybrid membranes [12]. However, despite the increasing computational power available to researchers and the improvements in the MD codes, atomistic simulations are still able to handle only systems with tens or hundreds of thousands of atoms and in the nanoseconds time scale. Several phenomena of interest at the material scale, however,cover time and space scales larger than those affordable with atomistic modeling. This is the case of normal diffusion regime. The diffusion coefficient D can be directly calculated from the motion of the particles extracted during a MD simulation, in particular from the mean square displacement (MSD) of the particles, using the Einstein equation [5]. This equation holds only in the case that the observation time (i.e., the simulation time) is large enough to allow the particles to show uncorrelated motion. This means that the MSD is linear with time, i.e., MSD∼t n where n=1. Conversely, if n<1 then the diffusion is in the anomalous diffusion regime. Therefore, in order to assess an accurate diffusion coefficient, MD simulations must reach the normal diffusive regime which, depending on the membrane and diffusive molecule, can be on time scales higher than few nanoseconds. This regime is therefore often difficult to reach for molecules larger than diatomic molecules, like water or benzene, hindering molecular simulations to assess an accurate diffusion coefficient [12, 13].Recently, the use of coarse grain (CG) modeling, in which a number of atoms are condensed into beads or interacting particles, has proven to be a suitable option to model large systems and long time scales, providing realistic results. The methods, assumptions and level of resolution greatly vary depending on the scope of the models and the properties of interests [14, 15]. CG models have been developed with particular focus on biomolecular systems, since biomolecules are often too large and their characteristic times too long to be treated with full atomistic simulations. However, there are no theoretical impediments to the application of CG methods to polymeric materials.In this view, of particular interest is the coarse grain force field developed by Marrink and co-workers and called MARTINI force field. This CG force field was originally developed to model the lipid bilayers forming the cellular membranes and then extended to proteins [16–18]. Unlike other CG models, which focus on accurate modeling of a particular state or a particular molecule, the philosophy of the MARTINI force field is to accurately parameterize the basic building blocks of the system (e.g., the single amino acids for proteins), thus allowing a broad spectrum of applications without the need of reparameterization.Relying on the same philosophy, in this work we present an atomistic-informed parameterization of the MARTINI force field for the modeling of penetrants diffusion in polymeric membranes. We used atomistic simulations to calculate the interaction free energy between the basic building blocks of the system, i.e., the penetrant molecule and the polymer monomers, and then we performed CG molecular dynamics simulations to assess the diffusion behavior. As a test case, we investigated the diffusion behavior of benzene in a matrix of Poly (vinyl alcohol), PVA. Benzene, an important industrial solvent and precursor in the production of drugs, plastics,synthetic rubber, and dyes, was chosen since it is a well known representative of medium-sized permeant molecules. On the other hand, the choice of PVA as the polymer matrix is based on the fact that this polymer is widely used in several fields and finds applications as membrane material due to its excellent chemical stability, film forming capacity, barrier properties and high hydrophilicity.Methods:Coarse grain mappingThe original MARTINI mapping scheme is based on the four-to-one rule, i.e., on average four heavy (nonhydrogen) atoms are grouped into a bead or interaction center. Here we used a similar mapping, where the benzene molecule is represented by one bead and the vinyl alcohol (VA) monomers are represented by a different bead (see Fig. 1). The mass of the two types of beads are calculated as the sum of the masses of the atoms grouped into the bead.Bonded and nonbonded interactionsThe chemically bonded beads interact through a bond interaction modeled as a harmonic potential Vbond(r):where r is the distance between two bonded beads, kbond is the force constant of the bond interaction and r0 is the equilibrium distance. In the system under investigation, only VA beads representing chemically bonded monomers along a PVA chain are subject to bond interactions.The beads i and j that are not chemically connected interact via nonbonded interactions, which are described by a Lennard-Jones 12-6 potential:where r is the distance between the two nonbonded beads, εij is the energy minimum depth (the strength of the interaction) and r0ij is the distance at the minimum of the potential.ParameterizationGiven the mapping scheme and the type of interaction, we needed to calculate one set of bonded parameters (for bonded VA–VA beads) and three sets of nonbonded parameters (VA–VA, benzene–benzene and VA–benzene). For each set we run a full atomistic simulation of the two groups involved in the interaction and we calculated the free energy of interaction between the two groups. The free energy calculationsare performed using the adaptative biasing force (ABF) framework [19] as implemented in the NAMD code [20, 21]. The atomistic MD simulations are carried out using the NAMD program and the all-atom CHARMM force field [22], for a simulation time of 40 ns (time step of 1 fs) at a temperature of 300 K. Nonbonded interactions are computed using a switching function between 20 and 22 Å. The free energy of interaction, computed via the ABF framework, is monitoredbetween the two groups of atoms as a function of their center-of-mass distance, in the range 2–20 Å using windows of 0.01 Å.Generation of the CG modelsWe generated three different molecular models: pure benzene, pure PVA and PVA with a small amount of benzene as penetrant molecule. All three systems were generated in the atomistic form using the Amorphous Cell construction tool of Materials Studio 4.4 (Accelrys, Inc.). The pure benzene system contained 500 benzene molecules in a cubic periodic box with initial density of 0.88 gcm−3. For the pure PVA system we considered six atactic PVA molecules (consisting of 200 repeat units) in a cubic periodic box with initial density of 1.25 gcm−3. Finally, the third system contained four PVA chains (of 200 repeat units) and 12 benzene molecules in a cubic periodic box with initial density of 1.25 gcm−3. The three atomistic systems are then converted into CG systems using the Coarse Grainer tool of Materials Studio according to the mapping scheme described above (see Fig. 2).CG simulationsCG molecular dynamics simulations are carried out using the Mesocite module and the MARTINI force field implemented in Materials Studio. Prior to the simulations, we modified the original force field including the parameters for bonded and nonbonded interactions between benzene and VA beads, as obtained from the ABF atomistic simulations. The CG systems are minimized for 1000 steps, then equilibrated for 1 ns (using a time step of 20 ps) at 300 K. Finally, production simulations are run for asimulated time of 10 ns (for pure benzene and pure PVA) and 200 ns (for benzene in PVA matrix). The diffusion coefficient Di of a single permeant molecule i is calculated by the Einstein relation, starting from the diffusion trajectory ~rietT which is determined during the production MD simulations:where represents the root mean square displacement (MSD) of the permeant molecule i averaged over all possible time origins and t represents the time. The computationally derived diffusion coefficient D for a given kind of permeant molecule is then obtained as average overthe diffusion coefficients for N permeant molecules:In this work the diffusion of all 500 benzene beads (for benzene self diffusion) and the 12 benzene beads (for benzene in PVA) was investigated during the CG simulations.Results:The parameters of the CG force field, i.e. the bonded and nonbonded interactions between the beads, are calculated through full atomistic simulations and by applying the ABF framework. The ABF calculations provide the free energy profile as a function of the distance between the group of atoms, as shown in Fig. 3. The free energy profile of two bonded VA monomers (Fig. 3a) is interpolated with a harmonic potential, giving the equilibrium distance and the force constant (see Table 1). On the other end, from the interaction free energy profiles between nonbonded VA monomers, benzene molecules and VA-benzene molecules (Fig. 3b–d) we obtained the three sets of r0 (energy minimum) and ε(energy minimum depth), used to feed the Lennard-Jones 12-6 potential of the CG force field (see Table 1).We used the CG approach to investigate three different systems: pure benzene, pure PVA and benzene molecules in a PVA matrix (see Fig. 2). The pure benzene system consisted of 500 benzene molecules, which were coarse grained into benzene beads. We measured the density of the system during the 1 ns equilibration obtaining a realistic value of 0.881±0.001 gcm−3 (where the experimental value is 0.876 gcm−3). After the equilibration we carried out a 10 ns simulation in which we monitored the MSD of the benzene molecules (see Fig. 4a) and, by applying Eq. 3, we determined the self diffusion coefficient of benzene, obtaining a value of 2.273±0.588·10−9m2s−1, very close to the experimental value of 2.203±0.004 ·10−9m2s−1 [23]. In the case of pure PVA the system consisted of a periodic box with six chains of 200 monomers each. The coarse grained system was equilibrated for 1 ns and the density of the CG PVA box was measured, giving a value of 1.305± 0.011 gcm−3, which lie in the experimental range (1.232– 1.329 gcm−3) [24]. Finally, the third system consisted of 12 benzene molecules diffusing in a PVA matrix. The density of the coarse grained system, measured at the end of 1 ns equilibration, was 1.293±0.003, similar to that of pure PVA. The MSD of the benzene beads was monitored during a 200 ns MD simulation (see Fig. 4b), and from the derivative of the curve, we calculated the diffusion coefficient of benzene in PVA. We obtained a diffusion coefficient of0.263±0.035·10−12m2s−1 which is in good agreement with the experimental value, that is 0.25·10−12m2s−1[12]. The 200 ns simulation of the 4 nm×4 nm×4 nm CG box (with 812 beads representative of ≈6000 atoms) took 36 hours on a single CPU. The results of the simulations as well as the experimental data are shown in Table 2.Table 1 Parameters of the CG force field, obtained fromfull atomistic free energy calculations.Within this approach bonded interactions (i.e., VA beads covalently connected) are modeled through a harmonic potential, while nonbonded interactions are approximated with a Lennard-Jones 12-6 potentialInteraction Bonded Nonbondedkbond (kcal/mol/Å2) r0 (Å) ε(kcal/mol) r0 (Å) VA–VA 40.36 2.76 1.306 4.115 VA–Benzene - - 0.957 5.51 Benzene–Benzene - - 0.9634 5.62 Table 2 Main results of the CG simulations. The conversion of the three systems under study fromatomistic to coarse grain reduces the interacting particles by a factor between 7 and 12, depending on the specific system. Despite the loss of atomistic details, the CG models feature realistic densities and are able to predict benzene diffusion coefficient very close to the experimentsSystems Totalatoms TotalbeadsFinal density(g/cm3)Experimentaldensity (g/cm3)PredictedDbenzene(m2/s)ExperimentalDbenzene(m2/s)500 benzene molecules 6000 500 0.881 0.876 2.273·10−9 2.203·10−9[23]6 PVA chains 8400 1200 1.305 1.23–1.32 [24] --4 PVA chains + 12 benzene 5744 812 1.293 -- 0.263·10−120.25·10−12[24]Discussion:In this work we present a multi-scale method for the parameterization of the MARTINI CG force field and its application for the calculation of the diffusivity of medium sized molecules in polymeric membranes. In the past, atomistic simulations have been already successfully applied for the calculation of diffusivity of small molecules in polymeric membranes. Nonetheless, the computational costs can hinder the ability of MD simulations to predict such a parameter. Indeed, the Einstein relation (Eq. 3) applied for the assessment of the diffusion coefficient can only be used when the simulation is in the regime of normal diffusion and this realm is reached when the slope of the function log[MSD(t)] = f [log(t)] equals 1. In the case of very small molecules, like oxygen or hydrogen, the normal diffusion regime can be reached within few nanoseconds [5] while, in the case of medium sized molecules like benzene [12] or even water [13], it cannot be reached within the limit of atomistic simulations. In this view, the use of CG simulations, where a number of atoms are condensed into beads or interacting particles, can be a useful approach to overcome the limitations of atomistic simulations.In order to test the feasibility of the CG approach, we investigated the self diffusion coefficient of benzene and its diffusivity in PVA matrix using an atomistic-informed CG force field (see Fig. 1). As shown in Table 2, the coarse graining reduces the number of interacting particles by a factor of ≈10. Furthermore,since the CG interactions are much smoother compared to atomistic interactions [16], it is possible to use a time step of 20–40 fs, much larger than that typical of classical MD (1–2 fs). Thus, the CG approach leads to a total speed-up factor of 200–400 with respect to atomistic simulations.In this work we did not rely on the standard MARTINI bead types but rather we defined two ad hoc bead types (one for benzene molecule and one for VA monomer) and we estimated the bonded and nonbonded parameters using atomistic free energy calculations.The predicted parameters are then used to feed the MARTINI force field. The extended force field is then used to perform CG molecular dynamics simulations of three different systems: pure benzene, pure PVA and benzene in PVA (see Fig. 2). The coarse grain systems underwent1 ns equilibration dynamics, during which they reached a stable density very close to the experimental values (Table 2), thus confirming that the outcome of the atomistic free energy calculations are reasonable. As a final validation of our approach, we ran longer CG simulations in order to assess the self diffusion coefficient of benzene and the diffusion coefficient of benzene in PVA. For the pure benzene, we ran a 10 ns simulations from which we estimated the diffusion coefficient. The calculated and the experimental values are shown in Table 2, and the comparison confirms that the CG model is able topredict the experimental value with good approximations. In the case of benzene diffusing in a PVA matrix, 10 ns of simulation were not enough to reach the normal diffusion regime, since the derivative of the function log[MSD(t)] =f [log(t)] was lower than 1. This result is in agreement with the observations of Pan et al. [12], which showed that MD simulations of a few nanoseconds are not long enough to reach the normal diffusion regime and provide a good estimation of benzene diffusivity in PVA. For this reason, we run a longer simulation of 200 ns, in order to reach the realm of normal diffusivity, as shown in Fig. 5. Indeed, the trajectory of this long simulation permitted us to obtain a diffusion coefficient very close to the experimental value (see Table 2). This result confirms the feasibility of the CG approach to reach the normal diffusion regime of medium sized molecules in polymer matrices and that our multi-scale approach is a valid method to treat this kind of problem.Fig. 5 Log(MSD) vs. log(t) plots (straight lines) and linear interpolation (dashed lines) for the self diffusion of benzene (panel a) and for the diffusion of benzene in PVA (panel b) obtained from CGsimulations. The plots show that in the case of pure benzene the normal diffusion regime is reached, as indicated by the slope very close to 1, already in the range from 10to 101ns, while in the case of benzene in PVA (panel b) a longer simulation time is required since the normal diffusion regime is reached in the range from 101.7 to 102.3ns (i.e., from 50 to 200 ns)The major limitation of atomistic computational techniques applied in the literature to solve diffusive problems is related to the restricted time scale and sample size which can be simulated, which are a few nanoseconds and a few nanometers, respectively. Thus, when the phenomena under investigation exceed these limits MD simulations fail to provide reliable values of the diffusivity. In order to overcome these limitations we developed a novel method, which consits of combining atomistic and coarse grain simulations in a multi-scale paradigm, where the parameters for the meso-scale model are derived from atomistic MD simulations. Similar techniques are increasingly applied for the study of biological problems, but to the best of our knowledge, have not been used for the investigation of diffusion problems. Here we showed that this technique can be successfully applied to investigate the diffusion of penetrant molecules in polymer matrices, reliably predicting experimental data. A similar method as used in this paper could be applied to study the diffusion of larger molecules, which require a longer time to reach the normal diffusion regime, or the study of complex polymeric materials, for which representative volumes are larger than a few cubic nanometersConclusions:In conclusion, the main focus of this work has been to develop and validate a novel multi-scale method for the prediction of diffusivity in polymer matrices. We demonstrated that atomistic-informed CG simulations can be a valid approach to treat problems where the computational limits of classical MD simulations are too restrictive while, at the same time, strictly atomistic details are not mandatory. Thus, the multi-scale approach presented in this work extends the application range of computational modeling and provide a useful tool to investigate phenomena at the micro-scale which determine macroscopic physical properties of polymeric materials.In this view, multi-scale paradigm here discussed can further help computation aided molecular modeling to reduce the extent of the experimental trial-and-error approach during the design and investigation of new materials, thus resulting in a more cost and time efficient process.Acknowledgments:This research was partially supported by the Italian Institute of Technology (IIT). The authors declare no conflict ofinterest of any sort.References:1. Gestoso P, Karayiannis NC (2008) Molecular simulation of the effect of temperature and architecture on polyethylene barrier properties. J Phys Chem B 112:5646–56602. Chiessi E, Cavalieri F, Paradossi G (2007) Water and polymer dynamics in chemically cross-linked hydrogels of poly(vinyl alcohol): a molecular dynamics simulation study. J Phys Chem B 111:2820–28273. Zhang QG, Liu QL, Chen Y, Wu JY et al (2009) Microstructure dependent diffusion of water-ethanol in swollen poly(vinyl alcohol): a molecular dynamics simulation study. Chem Eng Sci 64:334–3404. Hofmann D, Fritz L, Ulbrich J, Schepers C et al (2000) Detailedatomistic molecular modeling of small molecule diffusion and solution processes in polymeric membrane materials. Macromol Theory Simul 9:293–3275. Hofmann D, Fritz L, Ulbrich J, Paul D (2000) Molecular simulation of small molecule diffusion and solution in dense amorphous polysiloxanes and polyimides. Comput Theor Polymer Sci 10:419–4366. Tocci E, Hofmann D, Paul D, Russo N et al (2001) A molecular simulation study on gas diffusion in a dense poly(ether-etherketone) membrane. Polymer 42:521–5337. Pavel D, Shanks R (2003) Molecular dynamics simulation of diffusion of O-2 and CO2 in amorphous poly(ethylene terephthalate) and related aromatic polyesters. Polymer 44:6713–67248. Fermeglia M, Cosoli P, Ferrone M, Piccarolo S et al (2006) PET/ PEN blends of industrial interest as barrier materials. Part 1. Many-scale molecular modeling of PET/PEN blends. Polymer 47:5979–59899. Pavel D, Shanks R (2005) Molecular dynamics simulation of diffusion of O-2 and CO2 in blends of amorphous poly(ethylene terephthalate) and related polyesters. Polymer 46:6135–614710. Ionita M, Silvestri D, Gautieri A, Votta E et al (2006) Diffusion of smallmolecules in bioartificialmembranes for clinical use:molecular modelling and laboratory investigation. Desalination 200:157–15911. Prathab B, Aminabhavi TM (2007) Molecular modeling study on surface, thermal, mechanical and gas diffusion properties of chitosan. J Polym Sci B Polym Phys45:1260–127012. Pan FS, Peng FB, Lu LY,Wang JT et al (2008)Molecular simulation on penetrants diffusion at the interface region of organic-inorganic hybrid membranes. Chem Eng Sci 63:1072–108013. Entrialgo-Castaño M, Salvucci AE, Lendlein A, Hofmann D (2008) An atomistic modeling and quantum mechanical approach to the hydrolytic degradation of aliphatic polyesters. Macromol Symp 269:47–6414. Tozzini V (2005) Coarse-grained models for proteins. Curr Opin Struct Biol 15:144–15015. Chng C-P, Yang L-W (2008) Coarse-grained models reveal functional dynamics - II. Molecular dynamics simulation at the coarse-grained level—theories and biological applications. Bioinf Biol Insights 2:171–18516. Marrink SJ, de Vries AH, Mark AE (2004) Coarse grained model for semiquantitative lipid simulations. J Phys Chem B 108:750–76017. Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP et al (2007) The MARTINI force field: coarse grained model for biomolecular simulations. J Phys Chem B 111:7812–782418. Monticelli L, Kandasamy SK, Periole X, Larson RG et al (2008) The MARTINI coarse-grained force field: extension to proteins. J Chem Theory Comput 4:819–834 19. Darve E, Pohorille A (2001) Calculating free energies using average force. J Chem Phys 115:9169–918320. Darve E, Wilson MA, Pohorille A (2002) Calculating free energies using a scaled-force molecular dynamics algorithm. Mol Simul 28:113–14421. Phillips JC, Braun R, Wang W, Gumbart J et al (2005) Scalable molecular dynamics with NAMD. J Comput Chem 26:1781–180222. MacKerell AD, Bashford D, Bellott M, Dunbrack RL et al (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102:3586–361623. Mills R (2002) Search for isotope effects in the self-diffusion of benzene and cyclohexane at 25.deg. J Phys Chem 79:852–85324. Mark J (1999) Polymer data handbook. Oxford University Press, New York从原子理论到粗粒理论来进行模拟研究预测中等大小的分子在聚合物模型中的扩散摘要：由于小分子和中等大小的分子的正常扩散所需要的时间太长，而以至于不能很好通过原子理论的模似进行研究。

分子模拟中常用的结构分析与表征方法综述张世良;戚力;高伟;冯士东;刘日平【摘要】分子模拟技术是随着计算机技术发展而兴起的一项新技术，主要包括分子动力学和蒙特卡洛等方法。

通过分子模拟技术，利用计算机对材料的组成、性质、制备工艺、加工工艺等环节进行虚拟实验，获得大量数据，再与验证性实验进行对照，可以分析其中的物理现象和本质。

本文整理了目前分子模拟技术中常用的几种结构分析与表征方法，对其原理和分析要点进行综述，希望能够有利于分子模拟技术在国内的推广和应用。

%Molecular modeling is developed as the computering aibility is greatly enhanced,and it mainly includes the molecular dy⁃namics simulation and Monte Carlo. Molecular modeling simulation enables the determination of a large number of data regarding materials′composition,propertie s,preparation and processing by virtual experiments on computers. Compared with the experiment results,the physical nature behind the phenomena can be understood.This paper summarized some methods on the structural analy⁃ses and characterization in molecular modeling,and reviewed the basic principles and applications.This work is expected to promote the applications of molecular modeling.【期刊名称】《燕山大学学报》【年(卷),期】2015(000)003【总页数】8页(P213-220)【关键词】分子模拟;分子动力学;蒙特卡洛;结构分析;综述【作者】张世良;戚力;高伟;冯士东;刘日平【作者单位】燕山大学理学院，河北秦皇岛066004; 燕山大学亚稳材料制备技术与科学国家重点实验室，河北秦皇岛066004;燕山大学亚稳材料制备技术与科学国家重点实验室，河北秦皇岛066004;燕山大学亚稳材料制备技术与科学国家重点实验室，河北秦皇岛066004;燕山大学理学院，河北秦皇岛066004; 燕山大学亚稳材料制备技术与科学国家重点实验室，河北秦皇岛066004;燕山大学亚稳材料制备技术与科学国家重点实验室，河北秦皇岛066004【正文语种】中文【中图分类】TB303分子模拟技术是随着计算机技术发展而兴起的一项新技术，主要包括分子动力学（Molecular dynamics simulation，MD）和蒙特卡洛（Monte Carlo，MC）等方法。

1. Langmuir 影响因子4.186 (ACS)Langmuir is an interdisciplinary（多学科）journal publishing articles in the following subject categories:（1）Colloids: Surfactants and self-assembly, dispersions, emulsions, foams（2）Interfaces: Adsorption, reactions, films, forces.（3）Biological Interfaces: Bio-colloids, bio-molecular and bio-mimetic materials(生物仿生材料)（4）Materials: nano - structured and meso-structured materials（纳米和中间结构材料）, polymers, gels, liquid crystals（5）Electrochemistry: Interfacial charge transfer (界面电子转移), charge transport, electro-catalysis(电催化作用), electro-kinetic phenomena（电动力学现象）, bio-electrochemistry（生物电化学）（6）Devices and Applications: Sensors(传感器), fluidics（射流技术）, patterning （仿生）, catalysis（催化）, photonic crystals（光电子晶体）期刊地址：/journal/langd52. JPC (A)影响因子2.946(ACS)The Journal of Physical Chemistry A (Isolated Molecules, Clusters, Radicals（自由基）, and Ions; Environmental Chemistry, Geochemistry（地球化学）, and Astrochemistry（天体化学）; Theory) publishes studies on kinetics and dynamics; spectroscopy, photochemistry, and excited states（激发态）; environmental and atmospheric chemistry, aerosol processes（气溶胶过程）, geochemistry, and astrochemistry; and molecular structure, quantum chemistry, and general theory期刊地址：/journal/jpcafh3. JPC (B)影响因子3.696(ACS)The Journal of Physical Chemistry B (Biophysical Chemistry, Biomaterials, Liquids, and Soft Matter) publishes studies on biophysical chemistry and biomolecules; biomaterials, surfactants, and membranes（细胞膜）; liquids; chemical and dynamical processes in solution; glasses, colloids, polymers, and soft matter期刊地址：/journal/jpcbfk4. JPC (C)影响因子4.805(ACS)The Journal of Physical Chemistry C (Energy Conversion and Storage, Optical and Electronic Devices, Interfaces, Nanomaterials, and Hard Matter) publishes studies on energy conversion and storage; energy and charge transport; surfaces, interfaces, porous materials, and catalysis; plasmonics(等离子体), optical materials, and hard matter; physical processes in nanomaterials and nanostructures.期刊地址：/journal/jpccck5. Journal of Colloid and Interface Science 影响因子3.070(Elsevier)The Journal of Colloid and Interface Science publishes original research findings and insights regarding the fundamental principles of colloid and interface science, and conceptually novel applications of these principles in chemistry, chemical engineering, physics, applied mathematics, materials science, polymer science, electrochemistry, geology, agronomy, biology, medicine, fluid dynamics, and related fields The Journal of Colloid and Interface Science emphasizes fundamental scientific innovation within the following categories:A. Colloidal Materials and NanomaterialsB. Surfactants and Soft MatterC. Adsorption, Catalysis and ElectrochemistryD. Interfacial Processes, Capillarity（毛细管作用）and WettingE. Biomaterials and NanomedicineF. Novel Phenomena and Techniques期刊地址：/journal-of-colloid-and-interface-science/ 6. Journal of Surfactants and Detergents 影响因子1.545(Springer)Journal of Surfactants and Detergents（洗涤剂）, a journal of the American Oil Chemists Society (AOCS) publishes scientific contributions in the surfactants and detergents area. This includes the basic and applied science of petrochemical（石油化学）and oleochemical（油化学）surfactants, the development and performance of surfactants in all applications, as well as the development and manufacture of detergent ingredients（材料）and their formulation into finished products. Manuscripts involving performance, test method development, analysis, and the environmental fate of surfactants and detergent ingredients are welcome.期刊地址：/chemistry/journal/117437. Journal of Dispersion Science and Technology 影响因子0.628(Taylor & Francis Group content )Journal of Dispersion Science and Technology is an international journal covering fundamental and applied aspects of dispersions, emulsions, vesicles（囊泡）, microemulsions, liquid crystals, particle suspensions（悬浮液）and sol-gel processes. Fundamental areas that are covered include new surfactants, polymers and indigenous stabilizers; surfactant and polymer association as well as phase equilibria （相平衡）in systems water and oil; surfactant and polymer films, monolayers and interfacial films; adsorption and desorption onto solid surfaces; stability and destabilization of dispersions, emulsions and particle suspensions; collodal templates and sol-gel processing. Industrial applications cover chemicals (surfactants, polymers, stabilizers, inhibitors), crude oils, food, pharmaceuticals, agriculture, nanotechnology, and soft condensed materials.期刊地址：/action/aboutThisJournal?show=aimsScope&journalCode =ldis208. Journal of Molecular Modeling （J MOL MODEL，JMM）影响因子1.797The Journal of Molecular Modeling was founded in 1995 as the first purely electronic journal in chemistry with the aim of publishing original articles on all aspects of molecular modeling. One reason for the electronic format was the ability to publish in full color at no extra cost and to be able to provide multimedia features or supplemental material electronically. From January 1st 2003 the Journal of Molecular Modeling is also published six times per year as a classical, but still full color, print journal. The electronic publication in advance of the printed issues continues as for the purely electronic journal. Electronic supplementary material will also be available from Springer's internet service as before. To our knowledge, the Journal of Molecular Modeling is the first scientific journal to make the move from purely electronic (with subsequent publication of the Molecular Modeling Annuals) to a more classical print format. We have decided to use the opportunity of the birth of the print edition of theJournal of Molecular Modeling to redefine the aims and scope of the journal to fit the fast-changing field of molecular modeling.The Journal of Molecular Modeling publishes all quality science that passes the critical review of expert reviewers and falls within the scope of the journal coverage, including:Life Science Modeling· Computer-aided molecular design· Rational drug design, de novo ligand design, receptor modeling and docking· Cheminformatics（化学信息学）, data analysis, visualization and mining（采矿）· Computational medicinal chemistry· Homology modeling（同源建模）· Simulation of peptides, DNA and other biopolymers· Quantitative structure-activity relationships (QSAR)· Quantitative structure-property relationships (QSAR) and ADME-modeling· Modeling of biological reaction mechanisms·Combined experimental/computational studies in which calculations play a major roleMaterials Modeling· Classical or quantum mechanical modeling of materials· Modeling mechanical and physical properties· Computer-based structure determination of materials· Catalysis-modeling· Modeling zeolites（沸石）, layered minerals（矿物）etc.· Modeling catalytic reaction mechanisms and computational catalysis optimization · Polymer modeling· Nanomaterials, fullerenes（富勒烯）and nanotubes· Modeling stationary phases in separation scienceNew Methods· New classical modeling techniques and parameter sets·New quantum mechanical techniques, including ab inito DFT and semiempiricalMO-methods, basis sets etc.· New hybrid QM/MM techniques· New computer-based methods for interpreting experimental data· New visualization techniques· New statistical methods for treating biopolymers· New software and new versions of existing software· New techniques for simulating environments or solventComputational Chemistry· Classical and quantum mechanical modeling of chemical structures and reactions · Molecular recognition· Modeling sensors· New desktop modeling software and techniques· Theories of chemical structure and reactions· Neural nets and genetic algorithms in chemistry期刊地址：/chemistry/journal/894。

Crystallization of Amino Acids on Self-AssembledMonolayers of Rigid Thiols on GoldAlfred Y.Lee,†,‡Abraham Ulman,†,§and Allan S.Myerson*,‡Department of Chemical and Environmental Engineering,Illinois Institute of Technology, Chicago,Illinois60616,and Department of Chemical Engineering,Chemistry and Material Science,and the NSF MRSEC for Polymers at Engineered Interfaces,Polytechnic University,Brooklyn,New York11201Received March6,2002.In Final Form:May3,2002Self-assembled monolayers(SAMs)of rigid biphenyl thiols are employed as heterogeneous nucleants for the crystallization of L-alanine and DL-valine.Powder X-ray diffraction and interfacial angle measurements reveal that the L-alanine crystallographic planes corresponding to nucleation are{200}, {020},and{011}on SAMs of4′-hydroxy-(4-mercaptobiphenyl),4′-methyl-(4-mercaptobiphenyl),and4-(4-mercaptophenyl)pyridine on gold(111)surfaces,respectively.In the case of DL-valine,monolayer surfaces that act as hydrogen bond acceptors(e.g.,4′-hydroxy-(4-mercaptobiphenyl)and4-(4-mercaptophenyl)-pyridine)induce the racemic crystal to nucleate from the{020}plane whereas the nucleating plane for the4′-methyl-(4-mercaptobiphenyl)surface is the fast-growing{100}face.The observation of crystal nucleation and orientation can be attributed to the strong interfacial interactions,in particular,hydrogen bonding,between the surface functionalities of the monolayer film and the individual molecules of the crystallizing phase.Molecular modeling studies are also undertaken to examine the molecular recognition process across the interface between the surfactant monolayer and the crystallographic planes.Similar to binding studies of solvents and impurities on crystal habit surfaces,binding energies between SAMs and particular amino acid crystal faces are calculated and the results are in good agreement with the observed nucleation planes of the amino acids.In addition to L-alanine and DL-valine,the interaction of SAMs and mixed SAMs of rigid thiols on the morphology of R-glycine is examined(Kang,J.F.;Zaccaro, J.;Ulman,A.;Myerson,ngmuir2000,16,3791),and similarly the calculations are in good agreement. These results suggest that binding energy calculations can be a valid method to screen self-assembled monolayers as potential templates for nucleation and growth of organic and inorganic crystals.I.IntroductionCrystallization from solution is a two-step process: nucleation,the birth of a crystal,and crystal growth,the growth of the crystal to larger sizes.2In this process, prenucleation aggregates(or clusters)are formed by individual molecules,which become stable nuclei,upon reaching a critical size,and further grow into macroscopic crystals.Homogeneous nucleation is very rare and re-quires high supersaturation to surmount the activation barrier,∆G crit.However,for a fixed supersaturation the activation barrier can be lowered by decreasing the surface energy of the aggregate,for instance,by introducing a foreign surface or substance.3This foreign surface(or substance)includes“tailor-made”additives,4impurities,5 organic single crystals,6Langmuir monolayers7floating at the air-water interface,and self-assembled monolayers (SAMs)immersed in solution.1Tailor-made additives or auxiliaries are designer impurities that have one part which resembles the crystallizing species and another part that is chemically or structurally different from the solute molecule.4,8These additives disrupt the bonding sequence in the crystals,thereby lowering the growth rate of the affected faces as evident in the case of L-alanine where hydrophobic amino acids such as L-leucine and L-valine inhibited the development of specific crystal faces,while in the presence of hydrophilic amino acids the crystal morphology did not change.9In addition to being habit modifiers,these molecular additives can also control polymorphism,where the impurities inhibit the growth of one polymorph and,in turn,promote the growth of the other polymorph.10Nucleation promoters such as organic single crystals and self-assembled monolayers have also been used to control polymorph selectivity,based on geometric match-ing between the molecular clusters and the ledges of the crystal substrates11and interfacial hydrogen bonding between the monolayer film and solute clusters,12respec-*To whom correspondence should be addressed.Phone:312 5677010.Fax:3125677018.E-mail:myerson@.†Polytechnic University.‡Illinois Institute of Technology.§NSF MRSEC for Polymers at Engineered Interfaces.(1)Kang,J.F.;Zaccaro,J.;Ulman,A.;Myerson,ngmuir2000, 16,3791.(2)(a)Myerson,A.S.Handbook of Industrial Crystallization,2nd ed.;Butterworth-Heinemann:Boston,2002.(b)Myerson,A.S.Mo-lecular Modeling Applications in Crystallization;Cambridge Uni-versity Press:New York,1999.(c)Mullin,J.W.Crystallization,4th ed.;Butterworth-Heinemann:Boston,2001.(3)Turnbull,D.J.Chem.Phys.1949,18,198.(b)Fletcher,N.H.J. Chem.Phys.1963,38,237.(4)Weissbuch,I.;Lahav,M.;Leiserowitz,L.In Molecular Modeling Applications in Crystallization;Myerson, A.S.,Ed.;Cambridge University Press:New York,1999;p166.(5)Meenan,P.A.;Anderson,S.R.;Klug,D.L.In Handbook of Industrial Crystallization,2nd ed.;Myerson,A.S.,Ed.;Butterworth Heinemann:Boston,2002;p67.(6)Carter,P.W.;Ward,M.D.J.Am.Chem.Soc.1993,115,11521.(7)(a)Rapaport,H.;Kuzmenko,I.;Berfeld,M.;Kjaer,K.;Als-Nielsen, J.;Popovitz-Biro,R.;Weissbuch,I.;Lahav,M.;Leiserowitz,L.J.Phys. Chem.B2000,104,1399.(b)Frostman,L.M.;Ward,ngmuir 1997,13,330.(8)(a)Berkovitch-Yellin,Z.;Ariel,S.;Leiserowitz,L.J.Am.Chem. Soc.1985,105,765.(b)Addadi,L.;Weinstein,S.;Gate,E.;Weissbuch,I.;Lahav,M.J.Am.Chem.Soc.1982,104,4610.(9)Li,L.;Lechuga-Ballesteros,D.;Szkudlarek,B.A.;Rodriguez-Hornedo,N.J.Colloid Interface Sci.1994,168,8.(10)(a)Weissbuch,I.;Lahav,M.;Leiserowitz,L.Adv.Mater.1994, 6,952.(b)Davey,R.J.;Blagden,N.;Potts,G.D.;Docherty,R.J.Am. Chem.Soc.1997,119,1767.5886Langmuir2002,18,5886-589810.1021/la025704w CCC:$22.00©2002American Chemical SocietyPublished on Web06/22/2002tively.Similar to Langmuir monolayers,self-assembled monolayers can be used as an interface across which stereochemical matching13and hydrogen bonding14in-teraction can transfer order and symmetry from the monolayer surface to a growing crystal.However,SAMs and mixed SAMs15lack the mobility of molecules at an air-water interface and hence the possibility to adjust lateral positions to match a face of a nucleating crystal. This is clearly evident in the case of the SAMs of rigid biphenyl thiols,where even conformational adjustment is not possible.Recently,SAMs of4-mercaptobiphenyl have been shown to be more superior to those of al-kanethiolates and are stable model surfaces.16Further-more,the ability to engineer surface functionalities at the molecular level makes SAMs of rigid thiols very attractiveas templates for heterogeneous nucleation. Organosilane monolayer films have been used to promote nucleation and growth of calcium oxalate mono-hydrate crystals17and have been employed in“biomimetic”synthesis as observed in the oriented growth of CaCO318 and iron hydroxide crystals.19Functionalized SAMs of alkanethiols have also been shown to control the oriented growth of CaCO3.20This was also evident in the hetero-geneous nucleation and growth of malonic acid crystals21 on alkanethiolate SAMs on gold where the monolayer composition strongly influenced the orientation of the malonic acid crystals.Additionally,functionalized alkane-thiolate SAMs have enhanced the growth of protein crystals.22More recently,SAMs and mixed SAMs of rigid thiols served as templates.1It was observed that glycine nucleated in the R-form independent of the hydroxyl and pyridine surface concentration and the morphology of the glycine crystal was very sensitive to the OH and pyridine site densities.Self-assembled monolayers on solid surfaces offer many advantages for enhanced crystal nucleation.In this work, SAMs of rigid thiols on gold are employed to investigate the effects of interfacial molecular recognition on nucle-ation and growth of L-alanine and DL-valine crystals.In addition,molecular modeling techniques are employed to examine the affinity between monolayer surfaces and particular amino acid crystal faces and to gain a better understanding of the molecular recognition events oc-curring.The modeling techniques employed are similar to studies of solvent and additive interactions on crystal habit23but have never been applied to organic monolayer films as templates for nucleation.II.Experimental SectionMaterials.Anhydrous ethanol was obtained from Pharmco (Brookfield,CT).L-Alanine(CH3CH(NH2)CO2H),and DL-valine ((CH3)2CHCH(NH2)CO2H)were purchased from Aldrich and used without further purification.Distilled water purified with a Milli-Q water system(Millipore)was used.Details of the synthesis of the4′-substituted4-mercaptobiphenyl(see Figure1)are described elsewhere.24Gold Substrate and Monolayer Preparation.Glass slides were cleaned in ethanol in an ultrasonic bath at40°C for10min. The slides were next treated in a plasma chamber at an argon pressure of0.1Torr for30min.Afterward,they were mounted in the vacuum evaporator(Key High Vacuum)on a substrate holder,approximately15cm above the gold cluster.The slides were baked overnight in a vacuum(10-7Torr)at300°C.Gold (purity>99.99%)was evaporated at a rate of3-5Å/s until the film thickness reached1000Å;the evaporation rate and film thickness were monitored with a quartz crystal microbalance (TM100model from Maxtek Inc.).The gold substrates were annealed in a vacuum at300°C for18h.After cooling to room temperature,the chamber was filled with high-purity nitrogen and the gold slides were either placed into the adsorbing solution right after the ellipsometric measurement was performed or stored in a vacuum desiccator for later use.25Atomic force microscopy(AFM)studies24revealed terraces of Au(111)with typical crystalline sizes of0.5-1µm2.Monolayers were formed by overnight(∼18h)immersion of clean substrates in10µm ethanol solutions of the thiols.The substrates were removed from the solution,rinsed with copious amounts of absolute ethanol to remove unbound thiols,and blown dry with a jet of nitrogen. Contact angle measurements,IR spectroscopy,and ellipsometry showed that after1h,90%or more of the SAMs are formed.26 Thus,to ensure equilibrium SAMs,the gold substrates were left overnight in the dipping solution.Crystal Growth.Nucleation and growth experiments were carried out in Quartex jars(1oz.)at25°C.Supersaturated solutions(25%)of L-alanine and DL-valine were obtained by dissolving 4.58g and 1.95g in22.0g of Millipore water, respectively.The solutions were heated to65°C for90min in an ultrasonic bath to obtain complete dissolution.The solutions were cooled to room temperature for90min before the SAMs were carefully introduced and aligned vertically to the wall. Macrocrystals of L-alanine and DL-valine nucleated at the surfaces(11)(a)Bonafede,S.J.;Ward,M.D.J.Am.Chem.Soc.1995,117, 7853.(b)Mitchell,C.A.;Yu,L.;Ward,M.D.J.Am.Chem.Soc.2001, 123,10830.(12)Carter,P.W.;Ward,M.D.J.Am.Chem.Soc.1994,116,769.(13)(a)Landau,E.M.;Levanon,M.;Leiserowitz,L.;Lahav,M.;Sagiv, J.Nature1985,318,353.(b)Weissbuch,I.;Berfeld,M.;Bouwman,W.; Kjaer,K.;Als,J.;Lahav,M.;Leiserowitz,L.J.Am.Chem.Soc.1997, 119,933.(14)Weissbuch,I.;Popvitz,R.;Lahav,M.;Leiserowitz,L.Acta Crystallogr.1995,B51,115.(15)For a review on SAMs of thiols on gold see:(a)Ulman,A.An Introduction to Ultrathin Organic Films:From Langmuir-Blodgett to Self-Assembly;Academic Press:Boston,1991.(b)Ulman,A.Chem. Rev.1996,96,1533.(16)(a)Kang,J.F.;Ulman,A.;Liao,S.;Jordan,R.J.Am.Chem.Soc. 1998,120,9662.(b)Kang,J.F.;Jordan,R.;Ulman,ngmuir1998,14,3983.(17)Campbell,A.A.;Fryxell,G.E.;Graff,G.L.;Rieke,P.C.; Tarasevich,B.J.Scanning Microsc.1993,7(1),423.(18)Archibald,D.D.;Qadri,S.B.;Gaber,ngmuir1996,12, 538.(19)Tarasevich,B.J.;Rieke,P.C.;Liu,J.Chem.Mater.1996,8,292.(20)Aizenberg,J.;Black,A.J.;Whitesides,G.M.J.Am.Chem.Soc. 1999,121,4500.(21)Frostman,L.M.;Bader,M.M.;Ward,ngmuir1994, 10,576.(22)Ji,D.;Arnold,C.M.;Graupe,M.;Beadle,E.;Dunn,R.V.;Phan, M.N.;Villazana,R.J.;Benson,R.;Colorado,R.,Jr.;Lee,T.R.;Friedman, J.M.J.Cryst.Growth2000,218,390.(23)(a)Docherty,R.;Meenan,P.In Molecular Modeling Applications in Crystallization;Myerson,A.S.,Ed.;Cambridge University Press: New York,1999;p106.(b)Myerson,A.S.;Jang,S.M.J.Cryst.Growth 1995,156,459.(c)Walker,E.M.;Roberts,K.J.;Maginn,ngmuir 1998,14,5620.(d)Evans,J.;Lee,A.Y.;Myerson,A.S.In Crystallization and Solidification Properties of Lipids;Widlak,N.,Hartel,R.W.,Narine, S.,Eds.;AOCS Press:Champaign,IL,2001;p17.(24)Kang,J.F.;Ulman,A.;Liao,S.;Jordan,R.;Yang,G.;Liu,G. Langmuir2001,17,95.(25)(a)Jordan,R.;Ulman,A.J.Am.Chem.Soc.1998,120,243.(b) Jordan,R.;Ulman,A.;Kang,J.F.;Rafailovich,M.;Sokolov,J.J.Am. Chem.Soc.1999,121,1016.(26)Ulman,A.Acc.Chem.Res.2001,34,855.Figure1.Rigid4′-substituted4-mercaptobiphenyls.Crystallization of Amino Acids on Thiol SAMs Langmuir,Vol.18,No.15,20025887and near the edge of the substrates.Only crystals having visible SAM area around them were considered,and the rest were discarded.The chosen crystals attached to the substrates were removed from the solution and stored in a vacuum desiccator for later analysis.Due to the strong adhesion of the crystal face to the SAM surface,gold marks were often observed on the crystal face that nucleated on the SAM surface.Characterization.A Rudolph Research AutoEL ellipsometer was used to measure the thickness of the monolayer surface.The He -Ne laser (632.8nm)light fell at 70°on the sample and reflected into the analyzer.Data were taken over five to seven spots on each sample.The measured thickness of the SAMs of biphenyl thiols ranged from 12to 14Å,assuming a refractive index of 1.462for all films.Powder X-ray diffraction patterns of crystalline L -alanine and DL -valine were obtained with a Rigaku Miniflex diffractometer with Cu K R radiation (λ)1.5418Å).All samples were manually ground into fine powder and packed in glass slides for analysis.Data were collected from 5°to 50°with a step size of 0.1°.Crystal habits of L -alanine and DL -valine were indexed by measuring the interfacial angles using a two-circle optical goniometer.All possible measured interfacial angles were compared with the theoretical values derived from the unit cell parameters of L -alanine and DL -valine crystals.27,28III.Modeling SectionIII.1.General.All of the binding energy calculations,including molecular mechanics and dynamics simulations,are carried out with the program Cerius 2.The overall methodology and procedures are summarized in Figure 2.The crystal structures of each amino acid are obtained from the Cambridge Crystallographic Database (ref codes GLYCIN17,LALNIN12,and VALIDL for R -glycine,L -alanine,and DL -valine,respectively).To accurately predict the crystal morphology,molecular mechanics simulations using a suitable potential function (or force field)are performed.In this work,molecular simulations are carried out using the DREIDING 2.21force field.29The van der Waals forces are approximated with the Lennard-Jones 12-6expression,and hydrogen bonding energy is modeled using a Lennard-Jones-like 12-10expression.The Ewald summation technique is employed for the summation of long-range van der Waals and electrostatic interactions under the periodic boundary conditions,and the charge distribution within the molecule is calculated using the Gasteiger method.30ttice Energy Calculation.The lattice energy E lat,also known as the cohesive or crystal binding energy,is calculated by summing all the atom -atom interactions between a central molecule and all the surrounding molecules in the crystal.If the central molecule and the n surrounding molecules each have n ′atoms,thenwhere V kij is the interaction between atom i in the central molecule and atom j in the k th surrounding parison to the “experimental”lattice energy,V exp ,allows us to assess the accuracy of the intermolecular interactions between the molecules by the defined po-tential function.where the term 2RT represents a compensation factor for the difference between the vibrational contribution to the crystal enthalpy and gas-phase enthalpy 31and ∆H sub is the experimental sublimation energy.III.3.Morphological Predictions.The morphology of each amino acid crystal is predicted using the attach-ment energy (AE)32calculation and the Bravais -Friedel -Donnay -Harker (BFDH)law.33The habit or shape of the crystal depends on the growth rate of the faces present.Faces that are slow growing have the greatest morpho-logical importance,and conversely,faces that are fast growing have the least morphological importance and are the smallest faces on the grown crystal.The simplest morphological simulation is the BFDH law which assumes that the linear growth rate of a given crystal face is inversely proportional to the corresponding interplanar distance after taking into account the extinction conditions of the crystal space group.The attachment energy of a crystal face is the difference between the crystal energy and the slice energy.Hartman and Bennema 32found that the relative growth rate of a face is directly proportional to the attachment energy and as a result,the more negative the attachment energy (or more energy released)for a particular face,the less prominent that face is on the crystal.Conversely,faces with the lowest attachment energies are the slowest growing faces and thus have the greatest morphological importance .III.4.Molecular Modeling of SAMs of 4-Mercapto-biphenyls on a Au(111)Surface.Molecular dynamics (MD)simulations are useful techniques in gaining insights on the structural and dynamical properties of self-assembled monolayers.In contrast to molecular mechan-ics,molecular dynamics computes the forces and moves the atom in response to forces,while molecular mechanics computes the forces on the atoms and changes their position to minimize the interaction energy.Recently,MD simulations have been used to investigate the packing order and orientation of rigid 4-mercaptobiphenyl thiol monolayers on gold surfaces.Results show that hydrogen-terminated biphenylmercaptan packs in the herringbone conformation 34and suggest average tilt angles of 8°.(27)Simpson,H.J.;Marsh,R.E.Acta Crystallogr .1966,20,550.(28)Mallikarjunan,M.;Rao,S.T.Acta Crystallogr .1969,B25,296.(29)Mayo,S.L.;Olafson,B.D.;Goddard,W.A.,III J.Phys.Chem .1990,94,8897.(30)Gasteiger,J.;Marsili,M.Tetrahedron 1980,36,3219.(31)Williams,D.E.J.Phys.Chem .1966,45,3370.(32)(a)Hartman,P.;Bennema,P.J.Cryst.Growth 1980,49,145.(33)(a)Bravais,A.Etudes Crystallographiques ;Gauthier-Villars:Paris,1866.(b)Friedel,M.G.Bulletin de la Societe Francaise de Mineralogie 1907,30,326.(c)Donnay,J.D.;Harker,D.Am.Mineral.1937,22,446.Figure 2.Overall scheme showing the computational meth-odology adopted when calculating the binding energy betweenthe crystallographic plane and the monolayer surface.Elat)∑k )1n ∑i )1n ′∑j )1n ′V kij (1)V exp )-∆H sub -2RT(2)5888Langmuir,Vol.18,No.15,2002Lee et al.Based on this work,molecular mechanics simulations are performed for hydroxy-and methyl-terminated 4-mer-captobiphenyl along with 4-(4-mercaptophenyl)pyridine for binding studies with different crystallographic planes.In the periodic model,each unit cell contains four biphenyl molecules and the geometric parameters are a )10.02Å,b )42.25Å,c )10.11Åand R )138.3°, )119.9°,γ)95.7°.The length in the y -direction is set to ∼42Åto ensure two-dimensional periodicity.Also,the gold atoms are arranged in a hexagonal lattice along the XY plane with a nearest neighbor atom of 2.88Å,and the biphenyl occupied a ( 3× 3)R30°Au(111)lattice.To simulate different 4′-substituted 4-mercaptobiphenyls,minimiza-tion was carried out by fixing the biphenyl moiety and varying the substituents at the 4′-position.As a result,the simulated models yielded uniform ordered SAMs of 4′-substituted 4-mercaptobiphenyls and 4-(4-mercapto-phenyl)pyridine with identical packing structure and dynamics to those of a hydrogen-terminated monolayer of biphenylmercaptan (Figure 3).However,this is not true experimentally since adsorption of different 4′-substituted 4-mercaptobiphenyls on gold surfaces results in different monolayer structures and thus one of the main assump-tions made in this work.III.5.Binding of Crystal Habit Faces to SAMs of 4-Mercaptobiphenyls on a Au(111)Surface.Based on BFDH and attachment energy morphology prediction,crystal habit faces with the highest morphological im-portance are chosen for binding studies.The crystal surfaces of interest are cleaved and extended to a 3×3unit cell and partially fixed,allowing flexibility in the tail atoms of the amino acid molecules and a more accurate representation of the effects of SAMs of rigid thiols on the crystallographic plane in the calculation of binding energies.The crystal surface is then docked onto a 3×1×3partially fixed nonperiodic monolayer surface,and the conjugate gradient energy minimization technique is performed.Next,the crystal surface is moved to another site on the monolayer surface and the minimization calculations are again performed.This process was repeated 15-20times to obtain the global minimum.For each monolayer surface,numerous calculations are carried out with different crystallographic planes of each amino acid.The binding energy (φBE )of each crystallographic surface with the monolayer surface iswhere φIE is the minimum interaction energy of the monolayer and crystal surfaces,φM is the minimum energy of the monolayer surface in the absence of the crystal face but in the same conformation as it adopts on the surface,and φS is the minimum energy of the crystal surface with no monolayer surface present and in the same molecular conformation in which it docks on the surface.Negative values of binding energies indicate preferential binding of the crystallographic surfaces with SAMs of 4-mercaptobiphenyl.In cases where the binding energy is positive,there is a less likely chance that the particular crystal face will interact and nucleate on the monolayer surface.Thus,using this approach it is possible to screen self-assembled monolayers as possible templates for nucleation and growth of crystals.IV.Results and DiscussionIV.1.Crystallization of Amino Acids on SAMs on Gold.L -Alanine crystallizes from water in the ortho-rhombic space group P 21212(a )6.025Å,b )12.324Å,and c )5.783Å),27and the morphology of the crystals is bipyramidal,dominated by the {020},{120},{110},and {011}growth forms,35as shown in Figure 4.The crystal grown in aqueous solution is indexed by comparing the interfacial angles measured by optical goniometry and theoretical values based on the unit cell of L -alanine.Powder X-ray diffraction patterns (Figure 5)and inter-facial angle measurements reveal that L -alanine crystals nucleating on SAM surfaces crystallize in the ortho-rhombic space group with similar unit cell dimensions.However,functionalized SAMs induce the formation of L -alanine crystals in different crystallographic directions.L -Alanine crystals display the normal bipyramidal habit but are randomly oriented with the different surfaces.In methyl-terminated SAMs,L -alanine selectively nucle-ated on the {020}plane on the surface (Figure 6),whereas in 100%OH SAM surfaces,L -alanine nucleated on an unobserved {200}side face.The crystal exhibits a similar morphology as observed in aqueous solution with an appearance of a {200}face adjacent to the {110}planes (Figure 6).In both cases,the area of each crystal face is substantially larger than those of the other faces on the crystal.The SAM surfaces almost act as an additive or impurity molecule specifically interacting with the crystal face and consequently reducing the relative growth rate and modifying the habit.Crystallization of L -alanine on 4-(4-mercaptophenyl)pyridine surfaces resulted in the {011}face as the plane corresponding to nucleation (Figure 6).The preferential interaction of the monolayer with the {011}face can be attributed to hydrogen bonding at the crystal -monolayer interface.Unlike the other two sur-faces where they can serve as both hydrogen bond donors and acceptors (4′-hydroxy-4-mercaptobiphenyl)or solely as H-bond donors (4′-methyl-4-mercaptobiphenyl),the pyridine electron pair at the surface only serve as hydrogen bond acceptors.The binding of the pyridine surface and the {011}plane can be explained by the amino and methyl groups protruding out perpendicular to the plane (Figure 7)and forming N -H ‚‚‚N and C -H ‚‚‚N hydrogen bonds with the SAM surface,respectively.In contrast,the 100%(34)Ulman,A.;Kang,J.F.;Shnidman,Y.;Liao,S.;Jordan,R.;Choi,G.Y.;Zaccaro,J.;Myerson,A.S.;Rafailovich,M.;Sokolov,J.;Flesicher,C.Rev.Mol.Biotech .2000,74,175.(35)Lehmann,M.S.;Koetzle,T.F.;Hamilton,W.C.J.Am.Chem.Soc .1972.101,2657.Figure 3.Snapshots of (a)4′-methyl-4-mercaptobiphenyl,(b)4′-hydroxy-4-mercaptobiphenyl,(c)4-(4-mercaptophenyl)pyri-dine,and (d)mixed SAMs of 4′-methyl-4-mercaptobiphenyl and 4′-hydroxy-4-mercaptobiphenyl (top view).φBE )φIE -(φM +φS )(3)Crystallization of Amino Acids on Thiol SAMs Langmuir,Vol.18,No.15,20025889CH 3and 100%OH SAM surfaces do not interact as strongly with the hydrogen bond donating plane.In a similar manner,the appearance of an unobserved {200}face of L -alanine grown in aqueous solution on [Au]-S -C 6H 4-C 6H 4-OH can be attributed to hydrogen bonds forming between the two surfaces.The {200}surface contains alternating methyl (CH 3)and carboxylic groups (COO -)that form N -H ‚‚‚O and O ‚‚‚H -O with the hydroxide group of the monolayer film (Figure 7),ideal for binding with surfaces that can serve as both hydrogen bond donors and acceptors.As a result,the preferential interaction leads to the stabilization and appearance of the {200}face.The oriented nucleation of L -alanine crystals on func-tionalized SAMs arises due to the different molecular structures of each crystal face.Similar to the adsorption of additive onto a crystal face,the interaction (or binding)with the monolayer surface depends on the functional group that each crystal face possesses.As a result of preferential interactions with specific crystal faces,in-terfacial molecular recognition directs nucleation and subsequently influences the crystal growth.In addition to L -alanine,SAMs of rigid thiols are employed to investigate the possibility of inhibiting the racemic crystal and inducing the formation of one of its enantiomers.The powder X-ray diffraction pattern (Figure 8)reveals that DL -valine nucleates in the monoclinic form independent of the hydroxyl,methyl,or pyridine surface concentration and that there was no trace of conglomer-ates.DL -Valine crystallizes in the monoclinic space group P 21/c with a unit cell of dimensions a )5.21Å,b )22.10Å,c )5.41Å,and )109.2°.28Although the structural literature reports three separate space group assignments,Leiserowitz and co-workers 36have shown that two of the three space groups (P 21and P 1)are highly improbable for racemic crystals.Interfacial angle measurements and powder X-ray diffraction undertaken in this work agreed much better with the theoretical values and simulated pattern based on the unit cell of the monoclinic space group(36)Wolf,S.G.;Berkovitch-Yellin,Z.;Lahav,M.;Leiserowitz,L.Mol.Cryst.Liq.Cryst .1990,186,3.Figure 4.Crystallographic image (a)and morphology (b)of L -alanine crystal grown from aqueoussolution.Figure 5.X-ray diffractograms of L -alanine nucleated on functionalized SAMs,compared with L -alanine crystallized from aqueous solution (bottom).Indices of the crystallographic planes corresponding to the diffraction intensities of major peaks are indicated at the top.5890Langmuir,Vol.18,No.15,2002Lee et al.。

ORIGINAL PAPERTheoretical study on monometallic cyanide cluster fullerenes MCN@C 74(M=Y,Tb)Xu Gao 1&Li-Juan Zhao 1&Dong-Lai Wang 1Received:10August 2015/Accepted:19October 2015#Springer-Verlag Berlin Heidelberg 2015Abstract New monometallic cyanide cluster endohedral ful-lerenes MCN@C 74(M=Y ,Tb)have been investigated using density functional theory.Four isomers of MCN@C 74are con-sidered based on four lowest energy C 742−isomers,namely one cage with isolated pentagons and three isomers with a pentagon-pentagon junction.The results show that the variation of the cluster size has slight influence on the structures and relative stabilities of MCN@C 74.The MCN@D 3h (14246)-C 74derived from the only C 74cage with the isolated pentagons are predicted to possess the lowest energy.More importantly,in MCN@D 3h (14246)-C 74,the encapsulated YCN or TbCN clus-ter is triangular,similar to the results reported on YCN@C s (6)-C 82and TbCN@C 2(5)-C 82.Furthermore,IR spectra and 13C NMR spectra have also been explored to assist future experi-mental characterization.Keywords Endohedral fullerene .IR and 13C NMR spectra .MCN@C 74.StabilityIntroductionEndohedral metallofullerenes (EMFs)have attracted much at-tention as a new class of fullerene-based materials because of their unique structures and fascinating properties.They are promising for various applications in biomedicine,electron-ics,photovoltaics,and materials science [1–9].To date,a largenumber of EMFs have been synthesized and isolated by using various experimental techniques.According to the number of encaged metals,EMFs can be classified into mono-EMFs,di-EMFs,and cluster EMFs [4].The cluster EMFs have gained particular attention,because they can be obtained in high pro-duction yield and high stability.Since the first isolation of nitride clusterfullerene Sc 3N@C 80[10],enormous progress in synthesis and isolation of some stable cluster EMFs has been made.In addition to metal nitride,EMFs are also found with other metal clusters,such as metal carbide [11],metal sulfide [12],metal oxide [13],metal hydrocarbon [14],and metal carbonitride [15].The cluster EMFs always contain multiple (two to four)metal atoms and non-metallic atoms inside the fullerene cages.Very little is known about monometallic cluster endohedral fullerenes until the synthesis of a new kind of YCN@C s (6)-C 82[16]in ing a modified Krätschmer-Huffman DC-arc discharge method with the addition of N 2while TiO 2is added in the raw mixture,Yang et al.[16]have successfully synthesized the first monometallic cyanide clusterfullerene,YCN@C s (6)-C 82.The structure of YCN@C s (6)-C 82has been determined unambiguously by single-crystal X-ray diffraction crystallography and 13C NMR.The second monometallic cy-anide clusterfullerene family member,TbCN@C 2(5)-C 82[17]has also been synthesized by Yang ’s group recently.These experimental findings stimulated the theoretical researchers ’passion for this new endohedral fullerene family.In light of quantum calculations,the MCN (M=Y ,Tb)clusters were re-cently suggested to be stable in C 2v (9)-C 82cage [18].Our recent theoretical investigation revealed that two MCN@-C 76(M=Sc,Y)isomers utilize two non-IPR C 2v (19138)-C 76a n d C 1(17459)-C 76c a g e s [19].T h e s t ru c t u r e s YCN@D 3h (24109)-C 78and YCN@C 2v (24107)-C 78are the most probable isomers for the C 78monometallic cyanide clus-ter endohedrals [20].*Dong-Lai Wangdonglaiwang@1Department of Chemistry,Anshan Normal University,Anshan 114007,ChinaJ Mol Model (2015) 21:295 DOI 10.1007/s00894-015-2844-5C 74is called B missing fullerene ^because it has been observed in soot produced by arc discharge,but it has not yet been isolated in macroscopic amounts.Similar to C 60and C 70fullerenes,C 74possesses only one structural iso-mer [21],i.e.,D 3h (14246)-C 74,that obeys the isolated pentagon rule (IPR).Previous theoretical studies [22,23]on D 3h (14246)-C 74have predicted an unusually small highest occupied molecular orbital (HOMO)-lowest unoc-cupied molecular orbital (LUMO)energy gap,suggesting a high chemical reactivity.However,the C 74cage is sta-bilized significantly by encapsulating a divalent metal at-om,with two electrons transferred from the metal to the C 74.Experimentally,the C 74-related endohedral fullerenes M@C 74,where M=Ca [24],Sr [25],Ba [26],Sm [27],Eu [28],and Yb [29,30],have been isolated.The M@C 74(M=Ca,Sr,Ba,Sm,Eu)and one Yb@C 74EMFs are determined to utilize the IPR-satisfying D 3h (14246)-C 74isomer [24–37].Computational studies suggest that the minor isomer of Yb@C 74possesses the non-IPR C 1(13393)-C 74or C 1(14049)-C 74structure [33].The elec-tronic state of carbon cage in M@C 74(M=Ca,Sr,Ba,Sm,Eu,Yb)is the same as that of YCN@C s (6)-C 82[16]and TbCN@C 2(5)-C 82[17].Thus,it is very interesting to know if such a monometallic cyanide cluster can also be encapsulated into C 74to form endohedral fullerenes and what properties they possess.This information is essential for the further development of EMFs.In this paper,den-sity functional theory (DFT)computations were performed to explore the geometrical structures of MCN@C 74(M=Y ,Tb).Moreover,the electronic structures and properties for the lowest-energy isomers have been determined and reported.Computational detailsFollowing the previous researcher [31],four lowest energy C 742−isomers are considered,namely the unique D 3h (14246)-C 74IPR cage and three non-IPR cages with a pentagon-pentagon junction.V arious possible isomers were explored byplacing the MCN (M=Y ,Tb)clusters with different orientations within the C 74cage.Full geometry optimizations for the C 74isomers and their dianions were carried out using the B3LYP density functional [38,39]with the 6-31G*basis set.Optimizations on the YCN@C 74structures were per-formed at the B3LYP/6-31G*-lanl2dz level (6-31G*basis set for C and N atoms and Lanl2dz [40]basis set with the corresponding pseudopotential for Y atom).Geometries of TbCN@C 74isomers were optimized at the B3LYP/6-31G*-MWB54level (6-31G*basis set for C and N atoms and effective core potential basis set MWB54[41]for Tb at-om).On the basis of the optimized geometries,frequency calculations were done at the same level of theory.Vibra-tional analysis confirms that all the reported structures in this work correspond to an energy minimum on the poten-tial energy surface.NMR spectra were computed using gauge-independent atomic orbital (GIAO)method and the optimized geometries at the same theory level for the lowest-energy isomers.The computed 13C chemical shifts of MCN@C 74,relative to those of C 60,were converted to the tetramethylsilane (TMS)scale using the experimental value for C 60(142.5ppm)[42].For comparison,another hybrid density functional PBE1PBE [43]was also employed for the reoptimizations of four lowest energy MCN@C 74isomers with the same basis set.All the calcu-lations were carried out using the Gaussian 09program [44].Results and discussionRelative energies and stabilitiesC 74has only one IPR-satisfying isomer ofD 3h symme-try,while it also has 14,245isomers violating the IPR rule (but still have a surface comprised of 26hexagons and 12pentagons).Nagase et al.[31]searched through all 615,576cage structures (composed of pentagons,hexagons,and one heptagon)and predicted several low-est energy dianions (C 742−).The carbon cageisomerismD 3h (14246)-C 74C 1(14049)-C 74C 1(13393)-C 74C 2(14227)-C 74Fig.1Isomers of C 74.The pentagon-pentagon fusions are highlighted in red295 Page 2of 8J Mol Model (2015) 21:295of EMFs shows a good correlation with the relative stabilities of the corresponding negatively charged cages [45].For YCN@C s(6)-C82and TbCN@C2(5)-C82,two electrons are transferred from the inner cluster to the C82cage[16,17].Therefore,four lowest energy C742−isomers[31]are selected as the candidate cages to de-termine the cage structures of MCN@C74(M=Y,Tb). Figure1depicts geometries and symmetries of the four chosen C74isomers predicted at the B3LYP/6-31G*lev-el of theory.The calculated energy values and the rela-tive energies are given in Table1.The results from the B3LYP/6-31G*calculations show that D3h(14246)-C742−is the most stable among dianion isomers.Three non-IPR isomers,C1(14049)-C74,C1(13393)-C74,and C2(14227)-C74,are far less stable than the IPR D3h(14246)-C74in the dianionic state(23.56,27.90, and43.27kcal mol−1higher in energy,respectively). Our computations for the stability order of the C742−isomers is in agreement with the previous work[31]. The relative energies and HOMO-LUMO gaps of MCN@C74(M=Y,Tb)are presented in Table2.In the c a s e o f Y C N@C74E M F s,t h e I P R s t r u c t u r e YCN@D3h(14246)-C74is predicted as the most stable s tr uct ur e at b o th B3LY P/6-31G*-la n l2dz and PBE1PBE/6-31G*-lanl2dz levels.A non-IPR structure YCN@C1(14049)-C74is the second most stable one with the relative energy of7.27(B3LYP)and 6.58 (PBE1PBE)kcal mol−1.The other two YCN@C74iso-mers locate more than14kcal mol−1energy higher than the lowest one in both methods.For the TbCN@C74 EMFs,the encapsulation of the TbCN cluster does not change the order of isomer stability found for YCN@C74,indicating the increase of the cluster size might have slight influence on the relative stabilities of the two types of MCN@C74series.The B3LYP sep-aration energies agree quite well with the PBE1PBE computations.Moreover,the relative energy changes from B3LYP to PBE1PBE are less than 1.5kcal mol−1.Therefore,the energies are converged enough to give a qualitatively accurate picture of the stability of these four isomers.Electronic and geometric structuresThe HOMO-LUMO energy gap has been used as an index of kinetic stability for fullerenes and metallofullerenes[45,46].The HOMO-LUMO gap for neutral IPR D3h(14246)-C74is0.70eV.Smaller energy gap for D3h(14246)-C74isomer may result in its lower kinetic stability.This may explain its absence in the normal fullerene solvent extraction from primary soot.The B3LYP calculated HOMO-LUMO gaps are 1.19and 1.18eV for YCN@D3h(14246)-C74and TbCN@D3h(14246)-C74,respectively.The encapsulation of the MCN clusters increases the HOMO-LUMO gap, which suggests MCN@D3h(14246)-C74become much less reactive than the empty D3h(14246)-C74.The exper-imentally available divalent mono-EMFs M@C74 (M=Ca,Sr,Ba,Sm,Eu,Yb)all possess the IPR D3h(14246)-C74cage.Therefore,it is reasonable to speculate that MCN@D3h(14246)-C74should be the iso-mer obtained in the experiment.In addition,The HOMO-LUMO gaps of isomers MCN@C1(14049)-C74 are large and show their kinetic stability.Table2DFT-predicted relative energies(E rel,kcal mol−1)and HOMO-LUMO gaps(Gap,eV)of MCN@C74(M=Y,Tb)Isomers Symm a YCN@-C74TbCN@-C74B3LYP/6-31G*-lanl2dz PBE1PBE/6-31G*-lanl2dz B3LYP/6-31G*-mwb54PBE1PBE/6-31G*-mwb54E rel Gap E rel Gap E rel Gap E rel Gap14246(PA=0)C s0.00 1.190.00 1.390.00 1.180.00 1.39 14049(PA=1)C17.27 1.61 6.58 1.838.63 1.627.89 1.84 13393(PA=1)C115.79 1.4914.34 1.7117.35 1.4915.98 1.71 14227(PA=1)C124.83 1.2524.51 1.4524.85 1.2424.66 1.43a Symmetry of the MCN@C74EMFsTable1The B3LYP/6-31G*relative energies(E rel,kcal mol−1)andHOMO-LUMO gap energies(Gap,eV)of C74and C742−Isomers a Symmetry b C74C742−E rel Gap E rel Gap14246(PA=0)D3h0.000.700.00 1.6014049(PA=1)C119.58 1.0523.56 1.4513393(PA=1)C126.47 1.1527.90 1.4614227(PA=1)C215.70 2.1143.270.91a The numbering of the isomers follows the nomenclature of Fowler andManolopoulos[21].PA is the number of pentagon adjacenciesb Symmetry of the original empty cageJ Mol Model (2015) 21:295 Page3of8 295F i g u r e 2s h o w s t h e o p t i m i z e d s t r u c t u r e s o f YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74.The lowest-energy structures YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74exhibit similar geometries:the Y or Tb atom sits upon a [6,6]-bond of a pyracyclene unit,as found for divalent metal atoms (Ca,Sr,Ba,Sm,Eu,Yb)in D 3h (14246)-C 74cage;the inner N and C atoms nearly locate in the center of the cage.The endohedral YCN or TbCN cluster is triangular,similar to the result reported on YCN@C s (6)-C 82[16]and TbCN@C 2(5)-C 82[17].Some structural data are pre-sented in Table 3.From Table 3,it can be seen that the optimized bond lengths with B3LYP calculations are in reasonable agreement with those with PBE1PBE calculations.The C-N distance in the MCN moiety is almost constant (about 1.182Å)by the B3LYP and PBE1PBE calculations,which is in excellent agreement with the results from recent density functional studiesfor YCN@C s (6)-C 82[18,19],YCN@D 3h (24109)-C 78and YCN@C 2v (24107)-C 78[20](about 1.183Åat the same level of theory),but this value is slightly longer than the C-N distance (about 0.94Å)observed in YCN@C s (6)-C 82[16]and TbCN@C 2(5)-C 82[17].The calculated distances between M and the CN unit nitro-gen are 2.327and 2.397Åfor YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74with B3LYP calculations,and 2.336and 2.407Åwith PBE1PBE calculations re-spectively.These bond lengths are comparable to the corresponding bond distances in YCN@C s (6)-C 82[16]and TbCN@C 2(5)-C 82[17].The HOMO and LUMO orbitals of MCN@D 3h (14246)-C 74and D 3h (14246)-C 742−are depicted in Fig.3.It is revealed that in MCN@D 3h (14246)-C 74structures the HOMO is pre-dominately delocalized on the carbon cage and the LUMO is mainly localized on the pyracylene unit close to the M.The HOMO and LUMO orbitals of YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74resemble that of the empty D 3h (14246)-C 742−dianion.So the valence state of [M 3+(CN)−]2+@[C 74]2−(M=Y,Tb)can be assigned to MCN@C 74,as in the case of YCN@C s (6)-C 82[16]and TbCN@C 2(5)-C 82[17]EMFs.To get more information about the physical properties of new MCN@D 3h (14246)-C 74EMFs,the vertical ionization potential (VIP)(the energy difference between the cation and its neutral species at the same neutral geometry)and vertical electron affinity (VEA)(the energy difference be-tween the neutral species and its anion at the same neutral geometry)of MCN@D 3h (14246)-C 74and D 3h (14246)-C 74have also been computed (Table 3).Fullerenes,in general,exhibit relatively large EAs.The experimentally measured VEAs of C 60and D 3h (14246)-C 74are 2.67[47]and 3.28eV [48],respectively.The very large VEA value of D 3h (14246)-C 74compared with C 60is consistent with a re-markably high stability of C 74anion observed in the gas-phase experiments [48].The calculated VIP and VEA values of D 3h (14246)-C 74are 5.91and 2.97eV at the B3LYP/6-31G*level,and 6.09and 3.19eV at the PBE1PBE/6-31G*level,respectively.The predicted VEA for D 3h (14246)-C 74with the PBE1PBE method is close to the experimental val-ue.Insertion of the MCN clusters increases the cage IPs.Table 3Optimized structural parameters,VIP and VEA for MCN@D 3h (14246)-C 74and D 3h (14246)-C 74obtained using B3LYP method aStructureC-N bond M-C bond M-N bond M-C-N angle VIP VEA (Å)(Å)(Å)(deg.)(eV)(eV)YCN@D 3h (14246)-C 74 1.182(1.183) 2.585(2.565) 2.327(2.336)64.1(65.5) 6.08(6.28) 2.67(2.86)TbCN@D 3h (14246)-C 74 1.182(1.182)2.589(2.576)2.397(2.407)67.3(68.4)6.09(6.29) 2.68(2.87)D 3h (14246)-C 745.91(6.09)2.97(3.19)aData in parentheses obtained using PBE1PBE method(a)(b)Fig.2Two views of optimized structures of YCN@D 3h (14246)-C 74(a )and TbCN@D 3h (14246)-C 74(b ).Orange and blue balls denote C and N atoms of the inner CN unit,while red and purple balls represent Yand Tb atoms,respectively295 Page 4of 8J Mol Model (2015) 21:295The calculated VIPs of MCN@D 3h (14246)-C 74are about 0.17(B3LYP)and 0.19(PBE1PBE)eV higher than that of pristine C 74,indicating MCN@D 3h (14246)-C 74are more difficult to lose electrons.On the other hand,the VEAs of YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74are 2.67and 2.68eV at the B3LYP level,and 2.86and 2.87eV at the PBE1PBE level,respectively,smaller than that of C 74.However,compared with C 60,MCN@D 3h (14246)-C 74pos-sess large VEA values,suggesting that they are good electron acceptors.IR and 13C NMR spectraThe infrared (IR)spectra of YCN@D 3h (14246)-C 74,TbCN@D 3h (14246)-C 74,and D 3h (14246)-C 742−were com-puted at the B3LYP level.As shown in Fig.4,the spectra of YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74exhibit a high resemblance to the spectra of D 3h (14246)-C 742−.Two regions (200–1000cm −1and 1000–1700cm −1)in the IR spectra of MCN@D 3h (14246)-C 74are mainly attributed to the vibrations of the D 3h (14246)-C 742−cage.The strongest absorption peaks (1132and 1133cm −1for YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74)correspond to the tangential vibrations of the carbon cage.Several other relatively strong peaks (1048,1353,1416,1593cm −1for YCN@D 3h (14246)-C 74,1047,1352,1414,1592cm −1for TbCN@D 3h (14246)-C 74)are also caused by the stretching vibrations of the tangential carbon cage vibra-tional mode.In contrast,the C-N stretching frequencies (νCN )of the internal CN unit (2117and 2121cm −1for YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74,respec-tively)have very weak absorption intensities;similar results can also be found in YCN@C s (6)-C 82and YCN@C 78(νCN at 2115,2122,and 2121cm −1for YCN@C s (6)-C 82,YCN@D 3h (24109)-C 78,and YCN@C 2v (24107)-C 78,respec-tively,at the same level of theory)[20].(a)HOMOLUMO(b)HOMOLUMO(c)HOMOLUMOFig.3HOMO and LUMO of YCN@D 3h (14246)-C 74(a ),TbCN@D 3h (14246)-C 74(b ),and D 3h (14246)-C 742−(c )obtained using B3LYP method5001000150020002500*YCN@D 3h (14246)-C74Frequency/cm-1*TbCN@D 3h (14246)-C 74D 3h (14246)-C742-Fig.4Comparison of the IR spectrum of charged empty cage C 742−and the corresponding MCN@C 74(M=Y ,Tb).The asterisks mark νCN stretching frequenciesJ Mol Model (2015) 21:295 Page 5of 8 295The 13C NMR spectra of YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74EMFs are also computed (Fig.5).The overall molecular symmetry of MCN@D 3h (14246)-C 74has changed from D 3h to C s .Thus,MCN@D 3h (14246)-C 74display 41signals,including 34full intensity signals and seven half intensity ones.The chemical shifts of the cage carbons of YCN@D 3h (14246)-C 74are computed from 124to 165ppm at the B3LYP/6-31G*-lanl2dz level.For TbCN@D 3h (14246)-C 74,the chemical shifts of the cage carbons are from 126to 163ppm at the B3LYP/6-31G*-MWB54level,very close to the YCN@D 3h (14246)-C 74range.The cluster size influence is minor.The signals of the internal CN carbon atom are 189and 187ppm for YCN@D 3h (14246)-C 74and TbCN@D 3h (14246)-C 74respectively.These values are similar to those of YCN@C 78previously reported (194and 196ppm for YCN@D 3h (24109)-C 78and YCN@C 2v (24107)-C 78respec-tively,at the same level of theory)[20].ConclusionsIn summary,the geometrical structures and electronic properties of four endohedral MCN@C 74(M=Y,Tb)metallofullerenes have been computationally investigated.The B3LYP and PBE1PBE calculations agree in predicting the IPR-satisfying MCN@D 3h (14246)-C 74structures as the lowest energy isomer.Both YCN and TbCN clusters adopt the triangular structure within the D 3h (14246)-C 74cage as characterized in YCN@C s (6)-C 82and TbCN@C 2(5)-C 82.The calculated C-N and M-N bond lengths of the internal MCN moiety in MCN@D 3h (14246)-C 74are similar to those found in YCN@C s (6)-C 82and TbCN@C 2(5)-C 82.Molecular orbital analysis reveals that formal charge trans-fer of 2e takes place from MCN unit to the C 74cage.Therefore,structural determination of M@D 3h (14246)-C 74(M=Ca,Sr,Ba,Sm,Eu,Yb)allows the assignment of the same host cage for YCN@D 3h (14246)-C 74and20019018017016015014013012012YCN@D 3h (14246)-C 74D e g e n e r a c yChemical Shifts (ppm)20019018017016015014013012012TbCN@D 3h (14246)-C 74D e g e n e r a c yChemical Shifts (ppm)Fig.5The computed 13C NMR spectra.Intensities are given in atoms per cage.The blue lines denote chemical shifts of the CN carbon atoms295 Page 6of 8J Mol Model (2015) 21:295TbCN@D3h(14246)-C74.In addition,IR spectra and13C NMR spectra have been simulated theoretically to assist the future experimental exploration.Acknowledgments This work was supported by Natural Science Foun-dation of Liaoning Province,China(No.2013020096)and Department of Education of Liaoning Province,China(Grant No.L2015002). 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生物信息学－国内外书目1. Bioinformatics: sequence and genome analysis,影印本,David W. Mount，科学出版社,20022. DNA芯片和基因表达:从实验到数据分析与模建，鲍尔迪，科学出版社，20033. 分子进化与系统发育，MasatoshiNei（根井正利）SudhirKumar. 译者：吕宝忠，钟扬，高莉萍，高等教育出版社，20024. 蛋白质化学与蛋白质组学，夏其昌，科学出版社，2004年5. 蛋白质组学：从序列到功能,钱小红、贺福初等译科学出版社，2002年9月6. 蛋白质组学:理论与方法，钱小红，贺福初主编.科学出版社，20037. 蛋白质组学导论：生物学的新工具，（美）利布莱尔，科学出版社，20058. 蛋白质组学导论：生物学的新工具，张继仁（译）科学出版社，2004年12月出版9. 后基因组信息学,MinoruKanehisa著；孙之荣等译,清华大学出版社,200210. 基础生物信息学及应用,蒋彦等编清华大学出版社，科学出版社，200311. 基因VⅢ，卢因，科学出版社，200512. 基因表达序列标签（EST）数据分析手册，胡松年，浙江大学出版社,200513. 基因组,袁建刚等主译科学出版社，200214. 基因组数据分析手册,胡松年，薛庆中主编，浙江大学出版社,200315. 基因组研究与生物信息学16. 基因组研究与生物信息学，李越中闫章才高培基，山东大学出版社，200317. 基于WWW的生物信息学应用指南，李桂源,钱骏主编,中南大学出版社200418. 计算分子生物学:算法逼近，帕夫纳，化学工业出版社，200419. 计算分子生物学导论，(巴西)J.塞图宝，J.梅丹尼斯著，朱浩等译，科学出版社，200320. 纳米生物技术学，张阳德，科学出版社，200521. 生物芯片分析，张亮，M.谢纳[美]，科学出版社，200422. 生物信息学，(英)D.R.韦斯特海德(D.R.Westhead)等著；王明怡等译,科学出版社200423. 生物信息学，DavidW.Mount著钟扬，王莉，张亮主译，高等教育出版社，200324. 生物信息学,张阳德编，科学出版社，200425. 生物信息学,赵国屏等编科学出版社，200226. 生物信息学：机器学习方法，（法）皮埃尔•巴尔迪（PierreBaldi），(丹)索恩•布鲁纳克（SorenBrunak）著；张东晖等译，中信出版社，200327. 生物信息学:基因和蛋白质分析的实用指南,[美][巴森文尼斯]AndreasD.Baxevanis,[美]B.F.FrancisOuellette著；李衍达,孙之荣等译，清华大学出版社,200028. 生物信息学导论，李巍主编,郑州大学出版社，200429. 生物信息学方法指南，(加)S.米塞诺,(美)S.A.克拉维茨著；欧阳红生,阮承迈,李慎涛等译,科学出版社，200530. 生物信息学概论,(美)DanE.Krane,MichaelL.Raymer著,孙啸，陆祖宏，谢建明等译，清华大学出版社200431. 生物信息学基础,孙啸,陆祖宏,谢建明编著,清华大学出版社200532. 生物信息学若干前沿问题的探讨：中国科协第81次青年科学家论坛论文集／黄德双等主编,中国科学技术大学出版社200433. 生物信息学手册,第2版,郝柏林等编，上海科学技术出版社，200234. 生物信息学网络资源与应用,黄韧等中山大学出版社，200335. 生物信息学中的计算机技术,(美）CyntbiaGibas,PerJambecks著；孙超等译中国电力出版社，200236. 生物序列分析,蛋白质和核酸的概率论模型[M].DurbinR,EddyS,KroghA,etal.北京:清华大学出版社,200237. 生物序列突变与比对的结构分析，沈世镒著，科学出版社200438. 探索基因组学、蛋白质组学和生物信息学（中译版）孙之荣主译，科学出版社，2004年8月出版39. 现代生物信息学理论与实践，李霞主编，科学出版社，2005年11月出版40. 药物基因组学——寻找个性化治疗，蒋华良、钟扬、陈国强、罗小民等译科学出版社，2005年7月出版41. 药物生物信息学，郑珩,王非，化学工业出版社，200442. 医学生物信息学，赵雨杰主编，人民军医出版社，200243. 遗传算法的基本理论与应用.李敏强，寇纪淞，林丹，李书全，科学出版社.2002年4月44. 遗传学:基因与基因组分析，哈特尔，科学出版社,200245. DNA Sequencing: From Experimental Methods to BioinformaticsAuthor(s): Luke Alphey46. Introduction to BioinformaticsAuthor(s): Teresa Attwood, David Parry-Smith47. Bioinformatics: The Machine Learning ApproachAuthor(s): P.Baldi and S. Brunak48. DNA Microarrays and Gene Expression: From Experiments to Data Analysis and Modeling Author(s): Pierre Baldi, G. Wesley Hatfield49. Bioinformatics for GeneticistsAuthor(s): Michael Barnes, Ian C Gray50. Bioinformatics: A Practical Guide to the Analysis of Genes and Proteins, Second EditionAuthor(s): Andreas D. Baxevanis and B. F. Francis Ouellette (Eds)51. Bioinformatics ComputingAuthor(s): Bryan P. Bergeron52. Genetics DatabasesAuthor(s): M. J. Bishop53. Structural BioinformaticsAuthor(s): Philip E. Bourne, Helge Weissig54. Computational Modeling of Genetic and Biochemical NetworksAuthor(s): James M. Bower and Hamid Bolouri55. Bioinformatics: A Biologist's Guide to Biocomputing and the InternetAuthor(s): Stuart M. Brown56. Discovering Genomics, Proteomics, and BioinformaticsAuthor(s): A. Malcolm Campbell, Laurie J. Heyer57. Bioinformatics for DummiesAuthor(s): Jean-Michel Claverie and Cedric Notredame58. Computational Molecular Biology: An IntroductionAuthor(s): Peter Clote, Rolf Backofen59. Nonlinear Estimation and ClassificationAuthor(s): D.D. Denison, M.H. Hansen, C.C. Holmes, B. Mallick & B. Yu (Eds.)60.Author(s): Richard Durbin, Sean R. Eddy, Anders Krogh, Graeme Mitchison61. Genomic Perl: From Bioinformatics Basics to Working CodeAuthor(s): Rex A. Dwyer62. Protein Bioinformatics: An Algorithmic Approach to Sequence and Structure Analysis Author(s): Ingvar Eidhammer, Inge Jonassen, William R.T. Taylor63. Computational Cell BiologyAuthor(s): Christopher P. Fall, Eric S. Marland, John M. Wagner and John J. Tyson, Editors64. Evolutionary Computation in BioinformaticsAuthor(s): Gary B. Fogel, David W. Corne65. Developing Bioinformatics Computer SkillsAuthor(s): Cynthia Gibas, Per Jambeck66. Statistical Methods in Bioinformatics: An IntroductionAuthor(s): Gregory R. Grant, Warren J. Ewens67. Algorithms on Strings, Trees and SequencesAuthor(s): Dan Gusfield68. Bioinformatics : Sequence, Structure, and Databanks : A Practical ApproachAuthor(s): Des Higgins (Editor), Willie Taylor (Editor)69. Post-genome InformaticsAuthor(s): Minoru Kanehisa70. Foundations of Systems BiologyAuthor(s): Hiroaki Kitano71. Guide to Analysis of DNA Microarray Data72. Microarrays for an Integrative GenomicsAuthor(s): Isaac S. Kohane, Alvin Kho, Atul J. Butte73. BLASTAuthor(s): Ian Korf, Mark Yandell, Joseph Bedell74. Hidden Markov Models for BioinformaticsAuthor(s): Timo Koski75. Fundamental Concepts of BioinformaticsAuthor(s): Dan E. Krane, Michael L. Raymer76. Advances in Molecular BioinformaticsAuthor(s): Steffen Schulze-Kremer (Editor)77. Molecular Bioinformatics: Algorithms and ApplicationsAuthor(s): Steffen Schulze-Kremer78. Computational BiologyAuthor(s): Lecture Notes in Computer Science, Vol. 206679. Analysis of Microarray Gene Expression DatasAuthor(s): Mei-Ling Ting Lee80. Bioinformatics: From Genomes to DrugsAuthor(s): Thomas Lengauer81. Sequence Analysis in a Nutshell: A Guide to Common Tools and Databases Author(s): Darryl LeÛn, Scott Markel82. Introduction to BioinformaticsAuthor(s): Arthur M. Lesk83. Computational Molecular BiologyAuthor(s): J. Leszczynski84. Bioinformatics: Databases and SystemsAuthor(s): Stanley Letovsky (Editor)85. Computational Cell BiologyAuthor(s): Eric Marland, John Wagner, John Tyson86. Bioinformatics and Genome AnalysisAuthor(s): H.W. Mewes, B. Weiss, H. Seidel87. Bioinformatics: Methods and ProtocolsAuthor(s): Stephen Misener (Editor), Stephen A. Krawetz (Editor)88. Bioinformatics: Sequence and Genome AnalysisAuthor(s): David W. Mount89. Bioinformatics: Genes, proteins and computersAuthor(s): C.A. Orengo, D.T. Jones and J.M. Thornton90. Mathematics of Genome Analysis91. Computational Molecular Biology: An Algorithmic ApproachAuthor(s): Pavel A. Pevzner92. Bioinformatics Basics Applications in Biological Science and MedicineAuthor(s): Hooman H. Rashidi, Lukas K. Buehler93. The Phylogenetic Handbook: A Practical Approach to DNA and Protein PhylogenyEdited by Marco Salemi, Anne-Mieke Vandamme94. Computational Methods in Molecular BiologyAuthor(s): S.L. Salzberg, D.B. Searls, S. Kasif95. Comparative Genomics: Empirical and Analytical Approaches to Gene Order Dynamics, Map Alignment and the Evolution of Gene FamiliesAuthor(s): David Sankoff, Joseph H. Nadeau96. Molecular Modeling and Simulation: An Interdisciplinary GuideAuthor(s): Tamar Schlick97. Bioinformatics: From Nucleic Acids and Proteins to Cell MetabolismAuthor(s): Dietmar Schomburg (Editor), Uta Lessel (Editor)98. Introduction to Computational Molecular BiologyAuthor(s): Joao Carlos Setubal, Joao Meidanis, Jooao Carlos Setubal99. Likelihood, Bayesian and MCMC Methods in Quantitative GeneticsAuthor(s): Daniel Sorensen, Daniel Gianola100. Microarray BioinformaticsAuthor(s): Dov Stekel101. Protein Structure Prediction - A Practical ApproachAuthor(s): Michael J. E. Sternberg102. Beginning Perl for BioinformaticsAuthor(s): James Tisdall103. Pathway Analysis and Optimization in Metabolic Engineering Author(s): Néstor V. Torres, Eberhard O. Voit104. Gene Regulation and Metabolism: Post-Genomic Computational ApproachesAuthor(s): Julio Collado-Vides and Ralf Hofestadt105. Computational Analysis of Biochemical Systems A Practical Guide for Biochemists and Molecular Biologists Author(s): Eberhard O. Voit106. Pattern Discovery in Biomolecular Data - Tools, Techniques, and ApplicationsAuthor(s): Jason T. L. Wang, Bruce A. Shapiro, and Dennis Shasha107. Introduction to Computational Biology: Maps, Sequences and GenomesAuthor(s): Michael S Waterman108. Instant Notes BioinformaticsAuthor(s): D.R. Westhead, J. H. Parish, R.M. TwymanAuthor(s): Limsoon Wong110. Neural Networks and Genome InformaticsAuthor(s): Cathy H. Wu, Jerry W. McLarty111. Intelligent Bioinformatics: The Application of Artificial Intelligence Techniques to Bioinformatics ProblemsAuthor(s): Edward Keedwell, Ajit Narayanan112. Jonathan Pevsner，Bioinformatics and Functional Genomics，John Wiley & Sons, Inc，2003。