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Approaches to Global Minimum
Dihedral driving (manual or automated; a 3n) Randomization-minimization (Monte Carlo) Molecular dynamics Trial & error (poor)
pdf转word http://www.skycn.com/soft/appid/16287.html
Molecular Mechanics Part 2
Potential Energy Surfaces Input File Types Successes, Limitations & Caveats Glossary of Terms
to a designated pattern)
File Interconversion Methods
Many modeling programs will read and write several file types (Titan, Alchemy2000 and HyperChem will read and write .pdb files, but with slightly different formats Titan (.pdb) -> HyperChem (.pdb = .ent) -> (save as .hin) -> Alchemy2000 or Titan (.pdb) -> WebLabViewer (to visualize, copy into MS.doc for lab reports) Conversion programs exist: most common is BABEL Gaussian 03, which we will use for ab initio calculations, has a conversion utility called newzmat
Energy Minimization
Local minimum vs global minimum Many local minima; only ONE global minimum Methods: Newton-Raphson (block diagonal), steepest descent, conjugate gradient, others.
Successes of Molecular Mechanics...
Reasonable geometries are usually obtained: • Bond lengths within 0.1 Angstrom of experimental values • Bond angles within 2° of experimental values. Calculated energies are usually quite good: • Enthalpies of formation within 2 kcal/mol (8 kJ/mol) of experimental values Provides input structure for more involved calculations (molecular orbital methods).
Successes of Molecular Mechanics Calculations
Calculations are very fast Geometry optimizations of small to mediumsize molecules can be accomplished on a pc Conformations of macromolecules (including biomacromolecules such as peptides and polysaccharides) can be calculated using workstations or parallel processing computers.
Internal Coordinates (for NH3)
(sometimes called Z-matrix)
distance angle dihedral ref. atom #
ห้องสมุดไป่ตู้
N 0.0000 0 0.0000 0 0.0000 0 0 0 0 H 1.0200 1 0.0000 0 0.0000 0 1 0 0 H 1.0200 1 104.5368 1 0.0000 0 1 2 0 H 1.0200 1 104.5368 1 109.5796 1 1 2 3 0 (end of file) (1 means optimize, 0 means keep constant, -1 means vary according
Uses of “Steric Energy”
“Steric energy” has NO physical meaning, and it is defined differently in different programs Therefore it CAN NOT be used to compare structures calculated by different programs Its use is limited to comparing ISOMERIC structures having the SAME number and kinds of bonds (conformers, stereoisomers).
…bottom of .PDB file
CONECT 1 CONECT 2 CONECT 3 CONECT 4 CONECT 5 CONECT 6 CONECT 7 CONECT 8 CONECT 9 CONECT 10 CONECT 11 END 2 4 1 3 2 8 1 1 2 2 3 3 3 1 5 11 6 7 9 10
MM2 Atom Types (more than 60!)
1 2 3 4 5 6 7 8 9 10 11 12 C C C C H O O N N N F Cl sp3 carbon sp2 carbon (C=C) sp2 carbon (C=O) sp carbon hydrogen (see others) oxygen (single bonded) oxygen (double bonded) sp3 nitrogen sp2 nitrogen sp nitrogen fluorine chlorine 13 Br 14 I 15 S 16 S+ 17 S 18 S 19 Si 20 LP 21 H 22 C 23 H 24 H bromine iodine sulfide (-S-) sulfonium sulfoxide (use S=O) sulfone (use two S=O) silane lone pair of electrons hydroxyl hydrogen cyclopropane carbon amine hydrogen carboxylic acid hydrogen
Input is usually done graphically (by sketching or building structures atom-by-atom or by assembling component parts). This graphical model is converted to a mathematical model by the software. Each software package has its own file type, but most have some common features. The .pdb file is most common denominator.
global minimum
Potential Energy Surface
Extrema (stationary points, where the gradient is zero): saddle point
maxima
minimum
PES and Energy Minimization
First, some caveats: extrema (stationary points) are located by most methods; this includes maxima, minima, and saddle points. among the minima, local minima are found, not necessarily the global minimum. with shallow minima (flat PES), a lot of cpu time can be spent seeking the lowest energy structure.
Limitations of Molecular Mechanics
The calculations do not account for electrons! Orbital interactions are ignored! The selection of “atom type” is crucial to the computational result: • e.g., AMBER has 5 types of Oxygen: carbonyl , alcohol, acid, ester/ether, water (see next slide) • No consideration is given to the importance of delocalized p electron systems Only ground states are considered...not T.S. or *
PDB (protein data bank) file of propane (C3H8)
HETATM 1 C 1 -1.129 1.281 HETATM 2 C 2 -2.558 1.772 HETATM 3 C 3 -3.519 0.606 HETATM 4 H 4 -0.596 1.637 HETATM 5 H 5 -0.596 1.637 HETATM 6 H 6 -2.733 2.392 HETATM 7 H 7 -2.733 2.392 HETATM 8 H 8 -4.558 0.952 HETATM 9 H 9 -3.359 -0.017 HETATM 10 H 10 -3.359 -0.017 HETATM 11 H 11 -1.110 0.183 (not all columns utilized/recognized -0.000 -0.000 -0.000 0.890 -0.890 0.890 -0.890 0.000 -0.890 0.890 -0.000 continued... by all software)
All methods are tedious, but some attempt at searching for the minimum is absolutely necessary if the result is to be meaningful!
Input File Structure
Cartesian coordinate (XYZ) file
C 1 -1.129 1.281 -0.000 C 2 -2.558 1.772 -0.000 C 3 -3.519 0.606 -0.000 H 4 -0.596 1.637 0.890 H 5 -0.596 1.637 -0.890 H 6 -2.733 2.392 0.890 H 7 -2.733 2.392 -0.890 H 8 -4.558 0.952 0.000 H 9 -3.359 -0.017 -0.890 H 10 -3.359 -0.017 0.890 H 11 -1.110 0.183 -0.000 (this MAY be the same as the .PDB file, as shown here, or the orientation of the molecule may be different, making the numbers different)
