An ab-initio evaluation of the local effective interactions in the superconducting compound

The objective of the Management Trainee Program (MTP) is to recruit and develop highly qualified individuals for key positions of responsibility in the federal Public Service of Canada. It offers talented graduates and employees with high potential the opportunity to lead a representative and diversified Public Service into the future.The MTP provides hands-on work experience through assignments with federal departments and agencies. As well, an educational component complements and enhances the experience acquired on the job. Courses focus on the basic knowledge and skills required by Public Service managers, and content is set against a backdrop of larger issues including governance, policy-making, service to the public and values and ethics. Upon completion of the four-year Program (or five-year Program for those who started the Program before March 19, 1998), graduates will be qualified for managerial positions at the intermediate level.By participating in the Management Trainee Program, you are taking an important step forward in your own professional development, and are making a vital contribution to our country's future. As one of tomorrow's leaders, you can help enhance the ability of our government to serve the needs of a changing society and ensure that Canada's standards of public administration remain a model of excellence for countries around the world.History of the ProgramOne of the major issues facing the Public Service is having a sufficient pool of qualified middle managers from which the next generation of senior managers can be drawn. A study ofpost-secondary recruitment revealed that the Public Service was not competitive in hiring graduates with high potential for management, in part because it did not have an entry-level program aimed at training and developing such individuals. The Management Trainee Program (MTP) was created in response to this need.The MTP was proposed and subsequently approved by the Treasury Board Secretariat on June 20, 1990. The Public Service Commission (PSC), as delegated by the Treasury Board Secretariat (TBS), was to carry out annual recruitment campaigns, conduct screening and evaluation of candidates, match candidates with organizations, and oversee the development of participants in the Program.The Management Trainee Program was implemented in May 1991, as a five-year, entry-level Program. The objective was to recruit and develop exceptionally qualified university graduates interested in management careers in the federal Public Service. The Program also sought out promising leaders from among existing employees.The MTP has undergone many changes since its inception in 1991. On March 16, 1995, Ministers of the Treasury Board approved revisions to the MTP. One of these was theprecedes entry to the Program and appointment to the Public Service. During this period,TBS established a classification standard for the MM group. This standard consists of athree-level structure (MM-01, MM-02 and MM-03) based on a number of performance criteria. This new pay structure implies that participants are expected to demonstrate specific competencies as assessed by a Promotion Board.As part of the La Relève initiative, in 1997 the Committee of Senior Officials (COSO) and a subcommittee were charged with reviewing entry-level recruitment and development programs. Accordingly, the MTP was examined and recommendations were submitted and endorsed by the full COSO. Treasury Board ministers approved the recommendations on March 19, 1998. In consequence, the duration of the Program was changed to four years instead of five. Individuals hired in the MTP prior to March 19, 1998, are required to complete the Program under rules governing the five-year Program.An optional five-year program is still available for the MTPProgram Roles and ResponsibilitiesThe success of the Program is dependent on the strong partnership and collaboration of sponsoring organizations. While the managing partners, Treasury Board of Canada Secretariat (TBS), Public Service Commission of Canada (PSC) and Canadian Centre for Management Development (CCMD), have a strong influencing role, organizations have significant accountability and flexibility within the Program to manage the Trainees and provide a culture and experience specific to their own needs.MTP Collaborative Management CommitteeA collaborative management committee was established for MTP, based on the principlesThe MTP Collaborative Management Committee is composed of the Directors responsible for MTP from TBS, PSC and CCMD, and required program analysts. The TBS representative serves as chairperson for the meetings. This Committee meets regularly to review the status of the MTP work plans and budgets, and analyse and discuss information relating to the Program. The Committee addresses the development and implementation of initiatives and components which impact another organization's responsibilities, and determines the respective project leader, objectives and timelines in consideration of the nature of the project and relevant situational factors. Matters that require higher level input and/or authority for decision-making will be raised collectively with the respective senior managers responsible for corporate development programs in TBS, PSC, and CCMD.Shared ResponsibilitiesAll parties will respect the specific roles and responsibilities of each of the partners, while proactively sharing information and working together with a view to achieving Program goals and protecting Program integrity. While specific organizational roles and responsibilities are described in this chapter, it is recognized that certain aspects of Program management entail shared responsibility and collaboration of the partners.Examples of TBS, PSC and CCMD shared responsibilities include:∙Program design initiatives which have implications for Program delivery in other organizations;∙commitment and continuity of Program delivery. For example, changes to respective roles and responsibilities are to be made only as a result of negotiation with partners;∙revisions to Program components which impact the cost of Program delivery;∙consistent messaging for overall MTP marketing through agreed upon tools, presentations, and formal and informal networks;∙facilitation of assignments both at central agencies and organization and support of the "brokering" role of the PSC in the assignment process;∙ensuring the integration of all learning components to optimize the results and serve collective clients more effectively;∙learning enhancement activities, such as MTP Day and other special events;∙community development support activities such as Town Hall meetings, and Training Coordinators' Day; and∙ensuring that organizations and Trainees are aware of the roles and responsibilities of each partner in MTP.Work Planning and BudgetsAnnual work plans and budgets will be shared with partners at the MTP Collaborative Management Committee at a time agreed to by the partners in consideration of the Program cycle, as well as departmental work planning and budget cycles.Monitoring, Audits, Reports and EvaluationsMonitoring of the Program will be done through the review and analysis of the annual reports submitted by the PSC and CCMD to TBS, through periodic independent audit and evaluation, and as specified in the Results Framework.The MTP Collaborative Management Committee will report to Deputy Ministers once a year. It is recognized that MTP also provides information and reports to the Committee of Senior Officials (COSO), the Treasury Board Secretariat Advisory Committee (TBSAC), the MTP Consultative Committee members, and other stakeholders as required.PSC and CCMD are to maintain comprehensive records as would normally be required for evaluation and audit purposes.Each managing partner has its own particular role and responsibilities:Other partners in the Program also have their own particular role and responsibilities:∙∙∙The MentorMentoring is a highly desirable component of the MTP, but not a required one. The mentor should be prepared to act as a guide and role model. He/she should, therefore, have extensive work experience, know the organization and the MTP, be enthusiastic, and be willing to support the Trainee through such means as:∙meeting with the Trainee on a regular basis;∙inviting the Trainee to meetings or seminars as an observer;∙introducing the Trainee to key personnel;∙bringing to the Trainee's attention pertinent literature on current policy issues; and ∙providing advice and guidance to Trainees on assignments, development plans and career aspirations.Treasury Board of Canada SecretariatManagement Trainee Program PolicyManagement Trainee Program PolicyPolicy ObjectiveThe objective of the MTP is to develop highly qualified managers, eligible for appointment to positions at the EX-minus-2 level upon completion of the Program. This is to be done by giving participants experience in a variety of operational settings which will allow them to acquire the skills and knowledge necessary to be Public Service leaders. Graduates of the Program will comprise a pool of middle managers with extensive knowledge of the functions, operation and values of the Canadian Public Service from which senior management positions can be filled in the future.Policy StatementAs part of a larger renewal effort, the Management Trainee Program (MTP) is designed to enrich the pool of middle managers who have the potential to become future leaders of the Public Service. The MTP is an entry level program that generally runs on a 5 year (60 month) cycle, although a shortened 4 year program is possible. The Program recruits and develops qualified university graduates, as well as individuals already employed by the federal government, interested in management careers in the Public Service.The Program operates under the authority of Treasury Board as the employer, is managed by the Public Service Commission (PSC), and is administered by departments.ApplicationThis policy applies to departments and agencies listed in Schedule 1 Part 1 of the Public Service Staff Relations Act.Policy RequirementsThe five constituencies of the MTP are:- Treasury Board Secretariat (TBS)- Public Service Commission (PSC)- Canadian Centre for Management Development (CCMD)- Participating departments and agencies, and- Management trainee.Each has its own particular roles and responsibilities which are as follows:Treasury Board SecretariatThe Human Resources Branch (HRB) of the Secretariat acts as the policy centre for the MTP on behalf of the Treasury Board. Subject to the strategic direction of the Treasury Board, TBS will:- seek approval for the resources necessary for the sound functioning of the MTP; -create and monitor classification standards for the Program;- determine the terms and conditions of employment;- define the MTP policy by formulating Program objectives and operating principles to meet Public Service needs, in consultation with the PSC, CCMD and participatingdepartments and agencies;- ensure that the operating principles of the MTP are consistent with Public Servicepolicies including other management training; and,- evaluate the Program as appropriate.The Public Service CommissionThe Public Service Commission is responsible for the management of the marketing, promotion, recruitment, development and placement components of the MTP on behalf of the Treasury Board. Subject to the policy established by Treasury Board the PSC will:Market and Promote the MTP by:- identifying departmental staffing requirements;- developing and implementing a marketing strategy aimed at university students and public servants to stimulate interest in the Program;- developing and implementing a marketing strategy geared at placing up to 100candidates each year, including active promotion of the Program and its benefits tomanagers across the Public Service;- consulting with departments to plan and execute the annual recruitment and selection activities.Place trainees by:- Matching and placing suitably qualified candidates in participating departments,including co-ordinating initial relocation for candidates;Support the development of trainees by:- assisting with career planning and providing advice to help ensure trainees are matched with appropriate assignments; - co-ordinating central agency assignment opportunities and assignments for non-participating departments which are compatible with thedevelopmental needs of trainees, and providing advice and assistance to all parties in negotiating these assignments.Manage the MTP by:- consulting with departments, CCMD and TBS to establish, maintain and updateoperating principles and guidelines to meet Program objectives;- developing guidelines and tools for departments to use in the assessment of trainees for Promotion and Selection Boards, and assisting where necessary;- providing overall support to departments in the delivery of the Program, including the provision of an orientation and/or refresher course for Departmental MTP Co-ordinators;- maintaining a management information base on aspects of the Program relevant to the needs of the MTP co-ordinator, the PSC and TBS;- managing salary and non-salary dollars for assignments within central agencies and for small organizations requesting funds;- co-ordinating all aspects of the graduation of trainees from the Program;- developing the legal instruments with respect to the Public Service Employment Act, necessary to ensure the smooth operation of the Program;- monitoring Program performance and advising the TBS on feedback received fromvarious sources such as departments, trainees, universities etc., regarding Programdesign, in order to ensure that the MTP meets its objectives.Canadian Centre for Management DevelopmentCCMD is responsible for the development, delivery and evaluation of the formal training component of the MTP. Subject to the strategic direction of the Treasury Board, CCMD will:- consult with departments, PSC and TBS to develop and deliver training which enables participants to acquire: a common orientation to government and the Public Service, a broad understanding of the socio-economic factors which influence decision-making and an understanding of other contemporary management issues;- in consultation with departments, TBS and the PSC, determine the frequency andtiming of CCMD courses and ensure that participants are advised;- review courses periodically to ensure that they continue to meet Program objectives. Participating Departments and AgenciesTo ensure the smooth and effective functioning of the Program participating departments and agencies will:- identify a contact person to be known as the MTP Co-ordinator;- promote the MTP and provide information on the Program to managers and potential candidates;- establish departmental procedures for determining the number of trainees requiredannually;- identify executives or equivalent level managers to assist in the selection process and to act as mentors for trainees;- ensure that trainees have and follow individual development plans reflectingservice-wide MTP requirements, departmental competencies and individual needs;- provide assignments which are consistent with the objectives of the Programservice-wide and which provide a meaningful challenge to both trainees whom theysponsor and to trainees from other departments who may come on assignment to them;- ensure that assignment objectives and performance indicators are clearly identified and that work performance is frankly and accurately assessed in detail;- request the assistance of the PSC, if required, in identifying assignments outside the home organization;- maintain the obligations of a home organization for trainees on assignment outside the department including maintaining communication with them, passing along significant departmental information, periodically reviewing their progress and arranging for smooth re-entry;- provide trainees with a five year plan, and ensure they receive annual assignmentdescriptions, as well as regular evaluations throughout the MTP cycle;- provide the PSC with regular reports on trainee activities, including promotion board results and Performance Review Reports;- ensure that upon individual completion of the Program, participants are appointed to positions reflecting their qualifications; in the case of trainees who successfully complete all aspects of the Program, this should be to a position at the EX-minus-2 level, unless the deputy head has agreement to operate a four year version with an EX-minus-3outcome; - assist trainees in identifying a mentor and provide advice as required tomanagers and trainees; - organize MM2 and MM3 promotion boards; provide training on promotion boards to departmental managers.TraineesTo ensure the smooth functioning of the Program trainees will:- actively seek out assignments and other learning opportunities consistent with theirdevelopment plan;- participate in the development of a five year plan and annual assignment descriptions;- take full advantage of the training and assignment opportunities provided to further their career objectives;- develop and expand upon a network of contacts;- maintain communication with their Departmental Co-ordinator; - provide on a timely basis, all necessary documents pertinent to the promotion board ; - attend all mandatory CCMD and departmental training courses.MonitoringIn monitoring the MTP, TBS will rely upon management information from the PSC, CCMD, departments and agencies, trainees and periodic program evaluations.ReferencesEnquiriesEnquiries about this policy should be referred to the Departmental MTP Co-ordinator at departmental headquarters who may in turn, as appropriate, direct questions to:Management Trainee ProgramRecruitment and Development Programs DivisionRecruitment Programs and Priority Administration DirectoratePublic Service CommissionManagement Trainee ProgramHuman Resources Branch,Treasury Board SecretariatAppendix A - Management Trainee Program Policy Administration1. PurposeThis appendix presents guidelines for the consistent application of the Management Trainee Program policy.2. DefinitionsAb Initio (Ab Initio) - non-employee status conferred on external candidates who take initial language training prior to appointment to the Public Service as a trainee (MM classification group). Candidates who accept Ab Initio (AIO) status are not deemed to be trainees.Departmental Co-ordinator (Co-ordinateur ministériel) - an individual designated by a department to administer the Program within the department and attend to trainees' concerns.Extended leave (congé prolongé) - any continuous leave or combinations of leaves exceeding 60 consecutive working days (3 months).External (externe)- a participant in the MTP recruited from outside the Public Service.Home Organization (ministère d'attache) - a department or agency that assumes responsibility for a trainee, sponsors the trainee for the duration of the Program, andco-ordinates the final placement of the trainee.Internal (interne) - a participant in the MTP recruited from within the Public Service.Management trainee (stagiaire en gestion) - an individual recruited externally or internally to the Public Service and appointed to the Public Service under the MTP. They are classified in the MM group. Also referred to in this policy as "trainee".Public Service (Fonction publique) - the departments and agencies listed in Part I, Schedule I of the Public Service Staff Relations Act.3. Operating PrinciplesThe selection, education and assignment phases of the MTP will operate in a manner consistent with the following principles:3.1 SelectionEach year, up to 100 candidates are accepted into the Program. These people must:- have recently obtained a master's degree from a recognised university if applying from outside of the Public Service; or have a bachelor's degree and no more than three years experience if applying from within the Public Service;- show commitment to developing a professional management career in the federalPublic Service;- demonstrate the potential to develop the skills required to be effective Public Service managers;- be bilingual to the C-B-C level, or show both the willingness and ability to becomebilingual. Those not meeting the language requirements at the time of recruitment are provided with up to twelve months of government-sponsored language training before appointment to the Program;- be willing to relocate and travel as required;- successfully complete a rigorous recruitment process.3.2 Training and DevelopmentThe educational component of the MTP is an integral part of the Program that is mandatory for all participants. Its purpose is to provide trainees with a common orientation to government and the Public Service and to ensure that they acquire a broad understanding of the factors that influence government decision making. Formal training provides a foundation of knowledge to enable trainees to succeed in the Program and perform well in their home organizations. It includes courses provided by the Canadian Centre for Management Development (CCMD) as well as a Management Orientation Program run either by departments or by Training and Development Canada.The educational component is interspersed throughout the Program's 60 month cycle, which allows trainees to continually expand their understanding of contemporary management issues, and to actively reflect upon what is learned in assignments.3.3 Language TrainingCandidates who are not bilingual and who were recruited after March 1995 must complete language training and obtain a C-B-C level before formal entry into the Program and, in the case of those not already employed by the government, before appointment to the PublicService. External candidates on language training have Ab Initio status and will not be retained in the MTP or, with certain exceptions, in the Public Service generally, if they do not meet the C-B-C level within a maximum of 52 weeks. PSC co-ordinates language training for "ab-initio" candidates who do not meet the C-B-C requirement.Candidates who are not bilingual and who were recruited before March 1995 must complete language training and obtain a B-B-B level before exiting the Program. Language training must be completed at any time during the 60 month cycle within a maximum of 52 weeks. Since trainees may require up to a year for training purposes, departments must ensure that training is provided for within the prescribed period.3.4 AssignmentOn-the-job assignments form the core of the Program curriculum by allowing participants to apply the theories, principles and practices, presented during the educational phase. To develop knowledge, abilities and managerial skills, assignments must be progressively more challenging and should require trainees to work in a variety of different situations.4. Home OrganizationsTrainees are sponsored by one department or agency throughout their time on the Program, although they can have assignments in other departments and/or agencies. The sponsoring department or agency, also called the home organization, retains the responsibilities of an employing organization including the commitment to offer trainees having completed all requirements for successful graduation, positions that are consistent with the EX-minus-2 level.All assignments must be approved by the home organization although sponsorship of a participant may be transferred to another department or agency at any time, provided that all parties agree.5. GraduationTo be considered an MTP graduate, participants:- must complete 60 months of progressively more responsible assignments (including time spent on language training for trainees appointed before March 16, 1995, andexclusive of time spent on extended leave);- must be assessed "fully satisfactory" or higher during this period, with the exception of one lesser assessment;- must complete all mandatory CCMD training;- must complete the middle management orientation course;- must meet Official Language proficiency requirements;- must have experience in supervising or leading groups/teams;- must meet additional department-specific requirements as set by the homeorganization.- should have worked in the home department;- should have worked at a location outside and inside the National Capital Region;- should have worked in a central agency;- should have experience in serving the public;- should have experience in at least one of finance, human resources, materialmanagement, or policy development position; and,- should have experience in a related operational department (optional).Upon graduation trainees are expected to assume a managerial position at the EX-minus-2 level.6. TerminationParticipation in the MTP terminates under any of the following circumstances:- after five years (60 months) from the commencement of the Program exclusive of time spent on extended leave or official language training;- when a participant withdraws from the Program voluntarily;- upon premature termination of an assignment without the consent of the PSC's MTP program office or the departmental MTP co-ordinator who arranged the assignment; or,- when a trainee exhibits continued poor performance (i.e. has more than one evaluation of less than fully satisfactory) or fails to comply with the requirements for continuingparticipation as outlined in this policy or in any of the individual's assignment agreements.7. Four Year (48 month) MTPA department or agency can apply to the Secretary of Treasury Board for the authority to operate a four year (48 month) Program with an expected target outcome of EX-minus-3 for successful graduates. Once approved, the department or agency must inform the PSC so that it may recruit accordingly.DEVELOPMENT FRAMEWORK FOR THE MANAGEMENT TRAINEEPROGRAMCOMPETENCIES, EXPERIENCE, TRAINING AND LEARNING FOR THE MANAGEMENT TRAINEE PROGRAMCOMPETENCY REQUIREMENTSCompetencies for each of the three levels in the Management Trainee Program (MTP) are derived from a combination of the classification standards for the MTP and the management characteristics described in the “Profile of Public Service Leaders and Managers”. The Classification Standards may be found in the Treasury Board Manual (TBM). The “Profile” may be found in the Treasury Board Manual (TBM) , Human Resources Volume, Chapter 1–9, Appendix H–7. The Competency Requirements are provided here in this Development Framework and Trainees will be assessed against them to determine promotions to each succeeding level.EXPERIENCEIn general, assignments for Management Trainees must be consistent with the activities as outlined in “A Career Planning Guide from Supervisor to Assistant Deputy Minister” of the Treasury Board Policy on the Development of Supervisors, Managers and Executives in the Public Service (TBM, Human Resources Volume, chapter 1–9, Appendix A–7). Each succeeding assignment should have increased responsibility as well as increased complexity.Assignments must contribute to the acquisition and maintenance of the competencies needed to lead and manage in the federal government context.Over the five-year period, the assignments must provide increasing operational and management experience which will ultimately enable the Trainee to obtain a position in the home department. Ideally, assignments should include line and staff experience, experience in a region outside the NCR, experience in the NCR and experience in a central agency. Certain flexibility may be necessary in the case of smaller departments and agencies.TRAININGTraining will be provided to assist Management Trainees in acquiring the required competencies. A summary of MTP training/learning needs is provided in this Developmental Framework. It is based on the Framework of Generic Supervisory and Middle Management Learning Needs. This is。

Ab Initio Study of the Penultimate Effect for the ATRP Activation Step Using Propylene,Methyl Acrylate,and Methyl Methacrylate MonomersChing Yeh Lin,†Michelle L.Coote,*,†Alban Petit,‡Philippe Richard,‡Rinaldo Poli,*,§and Krzysztof Matyjaszewski⊥*,ARC Centre of Excellence in Free-Radical Chemistry and Biotechnology,Research School of Chemistry,Australian National Uni V ersity,Canberra ACT0200,Australia,Laboratoire de Synthe`se et d’Electrosynthe`se Organome´talliques,Faculte´des Sciences“Gabriel”,Uni V ersite´de Bourgogne,6 Boule V ard Gabriel,21000Dijon,France,Laboratoire de Chimie de Coordination,UPR CNRS8241lie´e par con V ention a`l’Uni V ersite´Paul Sabatier et a`l’Institut National Polytechnique de Toulouse,205 Route de Narbonne,31077Toulouse cedex,France,and Department of Chemistry,Carnegie Mellon Uni V ersity,4400Fifth A V enue,Pittsburgh,Pennsyl V ania15213Recei V ed April18,2007;Re V ised Manuscript Recei V ed June5,2007ABSTRACT:High-level ab initio molecular orbital calculations are used to study the magnitude and origin of the penultimate unit effect in atom transfer radical polymerization(ATRP)of dimers involving the comonomers methyl acrylate(MA),methyl methacrylate(MMA),and propylene(P).The penultimate unit effects depend on the nature of the terminal unit and the halogen and can be significant,with the MMA unit in particular altering the equilibrium constant for the bond dissociation equilibrium by as much as2orders of magnitude.Specifically, the ratios of the equilibrium constants(K)for the bond dissociation reactions of H-M2-M1-Cl at298K,relative to the equilibrium constant(K0)of the corresponding unimer H-M1-Cl,for penultimate units M2)P,MA,and MMA are respectively0.81,1.27,and92.46for M1)P;8.73,2.64,and32.69for M1)MA;and5.73,0.78, and1.57for M1)MMA.For the bromides,H-M2-M1-Br,the corresponding ratios K/K0for M2)P,MA, and MMA are respectively0.55,0.70,and54.79(M1)P);5.44,0.63,and2.38(M1)MA);and0.24,12.18, and43.77(M1)MMA).It is shown that the penultimate unit effects arise in both the entropy and enthalpy of the equilibrium and are the result of a complex interplay of stereoelectronic effects which,for the ester linkages, are heavily influenced by intramolecular hydrogen bonding.The penultimate unit effects have important implications for initiator design;for example,they can account for the experimental observation that the isobutyrate halide is an inefficient initiator for MMA polymerization.The results also imply that penultimate unit effects need to be taken into account in the synthesis of block,gradient,and random copolymers.IntroductionPenultimate unit effects are well-known in many types of polymerizing systems.Perhaps the most studied examples are in the propagation step of free-radical copolymerization,where, following Fukuda’s seminal study in1985,1it has been generally established that penultimate(rather than terminal)models are necessary for an accurate description of the copolymerization kinetics of most pairs of monomer.2Penultimate unit effects have also been documented in the transfer kinetics of free-radical copolymerizations,3in the activation/deactivation equilibria of controlled radical polymerizations,such as nitroxide-mediated polymerization,4and in reversible addition fragmentation chain transfer(RAFT)polymerization,where penultimate unit effects of as much as2-3orders of magnitude have been reported.5It is thought that the penultimate unit can influence the rate and equilibrium constants of these reactions by a variety of different mechanisms,including steric6and conformational7effects on both the enthalpy and entropy as well as via polar8and radical stabilization effects on the enthalpy.9Unsurprisingly,the relative importance of these various factors varies substantially with the type of reaction being studied and the substitution pattern and also according to whether it is the rate or equilibrium constant that is being studied.For example,in the case of propagation and transfer,radical stabilization effects are generally larger in the equilibrium constants,compared with rate coefficients,due to partial cancellation from the early transition structures;8 conversely,polar interactions are normally expected to be larger in the rate coefficients as the charge-transfer configurations are typically lowest in their relative energy in the vicinity of the transition state.10Atom transfer radical polymerization(ATRP)is based on an inner-sphere redox process that involves the reversible transfer of a halogen atom from a dormant species,P n-X,and a catalyst, typically a copper(I)species complexed by multidentate amine-based ligand,CuIY/L m.11This results in the formation of a radical which carries the chain growth and a metal complex in a higher oxidation state,X-Cu II Y/L m,which acts as spin trap. An understanding of this equilibrium is of paramount importance if one wants to fine-tune the ATRP process. Experimentation has highlighted an interesting penultimate effect that plays an important role in the activation of the dormant species in ATRP.12For the particular case of poly-*Corresponding authors.E-mail:mcoote@.au;km3b@ ;poli@lcc-toulouse.fr.†Australian National University.‡Universite´de Bourgogne.§Laboratoire de Chimie de Coordination.⊥Carnegie MellonUniversity.5985 Macromolecules2007,40,5985-599410.1021/ma070911u CCC:$37.00©2007American Chemical SocietyPublished on Web07/10/2007merizations initiated by organohalides that are structurally derived from the monomer(e.g.,2-halo-isobutyrate,or H-MMA-X,for the polymerization of methyl methacrylate),the dormant species containing more than one monomeric entity (e.g.,H-(MMA)n-X with n g2)display a higher activation rate constant relative to the initiator(n)1),for the atom transfer process in eq 1.This seems particularly evident for1,1-disubstituted monomers(e.g.,MMA)but is less important for monosubstituted monomers such as styrene or methyl acrylate (MA).The enthalpy of eq1(∆H1)can be related to the difference of two bond dissociation energies(BDEs),and since BDE(Mt-X)is obviously constant for a given halide as the chain grows,the increase in activation and/or equilibrium constants can be attributed to a decrease in the BDE(R-X)as R begins to add monomer units(eq2).In other words,the penultimate monomer unit can affect the homolytic strength of the carbon-halogen bond;however,contribution of entropy to the penultimate effect cannot be neglected. Understanding the energetic effect of the penultimate unit in ATRP is also relevant for the reinitiation by macromonomers for the generation of block copolymers as well as for controlling the microstructure for statistical and gradient copolymers.11g,13 Moreover,it would be interesting to determine whether bulky penultimate units such as MMA or MA could be exploited to enhance activation rate constant of the relatively inactive terminal alkyl halide derived from R-olefin,e.g.,propylene (P).14In an analogous manner,TEMPO has been shown to control the copolymerization of styrene with acrylonitrile, even though it is unable to control the homopolymerization of the latter monomer,4a and a similar situation was recently reported for methyl methacrylate copolymerization with sty-rene.15In the present work,we use computational chemistry to study the magnitude and origin of the penultimate unit effect in the ATRP of dimers involving the comonomers MA,MMA,and P.We have recently carried out a computational study of the BDEs(eq3)of a variety of commonly used ATRP initiators, including several ones that contain a single monomer unit,in order to evaluate their relative activities in ATRP.16The results of this study were found to be in excellent agreement with the available thermochemical data and could be qualitatively related to the experimentally known initiator activities.These compu-tational results can therefore be used as a valuable guide for the selection of an appropriate initiator for any given monomer.A more rigorous approach,however,must take into account the penultimate effect.In this contribution,we present a computational analysis of the effect of the penultimate monomer unit on the carbon-halogen homolytic bond strength.Since the relevant effect is believed to be limited to the penultimate monomer unit(namely the activities should be similar for H-(M)n-X,where M is the monomer,for n g2)and because of computational complexity as n increases,our study was limited to molecules that contain two monomer units(both homo-and heteroleptic).We have selected dormant species that contain propylene(P),methyl acrylate(MA),and methyl methacrylate(MMA),in all possible combinations,and either chlorine or bromine chain ends.The bond strengths and thermodynamic parameters will be compared with those of the initiators that contain only a single monomer unit,i.e.,H-P-X,H-MA-X,and H-MMA-X,and also with the C-H and C-F BDEs of the corresponding H-(M)n-H and H-(M)n-F systems.The latter comparison will help us in assessing the relative importance of radical stabilization,polar,and stericeffects.Computational MethodsBond dissociation energies(BDEs)were computed usingstandard density functional theory(DFT)and ab initio molecularorbital theory calculations.Initially,all conformations of the Rand R-X molecules were generated by a molecular mechanicsforce field(MMFF)conformational search by use of the Spartan04Macintosh(v.1.0.1)program.The MMFF force field doesnot include parameters for hydrocarbon radicals,so these weretreated as sp2-centers.All conformers were then reoptimized atthe B3-LYP/6-31G(d)level of theory in Gaussian03,17and theglobal minimum structure was selected on the basis of thesemore accurate results.Frequencies were also calculated at thislevel of theory on the global minimum-energy structures andscaled by the appropriate scale factors.18For the systemscontaining two chiral centers(H-M2-M1-X;M2)MA;M1 )P,MA,MMA;X)Cl,Br),full conformational searches were performed on both diastereomers,and the lowest energyspecies overall was selected for the study.For both the H-MA-M1-Cl and H-MA-M1-Br species,these lowest energydiastereomers were RR,RS,and RS for M1)P,MA,and MMA,respectively.For H-MA-M1-Cl,the energy differencesbetween the lowest energy conformations of each diastereomerwere1.35,0.29,and0.30kcal mol-1for M1)P,MA,andMMA,respectively;for H-MA-M1-Br,the correspondingvalues were1.24,0.72,and0.30kcal mol-1.Improved energies were calculated using a modified versionof the G3(MP2)-RAD level of theory using a combination ofMolpro2002.619and Gaussian03,17as described below.Toassist in the qualitative rationalization of the results,the chargedistributions(within the closed-shell species)and spin densitydistributions(within the radicals)were calculated using a naturalbond orbital(NBO)population analysis,carried out at theROHF/cc-pVTZ level of theory.It should be noted that all DFTcalculations on radicals were performed using the spin-unrestricted formalism;all ab initio calculations were performedusing restricted open-shell wave functions.In standard G3(MP2)-RAD,20coupled cluster calculations[URCCSD(T)]with a large triple- basis set(called G3MP2large)are approximated as the sum of calculations at the lower-costURCCSD(T)/6-31G(d)level of theory and a basis set correctionterm,calculated as the difference in the corresponding ROMP2/G3MP2large and ROMP2/6-31G(d)energies.A higher-levelcorrection term and spin-orbit corrections21for atoms are alsoincluded.This method has been shown to reproduce the heatsof formation of a large test of open-and closed-shell species towithin∼1kcal mol-120and provide excellent absolute andrelative values of R-X bond dissociation energies(R)Me,Et,i Pr,and t Bu;X)H,CH3,OCH3,OH,and F).22In ourmodified version of this method,we simply replace calculationswith the double- Pople basis set(6-31G(d))with equivalentcalculations using the double- Dunning basis set,cc-pVDZ,and calculations with the triple- Pople basis set(G3MP2large)with equivalent calculations using the triple- Dunning basisset,cc-pVTZ.This modification is made necessary because thereis no G3MP2large basis set defined for the Br atom.The higher-level correction term has not been reoptimized for our modifiedmethod;however,it constitutes only a small contribution to theabsolute BDEs(<2.23kcal mol-1)and always cancels entirelyfrom the relative BDEs(and hence penultimate unit effects),and we therefore do not expect it to influence the present results.∆H1)BDE(R-X)-BDE(Mt-X)(2)R-X h R•+X•(3)5986Lin et al.Macromolecules,Vol.40,No.16,2007Having obtained the geometries,frequencies,and improved energies,partition functions and corresponding thermodynamic functions(i.e.,enthalpy H,entropy S,and Gibb’s free energy G)were calculated at298K using the standard textbook formulas,based on the statistical thermodynamics of an ideal gas under the harmonic oscillator/rigid rotor approximation.23 The equilibrium constant for each dissociation reaction was then calculated using the standard formulawhere T is the absolute temperature(298K),c°is the standard unit of concentration(c°)0.040897mol L-1),R is the universal gas constant(8.3143J mol-1K-1),∆n is the change in moles upon reaction,Q i and Q j are the molecular partition functions of reactant i and product j,respectively,∆G is the Gibb’s free energy of reaction,and∆E is the zero-point vibrational energy corrected energy change for the reaction. In order to improve the accuracy of the calculations,all relevant low-frequency torsional modes in the C-Br and C-Cl dissociations were treated separately as hindered internal rota-tions using a standard procedure,described previously.24Full rotational barriers for these modes were calculated at the B3-LYP/6-31G(d)level of theory as relaxed scans in steps of10°and are provided in the Supporting Information.Since the C-H and C-F bond dissociation reactions were used merely to assist in the interpretation of the reaction enthalpies,the less compu-tationally intensive harmonic oscillator approximation was used for these systems.It should be noted that in the present work all BDEs were calculated using the global minimum-energy conformations(and, where relevant,the lowest energy stereoisomer)of each species. However,in some cases,the second lowest energy conformation obtained from the calculations was found to be very close to the most stable one and could be thermally populated at the temperature of the ATRP.Thus,to be rigorous,one should consider a Boltzmann-weighted-averaged energy for the purpose of calculating the thermodynamic parameters.However,we consider that the simple BDE estimation by using only the most stable conformation(and stereoisomer)for the halide and for the free radical provides a relevant value for the purpose of the present investigation.In essence,we expect that conformers that are close enough in energy to the global minimum to be significantly populated are likely to have very similar BDEs, and hence averaging their values is unlikely to affect the results. One might argue that the population of higher energy conforma-tions could have an important effect on the atom transfer kinetics (k act and k deact in eq1)because the conformational equilibrium is attained much more rapidly than the time scale for the atom transfer process.Therefore,there is the possibility that a less populated,higher energy conformation is more reactive than the lower energy one if its atom transfer barrier is lower.This issue,however,is beyond the scope of the present investigation. In any case,the apparent polymerization rate constant depends on rate coefficients of propagation step but only on the thermodynamics of the atom transfer process in eq1(namely, k act/k deact)and not on the individual values of the transfer rate constants.Results and DiscussionThe enthalpies,entropies,and free energies of the bond homolysis reactions(H-M2-M1-X f H-M2-M1•+•X)were calculated at the G3(MP2)-RAD level of theory for all combina-tions of M1,M2)P,MA,and MMA and X)Cl and Br(see Table1).Figure1shows the optimized conformations of the H-M2-M1-Cl,H-M2-M1-Br,and H-M2-M1•species;full geometries of all species are provided in the Supporting Information.Optimized Conformations.From the comparison of the various geometries in Figure1,it can be appreciated that theTable1.Thermodynamic Parameters for the Homolytic Bond Rupture of the M1-X Bond in H-M2-M1-X(M1,M2)P,MA,MMA;X)Cl,Br,F,and H)and H-M1-X aRM2M1X∆H298/kcal mol-1∆S298/cal mol-1K-1∆G298/kcal mol-1∆∆H298b/kcal mol-1∆∆S298c/cal mol-1K-1K/K0dP Cl84.6135.4474.04001 P P Cl85.1836.9574.170.57 1.500.81 MA P Cl85.8039.9073.90 1.19 4.46 1.27 MMA P Cl83.2439.8571.36-1.37 4.4092.46 MA Cl74.6628.3966.19001 P MA Cl75.0934.1464.910.43 5.758.73 MA MA Cl76.4836.4265.62 1.828.02 2.64 MMA MA Cl75.8239.2264.13 1.1610.8332.69 MMA Cl74.3636.7363.40001 P MMA Cl72.9135.3662.37-1.44-1.37 5.73 MA MMA Cl74.6437.1763.550.280.440.78 MMA MMA Cl72.2130.4463.14-2.14-6.29 1.57 P Br74.4435.2363.93001 P P Br75.2936.9164.280.85 1.690.55 MA P Br75.6738.6864.14 1.24 3.460.70 MMA P Br73.4739.9561.56-0.96 4.7354.79 MA Br65.3730.0156.43001 P MA Br66.0735.7155.420.70 5.70 5.44 MA MA Br67.1735.1256.70 1.80 5.110.63 MMA MA Br67.1837.7955.91 1.817.78 2.38 MMA Br64.4935.9153.78001 P MMA Br63.8430.8854.63-0.65-5.040.24 MA MMA Br64.9042.2752.300.41 6.3612.18 MMA MMA Br61.2032.4051.54-3.29-3.5143.77a Calculated at the G3(MP2)-RAD level of theory using the hindered rotor model to treat all low-frequency torsional modes.b∆∆H298)∆H298(H-M2-M1-X)-∆H298(H-M1-X).c∆∆S298)∆S298(H-M2-M1-X)-∆S298(H-M1-X).d K/K0)exp(-∆∆G298/RT).K(T))(c°)∆n e-∆G/RT)(c°)∆n(∏products Q j∏reactants Q i)e-∆E/RT(4)Macromolecules,Vol.40,No.16,2007Penultimate Effect for the ATRP Activation Step5987best conformation for a pair of related chloride and bromide compounds is always the same.However,a change is often observed on going from the halogenated compounds to the free radical.In particular,whenever two carboxylate moieties are present and one monomer unit is MMA,the carboxylate moieties tend to stack with each other for the halogenated compounds to form a sort of incomplete boat conformation,whereas they are part of a more open chain in the corresponding free radicals (see the H -MA -MMA -X and H -MMA -MA -X series in Figure 1).The transformation of an sp 3to sp 2C atom is certainly responsible for this variation.On the other hand,the H -MA -MA -X molecules form an open structure unlike those contain-ing one MMA unit.Thus,the additional CH 3group is also play-ing a role,probably disfavoring the open structure by way of an additional 1,3gauche interaction.Interestingly,the H -MMA -MMA -X molecules also prefer a more open conformation (possibly due to increased steric crowding),and in these cases it is the radical that forms the stackedconformation.Figure 1.Views of the lowest energy optimized geometries for all H -M 2-M 1•,H -M 2-M 1-Cl,and H -M 2-M 1-Br molecules.5988Lin et al.Macromolecules,Vol.40,No.16,2007Reaction Entropies.The bond breaking process entails an entropy increase,which can essentially be related to the additional translational component associated with the release of the X free atom,and also a small and constant electronic contribution of2.754cal mol-1K-1,due to the unpairing of two electrons and to the availability of the two degenerate R and states.However,it is interesting to examine all contribu-tions to the reaction entropy(translational,rotational,vibrational, and electronic)individually(see Table2).The translational contribution to the reaction entropy is restricted to a relatively narrow range,34.8-36.1cal mol-1K-1(for X)Cl)and35.9-38.0cal mol-1K-1(X)Br).As a reference,the calculated translational S298values for free Cl and Br are36.59and39.01 cal mol-1K-1,respectively.The increase of∆S298(transl)is less than the free halogen atom values because R-X has more translational entropy than the free radical R.The entropy of R-Br is slightly greater than that of the related R-Cl.The rotational contribution is always negative and small;i.e., the saturated R-X has slightly more rotational entropy than the R radical.The range is between-0.26cal mol-1K-1(H-MA-MMA-Cl)for the heavier systems and-3.80cal mol-1 K-1(H-P-Br)for the smaller ones.This parameter generally increases with the size of R;in particular,there is a drastic increase on going from the one-monomer to the two-monomer molecules.However,some minor deviations to this trend occur due to conformational differences.For example,when the terminal unit(i.e.,M1in H-M2-M1-X)is MMA,the contribution of the rotational entropy decreases when the MA penultimate unit(M2)is replaced with the larger MMA unit as the conformation of the radical product becomes less extended and the closed-shell species becomes more extended.However, the opposite occurs when the terminal unit is MA,as in this case it is the conformation of the reactant closed-shell species that becomes less extended when the MMA penultimate unit replaces an MA unit.The largest effect on the spread of∆S298(total)is due to the vibrational contribution,∆S298(vibr),which includes both the contribution from the true vibrational modes and also those low-frequency torsional modes treated as hindered internal rotations. The corresponding value,∆S298(vibr′),in which all modes are treated under the harmonic oscillator approximation is also shown in Table2for purposes of paring these values,it is seen that the harmonic oscillator approximation introduces a large error(as much as3cal mol-1in some cases), and these errors are typically largest in the dimer species(i.e., in the presence of a penultimate unit).This highlights the important contribution of hindered internal rotations to penul-timate unit effect,a feature originally discussed in the context of propagation reactions by Heuts et al.25These results also further reinforce the importance of treating low-frequency torsional modes of oligomeric radicals as hindered internal rotations in accurate thermochemical studies,a result also seen in computational studies of RAFT polymerization26and propa-gation.25,27,28For the remainder of this section,we will focus on the more accurate hindered rotor values.The contribution of∆S298(vibr)to the total entropy change can be either positive or negative and can vary by as much as 8cal mol-1as the penultimate unit is altered.In general,one might have expected the vibrational entropy to decrease upon dissociation,as the free radical contains one less vibrational degree of freedom.However,this small effect can be enhanced (or countered)by a decrease(or increase)in the flexibility of the oligomeric chain,associated with,for example,changes in the intramolecular hydrogen bonds and/or the alignment of various functional groups with the unpaired electron in the radical.Unsurprisingly,therefore,the most significant penul-timate unit effects occur when the terminal unit contains a carboxylic acid group(i.e.,MA or MMA).In the case of the methyl acrylate unimers,the vibrational contribution to the BDEs is large and negative,presumably due to the vibrational restrictions imposed by the need for theπ-accepting carboxylic acid group to align with the unpaired electron in the product radical.This contribution becomes much less negative when penultimate units are added,as other factors(such as increasedTable2.Contributions to the Homolytic Carbon-Halogen Bond Rupture Entropy for All H-M2-M1-X(M1,M2)P,MA,MMA;X)Cl,Br)Molecules aRM2M1X∆S298(trans)/cal mol-1K-1∆S298(rot)/cal mol-1K-1∆S298(vibr′)b/cal mol-1K-1∆S298(vibr)c/cal mol-1K-1P Cl34.81-3.000.990.87 P P Cl35.56-1.56-1.330.19 MA P Cl35.87-1.12-0.49 2.40 MMA P Cl35.93-1.100.23 2.25 MA Cl35.58-1.91-4.45-8.03 P MA Cl35.87-1.22-4.55-3.26 MA MA Cl36.04-0.66-4.62-1.72 MMA MA Cl36.08-0.32-2.960.71 MMA Cl35.70-1.31-0.52-0.42 P MMA Cl35.93-0.84 1.40-2.50 MA MMA Cl36.08-0.260.71-1.40 MMA MMA Cl36.11-0.83-2.46-7.59 P Br35.91-3.780.330.35 P P Br37.06-2.24-2.16-0.65 MA P Br37.59-1.78-2.120.12 MMA P Br37.70-1.88-1.16 1.38 MA Br37.09-2.70-5.05-7.13 P MA Br37.59-1.91-5.29-2.72 MA MA Br37.89-1.12-6.31-4.41 MMA MA Br37.96-1.02-5.76-1.91 MMA Br37.29-2.02-1.39-2.11 P MMA Br37.70-1.33-0.64-8.26 MA MMA Br37.96-0.96-1.05 2.51 MMA MMA Br38.03-1.40-4.03-6.98a Each reaction has a∆S298(electr)contribution of2.754cal mol-1K-1.b Includes contribution from low-frequency torsional modes,treated under the harmonic oscillator approximation.c Includes contribution from low-frequency torsional modes treated as hindered internal rotations. Macromolecules,Vol.40,No.16,2007Penultimate Effect for the ATRP Activation Step5989steric pressure in the closed-shell species and reduced flexibility due to intramolecular hydrogen bonding)take over.In contrast,the vibrational contribution for the methyl methacrylate-terminated species shows the opposite effect:the vibrational contribution for the unimers is relatively small (though still negative)and (with one exception)becomes much more negative with the introduction of penultimate units.It would appear that the steric pressure from the additional R -methyl group reduces the vibrational flexibility of the closed-shell unimeric species,while differing hydrogen-bonding interactions in the closed-and open-shell species lead to the differing penultimate unit effects.In that regard,we note that the combinations of methyl acrylate with methyl methacrylate units (in either order)lead to higher than expected vibrational contributions,presumably due to the increased hydrogen bonding (and hence reduced vibrational entropy)in the stacked conformations of the closed-shell species.In a similar manner,the species containing two methyl meth-acrylate units possess a lower than expected vibrational con-tribution as in those cases it is the open-shell species that forms the stacked conformation (see Scheme 1).In summary,the main conclusions that can be drawn from these data is that the entropic component of the penultimate unit effect is significant (as much as 10.83cal mol -1K -1),it arises predominantly in the vibrational (and internal rotational)partition functions,it depends on a complex interplay of stereoelectronic effects,and,in the case of acrylate and methacrylate units,it is heavily influenced by intramolecular hydrogen bonding.Reaction Enthalpies A close inspection of Table 1reveals that the penultimate unit effect on the enthalpy can be very significant in these systems,ranging from -3.29kcal mol -1(for H -MMA -MMA -Br,relative to H -MMA -Br)to 1.82kcal mol -1(for H -MA -MA -Cl,relative to H -MA -Cl).Although the penultimate unit effects depend on the nature of the terminal unit (and,to a lesser extent,the halogen),some generalizations may be made.In particular,it is seen that the MA penultimate unit strengthens the breaking bond,relative to hydrogen,with the strengthening effect being largest for the MA terminal unit.The MMA penultimate unit usually weakens the breaking bond relative to hydrogen,except when the terminal unit is MA.The propyl penultimate unit shows a relatively weak effect on bond dissociation enthalpy (typically less than 1kcal mol -1)and can either strengthen or weaken the bond,depending upon the nature of the terminal unit and the halogen.Previously,it has been found that both the polarity and radical stabilization ability of a substituent can affect the R -X bond dissociation energy of small molecules (R -X;R )Me,Et,iPr,and t -Bu;X )H,CH 3,OCH 3,OH,and F),with the radical stabilization effect of R being most dominant for the (relatively nonpolar)R -H compounds and the polar effect of R being dominant for the (more polar)R -F compounds.29One might expect the larger R -Cl and R -Br compounds of the present work to have intermediate polarities to these extremes and thus display intermediate behavior,though their BDEs are likely to be further complicated by steric effects.To help deconvolute these factors,the corresponding C -H and C -F bond dissocia-tion energies were calculated (see Table 3),together with the charges on the halogen in the closed-shell species and the spin densities on the nominal radical carbon in the open-shell species (see Table 4).The penultimate unit effects on the bond dis-sociation enthalpies for all systems are also plotted in Figure 2.Polar Effect.Considering first polar factors,it is seen in Table 4that the breaking alkyl -halogen bond shows some degree of polarity in all cases,and thus resonance between the covalent and ionic (i.e.,alkyl +X -)forms is likely to affect the strength of the breaking bond.Not unexpectedly,the fluorides show the largest degree of charge separation and have the strongest bonds,followed by the chlorides and then the bromides.Within each series,the degree of charge separation depends upon the nature of the terminal unit,with the propyl unit affording the most polar bonds and the acrylate and methacrylate units the least.This is readily understood in terms of the electron-donating properties of an alkyl substituent vs the electron-accepting properties of an ester substituent.How-ever,importantly,the polarity of the breaking bonds appears to be relatively unaffected by the nature of the penultimate unit.This is because the methyl and ester groups donate or accept electrons principally via hyperconjugation and resonance,respectively,and in these systems there is no possibility for conjugation between the chain end and the γ-carbon.Although the ester groups could in principle interact with the chain end inductively as well,they are relatively weak sigma acceptors (compared with,for example,a cyano group),and this weak effect diminishes rapidly with distance from the chain end.Thus,for these substituents at least,polar factors do not contribute significantly to the origin of the penultimate unit effect.Radical Stabilization Effect.The contribution of radical stabilization effects can be assessed through an examination ofScheme 1.Hydrogen-Bonding Contribution to the Penultimate Unit Effect of MMA vsMA5990Lin et al.Macromolecules,Vol.40,No.16,2007。

V ASP5.2RELEASEDWe are happy to announce the release of the new version of the Vienna ab-initio simula-tion package VASP–VASP5.2.The new release contains many additional features which enhance the functionality of the program package-we emphasize in particular the ability to perform calculations using exact non-local exchange or hybrid functionals and of many-body perturbation(GW)calculations.A list of all new features,including references to the pertinent publications is given below.New features in VASP5.2•Less memory demanding on massively parallel machines(support by the IBM Blue Gene team is gratefully acknowledged)•New gradient corrected functionals-AM05-PBEsol-new functionals can be applied using standard PBE POTCARfiles(improved one-center treatment)Reference:A.E.Mattsson,R.Armiento,J.Paier,G.Kresse,J.M.Wills,and T.R.Mattsson:The AM05density functional applied to solids,Journal of Chemical Physics128,084714(2008).•Finite differences with respect to changes in the-ionic positions-lattice vectorsThis allows the automated determination of second derivatives yielding-inter-atomic force constants and phonons(requires a supercell approach)-elastic constantsSymmetry is automatically considered and lowered during the calculations.•Linear response with respect to changes in the-ionic positions-electrostaticfieldsThis allows the calculation of second derivatives yielding-inter-atomic force constants and phonons(requires a supercell approach)-Born effective charge tensor-static dielectric tensor(electronic and ionic contribution)-internal strain tensors-piezoelectric tensors(electronic and ionic contribution)Linear response is only available for local and semi-local functionals.•Exact non-local exchange and hybrid functionals-Hartree-Fock method-hybrid functionals,specifically PBE0and HSE06-screened exchange-experimental:simple model GW-COHSEX(applies empirical screened exchange function-als)-experimental:hybrid functional B3LYPReferences:J.Paier,R.Hirschl,M.Marsman,and G.Kresse:The Perdew-Burke-Ernzerhof exchange-correlation functional applied to the G2-1test set using a plane-wave basis set,Journal of Chemical Physics122,234102(2005).J.Paier,M.Marsman,K.Hummer,G.Kresse,I.D.Gerber,and J.G.´Angy´a n,Screened hybrid density functionals applied to solids,Journal of Chemical Physics124,154709(2006). M.Marsman,J.Paier,A.Stroppa,G.Kresse:Hybrid functionals applied to extended systems,Journal of Physics:Condensed Matter20,064201(2008). J.Paier,M.Marsman,and G.Kresse:Why does the B3LYP HF/DFT hybrid functional fail for metals?,Journal of Chemical Physics127,024103 (2007).•Frequency dependent dielectric tensor by summation over eigenstates-in the independent particle approximation-in the random phase approximation(RPA)via GW routines-available for local,semi-local,hybrid functionals,screened exchange and Hartree-Fock References:M.Gajdoˇs,K.Hummer,G.Kresse,J.Furthm¨u ller,and F.Bechstedt:Linear optical properties in the PAW methodology,Physical Review B73,045112(2006).•Fully frequency dependent GW at the speed of the plasmon pole model-single shot G0W0-iteration of eigenvalues in G and W until selfconsistency is reached-experimental:self-consistent GW by iterating the eigenstates in G(and optionally W)-experimental:total energies from GW using the RPA approximation to the correlation energy-vertex corrections(localfield effects)in G and W in the LDA(available only non-spin polarized)-experimental:many-body vertex corrections in W(available only non-spin polarized) References:M.Shishkin and G.Kresse:Implementation and performance of frequency-dependent GW method within PAW framework Physical Re-view B74,035101(2006).M.Shishkin and G.Kresse:Self-consistent GW calculations for semiconductors and insulators,Physical Review B75,235102(2007). M.Shishkin,M.Marsman,and G.Kresse:Accurate quasiparticle spectra from self-consistent GW with vertex corrections,Physical Review Letters99, 246403(2007).J.Harl and G.Kresse:Cohesive energy curves for noble gas solids calculated by adiabatic connectionfluctuation-dissipation theo-rem,Physical Review B77,045136(2008).•Experimental:-TD-HF and TD-hybrid functionals by solving the Cassida equation(non-spinpolarized only using Tamm-Dancoffapproximation)-Bethe-Salpeter on top of GW(non-spinpolarized only using Tamm-Dancoffapproximation)Reference:J.Paier,M.Marsman,G.Kresse:Dielectric properties and excitons for extended systems from hybrid func-tionals,Physical Review B78,121201(R)(2008).For all features marked”experimental”,no support is available.These features are supplied”as is”,they are stable,but have not been widely applied and tested.IMPORTANT:The present version of the code has been tested only using the Intel Fortran compiler (ifc.10.X,ifc.11.X).Support for other compilers is presently not available.IMPORTANT:Certain features implemented in the new version of VASP(exact exchange,hybrid functionals,and GW calculations)are computationally very demanding.We advise all VASP users inter-ested in using these functionalities to consult the publications listed above.For all owners of a valid license for VASP4.6we offer an upgrade at the conditions described in the draftfor a new license agreement attached to this message.The fee for an upgrade will be1000Euro for academic (undergraduate teaching)institutions and2000Euro for other public non-profit research institutions.The license agreement for VASP5.2will replace the existing license agreement for VASP4.6-note that in certain license agreements upgraded from VASP4.4or older versions,the maximum number of users is higher than fixed in the current agreement.If these licenses are upgraded,the limit of six users will apply in the future. If owners of such licenses want to continue to profit of the more liberal terms for their use of VASP4.6,a new independent license for VASP5.2will be required.Licences for VASP4.4or older cannot be upgraded.The fee for new licenses to VASP5.2will4000Euro for academic and8000Euro for other non-profit institutions.Users interested in an upgrade of their licenses should complete the draft for a new license agreement attached to this message and send it signed(in duplicate),together with a purchase order on the license fee toDr.Doris VogtenhuberComputational Materials ScienceUniversit¨a t WienSensengasse8/12A-1090WIEN,AUSTRIAWe emphasize that the terms of the agreement are not negotiable,modifications of the agreement will not be accepted.Advance copies per fax(+43-1-4277-9514)are acceptable to speed up the procedure,but should be followed by the signed originals per air mail.Georg Kresse J¨u rgen Hafner。

Ultrafast transformation of graphite to diamond: An ab initio study of graphite under shock compressionChristopher J. Mundy, Alessandro Curioni, Nir Goldman, I.-F. Will Kuo, Evan J. Reed, Laurence E. Fried, and Marcella IanuzziCitation: The Journal of Chemical Physics 128, 184701 (2008); doi: 10.1063/1.2913201View online: /10.1063/1.2913201View Table of Contents: /content/aip/journal/jcp/128/18?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inLaser-induced versus shock wave induced transformation of highly ordered pyrolytic graphiteAppl. Phys. Lett. 106, 161902 (2015); 10.1063/1.4918929Molecular dynamics simulations of shock compressed heterogeneous materials. II. The graphite/diamond transition case for astrophysics applicationsJ. Appl. Phys. 117, 115902 (2015); 10.1063/1.4914481Ab initio study of shock compressed oxygenJ. Chem. Phys. 132, 154307 (2010); 10.1063/1.3402497AB INITIO MOLECULAR DYNAMICS SIMULATIONS OF WATER UNDER STATIC AND SHOCK COMPRESSED CONDITIONSAIP Conf. Proc. 955, 443 (2007); 10.1063/1.2833091Towards controlled production of specific carbon nanostructures— a theoretical study on structural transformations of graphitic and diamond particlesAppl. Phys. Lett. 79, 63 (2001); 10.1063/1.1382852Ultrafast transformation of graphite to diamond:An ab initio study of graphite under shock compressionChristopher J.Mundy,1,a͒Alessandro Curioni,2Nir Goldman,3I.-F.Will Kuo,3Evan J.Reed,3Laurence E.Fried,3and Marcella Ianuzzi41Chemical and Materials Science Division,Pacific Northwest National Laboratory,Richland,Washington99352,USA2IBM Research,Zurich Research Laboratory,CH-8803Ruesschlikon,Switzerland3Chemistry,Materials,Earth and Life Sciences,Lawrence Livermore National Laboratory,Livermore,California94550,USA4Paul Scherrer Institut,Winterthurerstrasse190,CH-5232PSI,Villigen,Switzerland͑Received16November2007;accepted1April2008;published online8May2008͒We report herein ab initio molecular dynamics simulations of graphite under shock compression inconjunction with the multiscale shock technique.Our simulations reveal that a novel short-livedlayered diamond intermediate is formed within a few hundred of femtoseconds upon shock loadingat a shock velocity of12km/s͑longitudinal stressϾ130GPa͒,followed by formation of cubicdiamond.The layered diamond state differs from the experimentally observed hexagonal diamondintermediate found at lower pressures and previous hydrostatic calculations in that a rapid bucklingof the graphitic planes produces a mixture of hexagonal and cubic diamond͑layered diamond͒.Direct calculation of the x-ray absorption spectra in our simulations reveals that the electronicstructure of thefinal state closely resembles that of compressed cubic diamond.©2008AmericanInstitute of Physics.͓DOI:10.1063/1.2913201͔INTRODUCTIONDespite being an area of intense research,the phaseboundaries and electronic properties of elemental carbon atextreme pressures and temperatures͑e.g.,10–100s of GPaand1000s of K͒are relatively poorly known.Diamond an-vil cell experiments have been used to study the transforma-tions of graphite under static compression at extreme condi-tions of temperature and pressure.1,2Shock compressiondynamically strains the sample in a uniaxial direction,whilesimultaneously heating the sample.Shock compression ex-periments can achieve nanosecond temporal resolution,andare thus well suited to study time-dependent phenomena.Shock compression experiments up toϳ20GPa have ob-served a martensitic phase transformation from graphite todiamond,3where the graphitic planes slide to form a hexago-nal diamond,which,in turn,forms a cubic diamond.Thetransition from graphite to diamond was observed to occur in10ns for a20GPa shock.Shock Hugoniot parameters forgraphite to diamond transitions have been measured up to120GPa using gas gun experiments.4͑The Hugoniot is the locus of thermodynamic states accessible by a shock.͒Laser-induced shock experiments have been used to study the melt-ing curve of diamond to significantly higher pressure condi-tions͑up to2000GPa͒.5However,experimental techniqueshave only recently been developed to perform in situ studiesof chemical transformations in shocks.6–8Molecular andatomic scale information are difficult to experimentally ob-tain,and theoretical studies are necessary in order to developsimple chemical pictures for the high pressure-temperature behavior of the phase transformations of carbon.A number of thermodynamic equilibrium simulations of carbon at extreme pressures and temperatures have been per-formed,where the pressure and temperature of the system are preset rather than simulating the numerous thermody-namic states induced by shock compression.Several studies have investigated the solid/liquid phase boundaries of carbon at high pressures and temperatures using both empirical9,10 and ab initio11,12potentials.Relatively few studies have in-vestigated the atomistic features of the martensitic phase transition of graphite to diamond.A previous density func-tional theory͑DFT͒study of hydrostatic constant pressure compression found that the sliding of graphite planes into an orthorhombic phase preceded the formation of diamond.13,14 It has been postulated that a layered diamond phase could be formed by direct buckling of hexagonal graphite without plane sliding at pressures above120GPa.13,14It was con-cluded that the experimental observation of this phase was very unlikely.These studies differ from shock compression experiments in that the simulations arefixed at a single state point,whereas shock compression causes a material to visit numerous thermodynamic states.An additional key differ-ence is that the stress in these simulations is hydrostatic, unlike shock waves,which contain regions of highly nonhy-drostatic stress due to the uniaxial nature of planar shock compression.Until recently,it has been extremely difficult to obtain a clear theoretical picture of chemistry behind shock fronts be-cause direct simulation of shock compression can require tens of millions of particles.15One empirical potential has been developed for the study of shock-induced melting of diamond,16although the parametrization of such potentialsa͒Electronic mail:chris.mundy@.THE JOURNAL OF CHEMICAL PHYSICS128,184701͑2008͒0021-9606/2008/128͑18͒/184701/6/$23.00©2008American Institute of Physics128,184701-1for high pressure carbon is still an active area of research.9,10 In order to accurately model the breaking and forming of chemical bonds behind shock fronts,we are generally re-quired to use DFT.Molecular dynamics͑MD͒calculations using DFT,however,are limited to only tens to hundreds of particles due to the extreme computational cost.This pre-cludes making a direct one-to-one comparison between simulations and shock compression experiments,where the nonhydrostatic conditions present in the steady shock front can produce novel intermediate species and mechanisms.In particular,we are interested in determining a molecular level picture of the graphite to diamond phase transformation in-duced by shock loading.Thus,a computational capability to access both electronic states and information on chemical bonding,while capturing the nonhydrostatic nature of a steady shock and the concomitant MD,is necessary to elu-cidate chemical processes at extreme pressures and temperatures.The multiscale shock technique17–20͑MSST͒is a simu-lation methodology based on the Navier–Stokes equations for compressibleflow.Instead of simulating a shock wave within a large computational cell with many atoms,15the MSST computational cell follows a Lagrangian point through the shock wave as if the shock were passing over it. This is accomplished by time-evolving equations of motion for the atoms and volume of the computational of cell to constrain the stress in the propagation direction␴xxϵp to the Rayleigh line and the energy of the system to the Hugoniot energy condition.17–19In the case of a shock,conservation of mass,momentum,and energy across the shock front leads tothe Hugoniot relation E−E0=12͑p+p0͒͑v0−v͒,where E is theenergy and v is the volume.A subscript0refers to the pre-shocked state,while quantities without subscripts refer to the postshocked state.The Rayleigh line p−p0=U2␳0͑1−␳0/␳͒͑where U is the shock velocity and␳is the density͒describesthe thermodynamic path connecting the initial state of the system to itsfinal͑Hugoniot͒state.For a given shock speed, these two relations describe a steady planar shock wave within continuum theory.By constraining the MD system to obey these relations,MSST enables simulation of the shock wave with significantly fewer atoms and,consequently,with significantly smaller computational cost.MSST has been shown to accurately reproduce the sequence of thermody-namic states throughout the reaction zone of shock com-pressed explosives with analytical equations of state.19Lin-ear scaling of computational work with simulation duration has enabled simulation lengths of up to0.2ns of tight-binding ab initio MD simulations of shock compressed nitromethane.20In this study,we present large scale ab initio DFT MD simulations of the transformation of graphite to diamond un-der shock compression normal to the basal planes.We study significantly higher longitudinal shock stress than previous experiments.3Wefind that the martensitic phase transforma-tion of graphite to diamond occurs much more rapidly as a result.We observe a novel mechanism for the phase trans-formation where the graphitic planes buckle directly,instead of sliding and forming an orthorhombic statefirst.13,14We identify this new intermediate as a layered diamond state,which is a mixture of hexagonal and cubic diamond.We thencalculate the x-ray absorption spectra͑XAS͒of the variousstages of our simulations and determine that the end state ofthe shock compression simulation has a diamondlike elec-tronic configuration.Our results provide a detailed atomicpicture from DFT of the chemistry behind shock fronts ingraphite for thefirst time.SIMULATION DETAILSWe have used Car–Parrinello͑CP͒and Born–Oppenheimer͑BO͒MD in conjunction with MSST to ensureaccurate simulation of the shock induced thermodynamicstates.We employed an optimized version of the CPMDcode21,22for the Blue Gene/L supercomputer at LawrenceLivermore National Laboratory.Four independent simula-tions using the CPMD software package21on360carbon at-oms in conjunction with the MSST method were performed.We performed two Born–Oppenheimer͑BO1,2͒calculations utilizing spin restricted DFT,and CPMD simulations23usingboth spin restricted and unrestricted DFT.A plane-wave cut-off of120Ry and the Perdew–Burke–Ernzerhof exchangeand correlation functional24was used for the BO simulations,although a smaller cutoff of90Ry was found to convergethe stress tensor and total energy for the CP simulations.Cutoffs were based on an uncompressed reference supercell.Subsequent shock compression yields a higher effective cut-off.We found the results for the spin unrestricted and spinrestricted CP calculations to be nearly identical for both andconsequently,only the spin restricted CP simulation is re-ported herein.The interaction between core and valenceelectrons are described by Martins–Troullier pseudo-potentials.25An initial supercell͑in cubic angstroms͒of hex-agonal graphite with size of20.10ϫ12.75ϫ12.30,corre-sponding to experimental graphite lattice parameters,wasused in conjunction with⌫-point sampling of the Brillouinzone.All calculations were performed on four midplanes ͑4096CPUs͒of the Blue Gene/Light supercomputer at LLNL.To compute the XAS spectra,we have used the all-electron half-hole transition potential method with Gaussian and augmented plane-wave treatment of DFT as imple-mented in CP2K.26,27For this calculation,we have used a 6-311G**all-electron basis set for carbon.28In order to investigatefinite size effects,we have con-ducted MSST simulations using the classical potential forcarbon from the work of Tersoff.30The resulting equations ofstate for system sizes of360,2880,and23040carbon atoms TABLE I.Table of simulation parameters andfinal thermodynamic states three calculations performed with different number of atoms͑N͒utilizing the Tersoff potential͑Ref.30͒for carbon in conjunction with the MSST at a shock speed of12km/s.The initial densities were identical to those per-formed with DFT interaction potentials.All three simulations were run for 100ps with a time step of0.1fs.N=360N=2880N=23040T final͑K͒491849814978P xx͑GPa͒130130130␳final͑g/cc͒ 3.5 3.6 3.6184701-2Mundy et al.J.Chem.Phys.128,184701͑2008͒are shown in Table I .Given the insensitivity of the thermo-dynamic end states to system size using the Tersoff potential,system size effects are unlikely to be present in our DFT simulations.The MSST simulations with the Tersoff poten-tial yielded an amorphous ͑e.g.,noncrystalline ͒state upon shock compression,unlike the diamond phase obtained from DFT.Consequently,we have omitted discussion of its result-ing structural parameters and molecular configurations.RESULTS AND DISCUSSIONWe chose a shock speed of 12km /s in order to produce a shock strong enough to see plastic deformations,and see chemistry on computationally accessible time scales.Our simulations using shock velocities under 12km /s did not yield a diamond phase on the time scale of the simulation ͑e.g.,5–10ps ͒.Simulation parameters for the DFT calcula-tions and final thermodynamic states including equation of state ͑EOS ͒calculations 29fit to experimental results are re-corded in Table II .We achieved longitudinal stresses in the shock propagation direction of ϳ134–140GPa in all three simulations.The total stresses ͑stress tensor trace ͒at the end of the simulations were 83–95GPa.The nonhydrostatic stress tensor indicates that full plastic relaxation of stress to a hydrostatic state has not yet occurred after 1ps of simulation and the simulation has not reached a final thermodynamic state.As a result of the Rayleigh line constraint and the high density of diamond relative to graphite,we expect the simu-lated pressures,temperatures,and densities to be below those of the EOS models in Table II which provide final shock states only.The time evolution of the thermodynamic prop-erties of the shock compressed graphite simulation are shown in Fig.1.After less than 200fs,the simulations all experienced a rise in temperature and pressure followed by a plateau,and second rise plateau after an additional 100fs.This is due to phase transformations and a rearranging of the chemical bonds of the system,discussed below.Shock experiments performed on graphite up to 20GPa have suggested that the transformation to the diamondlikestate is martensitic 3under the pressures studied,and occurs on a roughly nanosecond time scale.Our study,at 130GPa,is close to the melting line of diamond.Thus,a change in mechanism to a nonmartensitic transformation with an amor-phous intermediate is conceivable.An order parameter for tetrahedral configurations 31provides insight into the time evolution of the graphite to a cubic diamond ͑perfectly tet-rahedral state ͒phase transition.The order parameter contains an angular part and a distance part.The angular part S g is defined asS g =332͚j =13͚k =j +14ͩcos ␺j ,k +13ͪ2,͑1͒where ␺j ,k is the angle subtended between the j th and k thbonds.The distance part of the order parameter is defined asS k =13͚k =14͑r k −r ¯͒24r ¯2,͑2͒where r k is the radial distance from the central atom to thek th peripheral atom,r ¯is the arithmetic mean of the fourradial distances,and 13is a normalization factor.We consid-ered the total value order parameter S tot =S g +S k here.For a random configuration of bonds ͑e.g.,a liquid or amorphous solid ͒,S tot yields values of 0.25or greater.31For diamond,the order parameter is 0.We computed the initial value of S tot for graphite to be ϳ0.2.Consequently,we expect the value of S tot to decrease monotonically if our simulations exhibit a martensitic phase transformation.A nonmartensitic phaseTABLE II.Simulation parameters and final thermodynamic states for all three simulations.An electronic mass of 25a.u.was used for the CP runs.The EOS result is based on a fit to experiment ͑Refs.4and 29͒.The differ-ence averages of sp 2and sp 3percentages for the BO 2run is likely due to its short trajectory.Running averages of sp 2and sp 3fractions have been exam-ined and indicate that trajectories from all simulations are converging to the same values.BO 1BO 2CP EOS ͑Final state ͒Cell mass ͑a.u.͒7ϫ10717ϫ10717ϫ107N/A Time step ͑fs ͒0.0970.0970.012N/A Wavefunction cutoff ͑Ry ͒12012090N/A Wavefunction convergenceTolerance ͑a.u.͒5ϫ10−51ϫ10−6N/A N/A T final ͑K ͒4084.24058.83351.25300P xx ͑GPa ͒139.8134.4136.4150P tot ͑GPa ͒94.884.783.4N/A ␳final ͑g/cc ͒ 3.9 3.8 3.8 4.2sp final 2͑%͒183019N/A sp final 3͑%͒827081N/AFIG.1.Time evolution of the thermodynamic states induced by the 12km /s shock velocity.The results are shown for the BO 2simulation.The thermo-dynamic profiles of all three simulations were nearly identical.184701-3Ultrafast transformation of graphite to diamond J.Chem.Phys.128,184701͑2008͒transformation would exhibit an increase to a value equal to or greater than 0.25if a liquidlike intermediate is formed first,followed by a decrease to 0.Plots of S tot for all three DFT simulations clearly show a martensitic phase transformation ͑Fig.2͒.S tot decreases rap-idly and roughly monotonically to near-zero values as the graphite compresses to diamond.This indicates the absence of an amorphous intermediate state.The nonzero endpoints indicate that the final configurations are not perfectly tetra-hedral.It is interesting to note the ϳ100fs plateau observed for all three simulations,similar to Fig.1.This is due to the transient layered diamond phase,which is discussed below.All three simulations yield extremely similar results for the structural variation as a function of time.Thus,the observed martensitic transformation is reproducible with different simulation protocols ͑see Table II ͒.Our results suggest that the mechanism of the graphite to diamond remains marten-sitic between 20and 130GPa,although the time scale drops by three orders of magnitude.The CP simulation phase trans-formation is in good agreement with the BO simulations de-spite the electron heating issues in the CP simulation that cause the temperature to drift by ϳ180K from the target ͑Hugoniot ͒energy and the BO simulation temperature.In order to create a structural picture for the changes that occur during the shock compression,we have calculated the wide XAS ͑WAXS ͒͑Fig.3͒.The WAXS intensities I ͑Q ͒are calculated using the following formula:32I ͑Q ͒=͚ijf C 2͑Q ͒exp ͑i Q ·r ij ͒,͑3͒where f C ͑Q ͒are the standard carbon atomic form factors.33We have used an x-ray energy of 37.45keV for all calculations.1For the first few hundred femtoseconds of each simulation,the graphitic planes stay relatively intact,and weobserved single peaks at ϳ6°and 9.5°,and a doublet cen-tered at ϳ16°.This corresponds nearly exactly to experimen-tal results for compressed graphite.1Comparison of the WAXS of the middle plateau of our simulations to that of hexagonal diamond 14shows a mixture of hexagonal and cu-bic diamond spectra.Instead of a doublet at ϳ9°,we found a single peak,similar to what is found for cubic diamond.Our computed spectrum does exhibit the hexagonal diamond sin-glets at ϳ10°and 12.5°.However,the doublet found in hex-agonal diamond at ϳ16°appears to be coalescing into the single peak found in cubic diamond.This mixed cubic/hexagonal diamond phase is similar to what is found in static simulations of graphite compressed to much lower conditions.13The graphite layers likely buckle after rapid compression,allowing for sp 3-sp 3bonds to occur between the basal planes.14This represents a novel mechanism for the formation of cubic diamond from shock compression.The hexagonal diamond intermediate seen at lower shock velocities 3is not observed under the strong shock loading studied here.In all three DFT simulations,the layered dia-mond phase transforms to cubic diamond within ϳ100fs.FIG.2.Evolution of the tetrahedral order parameter as a function of time.The dashed curve corresponds to the BO 1simulation and the solid curve to the BO 2simulation.The dotted curve is the result from the CP simulation.The difference in the time scale to fully compress the simulation cell is dictated by the fictitious cell mass ͑see Table I ͒.Graphite corresponds to a value of 0.2and pure cubic diamond to a value of 0.A nonmartensitic transition to a liquid phase would have shown an increase in the value of the order parameter to 0.25or greater,followed a monotonic decrease to0.FIG.3.Wide angle x-ray scattering intensities of the compressed states ofgraphite.All results shown are from BO 1͑black curves ͒.The top panel ͑graphite ͒is averaged from zero to 300fs,with comparison to experimental results ͑dotted curve ͒at 3GPa ͑Ref.1͒.The middle panel ͑layered diamond ͒is averaged from 300to 500fs,shown with comparison to simulations for hexagonal diamond ͑Ref.14͒͑dotted curve ͒.The missing doublet at ϳ9°and the coalescence of peaks at ϳ16°indicates a mixture of hexagonal and cubic diamond phases.The bottom panel ͑cubic diamond ͒is averaged over the remainder of the simulation,with comparison made to simulations at 20GPa ͑Ref.14͒͑dotted curve ͒.184701-4Mundy et al.J.Chem.Phys.128,184701͑2008͒Snapshots of the three different phases found in our simula-tions ͑graphite,layered diamond,and cubic diamond ͒are shown in Fig.4.In addition to the above structural information,ab initio calculations also yield insight into the electronic states,which are not obtainable from empirical interaction poten-tials.In particular,we wish to investigate the effects of strong shock compression on the time evolution of the elec-tronic structure of the system.Although the final state of our simulation appears to be structurally diamondlike,this does not guarantee the existence of a diamondlike ͑insulating ͒electronic configuration.Recent advances in the techniques for computing XAS from ab initio calculations using all-electron methods allow us to directly compute the spectro-scopic signature of the final state achieved in our simulation.The XAS for our periodic supercell are shown in Fig.5.Our calculated XAS spectrum for graphite at 300K ͑top panel ͒shows a near-edge feature at ϳ287eV,which corre-sponds to a 1s to ␲*transition,indicative of a ␲-bonding network.1The higher energy remainder of the spectrum cor-responds to 1s to ␴*transitions ͑␴-bonding network ͒.How-ever,the XAS spectrum of the final state of our simulation ͑middle panel,black curve ͒has a marked the absence of the ␲*transition and an enhanced ␴*part of the spectrum.This is expected for a ␴bonded network structure such as cubic diamond.In addition,the spectrum exhibits a diffuse maxi-mum at ϳ290–300eV,a minimum at ϳ303eV,and a sec-ond maximum at ϳ306eV.The minimum at ϳ303eV very closely corresponds to the experimentally measured “second band gap”signature of a diamondlike material.34For refer-ence,we have computed the XAS of compressed cubic dia-mond in a hydrostatic state at the same density as our final compressed state ͑bottom panel ͒.We observe that the posi-tion of the second band gap of the hydrostatically com-pressed cubic diamond is in good agreement with both ex-periment and the end state of our simulations.In addition,we have also isolated the XAS of the simu-lation end state due to the sp 2-only carbon centers ͑middle panel,dashed curve ͒.Due to the significantly lower concen-tration of sp 2-only sites ͑Table II ͒,this normalized spectrum was then scaled by a factor of 0.6in order to be visible on the same scale.The ␲*signal of this compressed state is blueshifted relative to the ␲*signal of the uncompressed graphite.This blueshift can be seen,although in a less dra-matic,in the experiment 1and is likely due to the effects of the pressure applied normal to the basal planes.We also ob-serve a ␲*transition at ϳ288eV and a diminished ␴-bonding network.CONCLUSIONWe have used ab initio MD to provide a simple atomistic picture for the shock-induced phase transformation of graph-ite to diamond.Our results indicate that the transition is mar-tensitic at 130GPa,which is consistent with experiments at 20GPa.3This suggests that the mechanism may remain mar-tensitic from 20to 130GPa along the shock Hugoniot.However,we note two significant differences in our findings.First,we find that the graphite to diamond transition occurs four orders of magnitude faster at 130GPa than at the ex-perimental pressure of 20GPa ͑1ps versus 10ns ͒.Second,we observe a completely different transformation mechanism than found in hydrostatic ͑not shock ͒simulations.We find that a new intermediate layered diamond phase is formed without plane sliding,through buckling of the basal planes.From examination of Table II ,it is clear that the plastic re-laxation of stress is not complete at the final simulationtimeFIG.4.Snapshots of the BO 1simulation at various points during shock compression.The circled region in the layered diamond snapshot ͑b ͒corre-sponds to a likely hexagonal diamondregion.FIG.5.Calculated XAS of ͑top panel ͒graphite at 300K,͑middle panel ͒our final compressed state,͑bottom panel ͒hydrostatically compressed cubic dia-mond at the same density as the final compressed state.The XAS of graphite shows the ␲*pre-edge intensity at ϳ285eV and the ␴*intensity at ϳ295eV.The middle panel shows the XAS spectrum averaged over 200carbon centers.The dotted curve in the middle panel is the scaled partial XAS spectra of the sp 2-only carbon centers.This shows that the observed phase is more closely related to diamond than graphite.184701-5Ultrafast transformation of graphite to diamond J.Chem.Phys.128,184701͑2008͒of1ps even though the phase transition to diamond is nearly complete at this time.Our computed XAS spectra indicate that the end state of our simulation contains an electronic signature of cubic diamond.However,due to the elevated temperatures and pressures compared to the experiment,1the features of our spectrum are likely broadened.In addition, calculation of the spectrum from sp2-only sites in the system indicate trace amounts of␲-bonds. ACKNOWLEDGMENTSThis work was performed under the auspices of the U.S. Department of Energy by University of California LLNL un-der Contract No.W-7405-Eng-48.We would like to thank Tony Van Buuren,Trevor Willey,Dave Erskine,Jon Eggert, and Juerg Hutter for illuminating discussions.We also grate-fully acknowledge Mike McCoy and Dale Nielsen of the Center for Applied Scientific Computing for generous travel funds for A.C.and for supporting this research.1W.L.Mao,H.K.Mao,P.J.Eng,P.T.Trainor,M.Newville,C.C.Kao,D.L.Heinz,J.Shu,Y.Meng,and R.J.Hemley,Science302,425͑2003͒.2F.Bundy,W.Bassett,M.Weathers,R.Hemley,H.Mao,and A.Gon-charov,Carbon34,141͑1996͒.3D.J.Erskine and W.J.Nellis,Nature͑London͒349,317͑1991͒;J.Appl.Phys.71,4882͑1992͒.4W.H.Gust,Phys.Rev.B22,4744͑1980͒.5S.Brygoo,E.Henry,P.Loubeyre,J.Eggert,M.Koenig,B.Loupias,A.Benuzzi-Mounaix,and M.L.Gloahec,Nat.Mater.6,274͑2007͒.6Y.M.Gupta,Y.A.Gruzdkov,and G.I.Pangilinan,Chem.Phys.Lett.283,251͑1998͒.7M.D.Knudson,K.A.Zimmerman,and Y.M.Gupta,Rev.Sci.Instrum.70,1743͑1999͒.8P.A.Rigg and Y.M.Gupta,J.Appl.Phys.93,3291͑2003͒.9L.M.Ghiringhelli,J.H.Los,E.J.Meijer,A.Fasolino,and D.Frenkel, Phys.Rev.B69,100101͑2004͒.10L.M.Ghiringhelli,J.H.Los,E.J.Meijer,A.Fasolino,and D.Frenkel, Phys.Rev.Lett.94,145701͑2005͒.11A.Sorkin,J.Alder,and R.Kalish,Phys.Rev.B74,064115͑2006͒. 12A.A.Correa,S.A.Bonev,and G.Galli,Proc.Natl.Acad.Sci.U.S.A. 103,1204͑2006͒.13S.Scandolo,M.Bernasconi,G.L.Chiarotti,P.Focher,and E.Tosatti, Phys.Rev.Lett.74,4015͑1995͒.14F.J.Ribeiro,P.Tangney,S.G.Louie,and M.L.Cohen,Phys.Rev.B72, 214109͑2005͒.15K.Kadau,T.C.Germann,P.S.Lomdhal,and B.L.Holian,Science296, 1681͑2002͒.16S.V.Zybin,M.L.Elert,and C.T.White,Phys.Rev.B66,220102͑2002͒.17E.J.Reed,L.E.Fried,and J.D.Joannopoulos,Phys.Rev.Lett.90, 235503͑2003͒.18E.Reed,L.E.Fried,M.R.Manaa,and J.D.Joannopoulos,in Chemistry at Extreme Conditions,edited by M.Manaa͑Elsevier,New York,2005͒. 19E.J.Reed,L.E.Fried,W.D.Henshaw,and C.M.Tarver,Phys.Rev.E 74,056706͑2006͒.20E.J.Reed,M.R.Manaa,L.E.Fried,K.R.Glaesemann,and J.D. Joannopoulos,Nature Physics4,72͑2008͒.21CPMD code,Version3.11.1,Copyright IBM Corp1990–2006,Copyright MPI für Festkörperforschung Stuttgart,1997–2001.22J.Hutter and A.Curioni,ChemPhysChem6,1788͑2005͒.23R.Car and M.Parrinello,Phys.Rev.Lett.55,2471͑1985͒.24J.P.Perdew,K.Burke,and M.Ernzerhof,Phys.Rev.Lett.77,3865͑1996͒.25N.Troullier and J.L.Martins,Phys.Rev.B43,1993͑1991͒.26M.Ianuzzi and J.Hutter,Phys.Chem.Chem.Phys.9,1599͑2007͒.27CP2K code͑http://www.cpk2.berlios.de,Copyright CP2K developers group,2000–2006.28W.J.Hehre,R.Ditchfield,and J.A.Pople,J.Chem.Phys.56,2257͑1972͒.29L.Fried and W.M.Howard,Phys.Rev.B61,8734͑2000͒.30J.Tersoff,Phys.Rev.Lett.61,2879͑1988͒.31P.L.Chau and A.J.Hardwick,Mol.Phys.93,511͑1998͒.32B.E.Warren,X-Ray Diffraction͑Dover,New York,1990͒.33International Table for X-Ray Crystallography,edited by J.A.Ibers and W.C.Hamilton,3rd ed.͑Kluwer,Dordrecht,1989͒,V ol.3.34F.L.Coffman,R.Cao,P.A.Pianetta,S.Kapoor,M.Kelly,and L.J. Terminello,Appl.Phys.Lett.69,568͑1996͒.184701-6Mundy et al.J.Chem.Phys.128,184701͑2008͒。

Optical evidence of strong coupling between valence-band holes and d-localized spinsin Zn1−x Mn x OV.I.Sokolov,1A.V.Druzhinin,1N.B.Gruzdev,1A.Dejneka,2O.Churpita,2Z.Hubicka,2L.Jastrabik,2and V.Trepakov2,3 1Institute of Metal Physics,UD RAS,S.Kovalevskaya Str.18,620041Yekaterinburg,Russia2Institute of Physics,AS CR,v.v.i.,Na Slovance2,18221Praha8,Czech Republic3Ioffe Institute,RAS,194021St-Petersburg,Russia͑Received3December2009;revised manuscript received2March2010;published30April2010͒We report on optical-absorption study of Zn1−x Mn x O͑x=0–0.06͒films on fused silica substrates takingspecial attention to the spectral range of the fundamental absorption edge͑3.1–4eV͒.Well-pronounced exci-tonic lines observed in the region3.40–3.45eV were found to shift to higher energies with increasing Mnconcentration.The optical band-gap energy increases with x too,reliably evidencing strong coupling betweenoxygen holes and localized spins of manganese ions.In the3.1–3.3eV region the optical-absorption curve inthe manganese-containedfilms was found to shift to lower energies with respect to that for undoped ZnO.Theadditional absorption observed in this range is interpreted as a result of splitting of a localized Zhang-Rice-typestate into the band gap.DOI:10.1103/PhysRevB.81.153104PACS number͑s͒:78.20.ϪeI.INTRODUCTIONDilute magnetic semiconductor Zn1−x Mn x O is one of themost promising materials for the development of optoelec-tronic and spin electronic devices with ferromagnetism re-tained at practical temperatures͑i.e.,Ͼ300K͒.However,researchers are confronted with many complex problems.Ferromagnetic ordering does not always appear and the na-ture of its instability is a subject of controversy.In addition,optical properties of Zn1−x Mn x O appreciably differ fromthose in Zn1−x Mn x Se and Zn1−x Mn x S related compounds,where the intracenter optical transitions of Mn2+ions areconventionally observed in the optical-absorption and photo-luminescence spectra.1,2In contrast,a very intense absorp-tion in the2.2–3.0eV region was reported in Zn1−x Mn x Owithout any manifestations of intracenter transitions,3–5and photoluminescence due to4T1→6A1optical transition of Mn2+is absent as well.Interpretation of this absorption bandas a charge transfer3,5is complicated by the fact that Mn2+forms neither d5/d4donor nor d5/d6acceptor levels in the forbidden gap of ZnO.6,7To resolve this contradiction,Dietl8put forward the con-cept that the oxides and nitrides belong to the little studiedfamily of dilute magnetic semiconductors with strong corre-lations.Characteristic features of such compounds are an in-crease in the band gap with the concentration of magneticions and emergence of a Zhang-Rice͑Z-R͒-type state in theforbidden gap9arising as a result of strong exchange cou-pling of3d-localized spin of the impurity centers andvalence-band holes.According to Ref.8,fulfillment ofstrong hybridization condition depends on the ratio of theimpurity-center potential U to a critical value U c;a coupledhybrid state can be formed when U/U cϾ1.Existence of such electronic state has been verified by ab initio theoretical treatment of electron correlations using the local spin-density approximation͑LSDA+U model͒and calculation of the ex-change coupling values.10In Zn1−x Mn x O the hole can origi-nate by electron transfer from the Mn2+adjacent oxygen to the conduction band.The resulting hole localizes as the Z-R state leading to appearance of additional broad,intense ab-sorption band.In this way the study of optical-absorptionspectra can be used as a probe to identify the Z-R states.It is known that the optical band-edge absorption spec-trum of Mn-doped ZnO is characterized by the onset of astrong rise of the absorption coefficient in theϳ3.1eV spec-tral region.11In Refs.11and12,this absorption inZn1−x Mn x Ofilms was treated as a product of direct interbandoptical transitions using conventional formula␣2ϳ͑ប␻−E g͒.The resulting magnitudes of band gap for composition with x=0.05have been estimated as E g=3.10eV͑Ref.11͒and3.25eV,12which is appreciably less than E g=3.37eV inZnO.13Such“redshift”of the band gap was considered inRef.12as a result of p-d exchange interaction,in analogy tothe shift of the excitonic lines in reflectivity and lumines-cence spectra observed in Ref.14for Zn1−x Mn x Se.At thesame time theory predicts an increase in E g͑x͒with x for Zn1−x Mn x O.8Also excitonic absorption spectrum in Zn1−x Mn x O nanopowders,15appeared to be located at ener-gies higher than that in ZnO nanopowders,that does not confirm the shift of E g to lower energies for Zn1−x Mn x O films.In this work we report on the optical-absorption spectrastudies in thin Zn1−x Mn x Ofilms deposited on fused silicaing suchfilms we succeed to detect the absorp-tion spectra of excitons and to determine reliably the widthof the optical gap E g.This allowed us to elucidate the natureof the additional absorption band appearing atប␻ϽE g near the fundamental absorption edge as a result of splitting of one more Z-R-type state due to strong hybridization and ex-change coupling of3d-localized spin of the manganese and valence-band oxygen hole.II.EXPERIMENTALThin Zn1−x Mn x Ofilms with x=0–0.06,120–130,and 200–250nm of thicknesses were deposited on fused silica substrates by the atmospheric barrier-torch discharge tech-nique,as it was described in Refs.16and17.The substratePHYSICAL REVIEW B81,153104͑2010͒temperature during deposition was kept at ϳ200°C.Mn content was controlled by measurements of Mn and Zn emis-sion ͑␭em =4031Åand 4810Å,respectively ͒of plasma during deposition and crosschecked by the postgown EPMA ͑JEOL JXA-733device with Kevex Delta Class V mi-croanalyser ͒analysis with accuracy Ϯ0.3%.X-ray diffrac-tion ͑XRD ͒studies were performed with a Panalytical X’PertMRD Pro diffractometer with Eulerian cradle using Cu K ␣radiation ͑␭em =1.5405Å͒in the parallel beam ge-ometry.XRD profiles were fitted with the Pearson VII func-tion by the DIFPATAN code.18Correction for instrumental broadening was performed using NIST LaB6standard and V oigt function method.19Optical absorption within the 1.2–6.5eV spectral region was measured in unpolarized light at room temperature using a Shimadzu UV-2401PC spectrophotometer.The bare silica substrate and Zn 1−x Mn x O film on silica substrate were mounted into the reference and test channel,respectively.The optical density ␣d ͑product of optical-absorption coeffi-cient and film thickness ͒was calculated without taking into account multiple reflections as ␣d =ln ͑I 0/I ͒,where I 0and I are intensities of light passed through bare substrate and film/substrate structure.III.RESULTS AND DISCUSSIONFigure 1presents XRD pattern for ZnO and Zn 0.95Mn 0.05O films,as an example.All obtained films re-vealed crystalline block structure with dominant ͑002͒orien-tation of blocks’optical C -axes aligned normal to substrate.Observed reflexes correspond to wurtzite structure evi-dencing absence of extraneous phases.Both pure and Mn-doped ZnO films appeared to be compressively strained with 0.2%of strain,s =͑a 0−a S ͒/a 0,where a 0and a S are the lattice parameters of nonstrained and strained films.The analysis reveals that the value of compressive strain is controlled pre-dominantly by stresses,but not by presence of Mn ͑at least for Mn concentrations used ͒.Figure 2presents the optical-absorption spectra for Zn 1−x Mn x O films.A wide absorption line is seen in the re-gion of the band edge ͑Fig.2͒,whose energy appears to be shifted by about 100meV to higher energies in comparison with the excitonic line in ZnO ͓ϳ3.31eV at T =300K ͑Ref.13͔͒.The line shift is very likely connected with the com-pressive strain of Zn 1−x Mn x O films mentioned above.The wide and shifted line has been observed earlier in ZnO film on sapphire substrate 20,21and was identified as a shift of the excitonic line due to compressive strain of Zn 1−x Mn x O films.21The inset represents spectra of this line obtained in ZnO at T =300K and 77.3K.It is seen that the excitonic line is narrowed,split into two components and shifted to higher energies on lowering the temperature,clearly evidenc-ing its excitonic nature.The first line is a sum of A and B excitons,the second one is the C exciton appearing due to disorientation of blocks forming the film.16Analogous tem-perature evolutions have been reported for a wide excitonic line in ZnO nanocrystals.15As the concentration of Mn impurity increases,the exci-tonic line additionally broadens and shifts to higher energies.Figure 3shows the actual Mn concentration shift of the ex-citonic line energy ប␻exc .It is seen that the increase in Mn concentration leads to not only changes in the excitonic spec-trum but also exhibits enhancement of the band-gap energy in Zn 1−x Mn x O films ͑band-gap magnitude can be estimated as E g =ប␻exc +E exc ,where E exc =60meV is the excitonic binding energy 13͒.It is known that the band-gap magnitude in ZnO-MnO system varies from 3.37eV in ZnO up to 3.8eV in MnO.22According to the theoretical analysis 8per-formed taking into account inversion of ⌫7and ⌫9valence subbands in ZnO,23,24strong coupling of manganese spin and p states of valence band leads to appearance of a positiveI n t e n s i t y (c o u n t )2θ(degree)FIG.1.XRD pattern of ZnO ͑left scale ͒and Zn 0.95Mn 0.05O ͑right scale ͒films.E n e r g y (eV)αdFIG.2.Exciton absorption spectra of compressed Zn 1−x Mn x O films:1—x =0%,2—x =1.8%,and 3—x =5%;film thickness:d =͑120–130͒nm;and T =300K.Inset shows excitonic absorption lines for compressed ZnO:1—T =300K and 4—T =77.3K.01234563.403.413.423.433.44E n e r g y (e V )X (%)FIG.3.Mn-concentration dependence of the excitonic line en-ergies for Zn 1−x Mn x O films.additive in optical absorption of Zn 1−x Mn x O at small x val-ues.The sum of two contributions at sufficiently small x results in an increase in E g magnitude.The rise of the band-gap magnitude with the admixture of the second component E g ͑x ͒has been observed in Zn 1−x Co x O ͑Ref.25͒for exci-tonic lines registered in the reflection spectra at 1.6K.The shift of the excitonic line to higher energies was observed in Zn 0.99Fe 0.01O,too.20In the case of weak d -p coupling the additive into the band gap change appeared to be negative.8In this case the band-gap value E g decreases with x for x Յ0.1,as it was found for Zn 1−x Mn x Se ͑Fig.6in Ref.14͒and for Cd 1−x Mn x S.26Therefore,the observed rise of the E g ͑x ͒value with Mn addition provides the reliable experimental proof that the strong hybridization condition U /U c Ͼ1in Zn 1−x Mn x O is fulfilled.Figure 4presents optical absorption in Zn 1−x Mn x O films recorded in the spectral region 3.1–3.3eV .It is seen that the onset of optical absorption in Zn 1−x Mn x O films emerges at lower energies than that for ZnO ones.Analogous shift had been observed earlier in the spectrum of the photoluminescence excitation over deep im-purity centers in Zn 1−x Mn x O for Ref.15.Unlike authors of Refs.11and 12,we assume that addi-tional absorption of Zn 1−x Mn x O ͑in comparison with ZnO ͒in the 3.1–3.3eV range is a result of pushing the Z-R-type states out of valence band to the forbidden gap.9The essence of this state consists of localization of the valence-band hole within the first coordination sphere on the oxygen ions as a result of strong exchange interaction of manganese and hole spins.Such electronic state is similar to the Z-R-type state originally considered for La 2CuO 4oxidesuperconductor.9This state is a singlet one,because in La 2CuO 4the spins of d 9configuration of Cu 2+ion and oxy-gen holes are equal but of opposite direction.The situation is more complex in the case of Zn 1−x Mn x O since the top of valence band is formed by three close subbands:⌫7,⌫9,and ⌫7.23,24In such case we have serious reasons to assume that not only the presence of one deep Z-R-type state is respon-sible for optical absorption in the 2.2–3.0eV spectral region.We assume the presence of another,relatively shallow Z-R-type state too,which has been split off into the gap providing additional absorption in the 3.1–3.3eV region of Zn 1−x Mn x O.Tentatively,using results 11,12,15we estimate the splitting of the second Z-R level from the valence band as 0.12–0.27eV .More reliable determination of the split energy can be performed using more sensitive methods of absorp-tion spectra, e.g.,modulation methods,which are in progress.IV .CONCLUSIONThin Zn 1−x Mn x O films ͑x =0–0.06͒have been sintered and their optical-absorption spectra were investigated.The well-pronounced excitonic absorption lines in the fundamen-tal absorption spectral regions were observed.Position of excitonic absorption lines in Zn 1−x Mn x O films shifts to higher energies with increasing Mn content.This evidences an increase in the E g magnitude with x for small values x and reliably corroborates fulfillment of the strong coupling crite-rion ͑U /U c Ͼ1͒in Zn 1−x Mn x O.The last effect leads to emer-gence of an intense optical-absorption band in the 2.2–3.0eV region due to the presence of the band-gap Z-R-type state.The additional absorption observed in the range of 3.1–3.3eV is interpreted as a result of splitting of one more Z-R-type states into the band gap.ACKNOWLEDGMENTSAuthors thank T.Dietl,V .I.Anisimov,and A.V .Lukoy-anov for useful discussions and V .Valvoda for kind assis-tance in XRD experiments.This work was supported by Czech Grants No.A V0Z10100522of A V CR,No.KJB100100703of GA A V ,No.202/09/J017of GA CR,No.KAN301370701of A V CR,and No.1M06002of MSMT CR and Russian Grants No.08-02-99080r-ofiof RFBR,PP RAS “Quantum Physics of Condensed Matter”,and State Contract No.5162.nger and H.J.Richter,Phys.Rev.146,554͑1966͒.2T.Hoshina and H.Kawai,Jpn.J.Appl.Phys.19,267͑1980͒.3F.W.Kleinlein and R.Helbig,Z.Phys.266,201͑1974͒.4R.Beaulac,P.I.Archer,and D.R.Gamelin,J.Solid State Chem.181,1582͑2008͒.5T.Fukumura,Z.Jin,A.Ohtomo,H.Koinuma,and M.Kawasaki,Appl.Phys.Lett.75,3366͑1999͒.6K.A.Kikoin and V .N.Fleurov,Transition Metal Impurities in Semiconductors:Electronic Structure and Physical Properties ͑World Scientific,Singapore,1994͒,p.349.7T.Dietl,J.Magn.Magn.Mater.272-276,1969͑2004͒.8T.Dietl,Phys.Rev.B 77,085208͑2008͒.9F.C.Zhang and T.M.Rice,Phys.Rev.B 37,3759͑1988͒.10T.Chanier,F.Virot,and R.Hayn,Phys.Rev.B 79,205204͑2009͒.11V .Shinde,T.Gujar,C.Lokhande,R.Mane,and S.-H.Han,3.1253.2500.00.40.8αdEnergy (eV)12FIG.4.Spectral dependence of the optical density ␣d in the 3.1–3.3eV spectral region for Zn 1−x Mn x O,1—ZnO;2—x =0.3–0.5%;film thickness 200–250nm;and T =300K.Mater.Chem.Phys.96,326͑2006͒.12Y.Guo,X.Cao,n,C.Zhao,X.Hue,and Y.Song,J.Phys. Chem.C112,8832͑2008͒.13Zh.L.Wang,J.Phys.:Condens.Matter16,R829͑2004͒.14R.B.Bylsma,W.M.Becker,J.Kossut,U.Debska,and D. Yoder-Short,Phys.Rev.B33,8207͑1986͒.15V.I.Sokolov,A.Ye.Yermakov,M.A.Uimin,A.A.Mysik,V.A.Pustovarov,M.V.Chukichev,and N.B.Gruzdev,J.Lumin.129,1771͑2009͒.16M.Chichina,Z.Hubichka,O.Churpita,and M.Tichy,Plasma Processes Polym.2,501͑2005͒.17Z.Hubicka,M.Cada,M.Sicha,A.Churpita,P.Pokorny,L. Soukup,and L.Jastrabík,Plasma Sources Sci.Technol.11,195͑2002͒.18http://www.xray.cz/priv/kuzel/dofplatan/19R.Kuzel,Jr.,R.Cerny,V.Valvoda,and M.Blomberg,ThinSolid Films247,64͑1994͒.20Z.Jin,T.Fukumura,M.Kaasaki,K.Ando,H.Saito,T.Skiguchi, Y.Z.Yoo,M.Murakami,Y.Matsumoto,T.Hasegawa,and H. Koinuma,Appl.Phys.Lett.78,3824͑2001͒.21J.-M.Chauveau,J.Vives,J.Zuniga-Perez,ügt,M.Teis-seire,C.Deparis,C.Morhain,and B.Vinter,Appl.Phys.Lett.93,231911͑2008͒.d and V.E.Henrich,Phys.Rev.B38,10860͑1988͒. 23K.Shindo,A.Morita,and H.Kamimura,J.Phys.Soc.Jpn.20, 2054͑1965͒.24W.Y.Liang and A.D.Yoffe,Phys.Rev.Lett.20,59͑1968͒. 25W.Pacuski,D.Ferrand,J.Gibert,C.Deparis,J.A.Gaj,P.Ko-ssacki,and C.Morhain,Phys.Rev.B73,035214͑2006͒.26M.Ikeda,K.Itoh,and H.Sato,J.Phys.Soc.Jpn.25,455͑1968͒.。

Package‘EMT’February6,2023Type PackageTitle Exact Multinomial Test:Goodness-of-Fit Test for DiscreteMultivariate DataVersion1.3Date2023-02-06Author Uwe MenzelMaintainer Uwe Menzel<*******************>Description Goodness-of-fit tests for discrete multivariate data.It istested if a given observation is likely to have occurred underthe assumption of an ab-initio model.Monte Carlo methods are provided tomake the package capable of solving high-dimensional problems.License GPLLazyLoad yesRepository CRANDate/Publication2023-02-0622:32:31UTCNeedsCompilation noR topics documented:EMT-package (2)EMT-internal (2)multinomial.test (3)plotMultinom (6)Index712EMT-internalEMT-package Exact Multinomial Test:Goodness-of-Fit Test for Discrete Multivari-ate DataDescriptionThe package provides functions to carry out a Goodness-of-fit test for discrete multivariate data.It is tested if a given observation is likely to have occurred under the assumption of an ab-initio model.A p-value can be calculated using different distance measures between observed and ex-pected frequencies.A Monte Carlo method is provided to make the package capable of solving high-dimensional problems.The main user functions are multinomial.test and plotMultinom.DetailsPackage:CCPType:PackageVersion: 1.3Date:2013-02-06License:GPLAuthor(s)Uwe MenzelMaintainer:Uwe Menzel<*******************>EMT-internal Internal functions for the EMT packageDescriptionInternal functions for the EMT packageUsageExactMultinomialTest(observed,prob,size,groups,numEvents)ExactMultinomialTestChisquare(observed,prob,size,groups,numEvents)MonteCarloMultinomialTest(observed,prob,size,groups,numEvents,ntrial,atOnce)MonteCarloMultinomialTestChisquare(observed,prob,size,groups,numEvents,ntrial,atOnce)chisqStat(observed,expected)findVectors(groups,size)Argumentsobserved vector describing the observation:contains the observed numbers of items in each category.prob vector describing the model:contains the hypothetical probabilities correspond-ing to each category.expected vector containing the expected numbers of items in each category under the assumption that the model is valid.size sample size,sum of the components of the vector observed.groups number of categories in the experiment.numEvents number of possible outcomes of the experiment.ntrial number of simulated samples in the Monte Carlo approach.atOnce a parameter of more technical nature.Determines how much memory is used for big arrays.DetailsThese functions are not intended to be called by the user.multinomial.test Exact Multinomial Test:Goodness-of-Fit Test for Discrete Multivari-ate DataDescriptionGoodness-of-fit tests for discrete multivariate data.It is tested if a given observation is likely to have occurred under the assumption of an ab-initio model.Monte Carlo methods are provided to make the function capable of solving high-dimensional problems.Usagemultinomial.test(observed,prob,useChisq=FALSE,MonteCarlo=FALSE,ntrial=1e6,atOnce=1e6)Argumentsobserved vector describing the observation:contains the observed numbers of items in each category.prob vector describing the model:contains the hypothetical probabilities correspond-ing to each category.useChisq if TRUE,Pearson’s chisquare is used as a distance measure between observed and expected frequencies.MonteCarlo if TRUE,a Monte Carlo approach is used.ntrial number of simulated samples in the Monte Carlo approach.atOnce a parameter of more technical nature.Determines how much memory is used for big arrays.DetailsThe Exact Multinomial Test is a Goodness-of-fit test for discrete multivariate data.It is tested ifa given observation is likely to have occurred under the assumption of an ab-initio model.In theexperimental setup belonging to the test,n items fall into k categories with certain probabilities (sample size n with k categories).The observation,described by the vector observed,indicates how many items have been observed in each category.The model,determined by the vector prob, assigns to each category the hypothetical probability that an item falls into it.Now,if the obser-vation is unlikely to have occurred under the assumption of the model,it is advisible to regard the model as not valid.The p-value estimates how likely the observation is,given the model.In particular,low p-values suggest that the model is not valid.The default approach used by multinomial.test obtains the p-values by calculating the exact probabilities of all possible out-comes given n and k,using the multinomial probability distribution function dmultinom provided by R.Then,by default,the p-value is obtained by summing the probabilities of all outcomes which are less likely than the observed outcome(or equally likely as the observed outcome),i.e.by summing all p(i)<=p(observed)(distance measure based on probabilities).Alternatively,the p-value can be obtained by summing the probabilities of all outcomes connected with a chisquare no smaller than the chisquare connected with the actual observation(distance measure based on chisquare).The latter is triggered by setting useChisq=TRUE.Having a sample of size n in an experiment with k categories,the number of distinct possible outcomes is the binomial coefficient choose(n+k-1,k-1).This number grows rapidly with increasing parameters n and k.If the param-eters grow too big,numerical calculation might fail because of time or memory limitations.In this case,usage of a Monte Carlo approach provided by multinomial.test is suggested.A Monte Carlo approach,activated by setting MonteCarlo=TRUE,simulates withdrawal of ntrial samples of size n from the hypothetical distribution specified by the vector prob.The default value for ntrial is100000but might be incremented for big n and k.The advantage of the Monte Carlo approach is that memory requirements and running time are essentially determined by ntrial but not by n or k.By default,the p-value is then obtained by summing the relative frequencies of occurrence of unusual outcomes,i.e.of outcomes occurring less frequently than the observed one(or equally frequent as the observed one).Alternatively,as above,Pearson’s chisquare can be used as a dis-tance measure by setting useChisq=TRUE.The parameter atOnce is of more technical nature,witha default value of1000000.This value should be decremented for computers with low memoryto avoid overflow,and can be incremented for large-CPU computers to speed up calculations.The parameter is only effective for Monte Carlo calculations.Valueid textual description of the method used.size sample size n,equals the sum of the components of the vector observed.groups number of categories k in the experiment,equals the number of components of the vector observed.numEvents number of different events for the model considered.stat textual description of the distance measure used.allProb vector containing the probabilities(rel.frequencies for the Monte Carlo ap-proach)of all possible outcomes(might be huge for big n and k).criticalValue the critical value of the hypothesis test.ntrial number of trials if the Monte Carlo approach was used,NULL otherwise.p.value the calculated p-value rounded to four significant digits.NoteFor two categories(k=2),the test is called Exact Binomial Test.Author(s)Uwe Menzel<*******************>ReferencesH.Bayo Lawal(2003)Categorical data analysis with SAS and SPSS applications,V olume1,Chap-ter3ISBN:978-0-8058-4605-8Read,T.R.C.and Cressie,N.A.C.(1988).Goodness-of-fit statistics for discrete multivariate data.Springer,New York.See AlsoThe Multinomial Distribution:dmultinomExamples##Load the EMT package:library(EMT)##Input data for a three-dimensional case:observed<-c(5,2,1)prob<-c(0.25,0.5,0.25)##Calculate p-value using default options:out<-multinomial.test(observed,prob)#p.value=0.0767##Plot the probabilities for each event:plotMultinom(out)##Calculate p-value for the same input using Pearson s chisquare:out<-multinomial.test(observed,prob,useChisq=TRUE)#p.value=0.0596;not the same!##Test the hypothesis that all sides of a dice have the same probabilities:prob<-rep(1/6,6)observed<-c(4,5,2,7,0,1)out<-multinomial.test(observed,prob)#p.value=0.0357->better get another dice!#the same problem using a Monte Carlo approach:##Not run:out<-multinomial.test(observed,prob,MonteCarlo=TRUE,ntrial=5e+6)##End(Not run)6plotMultinom plotMultinom Plot the Probability distribution fot the Exact Multinomial TestDescriptionThis function takes the results of multinomial.test as input and plots the calculated probability distribution.UsageplotMultinom(listMultinom)ArgumentslistMultinom a list created by running the function multinomial.test.DetailsThe function plotMultinom displays a barplot of the probabilities for the individual events.The probabilities are shown in descending order from the left to the right.Events contributing to the p-value are marked red.Plots are only made if the number of different events is lower than or equal to100and for low number of trials in Monte Carlo simulations.ValueThefirst argument(listMultinom)is returned without modification.Author(s)Uwe Menzel<*******************>See AlsoThe Multinomial Distribution:multinomial.testExamples##Load the EMT package:library(EMT)##input and calculation of p-values:observed<-c(5,2,1)prob<-c(0.25,0.5,0.25)out<-multinomial.test(observed,prob)#p.value=0.0767##Plot the probability distribution:plotMultinom(out)Index∗htestEMT-package,2multinomial.test,3plotMultinom,6∗multivariateEMT-package,2multinomial.test,3plotMultinom,6chisqStat(EMT-internal),2dmultinom,4,5EMT(EMT-package),2EMT-internal,2EMT-package,2ExactMultinomialTest(EMT-internal),2 ExactMultinomialTestChisquare(EMT-internal),2findVectors(EMT-internal),2 MonteCarloMultinomialTest(EMT-internal),2 MonteCarloMultinomialTestChisquare(EMT-internal),2multinomial.test,3,6plotMultinom,67。

优秀英文简历格式【精彩5篇】光阴的迅速，一眨眼就过去了，我们又将打开新的篇章，寻求新的工作机会，这时一份好的简历可以起到很好的。

作用哦。

写简历需要注意哪些问题呢？牛牛范文的小编精心为您带来了5篇优秀英文简历格式，如果对您有一些参考与帮助，请分享给最好的朋友。

个人英文简历篇一一、千万别罗罗嗦嗦语言简练。

对于求职者来讲，目的明确、语言简练是其简历行之有效的基础。

如在教育背景中写相关课程，不要为了拼凑篇幅，把所有的课程一股脑儿地都写上，如体育等。

这样不会有效，别人也没耐心看。

二、千万别搞错顺序包括求职者的姓名、性别、出生年月等，与中文简历大体一致。

第二部分为教育背景(education)，必须注意的是在英文简历中，求职者受教育的时间排列顺序与中文简历中的时间排列顺序正好相反，也就是说，是从求职者的最高教育层次（学历）写起，至于低至何时，则无一定之规，可根据个人实际情况安排。

三、切记把“技能”写清楚在时间排列顺序上亦遵循由后至前这一规则，即从当前的工作岗位写起，直至求职者的第一个工作岗位为止。

求职者要将所服务单位的名称、自身的职位、技能写清楚。

把社会工作细节放在工作经历中，这样会填补工作经验少的缺陷。

例如，您在做团支书、学生会主席等社会工作时组织过什么活动，联系过什么事，参与过什么都可以一一罗列。

而作为大学生，雇主通常并不指望您在暑期工作期间会有什么惊天动地的。

成就。

当然如果您有就更好了。

四、切记列举所获奖励和发表的作品将自己所获奖项及所发表过的作品列举一二，可以从另一方面证实自己的工作能力和取得的成绩。

书写上，奖学金一项一行。

另外，大多数外企对英语（或其它语种）及计算机水平都有一定的要求，个人的语言水平、程度可在此单列说明。

语言简练对于求职者来讲，目的明确、语言简练的简历是求职外企行之有效的基础。

如在教育背景中写相关课程时，不要为了拼凑篇幅，把所有的课程一股脑儿地都写上，如体育等。

千万别搞错顺序包括求职者的姓名、性别、出生年月等，与中文简历大体一致。

国际商事争议解决研究术语摘录常设仲裁法院permanent court of arbitration 国际商会The International Chamber of Commerce，ICC 国际商会友好争议解决规则The ICC Amicable Dispute Resolution Rules 在线争议解决方法Online Dispute Resolution.，ODR 替代性争议解决Alternative Dispute Resolution，ADR 裁判adjudication 自然公正natural justice 正当程序due process 美国公众援救中心center of public sources，CPR 英国争议解决中心The Center for Effective Dispute Resolution，CEDR 管辖根据jurisdiction basis 直接国际裁判管辖权Direct international jurisdictional competence 间接国际裁判管辖权indirect international jurisdictional competence 欧洲自由贸易联盟European Free Trade Association，EFTA 取证嘱托书rogatory commission 审判前文件保留discovery of document 仲裁arbitration 实质性连结因素material connecting factors 联邦仲裁法federal arbitration act，FAA 产业化industry 国际的仲裁文化international arbitration culture程序公正procedural justice 实体公正substantive justice 显然漠视法律原则manifest disregard of law 仲裁协议arbitration agreement 往来函电in an exchange of letters or telegrams 临时仲裁ad hoc arbitration 自动移转规则automatic assignment rule 披露本人的代理agency of disclosed principal 未披露本人的代理agency of undisclosed principal 显名代理agency of named principal 隐名代理agency of unnamed principal 仲裁条款独立性理论doctrine of arbitration clause autonomy 又（称仲裁条款自治性理论reparability of arbitration clause 仲裁条款分离性理论severability of arbitration clause 仲裁条款分割性理论theory of autonomy of the arbitration clause）合同自始无效uoid ab initio 无中不能生有ex nitil nil fit 特殊类型sui genceris 管辖权自决学说compentence de la compentence（Kompetenz-kompetenz。