Implementing and evaluating a fictitious electron dynamics method for the calculation of electronic structure

[摘要] English: Quantum chemical calculations are an invaluable tool in the determination of electronic structure. However, the size of systems studied using these calculations are severely limited due to the highly unfavourable scaling of computational time - typically to the third or fourth order of the number of atoms in the system. Molecular dynamics calculations, on the other hand, can model systems consisting of thousands of atoms. They are, however, insufficient in describing chemical events - quantum chemical calculations are necessary for this. The quest for O(N) electronic structure calculation methods led to the investigation of a recently proposed fictitious electron dynamics method for calculating electronic structure which uses the idempotency of the density matrix to develop first and second order equations of motion. These equations are implemented in a semi-empirical environment, supplied by the MOPAC software package. The velocity Verlet scheme is used to integrate these equations and the enforcement of constraints is accomplished through McWeeny purification and the RATTLE algorithm. The essential role that parameters play in the effectiveness of the equations of motion is investigated and suggestions are made for these parameters. The requirements of energy conservation of the equations of motion, as well as the stability of the velocity Verlet integrator are addressed and the parameters are revised in order to comply to these requirements. The importance of the Si(100)2xl:H system as a test system is emphasized and the barriers for hydrogen atom diffusion are calculated using an existing parameter set in MOPAC. This system is used to determine the efficiency of the fictitious electron dynamics method to keep the calculated minimum energy close to the Born-Oppenheimer energy surface. Issues of relevance for further development of this method are discussed. These include the potential combination of this method with atomic dynamics to successfully describe chemical reactions on crystal surfaces as well as making use of the principle of nearsightedness of the density matrix to achieve linear scaling.

[发布机构] University of the Free State