Machine Learning Method In First Principle Calculation

Hartree-Fock method(HF)and density functional theory(DFT)are two fundamen-tal methods in studies of quantum chemistry and condensed matter physics.They're known as first principle method since they derive properties of materials directly from microscopic quantum theory and involve little empirical parameters.The development of first principle method greatly accelerates the exploration of novel materials.Recent advances in topological insulator and Weyl semimetal largely depend on the combina-tion of simulation methods with experiments.Although DFT has been developed over half of a centrary and widely used in var-ious of areas,there are still some open questions within DFT,one of them is about the kinetic energy functional.The orbital free DFT(OFDFT)based on a proper kinetic energy functional will enable DFT simulation on systems containing tens of thousands of atoms.In the second part of this thesis,we describe the idea of applying machine learning method to kinetic energy functional fitting.We utilize the periodicity within our system to reduce the dimensionality of the data,and design fitting algorithm based on Gaussian process method.The fitted functional performs well on estimating kinetic energy and it's functional derivative with respect to electron density.It can also be used in OFDFT to calculate the system's ground state electron density.HF method represents the many-electron quantum state as a Slater determinant of a set of single electron orbitals,and uses self-consistent field(SCF)method to evalu-ate these orbitals.Self-consistent field method is known to be sublinear in it's rate of convergence.In the third part of this thesis,we describe how to parametrize the single particle reduced density matrix(SRDM)using Thouless theorem.In the density matrix HF method designed by us,the SCF method is substituted with quasi-Newton method which has a faster convergence rate.We can also simultaneously optimize the param-eters inside the basis set of HF with SRDM.All the gradients used in the optimization process are evaluated by automatic differentiation method.