Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method

Abstract

The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.

Compact wavefunctions from compressed imaginary time evolution

“…[32][33][34][35] The path-integral renormalization group method also uses this approach to stochastically add non-orthogonal CI determinants, and has been applied to chemical systems such as H 2 . 36,37 Our method differs from this approach in the manner in which new determinants are t, and the performance benets of our method can be inferred from the data on H 2 in the appendix of this work.…”

Essentially exact ground-state calculations by superpositions of nonorthogonal Slater determinants

“…Also, Imada and co-workers [31-33] and Kojo and Hirose [34,35] employed nonorthogonal SDs in path integral renormalization group calculations. Goto and co-workers developed the direct energy minimization method using nonorthogonal SDs [36-39] based on the real-space finite-difference formalism [40,41]. In these previous studies, steepest descent directions and acceleration parameters are calculated to update one-electron wave functions on the basis of a variational principle [25-30,36-39].…”

“…Goto and co-workers developed the direct energy minimization method using nonorthogonal SDs [36-39] based on the real-space finite-difference formalism [40,41]. In these previous studies, steepest descent directions and acceleration parameters are calculated to update one-electron wave functions on the basis of a variational principle [25-30,36-39]. Although the steepest descent direction guarantees a secure approach to the ground state, a more effective updating process might be performed in a multi-direction search.…”