Kinetic energy-free Hartree-Fock equations: an integral formulation. (English) Zbl 1516.65076
The authors of this work designed and implemented a solver for Hartree-Fock (HF) equations which are considered as cornerstones of quantum chemistry. The equations are reformulated as coupled integral equations therefore making it possible to find the solution without implementing a differential operator. Convolution and derivative operators related to Multiwavelet (MW) framework were discussed and the descriptions of the Fock operator and iterative solution of the minimization problem are given. Usual strategies for obtaining the minimizer involves a finite basis representation of blocks of the Fock matrix. An integral representation of the HF equations is considered due to the concerns involving the use of differential operators within the MW approach. A detailed description of the integral representation that doesn’t require the explicit use of the kinetic energy operator and gives rise to development of efficient iterative algorithms is given. Extension of the procedure for a many-electron system is also discussed. Calculation of Fock matrix and energy, orbital orthonormalization, as well as the implementation details and the algorithm are provided. Numerical results with hydrogen and beryllium atoms demonstrating robust convergence patterns are presented.
Reviewer: Baasansuren Jadamba (Rochester)
MSC:
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65T60 | Numerical methods for wavelets |
| 65R20 | Numerical methods for integral equations |
| 65K10 | Numerical optimization and variational techniques |
| 65H10 | Numerical computation of solutions to systems of equations |
| 65F08 | Preconditioners for iterative methods |
| 65F10 | Iterative numerical methods for linear systems |
| 82M36 | Computational density functional analysis in statistical mechanics |
| 81V45 | Atomic physics |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q40 | PDEs in connection with quantum mechanics |
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