Friday, April 28, 2023
MLIT Room 310, Online seminar via Webinar
Danshin A.A.
(NRC «Kurchatov Institute»)

Development of numerical methods for solving problems of quantum mechanics based on the synthesis of stochastic and deterministic approaches

(based on the PhD thesis)

The main problem of the existing methods of quantum mechanical calculations of the properties of atoms, molecules, and crystals is the high computational complexity in cases where it is necessary to more fully take into account electronic correlations, which limits the possible range of calculated properties of such systems. Therefore, it is relevant to create new physical and mathematical models and program code based on them. The work presents an original quantum Monte Carlo method for solving the Schrödinger equation for fermion systems, verified on atoms containing s-electrons. An asymptotically accurate (in terms of a step of computational grid) algorithm for solving the Hartree-Fock and Kohn-Sham equations without the use of basis sets was created, implemented and verified on the full set of elements of the periodic table, the computational complexity of which is comparable to existing algorithms based on basis sets. A mathematical model has been developed and implemented for taking into account electronic correlations in the Hartree-Fock method, where the correlations are obtained from a stochastic calculation.

More information on the seminar and the link to connect via Webinar are available at Indico.