Title: New method for Electronic Structure Calculation: Information Entropy + Density Matrix Functional Theory

Speaker: Professor Wang Jian ,Huzhou University

Report Time:April 30th,2022，14:00

Tencent Meeting Number: 182-163-515

Meeting moderator: Professor Yan Bing

Hosted by:Institute of Atomic and molecular Physics,Jilin University

Abstract:

      Solving the Schrodinger equation for multi-electron systems is one of the most difficult problems in quantum mechanics.The Hartree-fock method approximates the wave function with a single determinant.Some physical phenomena, such as the decomposition of molecules, cannot be described by a single determinant, but generally need to be described by a linear combination of multiple determinants, which is called the CI method.Since the number of possible determinants increases rapidly as the number of electrons and orbitals increases, so does the computation of CI method, it is difficult to generalize this method to systems consisting of a dozen or more electrons.Density functional theory (DFT) can deal with multi-electron systems in principle, but the exact expression of the commutation-correlation function in the theory has not been found yet.There are hundreds of DFT approximate functional models in the literature, and new models are still being produced.

      In the Hartree-fock method, the orbital possession number can only be 1 or 0.In contrast, the number of orbits occupied in the CI method can be a fraction.The number of fractions allowed to occupy means that a first-order density matrix can be used as a variable.A functional method using first-order density matrices as variables is called density matrix functional theory (DMFT).In this theory, the kinetic energy can be rigorously expressed in terms of a first-order density matrix, and only a small part of the interaction between electrons needs to be simulated by a functional, which is the correlation energy.We use information entropy to simulate this part of energy, and use entropy maximization principle to minimize the correlation energy (negative value). The euler equation of single-electron orbital derived from this has the form of Hartree-Fock equation.This means that the quantum mechanics problem of multi-electron system can obtain the calculation result of CI precision only by solving a self-consistent field equation equivalent to Hartree-Fock.This new method can greatly facilitate or accelerate the calculation of molecular potential energy surface, the simulation of molecular dynamics, and the study of electronic structure of macromolecules.The work was recently published in Phys.Rev.Lett. (PRL, 128,013001) and selected by editors as a highlight article.

Introduction:

      Wang Jian, a professor at Huzhou University. He graduated from Zhejiang Normal University in 1983, completed his master's degree in Sichuan University in 1987 under the guidance of Professor Gou Qingquan, and completed his doctoral degree in University of Science and Technology Beijing  in 1991 under the guidance of Professor Fang Zhengzhi. After that, he followed Professor Xie Xide as a postdoctoral researcher at Fudan University, and worked in the Materials Department of Oxford University, Condensed Matter Theory Group of Cambridge University, Quantum Theory Institute of Florida University, Leibniz Institute of Solid Materials in Germany, Donostia International Physics Center in Spain, etc. He presided over the National Natural Science Foundation of China and other projects, and published many academic papers in Phys.Rev.Lett.,Phys.Rev.A and other magazines.