Free-complement local-Schrödinger-equation method for solving the Schrödinger equation of atoms and molecules: basic theories and features

The Journal of Chemical Physics
Hiroshi Nakatsuji, Hiroyuki Nakashima

Abstract

The free-complement (FC) method is a general method for solving the Schrödinger equation (SE): The produced wave function has the potentially exact structure as the solution of the Schrödinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local Schrödinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local Schrödinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule. The purpose of this paper is to formulate the basic theories of the LSE method and explain their basic features. First, we formulate three variants of the LSE method, the AB, HS, and H(T)Q methods, and explain their properties. Then, the natures of the LSE methods are clarified in some detail using the simple examples of the hydrogen atom and the Hooke's atom. Finally, the ideas obtained in this study are applied to solving the SE of the helium atom highly accurately with the FC-LSE method. The results are very encouraging: we could get the world's most accurate energy of the helium atom within the sampling-type methodologies, which is comparable to those obtained with the FC-VP method. Thus, the FC-LS...Continue Reading

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Citations

May 24, 2015·The Journal of Chemical Physics·Hiroshi Nakatsuji, Hiroyuki Nakashima
Aug 9, 2016·The Journal of Chemical Physics·Jerzy Cioslowski
Dec 7, 2018·The Journal of Chemical Physics·Sergei Manzhos, Tucker Carrington
Nov 15, 2019·The Journal of Physical Chemistry. a·Jonas KuSergei Manzhos

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