文档介绍：PHYSICAL REVIEW A 72, 062110 ͑2005͒
General method of solving the Schrödinger equation of atoms and molecules
Hiroshi Nakatsuji
Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Nishikyo-ku,
Kyoto 615-8510, Japan and Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano-Nishihiraki-cho, Sakyo-ku,
Kyoto 606-8103, Japan
͑Received 26 June 2005; published 13 December 2005͒
We propose a general method of solving the Schrödinger equation of atoms and molecules. We first construct
the wave function having the exact structure, using the ICI ͑iterative configuration plement interaction͒
method and then optimize the variables involved by the variational principle. Based on the scaled Schrödinger
equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a
general method of calculating the exact wave functions in an analytical expansion form. We choose initial
function 0 and scaling g function, and then the ICI method automatically generates the wave function that has
the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the
system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact
wave function. We explain putational procedure of the analytical ICI method routinely performed in
our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke’s
atom for the electron singularity case, and the helium atom for both cases.
DOI: .062110 PACS number͑s͒: , , ,
I. INTRODUCTION Furthermore, even if we could get the full-CI solutions, they
As noted by Dirac in 1929 ͓1͔, the Schrödinger equation are actually far from the true solutions of the SE, because the
͑SE͒ provides a fundamental mathematical law for chemistr