# General method of solving the Schroedinger equation of atoms and molecules

## Abstract

We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger 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 {psi}{sub 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 the computational 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.

- Authors:

- 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)

- Publication Date:

- OSTI Identifier:
- 20786261

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.062110; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; COMPLEMENT; CONFIGURATION INTERACTION; ELECTRONS; EXPANSION; HAMILTONIANS; HELIUM; HYDROGEN; ITERATIVE METHODS; MOLECULES; SCHROEDINGER EQUATION; SINGULARITY; VARIATIONAL METHODS; WAVE FUNCTIONS

### Citation Formats

```
Nakatsuji, Hiroshi.
```*General method of solving the Schroedinger equation of atoms and molecules*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Nakatsuji, Hiroshi.
```*General method of solving the Schroedinger equation of atoms and molecules*. United States. doi:10.1103/PHYSREVA.72.0.

```
Nakatsuji, Hiroshi. Thu .
"General method of solving the Schroedinger equation of atoms and molecules". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786261,
```

title = {General method of solving the Schroedinger equation of atoms and molecules},

author = {Nakatsuji, Hiroshi},

abstractNote = {We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger 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 {psi}{sub 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 the computational 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 = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 6,

volume = 72,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}