# Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory

## Abstract

The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, “electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science.” Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessarymore »

- Authors:

- Quantum Chemistry Research Institute, Kyodai Katsura Venture Plaza 107, Goryo Oohara 1-36, Nishikyo-ku, Kyoto 615-8245 (Japan)

- Publication Date:

- OSTI Identifier:
- 22415784

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 19; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; ATOMS; BASES; CHEMISTRY; ELECTRONS; INTERFERENCE; MATHEMATICAL SOLUTIONS; MOLECULES; OPERATION; SCHROEDINGER EQUATION; VALENCE; WAVE FUNCTIONS

### Citation Formats

```
Nakatsuji, Hiroshi, E-mail: h.nakatsuji@qcri.or.jp, and Nakashima, Hiroyuki.
```*Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory*. United States: N. p., 2015.
Web. doi:10.1063/1.4919843.

```
Nakatsuji, Hiroshi, E-mail: h.nakatsuji@qcri.or.jp, & Nakashima, Hiroyuki.
```*Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory*. United States. doi:10.1063/1.4919843.

```
Nakatsuji, Hiroshi, E-mail: h.nakatsuji@qcri.or.jp, and Nakashima, Hiroyuki. Thu .
"Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory". United States. doi:10.1063/1.4919843.
```

```
@article{osti_22415784,
```

title = {Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory},

author = {Nakatsuji, Hiroshi, E-mail: h.nakatsuji@qcri.or.jp and Nakashima, Hiroyuki},

abstractNote = {The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, “electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science.” Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules.},

doi = {10.1063/1.4919843},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 19,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}