# Loewdin alpha function and its application to the multi-center molecular integral problem over Slater-type orbitals

## Abstract

In this paper we trace the evolution of the Lowdin alpha-function method in its application to multi-center molecular integrals over Slater-type orbitals (STOs). As is well-known, any STO displaced from the origin can be expanded in an infinite series of spherical harmonics; the functional coefficients have been designated as Lowdin alpha functions. These alpha functions can be represented as exponentials multiplied by polynomials in the displacement distance and the radial distance. The polynomials are used to construct a C matrix with integer elements. To avoid cancellation errors in some cases, the exponentials are expanded to obtain E matrices for interior regions and F matrices for exterior regions. We believe that this careful approach to molecular integrals will succeed in producing accurate and rapid evaluation of the integrals needed in STO basis-set methods for quantum chemistry.

- Authors:

- Publication Date:

- Research Org.:
- Florida Agricultural and Mechanical Univ., Tallahassee, FL (USA). Dept. of Physics

- OSTI Identifier:
- 7003034

- Alternate Identifier(s):
- OSTI ID: 7003034

- Report Number(s):
- AD-A-218065/1/XAB

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Pub. in Jnl. of Molecular Structure (Theochem), Vol. 199, 233-243(1989)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; MOLECULAR STRUCTURE; CALCULATION METHODS; ACCURACY; CANCELLATION; DISTANCE; ERRORS; EVALUATION; INTEGRALS; MATRICES; MOLECULAR ORBITAL METHOD; MOLECULES; NUMERICAL SOLUTION; POLYNOMIALS; SLATER METHOD; SPHERICAL HARMONICS; FUNCTIONS 640302* -- Atomic, Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory

### Citation Formats

```
Jones, H.W., and Weatherford, C.A..
```*Loewdin alpha function and its application to the multi-center molecular integral problem over Slater-type orbitals*. United States: N. p., 1989.
Web.

```
Jones, H.W., & Weatherford, C.A..
```*Loewdin alpha function and its application to the multi-center molecular integral problem over Slater-type orbitals*. United States.

```
Jones, H.W., and Weatherford, C.A.. Sun .
"Loewdin alpha function and its application to the multi-center molecular integral problem over Slater-type orbitals". United States.
doi:.
```

```
@article{osti_7003034,
```

title = {Loewdin alpha function and its application to the multi-center molecular integral problem over Slater-type orbitals},

author = {Jones, H.W. and Weatherford, C.A.},

abstractNote = {In this paper we trace the evolution of the Lowdin alpha-function method in its application to multi-center molecular integrals over Slater-type orbitals (STOs). As is well-known, any STO displaced from the origin can be expanded in an infinite series of spherical harmonics; the functional coefficients have been designated as Lowdin alpha functions. These alpha functions can be represented as exponentials multiplied by polynomials in the displacement distance and the radial distance. The polynomials are used to construct a C matrix with integer elements. To avoid cancellation errors in some cases, the exponentials are expanded to obtain E matrices for interior regions and F matrices for exterior regions. We believe that this careful approach to molecular integrals will succeed in producing accurate and rapid evaluation of the integrals needed in STO basis-set methods for quantum chemistry.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Jan 01 00:00:00 EST 1989},

month = {Sun Jan 01 00:00:00 EST 1989}

}