DOI: 10.1063/1.1701315. Evaluation of Molecular Integrals by Solid Spherical Harmonic Expansions

Evaluation of Molecular Integrals by Solid Spherical Harmonic Expansions

10.1063/1.1701315

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The use of expansions of solid spherical harmonics, which are the functions (rn or r−n−1) Pnm (cosθ)(cosmφ or sinmφ),is discussed with respect to molecular integrals, and it is found that terms of the delta function type must be included in the expansion for the r−n−1 case if n—m≥2. These expansions are especially useful for operators involving inverse powers of r such as electromagnetic interaction operators. General formulas are given for integrals in which two atomic orbitals, e.g., Slater orbitals, are on one center, and one of these operators is on the other center. Formulas are also given for the corresponding one-center integrals, and methods of evaluating three-center integrals and other two-center integrals are discussed briefly.

Bibliography

Pitzer, R. M., Kern, C. W., & Lipscomb, W. N. (1962). Evaluation of Molecular Integrals by Solid Spherical Harmonic Expansions. The Journal of Chemical Physics, 37(2), 267â274.

Authors 3

Russell M. Pitzer (first)
C. William Kern (additional)
William N. Lipscomb (additional)

References 16 Referenced 145

10.1103/RevModPhys.32.239 / Revs. Modern Phys. (1960)
10.1063/1.1732236 / J. Chem. Phys. (1961)
{'key': '2024020820483293800_r3'}
10.1080/00268975900100121 / J. Mol. Phys. (1959)
10.1063/1.1730349 / J. Chem. Phys. (1959)
{'key': '2024020820483293800_r6'}
{'key': '2024020820483293800_r7'}
10.1063/1.1742457 / J. Chem. Phys. (1956)
10.1063/1.1731722 / J. Chem. Phys. (1961)
{'key': '2024020820483293800_r9'}
{'key': '2024020820483293800_r10', 'first-page': '221', 'volume': 'A243', 'year': '1951', 'journal-title': 'Phil. Trans. Soc.'} / Phil. Trans. Soc. (1951)
10.1017/S0305004100016820 / Proc. Camb. Phil. Soc. (1937)
{'key': '2024020820483293800_r11a'}
{'key': '2024020820483293800_r12', 'first-page': '148', 'volume': '22', 'year': '1954', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1954)
10.1063/1.1732550 / J. Chem. Phys. (1962)
{'key': '2024020820483293800_r14'}

Dates

Type	When
Created	20 years, 7 months ago (Jan. 5, 2005, 10:29 p.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 3:48 p.m.)
Indexed	1 month, 3 weeks ago (July 2, 2025, 3:47 p.m.)
Issued	63 years, 1 month ago (July 15, 1962)
Published	63 years, 1 month ago (July 15, 1962)
Published Print	63 years, 1 month ago (July 15, 1962)

Funders 0

None

BibTeX

@article{Pitzer_1962, title={Evaluation of Molecular Integrals by Solid Spherical Harmonic Expansions}, volume={37}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1701315}, DOI={10.1063/1.1701315}, number={2}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Pitzer, Russell M. and Kern, C. William and Lipscomb, William N.}, year={1962}, month=jul, pages={267–274} }

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