Use of Electron Repulsion Integral Approximations in Molecular Quantum Mechanics
- 1 April 1954
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 22 (4), 699-702
- https://doi.org/10.1063/1.1740153
Abstract
Straightforward theoretical calculation for molecular systems using eigenfunctions built up from atomic orbitals and employing actual and approximate methods for the evaluation of certain integrals have recently been widely applied with considerable success. Most of these calculations have evaluated the difficult multicentered electron repulsion integrals by use of an approximate formula suggested by Mulliken, in terms of Coulombic and overlap integrals. Previous work has indicated the general utility of this relationship. Here, direct numerical comparison is made of actual and approximate values of the multicenter 1s orbital integrals. The comparisons indicate that this approximation of integrals is moderately accurate over a wide range of internuclear configurations. Direct calculations of the energy of the linear triatomic hydrogen complex molecule with this approximate integral formula disclose that the total binding energy obtained by the two procedures is different by several kcal/mole. However the energy variation with internuclear separations obtained from the approximate calculations has its minimum very near that obtained using actual integrals. This indicates that energy minimization by variation of the parameters included in the trial eigenfunction may be accomplished using these approximate integrals. Single calculations may then be made using these ``best'' parametric values.Keywords
This publication has 11 references indexed in Scilit:
- On the Three- and Four-Center Integrals in Molecular Quantum MechanicsThe Journal of Chemical Physics, 1951
- Molecular Orbital Calculations for H3The Journal of Chemical Physics, 1951
- The evaluation of integrals occurring in the theory of molecular structure. Parts I & IIPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1951
- LCAO Self-Consistent Field Calculation of the Ground State of Carbon DioxideThe Journal of Chemical Physics, 1951
- Complete Molecular Orbital Treatment of the System H4Proceedings of the Physical Society. Section A, 1951
- The Energy of Interaction between Two Hydrogen AtomsThe Journal of Chemical Physics, 1950
- I. Calculation of Energy of H3 MoleculeThe Journal of Chemical Physics, 1936
- The Approximations Involved in Calculations of Atomic Interaction and Activation EnergiesThe Journal of Chemical Physics, 1934
- Zur Quantentheorie der homöopolaren ValenzzahlenThe European Physical Journal A, 1928
- Zur Quantenmechanik der homöopolaren ValenzchemieThe European Physical Journal A, 1928