On invariance requirements in approximate SCF MO Theory

Nanda, D. N. ; Narasimhan, P. T. (1977) On invariance requirements in approximate SCF MO Theory International Journal of Quantum Chemistry, 12 (1). pp. 215-223. ISSN 0020-7608

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/qua.560...

Related URL: http://dx.doi.org/10.1002/qua.560120117


The invariance question int he CNDO and INDO levels of approximation is discussed with particular reference to one-center and two-center two-electron integrals and rotation of molecule-fixed coordinate axes. It is shown that asufficient condition for rotational invariance for the cone-center two-electron integrals is Jμμ = Jμμ, +2Kμμ, where J and K are the Coulomb and exchange integrals over orbitals μ μ' with the same azimuthal quantum number. CNDO and INDO procedures, which explicitly employ Lowdin's orthogonalized basis set of atomic ortbitals (OAO) and differentiate between s-, p-, and d-orbitals on an atom in calculating various integrals, have also been examined in relation to the rotational invariance requirement. An expression which satisfies rotational invariance for two-electron Coulomb repulsion integrals over OAOS is also given.

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