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The perturbation theory of the extended Hartree–Fock approximation for two‐electron atoms
Author(s) -
Brown W. Byers,
Nazaroff G. V.
Publication year - 1967
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560010417
Subject(s) - atomic orbital , hartree–fock method , eigenvalues and eigenvectors , electronic correlation , quantum mechanics , perturbation theory (quantum mechanics) , physics , perturbation (astronomy) , homogeneous space , slater determinant , electron , atomic physics , mathematical physics , mathematics , geometry
The first‐order 1/ Z perturbation theory of the extended Hartree–Fock approximation for two‐electron atoms is described. A number of unexpected features emerge: ( a ) it is proved that the orbitals must be expanded in powers of Z −1/2 , rather than in Z −1 as expected; ( b ) it is shown that the restricted Hartree–Fock and correlation parts of the orbitals can be uncoupled to first order, so that second‐order energies are additive; ( c ) the equation describing the first‐order correlation orbital has an infinite number of solutions of all angular symmetries in general, rather than only one of a single symmetry as expected; ( d ) the first‐order correlation equation is a homogeneous linear eigenvalue‐type equation with a non‐local potential. It involves a parameter μ and an eigenvalue ω(μ) which may be interpreted as the probability amplitude and energy of a virtual correlation state. The second‐order correlation energy is 2μ 2 ω. Numerical solutions for the first‐order correlation orbitals, obtained variationally, are presented. The approximate second‐order correlation energy is nearly 90% of the exact value. The first‐order 1/ Z perturbation theory of the natural‐orbital expansion is described, and the coupled first‐order integro‐differential perturbation equations are obtained. The close relationship between the first‐order extended Hartree–Fock correlation orbitals and the first‐order natural correlation orbitals is discussed. A comparison of the numerical results with those of Kutzelnigg confirms the similarity.