Computational Chemistry and Molecular Modeling
Atomic, Molecular and Optical Physics
Wiley InterScience Backfile Collection 1832-2000
Chemistry and Pharmacology
This paper deals with the perturbation theory of an n-electron Hamiltonian of the general form H = ∑n ƒ(i) + λ∑n g(i, j) = H (f, g; n). In comparison to the Brueckner-Goldstone diagrammatic perturbation theory, we adopt the more general standpoint of admitting, for the construction of an n-particle state, component states of 1, 2, 3, and more particles [O. Sinanoglu, Phys. Rev. 122, 493 (1961) and C. D. H. Chisholm and A. Dalgarno, Proc. R. Soc. (London) Sec. A 292, 264 (1966)]. We show that this leads to the concept of a “partition” of a perturbational eigenstate (or energy) of H. A “partition” is a natural decomposition which: (i) is finite; (ii) relates the eigenvalue problem of the system H = H (f, g; n) to those of certain subsystems H (f, g; n1)(n1 〈 n); (iii) uses “nonseparable” components. We domonstrate (under the preliminary assumption of “strict” nondegeneracy) the second-order energy to possess a “partition.” The components therein are second-order energies of two- and three-particle states. The proof uses an extension of Racah's concept of the fractional-parentage expansion.
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