Quantum chemistry in Fock space. I. The universal wave and energy operators

摘要

The Fock space HamiltonianHhas a simpler structure than its projectionHntonhyphen;particle Hilbert space. It is therefore recommended to diagonalizeHmdash;to the extent that this is possiblemdash;before one specifiesn. Diagonalization ofHis possible if one defines the diagonal and nondiagonal parts of an operator appropriately. It is shown that the diagonalized Fock space HamiltonianL, called an energy operator, contains all information about the eigenvalues ofHin a simply coded form. For a spinfree Hamiltonian, spin can be completely eliminated and all interesting quantities are expressible in terms of spinfree excitation operators (generators of the unitary group). The construction of the wave operatorWand the energy operatorLis formulated in terms of perturbation theory both in the strictly degenerate and the quasidegenerate version. Three variants are discussed that differ in the normalization ofW, namely,aintermediate normalization,bandcunitary normalization with two additional conditions,b:thinsp;WD=WD+,c:sgr;D=(lnthinsp;W)D=0.The transformation of operator products to normal product form is achieved by means of a generalization of Wickrsquo;s theorem to spinfree quantum chemistry. The contributions to the various orders ofL,W, and sgr; are illustrated by means of diagrams. Only variantcguarantees a connectedhyphen;diagram expansion of the Fock space energy operatorL. None of the three variants satisfies a generalization of the Wigner(2n+1)rule, but with a slight change in the normalization frombtobprime; orctocprime; (that does, in the case ofcprime;, not affect the connectedness of the diagram expansion)L(2n)andL(2n+1)are expressible in terms of theW(k),kles;n.A generalization of the variation principle for the Fock space energy operator is given and its consequences are discussed. Generalized Fock space Brillouin conditions are derived and a variational scheme for the construction of the energy operator is proposed. We finally compare the present Fock space approach with the traditional degenerate perturbation theory innhyphen;particle Hilbert space. If the diagonal partOHgr;Dof an operator OHgr; is defined in the spirit of the theory of the universal wave and energy operators, then the two approaches lead to the same results (for the same normalization), but the Fock space approach looks simpler and more transparent.