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Structure of consistent ground state: Re—derivation of RPA vacuum and inclusion of higher RPA effects
Author(s) -
Toyoda Kaoru
Publication year - 1988
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.560340602
Subject(s) - random phase approximation , physics , ground state , formalism (music) , excitation , coupled cluster , operator (biology) , boson , symmetry (geometry) , quantum mechanics , mathematical physics , chemistry , mathematics , molecule , art , musical , biochemistry , geometry , repressor , transcription factor , visual arts , gene
Abstract Here is presented a method to determine the consistent ground state ( CGS ) which satisfies the so‐called killer condition for the excitation operator. This method may be called an extended application of the procedure employed by Weiner and Goscinski in deriving the random phase approximation ( RPA ) vacuum. The RPA vacuum is derived by solving the recurrence formula of the configuration coefficients of a multiconfigurational state vector. The role of boson approximation to the primitive p‐h excitation operator is also investigated and by using the present formalism the cluster‐expansion‐type CGS is derived as the RPA vacuum under the boson approximation. Inclusion of the effects of a higher RPA in the CGS leads to the simultaneous equations of the configuration coefficients of the CGS . In including the effect of the second RPA , only the symmetry‐broken CGS can exist. When the third RPA effect is involved instead of the second RPA , there can be a symmetry‐adapted CGS , in which the picture of electron pairs acquired in the standard RPA vacuum is modified. Thus the exact CGS vectors are analytically obtained in the case of simple model systems of two or four electrons.