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Evaluation of Suitable Mean‐Field (Hartree‐Fock) Representations for Perturbational Studies of Disordered Solids
Author(s) -
Böhm M. C.
Publication year - 1985
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221310132
Subject(s) - unitary transformation , unitary operator , wave function , slater determinant , subspace topology , hartree–fock method , operator (biology) , basis (linear algebra) , quantum mechanics , fock space , chemistry , atomic orbital , mathematics , physics , hilbert space , electron , mathematical analysis , biochemistry , geometry , repressor , transcription factor , quantum , gene
A unitary transformation scheme in Hartree‐Fock (HF) space is derived allowing for the definition of a “mixed” representation of the mean‐field operator which forms a suitable self‐consistent‐field (SCF) HF basis for perturbational studies of disordered solids and polymers. The transformed HF operator contains only a small number of off‐diagonal Lagrange multipliers (i.e. coupling terms) between properly defined “defect state(s)” in the filled or empty HF space and the remaining one‐particle functions of the Fermion system which are collected into a prediagonalized subspace. The unitary transformation scheme requires two numerical operations; in the first one the canonical one‐electron functions are transformed into a set of localized valence‐bond‐type orbitals. This one‐particle representation is then transferred into a mixed basis via elementary matrix diagonalizations and multiplications. The relevant theoretical steps are outlined in a few simple examples.