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Localized impurity states in the Hartree‐Fock, LCAO approximation. I.
Author(s) -
Martino F.
Publication year - 1968
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.560020205
Subject(s) - wave function , hamiltonian (control theory) , electron , linear combination of atomic orbitals , hartree–fock method , eigenvalues and eigenvectors , impurity , chemistry , crystal (programming language) , quantum mechanics , physics , eigenfunction , orthogonalization , atomic physics , condensed matter physics , mathematics , atomic orbital , geometry , mathematical optimization , computer science , programming language
One‐electron energies and wave functions for deep trap impurity electrons in a crystal are calculated by the Hartree‐Fock, single determinant method. The interactions arising from a many‐electron single determinant crystal wave function, with automatic inclusion of exchange effects, are those which determine the one‐electron functions and energies. The crystal plus impurity system has no translational symmetry and hence the Bloch theorem is not applicable for the solution of the essentially infinite Hartree‐Fock eigenvalue matrix. Thus we develop a technique in which the Hamiltonian and overlap matrices are written in terms of bordered matrices, with the interaction of the impurity functions with the rest of the crystal environment contained in the bordering rows and columns. The resulting secular equation explicitly includes the effects of orthogonalization of the entire basis set, including the impurity functions. This technique could be used in an iterative calculation of the electronic structure of a small number of electrons, assuming that the rest of the electrons in the environment are fixed according to an initial estimate.