Original scientific paper

Antialternant Perturbations of Alternant Systems

Tomislav P. Zivkovic ; »Ruder Boskovic«. Institute, University of Zagreb, P. 0 . Box; 1016, 41001 Zagreb, Yugoslavia

Abstract

Rayleigh - Schrodinger perturbation expansion is applied to
the system where the unperturbed Hamiltonian Ho is chosen to be
an alternant operator, while the perturbation J.. V is chosen to be
an antialternant operator. A configuration interaction space X ..
generated by n electrons moving over 2n orthonormalised orbitals
is considered. This space splits into two mutually complementary
subspaces x: and x.- containing alternant-like states. These states
have characteristic properteis of the eigenstates associated with
neutral alternant hydrocarbon systems. If the eigenstate «P E X.,
of the unperturbed Hamiltonian Ho is nondegenerate, then it is
alternant-like, i. e. either «P E X,,+ or «P E x.-, and without loss of
generality one can assume «P = cp+ E X,.+. In this case the eigenstate
'I' (A) of the total Hamiltonian H = Ho + J.. V , as expanded in the
power series of the expansion parameter J., is of the form 'I' (A) =
= cp+ + }. 'l'1-+ J..2 'l'2+ + J..3 'l'3- + ... , where corrections to all ordersare alternant-like states. In addition, all even corrections are containedin the space X,.+, while all odd corrections are contained in
the space x .. -. The corresponding eigenvalue E {J..) is an even functionof the expansion parameter J,, Also, the expectation value of
each alternant operator is an even function of J.., while the expectation
value of each antialternant operator is an odd function of
J... In particular, these results are applied to the matrix elements
of one- and two-particle density matrices, and a simple example
illustrating these properties is given.

Keywords

Hrčak ID:

194044

URI

https://hrcak.srce.hr/194044

Publication date:

21.5.1985.

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