AN ALTERNATIVE WAY OF SOLVING SECULAR EQUATIONS FOR THE HAMILTONIAN MATRICES OF REGULAR QUASI-ONE-DIMENSIONAL SYSTEMS

An alternative approach to secular problems for Hamiltonian matrices H of regular quasi-one-dimensional systems is suggested. The essence of this approach consists of the inverted order of operations against th at of the traditional solid-state theory, viz., taking into account th e local structure of the system is followed by regarding the translati onal symmetry of the whole chain. The first step is performed by reduc ing the initial system of secular equations into an effective N X N-di mensional secular problem, wherein a single equation corresponds to ea ch of N elementary fragments of the initial chain. An implicit form of the dispersion relation and the level density function follow directl y from the reduced problem without passing into the delocalized descri ption of the system. The resulting eigenfunctions of the matrix H prov e to be expressed as the Bloch sums of N nonorthogonal eigenvalue-depe ndent local-structure-determined orbitals of algebraic form, each of t hem corresponding to a definite elementary fragment of the chain. (C) 1996 John Wiley & Sons, Inc.