Studies on the Alternant Molecular Orbital Method. II. Application to Cyclic Systems

Abstract

Using the general energy expression for an alternant system with closed-shell structure, obtained in our previous paper on the alternant molecular orbital (AMO) method, a numerical analysis is presented of cyclic systems consisting of 2n=4v+2 electrons moving in the field of 2n[Complex chemical formula]centers. Special attention is paid to the case of large n, when we are essentially dealing with a linear chain with Born-von Karman periodicity condition. The most important result obtained is that the energy depression per electron (a measure for the effectiveness of the method to take into account electron correlation) decreases only slowly with increasing n and approaches a limit in the neighborhood of 0.4 ev. Hence the AMO method is useful even in the case of large systems and may provide a powerful tool for tackling certain problems in solid-state theory. A detailed discussion is given of the various approximations incorporated in our analysis and a critical comparison is made with some related results recently obtained by other investigators.