Application of molecular orbital graph theory to vibrational problems of finite chain systems

A generating function approach based on molecular orbital graph theory is presented that provides a straightforward way of obtaining the secular polynomials and energy bands for repeated unit systems from polynomial recurrence expressions. The possibility of obtaining the analytical energy-level spectrum of the system can also be predicted. These results are then used to discuss the vibrational problems of finite chain systems with single- and double-component lattices. It seems to be the first report describing the vibrational states of an (AB)_N chain.