Multiple solutions of coupled-cluster doubles equations for the Pariser-Parr-Pople model of benzene

To gain some insight into the structure and physical significance of the multiple solutions to the coupled-cluster doubles (CCD) equations corresponding to the Pariser-Parr-Pople model of cyclic polyenes, complete solutions to the CCD equations for the (1)A(1g)(-) states of benzene are obtained by means of the homotopy method. By varying the value of the resonance integral beta from -5.0 to -0.5 eV, we cover the so-called weakly, moderately, and strongly correlated regimes of the model. For each value of beta, 230 CCD solutions are obtained. It turned out, however, that only for a few solutions a correspondence with some physical states can be established. It has also been demonstrated that, unlike for the standard methods of solving CCD equations, some of the multiple solutions to the CCD equations can be attained by means of the iterative process based on Pulay's direct inversion in the iterative subspace approach.