A new approach to construct the three-body correlation matrices for correlated excited states

The calculations carried out with the G-particle-hole hypervirial equation (GHV) method for a set of ground-states dominated by a single determinant of electronic systems have yielded highly-accurate results when compared to the equivalent full configuration interaction (FCI) quantities [26,28,30]. However, the results obtained when calculating states dominated by several determinants were not satisfactory. This problem is common to other contracted equations methodologies. The reason for this apparent shortcoming is that in these cases the existing algorithms yield inaccurate approximations for the 3-body correlation matrices involved in the contracted equations. Here, we propose a new set of algorithms for constructing the 3-order correlation matrix in terms of the 2-order one when a singlet zero-order wave-function is formed by a single configuration state function (CSF) composed of two equally weighed Slater determinants. This type of correlated states are of great general interest but in particular in spectroscopy and quantum information. The results obtained are very satisfactory.