Coupled Cluster Methods
The Correlation Energy
The Hartree-Fock (HF) equations which describe the optimal Slater determinant representation of a molecular wave function and their computationally feasible solution via the SCF method were introduced in Chapter 2. Slater determinant representations have the advantage that they satisfy the Antisymmetry Principle and account for the indistinguishability of individual electrons; however, they do not correlate the motions of electrons with opposite spins, i. e. there exists a nonzero probability of two electrons with opposite spins occupying the exact same point in space. Moreover, the Fock operator which defines an optimal spin orbital, equation (1.33), does so by treating the electron within that orbital as if it were moving in the average field of the other electrons. For these reasons, HF/SCF wave functions are said to be uncorrelated and the HF model is described as a ``one-electron'' or ``independent particle'' model. Because in reality electrostatic forces prevent electrons from occupying an identical point in space, the exact non-relativistic energy must be lower than the variationally determined HF limit energy. The difference between the HF limit energy, EHF, and the exact non-relativistic energy, Eexact, is defined to be the correlation energy, Ecorr:
| Ecorr = Eexact - EHF. | (1) |
Many methods currently exist for recovering the correlation energy using both variational and non-variational approaches. Two of the most popular approaches are configuration interaction (CI) methods and coupled cluster (CC) methods.