An Alternative Algebraic Framework for the Simplification of Coupled Cluster Type Expectation Values

The Coupled-Cluster (CC) method is one of the most popular and efficient correlation methods in quantum chemistry. Especially the CCSD(T) approximation, which includes single and double excitations by means of the application of the cluster operator to a reference determinant and triple excitations via a perturbative treatment, has become a standard tool in quantum chemical applications. However, the method is restricted to relatively small system sizes due to its unfavourable scaling (N^7, where N is the number of basis functions applied). For the full treatment of triple excitations the scaling advances to N^8 and every further excitation level increases the exponent by two.

The goal of this work is to reduce the calculation time for closed shell systems at least by a factor growing with the excitation level for arbitrary truncation levels. This is done by restricting the spatial parts of the spin orbitals and thus treat pairs of spin orbitals on the same footing. The restrictions can be easily constructed for the CCSD model by spin integration. The derivation of the restrictions arising in higher excited case will be done employing the spatial orbital excitation operators E.

In the first part of this work an algorithm is derived that is capable of the derivation of the energy and amplitude equations for arbitrary excitation levels. In the second part an implementation of this algorithm is presented.