Iterative and Non-iterative Inclusion of Connected Triple Excitations in Coupled-Cluster Methods: Theory and Numerical Comparisons for Some Difficult Examples

In order to obtain quantitative accuracy from coupled-cluster (CC) methods, it is well known that connected triple excitations must be included in some manner. Since rigorous, full inclusion by the complete CC singles, doubles, and triples (CCSDT) method is computationally very demanding, a large number of approximate strategies have been proposed and used. These methods have varying degrees of complexity, computational cost, and success. The first purpose of this chapter is to give a clear and detailed description of the different methods. The intent is to enable the non-specialist to appreciate the origins of the different methods, the nature of the approximations involved, and the computational demands.

Among all the different methods for including connected triple excitations in CC methods, the most widely used by far is the CCSD(T) method. The reasons for this are that this method is very economical (in the context of CC methods that include triple excitations) and has been found to be rather reliable in many examples. For several reasons it is important to establish the limitations of the CCSD(T) method. The second part of this chapter addresses this issue by analyzing the performance of CCSD(T) method and several theoretically more complete methods, including the CCSDT method, for several difficult examples. In these comparisons, for the most part, basis sets of at least triple-zeta valence plus double polarization quality have been used, so as to make comparisons between advanced correlated methods as meaningful as possible. As well as providing benchmark comparisons, the results help to establish the limits of the CCSDT method, thereby assessing the need for connected quadruple and higher excitations.