Comparison of coupled-cluster methods which include the effects of connected triple excitations

Abstract

Electron correlation energies have been determined for 14 different molecules which represent a range of chemical bonding situations. These have been determined with the coupled‐cluster single, double, and triple (CCSDT) excitation model as well as with several coupled‐cluster methods that include only an approximate treatment of connected triple excitations, viz. CCSDT‐1a, CCSDT‐1b, CCSDT‐2, CCSDT‐3, CCSDT‐4, and the recently proposed CCSD(T) method. All of the CCSDT‐x methods include the effects of connected triple excitations in an iterative manner, whereas in CCSDT(T) these are included perturbationally. For chemical systems which are well represented by a single‐determinant reference function, some of the CCSDT‐x<s>methods (CCSDT‐1a, CCSDT‐1b, and CCSDT‐4) perform marginally better than the CCSD(T) approach in reproducing the CCSDT results. However, as nondynamical correlation becomes more important the good agreement from the CCSDT‐x methods deteriorates rapidly, while the error in CCSD(T) remains more consistent. For the 14 molecules considered in this work, the average error of the CCSD(T) method relative to CCSDT (667 μhartrees) is considerably below that obtained from any of the CCSDT‐x methods. It is concluded that CCSD(T) is to be preferred over any of the other approximate methods, both because it is the least expensive and also because it is generally the most accurate approximation to CCSDT.