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Content archived on 2024-05-29

Development and application of efficient explicitly correlated coupled cluster methods

Final Activity Report Summary - CCSD(T)R12 (Development and application of efficient explicitly correlated coupled cluster methods)

The CCSD(T) coupled-cluster electronic structure method is a standard tool for computational chemists, providing reliable predictions of molecular energies (such as thermochemical data, reaction pathways etc.) and properties (e.g. IR/NMR spectra etc.) by computing approximate numerical solutions to the quantum mechanical equations. However, large numbers of orbital basis functions are often required to obtain chemically useful accuracy, making these calculations very expensive. Explicitly-correlated (R12) electronic structure methods use additional two-particle basis functions that depend explicitly on the interelectronic distance. These methods require a relatively small number of orbital basis functions for highly accurate chemical predictions. However, the equations that must be solved are much more complex than the orbital-only counterparts and some of the approximations used to make the equations tractable carry the caveat that they are only valid if large orbital basis sets are used. The aim of the work carried out was to improve upon this method, increasing the efficiency to fully exploit the high performance potential of the R12 electronic structure methods.

In the months leading up to and during the initial stages of the working period it became clear, through our own investigations and those of other researchers, that the CCSD(T)(R12) method could be improved in three directions:
1. by introducing an auxiliary basis set to satisfy the requirements of the approximations inherent to the R12 methods;
2. by relaxing some of the constraints used to simplify the R12 terms in the coupled-cluster equations, i.e. by using Ansatz 2;
3. by using a new correlation factor for the two-particle basis functions, which was better able to reproduce the effects of correlation due to the Coulombic repulsion between electrons.

All of these three improvements were introduced to the explicity-correlated coupled-cluster CCSD(T)(R12) method. This new method was shown to yield accurate CCSD(T) energies using relatively small orbital basis sets. The computational cost of CCSD(T) calculations depended primarily on the size of the orbital basis set and the additional cost of the R12 terms in the CCSD(T)(R12) method only increased the time taken by a factor of three. Our new approach could therefore be applied to accurately probe much larger systems than those currently feasible with the conventional CCSD(T) method.