Toward an efficient implementation of internally contracted coupled-cluster methods

A new implementation of the internally contracted multireference coupled-cluster with singles and doubles (icMRCCSD) method is presented. The new code employs an efficient tensor contraction kernel and can also avoid full four-external integral transformations, which significantly extends the scope of the applicability of icMRCCSD. The new implementation is currently restricted to the simple case of two active electrons in two orbitals and also supports the computation of spin-adapted doublet and triplet coupled-cluster wavefunctions. This contribution describes the basic approach for the automated derivation of working equations and benchmarks the current code against efficient implementations of standard methods, such as single-reference coupled-cluster singles and doubles (CCSD) and internally contracted multireference configuration interaction (icMRCI). Run times for linearized variants of icMRCCSD are only twice as long as comparable CCSD runs and similar to those of the icMRCI implementation, while non-linear terms of more complete variants of icMRCCSD lead to an order of magnitude longer computation times. Nevertheless, the new code allows for computations at larger scales than it was possible previously, with less demands on memory and disk-space resources. This is exemplified by numerical structure optimizations and harmonic force field determinations of NC₂H₅ isomers and the singlet and triplet states of m-benzyne. In addition, the exchange coupling of a dinuclear copper complex is determined. This work also defines a new commutator approximation for icMRCCSD, which includes all terms that are also present in the single-reference CCSD method, thus yielding a consistent pair of single-reference and multireference coupled-cluster methods.