Multireference coupled cluster method for electronic structure of molecules

In this review we present a systematic derivation of the multireference coupled cluster theory based on the single reference formalism. The coupled cluster theories have recently emerged as one of the major method development activities in the electronic structure theory of atoms and molecules. Due to its size-extensive nature, using the coupled cluster method the total electronic energy of the system can be determined with the same relative accuracy as the total electronic energies of the fragments which the system separates into in the process of chemical decomposition. This feature is essential for the correct theoretical determination of dissociation energies as well as other molecular properties. One of the most difficult challenges in advancing the coupled cluster theory has been the development of the multireference coupled cluster methodology, i.e. generating a scheme which allows the reference function to incorporate more than one Slater determinant. Such development would enable a very accurate ab initio treatment of general categories of open-shell systems as well as the treatment of systems with stretched multiple bonds leading to a more precise determination of vibrational spectra. In this article we review our recent results in the development of a multireference coupled cluster theory. The reader will be first acquainted with the second quantization formalism, then guided through the derivation of the single reference coupled cluster theory, and finally presented with the multireference formalism. We have included several numerical examples illustrating the performance of the single reference and multireference coupled cluster methods.