Local correlation in the virtual space in multireference singles and doubles configuration interaction

We describe a multireference configuration interaction method that takes advantage of local correlation methods in both the internal ~originally occupied! and external ~originally unoccupied or virtual! orbital spaces. In the internal space, implementation of local correlation is trivial and involves neglecting configurations having simultaneous excitations out of widely separated orbitals. In the external space, the method involves restricting the space of allowed correlating orbitals to those localized near the hole orbitals. Of course, this necessitates the use of localized virtual orbitals which in turn requires one to sacrifice the orthogonality of the virtual space. This complicates the formalism substantially, and we discuss the necessary changes to the traditional expressions in detail. The scaling of the method with system size, basis set size, and the average number of allowed virtual orbitals is explored. An examination of systems having up to 8 heavy atoms reveals that the computational costs of the method scales somewhere between the third and fourth power of the size of the system. Furthermore, this reduced scaling method is capable of recovering greater than 97% of the correlation energy. Additionally, we demonstrate that the method can produce smooth potential energy surfaces and recover bond dissociation energies in organic molecules at a fraction of the cost ~>tenfold less expensive! while retaining accuracy. We go on to use this new reduced scaling approach to predict bond energies in several large organic molecules for which no experimental data are available. © 2003 American Institute of Physics. @DOI: 10.1063/1.1565314#