Perturbative triple and quadruple excitation corrections to MRCISD Yuriy G. Khait 1 , Jie Song 2 , Mark R. Hoffmann * Chemistry Department, Box 9024, University of North Dakota, Grand Forks, ND 58202-9024, USA Received 10 October 2002; in final form 6 March 2003 Abstract A non-iterative approximation to the effects of triple and quadruple excitations in the framework of the multire- ference configuration interaction method, including single and double excitations (MRCISD), for molecular electronic structure is suggested. The approximation is derived from perturbative expansions of lower and upper bounds of a self- consistent, second-order approximation to the MRCISDTQ energy. Numerical studies on a number of well studied model systems support the hypothesis that the suggested method, which can be referred to as MRCISD(TQ), is a new, viable, ultrahigh accuracy method. Ó 2003 Elsevier Science B.V. All rights reserved. 1. Introduction Although the quest for inclusion of dynamic electron correlation beyond the single- and double- excitation level has primarily found modern ex- pression in the context of coupled cluster methods, the configuration interaction (CI) framework does provide one essential advantage – a natural de- scription of excited electronic states. To be sure, multireference and quasidegenerate coupled clus- ter methods have been proposed, and some shown to have at least partial successes, in this direction [1–5], but it seems that CI, especially multirefer- ence CI (MRCI), remains a viable framework (for a recent review, see [6]). However, traditional CI in a configuration space larger than single and double excitations becomes computationally prohibitive for all but model studies or very small real systems. One avenue for inclusion of higher correlation is the CISD[TQ] method of Schaefer and co-workers [7,8], in which only triple and quadruple excita- tions that involve a relatively small subset of the one-electron basis are allowed. In this Letter, we suggest a new hybrid variational–perturbational approach that retains the advantages of the suc- cessful MRCISD method, and adds perturbatively dynamic electron correlation beyond the SD-level. Previous efforts to perturbatively include higher-than-double excitations in the framework of CISD (or MRCISD) have focused on so-called Chemical Physics Letters 372 (2003) 674–685 www.elsevier.com/locate/cplett * Corresponding author. Fax: 1-701-777-2331. E-mail address: mhoffmann@chem.und.edu (M.R. Hoff- mann). 1 Permanent address: 14 Dobrolyubova Ave., Russian Scien- tific Center ÔApplied ChemistryÕ, St. Petersburg 197198, Russia. 2 Present address: Department of Chemistry, Iowa State University, Ames, IA 50011, USA. 0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00478-0