A size-extensive state-specific multi-reference many-body approach using incomplete model spaces Dola Pahari a , Sudip Chattopadhyay a , Sanghamitra Das a , Debashis Mukherjee a,b, * a Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700032, India b Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India Received 29 June 2003; in final form 10 September 2003 Published online: Dedicated to Professor Werner Kutzelnigg on his 70th birthday Abstract We present a size-extensive and size-consistent state-specific multi-reference coupled-cluster approach based on an incomplete model space (IMS) and also discuss simplifications if the IMS is quasi-complete. Methods such as per- turbation theory or CEPA-like schemes follow naturally as suitable approximants. Intermediate normalization for the wave-operator, X is abandoned in the formalism and suitable excitations, defined as open and quasi-open – which excite out of the IMS by their action on at least one of the model functions – are incorporated in X. The effective operator W , leading to the energy on diagonalization, is a closed connected operator. Ó 2003 Elsevier B.V. All rights reserved. 1. Introduction Multi-reference (MR) many-body approach is one of the most promising avenues to describe electron correlation in molecular states which have varying degrees of nondynamical correlation. Most such traditional formulations were all based on the effective Hamiltonian framework [1–4] de- fined in a complete model space (CMS) (also called, a complete active space (CAS)). Both per- turbative [1] and coupled cluster (CC) [2–4] for- mulations were developed and their rigorous size- extensivity were established. The model functions furnish the nondynamical correlation and the vir- tual functions bring in the dynamical correlation. In molecular applications, their practical use re- mains somewhat restricted to this date due to the notorious Ôintruder problemÕ [5], which stems from near-degeneracy of some virtual functions with some high-lying model functions. One may imagine that a size-extensive formal- ism with an incomplete model space (IMS), where one leaves the potentially degenerate model func- tions intruded by the virtual functions out of the model space, will alleviate this problem. Such Chemical Physics Letters 381 (2003) 223–229 www.elsevier.com/locate/cplett * Corresponding author. Fax: 3324732805. E-mail address: pcdm@iacs.res.in (D. Mukherjee). 0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.09.117