5 November 1999 Ž . Chemical Physics Letters 313 1999 399–403 www.elsevier.nlrlocatercplett Intermediate Hamiltonian Fock-space coupled-cluster method Arie Landau, Ephraim Eliav, Uzi Kaldor ) School of Chemistry, Tel AÕiÕ UniÕersity, 69978 Tel AÕiÕ, Israel Received 9 August 1999; in final form 14 September 1999 Abstract An intermediate Hamiltonian Fock-space coupled-cluster method is presented, following the formalism developed by Malrieu in the context of perturbation theory. The method is expected to be applicable to many states not accessible by traditional FSCC. A pilot application to a large number of excited states of Sc q shows good convergence and agreement with experiment to a few hundredths of an eV, whereas the usual FSCC iterations diverge for all but the few lowest states. q 1999 Elsevier Science B.V. All rights reserved. 1. Introduction The coupled-cluster method is one of the most powerful tools for atomic and molecular calculations wx Ž . 1 . The Fock-space variant of the method FSCC wx Ž 2 provides highly accurate transition energies see, w x. e.g., Refs. 3,4 . A major limitation of the method, particularly of FSCC, results from convergence diffi- culties, due in many cases to the existence of in- w x truder states 5–12 . These are Q-space states which Ž . couple strongly with P or model states and lead to large excitation amplitudes and difficult or no con- vergence. The problem may sometimes be overcome w by introducing an incomplete model space 7– x 9,13,14 , selected so that intruders do not interfere. This is not always possible; in addition, an incom- plete space makes the method more complicated and is not always compatible with connectivity in the w x intermediate normalization formalism 14–17 . ) Corresponding author. Fax: q972-3-6428273; e-mail: kaldor@jade.tau.ac.il An alternative way of avoiding intruders is the intermediate Hamiltonian method, introduced by w x Malrieu et al. 12 in degenerate perturbation theory. Instead of the traditional division of the determinant space into P and Q sub-spaces, Malrieu has three subspaces: the main space P , the intermediate P , m i and the complementary Q. Bloch-type equations are obtained, which may be extended to the Fock-space coupled-cluster approach. Other intermediate Hamil- tonian schemes have been proposed in the frame- w x work of coupled-cluster 18,19 and configuration w x interaction 20 methods. A similar scheme has been w x proposed by Heuilly et al. 21 in the framework of quasidegenerate perturbation theory. In this Letter, w x we follow the basic ideas of Malrieu et al. 12 and take them further. While the original method as- sumed exact degeneracy of the model space, we allow more general spaces and, more important, instead of the perturbation theory framework, the method presented here is an all-order intermediate Ž . Hamiltonian Fock-space coupled-cluster IHFSCC scheme. 0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 99 01067-2