An MO-VB Approach for the Determination of Intermolecular Forces. Theory and Calculations on the He 2 , He-CH 4 , and He-H 2 O Systems Gabriele Calderoni, Fausto Cargnoni,* Antonino Famulari, and Mario Raimondi Dipartimento di Chimica Fisica ed Elettrochimica and Istituto CNR-ISTM, UniVersita` degli Studi di Milano, Via Golgi 19 -20133 Milano, Italy ReceiVed: March 12, 2002; In Final Form: April 8, 2002 We present the improvement of a previously developed strategy for the evaluation of intermolecu The approach defines a variational VB (valence bond) wave function, consisting of single and doub from the SCF-MI (self-consistent field for molecular interactions) determinant. The central idea o is the determination of optimal virtual orbitals, to contract the virtual space spanned by all singly excited localized configurations, by means of an iterative optimization procedure. The performance of the strategy is tested by comparison with results where the full virtual space is considered, and the e is also compared with more conventional quantum chemical methods. Testcalculations on three weakly interacting complexes, namely, He 2 , He-CH 4 , and He-H 2 O, are presented. Whatever the system studied, we found an overall agreement between VB, MP4,and CCSD(T) results. The VB welldepths estimates are somewhat larger than MP4 and CCSD(T) ones. Introduction Among the difficulties connected with the determination of intermolecular interactions by means of the supermolecular approach, the basis set superposition error (BSSE) represents a well-known inconvenience. 1 To avoid BSSE, two strategies can be followed. A first approach consists of making the monomer description consistent with that of the dimer, adopting a dimer centered basis set (DCBS); in the other approach, based on a monomer centered basis set (MCBS) scheme, the dimer descrip- tion is made consistent with that of the monomer. 2 During theyears,the computational quantum chemical methods that make use of a DCBS description have received the major interest, and the counterpoise correction 3 has been therefore commonly adopted to evaluate interaction energies. Among the reasons for this choice, we mention the difficulties to efficiently deal with the nonorthogonality, that naturally arises when a MCBS description is considered. Notwithstanding the great popularity received by the counterpoise method, there are someinconveniences associated with it. From a practical viewpoint, the need to calculate the energy of the isolated fragment in the DCBS framework leads to the tedious “3:1 rule” (i.e.,three energy calculations for eVery interaction energy to be evaluated), 3 with the situation getting worse if geometric relaxation is taken into account. 4 On the theoretical side,the upsetting of the multipole moments and polarizabilities of the monomers (secondary BSSE) was reported. 5 Over the pastfew years,we developed nonorthogonal approaches to the determination of intermolecular interactions. 6-9 Common to them is the partitioning of the global basis set into subsets centered on the interacting subsystems; the molecular orbitals of different fragments are then expanded only in their specific set, in the spirit of the MCBS approach. Because of this partitioning, orbitals belonging to different fragments are nonorthogonal and overlap,reflecting the physicsof the problem; in this way, BSSE is naturally avoided in a priori fashion. The firststep was the formulation of the SCF-MI(self- consistent field for molecular interactions) algorithm, 6 which has been successfully adopted in many investigations. 7 Later, we included electron correlation effects by means of a nonor- thogonal configuration interaction scheme (MO-VB). 8,9 Simi- larly to the ICF1 method proposed by Liu and McLean, 10 the essenceof theMO-VB scheme is the evaluation of the intermolecular part of the correlation energy only. In this pap we present a more rigorous formulation of the approach, alon with test calculations on three weakly bound complexes. To check the performances of this scheme, we carried out a thorough comparison with more standard Møller-Plesset and coupled cluster DCBS calculations. The paper is organized as follows.First,the theoretical framework of ourapproach is described and discussed. Ex- amples ofapplications to the He 2 , He-CH 4 , and He-H 2 O systemsare thenpresented. A final commentary section concludes. Theory Build-Up of the Wave Function. Consistent with the MCB approach, given the interacting system AB (fragments A and containing N A and N B electrons, respectively), the global basis setis partitioned into two subsets belonging to the isolated monomers: each set contains only the basis functions centered on the atoms of its fragment. Starting from the reference SCF MI 6 wave function, to avoid BSSE, the fullCI expansion is assumed in the form where 0 A/B stands for the reference state and S A/B , D A/B , ... N A/B represent singly,doubly,..., N-uply excited configurations localized on fragment A or B, respectively. The symbol X represents the direct product of the subspaces; in the contex Grassman or exterior algebra formalism, it is the exterior pro * To whom correspondence should be addressed. E-mail: fausto.cargnoni@ istm.cnr.it. [0 A x S A x D A x ‚‚‚ x N A ] X [0 B x S B x D B x ‚‚‚ x N B ] (1) 5521 J. Phys.Chem. A 2002, 106, 5521-5528 10.1021/jp020681f CCC: $22.00 © 2002 American Chemical Society Published on Web 05/07/2002