Dimers many-body forces

We may conclude that many-body forces are not important for the structure of solid hydrogen chloride (for further details see Sections 4.3 and 5). The energy of interaction in the dimer and in the solid fit very well into our relations. This is more a test of our assumptions of binary potentials in equations 8 and 18 than a limit on the role of many-body forces because the only available value was derived from cluster calculations based on the assumption of pairwise additivity. From the concepts and data discussed in this section it is obvious that an accurate description of clusters and condensed phases formed from polar molecules like HF and H20 which are both characteristic hydrogen bond donors and acceptors, requires a proper consideration of many-body forces. 

As a second model potential we shall briefly discuss the PES for the water dimer. Analytical potentials developed from ab initio calculations have been available since the mid seventies, when Clementi and collaborators proposed their MCY potential [49], More recent calculations by dementi s group led to the development of the NCC surface, which also included many-body induction effects (see below) [50]. Both potentials were fitted to the total energy and therefore their individual energy components are not faithfully represented. For the purposes of the present discussion we will focus on another ab initio potential, which was designed primarily with the interaction energy components in mind by Millot and Stone [51]. This PES was obtained by applying the same philosophy as in the case of ArCC>2, i.e., both the template and calibration originate from the quantum chemical calculations, and are rooted in the perturbation theory of intermolecular forces. 

The dimers of Be, Mg and Ca are very weakly bound by the electron correlation effects, at the self-consistent field (SCF) level they are not stable. The binding energy of alkaline earth dimers is only 2-4 times larger than that in Kr2 and Xe2 dimers. Thus, alkaline dimers can be attributed to the van der Waals molecules. The situation is changed in many-atom clusters, even in trimers (Table II). This is evidently a manifestation of the many-body effects. The crucial role of the 3-body forces in the stabilization of the Be clusters was revealed at the SCF level previously [3-5], and more recently was established at the Mpller-Plesset perturbation theory level up to the fourth order (MP4) [6,7]. The study of binding in the Ben clusters [8-10] reveals that the 3-body exchange forces are attractive and give an important contribution to... 

Electronic structure calculations have recently become capable to provide interaction potentials for medium-size dimers that can be used to predict properties of such dimers with accuracy approaching, and in a few favorable cases even surpassing, experimental accuracies [1-4]. The dimer (pair) potentials are the basic building blocks of potential surfaces for larger clusters represented in the form of many-body expansions. Such expansions decompose each surface into intramonomer contributions, i.e. the potentials within single molecules (monomers), the pair potentials, and the so-called nonadditive potentials. Since derivatives of potential energy surfaces define forces, one may alternatively use the term force helds equivalently with potentials . 

The concept of calculating the interaction energy of two chemical systems A and B perturbatively is not at all a new idea. The first intermolecular perturbation expansion was proposed [22] just a few years after the foundations of quantum mechanics had been laid. Since then, numerous other expansions, now known under a common name of symmetry-adapted perturbation theory, have been introduced and the perturbation theory of intermolecular forces is now a fully mature approach. Thanks to the development of the many-body SAPT [23] and of a general-utility closed-shell SAPT computer code [24], the perturbative approach to intermolecular interactions has been successfully applied to construct PESs for numerous interacting dimers of theoretical and experimental interest [19-21,25-27]. One of the notable achievements of SAPT is an accurate description of the interactions between water molecules [21,28-32]. A recent paper by Keutsch et al. [33] compares the complete spectra of the water dimer with theoretical predictions obtained using an empirical potential fitted to extensive spectroscopic data, and with the predictions from a SAPT potential. These comparisons show that the latter potential probably provides the best current characterization of the water dimer force field. In another recent application, an SAPT PES for heUum in-... 

Many applications of new force fields and new QM/MM methods of necessity focus on agreement with experimental or otherwise calculated results. Also in this section we will first show that DRF indeed gives a reliable model for static and response potentials and can lead to QM/MM—or even completely MM calculations—that are as good as, e.g., SCF calculations. To that end we point at some results for simple systems like the water and benzene dimers, and the three- and four-body interactions in several systems. 

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