Perturbation theory for intermolecular interactions

Van der Avoird A (1967) Perturbation theory for intermolecular interactions in the wave-operator formalism. J Chem Phys 47 3649-3653... 

P. R. Surjan, 1. Mayer, and 1. Lukovits, Chem. Phys. Lett., 119, 538 (1985). Second-Quantization-Based Perturbation Theory for Intermolecular Interactions Without Basis Set Superposition Error. 

Apparently, there is room for further research in this field. In the next section we shall review some many-body perturbation theories for intermolecular interactions which make use of one of the interaction operators discussed above. 

Until recently, and possibly still so for certain applications, one of the most successful perturbation theories for intermolecular interactions was the symmetry-adapted perturbation theory (S APT) (Jeziorski and Szalewicz 2002 Jeziorski et al. 1994). SAPT is a triple perturbation theory based on a Hartree-Fock description of the interacting monomers. Intramolecular correlation is buUt up using two of the perturbations, and intermolecular correlation by the third. SAPT has been applied to a large number of systems with very good success. See for example, applications... 

Distasio, R. A., Jr., 8c Head-Gordon, M. (2007). Optimized spin-component scaled second-order Moller-Plesset perturbation theory for intermolecular interaction energies. Molecular Physics, 105,1073-m3. 

The interaction energies of clusters of molecules can be decomposed into pair contributions and pairwise-nonadditive contributions. The emphasis of this chapter is on the latter components. Both the historical and current investigations are reviewed. The physical mechanisms responsible for the existence of the many-body forces are described using symmetry-adapted perturbation theory of intermolecular interactions. The role of nonadditive effects in several specific trimers, including some open-shell trimers, is discussed. These effects are also discussed for the condensed phases of argon and water. 

Adams WH (2002) Two new symmetry-adapted perturbation theories for the calculation of intermolecular interaction energies. Theor Chem Acc 108 225—231... 

The first chapter by Moszyliski presents in a systematic and comprehensive manner the current state-of-the-art theory of intermolecular interactions. Numerous examples illustrate how theoreticians and experimentalists working in tandem may gather valuable quantitative results related to intermolecular interactions, like accurate potential functions, interaction-induced properties, spectra and collisional characteristics or dielectric, refractive or thermodynamic properties of bulk phases. On the other hand the most advanced Symmetry Adapted Perturbation Theory (SAPT) enables validation of more approximate variation-pertubation models which could be applied to the analysis of specific interactions in much larger molecular systems, for example enzyme-drug interactions discussed in Chapter VIII by Berlicki et al. 

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. 

As Buckingham [18] has done, the intermolecular interaction can be formulated as a perturbing Hamiltonian and then elements of the interaction are associated with specific terms and specific orders of perturbation theory. For an ab initio... 

Halasz GJ, Vibok A, Mayer I (1999) Comparison of basis set superposition error corrected perturbation theories for calculating intermolecular interaction energies. J Comput Chem 20 274-283 Halgren TA, Lipscomb WN (1977) The synchronous-transit method for determining reaction pathways and locating molecular transition states. (3hem Phys Lett 49 225-232 Hammond GS (1955) A correlation of reaction rates. J Am Chem Soc 77 334-338... 

For the long-range intermolecular separations the perturbation theory can be applied. Within the perturbation theory using the interaction operator (2.2.3) one can obtain the energy of the pair of uncharged molecules A and B perturbed by a weak general static electric field as [5, 14] ... 

Yet another outstanding problem is the correct treatment of the interactions of small gap materials such as fullerenes. It is quite likely that second-order perturbation will not be adequate for such systems. Furthermore, the strong electron delocalization in these semi-conductor-like materials means that the standard atom-atom models of interaction fail due to their inherent assumption of locality (Misquitta et al. 2010). This is possibly the next hurdle to be faced by the theory of intermolecular interactions. 

For Inter Molecular Perturbation Theory (IMPT) see Hayes, I. C. Stone, A. J. An intermolecular perturbation theory for the region of moderate overlap, Mol. Phys. 1984, 53, 83-105 papers of this kind, however, contain a large amount of theoretical and mathematical detail and are not transparent to the uninitiated. For Symmetry-Adapted Perturbation Theory (SAPT) see e.g. Bukowski, R. Szalewicz, K. Chabalovski, C. F. Ab initio interaction potentials for simulations of dinitramine solutions in supercritical carbon dioxide with cosolvents, J. Phys. Chem. 1999, A103, 7322-7340, and references therein. The Morokuma decomposition scheme is described in Kitaura, K. Morokuma, K. A new energy decomposition scheme for molecular interactions within the Hartree-Fock approximation, Int. J. Quantum Chem. 1976,10, 325-340. 

A theory developed by Zimm, like Fixman s treatment of the expansion factor discussed above (which it antedates), is based on a perturbation expansion for weak interactions. For interacting polymer chains, Zimm assumes that intermolecular intersegmental potentials of average force between segments i i in molecule 1 and I2 in molecule 2 are additive... 

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-... 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

In order to ensure accurate CG potentials, one needs to conduct MD simulations with a reliable atomistic potential model. The most desirable theoretical approach for the atomistic-scale simulations would be to use a level of quantum mechanics (QM) that can treat both intermolecular and intramolecular interactions with acceptable accuracy. Realistically, the minimal QM levels of theory that can adequately treat all different types of chemical forces are second order perturbation theory [32] (MP2)... 

Considering only the interaction between HOMO of R and LVMO of S, elementary perturbation theory shows that the result of the orbital interaction is a repulsion of the levels, the occupied level becomes more stable, the unoccupied level less stable. The simplest Huckel-type formulation of PMO theory gives equations for the intermolecular perturbation energy change A that are quite simple in form, Eqs. 3—6 18,20,22,26-28) Q is a first-order Coulombic energy that can be calculated in terms of... 

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