Symmetry adapted perturbation theory intermolecular interactions

Rybak, S., Jeziorski,B. and Szalewicz, K. (1991)Many-body symmetry-adapted perturbation theory of intermolecular interactions. FhOandHF dimers,/. Chem. Phys., 95, 6576-6601. 

Contrary to the previously described supermolecular approach, perturbation theory treatment allows for the partition of the interaction energy into physically interpretable components. The most frequently used method for this purpose is symmetry-adapted perturbation theory (SAPT) [13]. More recently, great effort has also been invested in the development of DFT-SAPT [14-16], In the present contribution, we use the variational-perturbational scheme [17-20], In this approach, the intermolecular interaction energy components are determined based on the wave functions of the subsystems evaluated in the dimer-centered basis set. Thus, both interaction energy and its components are BSSE-free. More details about this scheme can be found elsewhere [21-23]. The total intermolecular interaction energy at the MP2 level of theory can be expressed as follows ... 

Application of the conventional wave function approach in the symmetry-adapted perturbation theory (SAPT) has been shown to give very accurate description of the dispersion interaction and has provided intermolecular potentials which performed... 

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

Bukowski R, Jankowski P, Jeziorski B, Jeziorska M, Kucharski SA, Moszynski R, Rybak S, Szalewicz K, Williams HL, Wormer PES (1996) SAPT96 An ab initio program for manybody symmetry-adapted perturbation theory calculations of intermolecular interaction energies. University of Delaware and University of Warsaw... 

Williams HL, Chabalowski CF (2001) Using Kohn-Sham orbitals in symmetry-adapted perturbation theory to investigate intermolecular interactions. J Phys Chem A 105 646-659... 

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. 

The HOH—NH3 complex served as a recent test for symmetry-adapted perturbation theory (SAFT). Basing their work on earlier formalism", which was further elaborated, Lan-glet et al. observed that a pure perturbation approach yielded an intermolecular separation that was somewhat too long, and underestimated the binding strength of the complex. Better correlation with experimental quantities, as well as with other acctirate computations, is obtained by a hybrid approach, wherein the dispersion energy, computed by SAPT, is added to the (counterpoise corrected) SCF portion of the interaction energy. This conclusion was found to apply not only to HOH—NH3, but also to the homodimers of HF, H O, andNH,. 

The present status of symmetry-adapted perturbation theory applied to intermolecular potentials and interaction-induced properties is presented, and illustrated by means of applications to the calculations of the collision-induced Raman spectra, rovibrational spectra of weakly bound dimers, and second (pressure and dielectric) virial coefficients. 

Recently, a new theoretical method of calculating potential energy and dipole/polarizability surfaces for van der Waals molecules based on symmetry-adapted perturbation theory (sapt) of intermolecular forces (12)— (15) has been developed (16)-(24). In this method, referred to as many-body symmetry-adapted perturbation theory, all physically important contributions to the potential and the interaction-induced properties, such as electrostatics, exchange, induction, and dispersion are identified and computed separately. By making a perturbation expansion in the intermolecular interaction as well as in the intramolecular electronic correlation, it is possible to sum the correlation contributions to the different physical... 

In the present paper we review recent advances in the symmetry-adapted perturbation theory calculations of interaction potentials and interaction-induced properties. We will give a brief description of the theoretical methods needed on the route from the intermolecular potential and properties to rovibrational spectra and collision-induced Raman spectra. We also discuss applications of the interaction potentials and interaction-induced polarizabilities to compute (thermodynamic and dielectric) second virial coefficients. Finally, we illustrate these theoretical approaches on several examples from our own work. 

Since the symmetry-adapted perturbation theory provides the basis for the understanding of weak intermolecular interactions, it is useful to discuss the convergence properties of the sapt expansion. High-order calculations performed for model one-electron (Hj) (30), two-electron (H2) (14, 15), and four-electron (He and He-Hz) (31) systems show that the sapt series converges rapidly. In fact, already the second-order calculation reproduces the exact variational interaction energies with errors smaller than 4%. Several recent applications strongly indicate that this optimistic result holds for larger systems as well. 

B. Jeziorski, R. Moszynski, A. Ratkiewicz, S. Rybak, K. Szalewicz, and H.L. Williams SAPT A Program for Many-Body Symmetry-Adapted Perturbation Theory Calculations of Intermolecular Interactions , in Methods and Techniques in Computational Chemistry METECC-94, vol. B Medium Size Systems, edited by E. Clementi, (STEP, Cagliari 1993), p. 79. 

Szalewicz K, Jeziorski B. Symmetry-adapted perturbation theory of intermolecular interactions. In Scheiner S, ed. Molecular Interactions. From van der Waals to Strongly Bound Complexes. New York Wiley, 1997 3 43. 

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. 

Understanding and Quantifying Intermolecular Interactions using Symmetry-Adapted Perturbation Theory... 

Symmetry-Adapted Perturbation Theory A perturbational method of calculating intermolecular interaction energy while taking into account the Pauli exclusion principle. 

Perturbation theories such as the MP2 method (McWeeny 1992) (see Sect. 3.2) have been appreciated as ab initio wavefunction theories reproducing dispersion interactions with relatively short computational times. Therefore, dispersion interactions can be incorporated in the Kohn-Sham method by combining with such perturbation theories, in principle. One of the methods based on this concept is the DFT symmetry-adapted perturbation theory (DFT-SAPT), which uses Kohn-Sham orbitals to calculate the perturbation energies (Williams and Chabalowski 2001). In contrast to ab initio SAPT, in which both intermolecular and intramolecular electron correlations are calculated, only intermolecular electron correlations are calculated as a dispersion correction for the Kohn-Sham method in DFT-SAPT. Consequently, this drastically reduces the computational cost, typically by one or two orders of magnitude, compared to an ab initio SAPT calculation, with similar accuracies. 

FIGURE 4 Components of the interaction energy for N2- HF shown as functions of the angle 62 formed by HF with the intermolecular axis (O2 = 0° for the N-N- F-H geometry) a R= 3.6 A, close to the minimum separation, and the N2 molecule lying on the intermolecular axis. SAPT, symmetry-adapted perturbation theory. (Data from Jankowski etal., 2000.)... 

A thick bible (1249 pages) of intermolecular interactions. We find there everything before the advent of computers and of the symmetry-adapted perturbation theory. 

Symmetry-adapted perturbation theory is a well-motivated theoretical approach to compute the individual components of intermolecular interactions, namely, the electrostatic, induction, dispersion, and exchange-repulsion terms. The approach is a double-perturbation theory that uses a Hartree-Fock reference, with a Fock operator F written as the sum of Fock operators for the individual molecules. Both the intramolecular correlation potential W) and the intermolecular interactions (V) are treated as perturbations, so that the Hamiltonian is expressed as... 

S. Rybak, B. Jeziorski, and K. Szalewicz, J. Chem. Phys., 95, 6576 (1991). Many-Body Symmetry-Adapted Perturbation Theory of Intermolecular Interactions. H2O and HF Dimers. 

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