Dispersion symmetry-adapted perturbation theory

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... 

In this section we will review the symmetry-adapted perturbation theory of pairwise nonadditive interactions in trimers. This theory was formulated in Ref. (302). We will show that pure three-body polarization and exchange components can be explicitly separated out and that the three-body polarization contributions through the third-order of perturbation theory naturally separate into terms describing the pure induction, mixed induction-dispersion, and pure dispersion interactions. 

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,. 

Apart from these supramolecular approaches to the interaction energy, advanced perturbation theory techniques, which combine symmetry-adapted perturbation theory and DFT and are thereby able to capture dispersion interactions, are also under development [89-91]. 

In order to analyze the interaction energy component, the symmetry-adapted perturbation theory (SAPT) [12] calculations were performed. SAPT have been used to analyze the interaction energies in terms of electrostatic, induction, dispersion, and exchange interaction components. The SAPT interaction energy (Dint) has been analyzed up to the second-order symmetry adapted perturbation theory the electrostatic energy (Dekt) consisting of and... 

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... 

There are theoretical approaches that compute the dispersion energy directly, so they do not suffer from the difficulty of extracting it from a jumble of other terms. Most of these are based on some form of perturbation theory. Szalewicz and Jeziorski [39] have summarized the basic equations and ideas of symmetry-adapted perturbation theory which has found wide use in studying noncovalent interactions. 

Misquitta, A. J., Podeszwa, R., Jeziorski, B., and Szalewicz, K. [2005]. Inter-molecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations,/ Chem. Phys. 123, p. 214103, doi 10.1063/l.2135288. 

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. 

Dispersion energy in the multipole representation Symmetry-Adapted Perturbation Theories (SAPT) ( U )... 

Becke has proposed a novel approach that formulates the dispersion interaction in terms of the dipole moment that would be created when considering an electron and its exchange hole. " ° Like DFT-D, these methods appear to be more reliable than MP2 for noncovalent interactions. Alternatively, other workers " " have combined DFT with symmetry-adapted perturbation theory (SAPT) (discussed below). These DFT-SAPT approaches evaluate the dispersion term via the frequency-dependent density susceptibility functions of time-dependent DFT, an approach that appears to be theoretically sound. 

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... 

Although electrostatics plays an important role in determining the geometry of the favorable nin interaction, recent high-level ab initio calculations show that dispersion is important for attraction in the benzene dimer. The absolute value of Ecorr is always considerabaly larger than the Ees value, as shown in Table 4, which reveals that dispersion is the major somce of attraction in the benzene dimer. Very recently reported symmetry-adapted perturbation theory (SAPT) calculations show that dispersion is the major source of attraction in the benzene dimer [60]. Similar results were also reported for other complexes of aromatic molecules (benzene-phenol, benzene-toluene, benzene-fluorobenzene and benzene-benzonitrile) [60]. 

In Fig. 9.1, it is possible to find the optimized geometries for six selected clusters, the ab initio structures were obtained at the MP2/AVDZ level [18] and the DFT ones at the B3LYP/AVTZ level. Only two of the three minima found for the 1 1 complex were considered in this work (the missing one differs only in the orientation of the water molecule). As expected the XB interaction leads to a more stable structure than the one stabilized by a XH. The decomposition of the interaction energy using the symmetry adapted perturbation theory (SAPT) for this two structures reveals that they are quite different the electrostatic component of the XB stmcture contributes with 60 % of the interaction energy, the induction with 10 % and dispersion with 30 % whereas for the XH bonded complex it was found that the main contribution to its stability was dispersion with 55 % followed by 31 % of electrostatic and 14 % of induction contribution. This difference between XB and XH interaction is useful to understand why this interaction is not that important in DFT optimized stmctures. The shifts calculated for small clusters are presented in Table 9.1. 

An alternative to the supermolecular approach is symmetry-adapted perturbation theory [19-21]. hi SAPT, the interaction energy is computed directly rather than by subtraction. SAPT provides both the conceptual framework and the computational techniques for describing intermolecular interactions, including the dispersion energy. However, the computer resources required by SAPT, similar to those of the methods with high-level treatment of correlation used in the supermolecular approach, make appHcations to monomers with more than about ten atoms impractical at the present time. For ten-atom or smaller molecules, SAPT has been very successful see [20,21], and Sect. 7 for a review of applications. 

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