Dispersion interaction SAPT

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... 

As discussed above, significant discrepancies were observed between quantum benchmarks and force fields for non-bonded interactions in the benzene dimer (Sherrill et al., 2009a). Analysis of the discrepancies was greatly aided by the use of energy component analysis, specifically the SAPT method. A detailed analysis of the parallel-displaced benzene dimer at a fixed vertical distance of 3.4 A is shown in Fig. 3.4. As seen from the figure, the London dispersion interaction computed by the force field through the attractive part of the Lennard-Jones potential is fairly accurate compared to the quantum SAPT results. Moreover, in this system, SAPT shows that... 

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. 

It is possible to note that the dispersion interaction plays the major role in the stabilization of different complexes. The interplay of electrostatic forces is also clearly evident from the DF-DFT-SAPT results. The interaction of carbon dioxide with the organic linkers has significant contribution from electrostatic and induction terms in the stabilization of these complexes. It is also worth noting that the interaction energies obtained from DF-DFT-SAPT results are in very good quantitative agreement with the BSSE-corrected MP2/aug-cc-pVTZ level of theory. This clearly indicates the usefulness of the method to decompose weakly bound complexes. 

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. 

However, the Cio model is rather elaborate and unwieldy. For many applications simpler models may suffice. Fortunately, the WSM method allows the construction of far simpler isotropic dispersion models. Even more simplifications can be made by scaling the isotropic Ce WSM model to best reproduce the SAPT(DFT) dispersion energies (Misquitta and Stone 2008b), and the results are quite acceptable. From O Fig. 6-3 we see that the scaled isotropic Ce dispersion model (damped) is quite acceptable for the benzene dimer and is a significant improvement over the empirical dispersion model from a popular and well parameterized empirical potential. The significant failure occurs at the stacked configurations where anisotropy is essential to describe the dispersion interaction correctly. 

The resulting SAPT(DFT) potential energy curves turn out to be very accurate in the wide range of intermolecular separations. For the benzene dimer225,228 the results are very close to those of the much more expensive CCSD(T) treatment. For systems of the size of the benzene dimer and for the triple-zeta quality basis sets, a SAPT(DFT) calculation actually takes less time than a conventional supermolecular DFT calculation. Due to the favorable computational scaling the SAPT(DFT) approach is applicable to much larger molecules than any method used thus far for a reliable calculation of dispersion-dominated interaction potential. 

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,. 

Figure 1 Comparison of argon interaction-potentials. The solid line is the empirical pair potential 100 the dashed line is the van der Waals + dispersion model of Dion et al. 485 the dot-dashed line is a CCSD(T) ab initio potential 77 and the dotted lines with circle and square symbols are the SAPT (DFT) potentials of Podeszwa and Szalewicz97 with different functionals. Reprinted from, 97, Copyright (2005) with permission from Elsevier...

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... 

The empirical intermolecular force fields are in most cases built of terms that are in a close correspondence with the interaction energy components described above. One may say that such force fields are simplest possible implementations of the SAPT approach. The functional forms used are based on SAPT analysis of the asymptotic behavior of the components. The electrostatic interactions are usually approximated by interactions of fractional charges located on atoms in each monomer. In simplest cases, the induction effects are not included explicitly but some more sophisticated force fields use the classical polarization model. The dispersion forces are accounted for by hnear combinations of l/R ab terms where R b are interatomic distances and the exchange forces by either exponential or 1 terms. 

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