Symmetry-adapted perturbation theory method

However, due to the availability of numerous techniques, it is important to point out here the differences and equivalence between schemes. To summarize, two EDA families can be applied to force field parametrization. The first EDA type of approach is labelled SAPT (Symmetry Adapted Perturbation Theory). It uses non orthogonal orbitals and recomputes the total interaction upon perturbation theory. As computations can be performed up to the Coupled-Cluster Singles Doubles (CCSD) level, SAPT can be seen as a reference method. However, due to the cost of the use of non-orthogonal molecular orbitals, pure SAPT approaches remain limited... 

If affordable, there is a range of very accurate coupled-cluster and symmetry-adapted perturbation theories available which can approach spectroscopic accuracy [57, 200, 201]. However, these are only applicable to the smallest alcohol cluster systems using currently available computational resources. Near-linear scaling algorithms [192] and explicit correlation methods [57] promise to extend the applicability range considerably. Furthermore, benchmark results for small systems can guide both experimentalists and theoreticians in the characterization of larger molecular assemblies. 

Binary Interaction-Induced Dipoles. Ab initio quantum chemical calculations of interaction-induced dipole surfaces are known for some time (Section 4.4, pp. 159 ff.) Such calculations were recently extended for the H2-He [17] and H2-H2 [18] systems, to account more closely for the dependencies of such data on the rotovibrational states of the H2 molecules [19]. New calculations of the kind and quality are now available also for the H-He system [20], the H2-H system [21], and the HD-He system [22]. New computational methods, called symmetry adapted perturbation theory (SAPT), were shown to be also successful for calculating interaction-induced dipole surfaces of such simple, binary van der Waals systems [23-26]. 

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 ... 

R. Podeszwa, R. Bukowski, K. Szalewicz, Density-fitting method in symmetry-adapted perturbation theory based on Kohn-Sham description of monomers. J. Chem. Theory Comput. 2, 400-412 (2006)... 

It should be stressed that the analysis presented above is general, and applies to any system. However, for the majority of Van der Waals complexes the electrostatic term E will not be as important as it is for the CO dimer. On the other hand, this analysis shows that any supermolecule method should be applied with great care, and an understanding of the supermolecule results in terms of contributions as defined by the symmetry-adapted perturbation theory is necessary. 

Jeziorski B, Moszynski R, Ratkiewicz A, Rybak S, Szalewicz K, Williams HL (1993) SAPT A program for many-body symmetry-adapted perturbation theory calculations of intermolecular interaction energies. In Clementi E (ed) Methods and techniques in computational chemistry METECC-94, vol B. STEF, Cagliari, pp 79-129... 

Current hybrid functionals do not improve this situation. Their non-local component (Hartree-Fock exchange) cannot give rise to any attraction. To describe quantitatively the long-range interactions, either a non-local approximation to Exc[p] must be applied within the Kohn-Sham framework or methods using other-than-Kohn-Sham formalism should be used. Some of such approaches will be discussed in the last section of this review. Here, we mention an especially promising combination of symmetry adapted perturbation theory with of the Kohn-Sham orbitals.125... 

On the theoretical side the H20-He systems has a sufficiently small number of electrons to be tackled by the most sophisticated quantum-chemical techniques, and in the last two decades several calculations by various methods of electronic structure theory have been attempted [77-80]. More recently, new sophisticated calculations appeared in the literature they exploited combined symmetry - adapted perturbation theory SAPT and CCSD(T), purely ab initio SAPT [81,82], and valence bond methods [83]. A thorough comparison of the topology, the properties of the stationary points, and the anisotropy of potential energy surfaces obtained with coupled cluster, Moller-Plesset, and valence bond methods has been recently presented [83]. 

DFT modeling has also been applied to the interaction energy calculations between nucleotide base pairs in DNA. Hesselmann et al. [32] examined the interaction energy between purines and pyrimidines using MP2, CCSD(T), and DFT in combination with symmetry-adapted perturbation theory (SAPT). This study demonstrated agreement between the results produced by the three methods, demonstrating the potential for DFT modified with SAPT. 

Because of the formal and practical problems with symmetry adapted perturbation theory, one mostly invokes variational methods applied to the total energy of the... 

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. 

In this paper we have given a short overview of the application of symmetry-adapted perturbation theory to intermolecular potentials and interaction-induced properties, and of the methods going directly from these intermolecular properties to experimentally measurable quantities such as collision-induced Raman spectra, rovibrational spectra, and second (pressure and dielectric) virial coefficients. The results presented in this paper show that intermolecular potentials and dipole/polarizability surfaces obtained from ab initio SAPT calculations can be used to correctly describe the spectroscopic and dynamical processes involving weakly bound complexes. 

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. 

MP2 calculations with large aug-cc-pVxZ basis sets yielded an estimate of -5.0 0.1 kcal/mol for the binding energy of the water dimer in the complete basis-set limit and the effect of going to the MP4 level was found to be negligible [M. W. Feyereisen, D. Feller, and D. A. Dixon,/. Phys. Chem., 100,2993 (1996)] essentially the same result was found by a method called symmetry-adapted perturbation theory, which treats the interactions between the monomers as a perturbation [E. M. Mas and K. Szalewicz, /. Chem. Phys., 104,7606 (1996)]. 

Flick, J. C., Kosenkov, D., Hohenstein, E. G Sherrill, C. D., and Slipchenko, L. V. (2012]. Accurate prediction of noncovalent interaction energies with the effective fragment potential method Comparison of energy components to symmetry-adapted perturbation theory for the S22 test set,/. Chem. Theory Comput 8, pp. 2835-2843, doi 10.1021/ct200673a. 

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. 

Symmetry-adapted perturbation theory (SAPT) The method describing the intermolecular forces including the hydrogen bonds. 

This method of generating perturbation theories has been called by the authors the symmetry forcing method in symmetry adapted perturbation theory (SAPT). 

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