Symmetry adapted perturbation theory calculations

Korona T, Williams HL, Bukowski R, Jeziorski B, Szalewicz K (1997) Helium dimer potential from symmetry-adapted perturbation theory calculations using large Gaussian geminal and orbital basis sets. J Chem Phys 106 5109—5122... 

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, Szalewicz K, Jeziorski B, Moszynski R, Rybak S (1993) Symmetry-adapted perturbation theory calculation of the Ar-H2 intermolecular potential energy surface. J Chem Phys 98 1279-1292... 

It is instructive to compare the SCF three-body interaction, represented by the solid curve in Fig. 5.21, with the induction energy, with which there is a tendency to approximate it in the literature. In this context, it should be noted that the induction curve is far too attractive, by a factor of more than 2 in the vicinity of 20°. Other characteristics of its shape differ from the full SCF curve or deformation energy in Fig. 5.21 as well. The three-body forces at the correlated MP2 level are very small in magnitude, and insensitive to angular characteristics of the trimer. Most of these conclusions have been verified by later calculations and by symmetry-adapted perturbation theory calculations, although there were a number of discepancies as welF. The issue is not entirely closed. 

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. 

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. 

Symmetry-Adapted Perturbation Theory Calculation of the Ar-Hi Intermo-lecular Potential Energy Surface. 

Bukowski, R., Cencek, W., Jankowski, P., Jeziorski, B., Jeziorska, M., Lotrich, V., Kucharski, S., Misquitta, A. J., Moszynski, R., Patkowski, K., Podeszwa, R., Rybak, S., Szalewicz, K., Williams, H., Wheatley, R. J., Wormer, P. E. S., 8c Zuchowski, P. S. (2002). SAPT2008 An ab initio program for many-body symmetry-adapted perturbation theory calculations of intermolecular interaction energies. University of Delaware and University of Warsaw, http //www.physics.udel. edu/ szalewic/. Accessed 18 July 2011... 

Misquitta, A. J., 8c Szalewicz, K. (2005). Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers. Journal of Chemical Physics, 122, 214109. 

Contents Introduction. - Symmetry An Excursion Through its Formal Apparatus. - Symmetry-Adapted Perturbation Theory A General Approach. - Why Symmetry-Adapted Perturbation Theories are Needed - Symmetry-Adapted Perturbation Theories at Low Orders From Ht to the General Case. - The Calculation of the 1-st Order Interaction Energy. - The Second-Order Contribution to the Interaction Energy. -Epilogue. - Appendix A. - Appendix B. -Appendix C. - Appendix D. - References. 

As the exchange energy, the polarization-exchange energy (.poi-txch is also nonadditive. The standard PT cannot be applied to the calculation of the poi-exch- The reason is that the antisymmetrized functions of zeroth order (Ai/>o. ..) are not eigenfunctions of the unperturbed Hamiltonian Ho as long as the operator Ho does not commute with the antisymmetrizer operator A. Many successful approaches for the symmetry adapted perturbation theory (SAPT) have been developed for a detailed discussion see chapter 3 in book, the modern achievements in the SAPT are described in reviews . 

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]. 

A symmetry-adapted perturbation theory approach for the calculation of the Hartree-Fock interaction energies has been proposed by Jeziorska et al.105 for the helium dimer, and generalized to the many-electron case in Ref. (106). The authors of Refs. (105-106) developed a basis-set independent perturbation scheme to solve the Hartree-Fock equations for the dimer, and analyzed the Hartree-Fock interaction energy in terms of contributions related to many-electron SAPT reviewed in Section 7. Specifically, they proposed to replace the Hartree-Fock equations for the... 

Moszynski R, Heijmen TGA, Jeziorski B (1996) Symmetry-adapted perturbation theory for the calculation of Hartree-Fock interaction energies. Mol Phys 88 741—758... 

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

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]. 

SAPT(ss) and SAPT(pp) are two functions obtained by best fitting high quality ab initio calculations carried out with symmetry adapted perturbation theory on a sample of over 1000 configurations. SAPT(ss) has the same form as the MCY model, while SAPT(pp) is a single-site model, located on the center of mass, with over 100 term for each contribution into which the energy can be decomposed according to the perturbative approach. The quality of the fit is better for SAPT(pp) (a=0.58 kcal/mol) than SAPT(ss), that underestimates the well depth by -15%, but more accurately fits the repulsive part, thanks to its exponential terms. The overall a of SAPT(ss) is roughly... 

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. 

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... 

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... 

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. 

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