Perturbation theory symmetry adaptation

A. HeBelmann, G. Jansen, M. Schtitz, Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting A new efficient method to study intermolecular interaction energies. J. Chem. Phys. 122, 014103 (2005)... 

R. Sedlak, P. Jurecka, P. Hobza, Density functional theory-symmetry adapted perturbation treatment energy decomposition of nucleic acid base pairs taken from DNA crystal geometry. J. Chem. Phys. 127, 075104 (2007)... 

Functional Theory-Symmetry-Adapted Intermolecular Perturbation Theory with Density Fitting A New Efficient Method to Study Intermolecular Interaction Energies. 

Bukowski R, Sadie] J, Jeziorski B, Jankowski P, Szalewicz K, Kucharski S A, Williams H L and Rice B M 1999 Intermolecular potential of carbon dioxide dimer from symmetry-adapted perturbation theory J. Chem. Phys. 110 3785... 

Milet A, Moszynski R, Wormer P E S and van der Avoird A 1999 Hydrogen bonding in water olusters pair and many-body interaotions from symmetry-adapted perturbation theory J. Phys. Chem. A 103 6811-19... 

Total number of spin and symmetry adapted configurations Number of spin and symmetry adapted configurations selected by second-order perturbation theory and treatedvariationally Property calculated with respect to the center of mass. 

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

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... 

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. 

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. 

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]. 

Symmetry-adapted perturbation theory applied to interaction-induced properties of collisional complexes. Molec. Phys., 89 81, 1996. 

K.E. Riley, P. Hobza, Investigations into the nature of halogen bonding including symmetry adapted perturbation theory analyses. J. Chem. Theor. Comput. 4, 232-242 (2008)... 

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)... 

A. Fiethen, G. Jansen, A. Hesselmann, M. Schiitz, Stacking energies for average B-DNA structures from the combined density functional theory and symmetry-adapted perturbation theory approach. J. Am. Chem. Soc. 130, 1802-1803 (2008)... 

To introduce the perturbation expansions corresponding to perturbation theories with different symmetry adaptation, it is useful to introduce a general concept of the interpolation function ve(t) defined such that86 ... 

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