Intermolecular interactions perturbation theory

Key words Molecular orbitals - Perturbation theory - Intermolecular interactions... 

Sundqvist B (2004) Polymeric Fullerene Phases Formed Under Pressure 109 85-126 Szalewicz K, Patkowski K, Jeziorski B (2005) Intermolecular Interactions via Perturbation Theory From Diatoms to Biomolecules 116 43-117... 

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

In order to ensure accurate CG potentials, one needs to conduct MD simulations with a reliable atomistic potential model. The most desirable theoretical approach for the atomistic-scale simulations would be to use a level of quantum mechanics (QM) that can treat both intermolecular and intramolecular interactions with acceptable accuracy. Realistically, the minimal QM levels of theory that can adequately treat all different types of chemical forces are second order perturbation theory [32] (MP2)... 

Considering only the interaction between HOMO of R and LVMO of S, elementary perturbation theory shows that the result of the orbital interaction is a repulsion of the levels, the occupied level becomes more stable, the unoccupied level less stable. The simplest Huckel-type formulation of PMO theory gives equations for the intermolecular perturbation energy change A that are quite simple in form, Eqs. 3—6 18,20,22,26-28) Q is a first-order Coulombic energy that can be calculated in terms of... 

Empirically corrected DFT theories almost invariably go back to second-order perturbation theory with expansion of the interaction Hamiltonian in inverse powers of the intermolecular distance, leading to R 6, R x, and R 10 corrections to the energy in an isotropic treatment (odd powers appear if anisotropy is taken into account [86]). 

This theory proves to be remarkably useful in rationalizing the whole set of general rules and mechanistic aspects described in the previous section as characteristic features of the Diels-Alder reaction. The application of perturbation molecular orbital theory as an approximate quantum mechanical method forms the theoretical basis of Fukui s FMO theory. Perturbation theory predicts a net stabilization for the intermolecular interaction between a diene and a dienophile as a consequence of the interaction of an occupied molecular orbital of one reaction partner with an unoccupied molecular orbital of the other reaction partner. 

Quantum mechanical calculations of intermolecular forces generally start from wave functions of the isolated particles. With regard to the actual treatment of the interaction, however, there is some competition between perturbation theory and MO methods. 

In intermolecular perturbation theory one of the major problems concerns electron exchange between molecules. In the method described here exchange is limited to single electrons. This simplification is definitely a good approximation at large intermolecular distances. The energy of interaction between the molecules, AE (R), is obtained as a sum of first order, second order, and higher order contributions ... 

Before we tarn to MO theory of molecular interactions a short discussion on the reliability of semiempirical calculations of the CNDO type by means of perturbation theory would be useful. For a better understanding of the possibilities and limitations of semiempirical MO approaches to intermolecular forces we calculated first-order perturbation energies for very simple complexes with and... 

The exchange contribution in an ab initio perturbation theory is the only repulsive term ) around the energy minimum in most of the stable complexes and consequently we would expect no net repulsion between two closed shell molecules in semiempirical calculations. On the other hand it is known from actual calculations that intermolecular interactions are described more or less correctly by the CNDO/2 procedure. Indeed, strong repulsion is obtained between closed shell molecules. Evidently there must be another approximation which compensates for the neglect of exchange energy. With regard to the simplifications of the CNDO/2 method we find that this is in fact the case. The approximation shown in Eq. (17) is responsible for the repulsive term. 

In order to leam more about the nature of the intermolecular forces we will start with partitioning of the total molecular energy, AE, into individual contri butions, which are as close as possible to those we defined in intermolecular perturbation theory. Attempts to split AE into suitable parts were undertaken independently by several groups 83-85>. The most detailed scheme of energy partitioning within the framework of MO theory was proposed by Morokuma 85> and his definitions are discussed here ). This analysis starts from antisymmetrized wave functions of the isolated molecules, a and 3, as well as from the complete Hamiltonian of the interacting complex AB. Four different approximative wave functions are used to describe the whole system ... 

Y.. Dappe, M.A. Basanta, F. Flores, J. Ortega, Weak chemical interaction and van der Waals forces between graphene layers A combined density functional and intermolecular perturbation theory approach, vol. 74, p. 205434-9, 2006. 

A fruitful approach to the problem of intermolecular interaction is perturbation theory. The wavefunctions of the two separate interacting molecules are perturbed when the overlap is nonzero, and standard treatment [49] yields separate contributions to the interaction energy, namely the Coulombic, polarization, dispersion, and repulsion terms. Basis-set superposition is no longer a problem because these energies are calculated directly from the perturbed wavefunction and not by difference between dimers and monomers. The separation into intuitive contributions is a special bonus, because these terms can be correlated with intuitive molecular... 

Fickett in "Detonation Properties of Condensed Explosives Calculated with an Equation of State Based on Intermolecular Potentials , Los Alamos Scientific Lab Rept LA-2712 (1962), pp 34-38, discusses perturbation theories as applied to a system of deton products consisting of two phases one, solid carbon in some form, and the other, a fluid mixt of the remaining product species. He divides these theories into two classes conformal solution theory, and what he chooses to call n-fluid theory. Both theories stem from a common approach, namely, perturbation from a pure fluid whose props are assumed known. They differ mainly in the choice of expansion variables. The conformal solution method begins with the assumption that all of the intermolecular interaction potentials have the same functional form. To obtain the equation of state of the mixt, some reference fluid obeying a common reduced equation of state is chosen, and the mixt partition function is expanded about that of the reference fluid... 

B. Jeziorski, K. Szalewicz, Intermolecular Interactions by Perturbation Theory, in Encyclopedia of Computational Chemistry, ed. by P. von Rague Schleyer, N.L. Allinger (Wiley, Chichester, 1998)... 

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 ... 

The most extensive analysis of the nature of intermolecular interaction components in hydrogen-bonded complexes of nucleic acid bases is that performed by Toczylowski et al. [26], The authors presented the results of calculations obtained on the basis of the intermolecular Mpller-Plesset perturbation theory using... 

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