Perturbation theory intermolecular

Adams W H 1994 The polarization approximation and the Amos-Musher intermolecular perturbation theories compared to infinite order at finite separation Chem. Phys. Lett. 229 472... 

Hayes I C and Stone A J 1984 An intermolecular perturbation theory for the region of moderate overlap Mol. Phys. 53 83... 

Note that, in contrast to other forms of intermolecular perturbation theory to be considered below, the NBO-based decomposition (5.8) is based on a full matrix representation of the supermolecule Hamiltonian H. All terms in (5.8) are therefore fully consistent with the Pauli principle, and both /7units(0, and Vunits(mt) are properly Hermitian (and thus, physically interpretable) at all separations. 

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 ... 

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 ... 

W Another type of energy partitioning in MO theory was proposed by Clementi 86>. This kind of partitioning called Bond Energy Analysis" (BEA) was found to be particularly useful in larger molecular clusters 87-90) Since the individual contributions of BEA are not directly related to the quantities discussed in intermolecular perturbation theory, dementi s technique will not be used here (see Chapter V). 

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. 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)... 

A. Hesselmann, G. Jansen, M. Schtitz, Interaction energy contributions of H-bonded and stacked structures of the AT and GC DNA base pairs from the combined density functional theory and intermolecular perturbation theory approach. J. Am. Chem. Soc. 128,11730-11731 (2006)... 

Figure 1-2. Schematic diagrammatic representation of the E correction (Brandow skeletons). The horizontal lines represent the denominators, while the vertical bar separates the monomers A and B. The two-electron integral corresponding to the dotted interaction line is a Coulomb integral. The dashed interaction lines represent antisymmetric two-electron integrals of the monomers. Diagram (a) is the intermolecular perturbation theory form of the MP5 contribution s, diagram (d) of qQ(/7), while (b) and (c) are combinations of 7s T and E (I)...

In the following, we will first present a formal derivation of the general PE equations rooted in intermolecular perturbation theory. Next follows a derivation of the PE scheme within the concepts of time-dependent density functional theory, and finally, we present a few illustrative examples. The PE model has been implemented in the Dalton program package [14]. 

I.C. Hayes, G.J.B. Hurst, and A.J. Stone, Intermolecular perturbation theory. Application to HeBe, ArHF, ArHCl and NeH2, Mol. Phys., 53 (1984) 107-127. 

Lessons from Intermolecular Perturbation Theory Calculations on Organic Molecules... 

Xantheas and co-workers [159,160] have incorporated polarization in a model scheme and have used that to provide a clear basis for the enhancement of water s dipole in ice. A model potential with polarization has been reported for the formaldehyde dimer [161]. It is an example of a carefully crafted potential, which is system-specific because of its application to pure liquid formaldehyde, but which has terms associated with properties and interaction elements as in the above models. As well, some of the earliest rigid-body DQMC work, which was by Sandler et al. [162] on the nitrogen-water cluster, used a potential expressed in terms of interaction elements derived from ab initio calculations with adjustment (morphing). Stone and co-workers have developed interaction potentials for HF clusters [163], water [164], and the CO dimer [165], which involve monomer electrical properties and terms derived from intermolecular perturbation theory treatment. SAPT has been used for constructing potentials that have enabled simulations of molecules in supercritical carbon dioxide [166]. There are, therefore, quite a number of models being put forth wherein electrical analysis and/or properties of the constituents play an essential role, and some where electrical analysis is used to understand property changes as well as the interaction energetics. 

The well-established perturbation theory of intermolecular interaction [53 59] can be applied to hydrogen-bonded systems in combination with the frozen molecule approximation, when the interaction is either sufficiently weak [60 62], or when the interaction is treated at a more qualitative level. When the interaction becomes larger, structural relaxations become sizable. Then the more usual approach to treat the hydrogen-bonded complex or cluster as a supermolecule becomes more practical and also more appropriate. However, also in this case, the detailed analysis of the interaction energy is often done with the aid of different variants of energy partitioning techniques [63,64] which closely follow the lines of intermolecular perturbation theory. 

As might be expected, the results of analyses that separate these terms as stringently as possible, such as Hayes and Stone s intermolecular perturbation theory (IMPT) [44], which uses a procedure [45] in which the difference between monomer and dimer basis sets is used to apportion induction (= polarization) and donor-acceptor contributions. Stone and Misquitta [46] point out that using this definition, the donor-acceptor energy would vanish if a complete basis set were used. The observed dependence for the water dimer is shown in Figure 18.6. 

If we have to use non-orthogonal wavefunctions, then the natural one-electron orbitals in which to express them are the SCF molecular orbitals of the non-interacting molecules. From these we can construct antisymmetrized (determinantal) wavefunctions in which some orbitals of each molecule are occupied. Because of the non-orthogonality of the orbitals, these determinant al wavefunctions will also be non-orthogonal. It is possible to construct a perturbation theory in which the wavefunction is expanded in terms of these determinants. Fortunately it is possible to formulate it in such a way that the separation of the Hamiltonian into an unperturbed part and a perturbation is unnecessary. The resulting Intermolecular Perturbation Theory (IMPT) has been incorporated into the Cambridge Analytical Derivatives Package (CADPAC)i ... 

Now the expression (19) is an uncoupled formulation of the polarizability. We can replace it by a polarizability derived from coupled Hartree-Fock perturbation theory, which is more accurate, because it takes account of the reorganisation of the electron distribution in a self-consistent manner. Better still would be to evaluate the monomer polarizability by a method that takes account of electron correlation as well . But whatever the level of calculation, we can once again perform a much better calculation of the monomer property than is possible for the dimer. In this way we arrive at a description of the induction energy that is far more accurate than we can obtain through either intermolecular perturbation theory, where the perturbation is treated in an uncoupled fashion, or from a supermolecule calculation, where the size of the basis is limited by the need to perform calculations at a large number of points on the potential energy surface. 

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

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