Dispersion energy coefficients

Kumar A, Fairley G R G and Meath W J 1985 Dipole properties, dispersion energy coefficients and integrated oscillator strengths for SFg J. Chem. Phys. 83 70... 

RJ. Wheatley, Time-dependent coupled-cluster calculations of polarizabilities and dispersion energy coefficients. J. Comput. Chem. 29, 445 150 (2008)... 

Mulder F, Thomas GF, Meath WJ (1980) A critical study of some methods for evaluating the C6, C8 and C10 isotropic dispersion energy coefficients using the first row hydrides, CO, C02 and N20 as models. Mol Phys 41 249-269... 

Jhanwar BL, Meath WJ (1982) Dipole oscillator strength distributions, sums, and dispersion energy coefficients for CO and C02. Chem Phys 67 185—199... 

Kumar A, Meath WJ (1985) Pseudo-spectral dipole oscillator strengths and dipole-dipole and triple-dipole dispersion energy coefficients for HF, HC1, HBr, He, Ne, Ar, Kr and Xe. Mol Phys 54 823-833... 

Kumar A, Fairley GRG, Meath WJ (1985) Dipole properties, dispersion energy coefficients, and integrated oscillator strengths for SF6. J Chem Phys 83 70-77... 

Pazur RJ, Kumar A, Thuraisingham RA, Meath WJ (1988) Dipole oscillator strength properties and dispersion energy coefficients for H2S. Can J Chem 66 615-619... 

Table 3. Isotropic dispersion energy coefficients and ratios Cg/C and C JC (in atomic units) for various methods, described in the text...

Kumar A, Meath W J, Bundgen P and Thakkar A J 1996 Reliable anisotropic dipole properties and dispersion energy coefficients for O2, evaluated using constrained dipole oscillator strength techniques J. 

McDowell SAC, Kumar A, Meath W1 (1996) Anisotropic and isotropic triple-dipole dispersion energy coefficients for all three-body interactions involving He, Ne, Ar, Kr, Xe, H2, N2, and CO. Canad J Chem 74 1180-1186... 

Wheatley, R. J., Lillestolen, T. C. (2008). Local polarizabilities and dispersion energy coefficients. Molecular Physics, 106,1545-1556. 

The parameter p is a function of the atom type (Table 12.3). This variable-ionization form of the theory amounts, in fact, to taking different dispersion energy coefficients according to the different kinds of interacting atomic basins. 

Some electric properties of molecules are described in section Al.5.2.2 because the coefficients of the powers of Mr turn out to be related to them. The electrostatic, mduction and dispersion energies are considered m turn in section Al.5.2.3, section Al.5.2.4 and section Al.5.2.5, respectively. 

Hence, the same teclmiques used to calculate are also used for Cg. Note that equation (A1.5.28) has a geometrical factor whose sign depends upon the geometry, and that, unlike tlie case of the two-body dispersion interaction, the triple-dipole dispersion energy has no minus sign in front of the positive coefficient Cg. For example, for an equilateral triangle configuration the triple-dipole dispersion is repulsive and varies... 

Recently Becke and Johnson [94] presented an elegant model for the evaluation of the C6, C8, and C10 coefficients characterizing the dispersion energy between two nonoverlapping systems A and B at distance R ... 

For practical purposes, the expansions (33), (34) may be truncated after the first few terms, e.g., from C10 = C10(l, 3) + C10(2,2) + C10(3,1) onwards in the case of the dispersion energy. Values of such dispersion coefficients, which have been calculated using dynamic polarizabilities represented by Pade approximants,56-60 have been reported in the literature for many systems of practical interest (see also Section V.A). 

Somewhat different is the case of the induction and dispersion energies. For these the expansion in inverse powers of r is only valid in the limit of vanishing orbital overlap, and in this case the expansions of equations (38), (39) are shown to overestimate the true value of the energy when such orbital overlap is taken into account. Indeed, studies carried out for small systems68-77 show that the values of the induction and dispersion coefficients decrease with decreasing r. Formally, it is possible to account for this effect by introducing the so-called damping functions as follows ... 

When the dispersion interaction coefficients are different for anions and cations, the different distributions of the two kinds of ions generate a potential even when the plates are neutral. The potential is obtained from the solution of the correspondingly modified Poisson-Boltzmann equation (Eqs. (1) and (2)) and the interaction free energy can be calculated via the numerical integration of Eq. (7). 

It should stressed that unlike in the case of the electrostatic energy, the expressions for the long-range coefficients and the angular function Aj defining the multicenter multipole expansions of the induction and dispersion energies are different. This difference is due to the fact that in the multicenter expansions the products of the D functions, (wj) ) and ( )... 

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