Polarizability dispersion coefficients

The empirical hydration free energy density is expressed by a linear combination of some physical properties calculated around the molecule with net atomic charges, polarizabilities, dispersion coefficients of the atoms in the molecule, and solvent accessible surface [Son, Han et al, 1999]. These physical properties are the result of the interaction of the molecule with its environment. To calculate the H F E D of a molecule a grid model was proposed a shell of critical thickness rc was defined around the solvent-accessible surface with a number of grid points inside (e.g., 8 points/A ). 

Adamovic, I., Gordon, M. S. (2005). Dynamic Polarizability, Dispersion Coefficient and Dispersion Energy in the Effective Fragment Potential Method, Mol Phys., 103,379-387. 

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). 

The parametrization procedure that we have opted for in the most recent works is as follows (1) Compute the intermolecular dynamic correlation energy for the ground state with a second-order Mpller-Plesset (MP2) expression that only contains the intermolecular part and which uses monomer orbitals. Fit the dispersion parameters to this potential. To aid in the distribution of the parameters, a version of the exchange-hole method by Becke and Johnson is sometimes used [154,155], Becke and Johnson show that the molecular dispersion coefficient can be obtained fairly well by a relation that involves the static polarizability and the exchange-hole dipole moment ... 

Kang, Y.K. and Jhon, M.S. (1982). Additivity of Atomic Static Polarizabilities and Dispersion Coefficients. Theor.Chim.Acta, 61,41-48. 

In this way, for each H atom, the calculated dipole pseudospectra a, si] i = 1,2, , N of Table 4.2 can be used to obtain better and better values for the C6 London dispersion coefficient for the H—H interaction a molecular (two-centre) quantity C6 can be evaluated in terms of atomic (one-centre), nonobservable, quantities, a, (a alone is useless). The coupling between the different components of the polarizabilities occurs through the denominator in the London formula (4.19), so that we cannot sum over i or / to get the full, observable,12 aA oraB. 

Bendazzoli, G.L., Magnasco, V., Figari, G., and Rui, M. (2000) Full-CI calculation of imaginary frequency-dependent dipole polarizabilities of ground state LiH and the Cg dispersion coefficients of LiH-LiH. Chem. Phys. Lett., 330, 146-151. 

The Ce dispersion coefficients for dipole dipole dispersion between pairs of interacting species, the coefficients for terms involving higher multipolar dispersion, and coefficients for three-body dispersion terms can be and have been evaluated by ab initio techniques [114 119] as well as through relations to experimental optical data based on moments of the dipole oscillator strength [120 122]. These are parameters of the interaction, not properties. However, as noted in Section IVA, values for Ce coefficients of like pairs (e.g., A-A), and possibly for other dispersion coefficients, can be used in simple [Eq. (4)] or in more complete forms [Eq. (2)] as an intrinsic property of a molecule. The basis set and correlation requirements for adequate evaluation show, in part, the same requirements for describing polarizabilities however, there are further needs and other than atom-centered functions are seen as being suited [49 52]. 

Permanent dipole moment Molecule (D) Polarizability (1 0 24cm3) Ionization potential (eV) London dispersion coefficient (1 0-79J m6) (Equation 80) Keesom polar orientation coefficient (1 0"79J m6) (Equation 86) Debye induced coefficient (1 0-79J m6) (Equation 88)... 

Doran [101] was the first to apply Goldstone diagrammatic techniques to the computation of frequency-dependent polarizabilities and dispersion coefficients. He applied his method to Ne2 and heavier noble gases, but owing to an inadequate basis, got results of fairly poor quality. Later Wormer and coworkers [87,93,102] derived and programmed all polarizability diagrams through second order of intramolecular correlation, so that dispersion (by definition second order in is completely... 

The complex polarization propagator method has been applied to the calculations of dipole-dipole dispersion coefficients of pyridine, pyrazine, and r-tetrazine. These calculations refer to the electronic ground states as well as the first excited states of 7t—>7t character <2004MI321>. Calculations of static and dynamic polarizabilities of excited states by means of DFT have been performed <2004JCP9795>. 

By suitable choices for the P, Q, R,... operators a whole variety of properties may be calculated. The polarizability corresponding to imaginary frequencies, for example, provides the van der Waals dispersion coefficients, with the leading term depending on the inverse sixth power of the interatomic distance between atoms A and... 

Osinga V, Ginsbergen SV, Snijders J, Baerends E (1997) Density fimctional results for isotropic and anisotropic multipole polarizabilities and C-6, C-7 and C-8 van der Waals dispersion coefficients for molecules. J Chem Phys 106 5091... 

A wide variety of molecular properties can be accurately obtained with ADF. The time-dependent DFT implementation " yields UV/Vis spectra (singlet and triplet excitation energies, as well as oscillator strengths), frequency-dependent (hyper)polarizabilities (nonlinear optics), Raman intensities, and van der Waals dispersion coefficients. Rotatory strengths and optical rotatory dispersion (optical properties of chiral molecules ), as well as frequency-dependent dielectric functions for periodic structures, have been implemented as well. NMR chemical shifts and spin-spin couplingsESR (EPR) f-tensors, magnetic and electric hyperfme tensors are available, as well as more standard properties like IR frequencies and intensities, and multipole moments. Relativistic effects (ZORA and spin-orbit coupling) can be included for most properties. 

Certain improvement in the efficiency of the CC calculations can be achieved by using the idea of local correlation effects [18, 33, 64, 67, 69]. In that approach the CC reference function is built using localized molecular orbitals (LMO) [62]. The use of the LMOs enables to significantly reduce the computational cost of the CCSD calculations [1, 32, 44, 53, 66, 70, 84]. Also, the local CC approach has been implemented in the calculations of electronic excited states [29, 30, 37, 52]. The use of the local CCSD approach in the calculations of the (hyper)polarizabilities has been described in Refs. [28, 35, 36, 38, 66]. For a description of the calculations of the frequency-dependent polarizability and dispersion-coefficients see Ref. [85]. 

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