Density functional results for isotropic and anisotropic multipole polarizabilities and C6, C7, and C8 Van der Waals dispersion coefficients for molecules

Abstract

The generalized gradient-approximated ͑GGA͒ energy functionals used in density functional theory ͑DFT͒ provide accurate results for many different properties. However, one of their weaknesses lies in the fact that Van der Waals forces are not described. In spite of this, it is possible to obtain reliable long-range potential energy surfaces within DFT. In this paper, we use time-dependent density functional response theory to obtain the Van der Waals dispersion coefficients C 6 , C 7 , and C 8 ͑both isotropic and anisotropic͒. They are calculated from the multipole polarizabilities at imaginary frequencies of the two interacting molecules. Alternatively, one might use one of the recently-proposed Van der Waals energy functionals for well-separated systems, which provide fairly good approximations to our isotropic results. Results with the local density approximation ͑LDA͒, Becke-Perdew ͑BP͒ GGA and the Van Leeuwen-Baerends ͑LB94͒ exchange-correlation potentials are presented for the multipole polarizabilities and the dispersion coefficients of several rare gases, diatomics and the water molecule. The LB94 potential clearly performs best, due to its correct Coulombic asymptotic behavior, yielding results which are close to those obtained with many-body perturbation theory ͑MBPT͒. The LDA and BP results are systematically too high for the isotropic properties. This becomes progressively worse for the higher dispersion coefficients. The results for the relative anisotropies are quite satisfactory for all three potentials, however.

Time-dependent density functional theory: Past, present, and future

“…(9) provides a route to van der Waals forces for separated pieces of matter, and so is being much studied by developers. In particular, the coefficient in the decay of the energy between two such pieces (C 6 in E → −C 6 /R 6 , where R is their separation) can be accurately (within about 20%) evaluated using a local approximation to the frequencydependent polarizability [21,120,121,122]. Recent work shows that the response functions of TDDFT can yield extremely accurate dispersion energies of monomers [123].…”

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

“…The recent success of the time-dependent density functional perturbation theory ͑TDDFPT͒ [1][2][3][4] in calculations of electron excitations [5][6][7][8][9][10][11][12] and other molecular response properties [13][14][15][16][17] is due to its efficient treatment of electron exchange and correlation. The exchange-correlation ͑xc͒ effects in the ground state are represented with the local, state independent exchange-correlation potential v xc in the oneelectron Kohn-Sham ͑KS͒ equations ͕Ϫ 1 2 ٌ 2 ϩv ext ͑ r͒ϩv H ͑ r͒ϩv xc ͑ r͖͒ i ͑ r͒ϭ⑀ i i ͑ r͒.…”

Excitation Energies for Transition Metal Compounds from Time-Dependent Density Functional Theory. Applications to MnO4-, Ni(CO)4, and Mn2(CO)10

“…By now, a whole range of frequency-dependent molecular properties have been obtained from this approach, such as frequency-dependent polarizabilities, [4][5][6][7] frequency-dependent hyperpolarizabilities, [8][9][10] van der Waals dispersion coefficients, 4,11 optical activity, 12 and Raman scattering intensities. 13,14 Perhaps the most popular application of time-dependent density functional theory (TD-DFT) in the molecular regime has been the calculation of excitation energies, in which many groups have, by now, been involved.…”