Density functional method including weak interactions: Dispersion coefficients based on the local response approximation

Abstract

A new method to calculate the atom-atom dispersion coefficients in a molecule is proposed for the use in density functional theory with dispersion (DFT-D) correction. The method is based on the local response approximation due to Dobson and Dinte [Phys. Rev. Lett. 76, 1780 (1996)], with modified dielectric model recently proposed by Vydrov and van Voorhis [J. Chem. Phys. 130, 104105 (2009)]. The local response model is used to calculate the distributed multipole polarizabilities of atoms in a molecule, from which the dispersion coefficients are obtained by an explicit frequency integral of the Casimir-Polder type. Thus obtained atomic polarizabilities are also used in the damping function for the short-range singularity. Unlike empirical DFT-D methods, the local response dispersion (LRD) method is able to calculate the dispersion energy from the ground-state electron density only. It is applicable to any geometry, free from physical constants such as van der Waals radii or atomic polarizabilities, and computationally very efficient. The LRD method combined with the long-range corrected DFT functional (LC-BOP) is applied to calculations of S22 weakly bound complex set [Phys. Chem. Chem. Phys. 8, 1985 (2006)]. Binding energies obtained by the LC-BOP+LRD agree remarkably well with ab initio references.

Long-range correlation energies from frequency-dependent weighted exchange-hole dipole polarisabilities

“…Note that a similar good performance is also found for the related XDM method by Becke and Johnson [31][32][33][34][35][36] and the LRD method by Sato et al 40 In case of the LRD method, the total mean absolute error for the S22 systems was found to be 0.27 kcal/mol if C 6 , C 8 and C 10 terms are accounted for 40 and thus the LRD method has an accuracy that is comparable to the present approach. In case of the XDM method, a very recent benchmark of Burns et al yields even a mean absolute deviation of only 0.19 kcal/mol for the combination of the XDM correction with the B3LYP functional.…”

“…Due to the nonlocality of the response function, in this work it is therefore necessary to apply a localisation method to the distributed polarisabilities in order to derive atomic polarisabilities, while in the LRD method the local form of the response function directly allows to transform the distributed polarisabilities into local ones, see Ref. 40.…”

“…Without the claim for completeness these may be categorised into hybrid methods combining elements of DFT with wave function methods, [14][15][16][17][18][19][20][21][22] methods which directly model the exchange-correlation functionals in terms of the density and its derivatives using nonlocal integral kernels, [23][24][25][26][27][28] or methods which employ the well-known asymptotic form of the dispersion interaction combined with proper damping functions. [29][30][31][32][33][34][35][36][37][38][39][40][41] Certainly, the first type of methods can be regarded as the most accurate methods, but their computational expense commonly exceeds the a) Author to whom correspondence should be addressed. Electronic mail:…”

“…II D. It should be noted that this approach is closely related to the local response dispersion (LRD) method by Sato and Nakai. 40 The LRD method uses a local approximation of the response function developed by Dobson and Dinte 49 which is based on a simple model of the density-density response function of the homogeneous electron gas (see also a related work by Andersson et al 50 ). From this response function Sato et al derive localised polarisabilites that are used in very much the same way as in the current work to calculate atom-atom dispersion energy contributions to the total correlation energy in a DFT+D scheme using a damping function for short ranges.…”

First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

“…211,212 Sato and Nakai developed an atomic pairwise method that can be considered a direct bridge to the class of nonlocal functionals, by directly expanding an ALL-like density functional into a multipole series around the atomic centers. 213,214 They used the general formula for the dynamic polarizability of an infinitesimal harmonic oscillator in eq 44, 215 combined with the characteristic excitation frequency from the vdW-DF-09 nonlocal functional of Vydrov and van Voorhis, 168 ω π λ π (59) where λ is an empirical parameter to be fitted to a set of C 6 coefficients. This formula shows yet another density functional for the effective local frequency which was the main topic in the section about nonlocal functionals.…”