Extending the applicability of the Tkatchenko-Scheffler dispersion correction via iterative Hirshfeld partitioning

Abstract

Recently we have demonstrated that the applicability of the Tkatchenko-Scheffler (TS) method for calculating dispersion corrections to density-functional theory can be extended to ionic systems if the Hirshfeld method for estimating effective volumes and charges of atoms in molecules or solids (AIM's) is replaced by its iterative variant [T. Bučko, S. Lebègue, J. Hafner, and J. Ángyán, J. Chem. Theory Comput. 9, 4293 (2013)]. The standard Hirshfeld method uses neutral atoms as a reference, whereas in the iterative Hirshfeld (HI) scheme the fractionally charged atomic reference states are determined self-consistently. We show that the HI method predicts more realistic AIM charges and that the TS/HI approach leads to polarizabilities and C6 dispersion coefficients in ionic or partially ionic systems which are, as expected, larger for anions than for cations (in contrast to the conventional TS method). For crystalline materials, the new algorithm predicts polarizabilities per unit cell in better agreement with the values derived from the Clausius-Mosotti equation. The applicability of the TS/HI method has been tested for a wide variety of molecular and solid-state systems. It is demonstrated that for systems dominated by covalent interactions and/or dispersion forces the TS/HI method leads to the same results as the conventional TS approach. The difference between the TS/HI and TS approaches increases with increasing ionicity. A detailed comparison is presented for isoelectronic series of octet compounds, layered crystals, complex intermetallic compounds, and hydrides, and for crystals built of molecules or containing molecular anions. It is demonstrated that only the TS/HI method leads to accurate results for systems where both electrostatic and dispersion interactions are important, as illustrated for Li-intercalated graphite and for molecular adsorption on the surfaces in ionic solids and in the cavities of zeolites.

Recent development of atom‐pairwise van der waals corrections for density functional theory: From molecules to solids

“…Therefore, Bučko et al [24,25] suggested using the iterative Hirshfeld partitioning scheme (the Hirshfeld-I algorithm) [31,32] to allow for a better description of the charge transfer. The Hirshfeld-I algorithm defines the Hirshfeld weight function at each step i as:…”

“…For consistent comparison under the same calculation conditions with the same program, we performed all of the calculations using the Vienna ab-initio simulation package (VASP) [43][44][45][46] and with the projector augmented wave (PAW) pseudopotentials, [47,48] although some of the current tests have already been reported in several previous publications. [23][24][25]41,[49][50][51] The implementation of the various methods in the VASP code is described elsewhere. [7,[23][24][25] Conditions for the kinetic energy cut-off (E cut ) of the plane waves and for the k-point sampling are listed in Table 1.…”

C6 Coefficients and Dipole Polarizabilities for All Atoms and Many Ions in Rows 1–6 of the Periodic Table

“…3,[17][18][19][20][21][22]25,26 But it has been more rarely (if ever) exploited directly in atom-in-molecule approaches. In part this is likely due to a lack of viable frequency-dependent data for atoms and ions.…”

“…6 To remedy this lack, a cornucopia of new approaches has been developed over the past twenty years 1,2,12-22 that allow van der Waals forces to be included alongside more conventional density functional approximations. 10,23,24 A number of these approaches -most notably those based around the work of Grimme [17][18][19] and Tkatchenko and Scheffler 3,[20][21][22]25,26 -are based on atom-in-molecule (AIM) approximations. These (arguably) semi-empirical approximations involve taking free atomic C 6 coefficients and using them to determine binding in more complex bulk and molecular systems.…”

“…7,25,27 A vital componment of these AIM approaches is the data set of C 6 coefficients. These must be pre-calculated elsewhere and tabulated for input into the AIM scheme.…”