Environmental Effects on Anion Polarizability:  Variation with Lattice Parameter and Coordination Number

Abstract

The results of ab initio calculations of in-crystal ionic polarizabilities, α, over a wide range of lattice parameters, R, are presented for LiF, NaF, KF, LiCl, NaCl, KCl, LiBr, NaBr, KCl, and MgO. The derivatives of the mean polarizability with respect to lattice parameters are compared with experimental values obtained from the variation of the refractive index with pressure. The environmental effects on the polarizability of an anion may be viewed as the consequence of imposition of a confining potential on its electron density whose origin includes Coulombic interactions and the exclusion of these electrons from the region occupied by the electron density of the first-neighbor shell of cations. This model suggests scaling relationships, between values of α(R) obtained at different levels of calculation and for a given anion with different cations, which are shown to be semiquantitative. These findings lead to the proposal of a universal representation of the polarizability of a given anion, which predicts the dependence on lattice parameter and crystal form and transfers from one substance to another.

Classical polarizable force fields parametrized from ab initio calculations

“…In the condensed phase the electronic distribution is more contracted, thus they are less polarizable and more strongly bound. 11,22,31,33,64,77 For instance, the oxide anion is unstable in the gas phase but confinement due to electrostatic and short-range interactions leads to a bound state for the in-crystal O 2Ϫ anion. The above discussion allows us to conclude that our DFT-LR calculation on the isolated anion underestimates its hardness ͑or, equivalently, overestimates its polarizability͒ with respect to the ''proper'' value exhibited in condensed phases.…”

“…Such procedures account for the effects of the overlap with the neighboring ions and the lattice confining potential ͑''environmental effects''͒ on the ion's polarizability and allows one to distinguish between pure Coulomb and shortrange contributions. [22][23][24] This class of models has proved to give excellent agreement with experiment for many closed shell oxides and halides. [25][26][27][28] In addition, potential parameters are transferable between chemically related materials.…”

Condensed phase ionic polarizabilities from plane wave density functional theory calculations

“…The method is easy to apply and does not involve the construction of pseudopotentials to describe the environmental potential 16 or the unraveling of dipole induced dipole and basis set superposition errors in cluster calculations. 3,15 It can therefore be applied to ions in arbitrary condensed phase environments, such as the asymmetric instantaneous coordination environments encountered in the course of thermal motion in a liquid, where anisotropic elements of the polarizability will be induced alongside the trace. In future work we will exploit this capability to calculate Raman spectra and to build transferable models of ionic interactions.…”

“…These problems are exacerbated by basis set superposition effects. 3,15 Nevertheless, in favorable cases, some information on the dependence of the polarizability on the identity of the neighboring ions, the number of coordinating ions and their geometrical arrangement, 9,16,17 on the polarizabilities of cations as well as anions, 18 and on the effect of taking an ion to surface sites 7 has emerged from the embedded cluster and pseudoenvironment calculations. This information has been used in the construction of polarizable interaction potentials, 19,20 in rationalizing the pressure dependence of the refractive index 9 and in calculating Raman spectra, 21 inter alia.…”

Including many-body effects in models for ionic liquids

“…This is due to differences in the confining potential, which affects the electron density around a given anion, and originates from both Coulombic interactions and the exclusion of electrons from the region occupied by the electron density of the first-neighbor shell of cations. 21,22,101 When passing from one cation to another (for example in the series Li + →Na + →K + →Cs + ), two effects are then competing: On the one hand, the anion-cation distance increases, which results in a diminution of the confining potential, but on the other hand, the volume occupied by the cation electron density also increases, with an opposite effect on the confining potential. Here, the observed increase of polarizability with the size of the cation tends to show that the first effect is the most important.…”