A Theoretical Modeling of the Static and Dynamic Polarizability of O^2- in Large and Complex Oxides

Abstract

A time-dependent approach is employed in conjunction with a crystal potential model to study the environment-specific optical linear response of the O 2-ions in a number of cubic oxides with varying number of constituents, unit-cell dimension and degree of complexity. It is shown that the static polarizability of the anion may vary significantly depending on the position of the anion within the unit-cell. Due to neglect of overlap compression, our method has limited success in predicting the refractive indices of large crystals of complex structures. For small binary oxides the frequency-dependent polarizability of the 0 :~ ion is found to exhibit the first poles close to the ultraviolet absorption edges ascribed to the lowest excitonic transitions in these crystals.

A simple semiempirical model for the static polarizability of ions

“…As can be deduced from Fig. 5, where the β obs values for the ions -without loss of generality of the discussionof the group 1 (alkali) atoms based on the α i data reported elsewhere [16,19,[24][25][26]28,59,73,82,86,87] are plotted as a function of N/Z (again, in the presence of different α i values for the same ion, weighted averaging was applied), the observed β (N/Z) function appears to have a pole at N/Z = 1. Indeed, for ions of heavy atoms, for which the N/Z argument is only slightly different from unity, there is a sharp increase in the apparent value of β function, and this β (N/Z) behavior can be described as an inverse power of |1 − N/Z| (see Fig.…”

“…To begin with, all the data we found for various charged atoms (ranging from H up to Ba as well as for several heavier elements including Pt, Au, Hg, Tl, Pb, At, Fr, Fr, and Ra) were involved for this purpose, namely, the results of multiple theoretical calculations [16,17,19,[21][22][23][24][25][26][27][28][29][30]44,51,59,82,86,87] and measurements [16,53] together with some expert estimates reported in related compendia. [73,75] Then, we introduced into the fit data set the theoretical [32][33][34][35][36][37][39][40][41][42][43][44] and experimental [38] cations adopted in reference [31] were used.…”

“…The relative polarizability ξ of ionized atoms, molecules, and clusters as extracted from Refs. [8,[11][12][13]16,17,19,53,59,73,75,82,[86][87][88] and DFT calculations of this work versus N/Z (N and Z are the electron and proton numbers).…”

“…( 1) is shown against N/Z in Fig. 3 as compared with the ξ values from the assembled data set for some monoatomic ions of some first-and second-row elements (B, C, N, O, Ne, Si, S, and Ar) [16,17,22,24,26,44,51,59,73,75,82,86,87] for which the ξ values are known in the broadest range of ionization degree (see Subsection 2.1). Note also that if there are different ξ values for the same ion in the data set, the weighted arithmetic means of relative polarizabilities we found in the literature (based on the weights assigned to these data points in Section 2) were used in the plotting of Fig.…”

“…(1) (solid curve) and its analogue -Eq. ( 2) -with a modified power exponent (dot for β = 2 and dash for β = 4) together with the actual ξ values for various atomic ions based on the data reported elsewhere [16,17,22,24,26,44,51,59,73,75,82,86,87] (symbols).…”