Computational Study of Polarizabilities and Second Hyperpolarizabilities of Inorganic Transition Metal Thiometalates and Metalates in Solution

Abstract

A systematic study of nonlinear optical (NLO) properties of inorganic transition metal (TM) thiometalates and metalates is reported. Polarizabilities (R) and second hyperpolarizabilities (γ) are calculated in solution within the polarizable continuum model. It is found that NLO properties of anionic inorganic complexes can be successfully modeled in solution, when this cannot be done so in the gas phase. Solvent effects are found to significantly increase R and γ. The effects are stronger on γ (up to 80%) than on R (up to 40%) and stronger on TM thiometalates than on metalates. For R, solvent effects are found to be more important than electron correlation effects. For γ, the two effects are similarly important. Solvent effects on R and γ caused by subordinate factors other than the dominant electrostatic solute-solvent interactions were studied and assessed to be negligible. Upon solvation, large TM and ligand modification effects on R and γ are found. One oxo-to-sulfido substitution results in an increase in R by 38 au and γ by 10 000 au.

Polarizabilities in the condensed phase and the local fields problem: A direct reaction field formulation

“…The continuum results are qualitatively the same as those coming from similar treatments, 8,11,55,56 i.e., all properties computed are numerically larger than their respective vacuum values. Local fields are only considered and applied in the work of Macac et al 56 but they use an expansion for the induced dipole ͓their Eqs.…”

Polarizabilities of hydrated and free ions derived from DFT calculations

“…For studies of heavier elements, treatment of relativistic effects is necessary, at least in the form of effective core potentials 103. Transition element coordination compounds were excluded, since more sophisticated modeling with at least the first coordination shell has to be taken into account 97–100, values for closed shell metalates and thiometalates can be found in the works of Cundari et al 96, 104. More values for ions in gas or condensed phase can be found in Refs.…”

“…73). For anions, this is not necessarily the case, as demonstrated in a PCM study on transition metal thiometalates and metalates 96. For metalates of charge −3 and −4, the authors found a decrease in polarizabilities which was rationalized by the unstable state of these highly charged ions in gas phase leading to relatively high gas phase polarizabilities.…”

“…It should be commented that experimental studies mostly deduce polarizability values below the theoretically obtained free ion values 43–45. Specifically, more studies have to be undertaken for multivalent anions for which a decrease of ion polarizabilities from PCM calculations has been noted 96 and will be shown below. More detailed studies are ongoing and out of the scope of this contribution.…”

Linear and nonlinear optical properties of some organoxenon derivatives

“…The usefulness and reliability of the pseudopotentials and, in particular, the large-core ones for the calculation of ͑hyper͒plarizabilities have been discussed by various authors. [19][20][21] The relativistic correction to the L&NLO properties has been estimated by employing the Douglas-Kroll approximation, 22 in connection with the HyPol basis, 17 which has been specifically developed for relativistic calculations.…”