Evaluation of the molecular static and dynamic first hyperpolarizabilities

Abstract

By considering two prototypical π‐conjugated compounds, several technical aspects associated with the evaluation of the first hyperpolarizabilities have been addressed in this article, that is, (i) the automatization of the Romberg's scheme to improve the numerical accuracy in the finite field method, (ii) the evaluation of the frequency dispersion at correlated levels using approximate schemes, and (iii) the deviations from Kleinman's symmetry conditions. It results from this study that accurate numerical derivatives can be obtained by resorting to the Romberg's method and by analyzing the Romberg's table in terms of two quantities, the field error and the iteration error. Indeed, the resulting first hyperpolarizability values are in close agreement with those obtained using an analytical differentiation procedure. The reliability of the multiplicative and additive approximate schemes to describe the frequency dispersion at correlated levels from using HF (Hartree‐Fock) frequency dispersion has been confirmed to be limited to large wavelengths or far‐from‐resonance wavelength regions. Kleinman's symmetry conditions have been assessed, showing that for off‐diagonal components of these two π‐conjugated compounds, the deviations could be substantial. Nevertheless, good accuracy can be achieved for experimentally related quantities like βHRS because the diagonal tensor components are dominant. © 2014 Wiley Periodicals, Inc.

Nonlinear optical properties in open‐shell molecular systems

“…For this broad range of methods, γ was evaluated using the finite‐field procedure, as the fourth‐order derivative of the energy with respect to the electric field. Analyses have been carried out for an adequate choice of the field amplitudes . Results were analyzed in terms of the γ density, highlighting the compounds moieties that contribute most to γ .…”

The Symmetries of Octupolar Tensors

“…2 When the frequencies of the applied fields are much smaller than the resonance frequency, χ (2) can safely be assumed to be independent of frequencies and fully symmetric in all its indices. Though this symmetry, which is often called Kleinman's symmetry after the name of the author who first introduced it [20], has been widely criticized [10] and also found in disagreement with some computational schemes [53], it is still often accepted as an approximation for its simplicity. Assuming Kleinman's symmetry to be valid, we can extract an octupolar tensor A = χ (2) out of χ (2) and rewrite the latter in the equivalent form χ (2)…”

Nonlinear response properties of atomic hydrogen under quantum plasma environment: A time‐dependent variation perturbation study on hyperpolarizability and two‐photon excitations

“…[31] However, such calculations on the hyperpolarizabilities of confined atomic systems are rather scanty and have been performed mostly on static hyperpolarizabilities. [64][65][66][67][68][69] Molecular static and dynamic first hyperpolarizabilities have been evaluated by de Wergifosse et al [70] Accurate density functional theory (DFT) calculations on linear and nonlinear electric properties of spatially confined molecules were performed by Chołuj et al [71] As molecules of different natures are, under many circumstances, surrounded by other environments, for example, solvent-solute systems or classical electrolytic environment, which has its origin for Debye shielding (SCP), it is worth mentioning the chemical implications of the present ideas with the existing literature. For example, extensive industrial applications of NLO organic, inorganic, and bio materials exist along with intrinsic theoretical understanding of macroscopic properties originating from electromagnetic field-induced NLO processes.…”