Problems in the comparison of theoretical and experimental hyperpolarizabilities

Abstract

Frequently it is useful to compare experimental values of the hyperpolarizabilities β and γ with calculated values. It is also often helpful to compare experimental values of β obtained from dc-electric field induced second harmonic generation (dc-SHG) experiments, e.g., with values obtained using the solvatochromism method. In order to do this the hyperpolarizabilities must be defined using consistent conventions. In this paper, four commonly used conventions are discussed and simple factors for converting between them presented. In addition, the sum-over-states expression for the calculation of β and γ is described and its correct use in comparing with hyperpolarizabilities obtained using other experimental and theoretical techniques discussed. As an illustration of the consistent use of conventions, ab initio and semiempirical calculations on para-nitroaniline are compared with experimental dc-SHG values. This comparison highlights the difference between theoretical values of the hyperpolarizability with the molecule in a gas phase environment and experimental values obtained in polar solvents−a difference that has in the past been obscured by inconsistent choice of conventions.

Can Gap Tuning Schemes of Long-Range Corrected Hybrid Functionals Improve the Description of Hyperpolarizabilities?

“…[58][59][60] To avoid these issues, we dedicate this section to clarify the conventions and hyperpolarizability measures employed here.…”

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Investigation of NLO properties of substituted (M)‐tetrathia‐[7]‐helicenes by semiempirical and DFT methods

“…The interaction of a molecule with an external electric field of component E i is typically expressed using the following Taylor series expansion of the induced dipole moment [13,14]:…”

Basis set effects on the hyperpolarizability of CHCl3: Gaussian-type orbitals, numerical basis sets and real-space grids

“…Here we use the Taylor convention for hyperpolarizabilities. 12 From our calculated tensor components we can calculate the isotropically averaged polarizabilityᾱ = 1 3 i α ii , the second-order hyperpolarizability coefficient, and the EFISH hyperpolarizability in the direction of the dipole moment β i = 1 5 j (β ijj + β jij + β jji ). In the C 3v point group, these relations reduce toᾱ = 1 3 (2α yy + α zz ), β z = 3 5 (2β yyz + β zzz ).…”