Coupled cluster evaluation of the second and third harmonic scattering responses of small molecules

  • Pierre Beaujean
  • Benoît ChampagneEmail author
Regular Article
Part of the following topical collections:
  1. Festschrift in honour of A. Rizzo


The static and dynamic second harmonic (\(\beta _{\mathrm{SHS}}\)) and third harmonic (\(\gamma _{\mathrm{THS}}\)) scattering hyperpolarizabilities and depolarization ratios of water, carbon tetrachloride, chloroform, dichloromethane, chloromethane, and acetonitrile have been evaluated at the coupled cluster response theory level of approximation. Following two recent publications on their measurements, this is the first quantum chemical investigation on \(\gamma _{\mathrm{THS}}\) and on its decomposition into its spherical tensor components. Substantial electron correlation and basis set effects are evidenced for \(\beta _{\mathrm{SHS}}\) and \(\gamma _{\mathrm{THS}}\) and for their depolarization ratios, and they depend on the nature of the molecule. Then, using the selected CCSD/d-aug-cc-pVDZ level, the chlorinated methane derivatives have been studied, showing that (i) the \(\gamma _{\mathrm{THS}}\) response is dominated by its isotropic contribution, whereas (ii) for \(\beta _{\mathrm{SHS}}\) the dipolar contribution increases from carbon tetrachloride to dichloromethane, chloroform, chloromethane, and acetonitrile. Comparisons with the experimental data obtained from measurements in liquid phase (i) show that the increase of \(\gamma _{\mathrm{THS}}\) with the number for chlorine atoms is well reproduced by the calculations and (ii) suggest that the solvation effects are smaller for \(\gamma _{\mathrm{THS}}\) than for \(\beta _{\mathrm{SHS}}\).


First and second hyperpolarizabilities Coupled cluster response functions Second and third harmonic scattering 



At the occasion of his 60th birthday, it is a pleasure to dedicate this paper to Prof. Antonio RIZZO, who is pioneering since several decades the evaluation of high-order optical effects and their confrontation with experiment, leading to an improved understanding of the interactions between light and matter. This work was supported by funds from the Francqui Foundation. The calculations were performed on the computers of the Consortium des Équipements de Calcul Intensif, including those of the Technological Platform of High-Performance Computing, for which we gratefully acknowledge the financial support of the FNRS-FRFC (Convention Nos. 2.4.617.07.F and 2.5020.11) and of the University of Namur.

Supplementary material

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Authors and Affiliations

  1. 1.Laboratory of Theoretical Chemistry, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured MatterUniversity of NamurNamurBelgium

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