Third-Order Nonlinear Optical Properties of The P-Nitroaniline Molecule: Electron Correlation Effects and Numerical Aspects

Komlanvi Sèvi Kaka1, Pierre Beaujean1, Frédéric Castet2, Benoît Champagne1

1 Laboratoire de Chimie Théorique (LCT), Unité de Chimie Physique Théorique et Structurale (UCPTS), Namur Institute of Structured Matter (NISM), Université de Namur.
2 Institut des Sciences Moléculaires (ISM, UMR CNRS 5255), Université de Bordeaux.


The third-order nonlinear optical responses are at the origin of phenomena such as the static and optical Kerr effects, the static electric field induced second harmonic generation, or the third harmonic scattering. It is characterized at the molecular level by the second hyperpolarizability (γ). Evaluating this quantity remains a challenge for quantum chemical methods because many effects have to be considered. My PhD thesis began with the study of these responses for conjugated organic systems. Although this work is carried out in a global multidisciplinary context, here we present the first results on the p-nitroaniline molecule, focusing attention on different aspects of the calculations:

  • the finite field (FF) method1 is an attractive scheme because of its simplicity. In fact, it only requires the calculation of the energy or lower-order properties (polarizability or the first hyperpolarizability) of the molecule undergoing the effects of external static electric fields of different amplitudes. Then, the derivatives are evaluated by finite differentiation using Romberg's2 quadrature procedure in order to improve the numerical precision. Depending on the order of the numerical differentiation, we discuss the choice of the static electric field amplitude and the numerical precision that can be achieved.
  • the electron correlation is known to impact the γ values3. If the CCSD(T) method can provide reference values, its application to systems of interest for nonlinear optics is difficult. Thus, it is important to gauge the precision of more approximate and computationally cheaper methods such as MP2, MP3, MP4 [D, DQ, SDQ and SDTQ], and CCSD methods.
  • density functional theory (DFT) represents an alternative to these wavefunction methods. It requires the choice of an exchange-correlation functional. Here, two aspects are known to be the origin of difficulties: the long-range nature of the responses4 to electric field and the choice of the numerical integration grid.

These different aspects are presented and discussed in our poster. In particular, the CCSD(T) reference values are shown to be well reproduced with the MP2 method (and the MP4 method) while γ values remain challenging for DFT exchange-correlation functionals.

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3         Champagne, B., Botek, E., Nakano, M., Nitta, T. and Yamaguchi, K. J. Chem. Phys., 2005, 112, 114315.
4         Champagne, B., Perpète, E. A., Van Gisbergen, S. J. A., Baerends, E. J., Snijders, J. G., Soubra-Ghaoui, C., Robins, K. A. and Kirtman, B. J. Chem. Phys., 1998, 109, 10489–10498.