Quantum Chemical Methods for Predicting and Interpreting Second-Order Nonlinear Optical Properties: From Small to Extended π-Conjugated Molecules

  • Benoît ChampagneEmail author
  • Pierre Beaujean
  • Marc de Wergifosse
  • Marcelo Hidalgo Cardenuto
  • Vincent Liégeois
  • Frédéric Castet


This chapter addresses the methodological and computational aspects related to the prediction of molecular second-order nonlinear optical properties, i.e., the first hyperpolarizability (β), by using quantum chemistry methods. Both small (reference) molecules and extended push-pull π-conjugated systems are considered, highlighting contrasted effects about (i) the choice of a reliable basis set together with the convergence of β values as a function of the basis set size, (ii) the amplitude of electron correlation contributions and its estimate using wave function and density functional theory methods, (iii) the description of solvent effects using implicit and explicit solvation models, (iv) frequency dispersion effects in off-resonance conditions, and (v) numerical accuracy issues. When possible, comparisons with experiment are made. All in all, these results demonstrate that the calculations of β remain a challenge and that many issues need to be carefully addressed, pointing out difficulties toward elaborating black-box and computationally cheap protocols. Still, several strategies can be designed in order to achieve a targeted accuracy, either for reference molecules displaying small β responses or for molecules presenting large β values and a potential in optoelectronics and photonics.


First hyperpolarizability Wave function versus density functional theory methods Solvation models Frequency dispersion Basis sets 



This work was supported by funds from the Belgian Government (IUAP N° P7/5 “Functional Supramolecular Systems”) and the Francqui Foundation. It has also been done in the frame of the Centre of Excellence LAPHIA (Investments for the future: Programme IdEx Bordeaux–LAPHIA (ANR-10-IDEX-03-02)). V.L. thanks the Fund for Scientific Research (F.R.S.-FNRS) for his Research Associate position and M.H.C. the IUAP N° P7/5. The calculations were performed on the computing facilities of the Consortium des Équipements de Calcul Intensif (CÉCI,, including those of the Technological Platform of High Performance Computing, for which we gratefully acknowledge the financial support of the FNRS- FNRC (Conventions 2.4.617.07.F and 2.5020.11) and of the University of Namur as well as on the “Mésocentre de Calcul Intensif Aquitain” (MCIA) of the University of Bordeaux, financed by the Conseil Régional d’Aquitaine and the French Ministry of Research and Technology.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Benoît Champagne
    • 1
    Email author
  • Pierre Beaujean
    • 1
  • Marc de Wergifosse
    • 1
  • Marcelo Hidalgo Cardenuto
    • 1
    • 2
  • Vincent Liégeois
    • 1
  • Frédéric Castet
    • 3
  1. 1.Laboratoire de Chimie Théorique, Unité de Chimie-Physique Théorique et StructuraleUniversité de NamurNamurBelgium
  2. 2.Instituto de Física, Universidade de São PauloSão PauloBrazil
  3. 3.UMR 5255 CNRSInstitut des Sciences Moléculaires (ISM), Université de BordeauxTalence CedexFrance

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