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

  • Benoît Champagne
  • Pierre Beaujean
  • Marc de Wergifosse
  • Marcelo Hidalgo Cardenuto
  • Vincent Liégeois
  • Frédéric Castet
Chapter

Abstract

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.

Keywords

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

Notes

Acknowledgements

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, http://www.ceci-hpc.be), 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.

References

  1. 1.
    D.P. Shelton, J.E. Rice, Chem. Rev. 94, 3–29 (1994)CrossRefGoogle Scholar
  2. 2.
    T. Verbiest, K. Clays, V Rodriguez, Second-Order Nonlinear Optical Characterization Techniques: An Introduction (Taylor & Francis, 2009)Google Scholar
  3. 3.
    D.R. Kanis, M.A. Ratner, T.J. Marks, Chem. Rev. 94, 195–242 (1994)Google Scholar
  4. 4.
    J.L. Brédas, C. Adant, P. Tackx, A. Persoons, B.M. Pierce, Chem. Rev. 94, 243–278 (1994)CrossRefGoogle Scholar
  5. 5.
    P.J. Campagnola, L.M. Loew, Nat. Biotechnol. 21, 1356–1360 (2003); Y.C. Liang, A.S. Dvornikov, P.M. Rentzepis, Proc. Natl. Acad. Sci. USA 100, 8109–8112 (2003)Google Scholar
  6. 6.
    P.C. Ray, Chem. Rev. 110, 5332–5365 (2010)CrossRefGoogle Scholar
  7. 7.
    R. Bersohn, Y.H. Pao, H.L. Frisch, J. Chem. Phys. 45, 3184–3198 (1966)CrossRefGoogle Scholar
  8. 8.
    S.Y. Liu, C.E. Dykstra, J. Phys. Chem. 91, 1749–1754 (1987)CrossRefGoogle Scholar
  9. 9.
    G.J.B. Hurst, M. Dupuis, E. Clementi, J. Chem. Phys. 89, 385–395 (1988)CrossRefGoogle Scholar
  10. 10.
    S. Yamada, M. Nakano, I. Shigemoto, S. Kiribayashi, K. Yamaguchi, Chem. Phys. Lett. 267, 445–451 (1997)CrossRefGoogle Scholar
  11. 11.
    T. Pluta, A.J. Sadlej, Chem. Phys. Lett. 297, 391 (1998); A. Baranowska, A.J. Sadlej, J. Comput. Chem. 31, 552–560 (2010); R. Zalesny, A. Baranowska-Laczkowska, M. Medved, J.M. Luis, J. Chem. Theor. Comput. 11,4119-4128 (2015)Google Scholar
  12. 12.
    G. Maroulis, J. Chem. Phys. 108, 5432–5448(1998); G. Maroulis, Theor. Chem. Acc. 129,437–445 (2011)Google Scholar
  13. 13.
    R.A. Kendall, T.H. Dunning Jr., R.J. Harrison, J. Chem. Phys. 96, 6796–6806(1992); D.E. Woon, T.H. Dunning Jr., J. Chem. Phys. 100, 2975–2988 (1994)Google Scholar
  14. 14.
    F. Castet, E. Bogdan, A. Plaquet, L. Ducasse, B. Champagne, V. Rodriguez, J. Chem. Phys. 136, 024506 (2012)CrossRefGoogle Scholar
  15. 15.
    F.D. Vila, D.A. Strubbe, Y. Takimoto, X. Andrade, A. Rubio, S.G. Louie, J.J. Rehr, J. Chem. Phys. 133, 034111 (2010)CrossRefGoogle Scholar
  16. 16.
    J.D. Talman, Phys. Rev. A 86, 022519 (2012)CrossRefGoogle Scholar
  17. 17.
    H.D. Cohen, C.C.J. Roothaan, J. Chem. Phys. 43, S34 (1965)CrossRefGoogle Scholar
  18. 18.
    D.M. Bishop, S.A. Solunac, Chem. Phys. Lett. 122, 567 (1985)CrossRefGoogle Scholar
  19. 19.
    A.A.K. Mohammed, P.A. Limacher, B. Champagne, J. Comput. Chem. 34, 1497–1507 (2013)CrossRefGoogle Scholar
  20. 20.
    M. de Wergifosse, V. Liégeois, B. Champagne, Int. J. Quantum Chem. 114, 900–910 (2014)CrossRefGoogle Scholar
  21. 21.
    J. Linderberg, Y. Öhrn, Propagators in Quantum chemistry (Wiley-Interscience, Hoboken, 2004)CrossRefGoogle Scholar
  22. 22.
    T. Helgaker, S. Coriani, P. Jørgensen, K. Kristensen, J. Olsen, K. Ruud, Chem. Rev. 112, 543 (2012)CrossRefGoogle Scholar
  23. 23.
    S. Karna, M. Dupuis, J. Comput. Chem. 12, 487 (1991)CrossRefGoogle Scholar
  24. 24.
    S.J.A. van Gisbergen, J.G. Snijders, E.J. Baerends, J. Chem. Phys. 109, 10657 (1998)CrossRefGoogle Scholar
  25. 25.
    P. Beaujean, B. Champagne, J. Chem. Phys. 145, 044311 (2016)CrossRefGoogle Scholar
  26. 26.
    H. Sekino, R.J. Bartlett, J. Chem. Phys. 94, 3665 (1991)CrossRefGoogle Scholar
  27. 27.
    J.E. Rice, N.C. Handy, J. Chem. Phys. 94, 4959 (1991)CrossRefGoogle Scholar
  28. 28.
    M. de Wergifosse, F. Castet, B. Champagne, J. Chem. Phys. 142, 194102 (2015)CrossRefGoogle Scholar
  29. 29.
    P. Kaatz, E.A. Donley, D.P. Shelton, J. Chem. Phys. 10, 849 (1998)CrossRefGoogle Scholar
  30. 30.
    J.F. Ward, C.K. Miller, Phys. Rev. A 19, 826 (1979)CrossRefGoogle Scholar
  31. 31.
    D.P. Shelton, J. Chem. Phys. 137, 044312 (2012)CrossRefGoogle Scholar
  32. 32.
    D.M. Bishop, F.L. Gu, S.M. Cybulski, J. Chem. Phys. 109, 8407 (1998)CrossRefGoogle Scholar
  33. 33.
    F. Castet, B. Champagne, J. Chem. Theor. Comput. 8, 2044 (2012)CrossRefGoogle Scholar
  34. 34.
    P. Karamanis, R. Marchal, P. Carbonnière, C. Pouchan, J. Chem. Phys. 135, 044511 (2012)CrossRefGoogle Scholar
  35. 35.
    K.Y. Suponitsky, S. Tafur, A.E. Masunov, J. Chem. Phys. 129, 044109 (2008)CrossRefGoogle Scholar
  36. 36.
    M. de Wergifosse, B. Champagne, J. Chem. Phys. 134, 074113 (2011)CrossRefGoogle Scholar
  37. 37.
    S.I. Lu, C.C. Chiu, Y.F. Wang, J. Chem. Phys. 135, 134104 (2011)CrossRefGoogle Scholar
  38. 38.
    H. Sun, J. Autschbach, ChemPhysChem 14, 2450–2461 (2013)CrossRefGoogle Scholar
  39. 39.
    K. Garrett, X.A. Sosa Vazquez, S.B. Egri, J. Wilmer, L.E. Johnson, B.H. Robinson, C.M. Isborn, J. Chem. Theory Comput. 10, 3821–3831 (2014)CrossRefGoogle Scholar
  40. 40.
    J. Tomasi, B. Mennucci, R. Cammi, Chem. Rev. 105, 2999–3094 (2005)Google Scholar
  41. 41.
    J.L. Oudar, D.S. Chemla, J. Chem. Phys. 66, 2664–2668 (1977)CrossRefGoogle Scholar
  42. 42.
    P. Kaatz, D.P. Shelton, Mol. Phys. 88, 683–691 (1996)CrossRefGoogle Scholar
  43. 43.
    K. Coutinho, S. Canuto, Adv. Quantum Chem. 28, 89–105 (1997)CrossRefGoogle Scholar
  44. 44.
    K. Coutinho, R. Rivelino, H.C. Georg, S. Canuto, in Solvation Effects in Molecules and Biomolecules: Computational Methods and Applications (Springer, 2008), pp. 159–189Google Scholar
  45. 45.
    M. Hidalgo Cardenuto, B. Champagne, Phys. Chem. Chem. Phys. 17, 23634–23642 (2015)CrossRefGoogle Scholar
  46. 46.
    M. Hidalgo Cardenuto, F. Castet, B. Champagne, RSC Adv. 6, 99558–99563 (2016)CrossRefGoogle Scholar
  47. 47.
    E. Deniz, J. Cusido, S. Swaminathan, M. Battal, S. Impellizzeri, S. Sortino, F.M. Raymo, J. Photochem. Photobiol., A 229, 20–28 (2012)CrossRefGoogle Scholar
  48. 48.
    M. Kamiya, H. Sekino, T. Tsuneda, K. Hirao, J. Chem. Phys. 122, 234111 (2005); F. Bulat, A. Toro-Labbé, B. Champagne, B. Kirtman, W. Yang, J. Chem. Phys. 123, 014319 (2005)Google Scholar
  49. 49.
    B. Champagne, K. Kirtman, J. Chem. Phys. 125, 024101 (2006)CrossRefGoogle Scholar
  50. 50.
    B. Champagne, E.A. Perpète, D. Jacquemin, S.J.A. van Gisbergen, E.J. Baerends, C. Soubra-Ghaoui, K.A. Robins, B. Kirtman, J. Phys. Chem. A 104, 4755–4763 (2000)CrossRefGoogle Scholar
  51. 51.
    L. Kronik, T. Stein, S. Refaely-Abramson, R. Baer, J. Chem. Theory Comput. 8, 1515–1531 (2012)CrossRefGoogle Scholar
  52. 52.
    B.J. Coe, Chem. Eur. J. 5, 2464–2471 (1999); J.A. Delaire, K. Nakatani K, Chem. Rev. 100, 1817–1845 (2000); I. Asselberghs, K. Clays, A. Persoons, M.D. Ward, J. McCleverty, J. Mater. Chem. 14, 2831–2839 (2004); F. Castet, V. Rodriguez, J.L. Pozzo, L. Ducasse, A. Plaquet, B. Champagne, Acc. Chem. Res. 46: 2656–2665 (2013)Google Scholar
  53. 53.
    A. Plaquet, M. Guillaume, B. Champagne, F. Castet, L. Ducasse, J.L. Pozzo, V. Rodriguez, Phys. Chem. Chem. Phys. 10, 3223–3232 (2008)CrossRefGoogle Scholar
  54. 54.
    A. Plaquet, B. Champagne, J. Kulhanek, F. Bures, E. Bogdan, F. Castet, L. Ducasse, V. Rodriguez, ChemPhysChem 12, 3245–3252 (2011)CrossRefGoogle Scholar
  55. 55.
    A. Plaquet, B. Champagne, F. Castet, L. Ducasse, E. Bogdan, V. Rodriguez, J.L. Pozzo, New J. Chem. 33, 1349–1356 (2009)CrossRefGoogle Scholar
  56. 56.
    E. Bogdan, A. Plaquet, L. Antonov, V. Rodriguez, L. Ducasse, B. Champagne, F. Castet, J. Phys. Chem. C 114, 12760–12768 (2010)CrossRefGoogle Scholar
  57. 57.
    A. Plaquet, B. Champagne, L. Ducasse, E. Bogdan, F. Castet, AIP Conf. Proc. 1642, 481–487 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Benoît Champagne
    • 1
  • 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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