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Vibrational Linear and Nonlinear Optical Properties: Theory, Methods, and Application

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Frontiers of Quantum Chemistry

Abstract

Methods for the calculation of vibrational contributions to nonresonant and resonant linear and nonlinear optical properties of molecules are reviewed. Both the Bishop–Kirtman perturbation theory and the finite-field/nuclear relaxation–curvature approach are treated. Emerging methods using variational approaches instead of perturbation theory and the methodology required to employ curvilinear coordinates instead of the more usual normal coordinates are briefly described, too. Finally, methods using a time-dependent approach are also treated.

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References

  1. A. Willetts, J.E. Rice, D.M. Burland, D. Shelton, Problems in the comparison of theoretical and experimental hyperpolarizabilities. J. Chem. Phys. 97, 7590–7599 (1992)

    Article  CAS  Google Scholar 

  2. H. Reis, Problems in the comparison of theoretical and experimental hyperpolarizabilities revisited. J. Chem. Phys. 125, 014506 (2006)

    Article  CAS  Google Scholar 

  3. P.N. Butcher, D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, Cambridge, 1990)

    Book  Google Scholar 

  4. G.S. Ezra, Symmetry Properties of Molecules. Lecture Notes in Chemistry Vol. 28, (Springer, Berlin 1982)

    Google Scholar 

  5. H. Reis, J.M. Luis, M. Garcia Borràs, B. Kirtman, Computation of nonlinear optical properties of molecules with large amplitude anharmonic motions. III. Arbitrary Double-Well Potentials, J. Chem. Theo. Comp. 10, 236–242 (2015)

    Google Scholar 

  6. D.M. Bishop, S.A. Solunac, Breakdown of the born-oppenheimer approximation in the calculation of electric hyperpolarizabilities. Phys. Rev. Lett. 55, 2627 (1985). erratum: Phys. Rev. Lett. 55, 2627

    Google Scholar 

  7. B.J. Orr, J.F. Ward, Perturbation theory of the non-linear optical polarization of an isolated system. Mol. Phys. 20, 513–526 (1971)

    Article  CAS  Google Scholar 

  8. D.M. Bishop, J.M. Luis, B. Kirtman, Additional compact formulas for vibrational dynamic dipole polarizabilities and hyperpolarizabilities. J. Chem. Phys. 108, 10013–10017 (1998)

    Google Scholar 

  9. B. Kirtman, B. Champagne, J.M. Luis, Efficient treatment of the effect of vibrations on electrical, magnetic, and spectroscopic properties. J. Comp. Chem. 21, 1572–1588 (2000)

    Article  CAS  Google Scholar 

  10. D.M. Bishop, Molecular vibration and nonlinear optics. Adv. Chem. Phys. 104, 1–40 (1998)

    CAS  Google Scholar 

  11. M. Torrent-Sucarrat, M. Sola, M. Duran, J.M. Luis, B. Kirtman, Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties. J. Chem. Phys. 116, 5363–5373 (2002)

    Article  CAS  Google Scholar 

  12. R. Zaleśny, Anharmonicity contributions to the vibrational first and second hyperpolarizability of para-disubstituted benzenes. Chem. Phys. Lett. 595–596, 109–112 (2014)

    Article  Google Scholar 

  13. B. Gao, M. Ringholm, R. Bast, K. Ruud, A.J. Thorvaldsen, M. Jaszunski, Analytic density-functional theory calculations of pure vibrational Hyperpolarizabilities: The first dipole Hyperpolarizability of retinal and related molecules. J. Phys. Chem. A 118, 748–756 (2014). Erratum: ibid, p. 2835 (2014)

    Google Scholar 

  14. M. Ringholm, D. Jonsson, R. Bast, B. Gao, A.J. Thorvaldsen, U. Ekström, T. Helgaker, K. Ruud, Analytic cubic and quartic force fields using density-functional theory. J. Chem. Phys. 140, 034103 (2014)

    Article  Google Scholar 

  15. Y. Cornaton, M. Ringholm, K. Ruud, Complete analytic anharmonic hyper-Raman scattering spectra. Phys. Chem. Chem. Phys. 18, 22331–22342 (2016)

    Article  CAS  Google Scholar 

  16. D.M. Bishop, J.M. Luis, B. Kirtman, Vibration and two-photon absorption. J. Chem. Phys. 116, 9729–9739 (2002)

    Article  CAS  Google Scholar 

  17. Lauvergnat, D.: Elvibrot-Tnum, http://pagesperso.lcp.u-psud.fr/lauvergnat/ElVibRot/ElVibRot.html

  18. P. Macak, Y. Luo, H. Ågren, Simulations of vibronic profiles in two-photon absorption. Chem. Phys. Lett. 330, 447–456 (2000)

    Article  CAS  Google Scholar 

  19. M. Drobizhev, N.S. Makarov, S.E. Tillo, T.E. Hughes, A. Rebane, Describing two-photon absorptivity of fluorescent proteins with a new vibronic coupling mechanism. J. Phys. Chem. B 116, 1736–1744 (2012)

    Article  CAS  Google Scholar 

  20. J.M. Luis, M. Duran, J.L. Andres, A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules, J. Chem. Phys. 107, 1501 (1997)

    Google Scholar 

  21. B. Kirtman, J.M. Luis, D.M. Bishop, Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: Curvature contributions. J. Chem. Phys. 108, 10008–10012 (1998)

    Article  CAS  Google Scholar 

  22. J.M. Luis, J. Martí, M. Duran, J.L. Andrés, B. Kirtman, Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6. J. Chem. Phys. 108, 4123 (1998)

    Google Scholar 

  23. J.M. Luis, M. Duran, B. Champagne, B. Kirtman, Determination of vibrational polarizabilities and hyperpolarizabilities using field–induced coordinated. J. Chem. Phys. 113 5203–5213 (2000); see also the correction in ref. 23 of [21]

    Google Scholar 

  24. J.M. Luis, M. Duran, B. Champagne, B. Kirtman, Field-induced coordinates for the determination of dynamic vibrational nonlinear optical properties. J. Chem. Phys. 115, 4473–4483 (2001)

    Article  CAS  Google Scholar 

  25. J.M. Luis, B. Champagne, B. Kirtman, Calculation of static zero-point vibrational averaging corrections and other vibrational curvature contributions to polarizabilities and hyperpolarizabilities using field-induced coordinates. Int. J. Quant. Chem. 80, 471–479 (2000)

    Article  CAS  Google Scholar 

  26. D.M. Bishop, M. Hasan, B. Kirtman, A simple method for determining approximate static and dynamic vibrational hyperpolarizabilities. J. Chem. Phys. 103, 4157–4159 (1995)

    Article  CAS  Google Scholar 

  27. J.M. Luis, M. Duran, J.L. Andrés, B. Champagne, B. Kirtman, Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: On the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations. J. Chem. Phys. 111, 875–884 (1999)

    Article  CAS  Google Scholar 

  28. M. Torrent-Sucarrat, M. Solà, M. Duran, J.M. Luis, B. Kirtman, Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties. J. Chem. Phys. 116, 5363–5373 (2002)

    Article  CAS  Google Scholar 

  29. M. Torrent-Sucarrat, M. Solà, M. Duran, J.M. Luis, B. Kirtman, Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules. J. Chem. Phys. 120, 6346–6355 (2004)

    Article  CAS  Google Scholar 

  30. U. Eckart, A. Sadlej, Vibrational corrections to electric properties of weakly bound systems. Mol. Phys. 99, 735–743 (2001)

    Article  CAS  Google Scholar 

  31. R.B. Gerber, J.O. Jung, The vibrational self-consistent field approach and extensions: Method and applications to spectroscopy of large molecules and clusters. In: Jensen, P., Bunker, P. R.: Computational Molecular Spectroscopy. (Wiley and Sons, Chichester, 2000)

    Google Scholar 

  32. M. Torrent-Sucarrat, J.M. Luis, B. Kirtman, Variational calculation of vibrational linear and nonlinear optical properties. J. Chem. Phys. 122, 204108 (2005)

    Article  Google Scholar 

  33. O. Christiansen, J. Kongsted, M.J. Paterson, J.M. Luis, Linear response functions for a vibrational configuration interaction state. J. Chem. Phys. 125, 124309 (2006)

    Article  Google Scholar 

  34. M.B. Hansen, O. Christiansen, C. Hättig, Automated calculation of anharmonic vibrational contributions to first hyperpolarizabilities: quadratic response functions from vibrational configuration interaction wave functions. J. Chem. Phys. 131, 154101 (2009)

    Article  Google Scholar 

  35. M.B. Hansen, O. Christiansen, Vibrational contributions to cubic response functions from vibrational configuration interaction response theory. J. Chem. Phys. 135, 154107 (2011)

    Article  Google Scholar 

  36. C. Eckart, Some studies concerning rotating axes and polyatomic molecules. Phys. Rev. 47, 552–558 (1935)

    Article  CAS  Google Scholar 

  37. C.R. Le Sueur, S. Miller, J. Tennyson, B.T. Sutcliffe, On the use of variational wavefunctions in calculating vibrational band intensities. Mol. Phys. 76, 1147–1156 (1992)

    Article  Google Scholar 

  38. S.N. Yurchenko, W. Thiel, P. Jensen, Theoretical ROVibrational Energies (TROVE): A robust numerical approach to the calculation of rovibrational energies for polyatomic molecules. J. Mol. Spectrosc. 245, 126 (2007)

    Article  CAS  Google Scholar 

  39. E. Mátyus, G. Czakó, A.G. Császár, Toward black-box-type full- and reduced-dimensional variational (ro)vibrational computations. J. Chem. Phys. 130, 28 (2009)

    Article  Google Scholar 

  40. D. Lauvergnat, A. Nauts, Torsional energy levels of nitric acid in reduced and full dimensionality with ElVibRot and Tnum. Phys. Chem. Chem. Phys. 12, 8405–12 (2010)

    Article  CAS  Google Scholar 

  41. Y. Scribano, D. Lauvergnat, D.M. Benoit, Fast vibrational configuration interaction using generalized curvilinear coordinates and self-consistent basis. J. Chem. Phys. 133, 94103 (2010)

    Article  Google Scholar 

  42. M.H. Beck, A. Jäckle, G.A. Worth, H.-D. Meyer, The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propagating wavepackets. Phys. Rep. 324, 1–105 (2000)

    Article  CAS  Google Scholar 

  43. G.A. Worth, K. Giri, G.W. Richings, M.H. Beck, A. Jäckle, H.-D. Meyer, QUANTICS Package, Version 1.1 (2015)

    Google Scholar 

  44. J.C.C. Light, Z. Bačić, Adiabatic approximation and nonadiabatic corrections in the discrete variable representation: Highly excited vibrational states of triatomic molecules. J. Chem. Phys. 87, 8007 (1987)

    Article  Google Scholar 

  45. A. Nauts, X. Chapuisat, Hamiltonians for constrained N-particle systems. Chem. Phys. Lett. 136, 164 (1987)

    Article  CAS  Google Scholar 

  46. R. Meyer, Flexible models for intramolecular motion, a versatile treatment and its application to glyoxal. J. Mol. Spectrosc. 76, 266 (1979)

    Article  CAS  Google Scholar 

  47. M.A. Harthcock, J. Laane, Calculation of kinetic energy terms for the vibrational Hamiltonian: Application to large-amplitude vibrations using one-, two-, and three-dimensional models. J. Mol. Spectrosc. 91, 300–324 (1982)

    Article  CAS  Google Scholar 

  48. Y. Smeyers, F. Melendez, M. Senent, Ab initio theoretical study of the methyl and phosphine torsion modes in ethylphosphine. J. Chem. Phys. 106, 1709–1717 (1997)

    Article  CAS  Google Scholar 

  49. D. Lauvergnat, A. Nauts, Exact numerical computation of a kinetic energy operator in curvilinear coordinates. J. Chem. Phys. 116, 8560–8570 (2002)

    Article  CAS  Google Scholar 

  50. E.B. Wilson, J.C. Decius, P.C. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra. McGraw-Hill (New York, 1955)

    Google Scholar 

  51. A. Nauts, X. Chapuisat, Momentum, quasi-momentum and hamiltonian operators in terms of arbitrary curvilinear coordinates, with special emphasis on molecular hamiltonians. Mol. Phys. 55, 1287–1318 (1985)

    Article  CAS  Google Scholar 

  52. D. Strobusch, C. Scheurer, Hierarchical expansion of the kinetic energy operator in curvilinear coordinates for the vibrational self-consistent field method. J. Chem. Phys. 135, 124102 (2011)

    Article  CAS  Google Scholar 

  53. W. Miller, N. Handy, J. Adams, Reaction path Hamiltonian for polyatomic molecules. J. Chem. Phys. 72, 99 (1980)

    Article  CAS  Google Scholar 

  54. P.R. Bunker, P. Jensen, Molecular Symmetry and Spectroscopy, NRC Press (Ottawa, 1998)

    Google Scholar 

  55. A.Y. Dymarsky, K.N. Kudin, Computation of the pseudorotation matrix to satisfy the Eckart axis conditions. J. Chem. Phys. 122, 124103 (2005)

    Article  Google Scholar 

  56. D. Lauvergnat, J.M. Luis, B. Kirtman, H. Reis, A. Nauts, Numerical and exact kinetic energy operator using Eckart conditions with one or several reference geometries: Application to HONO. J. Chem. Phys. 144, 084116 (2016)

    Article  Google Scholar 

  57. C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Natl. Bur. Stand. 45, 255 (1950)

    Article  Google Scholar 

  58. J.K. Cullum, R.A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations. Birkhäuser (Boston, 2002)

    Google Scholar 

  59. E.R. Davidson, The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J. Comput. Phys. 17, 87 (1975)

    Article  Google Scholar 

  60. F. Ribeiro, C. Iung, C. Leforestier, Calculation of highly excited vibrational levels: A prediagonalized Davidson scheme. Chem. Phys. Lett. 362, 199 (2002)

    Article  CAS  Google Scholar 

  61. J.M. Luis, H. Reis, M.G. Papadopoulos, B. Kirtman, Treatment of nonlinear optical properties due to large amplitude vibrational motions: Umbrella motion in NH\(_3\). J. Chem. Phys. 131, 034116 (2009)

    Article  Google Scholar 

  62. S. Garcia-Borràs, D. Lauvergnat, H. Reis, J.M. Luis, B. Kirtman, A full dimensionality approach to evaluate the nonlinear optical properties of molecules with large amplitude anharmonic tunneling motions. J. Chem. Theory Comput. 9, 520–532 (2013)

    Article  Google Scholar 

  63. M. Torrent-Sucarrat, J.M. Luis, B. Kirtman, Variational calculation of vibrational linear and nonlinear optical properties. J. Chem. Phys. 122, 204108 (2005)

    Article  Google Scholar 

  64. J.M. Luis, M. Torrent-Sucarrat, O. Christiansen, B. Kirtman, Variational calculation of static and dynamic vibrational nonlinear optical properties. J. Chem. Phys. 127, 084118 (2007)

    Article  Google Scholar 

  65. Y. Takimoto, F.D. Vila, J.J. Rehr, Real-time time-dependent density functional theory approach for frequency-dependent nonlinear optical response in photonic molecules. J. Chem. Phys. 127, 154114 (2007)

    Article  CAS  Google Scholar 

  66. E.J. Heller, The semiclassical way to molecular spectroscopy. Acc. Chem. Res. 14, 368–375 (1981)

    Article  CAS  Google Scholar 

  67. D.W. Silverstein, L. Jensen, Vibronic coupling simulations for linear and nonlinear optical processes: Theory. J. Chem. Phys. 136, 064111 (2012)

    Article  Google Scholar 

  68. T. Petrenko, F. Neese, Analysis and prediction of absorption band shapes, fluorescence band shapes, resonance Raman intensities, and excitation profiles using the time-dependent theory of electronic spectroscopy. J. Chem. Phys. 127, 164319 (2007)

    Article  Google Scholar 

  69. P.A. Weiss, D.W. Silverstein, L. Jensen, Non-condon effects on the doubly resonant sum frequency generation of Rhodamine 6G. J. Phys. Chem. Lett. 5, 329–335 (2014)

    Article  CAS  Google Scholar 

  70. F. Egidi, T. Giovannini, M. Piccardo, J. Bloino, C. Cappelli, V. Barone, Stereoelectronic, vibrational, and environmental contributions to polarizabilities of large molecular systems: A feasible anharmonic protocol. J. Chem. Theor. Comput. 10, 2456–2464 (2014)

    Article  CAS  Google Scholar 

  71. R. Zaleśny, R.W. Góra, J.M. Luis, W. Bartkowiak, On the particular importance of vibrational contributions to the static electrical properties of model linear molecules under spatial confinement. Phys. Chem. Chem. Phys. 17, 21782–21786 (2015)

    Article  Google Scholar 

  72. R. Zaleśny, M. Garcia-Borràs, R.W. Góra, M. Medved’, J.M. Luis, On the physical origins of interaction-induced vibrational (hyper)polarizabilities. Phys. Chem. Chem. Phys. 18, 22467–22477 (2016)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Biology, Medicinal Chemistry and Biotechnology, National Hellenic Research Foundation, 48 Vas. Constantinou Avenue, 11635, Athens, Greece

    Heribert Reis

  2. Laboratoire de Chimie Physique, CNRS, UMR 8000, Bâtiment 349, 91405, Orsay, France

    David Lauvergnat

  3. University of Paris-Sud, 91405, Orsay, France

    David Lauvergnat

  4. Institute of Computational Chemistry and Catalysis and Department of Chemistry, University of Girona, Campus de Montilivi, 17071, Girona, Catalonia, Spain

    Josep M. Luis

  5. Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wroclaw University of Science and Technology, Wyb. Wyspiańskiego 27, 50370, Wrocław, Poland

    Robert Zaleśny

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  1. Heribert Reis
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  2. David Lauvergnat
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  3. Josep M. Luis
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  4. Robert Zaleśny
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Correspondence to Heribert Reis .

Editor information

Editors and Affiliations

  1. Jagiellonian University, Kraków, Poland

    Marek J. Wójcik

  2. Quantum Chemistry Research Institute, Nishikyo-ku, Kyoto, Japan

    Hiroshi Nakatsuji

  3. University of California, Santa Barbara, California, USA

    Bernard Kirtman

  4. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Yukihiro Ozaki

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Reis, H., Lauvergnat, D., Luis, J.M., Zaleśny, R. (2018). Vibrational Linear and Nonlinear Optical Properties: Theory, Methods, and Application. In: Wójcik, M., Nakatsuji, H., Kirtman, B., Ozaki, Y. (eds) Frontiers of Quantum Chemistry. Springer, Singapore. https://doi.org/10.1007/978-981-10-5651-2_17

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