Abstract

The first- and second-order hyperpolarizabilities have been extensively studied to identify universal properties near the fundamental limit. Here, we employ the Monte Carlo method to study the fundamental limit of the second hyperpolarizability. As was found for the first hyperpolarizability, the largest values of the second hyperpolarizability approach the calculated fundamental limit. The character of transition moments and energies of the energy eigenstates are investigated near the second hyperpolarizability’s upper bounds using the missing state analysis, which assesses the role of each pair of states in their contribution. In agreement with the three-level ansatz, our results indicate that only three states (ground and two excited states) dominate when the second hyperpolarizability is near the limit.

© 2010 Optical Society of America

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  1. M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
    [CrossRef]
  2. M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183–1185 (2000).
    [CrossRef]
  3. M. G. Kuzyk, “Quantum limits of the hyper-Rayleigh scattering susceptibility,” IEEE J. Sel. Top. Quantum Electron. 7, 774–780 (2001).
    [CrossRef]
  4. J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
    [CrossRef]
  5. M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
    [CrossRef]
  6. M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities: erratum,” Opt. Lett. 28, 135–137 (2003).
    [CrossRef]
  7. M. G. Kuzyk, “Erratum: Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 90, 039902 (2003).
    [CrossRef]
  8. H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
    [CrossRef]
  9. H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
    [CrossRef]
  10. K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
    [CrossRef]
  11. J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
    [CrossRef]
  12. J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
    [CrossRef]
  13. J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
    [CrossRef]
  14. J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
    [CrossRef]
  15. M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
    [CrossRef]
  16. D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
    [CrossRef]
  17. M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
    [CrossRef]
  18. X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
    [CrossRef]
  19. A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810 (2004).
    [CrossRef]
  20. J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
    [CrossRef]
  21. J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
    [CrossRef]
  22. J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
    [CrossRef]
  23. M. G. Kuzyk, “A bird’s-eye view of nonlinear-optical processes: Unification through scale invariance,” Nonlinear Opt., Quantum Opt. 40, 1–13 (2010).
  24. S. P. Goldman and G. W. F. Drake, “Relativistic sum rules and integral properties of the Dirac equation,” Phys. Rev. A 25, 2877–2881 (1982).
    [CrossRef]
  25. P. T. Leung and M. L. Rustgi, “Relativistic corrections to Bethe sum rule,” Phys. Rev. A 33, 2827–2829 (1986).
    [CrossRef]
  26. S. M. Cohen, “Aspects of relativistic sum rules,” Adv. Quantum Chem. 46, 241–265 (2004).
    [CrossRef]
  27. J. J. Sakurai, Modern Quantum Mechanics—Revised Edition (Addison Wesley Longman, 1994).
  28. M. G. Kuzyk, “Truncated sum rules and their use in calculating fundamental limits of nonlinear susceptibilities,” J. Nonlinear Opt. Phys. Mater. 15, 77–87 (2006).
    [CrossRef]
  29. C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: A method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
    [CrossRef]

2010

M. G. Kuzyk, “A bird’s-eye view of nonlinear-optical processes: Unification through scale invariance,” Nonlinear Opt., Quantum Opt. 40, 1–13 (2010).

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

2009

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef]

M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
[CrossRef]

2008

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
[CrossRef]

M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
[CrossRef]

2007

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

2006

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef]

M. G. Kuzyk, “Truncated sum rules and their use in calculating fundamental limits of nonlinear susceptibilities,” J. Nonlinear Opt. Phys. Mater. 15, 77–87 (2006).
[CrossRef]

2005

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

2004

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810 (2004).
[CrossRef]

S. M. Cohen, “Aspects of relativistic sum rules,” Adv. Quantum Chem. 46, 241–265 (2004).
[CrossRef]

2003

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities: erratum,” Opt. Lett. 28, 135–137 (2003).
[CrossRef]

M. G. Kuzyk, “Erratum: Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 90, 039902 (2003).
[CrossRef]

2001

M. G. Kuzyk, “Quantum limits of the hyper-Rayleigh scattering susceptibility,” IEEE J. Sel. Top. Quantum Electron. 7, 774–780 (2001).
[CrossRef]

2000

M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183–1185 (2000).
[CrossRef]

1994

J. J. Sakurai, Modern Quantum Mechanics—Revised Edition (Addison Wesley Longman, 1994).

1989

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: A method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef]

1986

P. T. Leung and M. L. Rustgi, “Relativistic corrections to Bethe sum rule,” Phys. Rev. A 33, 2827–2829 (1986).
[CrossRef]

1982

S. P. Goldman and G. W. F. Drake, “Relativistic sum rules and integral properties of the Dirac equation,” Phys. Rev. A 25, 2877–2881 (1982).
[CrossRef]

Asselberghs, I.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Beratan, D. N.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Biaggio, I.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef]

Brown, E. C.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

Bures, F.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

Cariati, E.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Clays, K.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

Coe, B. J.

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

Cohen, S. M.

S. M. Cohen, “Aspects of relativistic sum rules,” Adv. Quantum Chem. 46, 241–265 (2004).
[CrossRef]

Diederich, F.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef]

Dirk, C. W.

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: A method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef]

Drake, G. W. F.

S. P. Goldman and G. W. F. Drake, “Relativistic sum rules and integral properties of the Dirac equation,” Phys. Rev. A 25, 2877–2881 (1982).
[CrossRef]

Eisler, S.

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810 (2004).
[CrossRef]

Elliot, E.

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810 (2004).
[CrossRef]

Facchetti, A.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Goldman, S. P.

S. P. Goldman and G. W. F. Drake, “Relativistic sum rules and integral properties of the Dirac equation,” Phys. Rev. A 25, 2877–2881 (1982).
[CrossRef]

Guo, K.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

Hao, J.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

Hegmann, F. A.

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810 (2004).
[CrossRef]

Ho, S. T.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Hu, X.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Jiang, H.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Kang, H.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Keinan, S.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Kelley, A. M.

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

Kuzyk, M. C.

Kuzyk, M. G.

M. G. Kuzyk, “A bird’s-eye view of nonlinear-optical processes: Unification through scale invariance,” Nonlinear Opt., Quantum Opt. 40, 1–13 (2010).

M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef]

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
[CrossRef]

M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef]

M. G. Kuzyk, “Truncated sum rules and their use in calculating fundamental limits of nonlinear susceptibilities,” J. Nonlinear Opt. Phys. Mater. 15, 77–87 (2006).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

M. G. Kuzyk, “Erratum: Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 90, 039902 (2003).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities: erratum,” Opt. Lett. 28, 135–137 (2003).
[CrossRef]

M. G. Kuzyk, “Quantum limits of the hyper-Rayleigh scattering susceptibility,” IEEE J. Sel. Top. Quantum Electron. 7, 774–780 (2001).
[CrossRef]

M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183–1185 (2000).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: A method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef]

Leung, P. T.

P. T. Leung and M. L. Rustgi, “Relativistic corrections to Bethe sum rule,” Phys. Rev. A 33, 2827–2829 (1986).
[CrossRef]

Lim, J. H.

Liu, Z.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Liu, Z. F.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

Macchioni, A.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Marks, T. J.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

May, J. C.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef]

Michinobu, T.

Moonen, N. N. P.

Pérez Moreno, J.

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

Pérez-Moreno, J.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

Qiu, L.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

Ratner, M. A.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

Righetto, S.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Rustgi, M. L.

P. T. Leung and M. L. Rustgi, “Relativistic corrections to Bethe sum rule,” Phys. Rev. A 33, 2827–2829 (1986).
[CrossRef]

Sakurai, J. J.

J. J. Sakurai, Modern Quantum Mechanics—Revised Edition (Addison Wesley Longman, 1994).

Shen, Y.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

Slepkov, A. D.

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810 (2004).
[CrossRef]

Stern, C. L.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Szafruga, U. B.

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

Therien, M. J.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Tripathy, K.

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

Tykwinski, R. R.

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810 (2004).
[CrossRef]

Ugo, R.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Watkins, D. S.

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef]

Xiao, D.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Yang, W.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Yang, Y.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Zhao, Y.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

Zhou, J.

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef]

Zhu, P.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Zuccaccia, C.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Adv. Quantum Chem.

S. M. Cohen, “Aspects of relativistic sum rules,” Adv. Quantum Chem. 46, 241–265 (2004).
[CrossRef]

Angew. Chem., Int. Ed.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Appl. Phys. Lett.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. G. Kuzyk, “Quantum limits of the hyper-Rayleigh scattering susceptibility,” IEEE J. Sel. Top. Quantum Electron. 7, 774–780 (2001).
[CrossRef]

J. Am. Chem. Soc.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: Synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

J. Chem. Phys.

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef]

J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810 (2004).
[CrossRef]

J. Mater. Chem.

M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

M. G. Kuzyk, “Truncated sum rules and their use in calculating fundamental limits of nonlinear susceptibilities,” J. Nonlinear Opt. Phys. Mater. 15, 77–87 (2006).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem. C

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, W. Yang, and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

Nonlinear Opt., Quantum Opt.

M. G. Kuzyk, “A bird’s-eye view of nonlinear-optical processes: Unification through scale invariance,” Nonlinear Opt., Quantum Opt. 40, 1–13 (2010).

Opt. Lett.

Phys. Rev. A

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: A method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef]

S. P. Goldman and G. W. F. Drake, “Relativistic sum rules and integral properties of the Dirac equation,” Phys. Rev. A 25, 2877–2881 (1982).
[CrossRef]

P. T. Leung and M. L. Rustgi, “Relativistic corrections to Bethe sum rule,” Phys. Rev. A 33, 2827–2829 (1986).
[CrossRef]

Phys. Rev. Lett.

M. G. Kuzyk, “Erratum: Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 90, 039902 (2003).
[CrossRef]

M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
[CrossRef]

Other

J. J. Sakurai, Modern Quantum Mechanics—Revised Edition (Addison Wesley Longman, 1994).

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