SOS Methods in Calculations of Electronic NLO Properties

Challenges and Advances in Computational Chemistry and Physics

Volumn 1, Issue , 2006, Pages 129-150

  Bartkowiak, Wojciech ^a   Zaleśny, Robert ^b  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b NICOLAUS COPERNICUS UNIVERSITY   (Poland)

Author keywords

First order hyperpolarizability; multiphoton absorption; nonlinear optics; second order hyperpolarizability; sum over states method

Indexed keywords

EID: 85073264749     PISSN: 25424491     EISSN: 25424483     Source Type: Book Series    
DOI: 10.1007/1-4020-4850-5_4     Document Type: Chapter

References (127)

1. Abe, J., Shirai, Y., Nemoto, N., Miyata, F., Nagase, Y.: Heterocyclic piridinium betaines, a new class of second-order nonlinear optical materials: Combined theoretical and experimental investigation of first-order hyperpolarizability through ab initio, INDO/S, and hyper-rayleigh scattering. J. Phys. Chem. B 101, 576–582 (1997)
2. Albert, I.D.L., Marks, T.J., Ratner, M.A.: Conformationally-induced geometric electron localization. Interrupted conjugation, very large hyperpolarizabilities, and sizable infrared absorption in simple twisted molecular chromophores. J. Am. Chem. Soc. 119, 3155–3156 (1997)
3. Albota, M., Beljonne, D., Brédas, J.-L., Ehrlich, J.E., Fu, J.-Y., Heikal, A.A., Hess, S.E., Kogej, T., Levin, M.D., Marder, S.R., McCord-Maughon, D., Perry, J.W., Röckel, H., Rumi, M.: Design of organic molecules with large two-photon absorption cross sections. Science 281, 1653–1656 (1998)
4. André, J.-M., Barbier, C., Bodart, V., Delhalle, J.: Trends in calculations of polarizabilities and hyperpolarizabilities of long molecules. In: Nonlinear Optical Properties of Organic Molecules and Crystals, vol. 2. Academc, New York (1987)
5. Åstrand, P.-O., Ruud, K., Sundholm, D.: A modified variation-perturbation approach to zero-point vibrational motion. Theor. Chem. Acc. 103, 365–373 (2000)
6. Bartkowiak, W.: Theoretical study of hyperpolarizabilities of aminobenzodifuranone. Synth. Met. 109, 109–111 (2000)
7. Bartkowiak, W., Lipiński, J.: Conformation and solvent dependence of the first molecular hyperpolarizability of piridinium-N-phenolate betaine dyes. Quantum chemical calculations. J. Phys. Chem. A 102, 5236–5240 (1998)
8. Bartkowiak, W., Lipiński, J.: Solvent effect on the nonlinear optical properties of para-nitroaniline studied by Langevin dipoles-Monte Carlo (LD/MC) approach. Computers Chem. 22, 31–37 (1998)
9. Bartkowiak, W., Strasburger, K., Leszczynski, J.: Studies of molecular hyperpolarizabilities (β, γ) for 4-nitroaniline (PNA). The application of quantum mechanical/Langevin dipoles/Monte Carlo (QM/LD/MC) and sum-over-orbitals (SOO) methods. J. Mol. Struct. (THEOCHEM) 549, 159–163 (2001)
10. Bartkowiak, W., Zaleśny, R., Leszczynski, J.: Relation between bond-length alternation and two-photon absorption of push-pull conjugated molecules: A quantum-chemical study. Chem. Phys. 287, 103–112 (2003)
11. Bartkowiak, W., Zaleśny, R., Niewodniczański, W., Leszczynski, J.: Quantum chemical calculations of the first-and second-order hyperpolarizability of molecules in solutions. J. Phys. Chem. A 105, 10702–10710 (2001)
12. Barzoukas, M., Runser, C., Fort, A., Blanchard-Desce, M.: A two-state description of (hyper) polarizabilities of push-pull molecules based on a two-form model. Chem. Phys. Lett. 257, 531–537 (1996)
13. Birge, R.R., Pierce, B.M.: A theoretical analysis of the two-photon properties of linear polyenes and the visual chromophores. J. Chem. Phys. 70, 165–178 (1979)
14. Bishop, D.M.: Molecular vibrational and rotational motion in static and dynamic electric field. Rev. Mod. Phys. 62, 343–374 (1990)
15. Bishop, D.M.: Explicit nondivergent formulas for atomic and molecular dynamic hyperpolarizabilities. J. Chem. Phys. 100, 6535–6542 (1994)
16. Bishop, D.M.: Molecular vibration and nonlinear optics. Adv. Chem. Phys. 104, 1–40 (1998)
17. Bishop, D.M., Champagne, B., Kirtman, B.: Relationship between static vibrational and electronic hyperpolarizabilities of σ-conjugated push-pull molecules within the two-state valence-bond charge-transfer model. J. Chem. Phys. 109, 9987–9994 (1998)
18. Bishop, D.M., Kirtman, B.: A peturbation method for calculating vibrational dynamic dipole polarizabilities and hyperpolarizabilities. J. Chem. Phys. 95, 2646–2658 (1991)
19. Bishop, D.M., Kirtman, B., Champagne, B.: Differences between the exact sum-over-states and the canonical approximation for the calculation of static and dynamic hyperpolarizabilities. J. Chem. Phys. 103, 365–373 (1997)
20. Bishop, D.M., Norman, P.: Calculations of dynamic hyperpolarizabilities for small and medium sized molecules. In: Handbook of Advanced Electronic and Photonic Materials and Devices, vol. 9. Academic, San Diego (2001)
21. Blanchard-Desce, M., Barzoukas, M.: Two-form two-state analysis of polarizabilities of push-pull molecules. J. Opt. Soc. Am. B 15, 302–307 (1998)
22. Bourhill, G., Brédas, J.L., Cheng, L.-T., Marder, S.R., Meyers, F., Perry, J.W., Tiemann, B.G.: Experimental demonstration of the dependence of the first hyperpolarizability of donor-acceptor-substituted polyenes on the ground-state polarization and bond length alternation. J. Am. Chem. Soc. 116, 2619–2620 (1994)
23. Brédas, J.L., Adant, C., Tackx, P., Persoons, A.: Third-order nonlinear optical response in organic materials: Theoretical and experimental aspects. Chem. Rev. 94, 243–278 (1994)
24. Bursi, R., Lankhorst, M., Feil, D.: Uncoupled Hartree-Fock calculations of the polarizability and hyperpolarizabilities of nitrophenols. J. Comp. Chem. 16, 545–562 (1995)
25. Champagne, B., Jacquemin, D., André, J.-M., Kirtman, B.: Ab initio coupled Hartree-Fock investigation of the static first hyperpolarizability of model all-trans-polymethineimine oligomers of increasing size. J. Phys. Chem. A 101, 3158–3165 (1997)
26. Champagne, B., Kirtman, B.: Theoretical approach to the design of organic molecular and polymeric nonlinear optical materials. In: Handbook of Advanced Electronic and Photonic Materials and Devices, vol. 9. Academic, San Diego (2001)
27. Chen, G., Lu, D., Goddard, III, W.A.: Valence-bond charge-transfer solvation model for nonlinear optical properties of organic molecules in polar solvents. J. Chem. Phys. 101, 5860–5864 (1994)
28. Cohen, H.D., Roothaan, C.C.J.: Electric dipole polarizability of atoms by the Hartree-Fock method. I. Theory for closed-shell systems. J. Chem. Phys. 43, S34–S39 (1965)
29. Cronstrand, P., Luo, Y., Ågren, H.: Generalized few-state models for two-photon absorption of conjugated molecules. Chem. Phys. Lett. 352, 262–269 (2002)
30. Cronstrand, P., Norman, P., Luo, Y., Ågren, H.: Few-states models for three-photon absorption. J. Chem. Phys. 121, 2020–2029 (2004)
31. Dalgarno, A.: Perturbation theory for atomic systems. Proc. Roy. Soc. (London) A251, 282–290 (1959)
32. Dalgarno, A., McNamee, J.M.: Calculation of polarizabilities and shielding factors. J. Chem. Phys. 35, 1517–1518 (1961)
33. Dehu, C., Meyers, F., Hendrickx, E., Clays, K., Persoons, A., Marder, S.R., Brédas, J.L.: Solvent effects on the second-order nonlinear optical response of -conjugated molecules: A combined evaluation through self-consistent reaction field calculations and hyper-Rayleigh scaterring measurements. J. Am. Chem. Soc. 117, 10127–10128 (1995)
34. Di Bella, S., Marks, T.J., Ratner, M.A.: Environmental efects on nonlinear optical chromophore performance. Calculation of molecular quadratic hyperpolarizabilities in solvating media. J. Am. Chem. Soc. 116, 4440–4445 (1994)
35. Dick, B., Hohlneicher, G.: Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules. J. Chem. Phys. 76, 5755–5760 (1982)
36. Dirk, C.W., Cheng, L.-T., Kuzyk, M.G.: A simplified three-level model describing the molecular third-order nonlinear optical susceptibility. Int. J. Quant. Chem. 43, 27–36 (1992)
37. Fanti, M., Fowler, P.W., Orlandi, G., Zerbetto, F.: Ab initio scaling of the second hyperpolarizability of carbon cages. J. Chem. Phys. 107, 5072–5075 (1997)
38. Freo, L. Del, Terenziani, F., Painelli, A.: Static nonlinear optical susceptibilities: Testing approximation schemes against exact results. J. Chem. Phys. 116, 755–761 (2002)
39. Hamada, T.: Ab initio estimation of quadratic hyperpolarizabilities of organic molecules: Sum over states vs. coupled perturbed Hartree-Fock. Nonlinear Optics 16, 279–289 (1996)
40. Hameka, H.F.: Calculation of linear and nonlinear electric susceptibilities of conjugated hydrocarbon chains. J. Chem. Phys. 67, 2935–2942 (1977)
41. Hrobarik, P., Zahradnik, P., Fabian, W.M.F.: Computational design of benzothiazole-derived push-pull dyes with high molecular quadratic hyperpolarizabilities. Phys. Chem. Chem. Phys. 6, 495–501 (2004)
42. Jacquemin, D., Champagne, B., André, J.-M.: Molecular orbital expressions for approximate uncoupled Hartree-Fock second hyperpolarizabilities. A Pariser-Parr-Pople assessment for model polyacetylene chains. Chem. Phys. 197, 107–127 (1995)
43. Kanis, D.R., Marks, T.J., Ratner, M.A.: Calculation and electronic description of molecular quadratic hyperpolarizabilities employing the ZINDO-SOS quantum chemical formalism. Chromophore architecture and substituent effects. Nonlinear Optics 6, 317–335 (1994)
44. Keinan, S., Zojer, E., Brédas, J.-L., Ratner, M.A., Marks, T.J.: Twisted -system electro-optic chromophores. A CIS vs. MRD-CI theoretical investigation. J. Mol. Struct. (Theochem) 633, 227–235 (2003)
45. Kobko, N., Masunov, A., Tretiak, S.: Calculations of the third-order nonlinear optical responses in push-pull chromophores with a time-dependent density functional theory. Chem. Phys. Lett. 392, 444–451 (2004)
46. Kogej, T., Beljonne, D., Meyers, F., Perry, J.W., Marder, S.R., Brédas, J.L.: Mechanism for enhancement of two-photon absorption in donor-acceptor conjugated chromophores. Chem. Phys. Lett. 298, 1–6 (1998)
47. Kurtz, H.J., Stewart, J.J.P., Dieter, K.M.: Calculation of the nonlinear optical properties of molecules. J. Comp. Chem. 11, 82–87 (1990)
48. Kuzyk, M.G., Dirk, C.W.: Effects of centrosymmetry on the nonresonant electronic third-order nonlinear optical susceptibility. Phys. Rev. A 41, 5098–5109 (1990)
49. Lalama, S.J., Garito, A.F.: Origin of the nonlinear second-order optical susceptibility of organic systems. Phys. Rev. A 20, 1179–1194 (1979)
50. Langhoff, P.W., Karplus, M., Hurst, R.P.: Approximations to Hartree-Fock perturbation theory. J. Chem. Phys. 44, 505–514 (1966)
51. Lee, W.-H., Lee, H., Kim, J.-A., Choi, J.-H., Cho, M., Jeon, S.-J., Cho, B.R.: Two-photon absorption and nonlinear optical properties of octupolar molecules. J. Am. Chem. Soc. 123, 10658–10667 (2001)
52. Li, D., Marks, T.J., Ratner, M.A.:  electron calculations for prediciting non-linear optical properties of molecules. Chem. Phys. Lett. 131, 370–375 (1986)
53. Li, D., Ratner, M., Marks, T.J.: Molecular and macromolecular nonlinear optical materials. Probing architecture/electronic structure/frequency doubling relationship via SCF-LCAO MECI π electron formalism. J. Am. Chem. Soc. 110, 1707–1715 (1988)
54. Liebmann, S.P., Moskowitz, J.W.: Polarizabilities and hyperpolarizabilities of small polyatomic molecules in the uncoupled Hartree-Fock approximation. J. Chem. Phys. 54, 3622–3631 (1971)
55. Lipiński, J.: Modified all-valence INDO/spd method for ground and excited state properties of isolated molecules and molecular complexes. Int. J. Quant. Chem. 34, 423–434 (1988)
56. Lipiński, J.: On the consequences of the violation of the Hellmann-Feynman theorem in calculations of electric properties of molecules. Chem. Phys. Lett. 363, 313–318 (2002)
57. Lipiński, J., Bartkowiak, W.: Conformation and solvent dependence of the first and second molecular hyperpolarizabilities of charge-transfer chromophores. Quantum-chemical calculations. Chem. Phys. 245, 263–276 (1999)
58. Liu, X.-J., Feng, J.-K., Ren, A.-M., Zhou, X.: Theoretical studies of the spectra and two-photon absorption cross section for porphyrin and carbaporphirin. Chem. Phys. Lett. 373, 197–206 (2003)
59. Lu, D., Chen, G., Perry, J.W., Goddard, III, W.A.: Valence-bond charge-transfer model for nonlinear optical properties of charge-transfer organic molecules. J. Am. Chem. Soc. 116, 10679– 10685 (1994)
60. Luis, J.M., Martí, J., Duran, M., Andrés, J.L.: Nuclear relaxation and vibrational contributions to the static electrical properties of polyatomic molecules: Beyond the Hartree-Fock approximation. Chem. Phys. 217, 29–42 (1997)
61. 1u two-photon spectrum of benzene. Chem. Phys. Lett. 209, 513–518 (1993)
62. Luo, Y., Ågren, H., Vahtras, O.: The hyperpolarizability dispersion of para-nitroaniline. Chem. Phys. Lett. 207, 190–194 (1993)
63. Luo, Y., Norman, P., Macak, P., Ågren, H.: Solvent-induced two-photon absorption of a push-pull molecule. J. Phys. Chem. A 104, 4718–4722 (2000)
64. Göppert-Mayer, M.: Über Elementarakte mit zwei Quantensprungen. Ann. Phys. 9, 273–294 (1931)
65. Macak, P., Luo, Y., Ågren, H.: Simulations of vibronic profiles in two-photon absorption. Chem. Phys. Lett. 330, 447–456 (2000)
66. Macak, P., Luo, Y., Norman, P., Ågren, H.: Electronic and vibronic contributions to two-photon absorption of molecules with multi-branched structures. J. Chem. Phys. 113, 7055–7061 (2000)
67. Marchese, F.T., Seliskar, C.J., Jaffé, H.H.: The use of CNDO in spectroscopy. XV. Two-photon absorption. J. Chem. Phys. 72, 4149–4203 (1980)
68. Marder, S.R., Beratan, D.N., Cheng, L.-T.: Approaches for optimizing the first electronic hyperpolarizability of conjugated organic molecules. Science 252, 103–106 (1991)
69. Marder, S.R., Cheng, L.-T., Tiemann, B.G., Friedli, A.C., Blanchard-Desce, M., Perry, J.W., Skindhøj, J.: Large first hyperpolarizability in push-pull polyenes by tuning of the bond length alternation and aromaticity. Science 263, 511–514 (1994)
70. Marder, S.R., Gorman, C.B., Meyers, F., Perry, J.W., Bourhill, G., Brédas, J.-L., Pierce, B.M.: A unified description of linear and nonlinear polarization in organic polymethine dyes. Science 265, 632–635 (1994)
71. Marder, S.R., Gorman, C.B., Tiemann, B.G., Cheng, L.-T.: Stronger acceptors can diminish nonlinear optical response in simple donor-acceptor polyenes. J. Am. Chem. Soc. 115, 3006–3007 (1993)
72. Marder, S.R., Perry, J.W., Bourhill, G., Gorman, C.B., Tiemann, B.G., Mansour, K.: Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules. Science 261, 186–189 (1993)
73. Marder, S.R., Perry, J.W., Tiemann, B.G., Gorman, C.B., Gilmour, S., Biddle, S.L., Bourhill, G.: Direct observation of reduced bond length alternation in donor/acceptor polyenes. J. Am. Chem. Soc. 115, 2524–2526 (1993)
74. Masunov, A., Tretiak, S.: Prediction of two-photon absorption properties for organic chromophores using time-dependent density-functional theory. J. Phys. Chem. B 108, 899–907 (2004)
75. McClain, W.M., Harris, R.A.: Two-photon molecular spectroscopy in liquid and gases. In: Excited States, vol. 3. Academc, New York (1977)
76. McIntyre, E.F., Hameka, H.F.: Calculation of nonlinear electric susceptibilities of aromatic hydrocarbon chains. J. Chem. Phys. 68, 5534–5537 (1978)
77. McIntyre, E.F., Hameka, H.F.: Extended basis set calculations of nonlinear susceptibilities of conjugated hydrocarbons. J. Chem. Phys. 69, 4814–4820 (1978)
78. McIntyre, E.F., Hameka, H.F.: Improved calculation of nonlinear electric susceptibilities of conjugated hydrocarbon chains. J. Chem. Phys. 68, 3481–3484 (1978)
79. Meyers, F., Brédas, J.L., Pierce, B.M., Marder, S.R.: Nonlinear optical properties of donor-acceptor polyenes: Frequency-dependent calculations of the relationship among molecular polarizabilities, (α, β and γ), and bond-length alternation. Nonlinear Optics 14, 61–71 (1995)
80. Meyers, F., Marder, S.R., Pierce, B.M., Brédas, J.L.: Electric field modulated nonlinear optical properties of donor-acceptor polyenes: Sum-over-states investigation of the relationship between molecular polarizabilities (α, β and γ) and bond length alternation. J. Am. Chem. Soc. 116, 10703–10714 (1994)
81. Monson, P.R., McClain, W.M.: Polarization dependence of the two-photon absorption of tumbling molecules with application to liquid 1-chloronaphtalene and benzene. J. Chem. Phys. 53, 29–37 (1970)
82. Morell, J.A., Albrecht, A.C.: Second-order hyperpolarizability of p-nitroaniline calculated from perturbation theory based expression using CNDO/S generated electronic states. Chem. Phys. Lett. 64, 46–50 (1979)
83. Morley, J.O., Pavlides, P., Pugh, D.: On the calculation of the hyperpolarizabilities of organic molecules by the sum over virtual excited states method. Int. J. Quant. Chem. 43, 7–26 (1992)
84. Mulliken, R.S.: Molecular compunds and their spectra. II. J. Am. Chem. Soc. 74, 811–824 (1952)
85. Musher, J.I.: Hartree-Fock theory of atomic properties. J. Chem. Phys. 46, 369–372 (1967)
86. Norman, P., Cronstrand, P., Ericsson, J.: Theoretical study of linear and nonlinear absorption in platinum-organic compounds. Chem. Phys. 285, 207–220 (2002)
87. Norman, P., Luo, Y., Ågren, H.: Large two-photon absorption cross sections in two-dimensional, charg-transfer, cumulene-containing aromatic molecules. J. Chem. Phys. 111, 7758–7765 (1999)
88. O’Hare, J.M., Hurst, R.P.: Hyperpolarizabilities of some polar diatomic molecules. J. Chem. Phys. 46, 2356–2366 (1967)
89. Olsen, J., Jørgensen, P.: Linear and nonlinear response functions for an exact state and for and MCSCF state. J. Chem. Phys. 82, 3235–3264 (1985)
90. Olsen, J., Jørgensen, P.: Time-dependent response theory with applications to self-consistent field and multiconfigurational self-consistent field wave functions. In: Modern Electronic Structure Theory, vol. 2. World Scientific, Singapore (1995)
91. Orr, B.J., Ward, J.F.: Perturbation theory of the non-linear optical polarization of an isolated system. Mol. Phys. 20, 513–526 (1971)
92. Otto, P., Gu, F.L., Ladik, J.: Calculation of ab initio dynamic hyperpolarizabilities of polymers. J. Chem. Phys. 110, 2717–2726 (1999)
93. Oudar, J.L.: Optical nonlinearities of conjugated molecules. Stilbene derivatives and highly polar aromatic compounds. J. Chem. Phys. 67, 446–457 (1977)
94. Oudar, J.L., Chemla, D.S.: Hyperpolarizabilities of the nitroanilines and their relations to the excited state dipole moment. J. Chem. Phys. 66, 2664–2668 (1977)
95. Pati, S.K., Marks, T.J., Ratner, M.A.: Conformationally tuned large two-photon absorption cross sections in simple molecular chromophores. J. Am. Chem. Soc. 123, 7287–7291 (2001)
96. Peticolas, W.L., Goldsborough, J.P., Rieckhoff, K.E.: Double photon exctation in organic crystals. Phys. Rev. Lett. 10, 43–45 (1963)
97. Peticolas, W.L., Rieckhoff, K.E.: Double-photon excitation on organic molecules in dilute solution. J. Chem. Phys. 39, 1347–1348 (1963)
98. Pierce, B.M.: A theoretical analysis of third-order nonlinear optical properties of linear polyenes and benzene. J. Chem. Phys. 91, 791–811 (1989)
99. Quinet, O., Kirtman, B., Champagne, B.: Analytical time-dependent Hartree-Fock evaluation of the dynamic zero-point vibrationally averaged (ZPVA) first hyperpolarizability. J. Chem. Phys. 118, 505–513 (2003)
100. Sadlej, A.J.: Perturbation theory of the electron correlation effects for atomic and molecular properties. J. Chem. Phys. 75, 320–331 (1981)
101. Sałek, P., Vahtras, O., Guo, J., Luo, Y., Helgaker, T., Ågren, H.: Calculations of two-photon absorption cross sections by means of density-functional theory. Chem. Phys. Lett. 374, 446–452 (2003)
102. Sałek, P., Vahtras, O., Helgaker, T., Ågren, H.: Density-functional theory of linear and nonlinear time-dependent molecular properties. J. Chem. Phys. 117, 9630–9645 (2002)
103. 70: A valence-effective-Hamiltonian study. Phys. Rev. B 46, 16135–16141 (1992)
104. Sim, F., Chin, S., Dupuis, M., Rice, J.E.: Electron correlation effects in hyperpolarizabilities of p-nitroaniline. J. Phys. Chem. 97, 1158–1163 (1993)
105. zxx. Chem. Phys. Lett. 215, 45–52 (1993)
106. zxx. J. Mol. Struct.: (Theochem) 311, 221–232 (1994)
107. Tomonari, M., Ookubo, N., Takada, T., Feyereisen, M.W., Almlöf, J.: Simplified sum-over-states calculations and missing-orbital analysis on hyperpolarizabilities of benzene derivatives. Chem. Phys. Lett. 203, 603–610 (1993)
108. Tretiak, S., Chernyak, V.: Resonant nonlinear polarizabilities in the time-dependent density functional theory. J. Chem. Phys. 119, 8809–8823 (2003)
109. Tretiak, S., Mukamel, S.: Density matrix analysis and simulation of electronic excitations in conjugated and aggregated molecules. Chem. Rev. 102, 3171–3212 (2002)
110. Tuan, D.F.-T., Epstein, S.T., Hirschfelder, J.O.: Improvements of uncoupled Hartree-Fock expectations values for physical properties. J. Chem. Phys. 44, 431–433 (1966)
111. Velders, G.J.M., Gillet, J.-M., Becker, P.J., Feil, D.: Electron density analysis of nonlinear optical materials. An ab initio study of different conformations of benzene derivatives. J. Phys. Chem. 95, 8601–8606 (1991)
112. Wang, C.-K., Macak, P., Luo, Y., Ågren, H.: Effects of π centers and symmetry on two-photon absorption cross sections of organic chromophores. J. Chem. Phys. 114, 9813–9820 (2001)
113. Ward, J.F.: Calculation of nonlinear optical susceptibilities using diagrammatic perturbation theory. Rev. Mod. Phys. 37, 1–18 (1965)
114. Warshel, A., Weiss, R.M.: An empirical valence bond approach for comparing reactions in solutions and in enzymes. J. Am. Chem. Soc. 102, 6218–6226 (1980)
115. Willets, A., Rice, J.E., Burland, D.M., Shelton, D.P.: Problems in the comparison of theoretical and experimental hyperpolarizabilities. J. Chem. Phys. 97, 7590–7599 (1992)
116. Xie, R.-H.: Empirical exponent law of the second-order hyperpolarizability in small armchair and zig–zag nanotubes. J. Chem. Phys. 108, 3626–3629 (1998)
117. 60 –derived nanotubes in infrared. Chem. Phys. Lett. 280, 66–72 (1997)
118. Zaleśny, R., Bartkowiak, W., Leszczynski, J.: Theoretical study of the two-photon absorption in phtochromic fulgides. J. Luminescence 105, 111–116 (2003)
119. Zaleśny, R., Bartkowiak, W., Styrcz, S., Leszczynski, J.: Solvent effects on conformationally induced enhancement of the two-photon absorption cross section of a pyridinium-N-phenolate betaine dye. A quantum-chemical study. J. Phys. Chem. A 106, 4032–4037 (2002)
120. Zaleśny, R., Sadlej, A.J., Leszczynski, J.: Size-nonextensive contributions in singles-only CI. Struct. Chem. 15, 379–384 (2004)
121. Zamani-Khamiri, O., Hameka, H.F.: Polarizability calculations with the SCF method. I. Linear and dynamic polarizabilities of conjugated hydrocarbons and aromatics. J. Chem. Phys. 71, 1607–1610 (1979)
122. Zamani-Khamiri, O., Hameka, H.F.: Polarizability calculations with the SCF method. IV. Various conjugated hydrocarbons. J. Chem. Phys. 73, 5693–5697 (1980)
123. Zamani-Khamiri, O., McIntyre, E.F., Hameka, H.F.: Polarizability calculations with the SCF method. II. The benzene molecule. J. Chem. Phys. 72, 1280–1284 (1980)
124. Zamani-Khamiri, O., McIntyre, E.F., Hameka, H.F.: Polarizability calculations with the SCF method. III. Ethylene, butadiene, and hexatriene. J. Chem. Phys. 72, 5906–5908 (1980)
125. Zhou, X., Ren, A.-M., Feng, J.-K., Liu, X.-J.: A comparative study of the two-photon absorption properties of a new octupolar molecule – truxeone derivative and relative molecules. Chem. Phys. Lett. 373, 167–175 (2003)
126. Zhou, X., Ren, A.-M., Feng, J.-K., Liu, X.-J., Zhang, J., Liu, J.: One-and two-photon absorption properties of novel multi-branched molecules. Phys. Chem. Chem. Phys. 4, 4346–4352 (2002)
127. Zhou, Y.-F., Wang, X.-M., Zhao, X., Jiang, M.-H.: A quantum-chemical INDO/CI method for calculating two-photon cross sections. J. Phys. Chem. Sol. 62, 1075–1079 (2001)