Abstract

Herein, we develop a phenomenological model for microscopic cascading and substantiate it with ab initio calculations. It is shown that the concept of local microscopic cascading of a second-order nonlinearity can lead to a third-order nonlinearity, without introducing any new loss mechanisms that could limit the usefulness of our approach. This approach provides a new molecular design protocol, in which the current great successes achieved in producing molecules with extremely large second-order nonlinearity can be used in a supra molecular organization in a preferred orientation to generate very large third-order response magnitudes. The results of density functional calculations for a well-known second-order molecule, (para)nitroaniline, show that a head-to-tail dimer configuration exhibits enhanced third-order nonlinearity, in agreement with the phenomenological model which suggests that such an arrangement will produce cascading due to local field effects.

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  25. A. Dreuw and M. Head-Gordon, “Single-reference ab initio methods for the calculation of excited states of large molecules,” Chem. Rev. 105(11), 4009–4037 (2005).
    [CrossRef] [PubMed]
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2009 (3)

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[CrossRef] [PubMed]

D. Bryce and J. Autschbach, “Relativistic hybrid density functional calculations of indirect nuclear spin-spin coupling tensors. comparison with experiment for diatomic alkali metal halides,” Can. J. Chem. 87(7), 927–941 (2009).
[CrossRef]

J. Autschbach, “Charge-transfer excitations and time-dependent density functional theory: problems and some proposed solutions,” Chem. Phys. Chem. 10(11), 1757–1760 (2009).
[CrossRef] [PubMed]

2007 (2)

K. Dolgaleva, R. W. Boyd, and J. E. Sipe, “Cascaded nonlinearity caused by local-field effects in the two-level atom,” Phys. Rev. A 76(6), 063806 (2007).
[CrossRef]

A. Ye, S. Patchkovskii, and J. Autschbach, “Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis,” J. Chem. Phys. 127(7), 074104 (2007).
[CrossRef] [PubMed]

2006 (1)

A. Ye and J. Autschbach, “Study of static and dynamic first hyperpolarizabilities using time-dependent density functional quadratic response theory with local contribution and natural bond orbital analysis,” J. Chem. Phys. 125(23), 234101 (2006).
[CrossRef] [PubMed]

2005 (2)

B. Jansik, P. Salek, D. Jonsson, O. Vahtras, and H. Ågren, “Cubic response function in time-dependent density functional theory,” J. Chem. Phys. 122(5), 054107 (2005).
[CrossRef]

A. Dreuw and M. Head-Gordon, “Single-reference ab initio methods for the calculation of excited states of large molecules,” Chem. Rev. 105(11), 4009–4037 (2005).
[CrossRef] [PubMed]

2004 (1)

C. Kolleck, “Cascaded second-order contribution to the third-order nonlinear susceptibility,” Phys. Rev. A 69(5), 053812 (2004).
[CrossRef]

2003 (1)

S. Grimme and M. Parac, “Substantial errors from time-dependent density functional theory for the calculation of excited states of large pi systems,” ChemPhysChem 4(3), 292–295 (2003).
[CrossRef] [PubMed]

2000 (1)

A. Adronov, J. M. J. Fréchet, G. S. He, K.-S. Kim, S.-J. Chung, J. Swiatkiewicz, and P. N. Prasad, “Novel Two-Photon Absorbing Dendritic Structures,” Chem. Mater. 12(10), 2838–2841 (2000).
[CrossRef]

1999 (1)

C. Adamo and V. Barone, “Toward reliable density functional methods without adjustable parameters: the PBE0 model,” J. Chem. Phys. 110(13), 6158 (1999).
[CrossRef]

1998 (1)

I. D. L. Albert, T. J. Marks, and M. A. Ratner, “Remarkable NLO response and infrared absorption in simple twisted molecular π-chromophores,” J. Am. Chem. Soc. 120, 11174 (1998).
[CrossRef]

1996 (3)

Ch. Bosshard, “Cascading of second-order nonlinearities in polar materials,” Adv. Mater. 8(5), 385–397 (1996).
[CrossRef]

J. P. Perdew, K. Burke, and Y. Wang, “Generalized gradient approximation for the exchange-correlation hole of a many-electron system,” Phys. Rev. B 54(23), 16533–16539 (1996).
[CrossRef]

I. Albert, T. J. Marks, and M. A. Ratner, “Rational design of molecules with large hyperpolarizabilities. electric field, solvent polarity, and bond length alternation effects on merocyanine dye linear and nonlinear optical properties,” J. Phys. Chem. 100(23), 9714–9725 (1996).
[CrossRef]

1995 (1)

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74(14), 2816–2819 (1995).
[CrossRef] [PubMed]

1994 (1)

K. V. Mikkelsen, Y. Luo, H. Ågren, and P. Jørgensen, “Solvent induced polarizabilities and hyperpolarizabilities of para-nitroaniline studied by reaction field linear response theory,” J. Chem. Phys. 100, 8240 (1994).
[CrossRef]

1993 (2)

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear-optical processes,” Opt. Lett. 18(1), 13–15 (1993).
[CrossRef] [PubMed]

C. B. Gorman and S. R. Marder, “An investigation of the interrelationships between linear and nonlinear polarizabilities and bond-length alternation in conjugated organic molecules,” Proc. Natl. Acad. Sci. U.S.A. 90(23), 11297–11301 (1993).
[CrossRef] [PubMed]

1992 (1)

J. H. Andrews, K. L. Kowalski, and K. D. Singer, “Pair correlations, cascading, and local-field effects in nonlinear optical susceptibilities,” Phys. Rev. A 46(7), 4172–4184 (1992).
[CrossRef] [PubMed]

1981 (1)

G. R. Meredith, “Cascading in optical third-harmonic generation by crystalline quartz,” Phys. Rev. B 24(10), 5522–5532 (1981).
[CrossRef]

1974 (1)

K. Rustagi and J. Ducuing, “Third-order optical polarizability of conjugated organic molecules,” Opt. Commun. 10(3), 258–261 (1974).
[CrossRef]

1973 (1)

B. Bedeaux and N. Bloembergen, “On the relation between microscopic and microscopic nonlinear susceptibilities,” Physica 69(1), 57–66 (1973).
[CrossRef]

Adamo, C.

C. Adamo and V. Barone, “Toward reliable density functional methods without adjustable parameters: the PBE0 model,” J. Chem. Phys. 110(13), 6158 (1999).
[CrossRef]

Adronov, A.

A. Adronov, J. M. J. Fréchet, G. S. He, K.-S. Kim, S.-J. Chung, J. Swiatkiewicz, and P. N. Prasad, “Novel Two-Photon Absorbing Dendritic Structures,” Chem. Mater. 12(10), 2838–2841 (2000).
[CrossRef]

Ågren, H.

B. Jansik, P. Salek, D. Jonsson, O. Vahtras, and H. Ågren, “Cubic response function in time-dependent density functional theory,” J. Chem. Phys. 122(5), 054107 (2005).
[CrossRef]

K. V. Mikkelsen, Y. Luo, H. Ågren, and P. Jørgensen, “Solvent induced polarizabilities and hyperpolarizabilities of para-nitroaniline studied by reaction field linear response theory,” J. Chem. Phys. 100, 8240 (1994).
[CrossRef]

Albert, I.

I. Albert, T. J. Marks, and M. A. Ratner, “Rational design of molecules with large hyperpolarizabilities. electric field, solvent polarity, and bond length alternation effects on merocyanine dye linear and nonlinear optical properties,” J. Phys. Chem. 100(23), 9714–9725 (1996).
[CrossRef]

Albert, I. D. L.

I. D. L. Albert, T. J. Marks, and M. A. Ratner, “Remarkable NLO response and infrared absorption in simple twisted molecular π-chromophores,” J. Am. Chem. Soc. 120, 11174 (1998).
[CrossRef]

Andrews, J. H.

J. H. Andrews, K. L. Kowalski, and K. D. Singer, “Pair correlations, cascading, and local-field effects in nonlinear optical susceptibilities,” Phys. Rev. A 46(7), 4172–4184 (1992).
[CrossRef] [PubMed]

Assanto, G.

Autschbach, J.

J. Autschbach, “Charge-transfer excitations and time-dependent density functional theory: problems and some proposed solutions,” Chem. Phys. Chem. 10(11), 1757–1760 (2009).
[CrossRef] [PubMed]

D. Bryce and J. Autschbach, “Relativistic hybrid density functional calculations of indirect nuclear spin-spin coupling tensors. comparison with experiment for diatomic alkali metal halides,” Can. J. Chem. 87(7), 927–941 (2009).
[CrossRef]

A. Ye, S. Patchkovskii, and J. Autschbach, “Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis,” J. Chem. Phys. 127(7), 074104 (2007).
[CrossRef] [PubMed]

A. Ye and J. Autschbach, “Study of static and dynamic first hyperpolarizabilities using time-dependent density functional quadratic response theory with local contribution and natural bond orbital analysis,” J. Chem. Phys. 125(23), 234101 (2006).
[CrossRef] [PubMed]

Barone, V.

C. Adamo and V. Barone, “Toward reliable density functional methods without adjustable parameters: the PBE0 model,” J. Chem. Phys. 110(13), 6158 (1999).
[CrossRef]

Bedeaux, B.

B. Bedeaux and N. Bloembergen, “On the relation between microscopic and microscopic nonlinear susceptibilities,” Physica 69(1), 57–66 (1973).
[CrossRef]

Bloembergen, N.

B. Bedeaux and N. Bloembergen, “On the relation between microscopic and microscopic nonlinear susceptibilities,” Physica 69(1), 57–66 (1973).
[CrossRef]

Bosshard, Ch.

Ch. Bosshard, “Cascading of second-order nonlinearities in polar materials,” Adv. Mater. 8(5), 385–397 (1996).
[CrossRef]

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74(14), 2816–2819 (1995).
[CrossRef] [PubMed]

Boyd, R. W.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[CrossRef] [PubMed]

K. Dolgaleva, R. W. Boyd, and J. E. Sipe, “Cascaded nonlinearity caused by local-field effects in the two-level atom,” Phys. Rev. A 76(6), 063806 (2007).
[CrossRef]

Bryce, D.

D. Bryce and J. Autschbach, “Relativistic hybrid density functional calculations of indirect nuclear spin-spin coupling tensors. comparison with experiment for diatomic alkali metal halides,” Can. J. Chem. 87(7), 927–941 (2009).
[CrossRef]

Burke, K.

J. P. Perdew, K. Burke, and Y. Wang, “Generalized gradient approximation for the exchange-correlation hole of a many-electron system,” Phys. Rev. B 54(23), 16533–16539 (1996).
[CrossRef]

Chung, S.-J.

A. Adronov, J. M. J. Fréchet, G. S. He, K.-S. Kim, S.-J. Chung, J. Swiatkiewicz, and P. N. Prasad, “Novel Two-Photon Absorbing Dendritic Structures,” Chem. Mater. 12(10), 2838–2841 (2000).
[CrossRef]

Dolgaleva, K.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[CrossRef] [PubMed]

K. Dolgaleva, R. W. Boyd, and J. E. Sipe, “Cascaded nonlinearity caused by local-field effects in the two-level atom,” Phys. Rev. A 76(6), 063806 (2007).
[CrossRef]

Dreuw, A.

A. Dreuw and M. Head-Gordon, “Single-reference ab initio methods for the calculation of excited states of large molecules,” Chem. Rev. 105(11), 4009–4037 (2005).
[CrossRef] [PubMed]

Ducuing, J.

K. Rustagi and J. Ducuing, “Third-order optical polarizability of conjugated organic molecules,” Opt. Commun. 10(3), 258–261 (1974).
[CrossRef]

Fréchet, J. M. J.

A. Adronov, J. M. J. Fréchet, G. S. He, K.-S. Kim, S.-J. Chung, J. Swiatkiewicz, and P. N. Prasad, “Novel Two-Photon Absorbing Dendritic Structures,” Chem. Mater. 12(10), 2838–2841 (2000).
[CrossRef]

Gorman, C. B.

C. B. Gorman and S. R. Marder, “An investigation of the interrelationships between linear and nonlinear polarizabilities and bond-length alternation in conjugated organic molecules,” Proc. Natl. Acad. Sci. U.S.A. 90(23), 11297–11301 (1993).
[CrossRef] [PubMed]

Grimme, S.

S. Grimme and M. Parac, “Substantial errors from time-dependent density functional theory for the calculation of excited states of large pi systems,” ChemPhysChem 4(3), 292–295 (2003).
[CrossRef] [PubMed]

Günter, P.

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74(14), 2816–2819 (1995).
[CrossRef] [PubMed]

He, G. S.

A. Adronov, J. M. J. Fréchet, G. S. He, K.-S. Kim, S.-J. Chung, J. Swiatkiewicz, and P. N. Prasad, “Novel Two-Photon Absorbing Dendritic Structures,” Chem. Mater. 12(10), 2838–2841 (2000).
[CrossRef]

Head-Gordon, M.

A. Dreuw and M. Head-Gordon, “Single-reference ab initio methods for the calculation of excited states of large molecules,” Chem. Rev. 105(11), 4009–4037 (2005).
[CrossRef] [PubMed]

Jansik, B.

B. Jansik, P. Salek, D. Jonsson, O. Vahtras, and H. Ågren, “Cubic response function in time-dependent density functional theory,” J. Chem. Phys. 122(5), 054107 (2005).
[CrossRef]

Jonsson, D.

B. Jansik, P. Salek, D. Jonsson, O. Vahtras, and H. Ågren, “Cubic response function in time-dependent density functional theory,” J. Chem. Phys. 122(5), 054107 (2005).
[CrossRef]

Jørgensen, P.

K. V. Mikkelsen, Y. Luo, H. Ågren, and P. Jørgensen, “Solvent induced polarizabilities and hyperpolarizabilities of para-nitroaniline studied by reaction field linear response theory,” J. Chem. Phys. 100, 8240 (1994).
[CrossRef]

Kim, K.-S.

A. Adronov, J. M. J. Fréchet, G. S. He, K.-S. Kim, S.-J. Chung, J. Swiatkiewicz, and P. N. Prasad, “Novel Two-Photon Absorbing Dendritic Structures,” Chem. Mater. 12(10), 2838–2841 (2000).
[CrossRef]

Kolleck, C.

C. Kolleck, “Cascaded second-order contribution to the third-order nonlinear susceptibility,” Phys. Rev. A 69(5), 053812 (2004).
[CrossRef]

Kowalski, K. L.

J. H. Andrews, K. L. Kowalski, and K. D. Singer, “Pair correlations, cascading, and local-field effects in nonlinear optical susceptibilities,” Phys. Rev. A 46(7), 4172–4184 (1992).
[CrossRef] [PubMed]

Luo, Y.

K. V. Mikkelsen, Y. Luo, H. Ågren, and P. Jørgensen, “Solvent induced polarizabilities and hyperpolarizabilities of para-nitroaniline studied by reaction field linear response theory,” J. Chem. Phys. 100, 8240 (1994).
[CrossRef]

Marder, S. R.

C. B. Gorman and S. R. Marder, “An investigation of the interrelationships between linear and nonlinear polarizabilities and bond-length alternation in conjugated organic molecules,” Proc. Natl. Acad. Sci. U.S.A. 90(23), 11297–11301 (1993).
[CrossRef] [PubMed]

Marks, T. J.

I. D. L. Albert, T. J. Marks, and M. A. Ratner, “Remarkable NLO response and infrared absorption in simple twisted molecular π-chromophores,” J. Am. Chem. Soc. 120, 11174 (1998).
[CrossRef]

I. Albert, T. J. Marks, and M. A. Ratner, “Rational design of molecules with large hyperpolarizabilities. electric field, solvent polarity, and bond length alternation effects on merocyanine dye linear and nonlinear optical properties,” J. Phys. Chem. 100(23), 9714–9725 (1996).
[CrossRef]

Meredith, G. R.

G. R. Meredith, “Cascading in optical third-harmonic generation by crystalline quartz,” Phys. Rev. B 24(10), 5522–5532 (1981).
[CrossRef]

Mikkelsen, K. V.

K. V. Mikkelsen, Y. Luo, H. Ågren, and P. Jørgensen, “Solvent induced polarizabilities and hyperpolarizabilities of para-nitroaniline studied by reaction field linear response theory,” J. Chem. Phys. 100, 8240 (1994).
[CrossRef]

Parac, M.

S. Grimme and M. Parac, “Substantial errors from time-dependent density functional theory for the calculation of excited states of large pi systems,” ChemPhysChem 4(3), 292–295 (2003).
[CrossRef] [PubMed]

Patchkovskii, S.

A. Ye, S. Patchkovskii, and J. Autschbach, “Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis,” J. Chem. Phys. 127(7), 074104 (2007).
[CrossRef] [PubMed]

Perdew, J. P.

J. P. Perdew, K. Burke, and Y. Wang, “Generalized gradient approximation for the exchange-correlation hole of a many-electron system,” Phys. Rev. B 54(23), 16533–16539 (1996).
[CrossRef]

Prasad, P. N.

A. Adronov, J. M. J. Fréchet, G. S. He, K.-S. Kim, S.-J. Chung, J. Swiatkiewicz, and P. N. Prasad, “Novel Two-Photon Absorbing Dendritic Structures,” Chem. Mater. 12(10), 2838–2841 (2000).
[CrossRef]

Ratner, M. A.

I. D. L. Albert, T. J. Marks, and M. A. Ratner, “Remarkable NLO response and infrared absorption in simple twisted molecular π-chromophores,” J. Am. Chem. Soc. 120, 11174 (1998).
[CrossRef]

I. Albert, T. J. Marks, and M. A. Ratner, “Rational design of molecules with large hyperpolarizabilities. electric field, solvent polarity, and bond length alternation effects on merocyanine dye linear and nonlinear optical properties,” J. Phys. Chem. 100(23), 9714–9725 (1996).
[CrossRef]

Rustagi, K.

K. Rustagi and J. Ducuing, “Third-order optical polarizability of conjugated organic molecules,” Opt. Commun. 10(3), 258–261 (1974).
[CrossRef]

Salek, P.

B. Jansik, P. Salek, D. Jonsson, O. Vahtras, and H. Ågren, “Cubic response function in time-dependent density functional theory,” J. Chem. Phys. 122(5), 054107 (2005).
[CrossRef]

Sheik-Bahae, M.

Shin, H.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[CrossRef] [PubMed]

Singer, K. D.

J. H. Andrews, K. L. Kowalski, and K. D. Singer, “Pair correlations, cascading, and local-field effects in nonlinear optical susceptibilities,” Phys. Rev. A 46(7), 4172–4184 (1992).
[CrossRef] [PubMed]

Sipe, J. E.

K. Dolgaleva, R. W. Boyd, and J. E. Sipe, “Cascaded nonlinearity caused by local-field effects in the two-level atom,” Phys. Rev. A 76(6), 063806 (2007).
[CrossRef]

Spreiter, R.

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74(14), 2816–2819 (1995).
[CrossRef] [PubMed]

Stegeman, G. I.

Swiatkiewicz, J.

A. Adronov, J. M. J. Fréchet, G. S. He, K.-S. Kim, S.-J. Chung, J. Swiatkiewicz, and P. N. Prasad, “Novel Two-Photon Absorbing Dendritic Structures,” Chem. Mater. 12(10), 2838–2841 (2000).
[CrossRef]

Vahtras, O.

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Figures (5)

Fig. 1
Fig. 1

Geometry of two beta-type chromophores interacting by means of near-field dipole-dipole mechanism.

Fig. 2
Fig. 2

Head-to-head (HH) and head-to-tail (HT) configurations of (para)nitroaniline (PNA) dimer.

Fig. 3
Fig. 3

Field-Free NLMOs whose contribution amounts for the enhancement of the averaged value of the second hyperpolarizability.

Fig. 4
Fig. 4

Orientationally averaged degenerate second hyperpolarizability of HT PNA dimer vs the distance, D, between the molecular planes computed with hybrid PBE0 functional.

Fig. 5
Fig. 5

Dispersion plots of γ av.

Tables (2)

Tables Icon

Table 1 Orientationally Averaged Degenerate First and Second Hyperpolarizabilities of Isolated PNA Molecule and the Dimer, and Second Hyperpolarizability Estimated by Means of Eqs. (11) and 12

Tables Icon

Table 2 Dispersion of Orientationally Averaged Degenerate First and Second Hyperpolarizabilities of the HT Dimer (Hybrid TDDFT)

Equations (12)

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μ i = α i j E j + 1 2 ! β i j k E j E k + 1 3 ! γ i j k l E j E k E l + ,
χ ( 3 ) = L 4 N γ + 2 3 L 5 N 2 β 2 ,
p 1 = β 1 ( E 0 β ^ 1 ) 2 β ^ 1 ,
E 2 = 3 n ^ ( p 1 n ^ ) p 1 4 π ε 0 D 3 .
p 2 = β 2 ( E 0 β ^ 2 ) ( E 2 β ^ 2 ) β ^ 2 ,
p 2 = γ e f f E 0 3 ,
p 2 = 2 γ i s o E 0 3 + 2 β 1 β 2 E 0 3 4 π ε 0 D 3 ,
γ e f f = 2 γ i s o + 2 β 1 β 2 4 π ε 0 D 3 ,
γ e f f = 2 γ i s o + 2 β 2 4 π ε 0 D 3 ,
γ e f f = 2 γ i s o 2 β 2 4 π ε 0 D 3 .
γ e f f = 2 γ i s o β 2 4 π ε 0 D 3 .
γ e f f = 2 γ i s o + β 2 4 π ε 0 D 3 .

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