Polymers for Second-Order Nonlinear Optics - American Chemical

Chapter 4

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Solvent Effects on the Molecular Quadratic Hyperpolarizabilites I. D. L. Albert, S. di Bella, D. R. Kanis, T. J. Marks, and M. A. Ratner Department of Chemistry and the Materials Research Center, Northwestern University, Evanston, IL 60208-3113

The Self-Consistent Reaction-Field (SCRF) theory has been employed to compute thefirsthyperpolarizability of a series of organic chromophores in the presence of a solvent. The solvent effect has been included in a self-consistent fashion, and hence the effect of the solvent has been included in calculating all the properties of the chromophores, namely the transition energies, the oscillator strengths of the associated transitions, the dipole moments of all relevant states, and the hyperpolarizabilities. The quadratic hyperpolarizability has been computed using the correction vector method. The results are then compared with the previously reported values of the hyperpolarizability and the experimentally observed Second-Harmonic Generation (SHG) coefficients at an excitation energy of 0.65 eV. The results show a good agreement with the experimentally observed values for many of the molecules, although there may be some overestimation of the hyperpolari zability values in cases where the ground state dipole moment of the chromophore is large. The earlier calculations, in which only the shifts in the transition energies in the presence of the solvent were used to compute the hyperpolarizabilities of the chromo phores, appears to slightly underestimate the solvent shifts. This can be attributed the neglect of the effect of the solvent on the oscillator strengths and the dipole moments of the various states, which occur in the numerator of the Sum Over States (SOS) expression.

The development of organic materials for nonlinear optical (NLO) applications has been the subject of substantial current research". In addition to having large nonlinear susceptibilities, these materials also have other optimal properties, such as high laser damage thresholds, low dielectric constants, and ultrafast response 1

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0097-6156/95/0601-0057$12.00A) © 1995 American Chemical Society Lindsay and Singer; Polymers for Second-Order Nonlinear Optics ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

58

POLYMERS FOR SECOND-ORDER NONLINEAR OPTICS

times, which are of importance in device applications. Organic materials provide an additional advantage in that the macroscopic NLO susceptibilities of these materials are in most cases governed by the NLO characteristics of the constituent molecular chromophores, which facilitates the modelling of novel systems with optimal properties. A number of quantum chemical methods have been directed towards the understanding and rationalization of such NLO characteristics. These methods have been routinely used to estimate the NLO response of many organic molecules and to design NLO materials exhibiting optimal microscopic hyperpolarizabilities. The theoretically-estimated NLO hyperpolarizabilities are in most cases lower than the experimentally measured values. A proper comparison of the two values has been difficult owing to the difference in the environmental effects for the two determinations. While most theoretical values are calculated for an isolated molecule in the gas phase, the experimental electricfield induced second harmonic generation (EFISH) measurements are made in solution. Besides the change in the hyperpolarizability values, the solvent effects can also be seen in linear optical properties such as the energy of the opticallyallowed transition (solvatochromism) and in the corresponding oscillator strengths. Thus to obtain a meaningful comparison with the experimentally observed linear and nonlinear optical properties of these systems, one must include the effect of solvent in the calculation. There are a number of procedures for computing molecular microscopic hyperpolarizabilities in literature. Of these methods, the SOS method has been used along with many semi-empirical quantum chemical model hamiltonians, such as the PPP, CNDO, INDO, and MNDO, for calculating the NLO response of both organic and metal-organic systems. The SOS method is simply a spectral representation of the response and, as such, would produce exact results if the exact eigenstates of the full hamiltonian were used. While SOS computations using semi-empirical models correlate very well with experiment, a better comparison would be possible if the environmental effects (solvent or polymer matrix) could also be included in the calculation. A number of methods have been proposed to include solvent effects in the description of linear optical properties using continuum or semi-continuum electrostatic models based on the reaction field model . These methods have been successfully used to predict the effect of solvent on the electronic and optical properties of many organic molecules. Recently, the reaction field model has been used to calculate the hyperpolarizability of a number of molecules including acetonitrile and /?-nitroaniline in the presence of solvent using the computationally intensive ab initio techniques. In our earlier study we estimated the shift in electronic energies of some of the low-lying states of several organic chromophores in a semi-quantitative approach, and used the shifted energies to calculate approximately the solvent-induced changes in the hyperpolarizability of these molecules. In this paper, we use the reaction field model, originally proposed by Zerner et. al. for linear optical response, to compute the effect of solvent on the quadratic hyperpolarizabilities of the high-(J chromophores studied earlier. In this 4

4

5,6

7

8

9

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Lindsay and Singer; Polymers for Second-Order Nonlinear Optics ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

4.

ALBERT ET AL.

Solvent Effects on Molecular Quadratic Hyperpolarizabilites

model, a SCRF calculation is followed by a configuration interaction calculation to generate all the excited states in the presence of a dielectric continuum. The hyperpolarizabilities are then computed using the correction vector approach. Computational Scheme We present here a brief outline of the SCRF model. The details of the calculation and the computational procedure for linear optical response can be found elsewhere. In this procedure, the solute is placed in a spherical cavity immersed in a dielectric continuum, characterized by its dielectric constant. The electric field of the solute molecule polarizes the surrounding medium, and this new field in turn acts on the solute molecular system. Quantum mechanically, this gives an additional term, H , in the Hamiltonian of the isolated molecule, H . The total Hamiltonian can now be written as 6

s

G

T

H =H H

(1)

0+

where H = -l/2g(e)u*

(2)

s

The total molecular energy in the presence of the solvent can now be written as (3) T

E

2

- E - l/2/?|(\|/|u|\|/>| o

where u is the electric dipole moment operator and \|/ is the molecular wave function (higher multipole interactions can also be included, but we do not do so here). The reactionfieldoperator R, which is proportional to the dipole moment of the solute, u, can be written as R

=

(4)

The proportionality constant g is the Onsager factor, which gives the strength of the reaction field and depends on the dielectric constant of the medium, e, and can be written, in the case of a spherical cavity of radius, ao, as 3

g=2(e-l)/a (2e+l) 0

(5)

After variation, with the normalitzation of the wave function and eq. 3 as the constraints, the Fock operator in the presence of the solvent can now be written as ( F ^ ^ V l u M ) ! ^ . ) = e.fo,)


(6)

59

60


where F is the effective one-electron Fock operator of the isolated solute molecule, and is a molecular orbital, and E is the corresponding energy. X can take the value of 1.0 or 0.5, and these values leads to two levels of including the solvent into the calculation. When the value of X is set to 1.0, the solvent is considered as just providing an isothermal bath; in this case the solvent "cost" energy of l/2gu has to be added separately. No such correction is needed if the value of X is set to 0.5, when the solvent is included in the calculation (see ref. 6 for more details). We have used a value of 0.5 in all of the present calculations, and in this case the total energy is given by eq. 3. The total energy of any state n can now be written in terms of the dipole moment, u^ of the excited state n as G

t

2

£/=£„°-l/2g(e)^

(7)

The energy of an electronic transition in the presence of a solvent can also be written as 5

2

= £/-£/-l/2^(Ti )u (u -up n

n

(»

The second term in eq. 8 corrects the energy of polarization due to the finite rate response of the solvent to the dipole of the excited state n. This correction has however not been included in ouf present calculation, as the NLO coefficients are calculated using the correction vector method, where the explicit values of the excitation energies of various states are not used (essentially, one simply solves the linear inhomogeneous equations). Here T| is the refractive index, and g(rj ) is given by 2

S(Ti )=2(Ti -l)/tfW l ) 2

2

+

( 9 )

In our earlier study (we call this Method A) of including the effects of solvent on the quadratic hyperpolarizability, an equation similar to eq. 8 (although the equation used appears similar, there are significant differences, for details see ref. 9 and ref. 6(a)) was used to estimate the shift in the transition energy of all the transitions, and the shifted energies were used in the SOS expression to compute the hyperpolarizability p. This procedure provides a reasonably good estimate of the shift in transition energies, but ignores any solvent-induced change in the dipole moment or the oscillator strengths of the associated transition. In the present study (hereafter called Method B) we have included the solvent effects in the SCF procedure itself, so that the shifts in the energies as well as the changes in dipole moments and the oscillator strengths are automatically included in the calculation. This is so because the solvent shift is automatically included while forming the CI matrix. Moreover, since the NLO coefficients are computed using the correction vector method, solvent effects are also automatically included in the calculation of the NLO coefficients. Details of the correction vector method for computing linear and nonlinear optical properties can be found elsewhere . It should be pointed out that although we have not included the electron polarization term (second term of eq. 8) in this calculation, this effect need not be small. 10


4.

ALBERT ET AL.


Results and Discussion In this paper we have examined two series of organic donor-acceptor chromo phores (Chart I) dissolved in the same polar solvent (chloroform) for second order NLO effects. This solvent is chosen as there cannot be any additional directed bonding interactions such as hydrogen-bonding, and we expect only small changes in geometry. The calculated shifts in the lowest CT transitions and the shifts in the hyperpolarizabilities calculated at an excitation energy of 0.65 eVfromthe two models are given in Table 1. The values calculated from model A are taken from our earlier paper. A plot of experimental vs calculated Pvec values for the two calculations are shown in Figure 1. It can be seenfromTable 1 and Figure 1 that, while there is a large shift in the hyperpolarizabilities of molecules 1-4 of the first series of compounds, the shifts for the molecules 5-12 are much less. This is to be expected as the solvent shift included in the SCRF procedure depends mainly on the dipole moment of the molecules and since the dipole moments of molecules 1-4 are large, we find a large shift in the hyper polarizability values The solvent-dependent hyperpolarizability of all these molecules has been studied using the same level of SCRF theory by Zerner et. al. (ref. 6c), however there are some differences in the two methodologies. While the geometry of the molecules used in their paper was optimized using the semi-empirical PM3 hamiltonian and the solvent-dependent hyperpolarizability was computed using the time-dependent Hartree-Fock theory, we have used idealized geometries and computed the hyperpolarizability using the correction vector method. In addition to the above differences in the methodology, we also find some differences in the conventions used in defining p. It is worth stressing that the comparison of theoretical and experimental values of P are further made difficult by the nature of conventions used in the literature in defining p. If a proper comparison of our values with the values of Zerner et. al. (ref 6c) is to be made, our calculated P values must be multiplied by a factor of 2 and the experimental P values we have used must be multiplied by a factor of 6*0.58. The factor of 2 comesfromthe definitions of P in the two cases and factor of 6*0.58 comes because of the revised value of d (LiI0 )=-4.1pm/V, used to measure the quartz reference instead of the previous value of -7.1pm/V. After making all the corrections, we find that our slope of the experimental vs calculated P curve is 0.92. This is in excellent agreement with both the experiment and with Zerner's value of 1.07, the difference being attributed to the difference in molecular input geometries. Table 1 also shows the close agreement between models A and B in estimating the CT transition energies. However the hyperpolarizability values from the two calculations show somewhat larger differences. This is so because in model A only the shift in the transition energies of the various energy levels used in the SOS procedure is calculated. However in model B, besides including the shifts in the transition energies, the shifts in the dipole moments and the oscillator strengths of the associated transitions are also included. This, in addition to decreasing the denominator of SOS expression (which is the only factor included in model A), increases the dipole moments and the oscillator strengths and hence, the numerator of the SOS expression. Thus we see a larger increase in the computed hyperpolarizability values for model B. 12

13

31

3


61


62

CHART I

1, D = N (CH ) , 2, D = N (CH ) , 3, D = N (CH ) , 4, D = N (CH ) , 5, D = OCH , 6, D = OCH , 7, D = OCH , 3

2

3

2

3

2

3

2

3

3

3

8, D = OCH3,

A = N0 , A = N0 , A = N0 , A = N0 , A = N0 , A = N0 , A = N0 , A = N0 , 2

2

2

2

2

2

2

2

9, D = OCH , 10, D = OCH ,

n=1 n=2 n=3 n= 4 n= l n=2 n=3 n=4

A = COH, n=l A = COH, n = 2

3

3

11, D = OCH3,

A = COH, n = 3

12, D = N (CH ) , A = N0 , n = 1 3

2

2


ALBERT ET AL.


Fig. 1 Plot of computed SHG hyperpolarizability at an excitation energy of 0.65eV in the gas phase and in chloroform solution using models A and B vs experimental chloroform solution values from ref. 11. Pvec values are in 10" cm esu" 30

5

1



b

7.95 4.08 4.70 5.15 9.66

87.84

9.96

19.22

32.38

33.13

4.12

3.71

3.42

3.37

9

10

11

12

2.83

3.33

3.61

4.03

2.77

2.85

2.98

3.17

55.6

32.6

18.8

8.9

102.1

82.9

62.1

41.3

162.0

2.62

3.61 3.31 3.11

6.41 11.02

4.04

2.77

2.89

3.04

3.23

2.56

2.65

2.79

2.94

30

Model B

5.56

4.57

9.94

9.44

8.92

8.39

14.27

13.41

12.44

104.4 135.2

11.61

K

77.1

b

Pvec

2.67

2.77

2.88

Model A

2.83 1

50.14 5

3.30

3.54

3.90

2.88

2.99

3.12

3.30

2.67

2.71

2.80

2.88

44.92

24.38

11.51

160.03

116.04

79.29

49.99

287.68

210.40

141.40

93.68

Pvec" v e c

b

50.0

42.0

28.0

12.0

101.0

76.0

47.0

34.0

190.0

131.0

107.0

73.0

P

Experimental

c

"CT transition energy in eV, Vector component of the 1st Hyperpolarizability (in 10 cm esu") at an excitation energy of 0.65 eV. Ground state dipole moment in Debye. The experimental data is takenfromRef. 11. The ground state dipole moments in the gas phase are the same as those in Model A.

b

7.79

69.27

51.34

3.15

6

3.08

7.58

35.11

3.41

5

2.96

7.34

120.98

2.97

2.89

4

8

10.53 10.76

98.62

3

7

10.23

76.28

3.08

2

9.85

54.82

3.23

Kvec

B

Gas Phase

1

Molecule

Table 1, Comparison of the experimental* and the calculated linear optical properties and 1st hyperpolarizabilities of the two series of organic chromophoresfrommodels A and B in chloroform solution. The numbering of the molecules are same in chart 1.

4.

ALBERT ET AL.


To conclude, we have estimated the solvent effects on the linear optical and the first hyperpolarizabilities of two series of donor-acceptor organic chromophores using the self consistent reactionfieldmethod. We have compared these values with the values obtained using a semi-quantitative method proposed earlier. The comparison shows that the semi-quantitative method is most suitable for estimating the solvent shifts of electronic spectra and the hyperpolarizability values of molecules having relatively small dipole moments. Acknowledgements We thank Professor M. C. Zerner for the original ZINDO program. This research was sponsored by the NSF through the Northwestern Materials Research Center (Grant DMR-9120521) and by the AFOSR (Contract 93-1-0114). References 1. Molecular Nonlinear Optics: Materials, Physics, and Devices; Zyss, J., Ed.; Academic Press: Boston, 1993. 2. Prasad, P. N.; Williams, D. J. Introduction to Nonlinear Optical Effects in Molecules and Polymers; Wiley: New York, 1991. 3. Nonlinear Optical Properties of Organic Molecules and Crystals; Chemla, D.

S., Zyss, J., Eds.; Academic Press: New York, 1987 Vols. 1 and 2. 4. (a)Kanis, D. R.; Ratner, M. A.; Marks, T. J., Chem. Rev., 1994, 94, 195,(b)Kurtz, H. A.; Stewart, J. J. P.; Dieter, K. M. J. Comput. Chem. , 1990, 11, 82, (c)Docherty, V. J.; Pugh, D.; Morley, J. O. J. Chem. Soc. Faraday Trans. 2 1985, 81, 1179, (d)Svendsen, E. N., Willand, C. S.; Albrecht, A. C. J. Chem. Phys. 1985, 83, 5760, (e)Lalama, S. J.; Garito, A. F. Phys. Rev. A 1979, 20, 1179, (f)Soos, Z. G.; Ramasesha, S. J. Chem. Phys., 1989, 89, 1067, (g)Kanis, D. R.; Ratner, M. A.; Marks, T. J.; Zerner, M. C. Chem. Mater. 1991, 3, 19. 5. (a)Amos, A. T.; Burrows, B. L. Adv. Quantum chem., 1973, 7, 289. (b)McRae, E. G. J. Phys. Chem., 1957, 61, 562.

6. (a)Karelson, M. M.; Zerner, M. C. J. Phys. Chem., 1992, 96, 6949. (b)Karelson, M. M.; Zerner, M. C., J. Am. Chem. Soc., 1990, 112, 9405, (c)Yu, J.; Zerner, M. C. J. Chem. Phys., 1994, 100, 7487. 7. Willets, A.; Rice, J. E. J. Chem. Phys., 1993, 99, 426 8. (a)Mikkelsen, K. V.; Luo, Y.; Agren, H.; Jorgensen, P. J. Chem. Phys., 1994, 100, 8240, (b)ibid, Adv. Quantum Chem. (in press) 9. Di Bella, S.; Marks, T. J.; Ratner, M. A. J. Am. Chem. Soc., 1994, 116, 4440. 10. Albert, I. D. L.; Morley, J. O.; Pugh, D. J. Chem. Phys., 1993, 99, 5197. 11. Cheng, L-T.; Tam, W.; Stevenson, S. H.; Meridith, G. R.; Rikken, G.; Marder, S. R. J. Phys. Chem., 1991, 95, 10631, (b)Cheng, L-T.; Tam, W.; Marder, S. R.; Steigman, A. E.; Rikken, G.; Spangler, C. W. ibid, 1991, 95, 10643. 12. Willets, A.; Rice, J. E.; Burland, D. M.; Shelton, D. P. J. Chem. Phys., 1992, 97, 7590. 13. Eckardt, R. C.; Masuda, H.; Fan, Y. X.; Byer, R. L. IEEE J. Quantum Electron., 1990, 26, 922. RECEIVED February 20, 1995


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Polymers for Second-Order Nonlinear Optics - American Chemical

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