Document Type




Embargo Period







Quadratic electro-optic effects (dc or low frequency Kerr effect) of bacteriorhodopsin dispersed in dried gelatin thin films are examined in the near resonance region at three wavelengths: 633, 647, and 676 nm. The films show relatively large quadratic electro-optic effects compared to other molecular dispersed systems. The purple membrane is fixed within the polymerized gelatin matrix, and we show that the electronic contribution to γ dominates over possible orientational contributions. At 676 nm. the quadratic electro-optic coefficient s1133( - ω;0,0,ω) is 6.7 × 10-20 m2/V2 and the third order nonlinear susceptibility X1133(3)(-ω;0,0,ω) is 7.0 × 10-13 cm4 statCoulomb-2, with both values obtained for a protein concentration of 6.9 × 1018 cm-3. The orientationally averaged second molecular hyperpolarizability 〈γ(-ω;0.0,ω)〉 determined from the quadratic electro-optic coefficients at 676 nm assuming an Onsager ellipsoidal local field factor is (10.8±5.1)×10-32 cm7 statCoulomb-2 [(1.34±0.63) × 10-56 F3 m4C-2]. The 〈γ(- ω;0,0,ω)〉 value increases roughly tenfold when the probe wavelength is decreased to 633 nm. The behavior of γ(-ω;0,0,ω), when fit to a two-state model, predicts that γ(- ω;0,0,ω) is strongly enhanced via type III processes. Thus, the magnitude of γ(-ω;0,0,ω) is dominated by a term (Δμ210×μ210)/(ω10-ω)3, where Δμ10 is the change in dipole moment, μ10 is the transition moment, and ω10 is the transition energy of the lowest-lying allowed 1Bw*+-like π,π* state. We calculate that Δμ10 is 12.8±1.2 D, in good agreement with previous Stark and two-photon experimental values. Time-dependent Hartree-Fock methods based on the MNDO Hamiltonian yield reasonable agreement with experiment, underestimating γ(-ω;0,0,ω) by factors of only 2-4, with the error increasing as the frequency approaches resonance.

Additional Information

Copyright 1998 Journal of Chemical Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and Journal of Chemical Physics.

The article may be found at


local input

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Chemistry Commons