Mechanisms of the excited state dynamics for the cis-trans photoisomerization of bacteriorhodopsin are investigated by analyzing the temperature dependence of the time-correlation function (tcf) of the modified vibrational wave packet which is obtained by the Fourier transform of the experimentally observed optical absorption spectra at 273,233, 193, 133, and 78 K. Remarkable temperature dependences of tcf are obtained, especially at the very initial time region up to about 60 fs: The peak at 27 fs, which is clearly observed at 78 K, becomes weak gradually as temperature increases, and instead a deep minimum is created around 30 fs at higher temperatures. We also observed a progression of some maxima with periods of 27-30 fs at lower temperatures (78 and 133 K) and a progression of global maxima with a period of about 60 fs at higher temperatures (233 and 273 K). The implication of these remarkable temperature dependent properties of tcf is discussed in relation to the possible role the protein environment played in the molecular mechanism of the specific, ultrafast photoisomerization reaction of bacteriorhodopsin.

We investigated the excited-state dynamics of the cis-trans photoisomerization of rhodopsin by analyzing deuterium substitution effects for hydrogen atoms bonded to C 11 and C 12 of the retinal chromophore by the method of Fourier transform of optical absorption spectra (FTOA). Plotting the absolute value of the time correlation function of modified vibrational wave packet, we found that the deuterium substitution effects do not appear in the excited-state dynamics until about 20 fs after photon absorption, weakly appear in the time range 20-60 fs, significantly appear in the time range 70-110 fs, and complicatedly appear in the time range 110-170 fs. By analyzing those deuterium substitution effects, we obtained a result that the concerted motions of hydrogen out-of-plane (HOOP) waggings at C 11 and C 12 , which are found to exist in native rhodopsin in the time range 20-60 fs, do not contribute to the excited-state dynamics in its time range appreciably and that the coupled motions of hydrogen atoms at C 11 and C 12 , which are significantly coupled with the skeletal twisting motion of the chromophore in the time range 70-110 fs, contribute to the excited dynamics in its time range substantially. The hydrogen motions after 110 fs contribute to the excited-state dynamics in a complicate way. This cis-trans photoisomerization process of rhodopsin is basically similar to that of bacteriorhodopsin, which was obtained by the comparative analysis of the FTOA of 13-trans-lockedbacteriorhodopsin with native bacteriorhodopsin. † Abbreviations: CHAPS, 3-[(3-cholamidopropyl)dimethylammonio]-1propanesulfonate; PC, L-R-phosphatidylcholine from fresh egg yolk; HEPES, N-(2-hydroxyethyl)piperazine-N′-2-ethanesulfonic acid.

Optical absorption spectra of 13-trans-locked-bacteriorhodopsin, which contains a chemically modified retinal chromophore inhibiting photoisomerization, were obtained at five temperatures. Analysis of the excitedstate dynamics of the time-correlation function (tcf) of the modified wavepacket was made by the Fourier transform of the optical absorption spectra. Even though the photoisomerization of the chromophore was inhibited, the normalized tcf decayed rapidly until the level of about 10 -6 at 200 fs almost independently of the temperature. The ratio of the tcf between 13-trans-locked-bacteriorhodopsin and native bacteriorhodopsin displayed some oscillations. Its mean value was close to 1 until about 100 fs, and it increased gradually up to the level of 10 0.5-10 1 at about 200 fs. Namely, the excited-state dynamics of 13-trans-lockedbacteriorhodopsin appears globally quite similar to that of native bacteriorhodopsin up to about 100 fs, and the difference of them becomes slightly evident after 100 fs up to about 200 fs. Those data suggest that the excited-state dynamics of bacteriorhodopsin is not solely determined by the conformation change of the chromophore but also by another factor such as the movement of the microenvironment of the protein.

Abstract— We significantly improved the analytical method for the study of excited state dynamics of pigments, by means of the time correlation function (tcf) of the vibrational wavepacket which is produced by the Fourier transform of experimentally obtained optical absorption spectra (FTOA). Applying the tcf method to the spectra of rhodopsin at 0°C and ‐180°C, we observed specific peaks which are slightly different between 0°C and ‐180°C in the early time region (1–130 fs) of the absolute value of tcf, representing a characteristic propagation of the wavepacket along a reaction coordinate pertinent to the cis‐trans photoisomerization of the chromophore accompanying the motion of protein moiety. From the analysis of phase angle propagation, we obtained a rather small relaxation energy, 6–7 kcal/mol. Based on these results, we can say that FTOA analysis is useful as one of the most powerful techniques for the study of very early procedures in the excited state dynamics of pigments.

Periodic trends in relativistic effects are investigated from 1 H through 103 Lr using Dirac–Hartree–Fock and nonrelativistic Hartree–Fock calculations. Except for 46 Pd (4d 10 ) (5s 0 ), all atoms have as outermost shell the ns or n’p spinors/orbitals. We have compared the relativistic spinor energies with the corresponding nonrelativistic orbital energies. Apart from 24 Cr (3d 5 ) (4s 1 ), 41 Nb (4d 4 ) (5s 1 ), and 42 Mo (4d 5 ) (5s 1 ), the ns + spinor energies are lower than the corresponding ns orbital energies for all atoms having ns spinor (ns + ) as the outermost shell, as some preceding works suggested. This indicates that kinematical effects are larger than indirect relativistic effects (the shielding effects of the ionic core plus those due to electron–electron interactions among the valence electrons). For all atoms having np + spinors as their outermost shell, in contrast, the np + spinor energies are higher than the corresponding np orbital energies as again the preceding workers suggested. This implies that indirect relativistic effects are greater than kinematical effects. In the neutral light atoms, the np – spinor energies are close to the np + spinor energies, but for the neutral heavy atoms, the np – spinor energies are considerably lower than the np + spinor energies (similarly, the np – spinors are considerably tighter than the np + spinors), indicating the importance of the direct relativistic effects in np – . In the valence nd and nf shells, the spinor energies are always higher than the corresponding orbital energies, except for 46 Pd (4d 10 ) (5s 0 ). Correspondingly, the nd and nf spinors are more diffuse than the nd and nf orbitals, except for 46 Pd.