Segment of Retinal Molecule

Retinal molecules are the basic element in human eyes that initiates our vision. Malfunctioning of these molecules could lead to eye illness or even blindness. In order to avoid such malfunctioning, one must first understand the so-called photo-induced isomerization in retinal, or conformation change of the molecule upon excitation of light.

Figure 10.2 shows the rhodopsin structure. Isomerization occurs around the bond 11-12 with angle 011j12. Here 11 and 12 refer to the numbers of the carbon

Figure 10.2. Rhodopsin. In the actual calculation, we only use a small segment, which contains nine carbon atoms and two methyl groups along the backbone.

Figure 10.3. Ground-state potential versus angle 011j12 in a segment of rhodopsin.

ra I

-425.65

-425.71

-425.73

-425.71

eii 12 (degrees)

eii 12 (degrees)

atoms counting from the left. In the present calculations, we have employed the multiconfiguration self-consistent field (MCSCF) [8] technique to compute the ground state and two excited states by the Molpro package [9]. The basis set used for hydrogen is (4S 1P)/[2S 1P], and for carbon, (9S 4P 1D)/[3S 2P 1D] is used, where both basis functions are correlation-consistent basis sets. After Hartree-Fock iterations, these basis sets are optimized for the later MCSCF calculations. We fully optimize the molecule structure and then calculate the ground-state and excited-state potentials as a function of the dihedral angle $11,12.

In Figure 10.3, we plot the ground-state potential as a function of the dihedral angle 011j12. Note that the configuration at 011j12 = 0°corresponds to a cw-structure. A potential surface shaped like the Greek letter n is noted. The figure shows that due to the steric hindrance, the ground state has an all-trans configuration.

Within MCSCF, the excited-state potential surfaces are obtained simultaneously. The excited-state potentials are plotted in Figure 10.4. Note that in order to

Figure 10.4. Potential for the excited state versus the angle around the bond 11-12. It is importantly to note, the transition matrix elements are also accurately obtained.

Figure 10.4. Potential for the excited state versus the angle around the bond 11-12. It is importantly to note, the transition matrix elements are also accurately obtained.

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have a clear view of the change of the excited-state potentials with respect to the ground-state potential, the ground-state energies have been subtracted from the excited-state energies at each dihedral angle 011j12. One prominent feature is that those surfaces are roughly symmetric with respect to 011>12 = 90°. For the first-excited state, a minimum appears around 011>12 = 60°-120°. This minimum is very important because it provides a barrierless decay channel for the isomerization. The traditional explanation of the efficient trans ^ cis isomerization is that there is no barrier for undergoing this isomerization on excited-state potentials. Indeed, our ab initio results confirm this picture. Furthermore, we wish to present an optical reason for isomerization by calculating the dipole-matrix elements between the ground and excited states.

Those strongly dipole-allowed transitions are marked with arrows (with solid lines) in Figure 10.4, where their respective transition matrix elements are also provided [11] in Debye units. One important message from the figure is that the dipole-allowed transitions are rather selective in our model system. We focus on the first-excited state for a moment. The allowed transitions from and to the ground state appear around 011>12 = 0°, 60°, 120° and 180°, with the corresponding transition moments of 0.10D, 0.123D, 0.11D, and 0.07D, respectively. Quite large transition moments at 011j12 = 0°and 180°ensure that the system can be easily excited, which activates the initial event of isomerization. For the trans ^ cisisomerization, the most important angles are 60° and 120°, as it is around these two angles that the trans ^ cisisomerization can effectively occur. We use dashed-line arrows to show two possible decay channels: one is around 60°, and the other is around 120°(also see Figure 10.2). It is easy to see that once one reaches 60°, the molecular configuration will tend to cis and the other reaches trans.

The success of decay to the ground state at these two desired configurations is ensured by the large transition matrix elements between the ground and excited states. Note that we only consider the radiative decay. More interesting, from 011>12 = 60°-120°, the potential surface of the excited state is rather flat. This greatly facilitates not only cis ^ trans but also trans ^ cis isomerization [10]. The highly selective transitions are further supported by the fact that for those undesired configurations, such as at 011j12 = 40°, which are not favorable to isomerization, the transition elements are basically zero [11]. This means that once an electron is excited to the excited state, it is hard to decay to the ground state at these unfavorable configurations. The high selectivity greatly improves the efficiency of isomerizations, a phenomenon which is very common in biological processes [12]. Here we show the optical aspect of the high selectivity in a short polyene, which is essential to many photoinduced processes.

There are some other reasons why the isomerization is so efficient. In Figure 10.4, we also plot the second-excited-state potential as a function of 011j12. This potential has a maximum instead of minimum around 011>12 = 60-120°. From the above, we know around 011j12 = 60-120°is the particular range where the isomerization from the trans to cis configuration happens. Consequently, for the second-excited state the isomerization is not favorable. This second-excited state, however, is also virtually dipole-forbidden from the ground state, as we find the transition matrix elements are very small. This guarantees that the second-excited state cannot be excited effectively. Interestingly, the transition matrix elements between the first- and second-excited states are fairly large, so that even if there are some electrons in the second-excited state, they can quickly transit to the first-excited state and finish the isomerization. This eventually ensures a very efficient isomerization.

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