Curl equations as substratum for the derivation of the electronic nonadiabatic coupling terms

The idea to derive the nonadiabatic coupling terms by solving the Curl equations (Avery, J.; Baer, M.; Billing, G. D. Mol Phys 2002, 100, 1011) is extended to a three‐state system where the first and second states form one conical intersection, i.e., τ₁₂ and the second and the third states form another conical intersection, i.e., τ₂₃. Whereas the two‐state Curl equations form a set of linear differential equations, the extension to a three‐state system not only increases the number of equations but also leads to nonlinear terms. In the present study, we developed a perturbative scheme, which guarantees convergence if the overlap between the two interacting conical intersections is not too strong. Among other things, we also revealed that the nonadiabatic coupling term between the first and third states, i.e., τ₁₃ (such interactions do not originate from conical intersection) is formed due to the interaction between τ₁₂ and τ₂₃. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

About the intrinsic photochemical properties of the 11-cis retinal chromophore: computational clues for a trap state and a lever effect in Rhodopsin catalysis

CASPT2//CASSCF/6-31G* computations are used on the singlet S ₁ and S ₂ states to map the photoisomerization process of the 11-cis retinal protonated Schiff base in vacuo and to characterize its optical properties. It is shown that the spectroscopic observations recorded in Rhodopsin are reproduced quite well, calling for a substantially neutral effect of the protein. Furthermore, a rationale is proposed for the unreactive population recently observed in Rhodopsin, which is here addressed to the accessible S ₂ state, behaving as a trap. The experimental transient absorption and (absorption-wavelength dependent) emission are discussed and interpreted under the light of this novel model. Finally, a planarization of the β-ionone ring is observed on S ₁, which may cause a steric lever effect into the protein pocket, thus assisting photoisomerization catalysis. The reported results constitute a solid reference for further studies aimed to rationalize the effect of the environment on the photochemical reactivity of retinal chromophores. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Contribution to the Fernando Bernardi Memorial Issue.     

Intersystem crossing at singlet conical intersections

The energy of the lowest triplet state of organic molecules is intermediate between the ground state and the first excited singlet. At the S₁/S₀ conical intersection, the two singlet states are degenerate. It is shown that for some molecules (ethylene, benzene, toluene and pyrrole) the T₁ state is also degenerate with the two singlet states. Moreover, the spin orbit coupling matrix element at this structure is necessarily large, so that intersystem crossing can be quite efficient. If the lowest triplet state is repulsive (as in the studied molecules) it may significantly contribute to the dissociation yield under certain experimental conditions.     

On the critical exponent for random walk intersections

The exponent _d for the probability of nonintersection of two random walks starting at the same point is considered. It is proved that 1/2<₂3/4. Monte Carlo simulations are done to suggest ₂=0.61 and ₃0.29.     

Femtochemistry of trans‐Azomethane: A Combined Experimental and Theoretical Study

The dissociation dynamics of trans‐azomethane upon excitation to the S₁(n,π*) state with a total energy of 93 kcal mol^?1 is investigated using femtosecond‐resolved mass spectrometry in a molecular beam. The transient signal shows an opposite pump–probe excitation feature for the UV (307 nm) and the visible (615 nm) pulses at the perpendicular polarization in comparison with the signal obtained at the parallel polarization: The one‐photon symmetry‐forbidden process excited by the UV pulse is dominant at the perpendicular polarization, whereas the two‐photon symmetry‐allowed process initiated by the visible pulse prevails at the parallel polarization. At the perpendicular polarization, we found that the two C? N bonds of the molecule break in a stepwise manner, that is, the first C? N bond breaks in ≈70 fs followed by the second one in ≈100 fs, with the intermediate characterized. At the parallel polarization, the first C? N bond cleavage was found to occur in 100 fs with the intensity of the symmetry‐allowed transition being one order of magnitude greater than the intensity of the symmetry‐forbidden transition at the perpendicular polarization. Theoretical calculations using time‐dependent density functional theory (TDDFT) and the complete active space self‐consistent field (CASSCF) method have been carried out to characterize the potential energy surface for the ground state, the low‐lying excited states, and the cationic ground state at various levels of theory. Combining the experimental and theoretical results, we identified the elementary steps in the mechanism: The initial driving force of the ultrafast bond‐breaking process of trans‐azomethane (at the perpendicular polarization) is due to the CNNC torsional motion initiated by the vibronic coupling through an intensity‐borrowing mechanism for the symmetry‐forbidden n–π* transition. Following this torsional motion and the associated molecular symmetry breaking, an S₀/S₁ conical intersection (CI) can be reached at a torsional angle of 93.1° (predicted at the CASSCF(8,7)/cc‐pVDZ level of theory). Funneling through the S₀/S₁ CI could activate the asymmetric C? N stretching motion, which is the key motion for the consecutive C? N bond breakages on the femtosecond time scale.     

The intersection seam between the 11A′ and 21A′ states of ozone

The intersection seam between the two lowest ¹A^′ states of ozone has been determined. The potential energy surfaces and the seam are calculated and discussed in perimetric coordinates which exhibit the full three-dimensional symmetry. The seam is shown to form a closed curve which crosses the C _{2 v} -restricted coordinate planes at six points. Three of these correspond to the previously determined intersection, the starting point of the present search. The other three correspond to highly repulsive regions on the potential energy surface where two atoms approach each other to within two-thirds of the O₂ bond length. At the former three points both states have ¹ A ₁ symmetry, but at the latter three points one state has ¹ A ₁ symmetry whereas the other has ¹ B ₂ symmetry. Consequently, there exist three additional branches of the intersection seam between these two states. Each of these branches lies entirely in one C _{2 v} -restricted coordinate plane and connects to the previously discussed C _s -seam at one point. The existence of a further intersection seam is established. A novel method for determining intersection points is described. Received: 10 January 1996 / Accepted: 2 January 1997     

The photophysics of 7H-adenine: A quantum chemical investigation including spin–orbit effects

Vertical and adiabatic electronic spectra have been investigated by means of combined density functional and multi-reference configuration interaction methods. Spin–orbit coupling has been determined employing a non-empirical spin–orbit mean-field operator. In the vertical absorption spectrum of isolated 7H-adenine, the transitions to the lowest ¹ state, the optically bright ¹ state, and a so far unknown ¹(π_H → (Ryd, σ^*)) state are predicted to lie very close to each other. The strong ¹ transition at 4.8 eV is the lowest excitation of ¹(π → π^*) type in 7H-adenine. It is red shifted by about 0.3 eV with respect to the corresponding excitation in the 9H-tautomer. We find the global minimum on the S₁ potential energy hypersurface at about 4.2 eV for a ¹ electronic structure. A potential well with a minimum at 4.3 eV exhibits mixed ¹ character. A planar ¹ structure with a potential energy of 4.6 eV constitutes a stationary point on the S₁ surface. At the present stage it is unclear whether it corresponds to a minimum or a saddle-point. The lowest-lying ¹(π → (Ryd, σ^*)) state is metastable with respect to N₇–H₁₄ bond dissociation. Its inner (Rydberg) potential well with an adiabatic excitation energy of 4.6 eV represents another minimum on the S₁ PEH. From the theoretical results presented in this work, we conclude that isolated 7H-adenine will be able to emit photons for excitation energies below 4.7 eV(264 nm). Above this threshold singlet excited 7H-adenine can undergo ultrafast non-radiative relaxation to the electronic ground state, either by hydrogen detachment via the ¹(π → (Ryd, σ^*)) channel or via a conical intersection of the ¹ state along a ring puckering mode. The ³ T₁ state can be efficiently populated via intersystem crossing from one of the S₁ potential energy wells. Large-amplitude motions in the T₁ state along an out-of-plane distortional coordinate lead to significant configuration interaction of the ¹ and ¹ structures which lend intensity to the phosphorescence.     

Mechanistic Insights into the Photophysics of Ortho-hydroxyl GFP Core Chromophores

Herein we have employed the MS-CASPT2//CASSCF method to study the S₁ excited-state intramolecular proton transfers (ESIPTs) of recently synthesized ortho-hydroxyl GFP core chromophores, i.e. OHIM, CHBDI, and MHBID, and their excited-state relaxation pathways. We have found that in OHIM and CHBDI, the ESIPT process is associated with small barriers of 3.4 and 4.2 kcal/mol; while, in MHBDI, it becomes essentially barrierless. Moreover, we have found two main S₁ excited-state radiationless channels. In the first one, the enol S₁ species decays to the S₀ state via the enol S₁/S₀ conical intersection after overcoming considerable barriers of 7.0 and 7.7 kcal/mol in OHIM and CHBDI (however, in MHBDI, it is nearly barrierless). In the second one, the keto S₁ species is first generated through the ESIPT event; then, it is de-excited into the S₀ state in the vicinity of the keto S₁/S₀ conical intersection. These energetically allowed excited-state decay channels rationalize experimentally observed ultralow fluorescence quantum yields. The insights gained from the present work may help to guide the design of new ortho-hydroxyl GFP core chromophores with improved fluorescence emission and brightness.     

Adiabatic Potential Energy Surfaces and Photodissociation Mechanisms for Highly Excited States of H2O

Full-dimensional adiabatic potential energy surfaces of the electronic ground state \begin{document}$ \tilde X $\end{document} and nine excited states \begin{document}$ \tilde A $\end{document}, \begin{document}$ \tilde I $\end{document}, \begin{document}$ \tilde B $\end{document}, \begin{document}$ \tilde C $\end{document}, \begin{document}$ \tilde D $\end{document}, \begin{document}$ \tilde D' $\end{document}, \begin{document}$ \tilde D'' $\end{document}, \begin{document}$ \tilde E' $\end{document} and \begin{document}$ \tilde F $\end{document} of H\begin{document}$ _2 $\end{document}O molecule are developed at the level of internally contracted multireference configuration interaction with the Davidson correction. The potential energy surfaces are fitted by using Gaussian process regression combining permutation invariant polynomials. With a large selected active space and extra diffuse basis set to describe these Rydberg states, the calculated vertical excited energies and equilibrium geometries are in good agreement with the previous theoretical and experimental values. Compared with the well-investigated photodissociation of the first three low-lying states, both theoretical and experimental studies on higher states are still limited. In this work, we focus on all the three channels of the highly excited state, which are directly involved in the vacuum ultraviolet photodissociation of water. In particular, some conical intersections of \begin{document}$ \tilde D $\end{document}-\begin{document}$ \tilde E' $\end{document}, \begin{document}$ \tilde E' $\end{document}-\begin{document}$ \tilde F $\end{document}, \begin{document}$ \tilde A $\end{document}-\begin{document}$ \tilde I $\end{document} and \begin{document}$ \tilde I $\end{document}-\begin{document}$ \tilde C $\end{document} states are clearly illustrated for the first time based on the newly developed potential energy surfaces (PESs). The nonadiabatic dissociation pathways for these excited states are discussed in detail, which may shed light on the photodissociation mechanisms for these highly excited states.