Conical intersection

Abstract: In the Born-Oppenheimer approximation for molecular dynamics as generalized by Born and Huang, nuclei move on multiple potential-energy surfaces corresponding to different electronic states. These surfaces may intersect at a point in the nuclear coordinates with the topology of a double cone. These conical intersections have important consequences for the dynamics. When an adiabatic electronic wave function is transported around a closed loop in nuclear coordinate space that encloses a conical intersection point, it acquires an additional geometric, or Berry, phase. The Schr\"odinger equation for nuclear motion must be modified accordingly. A conical intersection also permits efficient nonadiabatic transitions between potential-energy surfaces. Most examples of the geometric phase in molecular dynamics have been in situations in which a molecular point-group symmetry required the electronic degeneracy and the consequent conical intersection. Similarly, it has been commonly assumed that the conical intersections facilitating nonadiabatic transitions were largely symmetry driven. However, conical intersections also occur in the absence of any symmetry considerations. This review discusses computational tools for finding and characterizing the conical intersections in such systems. Because these purely accidental intersections are difficult to anticipate, they may occur more frequently than previously thought and in unexpected situations, making the geometric phase effect and the occurrence of efficient nonadiabatic transitions more commonplace phenomena. [S0034-6861(96)00404-7]

Abstract: The primary photochemical event in vision, isomerization of the 11-cis chromophore in rhodopsin to the all-trans form, is one of the fastest natural photochemical processes known, taking less than a millionth of a millionth of a second. The molecular details of reactions of such rapidity are a stiff challenge to experimenters, but Polli et al. now report the characterization of the reaction using ultrafast optical spectroscopy with sub-20-femtosecond time resolution and spectral coverage from the visible to the near infrared. The data confirm that rhodopsin's extreme reactivity results from a molecular funnel mechanism that involves a 'conical intersection' between the potential energy surfaces of the starting and product molecules. Chemical reactions are usually described in terms of the movement of nuclei between the potential energy surfaces of ground and excited electronic states. Crossings known as conical intersections permit efficient transitions between the surfaces. It is shown here that ultrafast optical spectroscopy, with sub-20-fs time resolution and spectral coverage from the visible to the near-infrared, can map the isomerization of rhodopsin with sufficient resolution to shown that a conical intersection is important in this crucial event in vision. Ever since the conversion of the 11-cis retinal chromophore to its all-trans form in rhodopsin was identified as the primary photochemical event in vision1, experimentalists and theoreticians have tried to unravel the molecular details of this process. The high quantum yield of 0.65 (ref. 2), the production of the primary ground-state rhodopsin photoproduct within a mere 200 fs (refs 3–7), and the storage of considerable energy in the first stable bathorhodopsin intermediate8 all suggest an unusually fast and efficient photoactivated one-way reaction9. Rhodopsin's unique reactivity is generally attributed to a conical intersection between the potential energy surfaces of the ground and excited electronic states10,11 enabling the efficient and ultrafast conversion of photon energy into chemical energy12,13,14,15,16. But obtaining direct experimental evidence for the involvement of a conical intersection is challenging: the energy gap between the electronic states of the reacting molecule changes significantly over an ultrashort timescale, which calls for observational methods that combine high temporal resolution with a broad spectral observation window. Here we show that ultrafast optical spectroscopy with sub-20-fs time resolution and spectral coverage from the visible to the near-infrared allows us to follow the dynamics leading to the conical intersection in rhodopsin isomerization. We track coherent wave-packet motion from the photoexcited Franck–Condon region to the photoproduct by monitoring the loss of reactant emission and the subsequent appearance of photoproduct absorption, and find excellent agreement between the experimental observations and molecular dynamics calculations that involve a true electronic state crossing. Taken together, these findings constitute the most compelling evidence to date for the existence and importance of conical intersections in visual photochemistry.

Abstract: The combined results of ab initio electronic-structure calculations and spectroscopic investigations of jet-cooled molecules and clusters provide strong evidence of a surprisingly simple and general mechanistic picture of the nonradiative decay of biomolecules such as nucleic bases and aromatic amino acids. The key role in this picture is played by excited singlet states of πσ* character, which have repulsive potential-energy functions with respect to the stretching of OH or NH bonds. The 1πσ* potential-energy functions intersect not only the bound potential-energy functions of the 1ππ* excited states, but also that of the electronic ground state. Via predissociation of the 1ππ* states and a conical intersection with the ground state, the 1πσ* states trigger an ultrafast internal-conversion process, which is essential for the photostability of biomolecules. In protic solvents, the 1πσ* states promote a hydrogen-transfer process from the chromophore to the solvent. Calculations for chromophore–water clusters have shown that a spontaneous charge-separation process takes place in the solvent shell, yielding a microsolvated hydronium cation and a microsolvated electron. These results suggest that the basic mechanisms of the complex photochemistry of biomolecules in liquid water can be revealed by experimental and theoretical investigations of relatively small chromophore–water clusters.

Abstract: We show how the presence of a conical intersection in the adiabatic potential energy hypersurface can be handled by including a new vector potential in the nuclear‐motion Schrodinger equation. We show how permutational symmetry of the total wave function with respect to interchange of nuclei can be enforced in the Born–Oppenheimer approximation both in the absence and the presence of conical intersections. The treatment of nuclear‐motion wave functions in the presence of conical intersections and the treatment of nuclear‐interchange symmetry in general both require careful consideration of the phases of the electronic and nuclear‐motion wave functions, and this is discussed in detail.