Minimum Energy Conical Intersections Research Articles

Photochemical dynamics simulations for trans–cis photoisomerizations of azobenzene and bridged azobenzene

Surface hopping dynamics simulations based on the Zhu–Nakamura theory were performed to investigate the trans–cis photoisomerization mechanisms of azobenzene and bridged azobenzene excited to S1 state. In geometry optimization, both for the two compounds, two minimum-energy conical intersections between the ground state and the lowest excited state are located. Two conical intersections are confirmed to be decay funnels in the trans–cis photoisomerization processes in azobenzene but only one plays important parts in the photoisomerization of bridged azobenzene. Due to the smaller slope of potential energy surface in the S1 state, the lifetime of the S1 state of azobenzene in our work is much longer than that of bridged azobenzene. We show that the torsion around the central NN bond is the preferred reaction mechanism in the isomerization of two molecules. Rotation around the central NN bond and twisting of phenyl rings around their NC bonds allows the molecule to move to a minimum-energy conical intersection, after which surface hopping from S1 to S0 occurs. In the ground state, further rotation occurs around the NN bond and two NC bonds until the azo moiety and phenyl rings complete their isomerization. The additional CH2CH2 bridge in bridged azobenzene starts to rotate toward the cis form after the azo moiety and two phenyl rings complete their reorientation. The bridge structure in bridged azobenzene makes the rotation of the azo moiety faster and the torsion of two phenyl rings slower.

Assessment of Density Functional Methods for Obtaining Geometries at Conical Intersections in Organic Molecules

A number of commonly available density functionals have been tested for their ability to describe the energetics and the geometry at conical intersections in connection with the spin-restricted ensemble referenced Kohn–Sham (REKS) method. The minimum energy conical intersections have been optimized for several molecular systems, which are widely used as paradigmatic models of photochemical rearrangements and models of biological chromophores. The results of the calculations are analyzed using the sign-change theorem of Longuet-Higgins and a method of elementary reaction coordinates of Haas et al. The latter approach helps to elucidate the differences between the geometries at conical intersections as predicted by the multireference wave function ab initio methods and by the density functional methods. Overall, the BH&HLYP density functional yields the best results for the conical intersection geometries and energetics.

Automated Search for Minimum Energy Conical Intersection Geometries between the Lowest Two Singlet States S0/S1-MECIs by the Spin-Flip TDDFT Method.

Automated search for minimum energy conical intersection geometries between the lowest two singlet states (S0/S1-MECIs) was performed by combining the anharmonic downward distortion following (ADDF) method, the seam model function (SMF) approach, and the spin-flip (SF) TDDFT method. SMF/ADDF has been employed previously in automated searches for MECIs on potential energy surfaces (PESs) with expensive multireference methods. In this work, we adopt the SF-TDDFT method that enables efficient optimization of S0/S1-MECIs in the framework of TDDFT. To evaluate the performance of the present approach, it was applied to ethylene and 1,3-butadiene. The present method automatically gave unknown S0/S1-MECIs as well as all previously reported ones. Therefore, the present hybrid method of SMF/ADDF and SF-TDDFT is shown to be a promising approach to locate S0/S1-MECIs of large systems automatically with modest computational costs.

On the electronic structure of the low lying electronic states of vanadium trioxide

The electronic structure of transition metal oxides is frequently studied using density functional theory. Nonetheless, the electronic structure of VO3 has been found to be sensitive to the choice of functional. As a consequence, the basic question of whether or not the ground electronic state exhibits a Jahn-Teller distortion has yet to be resolved. Using basis sets of triple zeta quality and multireference configuration interaction wave functions as large as 700 million configuration state functions, we determine that the ground electronic state of VO3 is a (2)A2 state in C3v symmetry. The first two excited electronic states are also characterized and found to be the components of a degenerate (2)E state, in C3v symmetry, which exhibits a small Jahn-Teller distortion. The Jahn-Teller stabilization energy is only 40 cm(-1) and the barrier to pseudo-rotation is 9 cm(-1). This (2)E state exhibits some unexpected properties. In the vicinity of the minimum energy conical intersection, the local topography appears almost quadratic, rather than linear, in the Jahn-Teller active coordinates. This gives rise to three symmetry-related seams of conical intersections in addition to the symmetry-required seam and results in the suppression of the geometric phase effect. These features, attributable to small linear Jahn-Teller parameters, are usually found in states characterized by e(2) (or e(3)e(')) electron configurations rather than the e(3) configuration found here. In addition to its Jahn-Teller minimum, the first excited state exhibits a second minimum with a structure significantly distorted from C3v. A conical intersection with Cs symmetry connects the two minima and puts an upper limit of 190 cm(-1) on the barrier connecting these minima.

Theoretical Study on the Photodissociation of Methylamine Involving S1, T1, and S0 States

Various photodissociation pathways of methylamine involving the three lowest electronic states, namely, singlet ground S0 state, singlet first excited S1 state, and triplet ground T1 state, were studied by the (MS-)CAS(8e,8o)PT2/6-31++G** method. All critical points, i.e., minima, transition states, minimum energy conical intersections, and minima on the seam of crossing, were explored systematically by the global reaction route mapping (GRRM) strategy utilizing the anharmonic downward distortion following (ADDF) and artificial force induced reaction (AFIR) methods. On the basis of obtained structures, we discuss the photodissociation mechanism of methylamine in the experimental excitation wavelength range 222-240 nm in detail. Especially, the T1 potential energy surface was explored systematically for the first time. The N-H bond rupture is a primary channel on the S1 state. Along the N-H dissociation path on S1, there is a low-energy conical intersection (CI), and through this CI the system can go back to the S0 state; from the CI the system can directly dissociate to CH3NH + H or reproduce the original CH3NH2 on S0. There is a seam of crossing between S0 and T1 in a partially dissociated CH3---NH2 geometry, and through this seam the system may go up to the T1. On the T1 state, a roaming-like pathway giving CH4 + NH (X(3)Σ(-)) products was found, which would explain the recently proposed intersystem crossing mediated roaming dynamics.

CASPT2 Study of Photodissociation Pathways of Ketene

The mechanism of various photodissociation channels of ketene involving the three lowest singlet states (S0, S1, and S2) and the three lowest triplet states (T1, T2, and T3) was investigated by means of the (MS-)CAS(8e,8o)PT2/6-31+G* method. Stationary structures, i.e., global minima (GMs), local minima (LMs), transition states (TSs), minimum energy conical intersections (MECIs), and minima on seam of crossing (MSXs), were explored systematically by the global reaction route mapping (GRRM) strategy. On the basis of these structures, we discussed related dissociation channels starting from S2 that have been studied experimentally with 193-215 nm excitation wavelength. Five working pathways were found for relaxation to the low-lying S0, S1, and T1 potential energy surfaces (PESs) from the Franck-Condon region of S2, and the relaxation is expected to occur very quickly. On these low-lying states, five dissociation channels are open: three CH2 + CO channels for different CH2 electronic states, H + HCCO, and H2 + C2O. Pathways for all of these five channels were identified and discussed, including new minor paths leading to H2 + C2O.

Exploring the Conical Intersection Seam: The Seam Space Nudged Elastic Band Method.

Conical intersections (CIs) play a fundamental role in photoreactions. Although it is widely known that CIs are not isolated points but rather multidimensional seams, there is a dearth of techniques to explore and characterize these seams beyond the immediate vicinity of minimum energy points within the intersection space (minimum energy conical intersections or MECIs). Here, we develop a method that connects these MECIs by minimal energy paths within the space of geometries that maintain the electronic degeneracy (the "seam space") in order to obtain a more general picture of a CI seam. This method, the seam space nudged elastic band (SS-NEB) method, combines the nudged elastic band method with gradient projected MECI optimization. It provides a very efficient way of finding minimum energy seam paths in the conical intersection seam. The method is demonstrated by application to two molecules: ethylene and the green fluorescent protein (GFP) chromophore. The results show that previously known MECIs for these molecules are connected within a single seam, adding further support to previous conjectures that all MECIs are topologically connected in the seam space. Analysis of the nonadiabatic dynamics further suggests that a broad range of seam geometries, not only the vicinity of MECIs, is involved in the nonadiabatic transition events. The current method provides a tool to characterize CI seams in different environments and to explore the importance of the seam in the dynamics.

Nonadiabatic ab initio molecular dynamics of photoisomerization in bridged azobenzene

The photoisomerization mechanisms of bridged azobenzene are investigated by means of surface hopping dynamics simulations based on the Zhu-Nakamura theory. In the geometry optimizations and potential energy surface calculations, four minimum-energy conical intersections between the ground state and the lowest excited state are found to play important roles in the trans-cis and cis-trans isomerization processes. The trans-cis photoisomerization proceeds through two minimum-energy conical intersections. Ultrafast pedal motion of the N atoms and twisting of phenyl rings around their N-C bonds allows the molecule to move to a minimum-energy conical intersection, after which surface hopping from S(1) to S(0) occurs. In the S(0) state, further rotation occurs around the N=N bond and two N-C bonds until the azo moiety and phenyl rings complete their isomerization. Finally, the cis form is achieved by subsequent adjustment of the ethylene bridge. In the cis-trans photodynamics, there is one rotational pathway, in the middle of which two CIs are responsible for the surface hopping to the S(0) state. After the nonadiabatic transition, the molecule reaches the trans form through a barrierless pathway and the two phenyl rings and the additional bridge complete their reorientation almost at the same time.

A Valence Bond Description of the Prefulvene Extended Conical Intersection Seam of Benzene.

The permutational isomers of the prefulvene-like minimum energy conical intersection lie on an extended conical intersection seam, where they are connected by higher symmetry structures. Here, we present a VB analysis of the electronic states involved along this extended seam. The VB method produces a spin-exchange density (ie. a bonding pattern) that provides the basis to assign resonance structures to the states. The results show that in the high symmetry region of the seam, the character of the states is dominated by the positive and negative combination of the Kekulé structures, (A+B) and (A-B). The low energy parts of the seam, comprised of lower symmetry conical intersection structures, are stabilized by mixing with the Dewar resonance structures. This feature is responsible for the stability of the benzvalene-like conical intersections. The validity of the VB model is confirmed by calculating the branching space vectors at this level of theory, which are in good agreement with the CASSCF calculated vectors. The VB analysis has also allowed us to complete our picture of the global seam, since it has provided the clue to locate a conical intersection saddle point that interconverts two minima of the prefulvene conical intersection where the carbon bent out of the plane is inverted and rotated by 60°. This saddle point has a benzvalene-like geometry, in agreement with the VB picture.

QM/MM Trajectory Surface Hopping Approach to Photoisomerization of Rhodopsin and Isorhodopsin: The Origin of Faster and More Efficient Isomerization for Rhodopsin

The photoinduced cis-trans isomerization dynamics of rhodopsin and isorhodopsin are studied using a newly developed hybrid QM/MM trajectory surface hopping MD scheme based on the Zhu-Nakamura theory for nonadiabatic transitions. Rhodopsin and isorhodopsin have 11-cis and 9-cis forms of retinal as chromophore and the two proteins are isomerized to bathorhodopsin enclosing the all-trans form. The simulation reproduced faster and more efficient isomerization in rhodopsin than in isorhodopsin. In the excited state, rhodopsin shows a straightforward dynamics, whereas isorhodopsin dynamics is rather complicated and in a back-and-forth manner. The latter complicated dynamics would be mainly due to a narrow space near the active dihedral angle ═C8-C9═C10-C11═ (ϕ9) created by Thr 118 and Tyr 268 in opsin. Rhodopsin gives bathorhodopsin only while isorhodopsin yields a byproduct. The rigorous selectivity in rhodopsin would be another reason why rhodopsin is selected biologically. Comparison with our previous opsin-free investigations reveals that opsin tends to confine the twist of the active dihedral to only one direction and funnels transitions into the vicinity of minimum energy conical intersections (MECI). The twist-confinement totally blocks simultaneous twisting of ϕ9 and ϕ11 (═C10-C11═C12-C13═) and enhances the quantum yields. The opposite rotation of ϕ9 and ϕ11 ("wring-a-wet-towel" motion) takes place upon photoexcitation, which also does without opsin. The wring-a-wet-towel motion is dynamically enhanced in comparison with the one expected from locations of the MECI. The present simulation reveals that the Weiss-Warshel model for cis-trans photoisomerization is not applicable for rhodopsin because the branching ratio after transition is crucial.

Automated Exploration of Photolytic Channels of HCOOH: Conformational Memory via Excited-State Roaming.

To elucidate the photodissociation mechanism of HCOOH, we systematically explored reaction pathways starting from the first excited singlet state (S1) by using automated reaction path search methods. All critical points, that is, minima, transition states, minimum energy conical intersections, and minima on seam of crossing, for the S0, T1, and S1 potential energy surfaces (PESs) obtained in the present search were optimized at the CASPT2 level. The structure list obtained by the search explained all experimentally reported photolytic channels. A new mechanism for the previously suggested but unexplained conformational memory in the 193 nm photolysis is proposed, which involves two steps: partial dissociation and succeeding roaming of one of H atoms on the S1 PES, followed by intramolecular recombination on the S0 PES after radiationless transition through a conical intersection at a partially dissociated geometry. This is partially similar to the excited-state roaming recently discovered for the NO3 radical.

Intramolecular Hydrogen Bonding Plays a Crucial Role in the Photophysics and Photochemistry of the GFP Chromophore

In commonly studied GFP chromophore analogues such as 4-(4-hydroxybenzylidene)-1,2-dimethyl-1H-imidazol-5(4H)-one (PHBDI), the dominant photoinduced processes are cis-trans isomerization and subsequent S(1) → S(0) decay via a conical intersection characterized by a highly twisted double bond. The recently synthesized 2-hydroxy-substituted isomer (OHBDI) shows an entirely different photochemical behavior experimentally, since it mainly undergoes ultrafast intramolecular excited-state proton transfer, followed by S(1) → S(0) decay and ground-state reverse hydrogen transfer. We have chosen 4-(2-hydroxybenzylidene)-1H-imidazol-5(4H)-one (OHBI) to model the gas-phase photodynamics of such 2-hydroxy-substituted chromophores. We first use various electronic structure methods (DFT, TDDFT, CC2, DFT/MRCI, OM2/MRCI) to explore the S(0) and S(1) potential energy surfaces of OHBI and to locate the relevant minima, transition state, and minimum-energy conical intersection. These static calculations suggest the following decay mechanism: upon photoexcitation to the S(1) state, an ultrafast adiabatic charge-transfer induced excited-state intramolecular proton transfer (ESIPT) occurs that leads to the S(1) minimum-energy structure. Nearby, there is a S(1)/S(0) minimum-energy conical intersection that allows for an efficient nonadiabatic S(1) → S(0) internal conversion, which is followed by a fast ground-state reverse hydrogen transfer (GSHT). This mechanism is verified by semiempirical OM2/MRCI surface-hopping dynamics simulations, in which the successive ESIPT-GSTH processes are observed, but without cis-trans isomerization (which is a minor path experimentally with less than 5% yield). These gas-phase simulations of OHBI give an estimated first-order decay time of 476 fs for the S(1) state, which is larger but of the same order as the experimental values measured for OHBDI in solution: 270 fs in CH(3)CN and 230 fs in CH(2)Cl(2). The differences between the photoinduced processes of the 2- and 4-hydroxy-substituted chromophores are attributed to the presence or absence of intramolecular hydrogen bonding between the two rings.

Theoretical study of the radiationless deactivation mechanisms of photo-excited thiophene

The radiationless deactivation mechanisms of photo-excited thiophene have been studied using the multi-reference second-order perturbation theory and linear response coupled cluster methods. The electronic spectrum has been established and various minimum energy structures and conical intersections involving the ground and lowest singlet excited states have been characterized. Simplified reaction paths connecting the optimized geometries have been calculated as well. Based on these investigations, several deactivation mechanisms have been identified leading from the lowest bright 1ππ∗ states back to the electronic ground state. The excited state depletion in each case is possible due to the existence of low-lying conical intersections formed by either cleavage of one of the CS bonds or out-of-plane deformations of the aromatic ring. The deactivation mechanisms suggested in this work should provide some very efficient decay channels after excitation into the first UV absorption band of thiophene, and are good candidates to explain why this compound is non-fluorescent.

Ultrafast non-adiabatic dynamics of methyl substituted ethylenes: The π3s Rydberg state

Excited state unimolecular reactions of some polyenes exhibit localization of their dynamics at a single ethylenic double bond. Here we present studies of the fundamental photophysical processes in the ethylene unit itself. Combined femtosecond time-resolved photoelectron spectroscopy (TRPES) and ab initio quantum chemical calculations was applied to the study of excited state dynamics in cis-butene, trans-butene, trimethylethylene, and tetramethylethylene, following initial excitation to their respective π3s Rydberg states. The wavelength dependence of the π3s Rydberg state dynamics of tetramethylethylene was investigated in more detail. The π3s Rydberg to ππ(∗) valence state decay rate varies greatly with substituent: the 1,2-di- and tri-methyl substituted ethylenes (cis-butene, trans-butene, and trimethylethylene) show an ultrafast decay (∼20 fs), whereas the fully methylated tetramethylethylene shows a decay rate of 2 to 4 orders of magnitude slower. These observations are rationalized in terms of topographical trends in the relevant potential energy surfaces, as found from ab initio calculations: (1) the barrier between the π3s state and the ππ∗ state increases with increasing methylation, and (2) the π3s∕ππ∗ minimum energy conical intersection displaces monotonically away from the π3s Franck-Condon region with increasing methylation. The use of systematic methylation in combination with TRPES and ab initio computation is emerging as an important tool in discerning the excited state dynamics of unsaturated hydrocarbons.

Probing Highly Efficient Photoisomerization of a Bridged Azobenzene by a Combination of CASPT2//CASSCF Calculation with Semiclassical Dynamics Simulation

Mechanism of phototriggered isomerization of azobenzene and its derivatives is of broad interest. In this paper, the S(0) and S(1) potential energy surfaces of the ethylene-bridged azobenzene (1) that was recently reported to have highly efficient photoisomerization were determined by ab initio electronic structure calculations at different levels and further investigated by a semiclassical dynamics simulation. Unlike azobenzene, the cis isomer of 1 was found to be more stable than the trans isomer, consistent with the experimental observation. The thermal isomerization between cis and trans isomers proceeds via an inversion mechanism with a high barrier. Interestingly, only one minimum-energy conical intersection was determined between the S(0) and S(1) states (CI) for both cis → trans and trans → cis photoisomerization processes and confirmed to act as the S(1) → S(0) decay funnel. The S(1) state lifetime is ∼30 fs for the trans isomer, while that for the cis isomer is much longer, due to a redistribution of the initial excitation energies. The S(1) relaxation dynamics investigated here provides a good account for the higher efficiency observed experimentally for the trans → cis photoisomerization than the reverse process. Once the system decays to the S(0) state via CI, formation of the trans product occurs as the downhill motion on the S(0) surface, while formation of the cis isomer needs to overcome small barriers on the pathways of the azo-moiety isomerization and rotation of the phenyl ring. These features support the larger experimental quantum yield for the cis → trans photoisomerization than the trans → cis process.

Surface Hopping Excited-State Dynamics Study of the Photoisomerization of a Light-Driven Fluorene Molecular Rotary Motor.

We report a theoretical study of the photoisomerization step in the operating cycle of a prototypical fluorene-based molecular rotary motor (1). The potential energy surfaces of the ground electronic state (S0) and the first singlet excited state (S1) are explored by semiempirical quantum-chemical calculations using the orthogonalization-corrected OM2 Hamiltonian in combination with a multireference configuration interaction (MRCI) treatment. The OM2/MRCI results for the S0 and S1 minima of the relevant 1-P and 1-M isomers and for the corresponding S0 transition state are in good agreement with higher-level calculations, both with regard to geometries and energetics. The S1 surface is characterized at the OM2/MRCI level by locating two S0-S1 minimum-energy conical intersections and nearby points on the intersection seam and by computing energy profiles for pathways toward these MECIs. Semiclassical Tully-type trajectory surface hopping (TSH) simulations with on-the-fly OM2/MRCI calculations are carried out to study the excited-state dynamics after photoexcitation to the S1 state. Fast relaxation to the ground state is observed through the conical intersection regions, predominantly through the lowest-energy one with a strongly twisted central C═C double bond and pyramidalized central carbon atom. The excited-state lifetimes for the direct and inverse photoisomerization reactions (1.40 and 1.79 ps) and the photostationary state ratio (2.7:1) from the TSH-OM2 simulations are in good agreement with the available experimental data (ca. 1.7 ps and 3:1). Excited-state lifetimes, photostationary state ratio, and dynamical details of the TSH-OM2 simulations also agree with classical molecular dynamics simulations using a reparametrized optimized potentials for liquid simulations (OPLS) all-atom force field with ad-hoc surface hops at predefined conical intersection points. The latter approach allows for a more extensive statistical sampling.

Molecular Driving Forces for Z/E Isomerization Mediated by Heteroatoms: The Example Hemithioindigo

A combined experimental and theoretical investigation of photoinduced Z/E isomerizations is presented. Unsubstituted Hemithioindigo is selected as a representative minimal model to unravel the reaction mechanism in the presence of heteroatoms on an atomic level. Time-resolved spectroscopy reveals multiexponential reaction dynamics on the few picoseconds time scale, which are interpreted by quantum chemical calculations at the CASSCF/CASPT2 level of theory. Detailed insight into the processes governing the ultrafast decay from the first excited state, mediated by a number of conical intersections, is provided. Charge separation and charge balance recovery on the reaction pathway play the leading role and are controlled by the electron-donating or -withdrawing character of the heteroatoms. The electronic and geometric structures of the individual minimum energy conical intersections governing the reaction are rationalized, and an extended energetically low lying conical intersection seam is extracted. Comparison to the experimental results permits linking the observed time constants to molecular intermediates and pathways. An explanation is provided for the pronounced differences of Z → E and the E → Z photoreactions upon excitation to the first excited singlet state.

Theoretical study of photoinduced ring-opening in furan

The potential energy surfaces (PESs) of the two lowest excited singlet states of furan [correlating with the Rydberg (1)A(2)(3s) and valence (1)B(2)(V) states at the C(2v) ground-state molecular configuration] have been studied in some detail with regard to the photoinduced ring-opening reaction. The surfaces have been characterized in terms of their stationary points and points of minimum energy conical intersections along the ring-opening pathway. The optimization of the geometrical parameters has been performed with the equation of motion coupled cluster singles and doubles method. The ab initio PESs have been modeled by energy grids and Taylor series. The resulting 11-dimensional PESs reproduce the ab initio results to a good accuracy and can be used in dynamical calculations.

Conical intersections of free energy surfaces in solution: Effect of electron correlation on a protonated Schiff base in methanol solution

The minimum energy conical intersection (MECI) optimization method with taking account of the dynamic electron correlation effect [T. Mori and S. Kato, Chem. Phys. Lett. 476, 97 (2009)] is extended to locate the MECI of nonequilibrium free energy surfaces in solution. A multistate electronic perturbation theory is introduced into the nonequilibrium free energy formula, which is defined as a function of solute and solvation coordinates. The analytical free energy gradient and interstate coupling vectors are derived, and are applied to locate MECIs in solution. The present method is applied to study the cis-trans photoisomerization reaction of a protonated Schiff base molecule (PSB3) in methanol (MeOH) solution. It is found that the effect of dynamic electron correlation largely lowers the energy of S(1) state. We also show that the solvation effect strongly stabilizes the MECI obtained by twisting the terminal C=N bond to become accessible in MeOH solution, whereas the conical intersection is found to be unstable in gas phase. The present study indicates that both electron correlation and solvation effects are important in the photoisomerization reaction of PSB3. The effect of counterion is also examined, and seems to be rather small in solution. The structures of free energy surfaces around MECIs are also discussed.

Insights into mechanistic photochemistry of urea

In this work, we have studied the mechanistic photochemistry of urea (NH(2)CONH(2)) by means of ab initio calculations on the stationary and intersection structures in the lowest three electronic states (S(1), T(1), and S(0)). Two dominant decay channels were found for NH(2)CONH(2) to decay from the S(1) state, internal conversion to the S(0) state via the S(1)/S(0) minimum-energy conical intersection, and intersystem crossing to the T(1) state in the vicinity of the S(1)/T(1) minimum-energy crossing point. Once in the S(0) state, the isomerization and deamination reactions prevail due to their low barrier heights. This is different from the mechanism proposed experimentally, in which the deamination and dehydration reactions proceed in the S(1) and T(1) states. The C-N bond cleavage was determined to occur mainly along the T(1) pathway as a result of the S(1)/T(1) intersystem crossing.