Minimum Energy Conical Intersections Research Articles

Ab initio reaction pathways for photodissociation and isomerization of nitromethane on four singlet potential energy surfaces with three roaming paths.

Photodissociation pathways of nitromethane following π → π(*) electronic excitation are reported. The potential energy surfaces for four lowest singlet states are explored, and structures of many intermediates, dissociation limits, transition states, and minimum energy conical intersections were determined using the automated searching algorism called the global reaction route mapping strategy. Geometries are finally optimized at CASSCF(14e,11o) level and energies are computed at CAS(14o,11e)PT2 level. The calculated preferable pathways and important products qualitatively explain experimental observations. The major photodissociation product CH3 and NO2 ((2)B2) is formed by direct dissociation from the S1 state. Important pathways involving S1 and S0 states for production of various dissociation products CH3NO + O ((1)D), CH3O(X(2)E) + NO (X(2)Π), CH2NO + OH, and CH2O + HNO, as well as various isomerization pathways have been identified. Three roaming processes also have been identified: the O atom roaming in O dissociation from CH3NO2, the OH radical roaming in OH dissociation from CH2N(O)(OH), and the NO roaming in NO dissociation from CH3ONO.

Conical intersections and low-lying electronic states of tetrafluoroethylene.

The low-lying electronic states of tetrafluoroethylene (C2 F4 ) are characterized theoretically for the first time using equation-of-motion coupled cluster theory (EOM-CCSD), and complete active space self-consistent field (CASSCF) and second-order perturbation theory (CASPT2). Computations are performed for vertical excitation energies, equilibrium geometries, minimum-energy conical intersections, and potential energy curves along three geometric coordinates: 1) twisting of the FCCF dihedral angle, 2) pyramidalization of the CF2 group, and 3) migration of a fluorine atom resulting in an ethylidene-like (CF3 CF) structure. The results suggest two relaxation pathways from the Rydberg-3s excited electronic state to the ground state. These relaxation pathways are discussed in conjunction with the femtosecond photoionization spectroscopy results of Trushin et al. [ChemPhysChem- 2004, 5, 1389].

Photodecarbonylation mechanism of cyclopropenone in the gas phase: electronic structure calculation and AIMS dynamics simulation.

In this article, structures and energies of cyclopropenone in the low-lying electronic states have been determined by the CASSCF and MS-CASPT2 calculations with different basis sets. Two minimum-energy conical intersections (CI-1 and CI-2) between S0 and S1 were obtained and their topographic characters were characterized by the SA4-CAS(10,9) calculated energy gradients and nonadiabatic coupling vectors. The AIMS method was used to carry out nonadiabatic dynamics simulation with ab initio calculation performed at the SA4-CAS(10,9) level. On the basis of time evolution of wave functions simulated here, the S1 lifetime is fitted to be 125 fs with a pure exponential decay for the S1 electronic population. The CI-1 intersection is mainly responsible for ultrafast S1→S0 nonadiabatic transition and the photoinduced decarbonylation is a sequential process, where the first C-C bond is broken in the S1 state and fission of the second C-C bond occurs in the S0 state as a result of the S1→S0 internal conversion via the CI-1 region. As a minor channel through the CI-2 region, the decarbonylation proceeds in an asynchronous concerted way. Effects of the S1 excess energies and the S1-S0 energy gap on the nonadiabatic dynamics were examined, which reveals that the S1→S0 nonadiabatic transition occurs within a small energy gap and high-energy conical intersection regions can play an important role. The present study provides new insights into mechanistic photochemistry of cyclopropenones and reveals that the AIMS dynamics simulation at a high-accuracy ab initio level is a powerful tool for exploring a mechanism of an ultrafast photochemical reaction.

Choosing RASSCF orbital active spaces for multiple electronic states

A systematic approach is introduced for defining Restricted Active Space Self-Consistent-Field (RASSCF) orbitals for treating multiple electronic states in a balanced way, based on an SCF state-averaging procedure (Thom and Head-Gordon, 2008). We start from an SCF density matrix averaged over the electronic states of interest and choose a RAS partition based on the corresponding natural orbital occupation numbers. In order to test this procedure, we apply it to naphthalene cation, previously studied as a potential interstellar Polycyclic Aromatic Hydrocarbon (PAH) because of its photo stability following electronic excitation (Hall et al., 2006). The results obtained with this method in terms of energies and bond lengths for the first three electronic states and the corresponding minimum energy conical intersections between potential energy surfaces compare very well with CASSCF results and suggest further testing of the method for RASSCF calculations.

Geometry deformation and mesomeric effect at the minimal-energy conical intersections and their relationship to the photoreactivity of indolylfulgides: A TD-DFT study

Minimum energy conical intersection (MECI) is the low-lying point on the CI hyperseam that facilitates ultrafast radiationless transition in photochromes. Time dependent density functional theory calculations using Maeda’s updated branching plane method were employed in the study of indolylfulgides’ structure at the MECI. Four criteria were used to effectively characterize the influence of the MECI structure on the photoreactivity of indolylfulgides; three of these criteria (molecular orbital, bond lengths and the height of C6 trigonal pyramid) were paramount to identifying one novel MECI structure and confirming 2 others previously reported.

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.