The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry--presented here for the first time--is found to be the global minimum in the intersection space.     

Theoretical Study on Photoisomerization of 2-Methylfuran to 3-Methylfuran

1 INTRODUCTION 2-Methylfuran belongs to the basic heteroaromatic compounds relevant to many fields of modern che- mistry, ranging from the study of natural products and biologically active substances to the develop- ment of building blocks for organic synthesis and conducting polymers[1]. Since the photochemistry ofR-furan was gradually recognized in 1960s[2～7], lots of interest has been aroused. Herein we only study one branch of photoche- mistry of R-furan: the isomerization of 2-methy…     

The photochemistry of formaldehyde: internal conversion and molecular dissociation in a single step?

A novel, nonadiabatic reaction path for H2 + CO molecular dissociation of formaldehyde via an extended S1/S0 conical intersection seam has been mapped out using the CAS-SCF method with a full valence active space (10 electrons, 9 orbitals). Two conical intersection geometries have been optimized, CsCoIn, a saddle point in the intersection space, and C1CoIn, which is the lowest-energy crossing point. A minimum-energy path connecting these points along a seam has also been characterized. In addition to the conventional and "roaming-atom" mechanisms--where internal conversion takes place before ground-state dissociation--we suggest that a strictly nonadiabatic mechanism can operate, where internal conversion and dissociation take place in concert.     

Controlling the mechanism of fulvene S(1)/S(0) decay: switching off the stepwise population transfer

Direct quantum dynamics simulations were performed to model the radiationless decay of the first excited state S(1) of fulvene. The full space of thirty normal mode nuclear coordinates was explicitly considered. By default, ultrafast internal conversion takes place centred on the higher-energy planar region of the S(1)/S(0) conical intersection seam, giving the stepwise population transfer characteristic of a sloped surface crossing, and leading back to the ground state reactant. Two possible schemes for controlling whether stepwise population transfer occurs or not-either altering the initial geometry distribution or the initial momentum composition of the photo-excited wavepacket-were explored. In both cases, decay was successfully induced to occur in the lower-energy twisted/peaked region of the crossing seam, switching off the stepwise population transfer. This absence of re-crossing is a direct consequence of the change in the position on the intersection at which decay occurs (our target for control), and its consequences should provide an experimentally observable fingerprint of this system.     

Ab initio nonadiabatic quantum dynamics of cyclohexadiene/hexatriene ultrafast photoisomerization

Reaction mechanisms of the ultrafast photoisomerization between cyclohexadiene and hexatriene have been elucidated by the quantum dynamics on the ab initio potential energy surfaces calculated by multireference configuration interaction method. In addition to the quantum wave-packet dynamics along the two-dimensional reaction coordinates, the semiclassical analyses have also been carried out to correctly estimate the nonadiabatic transition probabilities around conical intersections in the full-dimensional space. The reaction time durations of radiationless decays in the wave-packet dynamics are found to be generally consistent with the femtosecond time-resolution experimental observations. The nonadiabatic transition probabilities among the ground (S0), first (S1), and second (S2) excited states have been estimated by using the semiclassical Zhu-Nakamura formula considering the full-dimensional wave-packet density distributions in the vicinity of conical intersections under the harmonic normal mode approximation. The cyclohexadiene (CHD) ring-opening process proceeds descending on the S1(1 1B) potential after the photoexcitation. The major part of the wave-packet decays from S1(1 1B) to S1(2 1A) by the first seam line crossing along the C2-symmetry-breaking directions. The experimentally observed ultrafast S1-S0 decay can be explained by the dynamics through the S1-S0 conical intersection along the direction toward the five-membered ring. The CHD: hexatriene (HT) branching ratio is estimated to be approximately 5:5, which is in accordance with the experiment in solution. This branching ratio is found to be mainly governed by the location of the five-membered ring S1-S0 conical intersection along the ground state potential ridge between CHD and HT.     

Photophysics of intramolecularly hydrogen-bonded aromatic systems: ab initio exploration of the excited-state deactivation mechanisms of salicylic acid

Excited state reaction paths and the corresponding energy profiles of salicylic acid have been determined with the CC2 method, which is a simplified version of singles-and-doubles coupled cluster theory. At crucial points of the potential energy hypersurfaces, single-point energy calculations have been performed with the CASPT2 method (second-order perturbation theory based on the complete active space self-consistent field reference). Hydrogen transfer along the intramolecular hydrogen bond as well as torsion and pyramidization of the carboxy group have been identified as the most relevant photochemical reaction coordinates. The keto-type planar S(1) state reached by barrierless intramolecular hydrogen transfer represents a local minimum of the S(1) energy surface, which is separated by a very low barrier from a reaction path leading to a low-lying S(1)-S(0) conical intersection via torsion and pyramidization of the carboxy group. The S(1)-S(0) conical intersection, which occurs for perpendicular geometry of the carboxy group, is a pure biradical. From the conical intersection, a barrierless reaction path steers the system back to the two known minima of the S(0) potential energy surface (rotamer I, rotamer II). A novel structure, 7-oxa-bicyclo[4.2.0]octa-1(6),2,4-triene-8,8-diol, has been identified as a possible transient intermediate in the photophysics of salicylic acid.     

Monitoring the effect of a control pulse on a conical intersection by time-resolved photoelectron spectroscopy

We have previously shown how femtosecond angle- and energy-resolved photoelectron spectroscopy can be used to monitor quantum wavepacket bifurcation at an avoided crossing or conical intersection and also how a symmetry-allowed conical intersection can be effectively morphed into an avoided crossing by photo-induced symmetry breaking. The latter result suggests that varying the parameters of a laser to modify a conical intersection might control the rate of passage of wavepackets through such regions, providing a gating process for different chemical products. In this paper, we show with full quantum mechanical calculations that such optical control of conical intersections can actually be monitored in real time with femtosecond angle- and energy-resolved photoelectron spectroscopy. In turn, this suggests that one can optimally control the gating process at a conical intersection by monitoring the photoelectron velocity map images, which should provide far more efficient and rapid optimal control than measuring the ratio of products. To demonstrate the sensitivity of time-resolved photoelectron spectra for detecting the consequences of such optical control, as well as for monitoring how the wavepacket bifurcation is affected by the control, we report results for quantum wavepackets going through the region of the symmetry-allowed conical intersection between the first two (2)A' states of NO(2) that is transformed to an avoided crossing. Geometry- and energy-dependent photoionization matrix elements are explicitly incorporated in these studies. Time-resolved photoelectron angular distributions and photoelectron images are seen to systematically reflect the effects of the control pulse.     

A unified perspective on the hydrogen atom transfer and proton-coupled electron transfer mechanisms in terms of topographic features of the ground and excited potential energy surfaces as exemplified by the reaction between phenol and radicals

The relation between the hydrogen atom transfer (HAT) and proton-coupled electron transfer (PCET) mechanisms is discussed and is illustrated by multiconfigurational electronic structure calculations on the ArOH + R(*) --> ArO(*) + RH reactions. The key topographic features of the Born-Oppenheimer potential energy surfaces that determine the predominant reaction mechanism are the conical intersection seam of the two lowest states and reaction saddle points located on the shoulders of this seam. The saddle point corresponds to a crossing of two interacting valence bond states corresponding to the reactant and product bonding patterns, and the conical intersection corresponds to the noninteracting intersection of the same two diabatic states. The locations of mechanistically relevant conical intersection structures and relevant saddle point structures are presented for the reactions between phenol and the N- and O-centered radicals, (*)NH2 and (*)OOCH3. Points on the conical intersection of the ground doublet D0 and first excited doublet D1 states are found to be in close geometric and energetic proximity to the reaction saddle points. In such systems, either the HAT mechanism or both the HAT mechanism and the proton-coupled electron transfer (PCET) mechanism can take place, depending on the relative energetic accessibility of the reaction saddle points and the D0/D1 conical intersection seams. The discussion shows how the two mechanisms are related and how they blend into each other along intermediate reaction paths. The recognition that the saddle point governing the HAT mechanism is on the shoulder of the conical intersection governing the PCET mechanism is used to provide a unified view of the competition between the two mechanisms (and the blending of the two mechanisms) in terms of the prominent and connected features of the potential energy surface, namely the saddle point and the conical intersection. The character of the dual mechanism may be understood in terms of the dominant valence bond configurations of the intersecting states, which are zero-order approximations to the diabatic states.     

On the characterization of three state conical intersections: a quasianalytic theory using a group homomorphism approach

In this work, degenerate perturbation theory through second order is used to characterize the vicinity of a three state conical intersection. This report extends our recent demonstration that it is possible to describe the branching space (in which the degeneracy is lifted linearly) and seam space (in which the degeneracy is preserved) in the vicinity of a two state conical intersection using second order perturbation theory. The general analysis developed here is based on a group homomorphism approach. Second order perturbation theory, in conjunction with high quality ab initio electronic structure data, produces an approximately diabatic Hamiltonian whose eigenenergies and eigenstates can accurately describe the three adiabatic potential energy surfaces, the interstate derivative couplings, and the branching and seam spaces in their full dimensionality. The application of this approach to the minimum energy three state conical intersection of the pyrazolyl radical demonstrates the potential of this method. A Hamiltonian comprised of the ten characteristic (linear) parameters and over 300 second order parameters is constructed to describe the branching space associated with a point of conical intersection. The second order parameters are determined using data at only 30 points. In the vicinity of the conical intersection the energy and derivative couplings are well reproduced and the singularity in the derivative coupling is analyzed.     

On the characterization of three-state conical intersections using a group homomorphism approach: the two-state degeneracy spaces

Second-order degenerate perturbation theory, in conjunction with the group homomorphism method for describing a similarity transformation, are used to characterize the subspace of two-state conical intersections contained in the branching space of a three-state conical intersection. It is shown by explicit calculation, using the lowest three-state conical intersection of (CH)3N2, that a second-order treatment yields highly accurate absolute energies, even at significant distances from the reference point of three-state intersection. The excellent agreement between the second order and ab initio results depends on the average energy component, which is computed using 5 first-order terms and 15 second-order terms. The second-order absolute energy change over the range rho = 0.0-0.3 au, where rho is the distance from the three-state conical intersection in the branching space coordinates, is approximately 6500 and 9500 cm(-1) for the E(1=2) and E(2=3) seams, respectively, with the maximum ab initio energy deviation from degeneracy of 200 cm(-1) occurring at rho = 0.3 au. The characteristic parameters gIJ and hIJ are also predicted to great accuracy, even at large rho, with the error growing to only 10-15% at rho = 0.3 au.     

A CASSCF and CASPT2 study on the excited states of s-trans-formaldazine

The low-lying excited states of s-trans-formaldazine (H2CN-NCH2) have been investigated using the complete active space self-consistent field (CASSCF) and the multiconfigurational second-order perturbation (CASPT2) methods. The vertical excitation energies have been calculated at the state-average CASSCF and multistate CASPT2 levels employing the cc-pVTZ basis set. The photodissociation mechanisms starting from the S1 state have been determined. The lowest energy points along the seams of surface intersections have been located in both the Franck-Condon region and the N-N dissociation pathway in the S1 state. Once the system populates the S1 state, in the viewpoint of energy, the radiationless decay via S1/S0(3) conical intersection followed by the N-N bond fission in the ground-state is more favorable in comparison with the N-N dissociation process in the S1 state. A three-surface crossing region (S1/T1/T2), where the S1, T1, and T2 states intersect, was also found. However, the intersystem crossing process via S1/T1/T2 is not energetically competitive with the internal conversion via S1/S0(3).     

On the location of conical intersections in CH2BrCl using MS-CASPT2 methods

Multiconfigurational second-order perturbation theory has been employed to calculate two-dimensional potential energy surfaces for the lowest low-lying singlet electronic states of CH2BrCl as a function of the two carbon-halogen bonds. The photochemistry of the system is controlled by a nonadiabatic crossing occurring between the A and B bands, attributed to the b1A' and c1A' states, which are found almost degenerate and forming a near-degeneracy line of almost equidistant C-Br and C-Cl bonds. A crossing point in the near-degeneracy line is identified as a conical intersection in this reduced two-dimensional space. The positions of the conical intersection located at CASSCF, single-state (SS)-CASPT2, and multistate (MS)-CASPT2 levels of theory are compared, also paying attention to the nonorthogonality problem of perturbative approaches. To validate the presence of the conical intersection versus an avoided crossing, the geometrical phase effect has been checked using the multiconfigurational MS-CASPT2 wave function.     

Efficient photochemical merocyanine-to-spiropyran ring closure mechanism through an extended conical intersection seam. A model CASSCF/CASPT2 study

A mechanism of the thermal and photochemical bleaching of merocyanine to spiropyran is proposed on the basis of CASSCF/CASPT2 calculations on the 6-(2-propenyliden)cyclohexadienone model system. Our results suggest that this photochemical transformation takes place in two steps. First, the initially pumped 1(pi-pi) S2 undergoes radiationless decay to 1(n-pi) S1 via an extended S2/S1 conical intersection seam that runs approximately parallel to the trans-to-cis isomerization coordinate, a few kilocalories per mole higher in energy. Thus, S2 --> S1 internal conversion is possible at all values of the S2 trans-to-cis reaction coordinate. Second, on the S1 potential energy surface, there is a barrierless ring closure reaction path from the S1 cis minimum that leads to a peaked S1/S0 conical intersection where the deactivation to the ground state takes place. The inertia of the moving nuclei then drives the system toward the ground-state minimum of the 2H-chromene product. Thus, the extended seam topology of the S2/S1 conical intersection and the coordinate of the branching space of the S1/S0 conical intersection are essential to explain the efficiency and high speed of this reaction.     

Role of surface crossings in the photochemistry of nitromethane

The photodissociation dynamics of nitromethane (CH(3)NO(2)) starting at the S(3) excited state has been studied at the complete active space self-consistent field level of theory in conjunction with atomic natural orbital type basis sets. In addition, the energies of all the critical points and the energy profiles connecting them have been recomputed with the multiconfigurational second-order perturbation method. It is found that the key step in the reaction mechanism is a radiationless decay through an S(3)S(2) conical intersection. The branching space spanned by the gradient difference and nonadiabatic coupling vectors of this crossing point comprises dissociation into excited nitromethane plus singlet atomic oxygen [CH(3)NO(1A")+O((1)D)] and S(3)-->S(2) deactivation, respectively. Furthermore, deactivated nitromethane S(n (n<3)) can decompose in subsequent steps into CH(3)+NO(2), where NO(2) is generated at least in two different electronic states (1 (2)B(2) and 1 (2)A(1)). It is shown that formation of excited nitric oxide NO(A (2)Sigma) arises from CH(3)NO(1A") generated in the previous step. In addition, four crossings between singlet and triplet states are localized; however, no evidence is found for a relevant role of such crossings in the photochemistry of CH(3)NO(2) initiated at S(3) state in the gas phase.     

A fast photoswitch for minimally perturbed peptides: investigation of the trans-->cis photoisomerization of N-methylthioacetamide

Thio amino acids can be integrated into the backbone of peptides without significantly perturbing their structure. In this contribution we use ultrafast infrared and visible spectroscopy as well as state-of-the-art ab initio computations to investigate the photoisomerization of the trans form of N-methylthioacetamide (NMTAA) as a model conformational photoswitch. Following the S2 excitation of trans-NMTAA in water, the return of the molecule into the trans ground state and the formation of the cis isomer is observed on a dual time scale, with a fast component of 8-9 ps and a slow time constant of approximately 250 ps. On both time scales the probability of isomerization to the cis form is found to be 30-40%, independently of excitation wavelength. Ab initio CASPT2//CASSCF photochemical reaction path calculations indicate that, in vacuo, the trans-->cis isomerization event takes place on the S1 and/or T1 triplet potential energy surfaces and is controlled by very small energy barriers, in agreement with the experimentally observed picosecond time scale. Furthermore, the calculations identify one S2/S1 and four nearly isoenergetic S1/S0 conical intersection decay channels. In line with the observed isomerization probability, only one of the S1/S0 conical intersections yields the cis conformation upon S1-->S0 decay. A substantially equivalent excited-state relaxation results from four T1/S0 intersystem crossing points.     

Water effect on the excited-state decay paths of singlet excited cytosine

Two low-energy deactivation paths for singlet excited cytosine, one through a S₁/S₀ conical intersection of the ethylene type, and one through a conical intersection that involves the (n_N, π^*) state, are calculated in the presence of water. Water is included explicitly for several cytosine monohydrates, and as a bulk solvent, and the calculations are carried out at the complete active space self-consistent field (CASSCF) and complete active space second order perturbation (CASPT2) levels of theory. The effect of water on the lowest-energy path through the ethylenic conical intersection is a lowering of the energy barrier. This is explained by stabilization of the excited state, which has zwitterionic character in the vicinity of the conical intersection due to its similarity with the conical intersection of ethylene. In contrast to this, the path that involves the (n_N, π^*) state is destabilized by hydrogen bonding, although the bulk solvent effect reduces the destabilization. Overall, this path should remain energetically accessible.     

Ab initio molecular dynamics and time-resolved photoelectron spectroscopy of electronically excited uracil and thymine

The reaction dynamics of excited electronic states in nucleic acid bases is a key process in DNA photodamage. Recent ultrafast spectroscopy experiments have shown multicomponent decays of excited uracil and thymine, tentatively assigned to nonadiabatic transitions involving multiple electronic states. Using both quantum chemistry and first principles quantum molecular dynamics methods we show that a true minimum on the bright S2 electronic state is responsible for the first step that occurs on a femtosecond time scale. Thus the observed femtosecond decay does not correspond to surface crossing as previously thought. We suggest that subsequent barrier crossing to the minimal energy S2/S1 conical intersection is responsible for the picosecond decay.     

A theoretical characterization of the photoisomerization channels of 1,2-cyclononadienes on both singlet and triplet potential-energy surfaces

The ground-, (1)(pipi*)-, and (3)(pipi*)-state potential-energy surfaces of 1,2-cyclononadiene and isomeric C(9)H(14) species, as well as 1-methyl-1,2-cyclononadiene and isomeric C(10)H(16) species were all mapped using CASSCF and the 6-31G(d) basis set. Theoretical results were found to be in good agreement with the available experimental observations for both 1,2-cyclononadiene and 1-methyl-1,2-cyclononadiene isomerization reactions under singlet and triplet direct or sensitized irradiation. Extremely efficient decay occurs from the first singlet excited state to the ground state through at least three different conical intersections (surface crossings). The first of these crossing points is accessed by a one-bond ring closure. From this conical intersection point (CI-A or CI-C), some possible subsequent ground-state reaction paths have been identified: 1) intramolecular C--H bond insertion to form the bicyclic photoproduct and 2) intramolecular C--H bond insertion to form tricyclic photoproducts. An excited state [1,3]-sigmatropic shift leads to the second conical intersection (CI-B or CI-E), which can give a three-bond cyclononyne species. Besides these, in the singlet photochemical reactions of 1-methyl-1,2-cyclononadiene, excited-state, one allenic C--H bond insertion leads to a third conical intersection (CI-D). Possible ground-state reaction pathways from this structure lead to the formation of a diene photoproduct or to transannular insertion photoproducts. Moreover, in the case of triplet 1,2-cyclononadiene and 1-methyl-1,2-cyclononadiene photoisomerization reactions, both chemical reactions will adopt a 1,3-biradical (T(1)/S(0)-1, T(1)/S(0)-2, and T(1)/S(0)-3), which may undergo intersystem crossings leading to the formation of tricyclic or bicyclic photoproducts. The results obtained allow a number of predictions to be made.