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 study of conical intersections for the H3(+) system

A parametrization of the three asymptotic conical intersections between the energies of the H3(+) ground state and the first excited singlet state is presented. The influence of an additional, fourth conical intersection between the first and second excited states at the equilateral geometry on the connection between the three conical regions is studied, for both diatomics-in-molecules and ab initio molecular data.     

On the characterization of three state conical intersections using a group homomorphism approach: mapping the full N-5 dimensional seam space

A method for characterizing the degeneracy preserving seam space in the vicinity of a three state conical intersection is introduced. Second order degenerate perturbation theory is used to construct an approximately diabatic Hamiltonian whose eigenenergies and eigenstates accurately describe the vicinity of the three state conical intersection in its full dimensionality. The perturbative analysis enables the large number, 6(N(int)(N(int)+1)2), of unique second order parameters needed to construct this accurate Hamiltonian to be determined from ab initio data at a limited number of nuclear configurations, with (N(int)+10) being minimal. Using the minimum energy three state conical intersection of the pyrazolyl radical (N(int) = 18), the potential of this approach is illustrated. A Hamiltonian comprised of the ten characteristic (linear) parameters and over 1440 second order parameters is constructed and used to determine the locus of the conical intersection seam as well as to describe the 18 dimensional space in the vicinity of that point of intersection. Our results demonstrate the ability of this methodology to quantitatively reproduce the ab initio potential energy surfaces near a three state conical intersection.     

Conical intersection of the ground and first excited states of water: energies and reduced density matrices from the anti-Hermitian contracted Schrödinger equation

A conical intersection between the ground and first-excited states of water is computed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions of the anti-Hermitian contracted Schr?dinger equation (ACSE). This study is an extension of a previous study in which the ACSE was used to compute the energies around a conical intersection in the triplet excited states of methylene [Snyder, J. W., Jr.; Rothman, A. E.; Foley, J. J.; Mazziotti, D. A. J. Chem. Phys. 2010, 132, 154109]. We compute absolute energies of the 1(1)A' and 2(1)A' states of water (H(2)O) and the location of the conical intersection. The ACSE energies are compared to those from ab initio wave function methods. To treat multireference correlation, we seed the ACSE with an initial 2-RDM from a multiconfiguration self-consistent field (MCSCF) calculation. Unlike the situation for methylene, the two states in the vicinity of the conical intersection of water both have the same spatial symmetry. Hence, the study demonstrates the ability of the ACSE to resolve states of the same spatial symmetry that are nearly degenerate in energy. The 2-RDMs from the ACSE nearly satisfy necessary N-representability conditions. Comparison of the results from double-ζ and augmented double-ζ basis sets demonstrates the importance of augmented (or diffuse) functions for determining the location of the conical intersection.     

On the vibronic coupling approximation: a generally applicable approach for determining fully quadratic quasidiabatic coupled electronic state Hamiltonians

In this report we introduce an iterative procedure for constructing a quasidiabatic Hamiltonian representing N(state)-coupled electronic states in the vicinity of an arbitrary point in N(int)-dimensional nuclear coordinate space. The Hamiltonian, which is designed to compute vibronic spectra employing the multimode vibronic coupling approximation, includes all linear terms which are determined exactly using analytic gradient techniques. In addition, all [N(state)][N(int)] quadratic terms, where [n]=n(n+1)/2, are determined from energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. The use of energy gradient and derivative coupling information enables the large number of second order parameters to be determined employing ab initio data computed at a limited number of points (N(int) being minimal) and assures a maximal degree of quasidiabaticity. Numerical examples are given in which quasidiabatic Hamiltonians centered around three points on the C(3)H(3)N(2) potential energy surface (the minimum energy point on the ground state surface and the minimum energy points on the two- and three-state seams of conical intersection) were computed and compared. A method to modify the conical intersection based Hamiltonians to better describe the region of the ground state minimum is introduced, yielding improved agreement with ab initio results, particularly in the case of the Hamiltonian defined at the two-state minimum energy crossing.     

Ab initio based surface-hopping dynamics study on ultrafast internal conversion in cyclopropanone

Cyclopropanone exhibits an intriguing phenomenon that the fluorescence from the S(1) state disappears below 365 nm. This is ascribed to the ultrafast S(1) → S(0) internal conversion process via conical intersection, which deprives opportunity of the fluorescence emission. In this work, we have used ab initio based surface hopping dynamics method to study vibrational-mode-dependent S(1) → S(0) internal conversion of cyclopropanone. A new conical intersection between the S(1) and S(0) states is determined by the state-averaged CASSCF/cc-pVDZ calculations, which is confirmed to play a critical role in the ultrafast S(1) → S(0) internal conversion by the nonadiabatic dynamics simulations. It is found that the internal conversion occurs more efficiently when the initial kinetic energies are distributed in the four vibrational modes related to the C═O group, especially in the C-O stretching and the O-C-C-C out-of-plane torsional modes. Meanwhile, the S(1) lifetime and the time scale of the S(1) → S(0) internal conversion are estimated by the ab initio based dynamics simulations, which is consistent with the ultrafast S(1) → S(0) internal conversion and provides further evidence that the ultrafast internal conversion is responsible for the fluorescence disappearance of cyclopropanone.     

A new "spectroscopic" potential energy surface for formaldehyde in its ground electronic state

We report a new "spectroscopic" potential energy surface (PES) of formaldehyde (H(2)(12)C(16)O) in its ground electronic state, obtained by refining an ab initio PES in a least-squares fitting to the experimental spectroscopic data for formaldehyde currently available in the literature. The ab initio PES was computed using the CCSD(T)/aug-cc-pVQZ method at 30 840 geometries that cover the energy range up to 44 000 cm(-1) above equilibrium. Ro-vibrational energies of formaldehyde were determined variationally for this ab initio PES by means of the program TROVE [Theoretical ROtation-Vibration Energies; S. N. Yurchenko, W. Thiel, and P. Jensen, J. Mol. Spectrosc. 245, 126 (2007)]. The parameter values in the analytical representation of the PES were optimized in fittings to 319 ro-vibrational energies with J = 0, 1, 2, and 5. The initial parameter values in the fittings were those of the ab initio PES, the ro-vibrational eigenfunctions obtained from this PES served as a basis set during the fitting process, and constraints were imposed to ensure that the refined PES does not deviate unphysically from the ab initio one in regions of configuration space not sampled by the experimental data. The resulting refined PES, referred to as H(2)CO-2011, reproduces the available experimental J ≤ 5 data with a root-mean-square error of 0.04 cm(-1).     

Direct calculation of coupled diabatic potential-energy surfaces for ammonia and mapping of a four-dimensional conical intersection seam

We used multiconfiguration quasidegenerate perturbation theory and the fourfold-way direct diabatization scheme to calculate ab initio potential-energy surfaces at 3600 nuclear geometries of NH3. The calculations yield the adiabatic and diabatic potential-energy surfaces for the ground and first electronically excited singlet states and also the diabatic coupling surfaces. The diabatic surfaces and coupling were fitted analytically to functional forms to obtain a permutationally invariant 2 x 2 diabatic potential-energy matrix. An analytic representation of the adiabatic potential-energy surfaces is then obtained by diagonalizing the diabatic potential-energy matrix. The analytic representation of the surfaces gives an analytic representation of the four-dimensional conical intersection seam which is discussed in detail.     

Derivation of the electronic nonadiabatic coupling field in molecular systems: an algebraic-vectorial approach

In this Communication it is suggested that various elements of the nonadiabatic coupling matrix, tau(jk)(s) are created by the singular nonadiabatic coupling terms of the system. Moreover, given the spatial distribution of these coupling terms in the close vicinity of their singularity points yields, according to this approach, the integrated intensity of the field at every point in the region of interest. To support these statements we consider the conical intersections of the three lower states of the H+H(2) system: From an ab initio treatment we obtain the nonadiabatic coupling terms around each conical intersection separately (at its close vicinity) and having those, create the field at every desired point employing vector-algebra. This approach is also used to calculate the intensity of the Curl of those matrix elements that lack their own sources [tau(13)(s) in the present case]. The final results are compared with relevant ab initio calculations.     

Analytic three-dimensional 'MLR' potential energy surface for CO(2)-He, and its predicted microwave and infrared spectra

A three-dimensional, analytic potential energy surface for CO(2)-He that explicitly incorporates its dependence on the Q(3) asymmetric-stretch normal-mode coordinate of the CO(2) monomer has been obtained by least-squares fitting new ab initio interaction energies to a new three-dimensional Morse/Long-Range (3D-MLR) potential function form. This fit to 2832 points has a root-mean-square (RMS) deviation of 0.032 cm(-1) and requires only 55 parameters. The resulting pure ab initio potential provides a good representation of the experimental microwave and infrared data: for 51 pseudo microwave and 49 infrared transitions the RMS discrepancies are 0.0110 and 0.0445 cm(-1), respectively. Scaling this surface using only two morphing parameters yields an order of magnitude better agreement with experiments, with RMS discrepancies of only 0.0025 and 0.0038 cm(-1), respectively. The calculated infrared band origin shift associated with the nu(3) fundamental of CO(2) is 0.109 cm(-1), in good agreement with the (extrapolated) experimental value of 0.095 cm(-1).     

CVRQD ab initio ground-state adiabatic potential energy surfaces for the water molecule

The high accuracy ab initio adiabatic potential energy surfaces (PESs) of the ground electronic state of the water molecule, determined originally by Polyansky et al. [Science 299, 539 (2003)] and called CVRQD, are extended and carefully characterized and analyzed. The CVRQD potential energy surfaces are obtained from extrapolation to the complete basis set of nearly full configuration interaction valence-only electronic structure computations, augmented by core, relativistic, quantum electrodynamics, and diagonal Born-Oppenheimer corrections. We also report ab initio calculations of several quantities characterizing the CVRQD PESs, including equilibrium and vibrationally averaged (0 K) structures, harmonic and anharmonic force fields, harmonic vibrational frequencies, vibrational fundamentals, and zero-point energies. They can be considered as the best ab initio estimates of these quantities available today. Results of first-principles computations on the rovibrational energy levels of several isotopologues of the water molecule are also presented, based on the CVRQD PESs and the use of variational nuclear motion calculations employing an exact kinetic energy operator given in orthogonal internal coordinates. The variational nuclear motion calculations also include a simplified treatment of nonadiabatic effects. This sophisticated procedure to compute rovibrational energy levels reproduces all the known rovibrational levels of the water isotopologues considered, H(2) (16)O, H(2) (17)O, H(2) (18)O, and D(2) (16)O, to better than 1 cm(-1) on average. Finally, prospects for further improvement of the ground-state adiabatic ab initio PESs of water are discussed.     

Full-dimensional (15-dimensional) ab initio analytical potential energy surface for the H7+ cluster

Full-dimensional ab initio potential energy surface is constructed for the H(7)(+) cluster. The surface is a fit to roughly 160,000 interaction energies obtained with second-order M?llerPlesset perturbation theory and the cc-pVQZ basis set, using the invariant polynomial method [B. J. Braams and J. M. Bowman, Int. Rev. Phys. Chem. 28, 577 (2009)]. We employ permutationally invariant basis functions in Morse-type variables for all the internuclear distances to incorporate permutational symmetry with respect to interchange of H atoms into the representation of the surface. We describe how different configurations are selected in order to create the database of the interaction energies for the linear least squares fitting procedure. The root-mean-square error of the fit is 170 cm(-1) for the entire data set. The surface dissociates correctly to the H(5)(+) + H(2) fragments. A detailed analysis of its topology, as well as comparison with additional ab initio calculations, including harmonic frequencies, verify the quality and accuracy of the parameterized potential. This is the first attempt to present an analytical representation of the 15-dimensional surface of the H(7)(+) cluster for carrying out dynamics studies.     

Photochemistry of pyrrole: time-dependent quantum wave-packet description of the dynamics at the 1pi sigma*-S0 conical intersections

The photoinduced hydrogen-elimination reaction in pyrrole via the conical intersections of the two (1)pi sigma(*) excited states with the electronic ground states [(1)B(1)(pi sigma(*))-S(0) and (1)A(2)(pi sigma(*))-S(0)] have been investigated by time-dependent quantum wave-packet calculations. Model potential-energy surfaces of reduced dimensionality have been constructed on the basis of accurate multireference ab initio electronic-structure calculations. For the (1)B(1)-S(0) conical intersection, the model includes the NH stretching coordinate as the tuning mode and the hydrogen out-of-plane bending coordinate as the coupling mode. For the (1)A(2)-S(0) conical intersection, the NH stretching coordinate and the screwing coordinate of the ring hydrogens are taken into account. The latter is the dominant coupling mode of this conical intersection. The electronic population-transfer processes at the conical intersections, the branching ratio between the dissociation channels, and their dependence on the initial preparation of the system have been investigated for pyrrole and deuterated pyrrole. It is shown that the excitation of the NH stretching mode strongly enhances the reaction rate, while the excitation of the coupling mode influences the branching ratio of different dissociation channels. The results suggest that laser control of the photodissociation of pyrrole via mode-specific vibrational excitation should be possible. The calculations provide insight into the microscopic details of ultrafast internal-conversion processes in pyrrole via hydrogen-detachment processes, which are aborted at the (1)pi sigma(*)-S(0) conical intersections. These mechanisms are of relevance for the photostability of the building blocks of life (e.g., the DNA bases).     

Carbene formation in its lower singlet state from photoexcited 3H-diazirine or diazomethane. A combined CASPT2 and ab initio direct dynamics trajectory study

The potential energy surfaces of the ground and valence excited states of both 3H-diazirine and diazomethane have been studied computationally by mean of the CASSCF method in conjunction with the cc-pVTZ basis set. The energies of the critical points found on such surfaces have been recomputed at the CASPT2/cc-pVTZ level. Additionally, ab initio direct dynamic trajectory calculations have been carried out on the S(1) and S(2) surfaces, starting each trajectory run at the region dominated by the conformational molecular rearrangement of diazomethane. It is found that both isomers are interconnected along a C(s)() reaction coordinate on each potential surface. Radiationless deactivation of the corresponding S(1) state of each isomer occurs through the same point on the surface, an S(1)/S(0) conical intersection. Thereafter, the system has enough energy to surmount the barrier which leads to dissociation products (CH(2) + N(2)) on S(0) state. Therefore, photoexcitation to S(1) state of either diazirine of diazomethane produces methylene in its lower singlet state on a very short time scale (ca. 100 fs). Furthermore, both isomers can generate excited singlet carbene when they are excited onto the S(2) surface; in this case, they lose the activation energy passing through another common S(2)/S(1) conical intersection and then proceed to dissociation into carbene and N(2) on the S(1) surface. For the special case of methylene, it rapidly experiences deexcitation to S(0) state.     

Ultrafast deactivation of an excited cytosine-guanine base pair in DNA

Multiconfigurational ab initio calculations and QM/MM molecular dynamics simulations of a photoexcited cytosine-guanine base pair in both gas phase and embedded in the DNA provide detailed structural and dynamical insights into the ultrafast radiationless deactivation mechanism. Photon absorption promotes transfer of a proton from the guanine to the cytosine. This proton transfer is followed by an efficient radiationless decay of the excited state via an extended conical intersection seam. The optimization of the conical intersection revealed that it has an unusual topology, in that there is only one degeneracy-lifting coordinate. This is the central mechanistic feature for the decay both in vacuo and in the DNA. Radiationless decay occurs along an extended hyperline nearly parallel to the proton-transfer coordinate, indicating the proton transfer itself is not directly responsible for the deactivation. The seam is displaced from the minimum energy proton-transfer path along a skeletal deformation of the bases. Decay can thus occur anywhere along the single proton-transfer coordinate, accounting for the remarkably short excited-state lifetime of the Watson-Crick base pair. In vacuo, decay occurs after a complete proton transfer, whereas in DNA, decay can also occur much earlier. The origin of this effect lies in the temporal electrostatic stabilization of dipole in the charge-transfer state in DNA.     

Potential energy surface crossings and the mechanistic spectrum for intramolecular electron transfer in organic radical cations.

The structure of the potential energy surface for the intramolecular electron transfer (IET) of four different model radical cations has been determined by using reaction path mapping and conical intersection optimization at the ab initio CASSCF level of theory. We show that, remarkably, the calculated paths reside in regions of the ground-state energy surface whose structure can be understood in terms of the position and properties of a surface crossing between the ground and the first excited state of the reactant. Thus, in the norbornadiene radical cation and in an analogue compound formed by two cyclopentene units linked by a norbornyl bridge, IET proceeds along direct-overlap and super-exchange concerted paths, respectively, that are located far from a sloped conical intersection point and in a region where the excited-state and ground-state surfaces are well separated. A second potential energy surface structure has been documented for 1,2-diamino ethane radical cation and features two parallel concerted (direct) and stepwise (chemical) paths. In this case a peaked conical intersection is located between the two paths. Finally, a third type of energy surface is documented for the bismethyleneadamantane radical cation and occurs when there is, effectively, a seam of intersection points (not a conical intersection) which separates the reactant and product regions. Since the reaction path cannot avoid the intersection, IET can only occur nonadiabatically. These IET paths indicate that quite different IET mechanisms may operate in radical cations, revealing an unexpectedly enriched and flexible mechanistic spectrum. We show that the origin of each path can be analyzed and understood in terms of the one-dimensional Marcus-Hush model.     

The ring-opening reaction of chromenes: a photochemical mode-dependent transformation

The efficiency of the photochemical ring-opening of chromenes (or benzopyrans) depends on the vibronic transition selected by the chosen excitation wavelength. In the present work, ab initio CASPT2//CASSCF calculations are used to determine the excited-state ring-opening reaction coordinate for 2H-chromene (C) and 2,2-diethyl-2H-chromene (DEC) and provide an explanation for such an unusual mode-dependent behavior. It is shown that excited-state relaxation and decay occur via a multimodal and barrierless (or nearly barrierless) reaction coordinate. In particular, the relaxation out of the Franck-Condon involves a combination of in-plane skeletal stretching and out-of-plane modes, while the second part of the reaction coordinate is dominated exclusively by a different out-of-plane mode. Population of this last mode is shown to be preparatory with respect to both C-O bond breaking and decay via an S(1)/S(0) conical intersection. The observed mode-dependent ring-opening efficiency is explained by showing that the vibrational mode corresponding to the most efficient vibronic transition has the largest projection onto the out-of-plane mode of the reaction coordinate. To support the computationally derived mechanism, we provide experimental evidence that the photochemical ring-opening reaction of 2,2-dimethyl-7,8-benzo(2H)chromene, that similarly to DEC exhibits a mode-dependent photoreaction, has a low ( approximately 1 kcal mol(-1)) activation energy barrier.     

Intramolecular electron transfer in bis(methylene) adamantyl radical cation: a case study of diabatic trapping

Our characterization of the potential energy surface for electron transfer (ET) in the bis(methylene)adamantane (BMA) model radical cation shows that the surface topology is prone to diabatic trapping (competition between ET and upward hops to the excited state). The general conditions for this phenomenon have been derived. The surface is centered around a conical intersection, and diabatic trapping occurs because one of the branching space coordinates (coordinates that lift the degeneracy at first order) corresponds to a vector of small length. For BMA, this coordinate is an antisymmetric breathing mode of the rigid carbon framework. Other modes (including methylene torsions and pyramidalizations) may lift the degeneracy at second-order but do not affect the energy gap at the intersection region effectively. The resulting topology is similar to that of an (n - 1) dimensional seam (where n is the number of nuclear degrees of freedom of the molecule) that cannot be avoided along the reaction coordinate, thus favoring recrossing to the upper surface. This analysis is extended by ab initio semiclassical dynamics using an Ehrenfest and a trajectory surface hopping algorithm implemented at the CASSCF level. Examination of the trajectories shows that there is no single mode that controls the diabatic trap, in agreement with the condition that there is no predominant degeneracy-lifting coordinate. Thus the reactivity depends on a combination of small effects, where presumably higher-order effects come into play. This should be the general behavior of dynamics at a diabatic trapping situation.     

Photochemical Reaction Mechanism of Intramolecular H Transfer Reaction of H2C3O+⋅ Radical Cation

The photochemical reaction mechanism underlying the intramolecular H-transfer of the H₂C₃O⁺⋅ radical cation to the H₂CCCO⁺⋅ methylene ketene cation was elucidated using time-dependent density functional theory and high-level ab initio methods. Once the D₁ state of H₂C₃O⁺⋅ is populated, the reaction proceeds to form an intermediate (IM) in the D₁ state (IM4_D1). The molecular structure of the conical intersection (CI) was optimized using a multiconfigurational ab initio method. The CI is readily accessible because it lies slightly above the IM4_D1 in energy. In addition, the gradient difference vector of the CI is almost parallel to the intramolecular H-transfer reaction coordinate. Once the vibration mode of IM4_D1 which is parallel to the reaction coordinate is populated, the degeneracy of the CI is readily lifted and H₂CCCO⁺⋅ was formed via a relaxation pathway in the D₀ state. Our calculated results clearly describe the photochemical intramolecular H transfer reaction reported in a recent study.