Reactive chemical dynamics through conical intersections

Reaction dynamics of prototypical, D + H₂ and Cl (²P) + H₂, chemical reactions occurring through the conical intersections of the respective coupled multi-sheeted potential energy surfaces is examined here. In addition to the electronic coupling, nonadiabatic effects due to relativistic spin-orbit coupling are also considered for the latter reaction. A time-dependent wave packet propagation approach is undertaken and the quantum dynamical observables viz., energy resolved reaction probabilities, integral reaction cross-sections and thermal rate constants are reported.     

Intersystem crossing at singlet conical intersections

The energy of the lowest triplet state of organic molecules is intermediate between the ground state and the first excited singlet. At the S₁/S₀ conical intersection, the two singlet states are degenerate. It is shown that for some molecules (ethylene, benzene, toluene and pyrrole) the T₁ state is also degenerate with the two singlet states. Moreover, the spin orbit coupling matrix element at this structure is necessarily large, so that intersystem crossing can be quite efficient. If the lowest triplet state is repulsive (as in the studied molecules) it may significantly contribute to the dissociation yield under certain experimental conditions.     

Light-induced conical intersections: topological phase, wave packet dynamics, and molecular alignment

In previous publications (J. Phys. B: At., Mol. Opt. Phys.2008, 41, 221001; J. Phys. B: At., Mol. Opt. Phys. 2011, 44, 045603) a novel and physically interesting phenomenon was found in the field of light-matter interactions. It was shown theoretically that exposing a molecule to a laser field can give rise to the appearance of so-called light-induced conical intersections (LICIs). The existence of such LICIs may change significantly the field free physical properties of a molecular system. In this article we review the LICIs in diatomics and provide a new insight to the LICI phenomenon. The sodium dimer is chosen as an explicit sample system. We calculated the Berry phase for a contour that surrounds the point of LICI and found it to be π, which is the same value as for the case of a "natural" CI in triatomic or larger molecules. We also present results to stress the impact of LICIs on molecular wave packet dynamics and molecular alignment in different electronic states.     

Quantum dynamics through conical intersections: combining effective modes and quadratic couplings

We present a detailed study for the short-time dynamics through conical intersections in molecular systems related to the quadratic vibronic coupling (QVC) Hamiltonian [Müller, H.; K?ppel, H.; Cederbaum, L. S. New J. Chem. 1993, 17, 7-29] and the effective-mode formalism [Cederbaum, L. S.; Gindensperger, E.; Burghardt, I. Phys. Rev. Lett. 2005, 94, 113003]. Our approach is based on splitting the nuclear degrees of freedom of the whole system into system modes and environment modes. It was found that only three-effective environmental modes together with the system's modes are needed to describe the short-time dynamics of the complex system correctly. In addition, a detailed mathematical proof is given in the appendix to demonstrate that the exact cumulants are recovered up to the second order within the cumulant expansion of the autocorrelation function. The butatriene molecule is studied as an explicit showcase example to stress the viability of our proposed scheme and to compare with other systems.     

Complex dynamics at conical intersections: vibronic spectra and ultrafast decay of electronically excited trifluoroacetonitrile radical cation

An ab initio quantum dynamical study is performed here to examine the complex nuclear motion underlying the first two photoelectron bands of trifluoroacetonitrile. The highly overlapping structures of the latter are found to originate from transitions to the five lowest electronic states (viz., X(2)E, A(2)A1, B(2)A2, C(2)A1, and D(2)E) of the trifluoroacetonitrile radical cation. The Jahn-Teller (JT) instability of the doubly degenerate X and, D and their pseudo-Jahn-Teller (PJT) interactions with the nondegenerate A, B, and C electronic states along the degenerate vibrational modes lead to multiple multidimensional conical intersections and complex nuclear trajectories through them. It is found that the JT splitting is very weak in the X and relatively stronger in the D state. However, the PJT couplings play the pivotal role in the detailed shape of the vibronic bands of the radical cation. Ultrafast nonradiative decay of electronically excited radical cation has been examined. The findings of this paper are compared with the experimental data and are also discussed in relation to those observed for the methyl cyanide radical cation.     

Short-time dynamics through conical intersections in macrosystems. II. Applications

We present several numerical applications based upon the effective-mode formulation for the short-time dynamics through conical intersections in macrosystems, as detailed in the preceding paper and first proposed by Cederbaum et al. [Phys. Rev. Lett. 94, 113003 (2005)]. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective environmental modes are needed-together with the system's modes-to accurately calculate the low resolution spectra and the short-time dynamics of the entire macrosystem. For the systems discussed here, results are compared to those of a full quantum wave-packet propagation. Some rules are extracted to provide general tendencies; these rules allow one to understand and predict the dynamical properties in more general situations where the exact quantum dynamics of the macrosystem is out of reach.     

Beyond two-state conical intersections. Three-state conical intersections in low symmetry molecules: the allyl radical

Using multireference configuration interaction expansions comprised of over 7 million configuration state functions, three-state conical intersections are reported for the closely spaced, spectroscopically observed (tilde)B(2A1), (tilde)C(2B1), and (tilde)D(2B2) states (in C(2v) symmetry) of the allyl radical. These conical intersections of states which were previously assigned as the 3,4,5(2)A states and are here reassigned as the 4,5,6(2)A states, are expected to be accessible using optical probes. This conclusion is obtained from the structure of the minimum energy point on the 4,5,6(2)A three-state conical intersection seam which is similar to the equilibrium structure of the ground (tilde)X(2A2) state and only 1.1 eV above the (tilde)D(2B2) state at its equilibrium geometry. The seam of three-state degeneracies joins two two-state seams of conical intersection, the 4,5(2)A and 5,6(2)A conical intersection seams. The energy of the minimum energy point on the 4,5(2)A two-state seam is only 0.15 eV above that of the (tilde)D(2B2) state at its equilibrium structure. Three-state intersections are also reported for the 3,4,5(2)A states.     

Quantum dynamics through conical intersections in macrosystems: Combining effective modes and time-dependent Hartree

We address the nonadiabatic quantum dynamics of (macro)systems involving a vast number of nuclear degrees of freedom (modes) in the presence of conical intersections. The macrosystem is first decomposed into a system part carrying a few, strongly coupled modes, and an environment, comprising the remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment can be constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. The environment is described by a few effective modes augmented by a residual environment. In practice, the effective modes can be added to the system’s modes and the quantum dynamics of the entire macrosystem can be accurately calculated on a limited time-interval. For longer times, however, the residual environment plays a role. We investigate the possibility to treat fully quantum mechanically the system plus a few effective environmental modes, augmented by the dynamics of the residual environment treated by the time-dependent Hartree (TDH) approximation. While the TDH approximation is known to fail to correctly reproduce the dynamics in the presence of conical intersections, it is shown that its use on top of the effective-mode formalism leads to much better results. Two numerical examples are presented and discussed; one of them is known to be a critical case for the TDH approximation.     

Short-time dynamics through conical intersections in macrosystems. I. Theory: effective-mode formulation

The short-time dynamics through a conical intersection of a macrosystem comprising a large number of nuclear degrees of freedom (modes) is investigated. The macrosystem is decomposed into a "system" part carrying a limited number of modes, and an "environment" part. An orthogonal transformation in the environment's space is introduced, as a result of which a subset of three effective modes can be identified which couple directly to the electronic subsystem. Together with the system's modes, these govern the short-time dynamics of the overall macrosystem. The remaining environmental modes couple, in turn, to the effective modes and become relevant at longer times. In this paper, we present the derivation of the effective Hamiltonian, first introduced by Cederbaum et al. [Phys. Rev. Lett. 94, 113003 (2005)], and analyze its properties in some detail. Several special cases and topological aspects are discussed.     

Ultrafast dynamics through conical intersections and intramolecular vibrational energy redistribution in styrene

We report a femtosecond time-resolved photoelectron spectroscopy (TRPES) investigation of internal conversion in the first two excited singlet electronic states of styrene. We find that radiationless decay through an S(1)/S(0) conical intersection occurs on a timescale of ～4 ps following direct excitation to S(1) with 0.6 eV excess energy, but that the same process is significantly slower (～20 ps) if it follows internal conversion from S(2) to S(1) after excitation to S(2) with 0.3 eV excess energy (0.9 eV excess energy in S(1)).     

Hierarchy of effective modes for the dynamics through conical intersections in macrosystems

An extension of the effective-mode theory for the short-time dynamics through conical intersections in macrosystems [L. S. Cederbaum et al., Phys. Rev. Lett. 94, 113003 (2005)] is proposed. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective modes are needed-together with the system's modes-to accurately calculate low resolution spectra and the short-time dynamics of the entire macrosystem. Here, the authors propose an iterative scheme to construct a hierarchy of additional triplets of effective modes. This naturally extends the effective-mode formulation. By taking into account more and more triplets, the dynamics are accurately predicted for longer and longer times, and more resolved spectra can be calculated. Numerical examples are presented, computed using various numbers of additional effective modes.     

Gold-catalyzed reactions of 2-alkynyl-phenylamines with alpha,beta-enones

[reaction: see text] The gold-catalyzed reaction of 2-alkynyl-phenylamines with alpha,beta-enones represents a new general one-pot entry into C-3-alkyl-indoles by sequential reactions. Gold-catalyzed sequential cyclization/alkylation, N-alkylation/cyclization, or N-alkylation/cyclization/alkylation reactions leading to different indoles can be directed by changing the 2-alkynyl-phenylamine 1/alpha,beta-enone 3 ratio and the reaction temperature. Unusual gold-catalyzed rearrangement reaction of indoles are observed at 140 degrees C. New gold-catalyzed formation of propargyl-alkyl ether under mild conditions and the hydration reaction of N-acetyl-2-ethynyl-phenylamine are reported.     

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).     

The T(1) (3)(pi-pi*)/S(0) intersections and triplet lifetimes of cyclic alpha,beta-enones.

The ground and triplet excited states of cycloheptenone, cyclohexenone, and cyclopentenone have been studied using CASSCF calculations. For these three molecules, the difference in energy (DeltaE) between the twisted T(1) (3)(pi-pi*) minimum and T(1) (3)(pi-pi*)/S(0) intersection increases as the flexibility of the ring decreases. A strong positive correlation between DeltaE and the natural logarithm of the experimentally determined triplet lifetimes (ln tau) is found, suggesting that DeltaE predominantly determines the relative radiationless decay rates of T(1).     

Enantioselective epoxidation of alpha,beta-enones promoted by alpha,alpha-diphenyl-L-prolinol as bifunctional organocatalyst

[reaction: see text] An operationally simple and mild protocol for the catalytic enantioselective epoxidation of alpha,beta-unsaturated ketones has been estabilished using commercially available alpha,alpha-diphenyl-l-prolinol as bifunctional organocatalyst and tert-butyl hydroperoxide (TBHP) as oxidant. The epoxides have been obtained in good yields and with up to 80% ee.     

Dynamics at conical intersections: the influence of O-H stretching vibrations on the photodissociation of phenol

Comparing the recoil energy distributions of the fragments from one-photon dissociation of phenol-d(5) with those from vibrationally mediated photodissociation shows that initial vibrational excitation strongly influences the disposal of energy into relative translation. The measurements use velocity map ion imaging to detect the H-atom fragments and determine the distribution of recoil energies. Dissociation of phenol-d(5) molecules with an initially excited O-H stretching vibration produces significantly more fragments with low recoil energies than does one-photon dissociation at the same total energy. The difference appears to come from the increased probability of adiabatic dissociation in which a vibrationally excited molecule passes around the conical intersection between the dissociative state and the ground state to produce electronically excited phenoxyl-d(5) radicals. The additional energy deposited in electronic excitation of the radical reduces the energy available for relative translation.     

Theory of the photodissociation of ozone in the Hartley continuum: potential energy surfaces, conical intersections, and photodissociation dynamics

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.     

Geometrical and substituent effects in conical intersections: linking chemical structure and photoreactivity in polyenes

The knowledge of the intersection space topography of electronic states is essential for deciphering and predicting photoinduced reactions. Michl and Bonaci?-Koutecky developed a two-electron two-orbital model that allowed first systematic studies of the chemical origin of conical intersections in strongly polar systems. We generalize this approach to arbitrary functionalized and unfunctionalized polyene systems. For the extended model, a set of mathematical conditions for the formation of conical intersections are derived. These conditions are translated into geometrical motions and electronic effects, which help to explain and predict the structure and energetics of conical intersections. A three-step strategy for the conceptual search of conical intersections is outlined. Its universal validity is demonstrated using the textbook example cyclohexadiene and its functionalized derivative trifluoromethyl-indolylfulgide, a chromophore studied for possible application as a molecular switch.     

Exploring molecular complexity: conical intersections and NH3 photodissociation

The role of conical intersections in the photodissociation of the A 1A2" state of NH3 is investigated using extended atomic basis sets and a configuration state function expansion of approximately 8.5 million terms. A previously unknown portion of the 1 1A-2 1A seam of conical intersections with only C(s) symmetry is located. This portion of the seam is readily accessible from the equilibrium geometry of the A 1A2" state. These conical intersections are expected to play a role in the competition between adiabatic and nonadiabatic pathways for NH3(A 1A2") photodissociation.