Nonadiabatic transition and energy relaxation dynamics in the photoisomerization of s-trans butadiene

Excited state dynamics of cis,cis-1,3-cyclooctadiene: Non-adiabatic trajectory surface hopping

We have performed trajectory surface hopping dynamics for cis,cis-1,3-cyclooctadiene to investigate the photochemical pathways involved after being excited to the S₁ state. Our calculations reveal ultrafast decay to the ground state, facilitated by conical intersections involving distortions around the double bonds. The main distortions are localized on one double bond, involving twisting and pyramidalization of one of the carbons of that double bond (similar to ethylene), while a limited number of trajectories decay via delocalized (non-local) twisting of both double bonds. The interplay between local and non-local distortions is important in our understanding of photoisomerization in conjugated systems. The calculations show that a broad range of the conical intersection seam space is accessed during the non-adiabatic events. Several products formed on the ground state have also been observed.

Ultrafast Relaxation Dynamics in trans-1,3-Butadiene Studied by Time-Resolved Photoelectron Spectroscopy with High Harmonic Pulses

In trans-1,3-butadiene, the ultrafast relaxation from the doubly excited state 2(1)Ag and the corresponding recovery of the ground state 1(1)Ag were observed simultaneously for the first time by time-resolved photoelectron spectroscopy (TRPES) using 29.5 eV high harmonic pulses. The fast recovery of 1(1)Ag shows that the following dissociation upon photoexcitation takes place after returning to the ground state. At 427 fs after photoexcitation, only the ionization energy from the C═C σ bond was found to remain shifted. Accompanying theoretical calculations with an assumption of Koopmans' theorem show that the ionization energy of the C═C σ bond is modulated by vibrational excitation of the antisymmetric C═C stretching mode. TRPES by high harmonics can probe the changes in the molecular structure sensitively.

Quantum-classical dynamics of wave fields

An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled nonlinear equations that can be written by means of a suitable non-Hamiltonian bracket. As an example, the theory is applied to the relaxation dynamics of the spin-boson model. In the adiabatic limit, a good agreement with calculations performed by the operator approach is obtained. Moreover, the theory proposed in this paper can take nonadiabatic effects into account without resorting to surface-hopping approximations. Hence, the results obtained follow qualitatively those of previous surface-hopping calculations and increase by a factor of (at least) 2, the time length over which nonadiabatic dynamics can be propagated with small statistical errors. Moreover, it is worth to note that the dynamics of quantum-classical wave fields proposed here is a straightforward non-Hamiltonian generalization of the formalism for nonlinear quantum mechanics that Weinberg introduced recently.

A computational strategy for geometry optimization of ionic and covalent excited states, applied to butadiene and hexatriene

We propose a computational strategy that enables ionic and covalent pipi* excited states to be described in a balanced way. This strategy depends upon (1) the restricted active space self-consistent field method, in which the dynamic correlation between core sigma and valence pi electrons can be described by adding single sigma excitations to all pi configurations and (2) the use of a new conventional one-electron basis set specifically designed for the description of valence ionic states. Together, these provide excitation energies comparable with more accurate and expensive ab initio methods--e.g., multiconfigurational second-order perturbation theory and multireference configuration interaction. Moreover, our strategy also allows full optimization of excited-state geometries--including conical intersections between ionic and covalent excited states--to be routinely carried out, thanks to the availability of analytical energy gradients. The prototype systems studied are the cis and trans isomers of butadiene and hexatriene, for which the ground 1A(1/g), lower-lying dark (i.e., symmetry forbidden covalent) 2A(1/g) and spectroscopic 1B(2/u) (valence ionic) states were investigated.

A simple approach for improving the hybrid MMVB force field: application to the photoisomerization of s-cis butadiene

MMVB is a QM/MM hybrid method, consisting of a molecular mechanics force field coupled to a valence bond Heisenberg Hamiltonian parametrized from ab initio CASSCF calculations on several prototype molecules. The Heisenberg Hamiltonian matrix elements Q(ij) and K(ij), whose expressions are partitioned here into a primary contribution and second-order correction terms, are calculated analytically in MMVB. When the original MMVB force field fails to produce potential energy surfaces accurate enough for dynamics calculations, we show that significant improvements can be made by refitting the second-order correction terms for the particular molecule(s) being studied. This "local" reparametrization is based on values of K(ij) extracted (using effective Hamiltonian techniques) from CASSCF calculations on the same molecule(s). The method is demonstrated for the photoisomerization of s-cis butadiene, and we explain how the correction terms that enabled a successful MMVB dynamics study [Garavelli, M.; Bernardi, F.; Olivucci, M.; Bearpark, M. J.; Klein, S.; Robb, M. A. J Phys Chem A 2001, 105, 11496] were refitted.

A simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function

We devise and apply a simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function. These bonding schemes are close to resonance structures drawn by chemists. Firstly, a CASSCF wave function is computed. Secondly, the CASSCF computation is repeated but now the delocalized complete active space MOs are substituted by Weinhold's localized natural atomic orbitals. In this way the original CASSCF wave function is represented by a sequence of Slater determinants composed of localized natural atomic orbitals. Thus, a standard CASSCF wave function can be reinterpreted in terms of a local picture. To test the method we obtain localized bonding schemes and their weights for the ground and the pi-pi* excited state of ethylene. Moreover, bonding schemes and their weights are derived for the ground, the 1(1)B(u), and the 2(1)Ag pi-pi* excited states of trans-butadiene. The large weight bonding schemes are shown to be a qualitative indicator for the known photochemistry of butadiene. The remarkable stability of the Arduengo carbene is discussed by obtaining bonding schemes that indicate a stabilizing delocalization of the pi electrons. We illustrate that the large weight bonding schemes are in line with the observed reactivity of the Arduengo carbene.

H-vinyl conical intersections for dienes: a mechanism for the photochemical hula twists

The potential role of "H-vinyl" conical intersections in a photochemical process known as the hula twist has been evaluated. The H-vinyl conical intersections of butadiene are explored with complete active space self-consistent field calculations, and proposals about the geometries involved in the hula-twist mechanism are discussed and contrasted with the conventional one-bond flip mechanism of cis-trans isomerization.