Michael S. Schuurman

Role of Rydberg states in the photochemical dynamics of ethylene.

We use the ab initio multiple spawning method with potential energy surfaces and nonadiabatic coupling vectors computed from multistate multireference perturbation theory (MSPT2) to follow the dynamics of ethylene after photoexcitation. We introduce an analytic formulation for the nonadiabatic coupling vector in the context of MSPT2 calculations. We explicitly include the low-lying 3s Rydberg state which has been neglected in previous ab initio molecular dynamics studies of this process. We find that although the 3s Rydberg state lies below the optically bright ππ* state, little population gets trapped on this state. Instead, the 3s Rydberg state is largely a spectator in the photodynamics, with little effect on the quenching mechanism or excited state lifetime. We predict the time-resolved photoelectron spectrum for ethylene and point out the signature of Rydberg state involvement that should be easily observed.

Determining quasidiabatic coupled electronic state Hamiltonians using derivative couplings: A normal equations based method.

A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing N(state) coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a least-squares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a least-squares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the 1 (2)A(1) and 1 (2)E states of the 1-propynyl radical, CH(3)CC.

Tabletop imaging of structural evolutions in chemical reactions demonstrated for the acetylene cation

The introduction of femto-chemistry has made it a primary goal to follow the nuclear and electronic evolution of a molecule in time and space as it undergoes a chemical reaction. Using Coulomb Explosion Imaging, we have shot the first high-resolution molecular movie of a to and fro isomerization process in the acetylene cation. So far, this kind of phenomenon could only be observed using vacuum ultraviolet light from a free-electron laser. Here we show that 266 nm ultrashort laser pulses are capable of initiating rich dynamics through multiphoton ionization. With our generally applicable tabletop approach that can be used for other small organic molecules, we have investigated two basic chemical reactions simultaneously: proton migration and C=C bond breaking, triggered by multiphoton ionization. The experimental results are in excellent agreement with the timescales and relaxation pathways predicted by new and quantitative ab initio trajectory simulations.

On the simulation of photoelectron spectra in molecules with conical intersections and spin-orbit coupling : The vibronic spectrum of CH3S

A method to simulate photoelectron spectra for states coupled by conical intersections and the spin-orbit interaction is reported. The algorithm is based on the multimode vibronic coupling model and treats the spin-orbit interaction in a nonperturbative manner. Since the algorithm is not dependent on molecular symmetry, the approach is generally applicable to accidental conical intersections as well as the symmetry required intersections found in Jahn-Teller molecules. The method is also computationally efficient using energy gradient and derivative coupling information to limit the number of nuclear configurations at which ab initio data are required. This approach is applied to simulate the negative ion photoelectron spectrum of the methylthio radical. The two-state Hamiltonian employed to describe this system was determined employing ab initio gradients and derivative couplings at only 17 nuclear configurations.

Through-Bond Interactions and the Localization of Excited-State Dynamics

The influence of through-bond interactions on nonadiabatic excited-state dynamics is investigated by time-resolved photoelectron spectroscopy (TRPES) and ab initio computation. We compare the dynamics of cyclohexa-1,4-diene, which exhibits a through-bond interaction known as homoconjugation (the electronic correlation between nonconjugated double bonds), with the nonconjugated cyclohexene. Each molecule was initially excited to a 3s Rydberg state using a 200 nm femtosecond pump pulse. The TRPES spectra of these molecules display similar structure and time constants on a subpicosecond time scale. Our ab initio calculations show that similar sets of conical intersections (a [1,2]- and [1,3]-hydrogen shift, as well as carbon-carbon bond cleavage) are energetically accessible to both molecules and that the geometry and orbital composition at the minimum energy crossing points to the ground state are directly analogous. These experimental and computational results suggest that the excited-state dynamics of cyclohexa-1,4-diene become localized at a single double bond and that the effects of through-bond interaction, dominant in the absorption spectrum, are absent in the excited-state dynamics. The notion of excited-state dynamics being localized at specific sites within the nuclear framework is analogous to the localization of light absorption by a subsystem within the molecule, designated a chromophore. We propose the utility of the analogous concept, denoted here as a dynamophore.

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.

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.

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.

A method to reduce the size of the vibronic basis employed in the simulation of spectra using the multimode vibronic coupling approximation.

In the time-independent multimode approach for the determination of vibronic spectra involving strongly coupled electronic states, the equilibrium geometry and normal modes of the reference or precursor state are usually employed as the basis for the multimode expansion. This basis, while easily constructed, is generally ill-suited for determining the eigenstates of the observed species. Employing a more computationally effective basis requires the evaluation of Franck-Condon overlap integrals. Using established generalized Hermite polynomial generating function formalisms, an algorithm is developed that can efficiently determine the enormous requisite number of these overlap integrals. It is found that this flexibility in the choice of multimode basis can significantly reduce the size of the basis needed to obtain converged spectral simulations. The previously reported spectrum of the ethoxy (C(2)H(5)O) radical serves as an example of the efficacy of the new technique.

On the construction of quasidiabatic state representations of bound adiabatic state potential energy surfaces coupled by accidental conical intersections: incorporation of higher order terms.

The quadratic vibronic coupling model is an important computational tool for simulating photoelectron spectra involving strongly coupled electronic states in polyatomic molecules. However, recent work has indicated the need for higher order terms, with most of the initial studies focusing on molecules with symmetry-required degeneracies. In this study we report an extension of our approach for constructing fully quadratic representations of bound electronic states coupled by conical intersections, which allows for the inclusion of higher order terms, demonstrated here employing a quartic expansion. Procedures are developed that eliminate unphysical behavior for large displacements, a problem likely to be an endemic to anharmonic expansions. Following work on representing dissociative electronic states, Lagrange multipliers are used to constrain the constructed representation to reproduce exactly the energy, energy gradients, and∕or derivative couplings at specific points, or nodes, in nuclear coordinate space. The approach is illustrated and systematically studied using the four lowest electronic states of triazolyl, (CH)(2)N(3).