M. Ben-Nun

Photodynamics of ethylene: ab initio studies of conical intersections

Abstract We have used extended basis sets and configuration interaction wave functions to systematically characterize the excited state potential energy surfaces of ethylene, including conical intersections between electronic states. The results are consistent with our previous ab initio multiple spawning simulations of ethylene photodynamics and electronic spectra. The C–C bond on the optically accessible V state is extended in planar geometries, suggesting a role for C–C stretching in the electronic absorption spectrum. A cascade of conical intersections connecting the V state in the Franck–Condon region to each of the low-lying Rydberg states has been identified, in addition to intersections connecting the excited state manifold back to the ground state. The D 2d twisted geometry of ethylene is found to be a saddle point, not a local minimum. Pyramidalization of one of the methylene units in twisted ethylene is found to be favorable, leading to a conical intersection. We have identified and characterized eight conical intersections involving the V state which are likely to be relevant in the photochemistry of ethylene.

Ab initio molecular dynamics study of cis–trans photoisomerization in ethylene

Abstract We have used ab initio multi-electronic state molecular dynamics to study the photoinduced cis–trans isomerization of ethylene. The initial motion on the excited state is a stretching of the CC bond and the photoisomerization begins within ∼50 fs of optical excitation. Quenching to the ground electronic state is found to be ultrafast and proceeds from an ionic state via a conical intersection. Accessing the conical intersection requires pyramidalization of one of the methylene groups and this can happen only after energy is funneled from the twisting mode into the pyramidalization mode.

A multiple spawning approach to tunneling dynamics

Quantum mechanical tunneling effects are investigated using an extension of the full multiple spawning (FMS) method. The FMS method uses a multiconfigurational frozen Gaussian ansatz for the wave function and it allows for dynamical expansion of the basis set during the simulation. Basis set growth is controlled by allowing this expansion only when the dynamics signals impending failure of classical mechanics, e.g., nonadiabatic and/or tunneling effects. Previous applications of the FMS method have emphasized the modeling of nonadiabatic effects. Here, a new computational algorithm that accounts for tunneling effects is introduced and tested against exact solution of the Schrodinger equation for two multi-dimensional model problems. The algorithm first identifies the tunneling events and then determines the initial conditions for the newly spawned basis functions. Quantitative agreement in expectation values, tunneling doublets and tunneling splitting is demonstrated for a wide range of conditions.

Comparison of full multiple spawning, trajectory surface hopping, and converged quantum mechanics for electronically nonadiabatic dynamics

We present calculations employing the simplest version of the full multiple spawning method, FMS-M or minimal FMS, for electronically nonadiabatic quantum dynamics using three model potential energy matrices with different strengths and ranges for the diabatic coupling. We first demonstrate stability of the branching probabilities and final energy distributions with respect to the parameters in the FMS-M method. We then compare the method to a variety of other semiclassical methods, as well as to accurate quantum mechanical results for three-dimensional atom–diatom reactions and quenching processes; the deviations of the semiclassical results from the accurate quantum mechanical ones are averaged over nine cases. In the adiabatic electronic representation, the FMS-M method provides some improvement over Tully’s fewest switches trajectory surface hopping method. However, both methods, irrespective of electronic representation, systematically overpredict the extent of reaction in comparison to the exact qua...

The role of intersection topography in bond selectivity of cis-trans photoisomerization

Ab initio methods are used to characterize the ground and first excited state of the chromophore in the rhodopsin family of proteins: retinal protonated Schiff base. Retinal protonated Schiff base has five double bonds capable of undergoing isomerization. Upon absorption of light, the chromophore isomerizes and the character of the photoproducts (e.g., 13-cis and 11-cis) depends on the environment, protein vs. solution. Our ab initio calculations show that, in the absence of any specific interactions with the environment (e.g., discrete ordered charges in a protein), energetic considerations cannot explain the observed bond selectivity. We instead attribute the origin of bond selectivity to the shape (topography) of the potential energy surfaces in the vicinity of points of true degeneracy (conical intersections) between the ground and first excited electronic states. This provides a molecular example where a competition between two distinct but nearly isoenergetic photochemical reaction pathways is resolved by a topographical difference between two conical intersections.

Characterization of a conical intersection between the ground and first excited state for a retinal analog

Abstract Ab initio complete active space SCF calculations have been carried out to investigate the first excited electronic state of a retinal protonated Schiff base analog: all-trans-3,7-dimethylnona-2,4,6,8-tetraenmethylimminium cation. This model of the retinal chromophore in bacteriorhodopsin includes five conjugated double bonds as well as both pertinent backbone methyl groups. The excited state minimum that is relevant for isomerization in bacteriorhodopsin is investigated and is found to be in very close proximity to a Jahn–Teller conical intersection. The two (global) coordinates that are most effective in promoting efficient internal conversion back to the ground electronic state (by lifting the degeneracy between the ground and first excited state) are identified and discussed, and the distribution of the positive charge in the retinal analog as a function of these two coordinates is investigated.

Quantum dynamics of the femtosecond photoisomerization of retinal in bacteriorhodopsin

The membrane protein bacteriorhodopsin contains all-trans-retinal in a binding site lined by amino acid side groups and water molecules that guide the photodynamics of retinal. Upon absorption of light, retinal undergoes a subpicosecond all-trans-->13-cis phototransformation involving torsion around a double bond. The main reaction product triggers later events in the protein that induce pumping of a proton through bacteriorhodopsin. Quantum-chemical calculations suggest that three coupled electronic states, the ground state and two closely lying excited states, are involved in the motion along the torsional reaction coordinate phi. The evolution of the protein-retinal system on these three electronic surfaces has been modelled using the multiple spawning method for non-adiabatic dynamics. We find that, although most of the population transfer occurs on a timescale of 300 fs, some population transfer occurs on a longer timescale, occasionally extending well beyond 1 ps.

Photochemistry from first principles — advances and future prospects

Abstract Detailed simulation of photochemistry poses considerable challenges because quantum mechanical effects are important in determining both the electronic potential energy surfaces and the subsequent nuclear dynamics. We provide a brief overview of the ab initio multiple spawning (AIMS) method which addresses the problem by solving both the electronic and nuclear Schrodinger equations simultaneously. We discuss our recent AIMS simulations of cis–trans photoisoimerization in ethylene as an example application. The prospects of the method for modeling of photochemistry in large organic molecules and condensed phases are assessed.

EXPLOITING TEMPORAL NONLOCALITY TO REMOVE SCALING BOTTLENECKS IN NONADIABATIC QUANTUM DYNAMICS

An extension of the full multiple spawning (FMS) method for quantum non-adiabatic dynamics that capitalizes on the global nature of quantum mechanics and on the deterministic nature of the FMS method is discussed. The FMS method uses a classically motivated time-dependent basis set for the wave function and here we demonstrate that the choice of a temporally nonlocal basis set can reduce the scaling of the dominant effort in ab initio multiple spawning from O(N2) to O(N), where N is the number of basis functions describing the nuclear degrees of freedom. The procedure is applied to a two-dimensional two electronic state model problem and we show that the temporally nonlocal basis set provides accurate expectation values and branching ratios over a broad range of energies.

A Continuous Spawning Method for Nonadiabatic Dynamics and Validation for the Zero‐Temperature Spin‐Boson Problem

A four-dimensional spin-boson model is used to study the convergence and accuracy of the full multiple spawning (FMS) method using two spawning algorithms. The original spawning algorithm, based on the idea of effective non-adiabatic coupling, is expected to be optimal when the coupling between electronic states is either spatially or temporally localized. The new “continuous spawning” algorithm ensures that at all times there is a (user defined) minimal overlap between a basis function traveling on one electronic state and one (or more) basis functions traveling on the other electronic state. The algorithm is expected to be numerically efficient when the electronic states are coupled by a constant, position-independent term, as is the case in spin-boson models. The fast convergence of the algorithm is demonstrated by direct comparison to numerically converged results obtained using the multi-configuration time-dependent Hartree method. The results of the FMS dynamics are also compared to the more classical surface-hopping and Ehrenfest methods. The surface-hopping and Ehrenfest methods are shown to be sensitive to the particular method used to choose the trajectory initial conditions (quasi-classical vs. Wigner), while the FMS method is not very sensitive to this choice.