Michael A. Robb

Coupled electron-nuclear dynamics: charge migration and charge transfer initiated near a conical intersection.

Coupled electron-nuclear dynamics, implemented using the Ehrenfest method, has been used to study charge migration with fixed nuclei, together with charge transfer when nuclei are allowed to move. Simulations were initiated at reference geometries of neutral benzene and 2-phenylethylamine (PEA), and at geometries close to potential energy surface crossings in the cations. Cationic eigenstates, and the so-called sudden approximation, involving removal of an electron from a correlated ground-state wavefunction for the neutral species, were used as initial conditions. Charge migration without coupled nuclear motion could be observed if the Ehrenfest simulation, using the sudden approximation, was started near a conical intersection where the states were both strongly coupled and quasi-degenerate. Further, the main features associated with charge migration were still recognizable when the nuclear motion was allowed to couple. In the benzene radical cation, starting from the reference neutral geometry with the sudden approximation, one could observe sub-femtosecond charge migration with a small amplitude, which results from weak interaction with higher electronic states. However, we were able to engineer large amplitude charge migration, with a period between 10 and 100 fs, corresponding to oscillation of the electronic structure between the quinoid and anti-quinoid cationic electronic configurations, by distorting the geometry along the derivative coupling vector from the D6h Jahn-Teller crossing to lower symmetry where the states are not degenerate. When the nuclear motion becomes coupled, the period changes only slightly. In PEA, in an Ehrenfest trajectory starting from the D2 eigenstate and reference geometry, a partial charge transfer occurs after about 12 fs near the first crossing between D1, D2 (N(+)-Phenyl, N-Phenyl(+)). If the Ehrenfest propagation is started near this point, using the sudden approximation without coupled nuclear motion, one observes an oscillation of the spin density--charge migration--between the N atom and the phenyl ring with a period of 4 fs. When the nuclear motion becomes coupled, this oscillation persists in a damped form, followed by an effective charge transfer after 30 fs.

Polarizable QM/MM Multiconfiguration Self-Consistent Field Approach with State-Specific Corrections: Environment Effects on Cytosine Absorption Spectrum

We present the formulation and implementation of a polarizable quantum mechanics/molecular mechanics (QM/MM) strategy to describe environment effects in multiconfiguration self-consistent field calculations. The strategy is applied to the calculation of the vertical absorption spectrum of cytosine in water. In our approach, mutual polarization of the solute and the solvent is solved self-consistently at the complete-active-space self-consistent-field (CASSCF) level, and the resulting set of charges and dipoles is used to calculate vertical excitation energies using the complete-active-space second-order perturbative (CASPT2) approach and its multistate (MS-CASPT2) variant. In order to treat multiple excited states, we converge the solvent polarization with respect to the state-averaged density of the solute. In order to obtain the final energies, however, we introduce a state-specific correction, where the solvent polarization is recomputed with the density of each state, and demonstrate that this correction brings the excitation energies closer to the values obtained with state-optimized orbitals. Comparison with PCM and nonpolarizable QM/MM calculations shows the importance of specific solute-solvent interactions and environment polarization in describing experiments. Overall, the calculated excitations for the π → π* states in water show good agreement with the experimental spectrum, whereas the n → π* appear at energies above 6 eV, approximately 1 eV higher than in the gas phase. Beyond solvents, the new method will allow studying the impact of heterogeneous biological environments in multiple excited states, as well as the treatment of multichromophoric systems where charge transfer and exciton states play important roles.

Electron Dynamics upon Ionization of Polyatomic Molecules : Coupling to Quantum Nuclear Motion and Decoherence

Knowledge about the electronic motion in molecules is essential for our understanding of chemical reactions and biological processes. The advent of attosecond techniques opens up the possibility to induce electronic motion, observe it in real time, and potentially steer it. A fundamental question remains the factors influencing electronic decoherence and the role played by nuclear motion in this process. Here, we simulate the dynamics upon ionization of the polyatomic molecules paraxylene and modified bismethylene-adamantane, with a quantum mechanical treatment of both electron and nuclear dynamics using the direct dynamics variational multiconfigurational Gaussian method. Our simulations give new important physical insights about the expected decoherence process. We have shown that the decoherence of electron dynamics happens on the time scale of a few femtoseconds, with the interplay of different mechanisms: the dephasing is responsible for the fast decoherence while the nuclear overlap decay may actually help maintain it and is responsible for small revivals.

A valence bond description of the prefulvene extended conical intersection seam of benzene

The permutational isomers of the prefulvene-like minimum energy conical intersection lie on an extended conical intersection seam, where they are connected by higher symmetry structures. Here, we present a VB analysis of the electronic states involved along this extended seam. The VB method produces a spin-exchange density (ie. a bonding pattern) that provides the basis to assign resonance structures to the states. The results show that in the high symmetry region of the seam, the character of the states is dominated by the positive and negative combination of the Kekulé structures, (A+B) and (A-B). The low energy parts of the seam, comprised of lower symmetry conical intersection structures, are stabilized by mixing with the Dewar resonance structures. This feature is responsible for the stability of the benzvalene-like conical intersections. The validity of the VB model is confirmed by calculating the branching space vectors at this level of theory, which are in good agreement with the CASSCF calculated vectors. The VB analysis has also allowed us to complete our picture of the global seam, since it has provided the clue to locate a conical intersection saddle point that interconverts two minima of the prefulvene conical intersection where the carbon bent out of the plane is inverted and rotated by 60°. This saddle point has a benzvalene-like geometry, in agreement with the VB picture.

A generalised 17-state vibronic-coupling Hamiltonian model for ethylene

In a previous work [B. Lasorne, M. A. Robb, H.-D. Meyer, and F. Gatti, The electronic excited states of ethylene with large-amplitude deformations: A dynamical symmetry group investigation, Chem. Phys. 377, 30-45 (2010); and ibid. 382, 132 (2011) (Erratum)], we investigated the electronic structure of ethylene (ethene, C(2)H(4)) in terms of 17 dominant configurations selected at the multiconfiguration self-consistent field level of theory. These were shown to be sufficient to recover most of the static electron correlation among the first valence and Rydberg states at all geometries. We also devised a strategy to build a 17-quasidiabatic-state matrix representation of the electronic Hamiltonian for curvilinear coordinates using dynamical symmetry. Here, we present fitted surfaces in the form of a generalised vibronic-coupling Hamiltonian model for two nuclear coordinates, CC bond stretching and torsion. Dynamic electron correlation is included into the electronic structure to improve the energetics of the Rydberg states at the multireference configuration interaction level of theory. The chemical interpretation of the adiabatic states of interest does not change qualitatively, which validates our choice of underlying quasidiabatic states in the model. The absorption spectrum is calculated with quantum dynamics and partially assigned. This first two-dimensional model shows a surprisingly good agreement with the experimental spectrum.

The second-order Ehrenfest method

AbstractnThis article describes the Ehrenfest method and our second-order implementation (with approximate gradient and Hessian) within a CASSCF formalism. We demonstrate that the second-order implementation with the predictor–corrector integration method improves the accuracy of the simulation significantly in terms of energy conservation. Although the method is general and can be used to study any coupled electron–nuclear dynamics, we apply it to investigate charge migration upon ionization of small organic molecules, focusing on benzene cation. Using this approach, we can study the evolution of a non-stationary electronic wavefunction for fixed atomic nuclei, and where the nuclei are allowed to move, to investigate the interplay between them for the first time. Analysis methods for the interpretation of the electronic and nuclear dynamics are suggested: we monitor the electronic dynamics by calculating the spin density of the system as a function of time.

Communication: Oscillating charge migration between lone pairs persists without significant interaction with nuclear motion in the glycine and Gly-Gly-NH-CH3 radical cations

Coupled electron-nuclear dynamics has been studied, using the Ehrenfest method, for four conformations of the glycine molecule and a single conformation of Gly-Gly-NH-CH3. The initial electronic wavepacket was a superposition of eigenstates corresponding to ionization from the σ lone pairs associated with the carbonyl oxygens and the amine nitrogen. For glycine, oscillating charge migration (when the nuclei were frozen) was observed for the 4 conformers studied with periods ranging from 2 to 5 fs, depending on the energy gap between the lone pair cationic states. When coupled nuclear motion was allowed (which was mainly NH2 partial inversion), the oscillations hardly changed. For Gly-Gly-NH-CH3, charge migration between the carbonyl oxygens and the NH2 lone pair can be observed with a period similar to glycine itself, also without interaction with nuclear motion. These simulations suggest that charge migration between lone pairs can occur independently of the nuclear motion.

How the Conical Intersection Seam Controls Chemical Selectivity in the Photocycloaddition of Ethylene and Benzene

The photocycloaddition reaction of benzene with ethylene has been studied at the CASSCF level, including the characterization of an extended conical intersection seam. We show that the chemical selectivity is, in part, controlled by this extended conical intersection seam and that the shape of the conical intersection seam can be understood in terms of simple VB arguments. Further, the shape and energetics of the asynchronous segment of the conical intersection seam suggest that 1,2 (ortho) and 1,3 (meta) will be the preferred chemical products with similar weight. The 1,4 (para) point on the conical intersection is higher in energy and corresponds to a local maximum on the seam. VB analysis shows that the pairs of VB structures along this asynchronous seam are the same and thus the shape will be determined mainly by steric effects. Synchronous structures on the seam are higher in energy and belong to a different branch of the seam separated by a saddle point on the seam. On S1 we have documented three mechanistic pathways corresponding to transition states (with low barriers) between the reactants and the conical intersection seam: a mixed asynchronous/synchronous [1,2] ortho path, an asynchronous [1,3] meta path, and a synchronous [1,3] meta path.

Electron dynamics upon ionization: control of the timescale through chemical substitution and effect of nuclear motion.

Photoionization can generate a non-stationary electronic state, which leads to coupled electron-nuclear dynamics in molecules. In this article, we choose benzene cation as a prototype because vertical ionization of the neutral species leads to a Jahn-Teller degeneracy between ground and first excited states of the cation. Starting with equal populations of ground and first excited states, there is no electron dynamics in this case. However, if we add methyl substituents that break symmetry but do not radically alter the electronic structure, we see charge migration: oscillations in the spin density that we can correlate with particular localized electronic structures, with a period depending on the gap between the states initially populated. We have also investigated the effect of nuclear motion on electron dynamics using a complete active space self-consistent field (CASSCF) implementation of the Ehrenfest method, most previous theoretical studies of electron dynamics having been carried out with fixed nuclei. In toluene cation for instance, simulations where the nuclei are allowed to move show significant differences in the electron dynamics after 3 fs, compared to simulations with fixed nuclei.

Vertical transition energies vs. absorption maxima: Illustration with the UV absorption spectrum of ethylene

We revisit the validity of making a direct comparison between measured absorption maxima and computed vertical transition energies within 0.1 eV to calibrate an excited-state level of theory. This is illustrated on the UV absorption spectrum of ethylene for which the usual experimental values of 7.66 eV (V←N) and 7.11 eV (R(3s)←N) cannot be compared directly to the results of electronic structure calculations for two very different reasons. After validation of our level of theory against experimental data, a new experimental reference of 7.28 eV is suggested for benchmarking the Rydberg state, and the often-cited average transition energy (7.80 eV) is confirmed as a safer estimate for the valence state.