Is it really possible to control aromaticity of benzene with light?

Recent theoretical investigations claim that tailored laser pulses may selectively steer benzene's aromatic ground state to localized non-aromatic excited states. For instance, it has been shown that electronic wavepackets, involving the two lowest electronic eigenstates, exhibit subfemtosecond charge oscillation between equivalent Kekulé resonance structures. In this contribution, we show that such dynamical electron-localization in the molecule-fixed frame contravenes the principle of the indistinguishability of identical particles. This breach stems from a total omission of the nuclear degrees of freedom, giving rise to nonsymmetric electronic wavepackets under nuclear permutations. Enforcement of the latter leads to entanglement between the electronic and nuclear states. To obey quantum statistics, the entangled molecular states should involve compensating nuclear-permutation symmetries. This in turn engenders complete quenching of dynamical electron-localization in the molecule-fixed frame. Indeed, for the (six-fold) equilibrium geometry of benzene, group-theoretic analysis reveals that any electronic wavepacket exhibits a (D6h) totally symmetric electronic density, at all times. Thus, our results clearly show that the six carbon atoms, and the six C-C bonds, always have equal Mulliken charges, and equal bond orders, respectively. However, electronic wavepackets may display dynamical localization of the electronic density in the space-fixed frame, whenever they involve both even and odd space-inversion (parity) or permutation-inversion symmetry. Dynamical spatial-localization can be probed experimentally in the laboratory frame, but it should not be deemed equivalent to charge oscillation between benzene's identical electronic substructures, such as Kekulé resonance structures.

A quantum-mechanical tier model for phonon-driven vibrational relaxation dynamics of adsorbates at surfaces.

We present a quantum-mechanical tier model for vibrational relaxation of low-lying excited states of an adsorbate vibrational mode (system), coupled to surface phonons (bath), at zero temperature. The tier model, widely used in studies of intramolecular vibrational energy redistribution in polyatomics, is adapted here to adsorbate-surface systems with the help of an embedded cluster approach, using orthogonal coordinates for the system and bath modes, and a phononic expansion of their interaction. The key idea of the model is to organize the system-bath zeroth-order vibrational space into a hierarchical structure of vibrational tiers and keep therein only vibrational states that are sequentially generated from the system-bath initial vibrational state. Each tier is generated from the previous one by means of a successor operator, derived from the system-bath interaction Hamiltonian. This sequential procedure leads to a drastic reduction of the dimension of the system-bath vibrational space. We notably show that for harmonic vibrational motion of the system and linear system-bath couplings in the system coordinate, the dimension of the tier-model vibrational basis scales as ∼Nl×υ. Here, N is the number of bath modes, l is the highest-order of the phononic expansion, and υ is the size of the system vibrational basis. This polynomial scaling is computationally far superior to the exponential scaling of the original zeroth-order vibrational basis, ∼MN, with M being the number of basis functions per bath mode. In addition, since each tier is coupled only to its adjacent neighbors, the matrix representation of the system-bath Hamiltonian in this new vibrational basis has a symmetric block-tridiagonal form, with each block being very sparse. This favors the combination of the tier-model with iterative Krylov techniques, such as the Lanczos algorithm, to solve the time-dependent Schrödinger equation for the full Hamiltonian. To illustrate the method, we study vibrational relaxation of a D-Si bending mode, coupled via two- and (mainly) one-phonon interactions to a fully D-covered Si(100)-(2 × 1) surface, using a recent first-principles system-bath Hamiltonian. The results of the tier model are compared with those obtained by the Lindblad formalism of the reduced density matrix. We find that the tier model provides much more information and insight into mechanisms of vibration-phonon couplings at surfaces, and gives more reliable estimates of the adsorbate vibrational lifetimes. Moreover, the tier model might also serve as a benchmark for other approximate quantum-dynamics methods, such as multiconfiguration wavefunction approaches.

Isotopic effects in vibrational relaxation dynamics of H on a Si(100) surface.

In a recent paper [U. Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], we proposed a robust scheme to set up a system-bath model Hamiltonian, describing the coupling of adsorbate vibrations (system) to surface phonons (bath), from first principles. The method is based on an embedded cluster approach, using orthogonal coordinates for system and bath modes, and an anharmonic phononic expansion of the system-bath interaction up to second order. In this contribution, we use this model Hamiltonian to calculate vibrational relaxation rates of H-Si and D-Si bending modes, coupled to a fully H(D)-covered Si(100)-(2×1) surface, at zero temperature. The D-Si bending mode has an anharmonic frequency lying inside the bath frequency spectrum, whereas the H-Si bending mode frequency is outside the bath Debye band. Therefore, in the present calculations, we only take into account one-phonon system-bath couplings for the D-Si system and both one- and two-phonon interaction terms in the case of H-Si. The computation of vibrational lifetimes is performed with two different approaches, namely, Fermi's golden rule, and a generalized Bixon-Jortner model built in a restricted vibrational space of the adsorbate-surface zeroth-order Hamiltonian. For D-Si, the Bixon-Jortner Hamiltonian can be solved by exact diagonalization, serving as a benchmark, whereas for H-Si, an iterative scheme based on the recursive residue generation method is applied, with excellent convergence properties. We found that the lifetimes obtained with perturbation theory, albeit having almost the same order of magnitude-a few hundred fs for D-Si and a couple of ps for H-Si-, are strongly dependent on the discretized numerical representation of the bath spectral density. On the other hand, the Bixon-Jortner model is free of such numerical deficiencies, therefore providing better estimates of vibrational relaxation rates, at a very low computational cost. The results obtained with this model clearly show a net exponential decay of the time-dependent survival probability for the H-Si initial vibrational state, allowing an easy extraction of the bending mode "lifetime." This is in contrast with the D-Si system, whose survival probability exhibits a non-monotonic decay, making it difficult to define such a lifetime. This different behavior of the vibrational decay is rationalized in terms of the power spectrum of the adsorbate-surface system. In the case of D-Si, it consists of several, non-uniformly distributed peaks around the bending mode frequency, whereas the H-Si spectrum exhibits a single Lorentzian lineshape, whose width corresponds to the calculated lifetime. The present work gives some insight into mechanisms of vibration-phonon coupling at surfaces. It also serves as a benchmark for multidimensional system-bath quantum dynamics, for comparison with approximate schemes such as reduced, open-system density matrix theory (where the bath is traced out and a Liouville-von Neumann equation is solved) or approximate wavefunction methods to solve the combined system-bath Schrödinger equation.

Filtering reaction dynamics using nearside-farside theory and local angular momentum theory: application to the angular scattering of the H + D2(v(i) = 0, j(i) = 0) --> HD(v(f) = 3, j(f) = 0) + D reaction in the energy and time domains.

We investigate methods for filtering reaction mechanisms in the angular scattering of the state-to-state reaction, H + D(2)(v(i) = 0, j(i) = 0, m(i) = 0) --> HD(v(f) = 3, j(f) = 0, m(f) = 0) + D, where v(i), j(i), and m(i) and v(f), j(f), and m(f) are initial and final vibrational, rotational, and helicity quantum numbers, respectively. The input to our filtrations is a new set of accurate quantum scattering matrix elements for total energies in the range 1.52-2.50 eV (in steps of 0.01 eV) and for total angular momentum quantum numbers in the range, 0-40, in steps of unity. We filter reaction mechanisms in both the energy domain and the time domain. The time-domain calculations employ the plane wave packet formulation of time-dependent scattering. The theoretical tools used are nearside-farside (NF) analysis of partial wave series for scattering amplitudes, together with NF local angular momentum (LAM) theory. An energy-domain LAM analysis reveals the existence of an important dynamical feature in the N scattering, a "trench" which bisects the (energy, angle) plane. We use the location of this trench to approximately filter two reaction mechanisms. Transformation to the time domain demonstrates that the two reaction mechanisms correspond to direct and delayed (by about 25 fs) scattering. Further analysis, including filtration in the time domain, shows that the pronounced LAM trench arises from the interference of the energy-domain analogues of the time-direct and time-delayed scattering. Our theory and results provide the first successful demonstration of reaction mechanism filtering carried out directly in the (energy, angle) domain. The calculations and results in this paper extend and complement earlier research reported by Monks, Connor, and Althorpe (Monks, P. D. D.; Connor, J. N. L.; Althorpe, S. C. J. Phys. Chem. A 2006, 110, 741; J. Phys. Chem. A 2007, 111, 10302).

Calculations of near-threshold cross sections for photodissociation of CH+ using the Lanczos algorithm.

We combine the Lanczos algorithm with the absorbing-potential method, implemented in a discrete variable representation to calculate the near-threshold photodissociation cross sections of CH+. The method is iterative, based on a continued fraction representation of the Green function and avoids any explicit matrix diagonalization. A very good agreement is found with experiment and close-coupling calculations.