Time interferences and nonexponential decays of quasi-isolated molecules

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.

Enhancement of triplet stability in benzene by substituents with triple bonds

Excitation of phenylacetylene (PA) and benzonitrile to their lowest singlet states in a molecular beam has previously been shown to immediately (only during the 8 ns laser pulse) result in long-lived species with low ionization potentials (Hofstein, J.; Xu, H.; Sears, T.; Johnson, P.M. J. Phys. Chem. A 2008, 112, 1195-1201). Using the fragmentation of ions produced by photoionization at various times after initial excitation as a diagnostic for molecular geometry evolution, the long-lived species in phenylacetylene is shown to be a PA state (most likely a triplet) rather than an isomer. Delayed fluorescence and a delayed photoelectron signal indicative of S1 are also seen, indicating a singlet-triplet mixing process that is not quite in the statistical-coupling limit and is parallel to the long-lived species channel. Electronic structure calculations indicate that the lowest triplet state of phenylacetylene is nonplanar with the ethynyl group bent in a trans-configuration out of the plane of the ring. The substituent π-electrons are significantly conjugated into the ring, resulting in a tendency toward a quinoidal structure, which may be related to the unusual excited state stability. These molecules constitute the first members of a new class of excited state behaviors.

Line shape studies of a state coupled to a random background including large fluctuations of the couplings

Line shape functions of a model system are analyzed, describing an oscillator carrying state coupled to background states randomly distributed in energy and with random coupling constants. Depending on the energy distribution functions or the nature of the coupling distribution, different line shape functions, such as the Lorentzian, the Fano, or that related to the nonexponential decay of the Forster type are recovered as limiting cases. Conditions for the range of applicability of a specially introduced mean square coupling approximation are derived. It is shown that the appearance of a Lorentzian line shape does not imply directly a homogeneous decay mechanism and that, on the other hand, commonly accepted conditions for the so-called statistical limit, expressed in terms of an average density and an average coupling, do not necessarily lead to a Lorentzian line shape. This is illustrated analytically through a model with randomly distributed transition dipolar couplings. Other applications relate to spectral diffusion in proteins and to bridged charge transfer.