A new powerful computational method is introduced for the solution of the time dependent Schrödinger equation with time-dependent Hamiltonians (not necessarily time-periodic). The method is based on the use of the Floquet-type operator in an extended Hilbert space, which was introduced by H. Sambe [Phys. Rev. A 7, 2203 (1973)] for time periodic Hamiltonians, and was extended by J. Howland [Math Ann. 207, 315 (1974)] for general time dependent Hamiltonians. The new proposed computational algorithm avoids the need to introduce the time ordering operator when the time-dependent Schrödinger equation is integrated. Therefore it enables one to obtain the solution of the time-dependent Schrödinger equation by using computational techniques that were originally developed for cases where the Hamiltonian is time independent. A time-independent expression for state-to-state transition probabilities is derived by using the analytical time dependence of the time evolution operator in the generalized Hilbert space. Illustrative numerical examples for complex scaled time periodic model Hamiltonians are given.

We show that individual vibrational modes in single-molecule junctions with asymmetric molecule-lead coupling can be selectively excited by applying an external bias voltage. Thereby, a non-statistical distribution of vibrational energy can be generated, that is, a mode with a higher frequency can be stronger excited than a mode with a lower frequency. This is of particular interest in the context of mode-selective chemistry, where one aims to break specific (not necessarily the weakest) chemical bond in a molecule. Such mode-selective vibrational excitation is demonstrated for two generic model systems representing asymmetric molecular junctions and/or scanning tunneling microscopy experiments. To this end, we employ two complementary theoretical approaches, a nonequilibrium Green's function approach and a master equation approach. The comparison of both methods reveals good agreement in describing resonant electron transport through a single-molecule contact, where differences between the approaches highlight the role of non-resonant transport processes, in particular co-tunneling and off-resonant electron-hole pair creation processes.

A basic theoretical introduction is given for the phenomenon of electronic transport through molecular junctions. The electrode-molecule-electrode system is represented using a model Hamiltonian framework based on separation between the molecular and the electrode single-particle subspaces, using projection operators. The Landauer formulation of the steady-state current through the junction is introduced and the transmission function is derived from basic single-particle quantum scattering theory. Detailed implementations to a generic tight-binding model demonstrate the typical characteristics of the transmission function, and resonant transport through discrete quantum molecular states is analysed in detail. An alternative formulation based on the time-dependent Liouville-von Neumann equation leads to a quantum kinetic representation of the current in terms of rate constants for electron hopping between the molecule and the electrodes. The generalization of this approach to inelastic transport is discussed.

Using the (t,t′) method as introduced in Ref. [J. Chem. Phys. 99, 4590 (1993)] computational techniques which originally were developed for time independent Hamiltonians can be used for propagating an initial state for explicitly time dependent Hamiltonians. The present paper presents a time dependent integrator of the Schrödinger equation based on a Chebychev expansion, of the operator Û(x,t′,t0→t), and the Fourier pseudospectral method for calculating spatial derivatives [(∂2/∂x2),(∂/∂t′)]. Illustrative numerical examples for harmonic and Morse oscillators interacting with CW and short pulsed laser fields are given.

Response to "Comment on 'On the relation between unimolecular reaction rates and overlapping resonances'" [Comment on "On the relation between unimolecular reaction rates and overlapping resonances" [J. Chem. Unimolecular decay processes are studied in the regime of overlapping resonances with the goal of elucidating how. unimolecular reaction rates depend on resonances widths (the imaginary part of the Siegert eigenvalues). As illustrated analytically for one-dimensional models and numerically for a more general random matrix version of Feshbach's optical model, transition state theory (TST, Rice-Ramsperger-Kassel-Marcus) provides the correct average unimolecular decay rate whether the resonances are overlapping or not. For all studied cases, the explicit "universal" dependence of the TST average rate on the average resonance width (for a given energy, or an energy interval) is that of a saturation curve: in the regime of nonoverlapping resonances (i.e., weak coupling) the standard relation "unimolecular decay rate=resonance width Iii" holds, but as the resonance overlap increases (strong coupling) the rate saturates, becoming practically independent of the average resonance width in the strong overlapping limit. On the basis of these conclusions, a discussion of what has been or can be measured in experiments of unimolecular decay that relates to the average decay rate and to the resonance widths is given.