Real-time Quantum Dynamics Research Articles

Time-dependent Fourier grid Hamiltonian method for modelling real-time quantum dynamics: Theoretical models and applications

A local grid method for modelling real-time quantum dynamical events is formulated. The formulation is straightforward for 1-D systems. For more than one dimension, appeal has to be made to mean-field approximation of the appropriate kind. The simplest mean-field model results in time-dependent Hartree-Fourier grid method. The relationship of the proposed method with some other methods available in the literature is examined. A few examples of numerical applications dealing with (i) the dynamics of dissociation and ionization processes in diatoms and atoms respectively and (ii) tunnelling dynamics in the intramolecular H-atom transfer phenomenon are presented.

Path-integral treatment of multi-mode vibronic coupling

A path-integral (PI) approach to real-time quantum dynamics is developed which is suitable to treat the short-time dynamics of vibronic-coupling systems involving many degrees of freedom. The theory is formulated for the case of two electronic states which are coupled by a single active vibrational mode and whose energy separation is modulated by many so-called tuning modes. Time-dependent correlation functions are expressed as sums over all possible paths in the space of two electronic states in discretized time. For each electronic path, the multi-mode vibrational propagator factorizes into a product of single-mode propagators. Introducing the concept of classes of approximately equivalent paths, the summation over paths is replaced by a summation over classes and the computation of propagator averages within each class. It is shown that the propagator averages can efficiently be calculated by a recursive scheme. The performance of the PI method has been tested for a two-state four-mode model representing S1–S2 vibronic coupling in pyrazine. The PI results (time-dependent correlation functions and absorption spectra) are compared with numerically exact reference data which are available for this model. To demonstrate the potential of the path-integral approach for multi-mode problems, calculations are reported for a twenty-four-mode vibronic-coupling model.

Molecular quantum dynamics from high resolution spectroscopy and laser chemistry

Intramolecular kinetics is of central importance as a primary process in chemical reaction dynamics in general and laser chemistry in particular. High resolution molecular spectroscopy provides one approach to studying the real time quantum dynamics of molecules. This paper outlines the conceptual background and briefly summarizes some results from the last decade with particular emphasis on recent work from our group in Zürich on intramolecular kinetics in the femtosecond to nanosecond domain. New quantum phenomena in intramolecular vibrational (rotational) redistribution (IVR) are identified, leading to two types of redistribution times, one quasiclassical, one purely quantal. The fundamental importance of symmetry and conservation laws - and their violation by weak forces of nature - for the primary processes of intramolecular kinetics is discussed.

Multidimensional path integral calculations with quasiadiabatic propagators: Quantum dynamics of vibrational relaxation in linear hydrocarbon chains

This paper presents the first application of a new method for multidimensional real time quantum dynamics described in a previous Letter [Chem. Phys. Lett. 193, 435 (1992)]. The key feature of the method is the use of an improved zeroth order representation in the Feynman propagator, which allows large time steps in the path integral. Use of the adiabatic approximation in the case of a system coupled to a harmonic bath leads to a path integral over the system coordinate with a one-dimensional propagator which is constructed numerically and which corresponds to dynamics along the adiabatic path, and with a nonlocal influence functional that accounts for nonadiabatic effects. We have performed accurate quantum mechanical calculations on the dynamics of CH overtone relaxation in linear hydrocarbon chains by direct numerical evaluation of the path integral in the quasiadiabatic representation. Converged results for the survival probability of the υ=5 and υ=8 states of HC6 are reported up to five vibrational periods of the CH stretch and compared to those obtained from standard classical and semiclassical simulations.

A computational demonstration of the distributed approximating function approach to real time quantum dynamics

The authors report computational applications for the newly developed distributed approximating function (DAF) approach to real time quantal wavepacket propagation for several one-dimensional model problems. The DAF is constructed to fit all wavepackets accurately which can be represented, to the same accuracy, by a polynomial of degree M, or less, within the envelope of the DAF. (This defines the {open_quotes}DAF class{close_quotes} of functions.) By expressing the DAF (and thus the wavepacket to be propagated) in terms of Hermite functions (each a product of a Hermite polynomial and its Gaussian generating function), the DAF approximation to the wavepacket is propagated freely and exactly for a short time {tau}. The Hermite functions are the natural basis states for describing the free evolution of a localized particle and yield a highly banded representation for the free particle propagator. Combining the DAF class free propagation scheme with any of several short time approximations to the full propagator enables one to propagate the wavepacket through a potential. The DAF results for the propagated wavepacket and various scattering amplitudes are shown to be in good agreement with those obtained by more standard methods. 17 refs., 7 figs., 4 tabs.

A time-dependent Fourier grid Hamiltonian method. Formulation and application to the multiphoton dissociation of a diatomic molecule in intense laser field

A time-dependent Fourier grid Hamiltonian method is proposed for studying real-time quantum dynamics of simple systems. The method can work with an arbitrary number of grid points ( N). Convergence with respect to N is fast. Results of test calculations on the dynamics of dissociation of a diatomic species modelled by an appropriate Morse oscillator in a continuous high intensity non-resonant IR laser field are presented. The dissociation is predicted to be characterized by the presence of a definite threshold of laser intensity and an induction period preceeding the onset of dissociation.

Improved Feynman propagators on a grid and non-adiabatic corrections within the path integral framework

The idea of using a good representation as the zeroth order description of a problem, which is widely used in perturbation theory and in basis set calculations, is extended to the path integral formulation of quantum mechanics by constructing improved Feynman propagators. The best zeroth order propagators cannot be expressed in closed form in general, and are therefore constructed numerically and stored on one-dimensional grids. Use of improved propagators in discretized path integral calculations involves a trivial modification of Monte Carlo techniques and leads to convergence with fewer time slices. Application of a quasi-adiabatic propagator to a system coupled to a harmonic bath leads to a low-dimensional path integral with a non-local influence functional which incorporates the non-adiabatic corrections to the Born—Oppenheimer approximation and which (with parameters typical of chemical processes) can be evaluated by quadrature, providing an accurate method for investigating the real time quantum dynamics of system—bath Hamiltonians.

Monte Carlo methods for real-time quantum dynamics of dissipative systems

A numerical path integral technique based upon a quasiclassical Langevin equation is presented for the calculation of quantum mechanical properties of a system coupled to a dissipative bath. Fully quantum mechanical results are obtained by decorating quasiclassical paths with quantum fluctuations. The use of diophantine integration has been compared to Monte Carlo sampling of the fluctuation variables. Results are presented for several model systems.

Imaginary time path integral Monte Carlo route to rate coefficients for nonadiabatic barrier crossing

Nonadiabatic transitions such as some biological electron transfers are difficult to simulate on a computer because they seem to need long real time quantum dynamics simulations. In fact rates are often dominated by saddle point trajectories in imaginary time. This paper describes a way in which this observation can be exploited with path integral Monte Carlo methods.