Three‐dimensional Cartesian finite element method for the time dependent Schrödinger equation of molecules in laser fields

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields

A parallel quantum electron and nuclei wave packet computer code, LZH-DICP, has been developed to study laser-atom-molecule interaction in the nonperturbative regime with attosecond resolution. The nonlinear phenomena occurring in that regime can be studied with the code in a rigorous way by numerically solving the time-dependent Schrödinger equation of electrons and nuclei. Time propagation of the wave functions is performed using a split-operator approach, and based on a sine discrete variable representation. Photoelectron spectra for hydrogen and kinetic-energy spectra for molecular hydrogen ion in linearly polarized laser fields are calculated using a flux operator scheme, which testifies to the validity and the high efficiency of LZH-DICP.

Controlling HD+ and H+2 dissociation with the carrier-envelope phase difference of an intense ultrashort laser pulse

Carrier-envelope phase difference effects in the dissociation of the HD+ molecular ion in the field of an intense, linearly polarized, ultrashort laser pulse are studied in the framework of the time-dependent Schrödinger equation. We consider a reduced-dimensionality model in which the nuclei are free to vibrate along the field polarization and the electrons move in two dimensions. The laser has a central wavelength of 790 nm and a pulse length of 10 fs with intensities in the range 6x10(14) to 9x10(14) W/cm(2). We find that the angular distribution of dissociation to p+D and H+d can be controlled by varying the phase difference, generating differences between the dissociation channels of more than a factor of 2. Moreover, the asymmetry is nearly as large for H+2 dissociation.

Computational method for general multicenter electronic structure calculations

Here a three-dimensional fully numerical (i.e., chemical basis-set free) method [P. F. Batcho, Phys. Rev. A 57, 6 (1998)], is formulated and applied to the calculation of the electronic structure of general multicenter Hamiltonian systems. The numerical method is presented and applied to the solution of Schrödinger-type operators, where a given number of nuclei point singularities is present in the potential field. The numerical method combines the rapid "exponential" convergence rates of modern spectral methods with the multiresolution flexibility of finite element methods, and can be viewed as an extension of the spectral element method. The approximation of cusps in the wave function and the formulation of multicenter nuclei singularities are efficiently dealt with by the combination of a coordinate transformation and a piecewise variational spectral approximation. The complete system can be efficiently inverted by established iterative methods for elliptical partial differential equations; an application of the method is presented for atomic, diatomic, and triatomic systems, and comparisons are made to the literature when possible. In particular, local density approximations are studied within the context of Kohn-Sham density functional theory, and are presented for selected subsets of atomic and diatomic molecules as well as the ozone molecule.

Extension of the mapped Fourier method to time-dependent problems

A numerical method is described for integration of the time-dependent Schrödinger equation within the presence of a Coulomb field. Because of the singularity at r=0, the wave packet has to be represented on a grid with a high density of points near the origin; at the same time, because of the long-range character of the Coulomb potential, the grid must extend to large values of r. The sampling points are chosen, following E. Fattal, R. Baer, and R. Kosloff [Phys. Rev. E 53, 1217 (1996)], using a classical phase space criterion. Following those workers, the unequally spaced grid points are mapped to an equally spaced grid, allowing use of fast Fourier transform propagation methods that scale as N ln N, where N is the number of grid points. As a first test, eigenenergies for the hydrogen atom are extracted from short-time segments of the electronic wave-packet autocorrelation function; high accuracy is obtained by using the filter-diagonalization method. As a second test, the ionization rate of the hydrogen atom resulting from a half-cycle pulse is calculated. These results are in excellent agreement with earlier calculations.