Development of a general time-dependent absorbing potential for the constrained adiabatic trajectory method

The Constrained Adiabatic Trajectory Method (CATM) allows us to compute solutions of the time-dependent Schr\"odinger equation using the Floquet formalism and Fourier decomposition, using matrix manipulation within a non-orthogonal basis set, provided that suitable constraints can be applied to the initial conditions for the Floquet eigenstate. A general form is derived for the inherent absorbing potential, which can reproduce any dispersed boundary conditions. This new artificial potential acting over an additional time interval transforms any wavefunction into a desired state, with an error involving exponentially decreasing factors. Thus a CATM propagation can be separated into several steps to limit the size of the required Fourier basis. This approach is illustrated by some calculations for the $H_2^+$ molecular ion illuminated by a laser pulse.Comment: 8 pages, 7 figure

Global integration of the Schr\"odinger equation within the wave operator formalism: The role of the effective Hamiltonian in multidimensional active spaces

A global solution of the Schr\"odinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A: Math. Theor. 48, 225205 (2015)], is generalized to take into account the case of multidimensional active spaces. An iterative algorithm is derived to obtain the Fourier series of the evolution operator issuing from a given multidimensional active subspace and then the effective Hamiltonian corresponding to the model space is computed and analysed as a measure of the cyclic character of the dynamics. Studies of the laser controlled dynamics of diatomic models clearly show that a multidimensional active space is required if the wavefunction escapes too far from the initial subspace. A suitable choice of the multidimensional active space, including the initial and target states, increases the cyclic character and avoids divergences occuring when one-dimensional active spaces are used. The method is also proven to be efficient in describing dissipative processes such as photodissociation.Comment: 33 pages, 11 figure

Constrained Adiabatic Trajectory Method (CATM): a global integrator for explicitly time-dependent Hamiltonians

The Constrained Adiabatic Trajectory Method (CATM) is reexamined as an integrator for the Schr\"odinger equation. An initial discussion places the CATM in the context of the different integrators used in the literature for time-independent or explicitly time-dependent Hamiltonians. The emphasis is put on adiabatic processes and within this adiabatic framework the interdependence between the CATM, the wave operator, the Floquet and the (t,t') theories is presented in detail. Two points are then more particularly analysed and illustrated by a numerical calculation describing the $H_2^+$ ion submitted to a laser pulse. The first point is the ability of the CATM to dilate the Hamiltonian spectrum and thus to make the perturbative treatment of the equations defining the wave function possible, possibly by using a Krylov subspace approach as a complement. The second point is the ability of the CATM to handle extremely complex time-dependencies, such as those which appear when interaction representations are used to integrate the system.Comment: 15 pages, 14 figure

Investigation of the interaction of some astrobiological molecules with the surface of a graphite (0001) substrate. Application to the CO, HCN, H2O and H2CO molecules

Detailed semi-empirical interaction potential calculations are performed to determine the potential energy surface experienced by the molecules CO, HCN, H2O and H2CO, when adsorbed on the basal plane (0001) of graphite at low temperature. The potential energy surface is used to find the equilibrium site and configuration of a molecule on the surface and its corresponding adsorption energy. The diffusion constant associated with molecular surface diffusion is calculated for each molecule.Comment: 15 pages, 3 figure

Wave Operators And Active Subspaces; Tools For The Simplified Dynamical Description Of Quantum Processes Involving Many-Dimensional State Spaces

Time-dependent and stationary wave operators are presented as tools to define active spaces and simplified dynamics for the integration of the time-dependent Schrodinger equation in large quantum spaces. Within this framework a new light is thrown on the duality between time-dependent and time-independent approaches and a generalized version of the adiabatic theorem is given. For the Floquet treatment of photodissociation processes, the choice of the relevant subspaces and the construction of the effective Hamiltonians are carried out using the Bloch wave operator techniques. Iterative solutions of the basic equations associated with these wave operators are given, based on Jacobi, Gauss-Seidel and variational schemes

Computation of interior Eigenstates of Large Matrices using the quasiadiabatic evolution of instantaneous eigenvectors

A two-stage iterative scheme is proposed to handle a central problem of molecular dynamics, the computation of interior eigenvalues of large Hamiltonian matrices. The proposed method involves an initial propagation process for a time-dependent wave operator which is then inserted in an iterative process (R.D.W.A. or S.C.M.) to yield the exact stationary wave operator. The merits of the wave operator formalism for quasiadiabatic propagation are analysed, and possible improvements such as the use of partial adiabatic representations and spectral filters, are outlined. The proposed algorithm is applied to the test case of two coupled oscillators with variable coupling strength, and yields accurate results even with small switching times. 1 INTRODUCTION Numerous theoretical studies in molecular and chemical physics use discrete representations of the molecular continua and, via the Floquet treatment of the field-matter interaction, of the time variable. These Discrete Variable Represent..

Consistency between adiabatic and nonadiabatic geometric phases for nonselfadjoint hamiltonians

We show that the adiabatic approximation for nonselfadjoint hamiltonians seems to induce two non-equal expressions for the geometric phase. The first one is related to the spectral projector involved in the adiabatic theorem, the other one is the adiabatic limit of the nonadiabatic geometric phase. This apparent inconsistency is resolved by observing that the difference between the two expressions is compensated by a small deviation in the dynamical phases.Comment: 8 pages, 1 figur