Constrained adiabatic trajectory method: a global integrator for explicitly time-dependent Hamiltonians.

The constrained adiabatic trajectory method (CATM) is reexamined as an integrator for the Schrödinger 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 analyzed 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.

Dynamic and spectroscopic studies of single molecules physisorbed on graphite substrates. 2. Application to the ammonia molecule.

In the present paper, the theoretical approach developed in paper 1 is applied to an NH(3) molecule adsorbed on a graphite substrate. The potential energy surfaces (PESs) for the interaction between the molecule and the graphite crystal are described in detail. The molecule exhibits two quasi-equivalent angular position minima of energy ("up" and "down") along the perpendicular axis to the surface. The PES calculations also indicate that the NH(3) molecule has a rotational motion that is moderately hindered, with an energy barrier value of about 14 meV and also a quasi-free lateral translational motion above the surface, indicating a weak corrugation of the graphite (0001) surface. The isosteric heat of adsorption is calculated and is in agreement with the experimental one. Finally, the infrared absorption spectra for the vibrational mode frequency regions are obtained.

Internal eigenstate problem: the trial state method.

It is shown that the device of adding a special trial state to a basis set, thus augmenting by 1 the dimension of any complex matrix being studied, leads to a formalism that permits the application of the wave operator approach to calculating the internal spectrum of the matrix as well as the action of the resolvent operator (E-H)(-1) on an arbitrary vector in the original N-dimensional space. Two calculational variants of the method are described and both are tested by studying the problem of a short laser pulse interacting with a H+2 ion.