P. Dutta

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.

Fourier grid Hamiltonian method for bound states of multidimensional systems. Formulation and preliminary applications to model systems

A local grid method is proposed for computing the bound state eigenvalues and eigenvectors of multidimensional systems. The connection of the proposed methods with the one-dimensional Fourier grid Hamiltonian method is clarified. Results obtained with three different 2D Hamiltonians are compared with analytical and numerical results wherever available

Global optimization of molecular geometry: A new avenue involving the use of Metropolis simulated annealing

The viability of what has been known as the Metropolis simulated-annealing method (MSAM) in the optimization of molecular geometry is tested. The ability of MSAM to seek out the global energy minimum on a potential energy hypersurface with multiple minima is demonstrated in model calculations.

Applications of a local grid method for modeling chemical dynamics at a mean-field level

A local grid method proposed earlier is used to model chemical dynamical events in more than one dimension. Two different mean-field routes are applied to model problems representing dynamics of isomerization, H+-ion transfer, energy transfer, etc. The methods are seen to work with equal facility for both time-dependent and time-independent potentials.

Orthogonality-constrained variational calculation of excited state wavefunctions and energies. A new strategy based on the method of simulated annealing

A new method based on simulated annealing is developed for the variational determination of excited state wavefunctions which are constrained to remain orthogonal to the lower lying states of the same symmetry. The method is simple and effective. It does not require information about either the gradient or the Hessian matrix and is potentially capable of moving out of a local minimum and reaching a more global minimum. Encouraging results of some model calculations are reported.

A new strategy for the calculation of configuration interaction wavefunctions: direct search involving Metropolis simulated annealing

A Metropolis simulated annealing based method is developed for the variational determination of linear parameters in the trial function for the ground and excited states. One starts with the ground state and determines the excited states of the same symmetry sequentially, enforcing the relevant orthogonality constraints. The method is computationally economical and avoids explicit diagonalization of the CI matrix. Pilot scale calculations on the ground and excited states of a few members of the He-isoelectronic sequence are reported.

Orthogonality-constrained variational calculation of excited state wavefunctions and energies: a penalised-functional-based strategy

A viable strategy is developed for the general variational calculation of excited state wavefunctions which are constrained to remain orthogonal to all the lower lying states of the same symmetry. A key element of the strategy is to employ the penalised-functional procedure for enforcing the relevant orthogonality constraints and a gradient-based direct method to locate the constrained minima, bypassing the problem of Hessian singularity. The workability of the algorithm is tested on some model problems.

Simultaneous optimization of linear and non-linear parameters of a trial wavefunction: the efficacy of the method of simulated annealing

Abstract The method of simulated annealing in conjuction with the penalized functional method of constrained minimization is invoked for the simultaneous variational determination of both linear and non-linear parameters of a trial wavefunction for the ground and excited states. The method is applied to the ground and the singlet 1S2S states of a few members of the He-isoelectronic sequence. It is numerically demonstrated tha the computational labour involved in the extraction of one eigenvalue of the CI matrix goes as N 1.675 in the simulated annealing method, where N is the dimension of the CI space.

Localized quantum states on and above the top of a barrier

The quantum states of a particle moving in a symmetric double-well potential (SDW) both in the presence and absence of a constant electric field are investigated within the framework of a Fourier grid Hamiltonian method. It is shown that a few states, with energies close to or above the energy at the barrier top, are strongly localized within the width of the barrier. Comments are made on the nature of these states.

A linear least-squares variational recipe for the calculation of approximate energy eigenstates

The efficacy of the energy-spread minimization technique for solving the energy-eigenvalue equation in a linear variational framework is assessed with a 3×3 matrix perturbation problem with backdoor intruders, quartic anharmonic oscillator and the He-atom problems as prototypical examples. Both direct and indirect minimization schemes are considered and disadvantages of the latter pointed out. The relative merits and demerits of the conventional, vis-a-vis stochastic minimization routes are critically analyzed in the present context.