Satrajit Adhikari

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.

Dissociation dynamics of a model diatomic species in an intense pulsed laser field: a time dependent Fourier grid Hamiltonian approach

A time dependent Fourier grid Hamiltonian (TDFGH) method is employed to model the quantum dynamics of a pulsed Morse oscillator. The Morse oscillator is chosen to represent the bound states of the LiH molecule. The dissociation is seen to be characterized by a definite induction period and a threshold of peak laser intensity only beyond which noticeable dissociation takes place. The positive features of the present method are pointed out. Floquet state dynamics is invoked to explain some of the observed features.

Extended Born-Oppenheimer equation for a three-state system

We present explicit forms of nonadiabatic coupling (NAC) elements of nuclear Schrodinger equation (SE) for a coupled three-state electronic manifold in terms of mixing angles of real electronic basis functions. If the adiabatic-diabatic transformation (ADT) angles are the mixing angles of electronic bases, ADT matrix transforms away the NAC terms and brings diabatic form of SE. ADT and NAC matrices are shown to satisfy a curl condition with nonzero divergence. We have demonstrated that the formulation of extended Born-Oppenheimer (EBO) equation from any three-state BO system is possible only when there exists a coordinate-independent ratio of the gradients for each pair of mixing angles. On the contrary, since such relations among the mixing angles lead to zero curl, we explore its validity analytically around conical intersection(s) and support numerically considering two nuclear-coordinate-dependent three surface BO models. Numerical calculations are performed by using newly derived diabatic and EBO equations and expected transition probabilities are obtained.

The conical intersection effects and adiabatic single-surface approximations on scattering processes: A time-dependent wave packet approach

Using a quasi-Jahn-Teller model and an extended version of the approximate Born-Oppenheimer (BO) single surface equations, Baer, Charutz, Kosloff, and Baer [J. Chem. Phys. 105, 9141 (1996)] have performed time-independent scattering calculations to study a direct effect on the symmetry of the nuclear wave function due to conical intersections between BO potential energy surfaces. In this article, we have addressed the same problem using the same model by introducing either a vector potential in the nuclear Hamiltonian or by incorporating a phase factor in the nuclear wave function. The scattering calculations have been carried out by using a time-dependent wave packet approach.

The time-dependent discrete variable representation method in molecular dynamics

Abstract We discuss and present details of a newly formulated time-dependent discrete variable representation (DVR) method for molecular scattering. As a numerical example we consider the tunneling through an Eckart barrier.

Quantum-classical dynamics of scattering processes in adiabatic and diabatic representations.

We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn-Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schrodinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on an adiabatic surface with ordinary Born-Oppenheimer approximation. Excellent agreement between TDDVR and DVR results is obtained in both the representations.

A time-dependent discrete variable representation method

We have developed a novel discrete variable representation (DVR) method where not only the amplitudes of the wave function at the DVR grid points can change but also the positions of these grid points can move as a function of time. Since the Gauss–Hermite basis set is used as the primitive basis functions (PBF) to construct the DVR basis set, the method appears as a semiclassical one with a small number of PBF but converges very fast to the quantum with an increasing PBF. We have investigated the dynamics of a reaction coordinate with or without coupling to a heat bath of harmonic oscillators to demonstrate the validity of the proposed method. The excellent agreement of the calculated tunneling probabilities with numbers obtained by traditional quantum grid method (FFT) and the fast computability of the present method compared to the latter are remarkable.

THE HERMITE CORRECTION METHOD FOR NONADIABATIC TRANSITIONS

We have performed molecular dynamics simulations on a system where electronic transitions are allowed anywhere in configuration space among any number of coupled states. A classical path theory based on the Hermite correction to the Gaussian wave packet expansion, proposed by Gert D. Billing [J. Chem. Phys. 107, 4286 (1997)] has been used. The calculations are carried out on the same model used by J. C. Tully [J. Chem. Phys. 93, 1061 (1990)] and the transition probabilities agree well with corresponding exact quantum mechanical results.

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

A quantum-classical approach to the molecular dynamics of pyrazine with a realistic model Hamiltonian

We investigate the molecular dynamics of pyrazine after excitation to the S2 electronic state by using the time-dependent discrete variable representation (TDDVR) method. The investigation has been carried out with a realistic 24-mode model Hamiltonian consisting of all the vibrational degrees of freedom of pyrazine molecule. First, we perform the simulation on a basic four-mode model, and then by including additional eight important modes and finally, by introducing 20 bath modes on the basic model. This sequential inclusion of bath modes demonstrates the effect of weak modes on the subsystem, where the calculations of energy and population transfer from basic model to the bath quantify the same effect. The spectral profile obtained by using TDDVR approach shows reasonably good agreement with the results calculated by quantum mechanical approach. It appears that the TDDVR approach for those large systems where quantum mechanical description is needed in a restricted region is a good compromise between accuracy and speed.