S.P. Bhattacharyya

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.

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

Theoretical study of the nonlinear polarizabilities in H2N and NO2 substituted chromophores containing two hetero aromatic rings

Abstract The static first- and second-hyperpolarizabilities of a number of amino- and nitro-substituted chromophores containing two hetero aromatic rings have been calculated by ab initio time dependent Hartree–Fock (TDHF) method. The computed nonlinear polarizabilities correlate well with frontier orbital energies and hardness parameter ( η ). Furan and thiophene rings at the donor site and the thiazole and pyridine at the acceptor site are predicted to enhance the first hyperpolarizability ( β ) – but not 〈 γ 〉 values. The nature of the dependence of β and 〈 γ 〉 on the twist angle between the bridging rings have been explored.

Locating critical points on multi-dimensional surfaces by genetic algorithm: test cases including normal and perturbed argon clusters

Abstract It is demonstrated that Genetic Algorithm in a floating point realisation can be a viable tool for locating critical points on a multi-dimensional potential energy surface (PES). For small clusters, the standard algorithm works well. For bigger ones, the search for global minimum becomes more efficient when used in conjunction with coordinate stretching, and partitioning of the strings into a core part and an outer part which are alternately optimized The method works with equal facility for locating minima, local as well as global, and saddle points (SP) of arbitrary orders . The search for minima requires computation of the gradient vector, but not the Hessian, while that for SPs requires the information of the gradient vector and the Hessian, the latter only at some specific points on the path. The method proposed is tested on (i) a model 2-d PES (ii) argon clusters (Ar 4 –Ar 30 ) in which argon atoms interact via Lennard-Jones potential, (iii) Ar m X, m =12 clusters where X may be a neutral atom or a cation. We also explore if the method could also be used to construct what may be called a stochastic representation of the reaction path on a given PES with reference to conformational changes in Ar n clusters.

Direct solution of Schrödinger equation by genetic algorithm: test cases

A stable and generalizable recipe is proposed for directly solving Schrodinger equation by genetic algorithm. The recipe is tested for obtaining (i) the radial wave function of the H-atom in the ground and excited states, (ii) ground and excited states in a symmetric double well potential, (iii) ground and excited states of two coupled harmonic oscillators. The possibility of generalising and extending the recipe to more complex problems is analysed.

Spectral Signatures of Intramolecular Charge Transfer Process in β-Enaminones: A Combined Experimental and Theoretical Analysis

In this paper, we present spectroscopic signatures of intramolecular charge transfer (ICT) and effects of solvent on the ICT process in 3-(phenylamino)-2-cyclohexen-1-one (PACO), a member of the well-known molecular family, the beta-enaminones. The dual fluorescence in the steady state emission spectra of the molecule in polar solvents indicates the occurrence of ICT, which is further supported by time-resolved studies, using time correlated single photon counting technique with picosecond resolution. To understand the nature of the charge transfer, pH dependent studies of the probe in water were performed, where a quenching of fluorescence was observed even in the presence of very low concentrations of acids. Solvent induced fluorescence quenching was observed in ethanol and methanol. The ICT process was also investigated by quantum chemical calculations. To understand the role of solvents in the ICT process, we have theoretically studied the macroscopic and microscopic solvation of the probe in water. The absorption spectra of the molecule in the gas phase as well as in water were simulated using time dependent density functional theory with cc-pVTZ basis set and self-consistent reaction field theory that models macroscopic solvation. The possibility of microscopic solvation in water was probed theoretically and the formation of 1:3 molecular clusters by PACO with water molecules has been confirmed. Our findings could have a bearing on pH sensing applications of the probe.

A genetic algorithm based technique for locating first-order saddle point using a gradient dominated recipe

The present paper proposes and tests the workability of a genetic algorithm based search technique for locating the first-order saddle points on the potential energy surfaces of Lennard-Jones clusters with n6 30. A modified objective function using gradients only is used to locate the saddle points. The cost eAectiveness of the proposed method vis-a-vis that of an earlier formulation, where an explicit determination of Hessian eigenvalues was required, is demonstrated. The method could be useful in the construction and the analysis of the reaction paths in complex systems. ” 2000 Elsevier Science B.V. All rights reserved.

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.

Numerical solutions of the Schrodinger equation directly or perturbatively by a genetic algorithm: test cases

Abstract The workability of a genetic algorithm-based strategy to solve the Schrodinger equation directly is tested with reference to a screened Coulomb potential and an oscillator with quartic anharmonicity. The suitability of the same basic idea in solving the inhomogeneous differential equations of Rayleigh–Schrodinger perturbation theory is also examined in this context with particular reference to the ground state of a two-electron atom. Special advantages of the general approach are stressed.