Pinaki Chaudhury

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.

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.

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.

A simulated annealing based technique for locating first-order saddle points on multidimensional surfaces and constructing reaction paths: several model studies

Abstract We explore the workability of a simulated annealing based method for locating first-order saddle points (SP) on a potential energy surface, starting from a minimum. The search can proceed sequentially, exhausting all the saddle points of index one. It can also be tuned to trace the lowest first-order SP in one run. Four different model surfaces are investigated and the lowest first-order saddle point lying between two local minima are located in each case. Possible use of the technique in the construction of reaction paths is considered. A more realistic system involving six argon atoms interacting via Lennard-Jones potential (an 18 parameter problem) is investigated and the saddle point on the path of transformation of Ar6 cluster from its global minimum configuration to a neighbouring local minimum is traced out. The computational labour in the SAM-based search is examined vis-a-vis the traditionally used methods.

Structure and vibrational spectroscopy of halide ion hydrates: a study based on genetic algorithm

Abstract Genetic algorithm is used to locate the absolute minima on model potential energy surfaces of halide ion (X − ) ⋯ water [(H 2 O) n )] clusters of different sizes. Semi-empirical (AM1) calculations at the corresponding cluster geometries predict many of the prominent features of the experimental infrared spectra of these species that are sensitive to the cluster size. Some of the halide-ion sensitive features of the spectra, however remain elusive.

PHOTO-DISSOCIATION DYNAMICS OF A DIATOMIC MOLECULE : MODELLING OF THERMAL AND ENVIRONMENTAL EFFECTS

The quantum dynamics of photodissociation of a diatomic molecule interacting with ultrashort infrared laser pulses and modelled by an appropriate Morse oscillator with either a fixed or fluctuating well-depth is explored at non-zero temperatures by assuming an initial state vector consistent with the distribution of vibrational population at a given temperature. The time-dependent Schrodinger equation is solved by the time-dependent Fourier grid Hamiltonian method. The computed dissociation rate constant k(T) at a given intensity and frequency, of the driving field passes through a maximum at an intermediate temperature. If the well-depth of the Morse oscillator fluctuates randomly, mimicking medium-induced perturbations, k(T) shows a strong suppression at specific values of the fluctuation frequency and strength.

Diagonalization of a real-symmetric Hamiltonian by genetic algorithm: A recipe based on minimization of Rayleigh quotient

A genetic algorithm-based recipe involving minimization of the Rayleigh quotient is proposed for the sequential extraction of eigenvalues and eigenvectors of a real symmetric matrix with and without basis optimization. Important features of the method are analysed, and possible directions of development suggested

Bound states in screened and bare Coulomb potentials: A nonorthogonal CI‐based route to effective Hamiltonians for two‐electron systems

One- and two-electron bound states in screened and bare Coulomb potentials are calculated by adopting a discretized multiconfiguration generator coordinate (GC) method which leads to an iterative nonorthogonal configuration interaction procedure with the optimization of GCs. The GCs are optimized either by the method of simulated annealing or by a genetic algorithm. Critical scanning lengths for which bound states disappear in one-electron atoms are computed. A noninteracting model Hamiltonian for a two-electron atom based on the idea of screened Coulomb interaction is proposed and used for calculating electric dipole polarizability and establishing the threshold value of z for the appearance of autoionizing ground state of two-electron systems.

A random walk to local minima and saddle points on a potential energy surface. A strategy based on simulated annealing

We demonstrate how the Metropolis simulated annealing method, a global stochastic minimizer, can also be used as an all-purpose extremizer capable of locating all the local minima and saddle points on a given surface, in addition to the global minimum. The demonstration is done with reference to the well studied Muller-Brown potential and a one-dimensional spin glass with random nearest-neighbour interaction. The relevance of the present strategy in the construction of reaction paths is discussed.