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

We investigate the potential of numerical algorithms to decipher the kinetic parameters involved in multi-step chemical reactions. To this end, we study dimerization kinetics of protein as a model system. We follow the dimerization kinetics using a stochastic simulation algorithm and combine it with three different optimization techniques (genetic algorithm, simulated annealing and parallel tempering) to obtain the rate constants involved in each reaction step. We find good convergence of the numerical scheme to the rate constants of the process. We also perform a sensitivity test on the reaction kinetic parameters to see the relative effects of the parameters for the associated profile of the monomer/dimer distribution.

In this paper, we explore the use of stochastic optimizer, namely simulated annealing (SA) followed by density function theory (DFT)-based strategy for evaluating the structure and infrared spectroscopy of (H₂O)$_n$ OH⁻ clusters where 𝑛 = 1-6. We have shown that the use of SA can generate both global and local structures of these cluster systems.We also perform a DFT calculation, using the optimized coordinate obtained from SA as input and extract the IR spectra of these systems. Finally, we compare our results with available theoretical and experimental data. There is a close correspondence between the computed frequencies from our theoretical study and available experimental data. To further aid in understanding the details of the hydrogen bonds formed, we performed atoms in molecules calculation on all the global minimum structures to evaluate relevant electron densities and critical points.