A new method for optimizing a set of nonlinear parameters: application in total Hartree-Fock atomic energy calculations

摘要

A new method for optimizing a set of numerical parameters is presented. This method does not depend on prior knowledge of the goal function and of its derivatives. Besides, it is robust and does not require any other method to achieve result near the global extreme (maximum/minimum) of the goal function. However, as the computational time spent by our method increases with the number of numerical parameters and with the size of each parameter to be optimized, in this work, it is applied together with the IGCHF method to construct accurate uncontracted basis sets to describe the ground states of some atoms. In these cases, the parameters to be optimized are the exponents of the Gaussian functions and the minimum total HF energy criterion is guaranteed by the variational principle. It is verified that the results calculated with the proposed new method are better than those obtained with the Monte Carlo and particle swarm methods, although the computational times spent in some cases by it are larger than those of the other two methods.