Gaussian bases generated with the Simulated Annealing Monte Carlo and Particle Swarm Optimization Methods.

Name: Thiago Mello dos Reis
Type: PhD thesis
Publication date: 03/02/2017

Name Rolesort descending
Antônio Canal Neto Advisor *

Examining board:

Name Rolesort descending
Antônio Canal Neto Advisor *
Rene Felipe Keidel Spada External Examiner *
Cesar Turczyn Campos External Examiner *
Francisco Elias Jorge Internal Examiner *
Wanderlã Luis Scopel Internal Examiner *

Summary: The Monte Carlo Simulated Annealing and Particle Swarm Optimization methods were used to generate adapted Gaussian basis set for the atoms from H to Ar, in the ground state. A study about the eficiency and the reliability of each method was performed. In order to check the reliability of the proposed methods, we perform an specific study
considering a training set of 15 atoms, namely: N, Mg, Al, Cl, Ti, Ni, Br, Sr, Ru, Pd, Sb, Cs, Ir, Tl, At. First of all, the Improved Generator Coordinate Hartree-Fock Method was applied to generate adapted basis which was used as start point to generate new Gaussian basis sets. After that, the Monte Carlo Simulated Annealing and Particle Swarm Optimization methods were developed from parallel studies, however following the same procedure so as we could have the possibility to compare them. Previously applying of the developed methods we perform some calibrations in order to define the values of the parameters of the algorithms; we perform studies about annealing schedules (for the Monte Carlo Simulated Annealing method), the total of swarm's particle (for the
Particle Swarm Optimization method), and the total of steps for each algorithm. After the calibration procedure, both methods were applied, with the variational principle, to the Hartree-Fock wave function to give us the fully optimized Gaussian basis sets. Next, the basis sets were contracted by considering the lowest total energy loss, prioritizing the contraction of the most internal exponents. The last two steps of our procedure were the addition of polarized and difuse functions, respectively. These procedures were performed by using the methods which we developed in this work through calculations to the MP2 level. The basis sets that have been generated in this work were used in some
atomic and molecular calculations; we compare such results with relevant results from literature. We verified that, if we consider the same computational eficiency for both Monte Carlo Simulated Annealing and Particle Swarm Optimization methods, there is a small diference between them as regards the accuracy, so that by using the Monte Carlo Simulated Annealing method we obtain best results. When we compare the results of this work with those from literature we note similar results for the properties that were studied, however the proposed methods in this work are more eficient, and we can define a single total numbers of steps for the algorithms even though we are treating with diferent
atomic systems. In addition, we verify that the proposed methods in this work are more accurate than other similar methods presented in the literature, in the task of finding the global minima of the uncontracted basis sets to HF level of theory. It will be necessary to perform additional studies to check the real relationship between the accuracy of the methods. We do not verify the influence of several parameters of the Particle Swarm Optimization algorithm in this work. The fact that the developed methods in this work have been constructed through Double Zeta basis does not prevent them to be used for larger basis sets, the two methods are able to be applied to generate Gaussian basis sets
in the atomic environment for Gaussian basis sets with dierent qualities.

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