Problemas diretos e inversos em dinâmica molecular, espectroscopia vibracional, cinética química e espalhamento quântico

Abstract

Extracting physical information from experimental data is an inverse problem and its solution determines unknown causes based on observation of their effects. In contrast, the corresponding direct problem involves finding effects from the analyzes of their causes. If an inverse problem is ill-posed, i.e, one or more of three conditions; existence, uniqueness and continuity with respect to experimental errors are not satisfied, then, special numerical techniques are required for its solution. In this thesis, direct and inverse problems of chemical interest are discussed. In chapter 2, classical trajectories studies are applied to analyze the Coriolis coupling on the energy transfer to Ar+H2O and Ar+CO2 collisions. Partition of molecular kinetic energy into vibration, rotation and Coriolis coupling is made in a Cartesian coordinates system coupled to vibrational normal modes. Effects of rotational, vibrational and translational energies at different initial conditions are investigated in the molecular vibrational relaxation mechanism and the Coriolis influence on the energy transferred is characteri-zed. In chapter 3, stable structures and minima energies for ArnH2O van der Waals complexes are determined by performing a stochastic search method coupling to molecular dynamics calculations. A nonrigid intramolecular potential surface together with a pairwise-additive intermolecular potential are used to procedure the simulation and therefore, molecular relaxation effects on the growing pattern mechanism are quantified. Second differences on the clusters binding energy are calculated and the relative stabilities of the monomers are discussed and compared with previous rigid results. In chapter 4, a general method based on recursive neural networks is proposed to solve linear and nonlinear ill-posed inverse problems. The procedure is applied to chemical problems modeled by eigenvalue, differential and integral equations. Representative applications are discussed in vibrational spectroscopy, chemical kinetics and quantum scattering theory. As a first application, in chapter 5 force constants for water and benzene molecules, together with their main isotopes are obtained on symmetry coordinates basis from experimental vibrational frequencies. This is an ill-posed inverse problem in vibrational spectroscopy, called force field inverse problem, which can be represented by an eigenvalue matrix equation. As second example, in chapter 6, kinetic rate constants are calculated from the productconcentration for the hydrolysis mechanism of the 2,7-dicyanonaphthalene molecule in a first step. In a second moment, rate constants and absorption coefficients are obtained at the same time from ultraviolet absorbance data. The third application consists of the inverse quantum scattering problem. The inversion of intermolecular potential surfaces from scattering data is an ill-posed problemwhich can be write as a Fredholm integral equation in the elastic scattering quantum theory. In chapter 7, this problem is solved within the Born approximation. As physical example, the repulsive component of the potential surface for the interaction Ar-Ar is obtained from differential cross section data. The artificial intelligence method to solve inverse problems, presented in this thesis, is robust with respect to errors in the initial condition or in the experimental data; it is also numerically stable and has a broad range of applicability. The examples discussed inchapters 2 and 3 can be considered direct problems since observable properties (effects) such as transfer energies and nanostructures of van der Waals complexes are obtained from specific potential energies surfaces (causes). On other hand, in chapters 5-7, one obtainsindirect properties (causes) such as molecular force constants, kinetic rate constants and potential energy surface from experimental measurements (effects), i.e, vibrational frequencies, concentrations and differential cross section data. Thus, these examples are concerned about inverse problems.