This work presents a new implementation of the QP algorithm, a computer method to diagonalize the extremely large matrices arising in multimode vibronic problems. Benchmark calculations are included, showing the accuracy of the program. The QP algorithm is extended to treat multiple electronic surfaces for competitive control and this is demonstrated with an Hamiltonian including three electronic states, a model of the benzene radical cation. Finally, the evolution of zeroth-order states in a simple two electronic states, two dimensional model with a conical intersection is explored, towards building a time-dependent view of overlapping resonances coherent control.

This work presents a new implementation of the QP algorithm, a computer method to diagonalize the extremely large matrices arising in multimode vibronic problems. Benchmark calculations are included, showing the accuracy of the program. The QP algorithm is extended to treat multiple electronic surfaces for competitive control and this is demonstrated with an Hamiltonian including three electronic states, a model of the benzene radical cation. Finally, the evolution of zeroth-order states in a simple two electronic states, two dimensional model with a conical intersection is explored, towards building a time-dependent view of overlapping resonances coherent control.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This thesis will make a study of the conic, which can be defined as quadratic equations solutions with two variables, with the main objective recognition of same through a simplification of the quadratic form associated, whose procedure involves the diagonalization of symmetric matrices. Throughout this work, will address the prerequisites needed for the reader with little familiarity on the subject, can understand each stage of its development, as Euclidean spaces and matrix diagonalization. / Nesta dissertação faremos um estudo das cônicas, as quais podem ser definidas como soluções de equações do segundo grau com duas variáveis, tendo como objetivo principal o reconhecimento das mesmas por meio de uma simplificação da forma quadrática associada, cujo procedimento envolve a diagonalização de matrizes simétricas. Ao longo deste trabalho, serão abordados os pré-requisitos necessários para que o leitor, com pouca familiaridade no assunto, possa compreender cada etapa de seu desenvolvimento, como espaços euclidianos e diagonalização de matrizes.