Frederico V. Prudente

The fitting of potential energy surfaces using neural networks: Application to the study of vibrational levels of H3+

A back-propagation neural network is utilized to fit the potential energy surfaces of the H3+ ion, using the ab initio data points of Dykstra and Swope, and the Meyer, Botschwina, and Burton ab initio data points. We used the standard back-propagation formulation and have also proposed a symmetric formulation to account for the symmetry of the H3+ molecule. To test the quality of the fits we computed the vibrational levels using the correlation function quantum Monte Carlo method. We have compared our results with the available experimental results and with results obtained using other potential energy surfaces. The vibrational levels are in very good agreement with the experiment and the back-propagation fitting is of the same quality of the available potential energy surfaces.

A study of confined quantum systems using the Woods-Saxon potential

We propose the Woods-Saxon (WS) potential to simulate spatial confinement. The great advantage of our methodology is that it enables the study of a wide range of systems and confinement regimes by varying two parameters in the model potential. To test the methodology we have studied the confined harmonic oscillator in two different regimes: when the confinement potential exhibits a sudden jump; and when the confinement is described by a smooth function. We have also applied the present procedure to a realistic problem, a confined quantum dot-atom. The numerical calculation is performed with the equally spaced discrete variable representation (DVR). Our results are in close agreement with those available in the literature, and we believe our method to be a good alternative for studying confined quantum systems.

The fitting of potential energy surfaces using neural networks. Application to the study of the photodissociation processes

Abstract A back-propagation neural network is utilized to fit potential energy surfaces and the transition dipole moment of the HCl + ion, using the ab initio electronic energies calculated by Pradhan, Kirby and Dalgarno. These surfaces are used in the study of the photodissociation process. The photodissociation cross section is calculated utilizing the equally spaced discrete variable representation and the negative imaginary potential method.

A study of the confined hydrogen atom using the finite element method

The hydrogen atom confined by an infinite spherical potential barrier is studied employing a variational procedure based on the p-version of the finite element method. In such a procedure, the spherical spatial confinement is imposed straightforwardly by removing a local basis function. The calculations have been performed for estimating the energy spectrum, the dipole polarizability and the effective pressure for various confinement radii. The effect of the spatial confinement on these quantities is analysed. The results obtained are compared with those previously published in the literature and the efficiency of the finite element method to treat confined quantum systems is discussed.

A new genetic algorithm to be used in the direct fit of potential energy curves to ab initio and spectroscopic data

We propose a two-step genetic algorithm (GA) to fit potential energy curves to both ab initio and spectroscopic data. In the first step, the GA is applied to fit only the ab initio points; the parameters of the potential so obtained are then used in the second-step GA optimization, where both ab initio and spectroscopic data are included in the fitting procedure. We have tested this methodology for the extended-Rydberg function, but it can be applied to other functions providing they are sufficiently flexible to fit the data. The results for NaLi and Ar2 diatomic molecules show that the present method provides an efficient way to obtain diatomic potentials with spectroscopic accuracy.

A study of two-electron quantum dot spectrum using discrete variable representation method

A variational method called discrete variable representation is applied to study the energy spectra of two interacting electrons in a quantum dot with a three-dimensional anisotropic harmonic confinement potential. This method, applied originally to problems in molecular physics and theoretical chemistry, is here used to solve the eigenvalue equation to relative motion between the electrons. The two-electron quantum dot spectrum is determined then with a precision of at least six digits. Moreover, the electron correlation energies for various potential confinement parameters are investigated for singlet and triplet states. When possible, the present results are compared with the available theoretical values.

Optimized mesh for the finite-element method using a quantum-mechanical procedure

Abstract A quantum-mechanical procedure to define a mesh for the p-version of the finite-element method is proposed and utilized to calculate eigenvalues for three representative one-dimensional potentials. Comparisons are made with analytical results and calculations using other numerical methods to demonstrate its effectiveness. The methodology is shown to be accurate and allows mixing of the element sizes and polynomial order.

QUANTUM MONTE CARLO STUDY OF ROVIBRATIONAL STATES UTILIZING ROTATING WAVEFUNCTIONS : APPLICATION TO H2O

We applied the procedure developed by Prudente et al. [Chem. Phys. Lett. 302, 249 (1999)] to compute the rovibrational energy levels of the water molecule. The procedure utilizes rotating wavefunctions as the trial basis in the correlation-function quantum Monte Carlo method. The procedure originally tested for a rotating harmonic oscillator and rotating Morse potential, has been extended for triatomic systems, replacing the spherical harmonics by the Wigner functions. We computed the rovibrational levels of the water molecule and compared the results with the experiment, and they are shown to be accurate.

A novel finite element method implementation for calculating bound states of triatomic systems: Application to the water molecule

SummaryThe p-version of the finite element method is utilized in a fully three-dimensional bound state calculation of the vibrational spectrum of H2O. The algorithm shows the possibility of using the finite element method to calculate highly excited vibrational levels of triatomic molecules.

Ionization and Fragmentation of Formamide Induced by Synchrotron Radiation in the Valence Region via Photoelectron Photoion Coincidence Measurements and Density Functional Theory Calculations.

We have performed a theoretical and experimental study of the formamide (HCONH2) photofragmentation and photoionization processes in the gas phase. The experiment was perfomed by using a time-of-flight mass spectrometer using the photoelectron photoion coincidence (PEPICO) technique in the valence region, from photons with energy between 10 and 20 eV. We have obtained both mass and partial ion yield spectra, identified by the mass-to-charge ratio as a function of the photon energy. With this setup, we could ascertain the threshold energy for the production of formamide cation and its cationic fragments. The theoretical analysis of the formamide photofragmentation channels are fulfilled by the density functional theory (DFT) and the time-dependent density functional theory (TDDFT). The theoretical analysis allowed us to estimate, for example, which atoms are lost during the photofragmentation. We have also developed a theoretical-experimental analysis of the main fragments produced in the dissociation: m/q = 45 (HCONH2+), m/q = 44 (CONH2+), m/q = 29 (HCO+), m/q = 17 (NH3+), and m/q = 16 (NH2+).