J. J. Soares Neto

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.

Numerical Generation of Optimized Discrete Variable Representations

We develop a procedure for calculating an optimized Discrete Variable Representation (DVR) optimized for a given potential. The method leads to an efficient and compact way to obtain numerical solutions of quantum mechanical problems. The procedure is applied to several physical problems. To illustrate the strength of the algorithm in dealing with multidimensional calculations, we obtain accurate levels up to 19,000 cm-1 for the vibrational energies of the water molecule.

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.

Photodissociation of triatomic molecules: Formulation of the three‐dimensional problem

A variational approach for calculating the cross section of the photodissociation process of triatomic molecules is put forth as a generalization of a formulation used previously for fully three‐dimensional calculations of transition probabilities for the reaction H2+H→H+H2 and the rovibrational spectrum of H+3. It is based upon the generator coordinate method and the hyperspherical coordinates and the evaluation of the scattering wave function employs the R‐matrix theory.

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.

A numerical study of various finite-element method schemes applied to quantum mechanical calculations

Abstract This paper considers the performance of several finite-element method schemes used for solving two- and three-dimensional quantum mechanical problems. The study is performed on the adiabatic hyperangular functions for the ion H + 3 and the system H 2 + H.

A quantum Monte Carlo study of vibrational states of planar acetylene

Abstract This article reports the results of correlated function quantum Monte Carlo (CFQMC) calculations of the vibrational excited states of triatomic molecules, H2O, H3+ and HCN, and for the tetraatomic molecule of Acetylene (HCCH) restricted to vibrations on the plane. The results for the triatomic molecules are in good agreement with experiment and other calculations. We had to modify the wave functions used in other CFQMC calculations of the same kind, to account for the bending modes in the linear molecules, HCN and HCCH. The results of our calculations are in agreement with other theoretical work in the same potential energy surface and with the experimental results for the fundamental vibrational modes.

Non-zero total angular momentum calculations of rovibrational levels for triatomic molecules using generator coordinates

Abstract We demonstrate in this paper that the finite-element method can be used in the calculation of accurate rotational and vibrational levels for triatomic systems, and that the formation of rotational invariance using generator coordinates provides an adequate formalism for the determination of states with total angular momentum greater than zero. Results with several total angular momenta for H + 3 on the corrected Meyer, Botschwina and Burton (MBB) surface are presented.