Paulo H. Acioli

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.

Generation of pseudopotentials from correlated wave functions

The density matrix, or equivalently the natural orbitals play an essential role in determining the transferability of pseudopotentials to all orders of perturbation theory. In this work the one‐particle density matrix and natural orbitals of Li, C, and Ne atoms are obtained using variational and diffusion Monte Carlo. Using these a pseudopotential is computed for the lithium atom.

Review of quantum Monte Carlo methods and their applications

Abstract Correlation energy makes a small but very important contribution to the total energy of an electronic system. Among the traditional methods used to study electronic correlation are coupled clusters (CC), configuration interaction (CI) and manybody perturbation theory (MBPT) in quantum chemistry, and density functional theory (DFT) in solid state physics. An alternative method, which has been applied successfully to systems ranging from the homogeneous electron gas, to atoms, molecules, solids and clusters is quantum Monte Carlo (QMC). In this method the Schrodinger equation is transformed to a diffusion equation which is solved using stochastic methods. In this work we review some of the basic aspects of QMC in two of its variants, variational (VMC) and diffusion Monte Carlo (DMC). We also review some of its applications, such as the homogeneous electron gas, atoms and the inhomogeneous electron gas (jellium surface). The correlation energy obtained by Ceperley and Alder (D.M. Ceperley and B.J. Alder, Physical Review, 45 (1980) 566), as parameterized by Perdew and Zunger (J.P. Perdew and A. Zunger, Phys. Rev. B23 (1980) 5469), is one of the most used in DFT calculations in the local density approximation (LDA). Unfortunately, the use of the LDA in inhomogeneous systems is questionable, and better approximations are desired or even necessary. We present results of the calculations performed on metallic surfaces in the jellium model which can be useful to obtain better approximations for the exchange and correlation functionals. We have computed the electronic density, work function, surface energy and pair correlation functions for a jellium slab at the average density of magnesium ( r s = 2.66). Since there is an exact expression for the exchange and correlation functional in terms of the pair correlation functions, the knowledge of such functions near the edge of the surface may be useful to obtain exchange and correlation functionals valid for inhomogeneous systems. From the exchange and correlation functional we can conclude that the exchange-correlation hole is nearly spherical in the bulk region but elongated in the direction perpendicular to the surface as the electron approaches the edge of the surface, showing the anisotropic character of the electronic correlation near the surface.

Dynamics of charge transfer in molecular switches

With impurity molecules working as switches, the charge transfer on a single conducting polymer chain is studied. The chain is modeled by a modified tight-binding Hamiltonian extended to include the effects of an external field and the parameters of the switching molecules. The charge transfer through the sites that work like a switch is analyzed by the numerical integration of the equations of motion. Two basic types of molecular switches are studied: single and pairs of donor-acceptor molecules bonded to the chain. The main differences between these two models of switches are determined. We have found that the single radical switch has an anisotropic character and only works for solitons with the same parity of bonding site. For the donor-acceptor pair we have encountered that the chain offers a wider range of devices, from simple switches to perfect molecular rectifiers. The influence of the parameters of the molecules on the charge transfer and the changes they must undergo to characterize the molecular switch are obtained. The role of the length of separation between the sites where the donor and acceptor molecules bond is clarified. The optimum switch configuration is determined.

Estimating correlation energy of diatomic molecules and atoms with neural networks

The electronic correlation energy of diatomic molecules and heavy atoms is estimated using a back propagation neural network approach. The supervised learning is accomplished using known exact results of the electronic correlation energy. The recall rate, that is, the performance of the net in recognizing the training set, is about 96%. The correctness of values given to the test set and prediction rate is at the 90% level. We generate tables for the electronic correlation energy of several diatomic molecules and all the neutral atoms up to radon (Rn). © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 1407–1414, 1997

Charge Propagation on Branching off Conjugated Polymers

The propagation of charged solitons in a branching off conjugated polymer is studied. The soliton dynamics is numerically calculated using a 2-D extension of the Su-Schrieffer-Heeger Hamiltonian. We found that the propagation of a soliton through the bifurcation sites depends on the single-double bond configuration around these sites as well as the length of each branch. It is found that the soliton can be trapped, go through, or be reflected at the bifurcations. The implications for the setting up of molecular circuits are determined.

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.

Polaron Properties in Armchair Graphene Nanoribbons

By means of a 2-D tight-binding model with lattice relaxation in a first-order expansion, we report different polaron properties depending on the armchair graphene nanoribbons width family as well as on its size. We find that representatives of the 3p+2 family do not present a polaronic-mediated charge transport. As for 3p and 3p+1 families, the polaron behavior was completely dependent on the systems width. In particular, we observed a greater degree of delocalization for broader nanoribbons; narrower nanoribbons of both families, on the contrary, typically presented a more localized polaronic-type transport. Energy levels and occupation numbers analysis are performed to rigorously assess the nature of the charge carrier. Time evolution in the scope of the Ehrenfest molecular dynamics was also carried out to confirm the collective behavior and stability of the carrier as a function of time. We were able to determine that polarons in nanoribbons of 3p family present higher mobility than those in 3p+1 nanoribbons. These results identify the transport process that takes place for each system, and they allow the prediction of the mobility of the charge carriers as a function of the structural properties of the system, thus providing guidance on how to improve the efficiency of graphene nanoribbon-based devices.

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.