Using the Morse Potential to Understand Reaction Coördinates using Maple

The interactions employed in the “linear” reaction A(g)+BC(g) -> AB(g) + C(g) in a “one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum path on the surface created.“one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum path on the surface created.

A new type of confinement for the Morse potential

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Morse potential energy spectra through the variational method and supersymmetry

The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy and eigenfunction of the lowest levels of a Hamiltonian. The approach is illustrated by the case of the Morse potential applied to several diatomic molecules and the results are compared with stabilished results. (C) 2000 Elsevier Science B.V.

Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.

Solutions of the Fokker-Planck equation for a Morse isospectral potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The driving potential and cross sections for synthesizing super heavy nuclei with hot fusion

The dinuclear model of the formation mechanism of a superheavy compound nucleus assumes that when all nucleons of the projectile have been transferred in to the target nucleus the compound nucleus is formed. The nucleon transfer is determined by the driving potential. For some reaction channels, the relation between nucleon transfer and the evolution path of the neutron/proton ratio is rather complicated. In principle, both the dynamical equation and the driving potential should be a twodimensional explicit function of the neutron and proton. For the sake of simplicity we calculated the driving potential by choosing the path of the nucleon transfer which is related to the nutron/proton ratio, and the calculated evaporation residue cross-sections to synthesize the superheavy nuclei are much closer to the experimental data

États cohérents et comprimés du potentiel de Morse et intrication créée par un miroir semi-transparent

Pour décrire les vibrations à l'intérieur des molécules diatomiques, le potentiel de Morse est une meilleure approximation que le système de l'oscillateur harmonique. Ainsi, en se basant sur la définition des états cohérents et comprimés donnée dans le cadre du problème de l'oscillateur harmonique, la première partie de ce travail suggère une construction des états cohérents et comprimés pour le potentiel de Morse. Deux types d’états seront construits et leurs différentes propriétés seront étudiées en portant une attention particulière aux trajectoires et aux dispersions afin de confirmer la quasi-classicité de ces états. La deuxième partie de ce travail propose d'insérer ces deux types d’états cohérents et comprimés de Morse dans un miroir semi-transparent afin d'introduire un nouveau moyen de créer de l'intrication. Cette intrication sera mesurée à l’aide de l’entropie linéaire et nous étudierons la dépendance par rapport aux paramètres de cohérence et de compression.

Exact closed-form solutions of the Dirac equation with a scalar exponential potential

The problem of a fermion subject to a general scalar potential in a two-dimensional world for nonzero eigenenergies is mapped into a Sturm-Liouville problem for the upper component of the Dirac spinor. In the specific circumstance of an exponential potential, we have an effective Morse potential which reveals itself as an essentially relativistic problem. Exact bound solutions are found in closed form for this problem. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail, particularly the existence of zero modes. (c) 2005 Elsevier B.v. All rights reserved.

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solução analítica do potencial de Morse em mecânica clássica

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effects of oscillatory behavior of the dipole function on the dissociation dynamics of the classical driven Morse oscillator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Morse basis expansion applied to diatomic molecules

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Soluções da equação de Fokker-Planck para um potencial isoespectral ao potencial de Morse

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solução analítica da equação de movimento clássica para o potencial de Morse generalizado e potenciais de Morse simétricos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Uso de uma rede unidimensional harmônica com o potencial de Rosen-Morse on site para modelar o DNA

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)