Morse-like Potential Research Articles

Development of a semiempirical potential for simulations of thiol–gold interfaces. Application to thiol-protected gold nanoparticles

A new semiempirical potential, based on density functional calculations and a bond-order Morse-like potential, is developed to simulate the adsorption behavior of thiolate molecules on non-planar gold surfaces, including relaxing effects, in a more realistic way. The potential functions include as variables the metal-molecule separation, vibrational frequencies, bending and torsion angles between several pairs of atom types and the coordination number of both the metal (Au) and thiolate groups. The potential was parameterized based on a set of density functional calculations of molecular adsorption in several surface sites (i.e. hollow, bridge, top, on-top Au adatom and the novel staple motif) for different crystalline facets, i.e. Au(111) and (100). Langevin dynamics simulations have been performed to study the capping effects of alkanethiolates molecules on Au nanoparticles in the range 1-4 nm. The simulation results reveal an enhancement of the coverage degree whilst the nanoparticles diameter decreases. A high surface disorder due to the strong S-Au bond was found, in very good agreement with very recent experimental findings [M. M. Mariscal, J. A. Olmos-Asar, C. Gutierrez-Wing, A. Mayoral and M. J. Yacaman, Phys. Chem. Chem. Phys., 2010, 12, 11785].

On the thermal expansion of molecules

Experimental results for a variety of molecules have shown that their bond lengths expand appreciably when the molecules are heated, as expected from the asymmetric Morse-like potentials characterizing the bonds. However, in a series of papers on structures determined by gas-phase electron diffraction, Giricheva et al. claimed that, for very hot MX3 molecules, effects of out-of-plane vibrations cancel the thermal expansion of the M–X bonds. This is incorrect. Although the computations to support their claim were correct as far as they went, the authors neglected the effects of asymmetric vibrational modes and centrifugal stretches of the bonds. In the present report, we show that quantum chemical computations for LaI3 reveal the crucial roles played by the terms neglected by Giricheva et al., which terms are responsible for thermal bond stretches of approximately 0.023 A at 1142 K. In addition, because the iodine atoms in LaI3 are further apart in the mean structure than the sum of their Pauling van der Waals radii, the geminal nonbonded interactions are attractive. This accounts for the fact that the Morse asymmetry constant for the symmetric stretch mode is smaller than that for the asymmetric stretch. It also helps to explain the very large amplitude of the out-of-plane puckering mode, which tends to decrease the La–I bond length during the puckering trajectory.

Studies on the full vibrational energies and dissociation energies of some heteronuclear diatomic molecules

A parameter-free analytical formula for dissociation energies of diatomic molecules is proposed by Fan and Sun (2009) [20] based on LeRoy and Bernstein's vibrational energy expression near dissociation limit. Using three highest vibrational energies which may be generated by the algebraic method (AM) presented in our previous study and by some other physical methods, the new formula is applied to study the molecular dissociation energies of 10 electronic states of KH, 7LiD, 7LiH, 6LiH, NaK, NaLI and NaRb heteronuclear diatomic molecules which have regular (Morse-like) potentials in this work. The results show that the AM energies E υ A M and dissociation energies D e A M have excellent agreement with experimental values.

Studies on the full vibrational spectra and molecular dissociation energies for some diatomic electronic states

A parameter-free formula is suggested to evaluate the molecular dissociation energy of a stable diatomic electronic system. The full vibrational spectra { E υ A M } and theoretical dissociation energies D e A M are studied using the algebraic method ( AM) and the suggested analytical formula for some electronic states of Li 2, K 2, Na 2, and Sr 2 molecules which have regular (Morse-like) potentials. Both the { E υ A M } and the calculated D e A M agree excellently with known experimental values for each electronic state.

S−S Bond Mesolysis in α,α‘-Dinaphthyl Disulfide Radical Anion Generated during γ-Radiolysis and Pulse Radiolysis in Organic Solution

A dissociation mechanism of the S-S bond in the alpha,alpha'-dinaphthyl disulfide radical anion (NpSSNp*-) in organic solution was investigated on the basis of transient absorption measurements and DFT calculations. NpSSNp*- generated during gamma-radiolysis of NpSSNp in MTHF at 77 K showed the absorption band at 430 nm, which shifted to 560 nm with an increase of the ambient temperature up to room temperature. With the aid of DFT calculations at the B3LYP/6-31G(d) level, the shift of the absorption band was interpreted in terms of molecular conformational changes of NpSSNp*- due to the elongation of the S-S bond. It was observed that NpSSNp*- dissociates into naphthylthiyl radical and thionaphtholate anion in organic solution with a first-order rate constant in the magnitude of 10(6) s-1. From Arrhenius plots of the decay rate constants of NpSSNp*- in a temperature range of 160-293 K, an activation energy for the S-S bond cleavage in NpSSNp*- in solution was determined along with a frequency factor. Based on the state energies of NpSSNp*- calculated at the B3LYP/6-31G(d) level, a Morse-like energy potential for the S-S bond cleavage of NpSSNp*- is depicted as a function of the S-S bond distance.

Dirac equation exact solutions for generalized asymmetrical Hartmann potentials

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of vector and scalar generalized Hartmann potentials. This is done provided the vector potential is equal to or minus the scalar potential. The cases of some quasi-exactly solvable and Morse-like potentials are briefly commented.

The Linear Combination of Vibrational Wave Functions (LCVW) Method in a Morse–Gaussian Double Well Molecular Potential

The linear combinations of harmonic oscillator wave functions (LCWV) method is proposed to solve the Schrodinger equation, for a particle of a mass μ moving in a one dimensional double-well potential field, in which, the energy barrier has a gaussian shape. The general double well potential, whether symmetric or not, is constructed from appropriate combinations of Morse-like potentials and a Gaussian function and the problem is solved variationally, using as trial functions, linear combinations of harmonic oscillator wave functions (LCWV) centered at the two minima. The relevant matrix elements are calculated using the Harmonic Oscillator Tensor (HOT) technique. A generalization to multiple well problems is also advanced.

Algebraic approach to thermodynamic properties of diatomic molecules

A simple model extending Lie algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. Local anharmonic effects are described by means of a Morse-like potential and the corresponding anharmonic bosons are associated with the SU(2) algebra. The total number of anharmonic bosons, fixed by the potential shape, is determined for a large number of diatomic molecules. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation to the specific heat. A physical interpretation in terms of a quantum deformation associated with the model is given.

Pseudo-Hermiticity and some consequences of a generalized quantum condition

We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and allows access to a generalized quantum condition. Special cases lead to hyperbolic and Morse-like potentials in the framework of a coordinate-dependent mass model.

A principle of fractal-stochastic dualism and Gompertzian dynamics of growth and self-organization

The emergence of Gompertzian dynamics at the macroscopic, tissue level during growth and self-organization is determined by the existence of fractal-stochastic dualism at the microscopic level of supramolecular, cellular system. On one hand, Gompertzian dynamics results from the complex coupling of at least two antagonistic, stochastic processes at the molecular cellular level. It is shown that the Gompertz function is a probability function, its derivative is a probability density function, and the Gompertzian distribution of probability is of non-Gaussian type. On the other hand, the Gompertz function is a contraction mapping and defines fractal dynamics in time-space; a prerequisite condition for the coupling of processes. Furthermore, the Gompertz function is a solution of the operator differential equation with the Morse-like anharmonic potential. This relationship indicates that distribution of intrasystemic forces is both non-linear and asymmetric. The anharmonic potential is a measure of the intrasystemic interactions. It attains a point of the minimum ( U 0, t 0) along with a change of both complexity and connectivity during growth and self-organization. It can also be modified by certain factors, such as retinoids.

Bounded solutions of neutral fermions with a screened Coulomb potential

The intrinsically relativistic problem of a fermion subject to a pseudoscalar screened Coulomb plus a uniform background potential in two-dimensional space–time is mapped into a Sturm–Liouville. This mapping gives rise to an effective Morse-like potential and exact bounded solutions are found. It is shown that the uniform background potential determinates the number of bound-state solutions. The behaviour of the eigenenergies as well as of the upper and lower components of the Dirac spinor corresponding to bounded solutions is discussed in detail and some unusual results are revealed. An apparent paradox concerning the uncertainty principle is solved by recurring to the concepts of effective mass and effective Compton wavelength.

Theoretical and electrochemical analysis of dissociative electron transfers proceeding through formation of loose radical anion species: reduction of symmetrical and unsymmetrical disulfides.

The dissociative reduction of a series of symmetrical (RSSR, R = H, Me, t-Bu, Ph) and unsymmetrical disulfides (RSSR', R = H, R' = Me and R = Ph, R' = Me, t-Bu) was studied theoretically, by MO ab initio calculations and, for five of them, also experimentally, by convolution voltammetry in N,N-dimethylformamide. The reduction is dissociative but proceeds by a stepwise mechanism entailing the formation of the radical anion species. The electrochemical data led to estimated large intrinsic barriers, in agreement with an unusually large structural modification undergone by the disulfide molecules upon electron transfer. The theoretical results refer to MP2/3-21G*//MP2/3-21G*, MP2/3-21*G*//MP2/3-21G*, CBS-4M, and G2(MP2), the latter approach being used only for the molecules of small molecular complexity. A loose radical-anion intermediate was localized and the dissociation pattern for the relevant bonds analyzed. For all compounds, the best fragmentation pathway in solution is cleavage of the S-S bond. In addition, S-S bond elongation is the major structural modification undergone by the disulfide molecule on its way to the radical anion and eventually to the fragmentation products. The calculated energy of activation for the initial electron transfer was estimated from the crossing of the energy profiles of the neutral molecule and its radical anion (in the form of Morse-like potentials) as a function of the S-S bond length coordinate. The inner intrinsic barrier obtained in this way is in good agreement with that determined by convolution voltammetry, once the solvent effect is taken into account.

Elastic backscattering of hydrogen molecules from a plasma

Neutral gas measurements in the divertors of DIII-D and JET revealed very high neutral pressures on the wall in the private flux region in excess of expectations from DEGAS simulation for DIII-D and D α intensity measured at the same position in JET. This problem may be solved, if one takes into account an additional scattering process between H 2 molecules and plasma ions. This is caused by the polarization of molecules in the field of ions and becomes important at low temperature. Its consequences are:—Not all neutrals starting at the wall will be absorbed by the plasma.—Neutrals between plasma and wall will be heated and obtain an isotropic velocity distribution. Using a Morse-like potential, collision data for elastic scattering of H 2 -H + are calculated which can be used in Monte Carlo calculations, an example of which will be shown.

Muon bonding and antiferromagnetism in the 123 cuprates

Muon Spin Relaxation (μSR) is a microscopic technique which may help in understanding the mechanism of superconductivity in the high-temperature cuprates. A computational study indicates muon-probe sites in RBa 2Cu 3O x are strongly dependent on the oxygen content ( x), however, these μ sites are nearly independent of the rare earth (R). For x = 7, the majority of the μ sites lies near oxygen in the basal planes; for x = 6, near the oxygens in the CuO planes. The results are based upon potential-energy calculations using the Ewald method, ionic potentials and two different Morse-like potentials describing the μ-O bonding. Magnetic dipole fields are calculated for the candidate μ sites and compared with available zero-field μSR data. The obtained good agreement indicates that the ionic bonding assumption may be correct in describing the electronic p- and d-states in the insulating and superconducting cuprates.

Quantum Theory of Desorption of Adatoms from Solid Surfaces

We present a three-dimensional multiphonon theory of the desorption rate, for an atom adsorbed in a localized state on the surface of a solid, due to interactions with lattice vibrations. The central quantity in the theory is the time and position-dependent displacement-displacement correlation function of the lattice. The temperature dependent lifetime, and the angular and energy distributions, of desorbed adatoms are considered for model systems. Detailed numerical calculations are presented, employing a Debye model for the substrate lattice, and a Morse-like potential for the interaction between the adatom and each substrate atom.

Temperature-Dependent Activation Volumes in Zinc

Precision measurements of self-diffusion in zinc as a function of pressure indicate that the activation volumes $\ensuremath{\Delta}{V}_{c}$ and $\ensuremath{\Delta}{V}_{b}$ respectively associated with the nonbasal and basal vacancy jumps have a temperature dependence given by ${(\frac{\ensuremath{\partial}\ensuremath{\Delta}{V}_{c}}{\ensuremath{\partial}T})}_{p}=(6.2\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ${\mathrm{cm}}^{3}$/mole \ifmmode^\circ\else\textdegree\fi{}K and ${(\frac{\ensuremath{\partial}\ensuremath{\Delta}{V}_{b}}{\ensuremath{\partial}T})}_{p}=(7.6\ifmmode\pm\else\textpm\fi{}3.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ${\mathrm{cm}}^{3}$/mole \ifmmode^\circ\else\textdegree\fi{}K. A model calculation based on a Morse-like potential indicates that the frequencies of atomic vibrations in the vicinity of the defect vary with pressure in a way that is consistent with these experimentally measured quantities.

Classical Model for Vibrational and Rotational Excitation of Diatomic Molecules by Collision. II. Interaction with Arbitrary Potential Functions

Two classical models for vibrational energy transfer between a diatomic harmonic oscillator A-B and an atom C are examined in detail. The first model corresponds to a harmonic repulsion between B and C with a smooth cutoff at zero interaction. It can be solved exactly. The second corresponds to a Morse-like potential between B and C. In this case, the orbits for colinear collisions are followed on a digital computer, and ΔEv the inelastic energy transfer is ``measured'' from this numerical solution for the equation of motion. The results can be transformed into probabilities by defining excitation as the condition: 2hν>ΔEv≥hν. ΔEv is a strong function of the phase angle of the oscillator. The probability function for excitation is transformed into a rate constant by averaging over the temperature-dependent distribution functions for energies. In contrast to other ``classical'' solutions, it is found that P, the probability of excitation (or de-excitation), has a nearly Arrhenius type of dependence on temperature. The activation energy of P is quadratically sensitive to the range of the repulsive interaction between B and C. This arises from the result that the excitation probability P(ER) goes very sharply to zero as ER, the relative collisional energy, approaches some small limiting value. This is in marked contrast to present theories for which P(ER) goes asymptotically to zero with ER. Features of the classical model are discussed in some detail and comparisons are made with experimental data from shock tubes. Because of the extreme sensitivity of the model to the value for the range parameters, no absolute predictions of de-excitation probabilities are possible. However, it is possible to fit the temperature dependence reasonably well with physically acceptable Morse parameters.