Angle-dependent Potential Research Articles

Quantification of Anisotropy in Exchange and Dispersion Interactions: A Simple Model for Physics-Based Force Fields.

In some compounds, exchange repulsion is orientation dependent. However, in contrast to quantum chemical methods that treat exchange explicitly, empirical models assume exchange to be spherically symmetric, yielding an average description only. Here we quantify the anisotropy of exchange and dispersion energy for hydrogen halides and water by probing these compounds with a helium atom using the symmetry-adapted perturbation theory (SAPT). The exchange interaction is reduced by up to 33% due to the σ-hole in hydrogen iodide, depending on the location of the probe. We demonstrate how this anisotropy can be modeled in empirical force fields either using an angle-dependent potential or by introducing virtual sites, reducing the error in the empirical model by a factor of 5 compared to isotropic atoms. Lone-pairs on water, positioned close to perpendicular to the plane of the molecule, on a line with the oxygen atom, and, surprisingly, σ-holes on water both modulate the exchange interaction strongly. Both lone-pairs and σ-holes can be modeled by virtual sites, leading to an 80% reduced error.

Ben Naim's four-arm model with density anomaly: Theory and computer simulations.

Molecular dynamics, Wertheim's integral equationtheory (IET), and thermodynamics perturbation theory (TPT) were used to study the thermodynamics and structure of particles interacting through angle-dependent potential. The particles are modeled as two-dimensional Lennard-Jones disks with four hydrogen bonding arms arranged symmetrically. The model was introduced by Ben-Naim and we call it the BN4 model. The BN4 model exhibits density anomaly and other anomalous properties similar to those in water and in the Mercedes-Benz (MB) model. The IET is based on the orientationally averaged version of the Ornstein-Zernike equationand correctly predicts the pair correlation function of the model at high temperatures. Both TPT and IET are in semiquantitative agreement with the simulation values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity.

Theory of melting of glasses

ABSTRACT Glassy matter like crystals resists change in shape. Therefore a theory for their continuous melting should show how the shear elastic constant μ goes to zero. Since viscosity is the long wave-length low frequency limit of shear correlations, the same theory should give phenomena like the Volger-Fulcher dependence of the viscosity on temperature near the transition. A continuum model interrupted randomly by asymmetric rigid defects with orientational degrees of freedom is considered. Such defects are orthogonal to the continuum excitations, and are required to be imprisoned by rotational motion of the nearby atoms of the continuum. The defects interact with an angle dependent potential. A renormalisation group for the elastic constants, and the fugacity of the defects in 3D is constructed. The principal results are that there is a scale-invariant reduction of μ as a function of length at any temperature , above which it is 0 macrosopically but has a finite correlation length which diverges as . Viscosity is shown to be proportional to and has the Vogel-Fulcher form. The specific heat is . As , the Kauzman temperature from above, the configuration entropy of the liquid is exhausted. The theory also gives the ‘fragility’ of glasses in terms of their .

Investigation on the Origin of Spin and Pseudospin Symmetries in Atomic Nuclei

The spin and pseudo-spin symmetries are analytically investigated by solving the three-dimensional Dirac equation for the Kratzer potential plus a ring-shaped potential. Relativistic Schrödinger-like wave equations coupled in energy are derived from Dirac equation. The energy eigenvalues and eigenfunctions are calculated by solving the coupled relativistic radial, and angular wave equations in the framework of asymptotic iteration method. Our numerical results revealed that the spin and pseudo-spin symmetries are relativistic symmetries of the Dirac Hamiltonian. Effects of the angle-dependent potential on the relativistic energy spectra are also investigated. In addition, we include illustrative tables to examine the solutions in detail.

Raman signal from a hindered hydrogen rotor

We present a method for calculation of Raman modes of the quantum solid phase I hydrogen and deuterium. We use the mean-field assumption that the quantized excitations are localized on one molecule. This is done by explicit solution of the time-dependent Schroedinger equation in an angle-dependent potential, and direct calculation of the polarization. We show that in the free rotor limit, the ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ frequencies differ by a factor of 2, which evolves toward $\sqrt{2}$ as the modes acquire librational character due to stronger interactions. The ratio overshoots $\sqrt{2}$ if anharmonic terms weaken the harmonic potential. We also use density functional theory and molecular dynamics to calculate the ${\phantom{\rule{4pt}{0ex}}E}_{{2}_{g}}$ optical phonon frequency and the Raman linewidths. The molecular dynamics shows that the molecules are not free rotors except at very low pressure and high temperature, and become like oscillators as phase II is approached. We fit the interaction strengths to experimental frequencies, but good agreement for intensities requires us to also include strong preferred orientation and stimulated Raman effects between ${\phantom{\rule{4pt}{0ex}}S}_{0}$(1) and ${\phantom{\rule{4pt}{0ex}}S}_{0}$(0) contributions. The experimental Raman spectrum for phase II cannot be reproduced, suggesting that the mean-field assumption is invalid in that case.

Exact Solutions of Schrödinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

We propose improved ring shaped like potential of the form, V(r, θ) = V(r) + (ħ2/2Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2 and its exact solutions are presented via the Nikiforov–Uvarov method. The angle dependent part V(θ) = (ħ2 / 2 Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2, which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.

An angle-dependent potential and alpha-decay half-lives of deformed nuclei for 67≤Z≤91

The half-lives of deformed nuclei are reported for 67≤Z≤91. We consider an angle-dependent potential which yields multiple approximations. The results are in better agreement with the experimental data when the multiple approximation is solely considered for the daughter nuclei.

ALPHA-DECAY HALF-LIVES OF DEFORMED NUCLEI BY AN ANGLE-DEPENDENT POTENTIAL

The half-lives of deformed nuclei are reported. We consider an angle-dependent potential which yields multipole approximations. We see that the results are in better agreement with the experimental data when the multipole approximation is solely considered for the daughter nuclei.

A new Morse ring-shaped potential for diatomic molecules

Using the Pekeris approximation, the Schrödinger equation is solved analytically for the Morse plus a novel angle-dependent potential. The generalized parametric Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions. We present the effect of the angle-dependent part on radial solutions, and some numerical results for diatomic molecules are also given.

Exact Solutions of the Dirac Equation with Coulomb plus a Novel Angle-Dependent Potential

Abstract In this paper the Dirac equation is analytically solved for Coulomb plus a novel angle-dependent potential. The Nikiforov-Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions. We also discussed the effect of the angle-dependent part on radial solutions.

Spin and charge transport in U-shaped one-dimensional channels with spin-orbit couplings

A general form of the Hamiltonian for electrons confined to a curved one-dimensional (1D) channel with spin-orbit coupling (SOC) linear in momentum is rederived and is applied to a U-shaped channel. Discretizing the derived continuous 1D Hamiltonian to a tight-binding version, the Landauer--Keldysh formalism (LKF) for nonequilibrium transport can be applied. Spin transport through the U-channel based on the LKF is compared with previous quantum mechanical approaches. The role of a curvature-induced geometric potential which was previously neglected in the literature of the ring issue is also revisited. Transport regimes between nonadiabatic, corresponding to weak SOC or sharp turn, and adiabatic, corresponding to strong SOC or smooth turn, is discussed. Based on the LKF, interesting charge and spin transport properties are further revealed. For the charge transport, the interplay between the Rashba and the linear Dresselhaus (001) SOCs leads to an additional modulation to the local charge density in the half-ring part of the U-channel, which is shown to originate from the angle-dependent spin-orbit potential. For the spin transport, theoretically predicted eigenstates of the Rashba rings, Dresselhaus rings, and the persistent spin-helix state are numerically tested by the present quantum transport calculation.

Potential barrier of graphene edges

We calculated row resolved density of states, charge distribution and work function of graphene’s zigzag and armchair edge (either clean or terminated alternatively with H, O, or OH group). The zigzag edge saturated via OH group has the lowest work function of 3.76 eV, while the zigzag edge terminated via O has the highest work function of 7.74 eV. The angle-dependent potential barrier on the edge is fitted to a multipole model and is explained by the charge distribution.

Pseudospin symmetry for a new ring-shaped non-spherical harmonic oscillator potential

A new ring-shaped non-spherical harmonic oscillator potential is proposed, which consists of a generalized non-harmonic oscillator potential plus an angle-dependent potential, The pseudospin symmetry for a spin- particle moving in this potential is investigated by solving the Dirac equation with an equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained, and the algebraic property of the energy equation and some particular cases are also discussed.

On the exact solutions of the Dirac equation with a novel angle-dependent potential

We study the problem of the relativistic motion of a 1/2-spin particle in an exactly solvable potential, which consists of the harmonic oscillator potential plus a novel angle-dependent potential, The analytic bound state solutions of the Dirac equation for this potential are obtained by using the Nikiforov–Uvarov method. The wave functions of the radial and angle-dependent parts of the Dirac equation are derived in the form of the Laguerre and Jacobi polynomials. The contribution of the angle-dependent potential to the relativistic energy spectra is discussed under the condition that the scalar potential is equal to or minus the vector potential.

Modified ℓ-states of diatomic molecules subject to central potentials plus an angle-dependent potential

We present modified l-states of diatomic molecules by solving the radial and angle-dependent parts of the Schrodinger equation for central potentials, such as Morse and Kratzer, plus an exactly solvable angle-dependent potential V θ (θ)/r 2 within the framework of the Nikiforov–Uvarov (NU) method. We emphasize that the contribution which comes from the solution of the Schrodinger equation for the angle-dependent potential modifies the usual angular momentum quantum number l. We calculate explicitly bound state energies of a number of neutral diatomic molecules composed of a first-row transition metal and main-group elements for both Morse and Kratzer potentials plus an angle-dependent potential. We also compare the bound state energies for both potentials, taking into account spectroscopic parameters of diatomic molecules and arbitrary values of potential constants.

A novel angle-dependent potential and its exact solution

The quantum mechanics of a diatomic molecule in a noncentral potential of the type V (r) = Vθ(θ)/r2 + Vr(r) are investigated analytically. The θ-dependent part of the relevant potential is suggested for the first time as a novel angle-dependent (NAD) potential \({V_{\theta}(\theta)=\frac{\hbar^2}{2\mu}\left(\frac{\gamma +\beta \sin^2\theta +\alpha \sin^4 \theta}{\sin^2\theta \cos^2\theta}\right)}\) and the radial part is selected as the Coulomb potential or the harmonic oscillator potential, i.e., Vr(r) = − H/r or Vr(r) = Kr2, respectively. Exact solutions are obtained in the Schrodinger picture by means of a mathematical method named the Nikiforov–Uvarov (NU). The effect of the angle-dependent part on the solution of the radial part is discussed in several values of the NAD potential’s parameters as well as different values of usual quantum numbers.

Interatomic potential for the Cu-Ta system and its application to surface wetting and dewetting

An angle-dependent interatomic potential has been developed for the Cu-Ta system by crossing two existing potentials for pure Cu and Ta. The cross-interaction functions have been fitted to first-principles data generated in this work. The potential has been extensively tested against first-principles energies not included in the fitting database and applied to molecular dynamics simulations of wetting and dewetting of Cu on Ta. We find that a Cu film placed on a Ta (110) surface dewets from it, forming a Cu droplet on top of a stable Cu monolayer. We also observe that a drop of liquid Cu placed on a clean Ta (110) surface spreads over it as a stable monolayer, while the extra Cu atoms remain in the drop. The stability of a Cu monolayer and instability of thicker Cu films are consistent with recent experiments and first-principles calculations. This agreement demonstrates the utility of the potential for atomistic simulations of Cu-Ta interfaces.

Pseudospin symmetry solution of the Dirac equation with an angle-dependent potential

The pseudospin symmetry solution of the Dirac equation for spin 1/2 particles moving within the Kratzer potential connected with an angle-dependent potential is investigated systematically. The Nikiforov–Uvarov method is used to solve the Dirac equation. All of the studies are performed for the exact pseudospin symmetry (SU2) case and also the exact spin symmetry case is given briefly in the appendix. Bound-state solutions are presented to discuss the contribution of the angle-dependent potential to the relativistic energy spectra in the full description case which is either unavailable or excessively complicated.

Quantum scattering from the Coulomb potential plus an angle-dependent potential: a group-theoretical study

The nonrelativistic quantum scattering problem for a non-central potential which belongs to a class of potentials exhibiting an ‘accidental’ degeneracy is studied. We show that the scattering system under consideration admit the Lie algebra as the potential algebra. The scattering amplitude is then evaluated using purely algebraic techniques to give the closed result. It is expressed in terms of associated Legendre functions.

Spectrum of donor states in an ellipsoidal quantum dot

Introducing a method to exactly solve a set of coupled differential equations, different power-series solutions with matrix coefficients are given in different regions of the set of equations to be suitable for numerical calculations. By applying this method, the spectrum of donor states in an angle-dependent potential induced by an ellipsoidal quantum dot is obtained. The dot-shape and quantum-size effects on the spectrum are shown clearly.