Energy Difference Method Research Articles

Constant-NT? simulations: Free energy difference method for excess adsorption

Constant-NT? simulations: Free energy difference method for excess adsorption

Simulations of a confined polymer fluid at constant chemical potential

Monte Carlo simulations are reported of a polymer fluid confined between planar walls using the isotension ensemble, which allows one to perform simulations at constant chemical potential without the necessity of particle exchanges with a bulk polymer fluid. The pressure acting upon the walls and the free energy per unit area of the confined fluid as a function of separation between the walls are obtained, all at constant chemical potential. This is made possible by the use of the so-called free energy difference method. This method appears to be less susceptible to the difficulties that confront the simulation of confined fluids at high density in grand canonical ensemble simulations.

Excess Thermodynamic Properties of CO2+ C2H6Mixtures from MD Simulations

Abstract This paper reports excess Gibbs free energy, excess enthalpy, and excess volume from isothermal-isobaric molecular dynamics simulations of carbon dioxide + ethane mixtures at T = 230 K, 260 K, P = 15.5 MPa, and x = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9. The overall agreement of our calculations with experiments is excellent. The excess Gibbs free energies were calculated by two different methods. They showed that the energy difference method for swapping particles of CO2 into particles of C2H6 yields more reliable values.

Simulations of a confined polymer fluid at constant chemical potential

Monte Carlo simulations are reported of a polymer fluid confined between planar walls using the isotension ensemble, which allows one to perform simulations at constant chemical potential without the necessity of particle exchanges with a bulk polymer fluid. The pressure acting upon the walls and the free energy per unit area of the confined fluid as a function of separation between the walls are obtained, all at constant chemical potential. This is made possible by the use of the so-called free energy difference method. This method appears to be less susceptible to the difficulties that confront the simulation of confined fluids at high density in grand canonical ensemble simulations.

Methods of Single-Step and Multistep Particle Switching in Simulations of Mixtures

In an earlier paper, we applied a procedure combining the energy difference method with a modified Kirkwood−Buff fluctuation theory to extrapolate chemical potential differences in three directions (T, P, x). The results showed that the extrapolations in pressure and concentration were successful and the linear temperature extrapolations were moderate in determination of the phase separations. In this paper we have tried to calculate the second order of the temperature dependence of the chemical potential difference using the energy difference methods of single-step and multistep switchings. Due to large fluctuations in calculation of the second orders, the method can only predict qualitatively or semiquantitatively the second-order terms.

Simulations in planar slits at constant chemical potential

In this work we describe Monte Carlo simulations of a fluid confined between planar walls. We derive a free energy difference method (FEDM) in the isotension ensemble. We illustrate the method by varying the separation between the walls at constant chemical potential. It is shown that the FEDM is a viable alternative to grand canonical ensemble (GCE) simulations. Our method appears to be less susceptible to the difficulties that confront the simulation of confined fluids at high density in the GCE.

Relativistic self-consistent calculation for hafnium atoms and ions based on a relativistic local density functional theory

The Dirac equation for the spherical symmetrical potential of hafnium atoms and ions with various electron configurations has been calculated numerically by using a relativistic local density functional approximation. Electron binding energies, ionization potential, X-ray emission energies, and Auger electron energies are evaluated by the total energy difference (ΔSCF) method and Slater's transition-state method. The calculated results are in agreement with the experimental results measured by spectroscopies

Electron Density Distribution of a Single Hydrogen Perturbation in a Metal Lattice

The electronic structure of hydrogen centres stored in a metal crystal is described by a microscopic theory based on a functional energy difference method. That formalism works in a suitably chosen tensor product space built on a physical quasi-particle vacuum state. A transformation back to a bare Fock space representation is shown. This transformation operator divides the functional eigenvalue equation into a difference of two Schrödinger problems. The resulting state vectors can be used to calculate the electronic density distribution of a hydrogen excess electron in a metal lattice. The density function is obtained in a higher order approximation which considers the influence of three-particle correlations. A numerical solution is discussed for the case of a single hydrogen centre in a magnesium crystal. The plot shows that the excess electron is mainly localized in the surroundings of the corresponding hydrogen core. But with increasing host lattice extension there is more and more a non-vanishing probability to find the hydrogen electron dipped into the Fermi sea of metal electrons.

A Higher Order Approximation for the Electronic Structure of Hydrogen in Metals

A functional energy difference method based on first principles is used to calculate the electronic contribution to the storage energy of hydrogen impurities in metals. That electronic problem is treated in a higher order approximation which means considering the coupling between one-electron wavefunctions and three-particle amplitudes. A formalism is presented to eliminate all higher order correlations and to reduce the whole system to a one-particle Schrödinger equation with the help of a suitable G reen’s function. The resulting one-electron eigenvalue problem contains some logarithmic singularities due to the fact that there is no gap between occupied and unoccupied electron states in the band structure of a metal. In an electron gas model a convergent theory is reached by an improvement of the Green’s function leading to a screening of the long-range Coulomb potentials. The result is a complicated non-linear algebraic eigenvalue equation which is solved numerically for the special case of a single hydrogen perturbation in a magnesium crystal. The solution shows the influence of higher order electron correlations on the electronic energy eigenvalue of an interstitial hydrogen centre plot as a function of host lattice distortions.

Molecular-mechanical studies of hormone-protein interactions: the interaction of T4 and T3 with prealbumin.

AbstractWe present molecular‐mechanical calculations on the interactions of L‐thyroxine (T4) and 3,5,3′‐triiodo‐L‐thyronine (T3) with the binding site of human serum prealbumin. Energy refinement with restraints on the movement of the iodine atoms leads to reasonably low‐energy structures with the iodines within 0.2 Å of their x‐ray determined positions; removal of these restraints leads to larger (∼1.0 Å) deviations from these positions. However the relative energies of T3 and T4 complexation are similar in both cases, and the relative calculated energies for these complexes, when corrected by a simple empirical method for the solvation energy differences of the hormones, are in reasonable qualitative agreement with experiment.

The use of optimization techniques in the analysis of cracked members by the finite element displacement and stress methods

Abstract Mathematical programming is applied to the two-dimensional stationary crack problem of a body composed of nonlinear elastic incompressible material. Fully admissible displacement as well as stress formulations are used to discretize the problem. Crack tip singularity is introduced in the displacement formulation by enriched elements for plane stress and, in certain cases, by superposition for plane strain. Pointwise incompressibility is obtained through constrained displacement functions. For three crack geometries Rice's J integral is evaluated by the energy difference method for different values of the hardening index. The numerical results, which are also applicable to secondary creep problems, appear to suggest a bounding character.

Détermination du rayon de la distribution de neutrons de certains noyaux par l'étude de la diffusion élastique de particules alpha de 166 mev

The angular distributions for 166 MeV α-particle elastic scattering have been measured and are presented. The differential cross sections obtained are analysed with optical potentials whose real parts are derived from the convolution of nuclear-matter distributions with an effective α-nucleon interaction. This interaction is defined both from an analysis of α-scattering from N = Z light nuclei and from heavy nuclei whose matter distributions are supposedly well known. The imaginary parts of the optical potentials are either taken to be proportional to the real parts or to have a Woods-Saxon form. Using parameters for nuclear charge distributions derived from elastic electron scattering, radii of neutron matter distributions with errors varying between ±0.09 fm and ±0.16 fm are extracted for the following nuclei: 12C, 24Mg, 28Si, 32S, 40, 44, 48Ca, 48Ti, 56Fe, 59Co, 58, 60, 62Ni, 68Zn, 88Sr, 89Y, 90, 94Zr, 92Mo, 116, 118, 120, 124Sn, 140Ce 208Pb. The assumptions made in the present analysis and the resulting uncertainties are presented. Charge and neutron radii are compared in isotope and isotone families and to radii determinations from other sources. In particular, our results agree with those derived from proton-scattering analyses and with Hartree-Fock calculations but are not always in accord with the results obtained from Coulomb energy difference methods.

On the interpretation of k-shell electron binding energy chemical shifts in molecules

The relationship between the potential-at-a-point and orbital energy difference methods of computing K-shell electron binding energy chemical shifts, and their affinity to the nuclear shielding effect in NMR spectroscopy is demonstrated.