Non-Gaussian energy landscape of a simple model for strong network-forming liquids: Accurate evaluation of the configurational entropy

We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square-well potential, with an additional constraint that limits the maximum number of bonds Nmax per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and Nmax. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e., features defining strong glass-forming liquids. This model has two important features: (i) Landscape basins can be associated with bonding patterns. (ii) The configurational volume of the basin can be evaluated in a formally exact way, and numerically with an arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e., configurations in which all particles are bonded to Nmax neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state and show that it follows a logarithmic functional form, different from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior.     

Model investigations of network-forming materials

Recent advances in the study of network-forming materials are described for systems dominated both by ionic and covalent interatomic interactions. Modelling strategies are described which focus both on describing specific systems of interest and on modelling the systematic evolution of network topology. The effect of network topology on the presence of ordering both on intermediate- and extended-length-scales is discussed. The effect of the topology on the mechanical rigidity is also described and analysed in terms of a mean coordination model. In addition, the isomorphology between amorphous silicon and the silicon sub-lattice in SiO(2) is described. Polyamorphism in Si and ZnCl(2) is analysed and discussed. Finally, the study of reduced (two) dimensional systems is discussed for carbon, silicon and germanium.     

Mean spherical model approximation for the primitive model of sodium chloride

A calculation of the excess internal energy and the osmotic coefficient for a mixture of charged hard spheres of diameters equal to the ionic radii of NaCl, is done in the mean spherical approximation. The results are compared to the best available data, provided by the hypernetted chain theory. The agreement is better for the osmotic coefficient than for the internal energy, and improves at higher concentrations.     

On the closure conjectures for the Gibbsian approximation model of a binary droplet

Within the framework of Gibbsian thermodynamics, a binary droplet is regarded to consist of a uniform interior and dividing surface. The properties of the droplet interior are those of the bulk liquid solution, but the dividing surface is a fictitious phase whose chemical potentials cannot be rigorously determined. The state of the nucleus interior and free energy of nucleus formation can be found without knowing the surface chemical potentials, but the latter are still needed to determine the state of the whole nucleus (including the dividing surface) and develop the kinetics of nucleation. Thus it is necessary to recur to additional conjectures in order to build a complete, thermodynamic, and kinetic theory of nucleation within the framework of the Gibbsian approximation. Here we consider and analyze the problem of closing the Gibbsian approximation droplet model. We identify micro- and Gamma-closure conjectures concerning the surface chemical potentials and excess surface coverages, respectively, for the droplet surface of tension. With these two closure conjectures, the Gibbsian approximation model of a binary droplet becomes complete so that one can determine both the surface and internal characteristics of the whole nucleus and develop the kinetic theory, based on this model. Theoretical results are illustrated by numerical evaluations for binary nucleation in a water-methanol vapor mixture at T=298.15 K. Numerical results show a striking increase in the droplet surface tension with decreasing droplet size at constant overall droplet composition. A comparison of the Gibbsian approximation with density functional calculations for a model surfactant system indicate that the excess surface coverages from the Gibbsian approximation are accurate enough for large droplets and droplets that are not too concentrated with respect to the solute.     

Extension of the group-contribution lattice-fluid equation of state

This work focuses on the extension of the numbers of group parameters and application of the group-contribution lattice-fluid equation of state (GCLF EOS). The new group parameters of the GCLF EOS were evaluated by means of the volume translated Peng–Robinson equation of state (VTPR EOS) and the UNIFAC model. Values for 20 main groups and 33 subgroups are added into the current parameter matrix. The procedure used in this work can also be used to evaluate group parameters for the groups not present in the current matrix. Some examples are given to show the reliability of the new group parameters. Two new applications of the GCLF EOS are present: the effect of polymeric additive to solvents in extractive distillation and prediction of the crystallinity of polymers in the presence of gas.     

Generalized gradient approximation model exchange holes for range-separated hybrids

We propose a general model for the spherically averaged exchange hole corresponding to a generalized gradient approximation (GGA) exchange functional. Parameters are reported for several common GGAs. Our model is based upon that of Ernzerhof and Perdew [J. Chem. Phys. 109, 3313 (1998)]. It improves upon the former by precisely reproducing the energy of the parent GGA, and by enabling fully analytic evaluation of range-separated hybrid density functionals. Analytic results and preliminary thermochemical tests indicate that our model also improves upon the simple, local-density-based exchange hole model of Iikura et al. [J. Chem. Phys. 115, 3540 (2001)].     

Simple electrostatic model for the I — A approximation

Employing the approximation which replaces r _ij ^–1 by (r_i+r_j)^–1 we derive the relation 2/4l+5=I–A where is the orbital exponent of a Slater AO. This semiempirical relation appears to agree with experiment for the cases compared.     

Perturbation theory with model zero-order approximation for Li2 molecules

Odessa Engineering Institute. Translated from Zhurnal Strukturnoi Khimii, Vol. 29, No. 1, pp. 163–165, January–February, 1988.     

Improvement to the lattice-fluid prediction of gas solubilities in polymer liquids

Previously we have shown that the Lattice Fluid (LF) model can quantitatively predict, without adjustable parameters, gas solubilities for hydrocarbon and chlorinated hydrocarbon vapors in nonpolar polymers. For polar polymers, the model can also predict, with reasonable success, the solubilities of polar and aromatic vapors. However, the solubilities in polar/nonpolar combinations of gas and polymer are systematically overestimated. These are cases in which the geometric mean approximation for the interaction parameter is not expected to be valid. This paper demonstrates that with the addition of a simple empirical correlation for the interaction parameter based on Hansen's three-dimensional solubility parameters, the LF model is then able to quantitatively predict solubilities in all types of gas/polymer systems (excluding strongly self-associating systems, such as alcohols). No adjustable parameters are used; only the pure component equation-of-state and solubility parameters are required. © 1993 John Wiley & Sons, Inc.     

A semiempirical model for the two-center repulsion integrals in the NDDO approximation

A self-consistent formalism is proposed for the two-center electron repulsion integrals in the NDDO approximation, based on their expansion in terms of multipole-multipole interactions and free from adjustable parameters.     

Time-dependent density-functional theory beyond the adiabatic approximation: insights from a two-electron model system

Most applications of time-dependent density-functional theory (TDDFT) use the adiabatic local-density approximation (ALDA) for the dynamical exchange-correlation potential V(xc)(r,t). An exact (i.e., nonadiabatic) extension of the ground-state LDA into the dynamical regime leads to a V(xc)(r,t) with a memory, which causes the electron dynamics to become dissipative. To illustrate and explain this nonadiabatic behavior, this paper studies the dynamics of two interacting electrons on a two-dimensional quantum strip of finite size, comparing TDDFT within and beyond the ALDA with numerical solutions of the two-electron time-dependent Schrodinger equation. It is shown explicitly how dissipation arises through multiple particle-hole excitations, and how the nonadiabatic extension of the ALDA fails for finite systems but becomes correct in the thermodynamic limit.     

Separable approximation for diatomic transition operators: a variational approach

A general finite-rank separable approximation for the two-body transition operator has been obtained from the Lippmann--Schwinger variational principle. The method involves expansion of the off-shell wavefunction in a finite set of square integrable functions, and is applied to ¹Σ and ³Σ potentials of H₂ for thermal energies and momenta.     

Geometric approximation for molecular polarizabiities

Molecular polarizabilities calculated with the geometric approximation are shown to be independent of the type of perturbation theory used. Agreement with finite field calculations, including anisotropies, is obtained for small molecules. A modified procedure for including sigma and pi contributions in a differentiated way is developed within the CNDO scheme. Applications to planar conjugated systems are displayed.     

A simplified approach to vapor–liquid equilibria calculations with the group-contribution lattice-fluid equation of state

Equations of state that are based on the lattice-statistics approach use Guggenheim's quasi-chemical approximation to describe the non-randomness in the mixture due to the energetic interactions between the molecules. For ternary and higher-component systems the non-randomness expression is complex and requires an iterative calculation procedure. We have shown that the non-randomness parameters play a negligible role in the application of the GCLF-EoS model (based on the Panayiotou–Vera EoS) for predicting vapor–liquid equilibria. Omission of the non-randomness parameters from such calculations can significantly improve the computation efficiency. Binary, ternary, and quaternary vapor–liquid equilibria predictions were made including polystyrene, polyvinyl acetate, polyethylene, and polypropylene in polar and non-polar solvents to test the theory.     

Local-density-functional approximation for exchange-correlation potential

Local exchange-correlation potential has been derived starting from the free electron gas model.Ab initio way of calculating the parameter of the X method is presented. Self-consistent and statistical exchange-correlation parameters have been determined. The self-consistent parameters have been used to calculate the electron binding energies of Neon, Argon and Krypton. We suggest using statistical exchange-correlation parameter in molecular calculations. The statistical exchange-correlation parameter has been applied to study the electron binding energies of the molecules H₂O and HF. It is shown that the electron binding energies calculated with the self-consistent and the statistical parameters show agreement with the experimental values.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

A microscopic model of chemical reactions with reorganization. High-energy approximation

A dynamical model of a chemical reaction, accompanied by reorganization of the immediate environment of the isolated chemical subsystem, is proposed. The model enables studying the emergence of nonequilibrium distribution functions as a combined result of the interaction within the dynamical subsystem and the energy exchange with a subsystem of inactive degrees of freedom (thermal bath). The study is based on the quasiclassical high-energy approximation for nonadiabatic effects in the energy exchange within the dynamical subsystem, for strong and weak coupling of the oscillator mode with the thermal bath. Such an approximation allows for the important statement that nonequilibrium effects in thermal reactions are absent if the initial translational distribution along the reaction coordinate and the initial vibrational distribution in transversal degrees of freedom are Boltzmann-like with the same temperature. The results obtained in the absence of the initial equilibrium distribution have been used for interpreting the kinetics of endothermic plasmochemical reactions proceeding under nonequilibrium conditions.     

Applications of a quantum virial theorem to kronig and penney's model and to a diatomic molecule in static approximation

Kronig and Penney's model is used to test a new formulation of quantum virial theorem for periodic systems. It is shown that the corrective term to the usual formulation of the virial theorem corresponding to boundary conditions is of importance and gives correct energy values for the system. Application of the virial theorem to a diatomic molecule also shows an important boundary condition correction if the distance of the nuclei is slightly different from equilibrium position, in accordance with the above correction.