Pair correlation function of short-ranged square-well fluids

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths lambda-1 ranging from 0.1 to 1.0, in units of the diameter sigma of the particles. For each one of these widths, several densities rho and temperatures T in the ranges 0.1< or =rhosigma(3)< or =0.8 and T(c)(lambda) less or approximately T less or approximately 3T(c)(lambda), where T(c)(lambda) is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. 100, 3079 (1994); 100, 6665 (1994)] and the nonperturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. 101 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory works for long ranges and high densities.     

Direct determination of phase behavior of square-well fluids

We have combined Gibbs ensemble Monte Carlo simulations with the aggregation volume-biased method in conjunction with the Gibbs-Duhem method to provide the first direct estimates for the vapor-solid, vapor-liquid, and liquid-solid phase coexistences of square-well fluids with three different ranges of attraction. Our results are consistent with the previous simulations and verify the notion that the vapor-liquid coexistence behavior becomes metastable for cases where the attraction well becomes smaller than 1.25 times the particle diameter. In these cases no triple point is found.     

Direct correlation function for complex square barrier-square well potentials in the first-order mean spherical approximation

The direct correlation function of the complex discrete potential model fluids is obtained as a linear combination of the first-order mean spherical approximation (FMSA) solution for the simple square well model that has been reported recently [Hlushak et al., J. Chem. Phys. 130, 234511 (2009)]. The theory is employed to evaluate the structure and thermodynamics of complex fluids based on the square well-barrier and square well-barrier-well discrete potential models. Obtained results are compared with theoretical predictions of the hybrid mean spherical approximation, already reported in the literature [Guillen-Escamilla et al., J. Phys.: Condens. Matter 19, 086224 (2007)], and with computer simulation data of this study. The compressibility route to thermodynamics is then used to check whether the FMSA theory is able to predict multiple fluid-fluid transitions for the square barrier-well model fluids.     

Direct evaluation of the electron density correlation function of partially crystalline polymers

A discussion of the general properties of the one-dimensional electron density correlation function K(z) of a partially crystalline polymer with lamellar structure shows that application of a graphical extrapolation procedure permits direct determination of the crystallinity, the specific inner surface, and the electron density difference η_c ? η_a. The procedure is based upon the occurrence of a straight section in the “self-correlation” range of K(z). Curved and nonparallel lamellae do not invalidate the concept. In the case of heterogeneous samples composed of partially crystalline and totally amorphous regions, some of the parameters of the experimentally obtained correlation function, as for example the invariant K(0), are affected and may lose their definiteness. Use of the method is demonstrated in a detailed discussion of the correlation functions measured for a sample of lowdensity polyethylene at 25 and 100°C.     

Direct calculation of long time correlation functions using an optical potential

We present an ℒ︁² method aimed at directly computing autocorrelation functions 〈Φ₀|Φ_t〉 for systems displaying long time recurrences. By making use of a Lanczos scheme, as previously proposed by Wyatt [Chem. Phys. Lett. 121, 301 (1985)], the method avoids explicit time propagation of the wavefunction. The problem associated with spurious recurrences, due to the finite size of the ℒ︁²-box, is solved in terms of an optical potential located in the asymptotic region. The resulting complex representation of the Hamiltonian operator is handled by a complex symmetric Lanczos scheme, which retains the same basic advantages as its real version. The method is illustrated on the ozone photodissociation process which displays a very detailed recurrence structure over a long time period. It is shown that such a direct calculation of the correlation function is about one order of magnitude faster than an actual wavepacket propagation. The accuracy of the method is assessed by comparison to calculations performed without any optical potential but using a very large box size along the dissociation coordinate. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 317–328, 1998     

Second order of perturbation theory correction to the radial distribution function of a liquid with the interaction potential of hard spheres plus a square-well

A liquid with the interaction potential of hard spheres plus a square-well is analyzed using the Monte-Carlo technique. Numerical results for the perturbation theory series over a square-well potential are obtained in the form of the Barker and Henderson discrete representation. Approximating expressions for the correction to a liquid radial distribution function in the second order of perturbation theory are presented. The obtained results allow us to define this correction with a root-mean-square deviation of about 0.007. It is shown that the given approach provides a complete calculation in the second order of perturbation theory, and also the determination of the third order correction to the free energy for a liquid interacting with the potential of the Lennard-Jones type.     

Stokes-Einstein relations for a square-well fluid

A Stokes-Einstein relation, relating the shear viscosity eta to the self-diffusion coefficient D, is constructed for a classical fluid subject to an effective two-body intermolecular force, derived from a square-well potential, undergoing dynamics as described by a Smoluchowski equation for pair diffusion. The time correlation functions for eta and 1D are separated into contributions from delta function, hard-sphere forces, and from delta function, square-well soft forces. Furthermore, D is separated into its two- and three-body time correlation functions, and eta into its two- to four-body terms. D shows activated diffusion, as in Arrhenius behavior, and on the level of two-body dynamics, the Deta product adheres to the Stokes-Einstein relation, subject to a small correction for potential softness. Three-body time correlation functions increase D, whereas three- and four-body correlation functions in eta are partially offsetting. The deviation of Deta product from the Stokes-Einstein law arises from the three-body time correlations functions in D.     

Phase separation and percolation of reversibly aggregating spheres with a square-well attraction potential

Reversible aggregation of spheres is simulated using a novel method in which clusters of bound spheres diffuse collectively with a diffusion coefficient proportional to their radius. It is shown that the equilibrium state is the same as with other simulation techniques, but with the present method more realistic kinetics are obtained. The behavior as a function of volume fraction and interaction strength was tested for two different attraction ranges. The binodal and the percolation threshold were determined. The cluster structure and size distribution close to the percolation threshold were found to be consistent with the percolation model. Close to the binodal phase separation occurred through the growth of spherical dense domains, while for deep quenches a system spanning network is formed that coarsens with a rate that decreases with increasing attraction. We found no indication for arrest of the coarsening.     

The correlation potential for two-electron atomic ions

The correlation potential is computed for two electron atomic ions with atomic numbers from 1 to 10 using the charge density reconstructed from a natural orbital expansion of a Kinoshita-like atomic wave function. Over the wide range of densities involved, the correlation potentials are not even approximately a local function of the density.     

Symmetry-adapted correlation function for semiclassical quantization

We study a very simple method to incorporate quantum-mechanical symmetries, including the permutational symmetry on an equal footing with spatial symmetries, into the semiclassical calculation of correlation functions. This method is applied to the calculation of energy spectra to verify its validity by reproducing quantum energy levels for systems of bosons (symmetrized) and fermions (antisymmetrized). The mechanism of how the phase-space structure of classical dynamics is linked with the relevant quantum symmetry is discussed.     

Comparing ab initio density-functional and wave function theories: the impact of correlation on the electronic density and the role of the correlation potential

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order M?ller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.     

The flux-flux correlation function for anharmonic barriers

The flux-flux correlation function formalism is a standard and widely used approach for the computation of reaction rates. In this paper we introduce a method to compute the classical and quantum flux-flux correlation functions for anharmonic barriers essentially analytically through the use of the classical and quantum normal forms. In the quantum case we show that for a general f degree-of-freedom system having an index one saddle the quantum normal form reduces the computation of the flux-flux correlation function to that of an effective one-dimensional anharmonic barrier. The example of the computation of the quantum flux-flux correlation function for a fourth order anharmonic barrier is worked out in detail, and we present an analytical expression for the quantum mechanical microcanonical flux-flux correlation function. We then give a discussion of the short-time and harmonic limits.     

Viscosity for a dense fluid of square-well rough spheres

Shear viscosity is calculated for a dense fluid of square-well rough spheres. The results are compared with calculated shear viscosities for the familiar hard-sphere, square-well and rough-sphere models.     

Direct correlation analysis improves fold recognition

The extraction of correlated mutations through the method of direct information (DI) provides predicted contact residue pairs that can be used to constrain the three dimensional structures of proteins. We apply this method to a large set of decoy protein folds consisting of many thousand well-constructed models, only tens of which have the correct fold. We find that DI is able to greatly improve the ranking of the true (native) fold but others still remain high scoring that would be difficult to discard due to small shifts in the core beta sheets.     

The torsional potential function for n-butane

The energies of four different conformations for n-butane were calculated by the ab initio method using an STO-3G basis set. Fully relaxed molecular geometries obtained from molecular mechanics (MM2) were used. The two energy minima [anti (C_2h), gauche (C₂)] and the two maxima (C₂, C_2v) had the following relative energies: 0.0, 0.88, 3.56, 5.99 kcal/mole. These are approximate Hartree–Fock numbers. It is estimated that inclusion of electron correlation in the calculation would lower the last number to about 5.1 kcal/mole while leaving the first three values essentially unchanged.     

A stochastic model for the molecular dipole moment correlation function

An nth order truncation of the continued fraction representation of the molecular dipole moment correlation function is introduced from the free rotation representation and an interaction process which is supposed to be governed by a Poisson distribution. We can then derive a general expression for the correlation function, related both to the natural distribution of angular velocities and the successive time derivatives of the mean square torque due to molecular interactions. Some numerical results and comparisons with experiments are given in the second order truncation case.     

Calculating thermodynamic properties from perturbation theory: I. An analytic representation of square-well potential hard-sphere perturbation theory

The Barker–Henderson macroscopic compressibility approximation of the second-order perturbation term is improved by assuming that the numbers of molecules in every two neighbour shells are correlated, based upon the original assumptions. The results are better than those for the original macroscopic compressibility and local compressibility approximation, especially at high densities. A simple analytic representation of square-well potential hard-sphere perturbation theory is derived based upon this improvement. The method is tested by calculating thermodynamic properties with the four-term truncated form, and the results are in good agreement with those of Monte Carlo and Molecular Dynamics simulation.