Intermolecular Nuclear Relaxations and Molecular Site-Site Pair Correlation Functions in Liquids

Intermolecular nuclear relaxation studies of real liquids and the results of theoretical calculations for model potential functions have provided significant information on the role of molecular interactions in the structure of liquids. The intermolecular proton-proton paircorrelation function (pcf), obtained from the reference interaction site model (RISM) is used as the equilibrium distribution and is used to obtarn an effective force for the calculation of intermolecular proton relaxation rates in liquid benzene, 1,3,5-trideuterobenzene and ethane. For liquid ethane, better agreement with experiment is observed with the pcf obtained from the Monte Carlo simulation than with the RISM result.     

Application of Static Charge Transfer within an Ionic‐Liquid Force Field and Its Effect on Structure and Dynamics

The effects of linear scaling of the atomic charges of a reference potential on the structure, dynamics, and energetics of the ionic liquid 1,3‐dimethylimidazolium chloride are investigated. Diffusion coefficients that span over four orders of magnitude are observed between the original model and a scaled model in which the ionic charges are ±0.5 e. While the three‐dimensional structure of the liquid is less affected, the partial radial distribution functions change markedly—with the positive result that for ionic charges of ±0.7 e, an excellent agreement is observed with ab initio molecular dynamics data. Cohesive energy densities calculated from these partial‐charge models are also in better agreement with those calculated from the ab initio data. We postulate that ionic‐liquid models in which the ionic charges are assumed to be ±1 e overestimate the intermolecular attractions between ions, which results in overstructuring, slow dynamics, and increased cohesive energy densities. The use of scaled‐charge sets may be of benefit in the simulation of these systems—especially when looking at properties beyond liquid structure—thus providing an alternative to computationally expensive polarisable force fields.     

Radial behavior of gradient expansion approximation to atomic Fukui function and shell structure of atoms

An approximation to the Fukui function in atoms recently proposed in the form of a gradient correction to the local density approximation expression is here investigated. The spatial behavior of this function is analyzed, focusing on the gradient correction term. Physical information on the shell structure of atoms is shown to be conveyed by the radial distribution of that term. The analytically modeled densities (AMD) procedure is also implemented, and global atomic hardnesses are calculated with Hartree-Fock and AMD representations of atomic electron densities. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 488–503, 1998     

Structure and associated properties of concentrated SiO2 sols in dilute salt solutions

Using the Verwey-Overbeek potential (VO) function the various liquid-state properties of SiO₂ sols in dilute salt solutions have been evaluated under the mean spherical model approximation (MSMA). The structure factors of these SiO₂ sols predicted by this model are compared with results obtained from small-angle neutron scattering experiments by Ramsay et al. Fourier transformation of these structure factors have been performed to obtain the radial distribution functions (RDF), and from these RDF's we computed coordination numbers of the sol particles. The interparticle distanced _c of sol particles has been obtained from the peak position in structure factorS(k) by using the Bragg's equation. The surface potential _s of the oxide sols has been determined from the amplitude (A) of the VO potential. The present calculations clearly indicate some sort of ordering in the sols system. It is gratifying to note that the present theoretical calculations could reproduce the available observed results very satisfactorily with respect to structure factor and other data.     

Study of multipole contributions to the structure of water around ions in solution using the soft sticky dipole-quadrupole-octupole (SSDQO) model of water

The solvation of ions in the soft sticky dipole-quadrupole-octupole (SSDQO) model for liquid water is presented here. This new potential energy function for liquid water describes water-water interactions by a Lennard-Jones term plus a sticky potential consisting of an approximate moment expansion with point dipole, quadrupole, and octupole moments. The SSDQO potential energy function using the moments from extended simple point charge (SPC/E), TIP3P, or TIP5P reproduces the pair potential energy functions and radial distribution functions of the respective multipoint model but it is much faster than even the three-point models. Here, the solvation of ions in SSDQO water is studied using ion-water potential energy functions consisting of moment expansions up to the charge-quadrupole term, up to the charge-octupole term, and up to an approximate charge-hexadecapole term using the moments of SPC/E water. The radial distributions from Monte Carlo simulations show the best agreement with the results for ions in SPC/E water for the expansion up to the charge-hexadecapole term. Thus, the best results are obtained when the water-water and ion-water potentials are exact up to the 1r(4) term and also contain an approximate 1r(5) term. Overall, the simplicity, efficiency, and accuracy of the SSDQO potential make it potentially very useful for computer simulations of aqueous solvation.     

Anisotropic united atom model including the electrostatic interactions of benzene

An optimization including electrostatic interactions has been performed for the parameters of an anisotropic united atoms intermolecular potential for benzene for thermodynamic and transport property prediction using Gibbs ensemble, isothermal-isobaric (NPT) Monte Carlo, and molecular dynamic simulations. The optimization procedure is based on the minimization of a dimensionless error criterion incorporating various thermodynamic data (saturation pressure, vaporization enthalpy, and liquid density) at ambient conditions and at 350 and 450 K. A comprehensive comparison of the new model is given with other intermolecular potentials taken from the literature. Overall thermodynamic, structural, reorientational, and translational dynamic properties of our optimized model are in very good agreement with experimental data. The new model also provides a good representation of the liquid structure, as revealed by three-dimensional spatial density functions and carbon-carbon radial distribution function. Shear viscosity variations with temperature and pressure are very well reproduced, revealing a significant improvement with respect to nonpolar models.     

Modified all-valence INDO/spd method for ground and excited state properties of isolated molecules and molecular complexes

A new semiempirical all-valence method, GRINDOL (Ghost and Rydberg INDO ), based on the INDO approximation, is described. Linderberg–Seamans relation (extended to the d and Rydberg orbitals) for the resonance integrals and a new semitheoretical expression for the core-core repulsion term and energy correction including basis-set superposition error (intermolecular as well as intramolecular) has been applied. The proposed method enables calculation of ground and excited state properties. The ground state results (including intermolecular interactions) as well as the spectral properties are in reasonable agreement with relevant experimental (or ab initio) studies for isolated molecules, molecular complexes, and transition metal compounds. The method contains only one adjustable parameter, all two-center integrals and terms are only basis-set dependent. The one-center integrals are evaluated from the respective atomic terms.     

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.     

金属Cu液固转变及晶体生长的分子动力学模拟

采用分子动力学模拟研究了液态Ｃｕ在不同冷却速度下的凝固特点,模拟采用ＥＡＭ作用势,计算了不同温度,不同冷却速度下Ｃｕ的偶相关函数,结果表明ＥＡＭ作用势能很好地描述液态Ｃｕ的结构特征,当冷却速度较快时,液Ｃｕ形成非晶;当冷却速度较慢时,液Ｃｕ形成晶体,分析了不同冷却速度下体系的相变热力学及相变动力学过程,最后采用液固两层构型法,描述了Ｃｕ晶体的生长过程。     

Connection between the observable and centroid structural properties of a quantum fluid: application to liquid para-hydrogen

It is shown that the discrepancy between path integral Monte Carlo [M. Zoppi et al., Phys. Rev. B 65, 092204 (2002)] and path integral centroid molecular dynamics [F. J. Bermejo et al., Phys. Rev. Lett. 84, 5359 (2000)] calculations of the static structure factor of liquid para-hydrogen can be explained based on a deconvolution equation connecting centroid and physical radial distribution functions. An explicit expression for the kernel of the deconvolution equation has been obtained using functional derivative techniques. In the superposition approximation, this kernel is given by the functional derivative of the effective potential with respect to the pairwise classical potential. Results of path integral Monte Carlo calculations for the radial distribution function and the static structure factor of liquid para-hydrogen are presented.     

Molecular dynamic simulation of the structure of liquid chlorobenzene, <Emphasis Type="Italic">ortho</Emphasis>-chlorotoluene,and their mixtures

The molecular dynamics method is used to simulate the structure of liquid chlorobenzene, ortho-chlorotoluene, and their mixtures with concentrations of 0.03 ppm, 0.05 ppm, 0.1 ppm, 0.5 ppm, and 0.95 ppm chlorobenzene. Radial angular distribution functions (RADFs) were found for the distances between benzene ring planes and the angle between them in pure components and solutions. The data obtained from RADFs indicate that in the nearest environment of molecules the parallel orientation of benzene rings is the dominant configuration, while the fraction of perpendicular contacts is relatively small. In a concentration range of 0.03 ppm, 0.05 ppm, and 0.95 ppm chlorobenzene, conglomerates form with structural characteristics close to those of the dissolved substance. At a concentration of 0.1 ppm chlorobenzene, solute molecules start to agglomerate. In a concentration range from 0.15 ppm to 0.9 ppm chlorobenzene, both agglomerates and conglomerates of the same size are present in the mixture. The radial distribution functions of chlorine-chlorine distances calculated in pure components and mixtures indicate the presence of chlorine aggregates. The results obtained are compared with molecular light scattering data.     

An alternative multipolar expansion for intermolecular potential functions

We have derived a new multipolar expansion for intermolecular potential-energy functions with applications in molecular physics, theoretical chemistry, and mathematical physics. The new formulation employs a separation of radial and angular terms with a simple index structure that leads to computational efficiency and ease of physical interpretation. For the case of the Coulomb interaction, we compare the present formulation with two conventional multipole expansions: the Cartesian tensor and the irreducible spherical tensor expansions. The new formalism leads to efficient numerical algorithms that are useful for general applications beyond intermolecular potentials. In addition to the electrostatic Coulomb interaction, we illustrate the formalism with applications to special function theory and a bipolar expansion involved in potential theory.     

Exact solution of multidimensional hyper‐radial Schrödinger equation for many‐electron quantum systems

In quantum theory, solving Schrödinger equation analytically for larger atomic and molecular systems with cluster of electrons and nuclei persists to be a tortuous challenge. Here, we consider, Schrödinger equation in arbitrary N‐dimensional space corresponding to inverse‐power law potential function originating from a multitude of interactions participating in a many‐electron quantum system for exact solution within the framework of Frobenius method via the formulation of an ansatz to the hyper‐radial wave function. Analytical expressions for energy spectra, and hyper‐radial wave functions in terms of known coefficients of inverse‐power potential function, and wave function parameters have been obtained. A generalized two‐term recurrence relation for power series expansion coefficients has been established. © 2016 Wiley Periodicals, Inc.     

Tests of Monte Carlo perturbation theory for the free energy of liquid copper

Monte Carlo perturbation theory, in which terms in the thermodynamic perturbation series are evaluated by Monte Carlo averaging, has potentially large advantages in efficiency for calculating free energies of liquids from ab initio potential surfaces. In order to test the accuracy of perturbation theory for liquid metals, a series of calculations has been done on liquid copper, modeled by an embedded atom potential. A simple 1/r(12) pair potential is used as the reference system. The free energy is calculated to third order in perturbation theory, and the results are compared to an exact formula. It is found that for optimal reference potential parameters, second order perturbation theory is essentially exact. Second and third order theories give accurate results for significantly nonoptimal reference parameters. The relation between perturbation theory and reweighting is discussed, and an approximate formula is derived that shows an exponential dependence of the efficiency of reweighting on the second order free energy correction. Finally, techniques for application to ab initio potentials are discussed. It is shown that with samples of 100 configurations, it is possible to obtain accuracy and precision at the level of approximately 1 meV/atom.     

Liquid properties of dimethyl ether from molecular dynamics simulations using Ab Initio force fields

We have used molecular dynamic simulations to study the structural and dynamical properties of liquid dimethyl ether (DME) with a newly constructed ab initio force field in this article. The ab initio potential energy data were calculated at the second order Møller‐Plesset (MP2) perturbation theory with Dunning's correlation consistent basis sets (up to aug‐cc‐pVQZ). We considered 17 configurations of the DME dime for the orientation sampling. The calculated MP2 potential data were used to construct a 3‐site united atom force field model. The simulation results are compared with those using the empirical force field of Jorgensen and Ibrahim (Jorgensen and Ibrahim, J Am Chem Soc 1981, 103, 3976) and with available experimental measurements. We obtain quantitative agreements for the atom‐wise radial distribution functions, the self‐diffusion coefficients, and the shear viscosities over a wide range of experimental conditions. This force field thus provides a suitable starting point to predict liquid properties of DME from first principles intermolecular interactions with no empirical data input a priori. © 2012 Wiley Periodicals, Inc.     

Chemometric study of liquid water simulations. I. The parameters of the TIP4P model potential

The multivariate chemometric techniques two level factorial design (TLFD) and principal component analysis (PCA) were used to investigate the TIP4P model potential behavior with respect to perturbations on all intermolecular interaction parameters. The effects of these perturbations were calculated for the enthalpy of vaporization, the density, the first maximum of the radial distribution functions of the O-H and O-O pairs, and the second maximum of the radial distribution function of the O-H pair obtained from Monte Carlo simulations of liquid water at 25 degrees C. The principal effects were quantified and rationalized in terms of the pair-wise interaction potential of the TIP4P model. They also corroborate previously published sensitivity analysis results using molecular dynamics and other model potentials. In addition, significant interaction effects between some parameters of the TIP4P model potential were observed and quantified, which hardly could be obtained without such a statistic approach. These interaction effects are very regular and systematic, and their behavior has not been encountered in other chemometric studies and cannot be rationalized in terms of the functional form of the pair-wise potential.     

Ordering in homologous series of 4′-<Emphasis Type="Italic">n</Emphasis>-alkyl-4-cyanobiphenyl (<Emphasis Type="Italic">n</Emphasis>CB)—A comparative computational study

A comparative computational analysis of molecular ordering in homologous series of monotropic nematic liquid crystal 4′-n-alkyl-4-cyanobiphenyl (nCB) molecules with alkyl groups, butyl (4CB), pentyl (5CB), hexyl (6CB), heptyl (7CB), has been carried out with respect to translational and orientational motion. The atomic net charge and dipole moment at each atomic center were evaluated using the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh-Schrodinger perturbation theory and the multicenter-multipole expansion method were employed to evaluate long-range intermolecular interactions, while a 6-exp potential function was assumed for short-range interactions. Various possible geometrical arrangements of molecular pairs with regard to different energy components were considered, and the most favorable configuration was found. A comparative picture of molecular parameters, such as total energy, binding energy, and total dipole moment of 4CB, 5CB, 6CB, and 7CB, is given. The results are discussed in the light of other theoretical observations.     

Investigation of structure of liquid 2,2,2 trifluoroethanol: neutron diffraction, molecular dynamics, and ab initio quantum chemical study

The molecular conformation and intermolecular H bonding in liquid 2,2,2 trifluoroethanol (TFE) have been studied by neutron diffraction with hydrogen/deuterium isotopic substitution at room temperature. For comparison, conformations of molecules and their dimers in the gas phase have also been calculated, based on the density functional theory. Energies, geometry, and vibrational frequencies of dimers were analyzed. Diffraction data analyzed by the "Monte Carlo determination of g(r)" (MCGR) method resulted in a molecular structure in agreement with the findings from gas phase electron diffraction experiments and density functional calculations. The intermolecular structure functions were compared to the same functions obtained from a molecular dynamics simulation. All of the composite radial distribution functions are in good agreement with the simulation results. According to our calculation the hydrogen-bonded aggregation size is smaller in pure liquid TFE than in pure liquid ethanol.     

Chemical potential perturbation: a method to predict chemical potentials in periodic molecular simulations

A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of density in periodic molecular simulations. The CPP method applies a spatially varying external force field to the simulation, causing the density to depend upon position in the simulation cell. Following equilibration the homogeneous (uniform or bulk) chemical potential as a function of density can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. We compare three different methods of approximating this correction. The first method uses the van der Waals density gradient theory to approximate the inhomogeneous Helmholtz free energy density. The second method uses the local pressure tensor to approximate the homogeneous pressure. The third method uses the Triezenberg-Zwanzig definition of surface tension to approximate the inhomogeneous free energy density. If desired, the homogeneous pressure and Helmholtz free energy can also be predicted by the new method, as well as binodal and spinodal densities of a two-phase fluid region. The CPP method is tested using a Lennard-Jones (LJ) fluid at vapor, liquid, two-phase, and supercritical conditions. Satisfactory agreement is found between the CPP method and an LJ equation of state. The efficiency of the CPP method is compared to that for Widom's method under the tested conditions. In particular, the new method works well for dense fluids where Widom's method starts to fail.     

HUG and SQUEEZE: using CRYSTALS to incorporate resonant scattering in the SQUEEZE structure‐factor contributions to determine absolute structure

The resonant‐scattering contributions to single‐crystal X‐ray diffraction data enable the absolute structure of crystalline materials to be determined. Crystal structures can be determined even if they contain considerably disordered regions because a correction is available via a discrete Fourier transform of the residual electron density to approximate the X‐ray scattering from the disordered region. However, the corrected model cannot normally account for resonant scattering from atoms in the disordered region. Straightforward determination of absolute structure from crystals where the strongly resonantly scattering atoms are not resolved has therefore not been possible. Using an approximate resonant‐scattering correction to the X‐ray scattering from the disordered regions, we have developed and tested a procedure (HUG) to recover the absolute structure using conventional Flack x refinement or other post‐refinement determination methods. Results show that in favourable cases the HUG method works well and the absolute structure can be correctly determined. It offers no useful improvement in cases where the original correction for the disordered region scattering density is problematic, for example, when a large fraction of the scattering density in the crystal is disordered, or when voids are not occupied equally by the disordered species. Crucially, however, if the approach does not work for a given structure, the statistics for the absolute structure measures are not improved, meaning it is unlikely to lead to misassignment of absolute structure.