Site-site Distribution Functions Research Articles

Structural analysis of hydrazinium trifluoroacetate aqueous solution by X-ray diffraction and empirical potential structure refinement modeling in the temperature range of 25 to −125 °C

X-ray diffraction of a hydrazinium trifluoroacetate ([N2H5]+ [TFA]-) aqueous solution at 14.4 mol% of N2H5TFA is measured in a temperature range from 25 to −125 °C. The solution in a supercooled region exhibits an anomalous temperature behavior of the heat capacity without ice crystallization taken place for neat water. The X-ray interference functions of an N2H5TFA solution are subjected to empirical potential structure refinement (EPSR) modeling to obtain the site-site pair distribution functions, the coordination number distribution, the angle distribution, and the spatial density function (3D structure). The tetrahedral-like network structure as observed for neat water remains for an N2H5TFA aqueous solution, and the structure is enhanced at temperatures below −75 °C, although the solution does not freeze. The enhancement of the tetrahedral-like network structure could be responsible for the anomalous behavior of the heat capacity of the solution at a low temperature. It is consistent with the scenario of the second critical point of neat water where the transition from high-density water to low-density water is considered to take place.

Structure of liquid ammonia at high pressures and temperatures

The structure of liquid ammonia (${\mathrm{NH}}_{3}$) is investigated from 1 to 6.3 GPa and up to 800 K by means of synchrotron x-ray diffraction (XRD) and ab initio molecular dynamics (AIMD) simulations. The XRD data are used to extract the molecular structure factor ${S}_{\mathrm{mol}}(Q)$, pair distribution function (PDF) ${g}_{\mathrm{mol}}(r)$, and the density of ${\mathrm{NH}}_{3}$. There is an excellent agreement between present ${S}_{\mathrm{mol}}(Q)$ and ${g}_{\mathrm{mol}}(r)$ at our lowest density and those reported in reference neutron experiments. Our densities agree better with the equation of state (EoS) of Tillner-Roth et al. [DKV-Tagungsbericht (Hannover, New York, 1993), Vol. 20, p. 167] than with more recent EoS models. The experimental structure factor and PDF are well reproduced by AIMD simulations using either the Becke-Lee-Yang-Parr or the Perdew-Burke-Ernzerhof exchange-correlation functional. The shapes of ${S}_{\mathrm{mol}}(Q)$ and ${g}_{\mathrm{mol}}(r)$ vary little over the investigated pressure range and suggest a compact liquid with weak orientational correlations between molecules, which is corroborated by the coordination number varying from 12.7 to $\ensuremath{\sim}14$. The simulations are used to study the evolution of the site-site pair distribution functions, which reveals that the number of H bonds per molecule (between 1.5 and 2) do not evolve with density and that the distribution of H atoms around N atoms becomes more and more anisotropic with pressure.

Size distribution of associated clusters in liquid alcohols: Interpretation of simulation results in the frame of SAFT approach

The size distribution and topology of associated clusters for primary alcohols is studied using molecular dynamics simulations. Liquid ethanol, propanol, butanol, hexanol, and octanol are simulated at pressure P = 1 bar and temperatures T = 300 K, T = 350 K, and T = 400 K. The fractions of molecules with different sets of hydrogen bonded partners, the size of associated cluster and the site-site distribution functions between atoms participating on hydrogen bonding are extracted from simulated trajectories. For all alcohols longer than ethanol, the length of the alkyl chain has only a marginal effect on the association. Consequently, related properties like coordination numbers of hydroxyl group, size distribution of associates, or fractions of differently coordinated alcohol molecules are independent on the molecular size. Although we employed a force-field without involved polarizability, we observe a positive cooperativity of hydrogen bonding simply as a consequence of steric and electrostatic interactions. The size and topology of associates is analyzed within the frame of 3B model of statistical association fluid theory. Although this approach enables good thermodynamic description of systems containing associating compounds, several insufficiencies appear in the description at molecular level.

High Density Amorphous Ice from Cubic Ice

Supercooled water does not behave like a simple liquid, but instead shows a number of anomalous properties. These include the diffusion coefficient [2] or the kinematic viscosity [3] which show anomalous pressure dependencies on compression up to 200MPa, whereas beyond 200 MPa the expected behaviour is observed. To explain these anomalies the second critical point hypothesis has been put forward, in which a first-order-like phase transition between a low(LDL) and high-density liquid (HDL) is thought to occur. LDL and HDL become indistinguishable above the second critical point, which is postulated to be in the “no man’s land” around 180– 220 K and 100–340 MPa, where only crystalline ice has been observed experimentally. This model is supported by the observation that there are (at least) two different phases of amorphous water called low-(LDA) and high-density amorphous ice (HDA), which have been found to show a first-order like transformation in compression/decompression experiments. On heating, LDA and HDA experience a glass-transition to the highly viscous, supercooled liquids denoted low(LDL) and high-density liquid (HDL), respectively. The role of HDA in this model has become unclear since the discovery of a further distinct structural state called very-high density amorphous ice (VHDA). It has lately been argued that only VHDA and LDA are homogeneous disordered structures, whereas HDA does not constitute a particular state of the HDA network. This issue is still under debate, since the transition from HDA to VHDA on isothermal compression at 125 K has been found recently to be similar to the transition from LDA to HDA. The detailed structures of recovered HDA and VHDA have been determined at ambient pressure and 77 K by means of neutron diffraction with isotope substitution. These two studies contain the first experimental determination of the three site-site distribution functions (H H, O O, O H). For both HDA and VHDA there is no evidence in the diffraction pattern to show that it is microcrystalline rather than a genuinely amorphous structure. Herein, we show that HDA produced by pressure-induced amorphization of cubic ice (Ic) at 77 K is not the same material as “traditional” HDA produced by pressure-induced amorphization of hexagonal ice (Ih) at 77 K. The density of both amorphous states recovered at ambient pressure is very similar; however, the X-ray structure factor as well as the phase transition characteristics in differential scanning calorimetry scans, differ in the onset temperature, enthalpy and sharpness of the exotherms. Hexagonal ice was prepared by either pipetting 0.300 mL of deionized water directly into the piston-cylinder apparatus lined with an indium container kept at 77 K, or by heating HDA close to ambient pressure to 260 K and recovering to 77 K and 1 bar, or by Johari’s procedure of decompressing HDA to 0.06 GPa and heating to 235 K. Cubic ice was prepared by hyperquenching small liquid droplets of 3 mm diameter on a cryoplate kept at 190 K in the same way reported earlier. The deposit was then transferred to the piston–cylinder apparatus and filled into the indium–lined cylinder by spooning, under liquid nitrogen. Alternatively, cubic ice was prepared by heating HDA to 185 K at 0.025 GPa and recovering to 77 K and 1 bar. HDA was produced by compressing 300 mg of Ih to 1.5 GPa at 77 K in a similar way to our previous studies. These starting materials for the pressure-induced amorphization process have been characterized using powder X-ray diffractograms, which are depicted in Figure 1. The posi-

Molecular-dynamics simulations of dimethylsulfoxide-methanol mixtures

We present molecular-dynamics (MD) computer simulation results for the local structures, hydrogen (H)-bond distribution, and dynamical properties of methanol (MeOH) and dimethylsulfoxide (DMSO) binary mixtures at ambient conditions over the entire composition range. The simulated heat of mixing and site-site pair distribution functions suggest that the intermolecular structures of the pure liquids are not markedly altered upon mixing. Nevertheless, H-bonding statistics show that aggregates of the type 1DMSO:1MeOH are formed and represent the predominant form of molecular association in these mixtures. Only a small fraction (10%) of DMSO molecules in MeOH-rich mixtures (85% in mole) forms H-bonding trimers of type 1DMSO:2MeOH. No evidence of other types of interspecies association is found. The self-diffusion coefficient for DMSO (MeOH) increases (decreases) upon mixing. The characteristic reorientation time tau1 of both species increases in the mixture, but the composition dependence is weak. The frequency spectrum of MeOH reorientational time-correlation function shows significant redshifts of the principal librational band as DMSO is added to the system, whereas the librational band of DMSO shows small alterations upon mixing. Our results are discussed in the light of previous simulation analyses for a similar system, DMSO-water mixtures, and compared with available experimental results.

Pressure and Temperature Dependence of the Hydrogen Bonding in Supercritical Ethanol: A Computer Simulation Study

As a step toward deeper insight on the "hydrogen bonding" in supercritical ethanol (scEtOH), we carried out NVT molecular dynamics simulations of the fluid over a wide range of temperatures and pressures. The fluid was studied at SC conditions for which thermodynamic and spectroscopic (NMR, infrared, Raman, dielectric) data are available. The various site-site pair distribution functions (pdf's) were calculated, and their temperature and pressure dependence was obtained. It was found that over the thermodynamic conditions investigated here, scEtOH remains highly structured. Moreover, the characteristic behavior of the first peaks in H-H, O-O, and H-O pdf's reveals that hydrogen bonds still exist in scEtOH. The analysis focuses also on the reorientational dynamics of the bond unit vectors O-H, C-O, and of the permanent dipole moment of the molecules as well as the total dipole moment of the sample. The corresponding Legendre time correlation functions were discussed in connection to the "hydrogen bonding" in the fluid and in the context of experimental results. Specifically, the behavior of the O-H dynamics exhibits the well-known associative nature of the molecules in the system. A further analysis of the hydrogen bonds was carried out, and the degree of aggregation (average number of H-bonds per molecule) was obtained and compared with results from NMR chemical shift studies. Also the estimated monomer and free O-H groups in the fluid were compared with results from IR and Raman vibrational spectroscopy. The percentage analysis fi of the liquid and scEtOH molecules, with i = 0, 1, 2, 3, ... hydrogen bonds per molecule, has been obtained. The results show the existence of small, linear-chain oligomers formed mainly by two molecules, whereas the number of the three body oligomers, and specifically that of four body oligomers in the sample, is relatively small.

Molecular dynamics simulations of the liquid mixtures N, N-dimethylformamide-water using available potential models

This work reports the first computational study of N, N-dimethylformamide (DMF)-water mixtures performed by the molecular dynamics simulation (MDS) technique over the entire concentration range. The MDS results obtained have been used to assess the effectiveness of previously proposed potential models for pure liquid water (SPC, SPCE, TIPS2) and DMF (CS2) in predicting certain properties of the DMF-water mixtures at ambient conditions. Thus, the sensitivity of the bulk thermodynamic and transport properties of the mixture to the details of the combined intermolecular potentials (CS2/SPC, CS2/SPCE, CS2/TIPS2) used has been obtained and discussed. Specifically, hydrogen bonds among the DMF and water molecules in the mixture are revealed in the behaviour of the concentration dependent appropriate (O DMF-H water, O DMF-O water) site-site pair distribution functions. Finally, the bulk thermodynamic results obtained have shown that among the three aforementioned potentials for water used, the SPC model, and TIPS2 to a lower extent, in combination with our CS2 model for pure liquid DMF provides the most accurate descriptions of the DMF-water mixtures.

A generalized self-consistent mean-field theory for fluids of molecules with distributed polarizabilities: Comparisons with computer simulations

Abstract The generalized self-consistent mean field (GSCMF) approximation recently proposed provides a systematic approach for finding an effective pair potential for a fluid of molecules with atom, bond or other distributed polarizabilities. The GSCMF theory is combined with the molecular Ornstein-Zernike (MOZ) theory using the hypernetted chain (HNC) approximation to compute the liquid properties of polarizable interaction models of water, acetonitrile, and methanol. The average moments, the excess energies, the dielectric constants, and the site-site distribution functions are studied for models with a distributed polarizability or with an overall polarizability at the molecular centre. The MOZ(HNC)/GSCMF results are compared to the data of simulations using exact procedures to handle the molecular polarizabilities. Comparison of the results obtained by the MOZ/GSCMF theory and by simulations shows that the MOZ/GSCMF approach correctly predicts the relative changes of the liquid properties caused by a distribution of the polarizability. For the acetonitrile models, the MOZ/GSCMF and simulation results are in good agreement. In contrast for water and methanol, the MOZ/GSCMF theory gives strongly underestimated total excess energies and average dipoles and the liquid structure is less pronounced. However, this mainly occurs because the HNC approximation only provides a semi-quantitative description of H bonding liquids as recently observed for non polarizable models of water and methanol. The results suggest that the GSCMF approach is capable of providing accurate effective pair potentials for fluids of molecules with distributed polarizabilities.

Modifications of the hydrogen bond network of liquid water in a cylindrical SiO2 pore

We present results of molecular dynamics simulations of water confined in a silica pore. A cylindrical cavity is created inside a vitreous silica cell with geometry and size similar to the pores of real Vycor glass. The simulations are performed at different hydration levels. At all hydration levels water adsorbs strongly on the Vycor surface; a double layer structure is evident at higher hydrations. At almost full hydration the modifications of the confinement-induced site-site pair distribution functions are in qualitative agreement with neutron diffraction experiment. A decrease in the number of hydrogen bonds between water molecules is observed along the pore radius, due to the tendency of the molecules close to the substrate to form hydrogen-bonds with the hydrophilic pore surface. As a consequence we observe a substrate induced distortion of the H-bond tetrahedral network of water molecules in the regions close to the surface.

Water confined in Vycor glass. I. A neutron diffraction study

Neutron diffraction experiments with isotopic substitution on water confined in porous Vycor glass at two hydration states are presented and analyzed in terms of the experimentally accessible site-site distribution functions. The bias on these functions as well as their limitations, due to the presence of regions where water molecules are not allowed (excluded volume effects), and to the contribution of water–Vycor interference to the measured cross sections, are discussed. In particular the relative weight of these cross correlation terms is estimated for the first time. It is shown that the traditional analysis of diffraction data of these kinds which ignore cross correlations may be erroneous. A full account of the excluded volume effects is reported in paper II [A. Soper, F. Bruni, and M. A. Ricci, J. Chem. Phys. 109, 1486 (1998), following paper].

A molecular dynamics simulation of water confined in a cylindrical SiO2 pore

A molecular dynamics simulation of water confined in a silica pore is performed in order to compare it with recent experimental results on water confined in porous Vycor glass at room temperature. A cylindrical pore of 40 Å is created inside a vitreous SiO2 cell, obtained by computer simulation. The resulting cavity offers water a rough hydrophilic surface and its geometry and size are similar to those of a typical pore in porous Vycor glass. The site-site distribution functions of water inside the pore are evaluated and compared with bulk water results. We find that the modifications of the site-site distribution functions, induced by confinement, are in qualitative agreement with the recent neutron diffraction experiment, confirming that the disturbance to the microscopic structure of water mainly concerns orientational arrangement of neighboring molecules. A layer analysis of MD results indicates that, while the geometrical constraint gives an almost constant density profile up to the layers closest to the interface, with a uniform average number of hydrogen bonds (HB), the hydrophilic interaction produces the wetting of the pore surface at the expenses of the adjacent water layers. Moreover, the orientational disorder together with a reduction of the average number of HB persists in the layers close to the interface, while water molecules cluster in the middle of the pore at a density and with a coordination similar to bulk water.

Liquid acetone and chloroform: a comparison between Monte Carlo simulation, molecular Ornstein-Zernike theory, and site-site Ornstein-Zernike theory

Site-site distribution functions, internal energies, compressibilities, and dielectric constants of liquid acetone and chloroform are computed and compared. The hypernetted chain approximation is used for the molecular Ornstein-Zernike (MOZ) and site-site Ornstein-Zernike (SSOZ) theories. Both solvent molecules are described as sets of interaction sites, which are the centres of Lennard-Jones potentials and which carry partial electric charges. How the approximations inherent in both OZ theories affect the calculated liquid properties is discussed. In contrast to SSOZ theory, MOZ theory yields a correct description of the liquid structure as defined by the site-site distribution functions of simulations. The MOZ results for the dielectric constants are in good agreement with simulation, but both OZ theories slightly underestimate the internal excess energies. In contrast to the SSOZ formalism and to the simulations, the molecular pair distribution of MOZ theory can be computed readily for all two-molecule configurations, allowing a detailed study of the complex relief of this distribution. A search was performed for configurations that are highly probable in the liquid. They can be assigned to a small number of peaks of the molecular distribution function. These peaks have major contributions to the Kirkwood factors, which measure the orientational order in the liquid, and to the electrostatic part of the excess energies. The partitioning of the whole two-molecule configuration space makes it possible to study the details of the site-site distribution functions. For instance, a sharp peak in the oxygen-oxygen distribution in acetone results from many superimposed contributions of acetone-acetone arrangements of low and medium statistical weights, and not from the highly probable arrangements.

Structure and thermodynamics of liquid acetonitrile via Monte Carlo simulation and Ornstein-Zernike theories

Abstract Acetonitrile is modeled by a system of three sites, which are the centres of short-range Lennard-Jones interactions and which carry partial electric charges. Site-site distribution functions, internal energies, and dielectric constants are computed, using three theoretical methods: Monte Carlo simulation, molecular Ornstein-Zernike theory and site-site Ornstein-Zernike theory. The results of these calculations are compared and discussed in the light of the approximations inherent in the various approaches. The molecular pair distribution function is analysed to find pair configurations occuring in the liquid with a high probability. The effects of these configurations on the thermodynamic and structural properties are studied.

Microscopic structure of the hydrogen-xenon mixture

We report a neutron-diffraction study of the microscopic structure of the ${\mathrm{H}}_{2}\ensuremath{-}\mathrm{X}\mathrm{e}$ binary mixture in the Xe-rich phase, ${x}_{\mathrm{Xe}}=0.78,$ at $T=283$ K and $P=170$ bars, i.e., in the vicinity of the second-type gas-gas demixing surface. The site-site distribution functions are extracted employing the H-D isotopic substitution technique. We report also molecular-dynamics simulations for a mixture of equivalent Lennard-Jones (LJ) atoms. The experimental results are compared with previous ones obtained for the He-Xe and Ne-Xe mixtures, which show a first- and a second-type gas-gas transition, respectively. The general picture already suggested by the other two mixtures agrees also with the present results, although in this case the center-center distribution functions ${\mathrm{H}}_{2}$-${\mathrm{H}}_{2}$ and ${\mathrm{H}}_{2}\ensuremath{-}\mathrm{X}\mathrm{e}$ are clearly modulated by the Xe-Xe correlations. In particular the features found in the distribution functions of the mixture suggest that the LJ potential model is not able to reproduce at a satisfactory level the ${\mathrm{H}}_{2}$-${\mathrm{H}}_{2}$ and the ${\mathrm{H}}_{2}\ensuremath{-}\mathrm{X}\mathrm{e}$ correlation functions and that a $({\mathrm{XeH}}_{4})$ chemical complex is present.

Configurational statistics for isolated square-well chain molecules: exact results for short chains

Exact results are obtained for the configurational statistical properties of isolated square-well chain molecules of lengths 3 and 4. The chain molecules considered here are composed of square-well spheres with hard-core diameter σ and well diameter λσ (1 ˇ- λ ˇ- 2) connected by ‘universal joints’ with bond length σ. Exact analytical and semi-analytical expressions are obtained for the intramolecular site-site distribution functions for these chain molecules. From the intramolecular distribution functions one can determine all average equilibrium configurational and energetic properties. In particular, the mean-square site-site separations, mean-square radius of gyration, average energy, and specific heat are calculated. With decreasing temperature the chain molecules undergo a collapse transition identified by a sudden reduction in chain dimensions and a peak in the specific heat. For both square-well 3-mers and 4-mers the reduced transition temperature is in the range 0·2 ≲T c* ≲ 0·5.

Computer simulation of solvation dynamics in hydrogen-bonding liquids

The dynamics of solvation following an instantaneous reversal of the dipole moment, ( e 2 , −e 2 ) → ( −e 2 , e 2 ) , of diatomic solutes immersed in methanol-water mixtures is investigated through molecular dynamics simulations. We study the solvation response functions for two different solute sizes in an equimolar methanol-water mixture and compare them with the corresponding responses in pure methanol. The total response functions for the mixture are separated into methanol and water contributions in order to identify methanol- and water-like features of the response. Several equilibrium solute-solvent site-site pair distribution functions are also calculated to help elucidate the effects of the solute size on the solvation response.

Comparison of the Structure of Liquid Amides as Determined by Diffraction Experiments and Molecular Dynamics Simulations

The intermodular structures of liquid formamide, N-methylformamide and N,N-dimethylformamide at room temperature are studied by means of NVE molecular dynamics computer simulations. Newly developed flexible models are used. X-ray and neutron weighted structure and total radial pair distribution functions are computed from the simulated site-site pair distribution functions. They are compared with experimental results. The agreement is usually satisfactory as far as heavy atom pairs are concerned while the lengths of the hydrogen bonds are found to be systematically too long in the simulations.

Molecular fluids: site-site analysis and hypernetted chain results with bridge functions for Lennard-Jones dimers

Rigid site-site molecular fluids are analysed, and a formally exact expression for the virial pressure is obtained that involves the triplet site correlation function, which may be evaluated using a superposition approximation. Numerical results for a Lennard-Jones dimer are obtained using the hypernetted chain (HNC) closure with all bridge diagrams with two field points. The bridge diagrams induce the secondary peak in the site-site distribution function that is missing in the HNC. Although the internal energy and the pressure are improved by the inclusion of bridge functions, the latter is most reliably given by the bare HNC and the compressibility route.

Square-well diatomics Exact low density results

Exact semi-analytical expressions are obtained for the zero density site-site distribution function and the second virial coefficient for homonuclear square-well diatomics. The diatomic molecules considered here are composed of two fused square-well spheres with hard core diameter σ, well diameter λσ, and dimer bond length L, such that 0<Lˇ-σ and 1ˇ-λˇ-1+L/σ. Very accurate, although approximate, analytical expressions are also given for these functions.

Computer simulation of liquid methyl chloride

Molecular dynamics and Monte Carlo methods were applied, in the isobaric-isothermal NPT ensemble to study several thermodynamic states of CH 3 Cl in liquid phase. An intermolecular site-site (CH 3 and Cl) model was used. The thermodynamical properties were studied in the 175 K (mp)-250 K (bp) range. The calculated densities and vaporization enthalpies for the liquid are in good agreement with experimental results. The analysis of the site-site distribution functions indicates the presence in the liquid of some energetically favored relative configurations as antiparallel and linear dimers