Applications of the RISM equation to diatomic fluids: the liquids nitrogen,oxygen and bromine

The reference interaction site model (RISM) integral equation is used to study the equilibrium pair correlation for one-component liquids composed of homonuclear diatomic molecules. The integral equation is first tested by comparing the results obtained from it with those of computer simulation calculations. An internal consistency test is developed which seems to provide an a priori measure of the accuracy of the RISM equation. Then the theory is used to interpret the neutron scattering structure factor data taken on the liquids nitrogen and oxygen. For both of these liquids, a satisfactory explanation of the data is obtained by assuming that the short ranged repulsive forces between molecules are mimicked by a two-site hard core model. However, this simple model does not provide a satisfactory explanation of the data taken from liquid bromine. But, it is shown that a slightly more sophisticated model for the short-ranged repulsion between Br₂ molecules does provide an adequate explanation. With the molecular models determined by fitting the neutron scattering data, the RISM equation provides a method for determining the atom, atom to center-of-mass, and center-of-mass to center-of-mass intermolecular distribution functions in the diatomic liquids. From these functions, the local structures in the three liquids are analyzed. While orientational pair correlations are nearly negligible in both the liquids nitrogen and oxygen, these correlations are fairly substantial in liquid bromine. Furthermore, even when the orientation of a molecule does not greatly influence the orientation of its neighbors, it is found that the orientation of a molecule does have an important effect on the location of its neighbors. Thus, the coupling of translational and orientational coordinates is significant, even in the liquids nitrogen and oxygen.     

Towards a more accurate reference interaction site model integral equation theory for molecular liquids

A systematic approach for increasing the accuracy of the reference interaction site model (RISM) theory is introduced that uses input from simulation results to produce very accurate site-site pair correlation functions for single component molecular liquids. The methodology allows the computation of the "RISM bridge function." Realistic molecular liquids such as water, alcohols, amides, and others are investigated, and the merits and limitations of the method for each of these liquids are examined in relation to the known deficiencies of the RISM theory.     

Multiphonon vibrational relaxation in liquids: should it lead to an exponential-gap law?

The profound differences between solids and liquids notwithstanding, high-frequency vibrational energy relaxation in liquids seems to be well described by assuming that the excess energy is being transferred into discrete overtones of some fundamental intermolecular vibrations-precisely the way it is in crystalline solids. In a solid-state context, this kind of analysis can be used to justify the observation that relaxation rates fall off exponentially with the energy being transferred. Liquids, however, have a substantial degree of disorder, causing their relevant intermolecular spectra to have correspondingly diffuse band edges and large bandwidths. It is therefore not at all obvious what should become of this exponential-gap-law phenomenology. We show in this paper how near exponential-gap-law behavior can still be derived for vibrational energy relaxation in liquids. To do so, we take advantage of the simple dynamics that the high-frequency relaxation has when it is launched from an individual instantaneous configuration. Interestingly, the physically relevant region turns out not to be true asymptotic limit of our formalism, but for realistic liquid parameters the behavior in the physical regime differs only slightly from an exact exponential-gap law and is strikingly independent of the details of the intermolecular spectra.     

A RISM approach to the liquid structure and solvation properties of ionic liquids

We test for the first time the performance of the reference interaction site model (RISM) to predict the liquid structure and solvation of room-temperature ionic liquids (RTILs) represented with different degrees of accuracy. The model gives satisfactory results, proposing itself as a possible method to explore and to describe at a chemically realistic level the solvation shell in ionic liquids, which is believed to play a fundamental role in the static electronic and vibrational properties of these systems.     

Solvent dependence of OH bend vibrational relaxation of monomeric water molecules in liquids

The vibrational relaxation rates of the OH bending mode of monomeric H(2)O molecules diluted in various liquid halogenated methane and ethane derivates have been determined by a picosecond infrared pump-probe study. Relaxation time constants between 4.8 and 40.5 ps have been obtained. The discussion of the general solvent dependence suggests that in all cases the solvent fundamental with the smallest energy mismatch is favorably populated by this intermolecular energy transfer process.     

On the density scaling of liquid dynamics

Superpositioning of relaxation data as a function of the product variable TV(γ), where T is temperature, V the specific volume, and γ a material constant, is an experimental fact demonstrated for approximately 100 liquids and polymers. Such scaling behavior would result from the intermolecular potential having the form of an inverse power law (IPL), suggesting that an IPL is a good approximation for certain relaxation properties over the relevant range of intermolecular distances. However, the derivation of the scaling property of an IPL liquid is based on reduced quantities, for example, the reduced relaxation time equal to T(1∕2V - 1∕3) times the actual relaxation time. The difference between scaling using reduced rather than unreduced units is negligible in the supercooled regime; however, at higher temperature the difference can be substantial, accounting for the purported breakdown of the scaling and giving rise to different values of the scaling exponent. Only the γ obtained using reduced quantities can be sensibly related to the intermolecular potential.     

Estimating the Gibbs energy of hydration from molecular dynamics trajectories obtained by integral equations of the theory of liquids in the RISM approximation

A method of integral equations of the theory of liquids in the reference interaction site model (RISM) approximation is used to estimate the Gibbs energy averaged over equilibrium trajectories computed by molecular mechanics. Peptide oxytocin is selected as the object of interest. The Gibbs energy is calculated using all chemical potential formulas introduced in the RISM approach for the excess chemical potential of solvation and is compared with estimates by the generalized Born model. Some formulas are shown to give the wrong sign of Gibbs energy changes when peptide passes from the gas phase into water environment; the other formulas give overestimated Gibbs energy changes with the right sign. Note that allowance for the repulsive correction in the approximate analytical expressions for the Gibbs energy derived by thermodynamic perturbation theory is not a remedy.     

Intermolecular vibrations and fast relaxations in supercooled ionic liquids

Short-time dynamics of ionic liquids has been investigated by low-frequency Raman spectroscopy (4 < ω < 100 cm(-1)) within the supercooled liquid range. Raman spectra are reported for ionic liquids with the same anion, bis(trifluoromethylsulfonyl)imide, and different cations: 1-butyl-3-methylimidazolium, 1-hexyl-3-methylimidazolium, 1-butyl-1-methylpiperidinium, trimethylbutylammonium, and tributylmethylammonium. It is shown that low-frequency Raman spectroscopy provides similar results as optical Kerr effect (OKE) spectroscopy, which has been used to study intermolecular vibrations in ionic liquids. The comparison of ionic liquids containing aromatic and non-aromatic cations identifies the characteristic feature in Raman spectra usually assigned to librational motion of the imidazolium ring. The strength of the fast relaxations (quasi-elastic scattering, QES) and the intermolecular vibrational contribution (boson peak) of ionic liquids with non-aromatic cations are significantly lower than imidazolium ionic liquids. A correlation length assigned to the boson peak vibrations was estimated from the frequency of the maximum of the boson peak and experimental data of sound velocity. The correlation length related to the boson peak (～19 A?) does not change with the length of the alkyl chain in imidazolium cations, in contrast to the position of the first-sharp diffraction peak observed in neutron and X-ray scattering measurements of ionic liquids. The rate of change of the QES intensity in the supercooled liquid range is compared with data of excess entropy, free volume, and mean-squared displacement recently reported for ionic liquids. The temperature dependence of the QES intensity in ionic liquids illustrates relationships between short-time dynamics and long-time structural relaxation that have been proposed for glass-forming liquids.     

Intermolecular relaxation in glycerol as revealed by field cycling 1H NMR relaxometry dilution experiments

(1)H spin-lattice relaxation rates R(1) = 1/T(1) have been measured for partly deuterated glycerol-h(5) diluted in fully deuterated glycerol-h(0) for progressively lower concentrations of glycerol-h(5). By means of the field cycling (FC) technique relaxation dispersion data, R(1)(ω), have been collected for several temperatures in the frequency range of 10 kHz-20 MHz. In order to disclose the spectral shape of the intra- and intermolecular relaxation, extrapolation of the relaxation data to the zero concentration limit has been performed. The paper confirms that the low frequency excess contribution to the total relaxation rate R(1)(ω) previously reported for several liquids is of intermolecular origin and reflects translational motion, whereas the high-frequency part is attributed to molecular rotation. Thus, intra- and intermolecular relaxation contributions are spectrally separated. The intermolecular relaxation itself contains also a contribution from rotational motion, which is due to non-central positions of the interacting nuclei in the molecule. This eccentricity effect is quantitatively reproduced by treating the intermolecular spectral density as a sum of translational-like (described by the free diffusion model) and rotational-like contributions (described by a Cole-Davidson function). Applying frequency-temperature superposition master curves as well as individual relaxation dispersion data, R(1)(ω), are analyzed. It is demonstrated that, in spite of the rotational influence, the translational diffusion coefficients, D(T), can be extracted from the (1)H relaxation dispersion which gives (1)H NMR relaxometry the potential to become a routine technique determining the diffusion coefficient in liquids.     

Vibrational energy relaxation of large-amplitude vibrations in liquids

Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response. This observation seems to be a generic feature of large-moment-arm vibrational degrees of freedom and is therefore probably not specific to our choice of model system: The lowest frequency (largest amplitude) cases probably dissipate energy too quickly and the higher frequency (more slowly relaxing) cases most likely have solvent displacements too small to generate significant nonlinearities in simple nonpolar solvents. Vibrational kinetic energy relaxation, in particular, seems to be especially and surprisingly linear.     

Intermolecular vibrational relaxation in liquids

The influence of intermolecular vibrational relaxation on dipole moment correlation functions, as obtained from IR band shapes, is discussed. It is explicitly shown that vibrational relaxation due to intermolecular interactions depends on the reorientational behaviour of the molecules in the liquid.Therefore, an a priori separation of the dipole moment correlation function into independent reorientational and vibrational factors is not generally possible. The implications for various procedures used to “correct” Raman and IR band shapes for vibrational relaxation are discussed.The expression derived for the intermolecular vibrational relaxation is used to calculate theoretically the effect of transition dipole-transition dipole coupling on dipole moment correlation functions.Experimental data obtained from isotopic dilution measurements support the interpretation of the isotopic dilution effect in terms of the transition dipole-transition dipole coupling.     

Nuclear magnetic resonance study of alkane conformational statistics

NMR spectra of ethane, propane, and n-butane as solutes in the nematic liquid crystals 4-n-pentyl-4(')-cyanobiphenyl (5CB) and Merck ZLI 1132 (1132) are investigated over a wide temperature range. The ratios of dipolar couplings of ethane to propane are constant over the entire temperature range. Assuming that this constancy applies to the butane conformers facilitates the separation of probability from order parameter. This separation allows the investigation of conformational distribution without the need of invoking any model for the anisotropic intermolecular potential. The results give an order matrix that is consistent with that predicted from model potentials that describe the orientational potential in terms of short-range size and shape effects. The isotropic intermolecular potential contribution to the trans-gauche energy difference E(tg) is found to be temperature dependent with the values and variation in agreement with that found when the same results are analyzed using the chord model for anisotropic interactions [A. C. J. Weber and E. E. Burnell, Chem. Phys. Lett. 506, 196 (2011)]. The fit obtained for 9 spectra in 5CB (63 dipolar couplings) has an RMS difference between experimental and calculated dipolar couplings of 2.7 Hz, while that for the 16 spectra in 1132 (112 couplings) is 6.2 Hz; this excellent fit with nine adjustable parameters suggests that the assumption of equal temperature dependencies of the order parameters for ethane, propane, and each conformer of butane is correct. Also the fit parameters (E(tg) and the methyl angle increase) obtained for 1132 and 5CB agree. The results indicate that the chord model, which was designed to treat hydrocarbon chains, is indeed the model of choice for these chains. The temperature variation of E(tg) provides a challenge for theoreticians. Finally, even better fits to the experimental dipolar couplings are obtained when the energy in the Boltzmann factor is used for scaling ethane to butane results. However, in this case the values obtained for E(tg) differ between 1132 and 5CB.     

Molecular dynamics study of polarizability anisotropy relaxation in aromatic liquids and its connection with local structure

The collective polarizability anisotropy dynamics in a set of three aromatic liquids, benzene (Bz), hexafluorobenzene (HFB), and 1,3,5-trifluorobenzene (TFB), has been studied by molecular dynamics simulation. These liquids have very similar shapes, but different electrostatic interactions due to opposite polarities of C-H and C-F bonds, giving rise to different local intermolecular structures in the liquid phase. We have investigated how these structural arrangements affect polarizability anisotropy dynamics observed in optical Kerr-effect (OKE) spectroscopy. We have modeled the interaction-induced polarizability with the first-order dipole-induced dipole approximation, with the molecular polarizability distributed over the carbon sites. Local contributions to the librational OKE spectrum were computed separately for molecules participating in parallel or perpendicular relative orientations within the first coordination shell. We found that the relative locations of parallel and perpendicular librational bands of the OKE spectra are closely related to the corresponding pair energy distributions of the closest four neighbors of a given molecule, corresponding to a model of a harmonic oscillator in a cage of nearest neighbors. This model predicts higher librational frequencies for more attractive intermolecular interactions, which in all three liquids correspond to parallel local arrangements. On the diffusive orientational time scale, all three liquids exhibit slower relaxation of molecules in parallel arrangements, although the difference in relaxation rates is substantial only in TFB, which has the strongest tendency toward parallel stacking. The analysis of the collective polarizability relaxation was performed using two different approaches, the projection scheme (J. Chem. Phys. 1980, 72, 2801) and the theory developed by Steele (Mol. Phys. 1987, 61, 1031) for the second time derivatives applied to collective time correlations. Both approaches allow the decomposition of the OKE response into contributions from orientational relaxation and other dynamical processes. We find that they lead to different predictions on how the response depends on collective reorientation and processes arising from fluctuations in the interaction-induced polarizability. We discuss the reasons for these differences and the advantages and disadvantages of the two analysis schemes.     

Critical cavities and the kinetic spinodal for superheated liquids

We present density-functional theory (DFT) calculations for critical cavities inside model superheated liquids with varying intermolecular potentials. Our calculations show that the radius of the critical cavity and the ratio of the work of formation of the critical cavity to the work of formation of the critical bubble as predicted by the classical nucleation theory exhibit universal scaling across similar intermolecular potentials. We then utilize this observed scaling behavior by proposing two new criteria for the kinetic spinodal of superheated liquids. These criteria are based on various properties of the critical cavity as obtained from our DFT studies of the superheated Lenanrd-Jones liquid. Our predictions of the kinetic spinodal compare favorably with experimental data of the limits of superheating for various organic liquids.     

Site-site memory equation approach in study of density/pressure dependence of translational diffusion coefficient and rotational relaxation time of polar molecular solutions: acetonitrile in water, methanol in water, and methanol in acetonitrile

We present results of the theoretical study and numerical calculation of the dynamics of molecular liquids based on the combination of the memory equation formalism and the reference interaction site model (RISM). Memory equations for the site-site intermediate scattering functions are studied in the mode-coupling approximation for the first-order memory kernels, while equilibrium properties such as site-site static structure factors are deduced from RISM. The results include the temperature-density (pressure) dependence of translational diffusion coefficients D and orientational relaxation times tau for acetonitrile in water, methanol in water, and methanol in acetonitrile--all in the limit of infinite dilution. Calculations are performed over the range of temperatures and densities employing the extended simple point charge model for water and optimized site-site potentials for acetonitrile and methanol. The theory is able to reproduce qualitatively all main features of temperature and density dependences of D and tau observed in real and computer experiments. In particular, anomalous behavior, i.e, the increase in mobility with density, is observed for D and tau of methanol in water, while acetonitrile in water and methanol in acetonitrile do not show deviations from the ordinary behavior. The variety exhibited by the different solute-solvent systems in the density dependence of the mobility is interpreted in terms of the two competing origins of friction, which interplay with each other as density increases: the collisional and dielectric frictions which, respectively, increase and decrease with increasing density.     

Intermolecular vibrations and diffusive orientational dynamics of Cs condensed ring aromatic molecular liquids

The ultrafast dynamics, including the intermolecular vibrations and the diffusive orientational dynamics, of the neat C(s) symmetry condensed ring aromatic molecular liquids benzofuran, 1-fluoronaphtalene, and quinoline were investigated for the first time by means of femtosecond Raman-induced Kerr effect spectroscopy. To understand the features of these C(s) condensed ring aromatic molecular liquids, reference singular aromatic molecular liquids, furan, fluorobenzene, pyridine, and benzene, were also studied. High quality low-frequency Kerr spectra of the aromatic molecular liquids were obtained by Fourier-transform deconvolution analysis of the measured Kerr transients. The Kerr spectra of the C(s) condensed ring aromatic molecular liquids are bimodal, as are those of the reference singular aromatic molecular liquids. The first moment of the intermolecular vibrational spectrum and the peak frequencies of the high- and low-frequency components in the broad spectrum band were compared with their molecular properties such as the rotational constants, molecular weight, and intermolecular (bimolecular) force. The comparisons show that the molecular volume (related to molecular weight and rotational constants) is a dominant property for the characteristic frequency of the entire intermolecular vibrational spectrum. The observed intramolecular vibrational modes in the Kerr spectra of the aromatic molecular liquids were also assigned on the basis of the ab initio quantum chemical calculation results. In their picosecond diffusive orientational dynamics, the slowest relaxation time constant for both the condensed ring and singular aromatic molecular liquids can be accounted for by the simple Stokes-Einstein-Debye hydrodynamic model.     

Thermodynamic scaling of the viscosity of van der Waals, H-bonded, and ionic liquids

Viscosities eta and their temperature T and volume V dependences are reported for seven molecular liquids and polymers. In combination with literature viscosity data for five other liquids, we show that the superpositioning of relaxation times for various glass-forming materials when expressed as a function of TV(gamma), where the exponent gamma is a material constant, can be extended to the viscosity. The latter is usually measured to higher temperatures than the corresponding relaxation times, demonstrating the validity of the thermodynamic scaling throughout the supercooled and higher T regimes. The value of gamma for a given liquid principally reflects the magnitude of the intermolecular forces (e.g., steepness of the repulsive potential); thus, we find decreasing gamma in going from van der Waals fluids to ionic liquids. For some strongly H-bonded materials, such as low molecular weight polypropylene glycol and water, the superpositioning fails, due to the nontrivial change of chemical structure (degree of H bonding) with thermodynamic conditions.     

Selectivity of stationary phases based on pyridinium ionic liquids for capillary gas chromatography

A number of capillary columns with stationary liquid phases based on mono- and dication pyridinium ionic liquids (ILs) were prepared. Their polarity was evaluated using McReynolds system and the selectivity was estimated from intermolecular interactions. The parameters of intermolecular interactions were obtained from retention data using the (Abraham) model of the linear free energy relationship. The dependences of intermolecular interactions on the structure of the cation in the ILs under study were revealed. The results were compared with the data for the traditional phases (HP-5, ZB-WAX). Examples of separation of mixtures of oxygen-containing compounds on the phases under study are given.     

Temperature- and solvation-dependent dynamics of liquid sulfur dioxide studied through the ultrafast optical Kerr effect

The ultrafast dynamics of liquid sulphur dioxide have been studied over a wide temperature range and in solution. The optically heterodyne-detected and spatially masked optical Kerr effect (OKE) has been used to record the anisotropic and isotropic third-order responses, respectively. Analysis of the anisotropic response reveals two components, an ultrafast nonexponential relaxation and a slower exponential relaxation. The slower component is well described by the Stokes-Einstein-Debye equation for diffusive orientational relaxation. The simple form of the temperature dependence and the agreement between collective (OKE) and single molecule (e.g., NMR) measurements of the orientational relaxation time suggests that orientational pair correlation is not significant in this liquid. The relative contributions of intermolecular interaction-induced and single-molecule orientational dynamics to the ultrafast part of the spectral density are discussed. Single-molecule librational-orientational dynamics appear to dominate the ultrafast OKE response of liquid SO2. The temperature-dependent OKE data are transformed to the frequency domain to yield the Raman spectral density for the low-frequency intermolecular modes. These are bimodal with the lowest-frequency component arising from diffusive orientational relaxation and a higher-frequency component connected with the ultrafast time-domain response. This component is characterized by a shift to higher frequency at lower temperature. This result is analyzed in terms of a harmonic librational oscillator model, which describes the data accurately. The observed spectral shifts with temperature are ascribed to increasing intermolecular interactions with increasing liquid density. Overall, the dynamics of liquid SO2 are found to be well described in terms of molecular orientational relaxation which is controlled over every relevant time range by intermolecular interactions.