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.     

Molecular dynamics simulations for CO2 spectra. III. Permanent and collision-induced tensors contributions to light absorption and scattering

Classical molecular dynamics simulations have been performed for gaseous CO(2) starting from an accurate anisotropic intermolecular potential. Through calculations of the evolutions of the positions and orientations of a large number of molecules, the time evolutions of the permanent and collision-induced electric dipole vector and polarizability tensor are obtained. These are computed from knowledge of static molecular parameters taking only the leading induction terms into account. The Laplace transforms of the auto-correlation functions of these tensors then directly yield the light absorption and scattering spectra. These predictions are, to our knowledge, the first in which the contributions of permanent and collision-induced tensors are simultaneously taken into account for gaseous CO(2), without any adjusted parameter. Comparisons between computations and measurements are made for absorption in the region of the ν(3) infrared band and for depolarized Rayleigh scattering in the roto-translational band. They demonstrate the quality of the model over spectral ranges from the band center to the far wings where the spectrum varies by several orders of magnitude. The contributions of the permanent and interaction-induced (dipole and polarizability) tensors are analyzed for the first time, through the purely permanent (allowed), purely induced, and cross permanent∕induced components of the spectra. It is shown that, while the purely induced contribution is negligible when compared to the collision-broadened allowed component, the cross term due to interferences between permanent and induced tensors significantly participates to the wings of the bands. This successfully clarifies the long lasting, confusing situation for the mechanisms governing the wings of the CO(2) spectra considered in this work.     

Preface

The anisotropic rototranslational scattering spectra of nitrogen gas at high frequency up to 700 cm⁻¹ for several temperatures and from low densities are analyzed in terms of new site–site (M3SV) intermolecular potential and interaction-induced pair polarizability models, using quantum spectral shapes computations. Our theoretical calculations take into account multipole contributions from the mean value and anisotropy of the dipole–dipole polarizability tensor α, two independent components of the dipole–octopole polarizability tensor E and dipole–dipole–quadrupole hyperpolarizability tensor B. The high-frequency wings are discussed in terms of the collision-induced rotational Rayleigh effect and estimates for the dipole–octopole polarizability |E₄| are obtained and checked with recent ab initio theoretical value. Good comparison is found in the frequency range 0–400 cm⁻¹ between the theoretical and experimental spectra. When an exponential contribution [exp(−ν/ν₀)] with ν₀ = 425 cm⁻¹ is considered to model very short-range light scattering mechanisms at room temperature, good agreement is found over the whole frequency range.     

Electronic polarization effect on low-frequency infrared and Raman spectra of aprotic solvent: molecular dynamics simulation study with charge response kernel by second order Møller-Plesset perturbation method

Low-frequency infrared (IR) and depolarized Raman scattering (DRS) spectra of acetonitrile, methylene chloride, and acetone liquids are simulated via molecular dynamics calculations with the charge response kernel (CRK) model obtained at the second order M?ller-Plesset perturbation (MP2) level. For this purpose, the analytical second derivative technique for the MP2 energy is employed to evaluate the CRK matrices. The calculated IR spectra reasonably agree with the experiments. In particular, the agreement is excellent for acetone because the present CRK model well reproduces the experimental polarizability in the gas phase. The importance of interaction induced dipole moments in characterizing the spectral shapes is stressed. The DRS spectrum of acetone is mainly discussed because the experimental spectrum is available only for this molecule. The calculated spectrum is close to the experiment. The comparison of the present results with those by the multiple random telegraph model is also made. By decomposing the polarizability anisotropy time correlation function to the contributions from the permanent, induced polarizability and their cross term, a discrepancy from the previous calculations is observed in the sign of permanent-induce cross term contribution. The origin of this discrepancy is discussed by analyzing the correlation functions for acetonitrile.     

Two-dimensional measurements of the solvent structural relaxation dynamics in dipolar solvation

Resonant-pump polarizability response spectroscopy (RP-PORS) is based on an optical heterodyne detected transient grating (OHD-TG) method with an additional resonant pump pulse. In RP-PORS, the resonant pump pulse excites the solute-solvent system and the subsequent relaxation of the solute-solvent system is monitored by the OHD-TG spectroscopy. RP-PORS is shown to be an excellent experimental tool to directly measure the solvent responses in solvation. In the present work, we extended our previous RP-PORS (Park et al., Phys. Chem. Chem. Phys., 2011, 13, 214-223) to measure time-dependent transient solvation polarizability (TSP) spectra with Coumarin153 (C153) in acetonitrile. The time-dependent TSP spectra showed how the different solvent intermolecular modes were involved in different stages of the solvation process. Most importantly, the inertial and diffusive components of the solvent intermolecular modes in solvation were found to be spectrally and temporally well-separated. In a dipolar solvation of C153, high-frequency inertial solvent modes were found to be driven instantaneously and decay on a subpicosecond timescale while low-frequency diffusive solvent modes were induced slowly and decayed on a picosecond timescale. Our present result is the first experimental manifestation of frequency-dependent solvent intermolecular response in a dipolar solvation.     

Solvent structural relaxation dynamics in dipolar solvation studied by resonant pump polarizability response spectroscopy

Resonant pump polarizability response spectroscopy (RP-PORS) was used to study the isotropic and anisotropic solvent structural relaxation in solvation. RP-PORS is the optical heterodyne detected transient grating (OHD-TG) spectroscopy with an additional resonant pump pulse. A resonant pump excites the solute-solvent system and the subsequent relaxation of the solute-solvent system is monitored by the OHD-TG spectroscopy. This experimental method allows measuring the dispersive and absorptive parts of the signal as well as fully controlling the beam polarizations of incident pulses and signal. The experimental details of RP-PORS were described. By performing RP-PORS with Coumarin 153(C153) in CH(3)CN and CHCl(3), we have successfully measured the isotropic and anisotropic solvation polarizability spectra following electronic excitation of C153. The isotropic solvation polarizability responses result from the isotropic solvent structural relaxation of the solvent around the solute whereas the anisotropic solvation polarizability responses come from the anisotropic translational relaxation and orientational relaxation. The solvation polarizability responses were found to be solvent-specific. The intramolecular vibrations of CHCl(3) were also found to be coupled to the electronic excitation of C153.     

The influence of molecular shape and charge distribution on the molecular approach in solution. NMR dipolar relaxation studies of the many-body effects

The paramagnetic dipolar spin-lattice relaxation of nuclear spins is expressed in terms of the geometrical and dynamical parameters of the molecules and used to analyze the intra- and intermolecular microdynamics. The possible conformational changes of a TEMPOL nitroxide-labelled sugar in deuterated chloroform are studied and then the intermolecular processes are considered. The influence of the discrete polar natures of acetonitrile, chloroform, and methanol on the TEMPOL solvation dynamics is recognized. The importance of the water structure on the collisional approach of two attractive ions is emphasized. Finally, the attractive effects of the dipole-dipole electrostatic forces are shown for the water/TEMPOL pair. Diffusion and jump analytical theories, integral equations of statistical mechanics, and Monte-Carlo simulations of the diffusion are combined to treat the anisotropic interactions and the many-body effects.     

Effects of molecular association on polarizability relaxation in liquid mixtures of benzene and hexafluorobenzene

In this work we have studied the relaxation dynamics of the many-body polarizability anisotropy in liquid mixtures of benzene (Bz) and hexafluorobenzene (Hf) at room temperature by femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) experiments and molecular dynamics (MD) simulations. The computed polarizability response arising from intermolecular interactions was included using the first-order dipole-induced-dipole model with the molecular polarizability distributed over the carbon sites of each molecule. We found good qualitative agreement between experiments and simulations in the features exhibited by the nuclear response function R(t) for pure liquids and mixtures. The long-time diffusive decay of R(t) was observed to vary substantially with composition, slowing down noticeably with dilution of each of the species as compared with that in the corresponding pure liquids. MD simulation shows that the effect on R(t) is due to the formation of strong and localized intermolecular association between Bz and Hf species that hinder the rotational diffusive dynamics. The formation of these Bz-Hf complexes in the liquid mixtures also modifies the rotational diffusive dynamics of the component species in such a way that cannot be explained solely in terms of a viscosity effect. Even though the computed orientational diffusive relaxation times associated with Bz and Hf are larger by a factor of approximately 2 than those from experiments, we found similar trends in experiments and simulations for these characteristic times as a function of composition. Namely, the collective and single-molecule orientational correlation times associated with Bz are observed to grow monotonically with the dilution of Bz, while those corresponding to Hf species exhibit a maximum at the equimolar composition. We attribute the quantitative discrepancy between experiments and simulations to the use of the Williams potential, which seems to overestimate the intermolecular interactions and thus predicts not only a slower translational dynamics but also a slower rotational diffusion dynamics than in real fluids.     

On the relation of the non-linear dielectric effect to the kerr effect: closing a gap

A simple and uniform procedure is used to determine the non-linear dielectric effect in static fields, for probing fields with frequency either below or above the rotational relaxation region. Contributions from the permanent moment and the linear and non-linear polarizability of non-interacting particles are considered. A quantitative link with the Kerr effect is established. The different weight of contributions due to anisotropic polarizability and hyperpolarizability in both effects is emphasized.     

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.     

Formation of hydrogen-bonded complexes of 3,3′,5,5′-tetrabromo-2,2′-biphenol with MTBD and triethylamine

The complexes of 3,3′,5,5′-tetrabromo-2,2′-biphenol (TBBPh) with 7-methyl-1,5,7-triazabicyclo[4.4.0]dec-5-ene (MTBD) and triethylamine (TEA) were studied by FTIR spectroscopy. In chloroform and in acetonitrile a proton transfer from TBBPh to N-bases (MTBD, TEA) occurs. In chloroform solution the protonated N-base molecules are hydrogen-bonded to the deprotonated TBBPh molecules, whereas in acetonitrile the complexes dissociate. The intra- as well as intermolecular hydrogen bonds within the chains show large proton polarizability.     

Intermolecular polarizability dynamics of aqueous formamide liquid mixtures studied by molecular dynamics simulations

A molecular dynamics simulation study is presented for the relaxation of the polarizability anisotropy in liquid mixtures of formamide and water, using a dipolar induction scheme that involves the intrinsic polarizability and first hyperpolarizability tensors of the molecules, and the dipole-quadrupole polarizability of water species. The long time diffusive decay of the collective polarizability anisotropy correlations exhibits a substantial slowing down as the formamide mole fraction increases in the mixture. The diffusive times for the polarizability relaxation obtained from the authors' simulations are in good agreement with optical Kerr effect experimental data, and they are found to correlate nearly linearly with the estimated mean lifetimes of the hydrogen bonds within the mixture, suggesting that the relaxation of the hydrogen bond network is responsible to some extent for the collective relaxation of the polarizability anisotropy of the mixture. The short time behavior of the polarizability anisotropy relaxation was investigated by computing the nuclear response function, R(t), which is very rapidly dominated by the formamide contribution as it is added to water, due to the much larger polarizability anisotropy of formamide molecules compared to that of water. Several contributions to the Raman spectrum were also analyzed as a function of composition, and the dynamical origin of the different bands was determined.     

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.     

Molecular dynamics of liquid acetone determined by depolarized Rayleigh and low-frequency Raman scattering spectroscopy

Slow to ultrafast dynamics of liquid acetone at variable temperature was investigated by depolarized Rayleigh and low-frequency Raman scattering spectroscopy, in the region 0-200 cm(-1). A detailed analysis was performed on the spectra and corresponding time responses, and a consistent view of the molecular dynamics of this dipolar solvent was obtained. The effects of temperature on the spectra were interpreted, and distinct dynamical processes identified. At very low frequencies, or long time scales, acetone dynamics is characterized by a slow diffusive reorientation obeying the Stokes-Einstein-Debye hydrodynamic theory only in the limit of subslip boundary conditions. An alternative model based on the microviscosity concept proved to be able to reproduce this correlation time and its temperature dependence. A comparative analysis of collective and single-molecule reorientational times, these latter estimated from intramolecular Raman spectra, led to an orientational correlation parameter g(2) of unity, which denotes a statistical disorder of molecular polarizability tensors. A fast local restructuring process is putatively responsible for an additional contribution at subpicosecond time scales often referred to as intermediate response in other molecular liquids. The high frequency portion of the dynamical susceptibility showed the signature of librational intermolecular motions, giving rise to an ultrafast decay of the time correlation function of polarizability anisotropy. The overall approach, which provided valuable information on dynamics, structure and molecular interactions of neat acetone, will be applied to acetone electrolytic solutions.     

Orientational and interaction induced dynamics in the isotropic phase of a liquid crystal: polarization resolved ultrafast optical Kerr effect spectroscopy

The ultrafast dynamics of the isotropic phase of a liquid crystal 4'-pentyl-4-p-biphenylcarbonitrile (5CB) have been investigated using polarization resolved optical Kerr effect spectroscopy. Measurements were made as a function of both temperature and dilution in nonpolar solvents. To separate single molecule and interaction induced components to the relaxation of the induced birefringence, measurements of both the anisotropic and isotropic response were made. The isotropic response was found to be dominated by a damped low-frequency mode of intramolecular origin. There is a minor additional component assigned to an interaction induced contribution. There is at most an extremely weak isotropic signal beyond 1 ps, showing that the picosecond time scale dynamics of 5CB are dominated by orientational relaxation. The isotropic response is independent of temperature in the range studied (0.2-50 K above the nematic to isotropic phase-transition temperature). The anisotropic response exhibits relaxation dynamics on time scales spanning subpicosecond to several hundred picoseconds and beyond. The fastest components are dominated by a librational response, but there are smaller contributions from three low-frequency intramolecular modes, and a contribution from interaction induced effects. The low-frequency spectral density extracted from these data are independent of temperature in the range studied, 0.2-30 K above the phase-transition temperature, but shift to lower frequency on dilution in alkane solvents. In neat 5CB the picosecond time scale orientational dynamics are dominated by temperature-independent reorientation within the pseudonematic domains, while in solution these are disrupted, and the orientational response becomes faster and temperature dependent.     

Molecular dynamics simulations for CO2 spectra. II. The far infrared collision-induced absorption band

Classical molecular dynamics simulations have been carried out for gaseous CO(2) starting from various anisotropic intermolecular potential energy surfaces. Through calculations for a large number of molecules treated as rigid rotors, the time evolution of the interaction-induced electric dipole vector is obtained and the Laplace transform of its autocorrelation function gives the collision-induced absorption rototranslational spectrum. The results are successfully compared with those of previous similar calculations before studies of the influences of the intermolecular potential and induced-dipole components are made. The calculated spectra show a significant sensitivity to anisotropic forces consistently with previous analyses limited to the spectral moments. The present results also demonstrate the importance of vibrational and back-induction contributions to the induced dipole. Comparisons between measured far infrared (0-250 cm(-1)) spectra at different temperatures and results calculated without the use of any adjustable parameter are made. When the best and more complete input data are used, the quality of our predictions is similar to that obtained by Gruszka et al. [Mol. Phys. 93, 1007 (1998)] after the introduction of ad hoc short-range overlap contributions. Our results thus largely obviate the need for such contributions the magnitudes of which remain questioned. Nevertheless, problems remain since, whereas good agreements with measurements are obtained above 50 cm(-1), the calculations significantly underestimate the absorption below, a problem which is discussed in terms of various possible error sources.     

Induced contributions in the rayleigh spectra of water: A molecular dynamics simulation

A molecular dynamics simulation of TIP4P water at T=280 K has been performed to calculate the depolarized and isotropic Raman spectra in the translational and librational region. Comparison of the isotropic spectra with experiment confirms the assignment of the low-frequency scattered light to collision-induced phenomena and allows identification of the spectral contributions arising from polarizability modulation due to short-range interactions.     

Intermolecular vibrational spectra of C3v CXY3 Molecular Liquids, CHCl3, CHBr3, CFBr3, and CBrCl3

We report the quality anisotropic intermolecular vibrational spectra within the frequency range 0.5-800 cm(-1) of four C(3v) CXY(3) molecular liquids, CHCl(3), CHBr(3), CFBr(3), and CBrCl(3), by means of femtosecond optical-heterodyne-detected Raman-induced Kerr effect spectroscopy. The results show that the first moment of the intermolecular vibrational spectrum is proportional to the square root of the value of the surface tension divided by the liquid density. This implies that the intermolecular vibrational spectrum reflects the bulk properties of the liquids. To understand the molecular-level aspects of the intermolecular vibrational spectra of the liquids, the spectra are compared with the molecular properties such as molecular weight, rotational constants, and bimolecular interaction energy. Overall, the first moment of the spectrum moderately correlates to the inverse square roots of both the molecular weight and the fast rotational constant. Therefore, the molecular properties are responsible for the intermolecular vibrational spectrum. Plots of the first moment of the intermolecular vibrational spectrum vs the square root of the value of the simple bimolecular interaction energy divided by the molecular surface area and the molecular weight show a linear correlation in the case of the oblate symmetric top molecular liquids, CHCl(3), CHBr(3), and CFBr(3). However, CBrCl(3), which is a prolate symmetric top molecular liquid, does not show the same correlation for the oblate molecular liquids.     

Application of proton field-cycling NMR relaxometry for studying translational diffusion in simple liquids and polymer melts

With the availability of commercial field-cycling relaxometers together with progress of home-built instruments nuclear magnetic resonance relaxometry has gained new momentum as a method of investigating the dynamics in viscous liquids and polymer melts. The method provides the frequency dependence of the spin–lattice relaxation rate. In the case of protons, one distinguishes intramolecular and intermolecular relaxation pathways. Whereas the intramolecular contribution prevails at high frequencies and reflects rotational dynamics, the often ignored intermolecular relaxation contribution dominates at low-frequency and provides access to translational dynamics. A universal low-frequencies dispersion law holds which in pure systems allows determining the diffusion coefficient in a straightforward way. In addition, the rotational time constant is extracted from the high-frequency relaxation contribution. This is demonstrated for simple and ionic liquids and for polymer melts.