A study of molecular vibrational relaxation mechanism in condensed phase based upon mixed quantum-classical molecular dynamics. II. Noncollisional mechanism for the relaxation of a polar solute in supercritical water

Mixed quantum-classical molecular dynamics method has been applied to vibrational relaxation of a hydrophilic model NO in supercritical water at various densities along an isotherm above the critical temperature. The relaxation rate was determined based on Fermi's golden rule at each state point and showed an inverse S-shaped curve as a function of bulk density. The hydration number was also calculated as a function of bulk density based on the calculated radial distribution function, which showed a good correlation with the relaxation rate. Change of the survival probability of the solute vibrational state was analyzed as a function of time together with the trajectory of the solvent water and the interaction with it. We will show that the solvent molecule resides near the solute molecule for a while and the solvent contributes to the relaxation by the random-noiselike Coulombic interaction only when it stays near the solute. After the solvent leaves the solute, it shows no contribution to the relaxation. The relaxation mechanism for this system is significantly different from the collisional one found for a nonpolar solute in nonpolar solvent in Paper I. Then, the relaxation rate is determined, on average, by the hydration number or local density of the solvent. Thus, the density dependence of the relaxation rate for the polar solute in supercritical water is apparently similar to that found for the nonpolar solute in nonpolar solvent, although the molecular process is quite different from each other.     

Vibrational relaxation of OH and CH fundamentals of polar and nonpolar molecules in the condensed phase

Studies of vibrational energy flow in various polar and nonpolar molecules that follows the ultrafast excitation of the CH and OH stretch fundamentals, modeled using semiclassical methods, are reviewed. Relaxation rates are calculated using Landau-Teller theory and a time-dependent method, both of which consider a quantum mechanical solute molecule coupled to a classical bath of solvent molecules. A wide range of decay rates are observed, ranging from 1 ps for neat methanol to 50 ps for neat bromoform. In order to understand the flow rates, it is argued that an understanding of the subtle mixing between the solute eigenstates is needed and that solute anharmonicities are critical to facilitating condensed phase vibrational relaxation. The solvent-assisted shifts of the solute vibrational energy levels are seen to play a critical role of enhancing or decreasing lifetimes.     

Vibrational relaxation of azide ions in liquid-to-supercritical water

The dynamics of vibrational energy relaxation (VER) of the aqueous azide anion was studied over a wide temperature (300 K ≤ T ≤ 663 K) and density (0.6 g cm(-3) ≤ ρ ≤ 1.0 g cm(-3)) range thereby covering the liquid and the supercritical phase of the water solvent. Femtosecond mid-infrared spectroscopy on the ν(3) band associated with the asymmetric stretching vibration of the azide anion was used to monitor the relaxation dynamics in a time-resolved fashion. The variation of the vibrational relaxation rate constant with temperature and density was found to be rather small. Surprisingly, the simple isolated binary collision model is able to fully reproduce the experimentally observed temperature and density dependence of the relaxation rate provided a local density correction around the vibrationally excited solute based on classical molecular dynamics simulations is used. The simulations further suggest that head-on collisions of the solvent with the terminal nitrogen atoms rather than side-on collisions with the central nitrogen atom of the azide govern the vibrational energy relaxation of this system. Finally, the importance of hydrogen bonding for the VER dynamics in this system is briefly discussed.     

A novel approach to solvation time scale in nonpolar solvents via instability of solvent density modes

We perform linear stability analysis of solvent density modes in the presence of nonpolar solute-solvent interaction in a nonpolar solvent. The dominant instability given by the maximum positive eigenvalue of the stability matrix provides the time scale of the solvent rearrangement around a solute. Our theory predicts two long time scales for both in normal nonpolar and supercritical fluids. We discuss the existing experimental results on nonpolar solvation dynamics in light of our prediction.     

Solute dependence of mobility of solvent molecules in solvophobic solute solutions: Dielectric relaxation of nonpolar solute/alcohol mixtures

The dielectric relaxation spectra of alcohol/nonpolar solute mixtures are measured at several temperatures (-15 degrees C < or = T < or = 25 degrees C) and for several molar fractions of solute (0 < or = X(s) < or = 0.114) in the frequency range of 200 MHz < or = nu < or = 20 GHz. The double-Debye-type function is used for fitting of the spectra of mixtures, and the mean dielectric relaxation times (tau(mean)) of alcohol molecules are determined. In the systems having strong interaction between alcohol and nonpolar solutes, tau(mean) becomes shorter with an increase in the concentration of the solutes. On the other hand, tau(mean) becomes longer in the system having weak interaction between alcohol and nonpolar solutes. These results contradict with our intuitive predictions, do not correspond to mixing enthalpy, and are not explained by the hydrodynamic theory. They are attributed to the mechanism of the coupling between long-range electrostatic interactions and concentration fluctuation caused by the addition of solutes, which is suggested by Yamaguchi et al. based on the mode-coupling theory (Yamaguchi, T.; Matsuoka, T.; Koda, S. J. Chem. Phys. 2004, 120, 7590).     

Extended rotational diffusion and orientational relaxation of symmetric top molecules in a strong dc electric field: second-rank orientational correlation functions

Second-rank orientational correlation functions (pertaining to Kerr effect relaxation and Raman scattering) are obtained using the extended rotational diffusion (J-diffusion) model of symmetric top polar molecules in a strong constant external field. It is shown that the shape of the molecule noticeably affects all second-rank correlation functions and relaxation times in the rare collision limit. In the opposite limit of frequent collisions, the quantities of interest are shown to be shape independent as a consequence of vanishingly small inertial effects. An interpolation formula for the orientation relaxation times in the intermediate regime between the rare and frequent collision limits is also given.     

Theoretical studies of solute vibrational energy relaxation at liquid interfaces

Recent advances in the theoretical understanding of solute vibrational energy relaxation at liquid interfaces and surfaces are described. Non-equilibrium molecular dynamics simulations of the relaxation of an initially excited solute molecule are combined with equilibrium force autocorrelation calculations to gain insight into the factors that influence the vibrational relaxation rate. Diatomic and triatomic nonpolar, polar, and ionic solute molecules adsorbed at the liquid/vapor interface of several liquids as well as at the water/CCl(4) liquid/liquid interface are considered. In general, the vibrational relaxation rate is significantly slower (a factor of 3 to 4) at the liquid/vapor and liquid/liquid interface than in the bulk due to the reduced density, which gives rise to a reduced contribution of the repulsive solvent-solute forces on the vibrational mode. The surface effects on the ionic solutes are much smaller (50% or less slower relaxation relative to the bulk). This is due to the fact that ionic solutes at the interface are able to keep part of their solvation shell to a degree that depends on their size. Thus, a significant portion of the repulsive forces is maintained. A high degree of correlation is found between the peak height of the solvent-solute radial distribution function and the vibrational relaxation rate. The relaxation rate at the liquid/liquid interface strongly depends on the location of the solute across the interface and correlates with the change in the density and polarity profile of the interface.     

Dispersion corrected interaction of polar and nonpolar fluids confined within carbon nanotubes: Density functional theoretical analysis using Grimme's D3 scheme

The structural and flow characteristics of fluids within carbon nanotube (CNT) is dictated by the interaction of fluid molecules within the nanocavity of CNT. Therefore, in the present study, dispersion corrected density functional theory has been used to investigate the structure and interaction of polar and nonpolar molecules within CNT. The present study shows that there is profound effect on the interaction due to dispersion. The interaction energy of the confined water was found to be reduced with increasing distance of the water molecule from the wall of the CNT. The water is preferentially adsorbed over methane due to stronger interaction with CNT over methane. Further, water is preferentially adsorbed over methanol molecule when interaction is calculated without dispersion but after inclusion of dispersion interaction, the calculated results show that the methanol–CNT interaction is stronger than that of water molecule and hence preferentially adsorbed within the CNT as revealed from MD simulation. The present calculation reveals that that the effect of CNT confinement on the IR spectra of the single file water is quite considerable compared to the IR spectra of tetrahedral bulk water cluster. Therefore, the present results might be useful for the separation of polar molecule from nonpolar molecule during fabrication of CNT‐based filter and purification system.     

On the choice of a reference state for one‐step perturbation calculations between polar and nonpolar molecules in a polar environment

One‐step perturbation is an efficient method to estimate free energy differences in molecular dynamics (MD) simulations, but its accuracy depends critically on the choice of an appropriate, possibly unphysical, reference state that optimizes the sampling of the physical end states. In particular, the perturbation from a polar moiety to a nonpolar one and vice versa in a polar environment such as water poses a challenge which is of importance when estimating free energy differences that involve entropy changes and the hydrophobic effect. In this work, we systematically study the performance of the one‐step perturbation method in the calculation of the free enthalpy difference between a polar water solute and a nonpolar “water” solute molecule solvated in a box of 999 polar water molecules. Both these polar and nonpolar physical reference states fail to predict the free enthalpy difference as obtained by thermodynamic integration, but the result is worse using the nonpolar physical reference state, because both a properly sized cavity and a favorable orientation of the polar solute in a polar environment are rarely, if ever, sampled in a simulation of the nonpolar solute in such an environment. Use of nonphysical soft‐core reference states helps to sample properly sized cavities, and post‐MD simulation rotational and translational sampling of the solute to be perturbed leads to much improved free enthalpy estimates from one‐step perturbation. © 2012 Wiley Periodicals, Inc.     

Transient molecular dynamics simulations of liquid viscosity for nonpolar and polar fluids

A transient molecular dynamics (TMD) method for obtaining fluid viscosity is extended to multisite, force-field models of both nonpolar and polar liquids. The method overlays a sinusoidal velocity profile over the peculiar particle velocities and then records the transient decay of the velocity profile. The viscosity is obtained by regression of the solution of the momentum equation with an appropriate constitutive equation and initial and boundary conditions corresponding to those used in the simulation. The transient velocity decays observed appeared to include both relaxation and retardation effects. The Jeffreys viscoelastic model was found to model accurately the transient responses obtained for multisite models for n-butane, isobutane, n-hexane, water, methanol, and 1-hexanol. TMD viscosities obtained for saturated liquids over a wide range of densities agreed well for the polar fluids, both with nonequilibrium molecular dynamics (NEMD) results using the same force-field models and with correlations based on experimental data. Viscosities obtained for the nonpolar fluids agreed well with the experimental and NEMD results at low to moderate densities, but underpredicted experimental values at higher densities where shear-thinning effects and viscous heating may impact the TMD simulations.     

Dielectric relaxation in coexisting nematic and smectic B phases

Mixtures of a polar solute 4-n-pentyl-4'-cyanobiphenyl in a non-polar nematic solvent exhibit two separated low frequency dielectric relaxations for concentrations of the solute between 2 mol% and 20 mol% over a limited temperature range. This behaviour is attributed to coexisting nematic and smectic B phases, in which the polar solute probe has different relaxation frequencies. The observed dielectric spectra can be accurately fitted to two Debye-like relaxations, and the strengths of the absorptions are proportional to the amounts of the coexisting phases. A microscopic determination of the phase diagram confirms the assignment of the coexisting phases, and it is concluded that there is a preference of the dipolar probe molecule for the smectic B phase, which is induced as a result of solute-solvent interactions.     

Simple models for nonpolar solvation: Parameterization and testing

Implicit solvent models are important for many biomolecular simulations. The polarity of aqueous solvent is essential and qualitatively captured by continuum electrostatics methods like Generalized Born (GB). However, GB does not account for the solvent‐induced interactions between exposed hydrophobic sidechains or solute‐solvent dispersion interactions. These “nonpolar” effects are often modeled through surface area (SA) energy terms, which lack realism, create mathematical singularities, and have a many‐body character. We have explored an alternate, Lazaridis–Karplus (LK) gaussian energy density for nonpolar effects and a dispersion (DI) energy term proposed earlier, associated with GB electrostatics. We parameterized several combinations of GB, SA, LK, and DI energy terms, to reproduce 62 small molecule solvation free energies, 387 protein stability changes due to point mutations, and the structures of 8 protein loops. With optimized parameters, the models all gave similar results, with GBLK and GBDILK giving no performance loss compared to GBSA, and mean errors of 1.7 kcal/mol for the stability changes and 2 Å deviations for the loop conformations. The optimized GBLK model gave poor results in MD of the Trpcage mini‐protein, but parameters optimized specifically for MD performed well for Trpcage and three other small proteins. Overall, the LK and DI nonpolar terms are valid alternatives to SA treatments for a range of applications. © 2017 Wiley Periodicals, Inc.     

Molecular dynamics study on the solvent dependent heme cooling following ligand photolysis in carbonmonoxy myoglobin

The time scale and mechanism of vibrational energy relaxation of the heme moiety in myoglobin was studied using molecular dynamics simulation. Five different solvent models, including normal water, heavy water, normal glycerol, deuterated glycerol and a nonpolar solvent, and two forms of the heme, one native and one lacking acidic side chains, were studied. Structural alteration of the protein was observed in native myoglobin glycerol solution and native myoglobin water solution. The single-exponential decay of the excess kinetic energy of the heme following ligand photolysis was observed in all systems studied. The relaxation rate depends on the solvent used. However, this dependence cannot be explained using bulk transport properties of the solvent including macroscopic thermal diffusion. The rate and mechanism of heme cooling depends upon the detailed microscopic interaction between the heme and solvent. Three intermolecular energy transfer mechanisms were considered: (i) energy transfer mediated by hydrogen bonds, (ii) direct vibration-vibration energy transfer via resonant interaction, and (iii) energy transfer via vibration-translation or vibration-rotation interaction, or in other words, thermal collision. The hydrogen bond interaction and vibration-vibration interaction between the heme and solvent molecules dominates the energy transfer in native myoglobin aqueous solution and native myoglobin glycerol solutions. For modified myoglobin, the vibration-vibration interaction is also effective in glycerol solution, different from aqueous solution. Thermal collisions form the dominant energy transfer pathway for modified myoglobin in water solution, and for both native myoglobin and modified myoglobin in a nonpolar environment. For native myoglobin in a nonpolar solvent solution, hydrogen bonds between heme isopropionate side chains and nearby protein residues, absent in the modified myoglobin nonpolar solvent solution, are key interactions influencing the relaxation pathways.     

Skeletal relaxation effect on the charge transfer state formation of 4-dimethylamino,4'-cyanostilbene

Ab initio complete active space self-consistent field (CASSCF) calculations combined with polarized continuum model (PCM) have been performed to examine the charge transfer (CT) state formation of trans-4-dimethylamino,4'-cyanostilbene (DCS) in a solvent. In a polar solvent, the globally stable geometry in S1 takes a twisted conformation where the electron-donating dimethylanilino group is highly twisted against the other part of the electron-withdrawing 4-cyanostyryl group. In addition, skeletal relaxation where the aromatic benzene rings turn to be a nonaromatic quinoid structure is essential to stabilize the CT state. In a nonpolar solvent, the stable geometry in S1 takes a nontwisted conformation, though the skeletal relaxation is also an essential factor. By means of the free energy decomposition analysis, it is found that the stable CT geometry which depends on solvent polarity mainly comes from two factors: the linkage bond between the dimethylanilino and the 4-cyanostyryl group and the electrostatic interaction. In a polar solvent, the linkage bond has a single bond character to slightly prevent the torsional motion. This twist geometrically assists the charge separation so as to reinforce the electrostatic interaction. In consequence, the twisted internal CT (TICT) conformation is stable. In a nonpolar solvent, on the other hand, a nontwisted CT state is stable because the linkage bonds greatly increase a double bond character so as to prevent the torsional motion, while the electrostatic interaction is not so enhanced even by the geometrical twist.     

Particle charging and charge screening in nonpolar dispersions with nonionic surfactants

The electrostatic stabilization of colloidal dispersions is usually considered the domain of polar media only because of the high energetic cost associated with introducing electric charge in nonpolar environments. Nevertheless, some surfactants referred to as "charge control agents" are known to raise the conductivity of liquids with low electric permittivity and to mediate charge stabilization of nonpolar dispersions. Here we study an example of the particularly counterintuitive charging and electrostatic interaction of colloidal particles in a nonpolar solvent caused by nonionic surfactants. PMMA particles in hexane solutions of nonionic sorbitan oleate (Span) surfactants are found to exhibit a field-dependent electrophoretic mobility. Extrapolation to zero field strength yields evidence for large electrostatic surface potentials that decay with increasing surfactant concentration in a fashion reminiscent of electrostatic screening caused by salt in aqueous solutions. The amount of surface charge and screening ions in the nonpolar bulk is further characterized via measurements of the particles' pair interaction energy. The latter is obtained by liquid structure analysis of quasi-2-dimensional equilibrium particle configurations studied with digital video microscopy. In contrast to the behavior reported for systems with ionic surfactants, we observe particle charging and a screened Coulomb type interaction both above and below the surfactant's critical micelle concentration.     

Solvatochromic and thermochromic shifts of electronic spectra of polar solute molecules in a mixture of polar and nonpolar solvent; the role of solvent-solvent interactions

A theoretical model is proposed to describe the influence of the concentration of a polar solvent and the temperature of a solution on the electronic spectra of a polar solute in a binary solvent mixture. It is shown that the interaction between molecules of the polar solvent in the first solvation shell makes the significant contribution to the formation of absorption and fluorescence bands of the solute. An experimental study of solvatochromic and thermochromic shifts of steady-state fluorescence spectra of 3-amino-N-methylphthalimide in decalin--propanol mixture for different values of propanol mole fraction is carried out. Good qualitative agreement between the experimental data and calculation results is observed.     

Vibrational relaxation in hydrogen bonded systems: I. Theory

A theory is proposed which expresses the influence of intermolecular interaction in H-bonded solutions on the solute IR band shape in terms of parameters characterising the modulation and strength of this interaction. It is found that appreciable vibrational relaxation can occur by interaction between oscillators with different frequencies, provided that the energy gap is closed by the hydrogen bond spectral density. Isotopic substitution of the solvent provides a means for experimental verification, which is the subject of a subsequent paper.     

Evidences of nonideal mixing in poly(ethylene glycol)/organic solvent mixtures by Brillouin scattering

The concentration dependence of the hypersonic properties of solutions of poly(ethylene glycol) of mean molecular mass 600 g/mol (PEG600) in benzene and toluene has been investigated by Brillouin scattering. The two solvents are very similar in structure and chemical properties, but while benzene is nonpolar, toluene possess a modest dipole. In both solvents a high-frequency relaxation process has been observed at high concentrations which has been assigned to conformational rearrangements of the polymeric chains, triggered by reorientation of the side groups. In both cases, the concentration dependence of the adiabatic compressibility deviates significantly from linearity, indicating the existence of nonideal mixing phenomena driven by aggregation processes taking place in the systems. However, there is no temperature dependence for solutions of PEG600 in benzene; on the contrary, the results obtained for solutions of PEG600 in toluene are noticeably dependent on the temperature. The comparison of the experimental data with the results of previous experiments on similar systems allows a general picture for weakly interacting mixtures of hydrogen-bonded systems and organic solvents to be developed. In particular, in the presence of a nonpolar solvent molecule the local structure of the mixture is dominated by solute self-association processes and any resulting solute-solvent correlation is barely induced by excluded volume effects. At high enough dilution the self-aggregation of solute molecules produces a variety of new local topologies that cannot be observed in bulk solute, and as a consequence, the concentration evolution of the system is too rich to be described in terms of a linear combination of a few components over the whole concentration range. The situation seems to be simpler for the polar toluene solvent molecules, where a three-component model seems able to fit the experimental concentration dependence of the hypersonic velocity. This result is interpreted to imply that the interaction between the solvent dipoles and the active sites of the solute produces a relatively stable heterocoordination, while the relevance of self-association is partially reduced.