Time-dependent fluorescence in nanoconfined solvents: linear-response approximations and Gaussian statistics

The time-dependent fluorescence of a model dye molecule in a nanoconfined solvent is used to test approximations based on the dynamic and static linear-response theories and the assumption of Gaussian statistics. Specifically, the results of nonequilibrium molecular-dynamics simulations are compared to approximate expressions involving time correlation functions obtained from equilibrium simulations. Solvation dynamics of a model diatomic dye molecule dissolved in acetonitrile confined in a spherical hydrophobic cavity of radius 12, 15, and 20 A? is used as the test case. Both the time-dependent fluorescence energy, expressed as the normalized dynamic Stokes shift, and the time-dependent position of the dye molecule after excitation are examined. While the dynamic linear-response approximation fails to describe key aspects of the solvation dynamics, assuming Gaussian statistics reproduces the full nonequilibrium simulations well. The implications of these results are discussed.     

Theory of the time development of the stokes shift in polar media

We present a theory for the time evolution of the Stokes shift of a polar molecule in a polar solvent. The time-dependent solute—solvent interaction is calculated in a continuum model by replacing the surrounding solvent by a frequency-dependent dielectric continuum. An expression for the time dependence of the fluorescence maximum is derived. This expression can be considered a direct generalization of the well-known Ooshika—Lippert—Mataga equation to the time domain. We also present an approximate expression for the wavelength dependence of the dynamics of the Stokes shift, and find it to be consistent with recent experimental results. We have investigated the effect of polarizability of the solute molecule and found that for many molecules this effect is not negligible.     

分子动力学模拟纳米尺寸限制体系下氩溶液中I2的振动能量弛豫

利用平衡态分子动力学方法(EMD)模拟了纳米尺寸限制球壳内I2在Ar溶液中的振动能量转移. 计算并讨论了I2振动能量弛豫时间T1随球壳半径、溶剂密度的变化规律. 通过分子间相互作用分析, 在原子、分子水平上, 揭示了随着球壳半径的减小, T1呈逐渐增大趋势的原因. 结果表明, 球壳的几何限制效应和表面作用对受限溶液密度分布的影响较大, 从而导致溶质振动弛豫的显著变化. 此外, 非限制体系模拟显示, 非平衡态分子动力学(NEMD)方法可以得到与平衡态分子动力学方法较一致的振动能量弛豫时间T1.     

DFT and TD‐DFT investigation of IR and UV spectra of solvated molecules: Comparison of two SCRF continuum models

We report the calculation of liquid‐phase infrared (IR) and ultraviolet (UV) spectra in the framework of the solute's response to the reaction field of several solvents. In particular, we compare these two properties for the multipolar expansion model developed in the Nancy continuum model (NCM) and the polarized continuum model (PCM) scheme developed in Pise and Naples. All calculations are carried out at the (TD‐)DFT/6–311G(2d,2p) level of theory. The cavity size used for modeling the solute effects on the IR and UV spectra are examined. To calibrate the solute cavity size, we have investigated the IR spectra of coumarin and of a set of 14 additional solutes of different size and polarity in several dielectrical surroundings. It turns out that: (i) PCM and NCM present an identical behavior when a common cavity is used to calibrate the models; and (ii) for both NCM and PCM models, the IR spectra are highly sensitive to the solute and solvent polarity. The UV/VIS investigation of coumarin derivatives demonstrates that both models provide close estimates of λ_max independent of the solute cavity size. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Solvent effects in density functional calculations of uracil and cytosine tautomerism

The effects of the solvent on the tautomeric equilibria of cytosine and uracil are studied using Onsager's reaction field model in the framework of density functional theory. In this model, the solute molecule is placed in a spherical cavity of radius ao immersed in a continuous medium with a dielectric constant e, treating the solute-solvent electrostatic interactions at the dipole level. The cavity radius is evaluated by determining the molecular volume with a quantum mechanical approach. The solvent effect brings significant changes in the geometrical parameters of some cytosine tautomers, but only very small changes to those of the uracil tautomers. Our results are in good agreement with available experimental results and confirm that the polarization of the solute by the continuum has important effects on the absolute and relative solvation energies. Frequency shifts and intensity variations in the infrared spectra due to the presence of the solvent are also presented. © 1995 John Wiley & Sons, Inc.     

Excitation energy transfer (EET) between molecules in condensed matter: a novel application of the polarizable continuum model (PCM)

We present a quantum-mechanical theory to study excitation energy transfers between molecular systems in solution. The model is developed within the time-dependent (TD) density-functional theory and the solvent effects are introduced in terms of the polarizable continuum model (PCM). Unique characteristic of this model is that both "reaction field" and screening effects are included in a coherent and self-consistent way. This is obtained by introducing proper solvent-specific operators in the Kohn-Sham equations and in the corresponding TD scheme. The solvation model exploits the integral equation formalism (IEF) version of PCM and it defines the solvent operators on a molecular cavity modeled on the real three-dimensional (3D) structure of the solute systems. Applications to EET in dimers of ethylene and naphtalene are presented and discussed.     

Hydrophobic and ionic interactions in nanosized water droplets

A number of situations such as protein folding in confined spaces, lubrication in tight spaces, and chemical reactions in confined spaces require an understanding of water-mediated interactions. As an illustration of the profound effects of confinement on hydrophobic and ionic interactions, we investigate the solvation of methane and methane decorated with charges in spherically confined water droplets. Free energy profiles for a single methane molecule in droplets, ranging in diameter (D) from 1 to 4 nm, show that the droplet surfaces are strongly favorable as compared to the interior. From the temperature dependence of the free energy in D = 3 nm, we show that this effect is entropically driven. The potentials of mean force (PMFs) between two methane molecules show that the solvent separated minimum in the bulk is completely absent in confined water, independent of the droplet size since the solute particles are primarily associated with the droplet surface. The tendency of methanes with charges (M(q+) and M(q-) with q(+) = |q(-)| = 0.4e, where e is the electronic charge) to be pinned at the surface depends dramatically on the size of the water droplet. When D = 4 nm, the ions prefer the interior whereas for D < 4 nm the ions are localized at the surface, but with much less tendency than for methanes. Increasing the ion charge to e makes the surface strongly unfavorable. Reflecting the charge asymmetry of the water molecule, negative ions have a stronger preference for the surface compared to positive ions of the same charge magnitude. With increasing droplet size, the PMFs between M(q+) and M(q-) show decreasing influence of the boundary owing to the reduced tendency for surface solvation. We also show that as the solute charge density decreases the surface becomes less unfavorable. The implications of our results for the folding of proteins in confined spaces are outlined.     

Solute-solvent interaction in liquids. I. Long-range forces and vibrational solvent shifts

The model of solute— solvent interaction based on dipole-induced-dipole forces (Kirkwood-Bauer-Magat) has been generalized, yielding an expression for the energy as a function of solute position and orientalion within a spherical cavity in a dielectric medium. An analogous relation has been derived for the dispersion energy. Barriers to rotation of the solute molecule and shifts in its vibrational frequency are calculated as functions of cavity radius and eccentricity for the case of dilute solutions of HCl in CCl₄. It is found that the effect of dispersion forces on the vibrational frequency of HCl is two-to-three times more important than the traditional dipole-induced-dipole contribution.     

Correlation and solvation effects. IV. A systematic analysis of the influence of cavity size and shape on solvation properties in the polarizable continuum model with electron correlation

From the standpoint of models that use a polarizable continuum to represent the solvent in studying the phenomenon of solvation, a systematic and detailed analysis is made of the influence of the cavity size and shape on calculated energies. The solute is represented by its ab initio wavefunction, and the electronic part of the solvation energy is calculated including terms that take into account electron correlation up to third order. The analysis shows the convenience of modeling the cavity according to considerations of homogeneity, which are based fundamentally on how the solute wavefunction is constructed, i.e., the basis set used.     

Hydrophobic effects on partial molar volume

The hydrophobic effects on partial molar volume (PMV) are investigated as a PMV change in the transfer of a benzenelike nonpolar solute from the nonpolar solvent to water, using an integral equation theory of liquids. The volume change is divided into two effects. One is the "packing" effect in the transfer from the nonpolar solvent to hypothetical "nonpolar water" without hydrogen bonding networks. The other is the "iceberg" effect in the transfer from nonpolar water to water. The results indicate that the packing effect is negative and a half compensated by the positive iceberg effect. The packing effect is explained by the difference in the solvent compressibility. Further investigation shows that the sign and magnitude of the volume change depend on the solute size and the solvent compressibility. The finding gives a significant implication that the exposure of a hydrophobic residue caused by protein denaturation can either increase or decrease the PMV of protein depending on the size of the residue and the fluctuation of its surroundings.     

定标粒子理论在萃取化学中的应用——Ⅰ.惰性气体分配常数的计算

萃取过程的分配常数∧,可由Nernst分配定律导出: (1) (2)α和μ°分别为被萃取物的活度和标准态化学势,脚注s和w表示有机相和水相,△G°为萃取过程的标准吉布斯自由能。在萃取化学中,迄今尚未见到直接从理论上来推算△G°及∧的报道。本文试图引用定标粒子理论和物质标准迁移吉布斯自由能来计算萃取过程的△G°和分配常数∧。萃取过程可以看作是被萃取物M在有机相和水相中两个溶解过程之间的竞争。M溶于水相或有机相,首先必须破坏相同溶剂分子之间的结合,形成一个适合溶质分子大小的空腔来容纳M,同时又产生溶质与溶剂分子之间w-M和s-M相互作用。所以萃取过程可以表示为     

Dissipative particle dynamics simulations of polymer-protected nanoparticle self-assembly

Dissipative particle dynamics simulations were used to study the effects of mixing time, solute solubility, solute and diblock copolymer concentrations, and copolymer block length on the rapid coprecipitation of polymer-protected nanoparticles. The simulations were aimed at modeling Flash NanoPrecipitation, a process in which hydrophobic solutes and amphiphilic block copolymers are dissolved in a water-miscible organic solvent and then rapidly mixed with water to produce composite nanoparticles. A previously developed model by Spaeth et al. [J. Chem. Phys. 134, 164902 (2011)] was used. The model was parameterized to reproduce equilibrium and transport properties of the solvent, hydrophobic solute, and diblock copolymer. Anti-solvent mixing was modeled using time-dependent solvent-solute and solvent-copolymer interactions. We find that particle size increases with mixing time, due to the difference in solute and polymer solubilities. Increasing the solubility of the solute leads to larger nanoparticles for unfavorable solute-polymer interactions and to smaller nanoparticles for favorable solute-polymer interactions. A decrease in overall solute and polymer concentration produces smaller nanoparticles, because the difference in the diffusion coefficients of a single polymer and of larger clusters becomes more important to their relative rates of collisions under more dilute conditions. An increase in the solute-polymer ratio produces larger nanoparticles, since a collection of large particles has less surface area than a collection of small particles with the same total volume. An increase in the hydrophilic block length of the polymer leads to smaller nanoparticles, due to an enhanced ability of each polymer to shield the nanoparticle core. For unfavorable solute-polymer interactions, the nanoparticle size increases with hydrophobic block length. However, for favorable solute-polymer interactions, nanoparticle size exhibits a local minimum with respect to the hydrophobic block length. Our results provide insights on ways in which experimentally controllable parameters of the Flash NanoPrecipitation process can be used to influence aggregate size and composition during self-assembly.     

Transient cavities and the excess chemical potentials of hard-spheroid solutes in dipolar hard-sphere solvents

Monte Carlo computer simulations are used to study transient cavities and the solvation of hard-spheroid solutes in dipolar hard-sphere solvents. The probability distribution of spheroidal cavities in the solvent is shown to be well described by a Gaussian function, and the variations of fit parameters with cavity elongation and solvent properties are analyzed. The excess chemical potentials of hard-spheroid solutes with aspect ratios x in the range of 15< or =x< or =5, and with volumes between 1 and 20 times that of a solvent molecule, are presented. It is shown that for a given molecular volume and solvent dipole moment (or temperature) a spherical solute has the lowest excess chemical potential and hence the highest solubility, while a prolate solute with aspect ratio x should be more soluble than an oblate solute with aspect ratio 1x. For a given solute molecule, the excess chemical potential increases with increasing temperature; this same trend can be observed in hydrophobic solvation. A scaled-particle theory based on the solvent equation of state and a fitted solute-solvent interfacial tension shows excellent agreement with the simulation results over the whole range of solute elongations and volumes considered. An information-theoretic model based on the solvent density and radial distribution function is less successful, being accurate only for small solute volumes and low solvent densities.     

Excited-state dipole moments from absorption/fluorescence solvatochromic ratios

The permanent dipole moments of excited molecules can be obtained from the ratio of the solvent shifts of absorption and fluorescence spectra. This ratio method eliminates the uncertain solute cavity radius parameter, as well as the solvent polarity function. In the case of the first excited singlet state of aniline the dipole moment is 5 D (versus 1.57 D in the ground state).     

An improved algorithm for the analytical computation of solvent-excluded volume. The treatment of singularities in solvent-accessible surface area and volume functions

An algorithm for the analytical computation of solvent-excluded volume is presented as part of our efforts to develop an improved computational model for a solvent effect term, in which the work required to create a cavity in the solvent is expressed as a function of the solvent-excluded volume. In this article we describe mathematical developments in the analytical integration of solvent-accessible surface (SAS) area, the singularities in SAS area and volume functions, and the procedures required to detect and treat singularities. Techniques to increase algorithm performance are presented, which improve computational speed by about five times, on the average. The accuracy of the analytical method for volume computation is compared with the accuracy of two numerical methods: the numerical integration of SAS area and the point-by-point scanning method. This algorithm calculates the volume of the spheres confined among their intersection planes and resembles a numerical integration of surface area by summing up volume layers. These characteristics make the algorithm useful in analytically calculating the work required to create a convex cavity in a solvent and the work (pΔV) associated with a change in the solvent-excluded volume of the solute due to solvent pressure. © 1995 by John Wiley & Sons, Inc.     

Electrostatic interaction of a solute with a continuum. A direct utilizaion of AB initio molecular potentials for the prevision of solvent effects

A method is presented which utilizes the calculation of the molecular electrostatic potential or the electric field at a discrete number of preselected points to evaluate the environmental effects of a solvent on the properties of a molecular system. No limitations are imposed on the composition and dimension of the solute, on the goodness of the corresponding wavefunction, or on the shape of the cavity in the dielectric. Several levels of approximation, which evidence the effect of self-polarization of the system of surface charges, the influence of the tails of the solute charge distribution going beyond the limits of the cavity, and the effect of the polarization of the solute, are examined and discussed.     

Hybrid supermolecule-polarizable continuum approach to solvation: Application to the mechanism of the Stevens rearrangement

Semiempirical molecular orbital theory has been used to study the effects of solvation by acetonitrile on the Stevens rearrangement of methylammonium formylmethylide to 2-aminopropanal. Three methods of solvation have been used to investigate both the electrostatic and specific solvent–solute effects of solvation: a supermolecule calculation involving the complete geometry optimization of up to six solvent molecules about the solute, the conductor-like screening model (COSMO) polarizable continuum method which allows for geometry optimization of the solute in a solvent defined by its dielectric constant, and a hybrid method in which up to five solvent molecules are incorporated inside the solute cavity and complete geometry optimization of the complex is carried out within the polarizable continuum. A comparison of the calculated geometries, rearrangement activation energies, and enthalpies of solvation from these approaches is presented, and the explicit versus bulk solvation effects are discussed. The overall effect of all methods for incorporating solvation effects is that the radical pair pathway is perferred over the concerted mechanism. © 1996 by John Wiley & Sons, Inc.     

圆柱形纳米孔道内受限溶液I2/Ar的分子动力学模拟研究

利用分子动力学模拟方法, 考察了受限于圆柱形纳米孔道内I2/Ar溶液的振动传能及扩散动力学. 计算得到了溶质振动弛豫时间T1、溶剂轴向扩散系数Dz随孔道半径变化的规律. 结果表明: T1随着孔道半径的增大而减小; 而Dz随着孔道半径的增大而增大; 与预期的一致, 随着孔道半径的增大, 孔道的限制作用逐渐减小, T1与Dz趋近于相应的非受限溶液体相值. 此外, 通过考察溶质、溶剂与孔道的相互作用, 在原子、分子层次上揭示了限制作用对传能与传质影响的机制.