Molecular dynamics of phenol at the liquid-vapor interface of water

Molecular dynamics results are presented for phenol at the water liquid-vapor interface at 300 K. The calculated excess free energy of phenol at the interface is -2.8 +/- 0.4 kcal/mol, in good agreement with the recent experimental results of Eisenthal and co-workers. The most probable orientation of the phenol molecule at the surface is such that the aromatic ring is perpendicular to the interface and the OH group is fully immersed in water. The hydroxyl substituent has a preferred orientation which is similar to the orientation of OH bonds of water at the pure water liquid-vapor interface. The transition between interfacial and bulk-like behavior of phenol is abrupt and occurs when the center of mass of the solute is located about 6 angstroms from the Gibbs surface of water. In this region the para carbon atom of the hydrophobic benzene ring can reach the interface and become partially dehydrated. This result suggests that the width of the interfacial region in which the behavior of a simple amphiphilic solute in water is influenced by the presence of the surface depends primarily on the size of its hydrophobic part. The role of the OH substituent was investigated by comparing phenol at the interface with two model systems: benzene with and without partial charges on carbon and hydrogen atoms. It is shown that in the absence of the hydrophilic substituent the solute is located further away from the liquid phase and is more likely to be oriented parallel to the interface. However, when the center of mass of the solute is moved into the interfacial region where the density of water approaches that of the bulk solvent, all three molecules become oriented perpendicularly to the surface. In this orientation the work of cavity formation needed to accommodate the hydrophobic ring in aqueous solvent is minimized.     

Molecular macrocluster formation on silica surfaces in phenol-cyclohexane mixtures

The adsorption of phenol, an aromatic compound with a hydrogen-bonding group, onto a silica surface in cyclohexane was investigated by colloidal probe atomic force microscopy (AFM), attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), and adsorption isotherm measurements. ATR-FTIR measurements on the silica surface indicated the formation of surface macroclusters of phenol through hydrogen bonding. The ATR-FTIR spectra were also measured on the H-terminated silicon surface to observe the effect of the silanol groups on the phenol adsorption. The comparison of the ATR-FTIR spectra for both the silicon oxide and H-terminated silicon surfaces proved that the silanol groups are necessary for the formation of phenol clusters on the surface. The surface force measurement using colloidal probe AFM showed a long-range attraction between the two silica surfaces in phenol-cyclohexane mixtures. This long-range attraction resulted from the contact of the adsorbed phenol layers for the phenol concentrations below 0.6 mol %, at which no significant phenol clusters formed in the bulk solution. The attraction started to decrease at 0.6 mol % phenol due to the exchange of the phenol molecules between the clusters in the bulk phase and on the surface. The surface density of phenol in the adsorbed layer was calculated on the basis of the long-range attraction and found to be much smaller than the liquid phenol density. The plausible structure of the adsorbed phenol layer was drawn by referring to the crystal structure of the bulk phenol and orientation of the phenol molecules on the surface, estimated by the dichroic analysis of ATR-FTIR spectroscopy. The investigation of the phenol adsorption on the silica surface in a nonpolar solvent using this novel approach demonstrated the effect of the aromatic ring on the surface packing density.     

Oligomeric cholates: amphiphilic foldamers with nanometer-sized hydrophilic cavities

The hydroxyl at the C-3 of cholic acid was converted to an amino group, and the resulting amino-functionalized cholic acid was used as a monomer to prepare amide-linked oligomeric cholates. These cholate oligomers fold into helical structures with nanometer-sized hydrophilic internal cavities in solvent mixtures consisting of mostly nonpolar solvents such as carbon tetrachloride or ethyl acetate/hexane and 2-5% of a polar solvent such as methanol or DMSO. The conformations of the foldamers were studied by UV, fluorescence, fluorescence quenching, and fluorescence resonance energy transfer. The nature of the polar/nonpolar solvents and their miscibility strongly influenced the folding reaction. Folding was cooperative, as evidenced by the sigmoidal curves in solvent denaturation experiments. The folded conformers became more stable with an increase in the chain length. The folding/unfolding equilibrium was highly sensitive toward the amount of polar solvent. One percent variation in the solvent composition could change the folding free energies by 0.5-1.4 kcal/mol.     

Monte Carlo simulations of Lennard-Jones nonionic surfactant adsorption at the liquid/vapor interface

We present Monte Carlo simulations of nonionic surfactant adsorption at the liquid/vapor interface of a monatomic solvent. All molecules in the system, solvent and surfactant, are characterized by the Lennard-Jones (LJ) potential using differing interaction parameters. Surfactant molecules consist of an amphiphilic chain with a solvophilic head and a solvophobic tail. Adjacent atoms along the surfactant chain are connected by finitely extensible harmonic springs. Solvent molecules move via the Metropolis random-walk algorithm, whereas surfactant molecules move according to the continuum configurational bias Monte Carlo (CBMC) method. We generate quantitative thermodynamic adsorption and surface tension isotherms in addition to surfactant radius of gyration, tilt angles, and potentials of mean force. Surface tension simulations compared to those calculated from the simulated adsorbed amounts and the Gibbs adsorption isotherm agree confirming equilibrium in our simulations. We find that the classical Langmuir isotherm is obeyed for our LJ surfactants over the range of head and tail lengths studied. Although simulated surfactant chains in the bulk solution exhibit random orientations, surfactant chains at the interface orient roughly perpendicular and the tails elongate compared to bulk chains even in the submonolayer adsorption regime. At a critical surfactant concentration, designated as the critical aggregation concentration (CAC), we find aggregates in the solution away from the interface. At higher concentrations, simulated surface tensions remain practically constant. Using the simulated potential of mean force in the submonolayer regime and an estimate of the surfactant footprint at the CAC, we predict a priori the Langmuir adsorption constant, KL, and the maximum monolayer adsorption, Gammam. Adsorption is driven not by proclivity of the surfactant for the interface, but by the dislike of the surfactant tails for the solvent, that is by a "solvophobic" effect. Accordingly, we establish that a coarse-grained LJ surfactant system mimics well the expected equilibrium behavior of aqueous nonionic surfactants adsorbing at the air/water interface.     

Adsorption of organosilanes at a Zn-terminated ZnO (0001) surface: molecular dynamics study

Four different organosilanes (octyltrihydroxysilane, butyltrihydroxysilane, aminopropyltrihydroxysilane, and thiolpropyltrihydroxysilane) adsorbed at a reconstructed Zn-terminated polar ZnO (0001) surface are studied via constant temperature (298 K) molecular dynamics simulations. Both single adsorbed silane molecules as well as adsorbed silane layers are modeled, and the energy, distance, orientation, and alignment of these adsorbates are analyzed. The adsorbed silane molecules exhibit behavior depending on the chemical nature of their tail (nonpolar or polar) as well as on the silane concentration at the solid surface (single adsorption or silane layer). In contrast to the O-terminated ZnO surface studied previously, now adsorption can only occur at the vacancies of this reconstructed crystal surface, thus leading to an arched structure of the liquid phase near the crystal surface. Nevertheless, both nonpolar and polar single adsorbed silanes show a similar orientation and alignment at the surface (orthogonal in the former, parallel in the latter case) as for the O-terminated ZnO surface, although the interaction energy with the surface is considerably increased for nonpolar silanes while it is nearly unaffected for the polar ones. For adsorbed silanes within silane layers, the difference to single adsorbed silanes depends on the polarity of the tail: nonpolar silanes again show an orthogonal alignment, while polar silanes exhibit two different orientations at the solid surface-a head and a tail down configuration. This leads to two completely different but nevertheless stable orientations of these silanes at the Zn-terminated ZnO surface.     

Hydrogen bond dynamics at water/organic liquid interfaces

Hydrogen bond dynamics at the neat interface between water and a series of organic liquids are studied with molecular dynamics computer simulation. The organic liquids are nonpolar (carbon tetrachloride), weakly polar (1,2-dichloroethane), and polar (nitrobenzene). The effect of surface polarity and surface roughness is examined. The dynamics are expressed in terms of the hydrogen bond population autocorrelation functions and are found to be nonexponential and strongly dependent on the nature of the organic phase. In particular, at all interfaces, the dynamics are slower at the interface than in the bulk and sensitive to the location of the water molecules along the interface normal.     

Molecular orbital theory of the hydrogen bond. 26. The hydration of uracil

Ab initio SCF calculations with the STO -3G basis set have been performed to determine the structure and stability of a 6:1 water:uracil heptamer in which water molecules are hydrogen bonded to uracil at each of the six hydrogen-bonding sites in the uracil molecular plane. The structure of the heptamer describes a stable arrangement of these six water molecules, which are the primary solvent molecules in the first solvation shell, and is suggestive of the arrangement of secondary solvent molecules in that shell in the nonpolar region of the uracil molecular plane. The stabilization energy of the heptamer is 49.6 kcal/mol, or 8.3 kcal/mol per water molecule. The hydrogen bonds between uracil and water are the primary factor in the stabilization of the complex, although water–water interactions and nonadditivity effects are also significant.     

Conformational equilibria of terminally blocked single amino acids at the water-hexane interface. A molecular dynamics study

The conformational equilibria of the acetyl and methyl amide terminally blocked L-alanine, L-leucine and L-glutamine amino acids are examined in vacuum, in bulk water, and at the water-hexane interface, using multi-nanosecond molecular dynamics simulations. The two-dimensional probability distribution functions of finding the peptides at different dihedral angles of the backbone, phi and psi, are calculated, and free energy differences between different conformational states are determined. All three peptides are interfacially active, i.e. tend to accumulate at the interface even though they are not amphiphilic. Conformational states stable in both gas phase and water are also stable in the interfacial environment. Their populations, however, cannot be simply predicted from the knowledge of conformational equilibria in the bulk phases, indicating that the interface exerts a unique effect on the peptides. Conformational preferences in the interfacial environment arise from the interplay between electrostatic and hydrophobic effects. As in an aqueous solution, electrostatic solute-solvent interactions lead to the stabilization of more polar peptide conformations. The hydrophobic effect is manifested at the interface by a tendency to segregate polar and nonpolar moieties of the solute into the aqueous and the hexane phases, respectively. For the terminally blocked glutamine, this favors conformations for which such a segregation is compatible with the formation of strong, backbone-side chain intramolecular hydrogen bonds on the hexane side of the interface. The influence of the hydrophobic effect can be also noted in the orientational preferences of the peptides at the interface. The terminally blocked leucine is oriented such that its nonpolar side chain is buried in hexane, whereas the polar side chain of glutamine is immersed in water. The free energies of rotating the peptides along the axis parallel to the interface by more than 90 degrees are substantial. This indicates that peptide folding at interfaces is strong by driven by the tendency to adopt amphiphilic structures.     

Behavior of β-amyloid 1-16 at the air-water interface at varying pH by nonlinear spectroscopy and molecular dynamics simulations

The adsorption and aggregation of β-amyloid (1-16) fragment at the air-water interface was investigated by the combination of second harmonic generation (SHG) spectroscopy, Brewster angle microscopy (BAM), and molecular dynamics simulations (MD). The Gibbs free energy of surface adsorption was measured to be -10.3 kcal/mol for bulk pHs of 7.4 and 3, but no adsorption was observed for pH 10-11. The 1-16 fragment is believed not to be involved in fibril formation of the β-amyloid protein, but it exhibits interesting behavior at the air-water interface, as manifested in two time scales for the observed SHG response. The shorter time scale (minutes) reflects the surface adsorption, and the longer time scale (hours) reflects rearrangement and aggregation of the peptide at the air-water interface. Both of these processes are also evidenced by BAM measurements. MD simulations confirm the pH dependence of surface behavior of the β-amyloid, with largest surface affinity found at pH = 7. It also follows from the simulations that phenylalanine is the most surface exposed residue, followed by tyrosine and histidine in their neutral form.     

Determination of structure and energetics for gibbs surface adsorption layers of binary liquid mixture 1. Acetone + water

The orientation, structure, and energetics of the vapor/acetone-water interface are studied with sum frequency generation vibrational spectroscopy (SFG-VS). We used the polarization null angle (PNA) method in SFG-VS to accurately determine the interfacial acetone molecule orientation, and we found that the acetone molecule has its C=O group pointing into bulk phase, one CH3 group pointing up from the bulk, and the other CH3 group pointing into the bulk phase. This well-ordered interface layer induces an antiparallel structure in the second layer through dimer formation from either dipolar or hydrogen bond interactions. With a double-layer adsorption model (DAM) and Langmuir isotherm, the adsorption free energies for the first and second layer are determined as deltaG degrees (ads,1) = - 1.9 +/- 0.2 kcal /mol and deltaG degrees (ads,2) = - 0.9 +/- 0.2 kcal /mol, respectively. Since deltaG degrees (ads,1) is much larger than the thermal energy kT = 0.59 kcal /mol, and deltaG degrees (ads,2) is close to kT, the second layer has to be less ordered. Without either strong dipolar or hydrogen bonding interactions between the second and the third layer, the third layer should be randomly thermalized as in the bulk liquid. Therefore, the thickness of the interface is not more than two layers thick. These results are consistent with previous MD simulations for the vapor/pure acetone interface, and undoubtedly provide direct microscopic structural evidences and new insight for the understanding of liquid and liquid mixture interfaces. The experimental techniques and quantitative analysis methodology used for detailed measurement of the liquid mixture interfaces in this report can also be applied to liquid interfaces, as well as other molecular interfaces in general.     

银纳米粒子表面油酸盐吸附的分子模拟

采用分子力学方法模拟了油酸盐分子在银纳米粒子(111)表面的两种主要吸附形态: 双键吸附和羧基吸附, 计算了不同溶剂环境中油酸盐分子的吸附能和振动频率. 结果表明: 作为银纳米粒子保护剂的油酸盐能够稳定地存在于极性和非极性溶剂环境中, 与银表面的作用方式随溶剂极性的改变而改变, 水相中以双键吸附为主, 而在有机相中主要是羧基吸附. 这与红外光谱实验的推论基本吻合. 从而在分子水平上为实验结果提供了有价值的理论支持和微观信息.     

Sum frequency vibrational spectroscopy of leucine molecules adsorbed at air-water interface

Sum frequency vibrational spectroscopy was used to study adsorption of leucine molecules at air-water interface from solutions with different concentrations and pH values. The surface density and the orientation of the isopropyl head group of the adsorbed leucine molecules could be deduced from the measurements. It was found that the orientation depends on the surface density, but only weakly on bulk pH value at the saturated surface density. The vibrational spectra of the interfacial water molecules appeared to be strongly affected by the charge state of the adsorbed leucine molecules. Enhancement and inversion of polar orientation of interfacial water molecules by surface charges or field controllable by the bulk pH value were observed.     

Dynamics and thermodynamics of water in PAMAM dendrimers at subnanosecond time scales

Atomistic molecular dynamics simulations are used to study generation 5 polyamidoamine (PAMAM) dendrimers immersed in a bath of water. We interpret the results in terms of three classes of water: buried water well inside of the dendrimer surface, surface water associated with the dendrimer-water interface, and bulk water well outside of the dendrimer. We studied the dynamic and thermodynamic properties of the water at three pH values: high pH with none of the primary or tertiary amines protonated, intermediate pH with only the primary amines protonated, and low pH with all amines protonated. For all pH values we find that both buried and surface water exhibit two relaxation times: a fast relaxation ( approximately 1 ps) corresponding to the libration motion of the water and a slow ( approximately 20 ps) diffusional component related to the escaping of water from one domain to another. In contrast for bulk water the fast relaxation is approximately 0.4 ps while the slow relaxation is approximately 14 ps. These results are similar to those found in biological systems, where the fast relaxation is found to be approximately 1 ps while the slow relaxation ranges from 20 to 1000 ps. We used the 2PT MD method to extract the vibrational (power) spectrum and found substantial differences for the three classes of water. The translational diffusion coefficient for buried water is 11-33% (depending on pH) of the bulk value while the surface water is about 80%. The change in rotational diffusion is quite similar: 21-45% of the bulk value for buried water and 80% for surface water. This shows that translational and rotational dynamics of water are affected by the PAMAM-water interactions as well as due to the confinement in the interior of the dendrimer. We find that the reduction of translational or rotational diffusion is accompanied by a blue shift of the corresponding libration motions ( approximately 10 cm(-1) for translation, approximately 35 cm(-1) for rotation), indicating higher local force constants for these motions. These effects are most pronounced for the lowest pH, probably because of the increased rigidity caused by the internal charges. From the vibrational density of states we also calculate the enthalpies and entropies of the various waters. We find that water molecules are enthalpically favored near the PAMAM dendrimer: energy for surface water is approximately 0.1 kcal/mol lower to that in the bulk, and approximately 0.5-0.9 kcal/mol lower for buried water. In contrast, we find that both the buried and surface water are entropically unfavored: buried water is 0.9-2.2 kcal/mol lower than the bulk while the surface water is 0.1-0.2 kcal/mol lower. The net result is a thermodynamically unfavored state of the water surrounding the PAMAM dendrimer: 0.4-1.3 kcal/mol higher for buried water and 0.1-0.2 kcal/mol for surface water. This excess free energy of the surface and buried waters is released when the PAMAM dendrimer binds to DNA or metal ions, providing an extra driving force.     

What can you learn from a molecular probe? New insights on the behavior of C343 in homogeneous solutions and AOT reverse micelles

The behavior of C343, a common molecular probe utilized in solvation dynamics experiments, was studied in homogeneous media and in aqueous and nonaqueous reverse micelles (RMs). In homogeneous media, the Kamlet and Taft solvatochromic comparison method quantified solute-solvent interactions from the absorption and emission bands showing that the solvatochromic behavior of the dye depends not only on the polarity of the medium but also on the hydrogen-bonding properties of the solvent. Specifically, in the ground state the molecule displays a bathochromic shift with the polarity polarizability (pi) and the H-bond acceptor (beta) ability of the solvents and a hypsochromic shift with the hydrogen donor ability (alpha) of the media. The carboxylic acid group causes C343 to display greater sensitivity to the beta than to the pi polarity parameter; this sensitivity increases in the excited state, while the dependence on alpha vanishes. This demonstrates that C343 forms a stable H-bond complex with solvents with high H-bond acceptor ability (high beta) and low H-bond donor character (low alpha). Spectroscopy in nonpolar solvents reveals J-aggregate formation. With information from the Kamlet-Taft analysis, C343 was used to explore RMs composed of water or polar solvents/sodium 1,4-bis-2-ethylhexylsulfosuccinate (AOT)/isooctane using absorption, emission, and time-resolved spectroscopies. Sequestered polar solvents included ethylene glycol (EG), formamide (FA), N,N-dimethylformamide (DMF), and N,N-dimethylacetamide (DMA). Dissolved in the AOT RM systems at low concentration, C343 exists as a monomer, and when introduced to the RM samples in its protonated form, C343 remains protonated driving it to reside in the interface rather than the water pool. The solvathochromic behavior of the dye depends the specific polar solvent encapsulated in the RMs, revealing different types of interactions between the solvents and the surfactant. EG and water H-bond with the AOT sulfonate group destroying their bulk H-bonded structures. While water remains well segregated from the nonpolar regions, EG appears to penetrate into the oil side of the interface. In aqueous AOT RMs, C343 interacts with neither the sulfonate group nor the water, perhaps because of intramolecular H-bonding in the dye. DMF and DMA interact primarily through dipole-dipole forces, and the strong interactions with AOT sodium counterions destroy their bulk structure. FA also interacts with the Na+ counterions but retains its H-bond network present in bulk solvent. Surprisingly, FA appears to be the only polar solvent other than water forming a "polar-solvent pool" with macroscopic properties similar to the bulk.     

十二烷基苯磺酸钠在SiO2表面聚集的分子动力学模拟

采用分子动力学方法研究了阴离子表面活性剂十二烷基苯磺酸钠(SDBS)在无定形SiO2固体表面的吸附. 设置不同的水层厚度, 观察固液界面和气液界面吸附的差异. 模拟发现表面活性剂分子能够在短时间内吸附到SiO2表面, 受碳链和固体表面之间相互作用的影响形成表面活性剂分子层, 并依据吸附量的大小形成不同的聚集结构; 在水层足够厚的情况下, 由于有较多的表面活性剂分子吸附在固体表面,从而形成带有疏水核心的半胶束结构; 计算得到的成对势表明极性头与钠离子或水分子之间的结合或解离与二者之间的能垒有关, 解离能垒远大于结合能垒, 引起更多Na+聚集在极性头周围而只有少数Na+存在于溶液中; 无论气液还是固液界面, 极性头均伸向水相, 与水分子形成不同类型的氢键. 模拟表明, 分子动力学方法可以作为实验的一种补充, 为实验提供必要的微观结构信息.     

Anisotropic solvent model of the lipid bilayer. 1. Parameterization of long-range electrostatics and first solvation shell effects

A new implicit solvation model was developed for calculating free energies of transfer of molecules from water to any solvent with defined bulk properties. The transfer energy was calculated as a sum of the first solvation shell energy and the long-range electrostatic contribution. The first term was proportional to solvent accessible surface area and solvation parameters (σ(i)) for different atom types. The electrostatic term was computed as a product of group dipole moments and dipolar solvation parameter (η) for neutral molecules or using a modified Born equation for ions. The regression coefficients in linear dependencies of solvation parameters σ(i) and η on dielectric constant, solvatochromic polarizability parameter π*, and hydrogen-bonding donor and acceptor capacities of solvents were optimized using 1269 experimental transfer energies from 19 organic solvents to water. The root-mean-square errors for neutral compounds and ions were 0.82 and 1.61 kcal/mol, respectively. Quantification of energy components demonstrates the dominant roles of hydrophobic effect for nonpolar atoms and of hydrogen-bonding for polar atoms. The estimated first solvation shell energy outweighs the long-range electrostatics for most compounds including ions. The simplicity and computational efficiency of the model allows its application for modeling of macromolecules in anisotropic environments, such as biological membranes.     

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.     

Assessment of the Surface Heterogeneity of Talc Materials

The hydrophobic and hydrophilic components of the surface of talc materials in aqueous solution were determined using ionic surfactants and their polar headgroup adsorption isotherms. The hydrophilic and hydrophobic surface areas are inferred from the amount of probe molecule adsorbed and the structure of the adsorbed layer. Natural dispersion of talc shows at 298 K a pH of 9.4 and the electrophoretic measurements indicate that the particles are negatively charged. The hydrophilic surface area is estimated from the adsorption of benzyltrimethylammonium ions (BTMA(+)) through electrostatic interactions as supported by the increase of divalent ions in the bulk phase and the decrease in the exothermic displacement enthalpy. It was also observed from the adsorption isotherm of benzene sulfonate anions that the density of positive surface sites is very low and is thus neglected. The adsorption of an anionic surfactant essentially occurs through dispersive interactions between the nonpolar organic tail of the molecule and the hydrophobic surface. Furthermore, some assumptions on the structure of dodecyl sulfate surfactant aggregates at the interface allow the hydrophobic part of the talc particles to be estimated. The cationic surfactant adsorption has been investigated and found to corroborate the hydrophilic and hydrophobic area values first obtained. Copyright 2001 Academic Press.     

Solvent dynamics following charge transfer at the liquid-liquid interface

The dynamics of solvent reorganization following charge transfer at the interface between two immiscible liquids, one polar and the other non-polar are investigated by molecular dynamics. Both charge separation and charge recombination processes in two different orientations at the surface are considered and are compared with the same processes in the bulk polar solvent. The relaxation at the surface is significantly slower than in the bulk, in contrast to predictions of continuum models. The linear response approximation works reasonably well in the bulk but fails at the interface. The Langevin model is in poor agreement with the exact equilibrium correlations, especially at short time, but can qualitatively account for the overall rate.