Equation of state for the phase coexistence region of insoluble monolayers under consideration of the entropy nonideality

The equation of state for the monolayer with a fluid (G, LE)/condensed (LC) phase transition derived earlier (Fainerman, V.B.; Vollhardt, D. J. Phys. Chem. B 1999, 103, 145) in the framework of a quasichemical approach is generalized. A term is added that takes into account the entropy nonideality of mixing of the monomers and clusters of amphiphilic molecules. The results calculated from the proposed equations agree well with the experimental Pi-A isotherms obtained for various types of amphiphilic monolayers. The values of molecular areas of the amphiphilic molecules estimated from the fitting of experimental data to the proposed equation are quite similar to the real values. Another equation of state capable of describing the fluid state of insoluble monolayers and based on equations for the chemical potential of the solvent in the bulk phase and in the surface layer (Fainerman, V. B.; Vollhardt, D. J. Phys. Chem. B 2006, 110, 10436) is also generalized to be extended to the fluid/condensed phase transition region (A < A(c)), taking into account entropy nonideality for mixing solvent molecules, monomers, and clusters of amphiphilic molecules. The values calculated on this basis agree also well with the experimental data.     

The ionic work function and its role in estimating absolute electrode potentials

The experimental determination of the ionic work function is briefly described. Data for the proton, alkali metal ions, and halide ions in water, originally published by Randles (Randles, J. E. B. Trans Faraday Soc. 1956, 52, 1573) are recalculated on the basis of up-to-date thermodynamic tables. These calculations are extended to data for the same ions in four nonaqueous solvents, namely, methanol, ethanol, acetonitrile, and dimethyl sulfoxide. The ionic work function data are compared with estimates of the absolute Gibbs energy of solvation obtained by an extrathermodynamic route for the same ions. The work function data for the proton are used to estimate the absolute potential of the standard hydrogen electrode in each solvent. The results obtained here are compared with those published earlier by Trasatti (Trasatti, S. Electrochim. Acta 1987, 32, 843) and more recently by Kelly et al. (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 2006, 110, 16066. Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 2007, 111, 408). A comparison of the ionic work function with the absolute Gibbs solvation energy permits an estimation of the surface potential of the solvent. The results show that the surface potential of water is small and positive whereas the surface potential of the nonaqueous solvents considered is negative. The sign of the surface potential is consistent with the known structure of each solvent.     

Scaled particle theory study of the length scale dependence of cavity thermodynamics in different liquids

It has been noted that the work of cavity creation in water exhibits a crossover behavior, in that its cavity size dependence changes from volume dependence for small cavities to area dependence for larger cavities [Lum, K.; Chandler, D.; Weeks, J. D. J. Phys. Chem. B 1999, 103, 4570]. It is shown here that this behavior can be reproduced using the scaled particle theory in a straightforward manner for six different liquids (water, methanol, ethanol, benzene, cyclohexane, and carbon tetrachloride). It has also been suggested that the crossover is due to a change in the physical mechanism of the process, from one entropy-dominated to another enthalpy-dominated. However, the crossover behavior can be produced using the scaled particle theory without invoking any change in any physical mechanism. Also, the crossover occurs at a length scale of the size of the liquid molecules, as has been pointed out by others. This is the length regime where the work of cavity creation bears little relation to the bulk liquid surface tension. In addition, it is pointed out that cavity creation can always be considered as a purely entropy-driven process, which is usually accompanied by another process with compensating enthalpy and entropy changes.     

VBSM: a solvation model based on valence bond theory

A new solvation model, called VBSM, is presented. The model combines valence bond (VB) theory with parameters determined for the SM6 solvation model (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). VBSM, like SM6, is based on the generalized Born (GB) approximation for bulk electrostatics and atomic surface tensions to account for cavitation, dispersion, and solvent structure (CDS). The solvation free energy of VBSM includes (i) a self-consistent polarization term obtained by using VB atomic charges in a GB reaction field with a VB self-consistent field procedure that minimizes the total energy of the system with respect to the valence bond orbitals and (ii) a geometry-dependent CDS term to account for deviations from bulk-electrostatic solvation. Test calculations for a few systems show that the liquid-phase partial atomic charges obtained by VBSM are in good agreement with liquid-phase charges obtained by charge model CM4 (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). Free energies of solvation are calculated for two prototype test cases, namely, for the degenerate S(N)2 reaction of Cl(-) with CH(3)Cl in water and for a Menshutkin reaction in water. These calculations show that the VBSM method provides a practical alternative to single-configuration self-consistent field theory for solvent effects in molecules and chemical reactions.     

Structure and dynamics of the hydrogen-bond network around (R,R)-pterocarpans with biological activity in aqueous solution

Molecular dynamics simulations were carried out in the presence of 2380 water molecules (TIP3P) to explore the conformational preferences of 3,9-dimethoxy-4-prenylpterocarpan (bitucarpin A) and 3,9-dihydroxy-4,8-diprenylpterocarpan (erybraedin C) and the H-bond network around them, using the empirical general AMBER force field (GAFF). Specific angle and torsional parameters have been improved in order to match the geometries of the minimum energy structures obtained from an earlier DFT/ab initio study in vacuo, taking into account a few configurations [Alagona, G.; Ghio, C.; Monti, S. Phys. Chem. Chem. Phys. 2004, 6, 2849-2857]. RESP partial charges were assigned to reproduce the electrostatic potential determined at the HF/6-31G level of theory. The analysis of trajectories allowed the conformations of bitucarpin and erybraedin as well as the distribution of water molecules around them to be elucidated. During one of the simulations only, the scaffold of erybraedin undergoes interconversion from its most stable Ht conformation to the Ot one and vice versa. Radial distribution functions, coordination numbers, and angular distributions put forward the extent of solvent structure and the hydrogen bonding behavior of their various (methoxy, hydroxyl, or ethereal) oxygen atoms. The distribution of solvent molecules in the first and second solvation shells as well as the residence times for the different solute-solvent interacting sites have been considered.     

Molecular dynamics simulation of the energetic room-temperature ionic liquid, 1-hydroxyethyl-4-amino-1,2,4-triazolium nitrate (HEATN)

Molecular dynamics (MD) simulations have been performed to investigate the structure and dynamics of an energetic ionic liquid, 1-hydroxyethyl-4-amino-1,2,4-triazolium nitrate (HEATN). The generalized amber force field (GAFF) was used, and an electronically polarizable model was further developed in the spirit of our previous work (Yan, T.; Burnham, C. J.; Del Popolo, M. G.; Voth, G. A. J. Phys. Chem. B 2004, 108, 11877). In the process of simulated annealing from a liquid state at 475 K down to a glassy state at 175 K, the MD simulations identify a glass-transition temperature region at around 250-275 K, in agreement with experiment. The self-intermediate scattering functions show vanishing boson peaks in the supercooled region, indicating that HEATN may be a fragile glass former. The coupling/decoupling of translational and reorientational ion motion is also discussed, and various other physical properties of the liquid state are intensively studied at 400 K. A complex hydrogen bond network was revealed with the calculation of partial radial distribution functions. When compared to the similarly sized 1-ethyl-4-methyl-1,4-imidazolium nitrate ionic liquid, EMIM+/NO3-, a hydrogen bond network directly resulting in the poorer packing efficiency of ions is observed, which is responsible for the lower melting/glass-transition point. The structural properties of the liquid/vacuum interface shows that there is vanishing layering at the interface, in accordance with the poor ion packing. The effects of electronic polarization on the self-diffusion, viscosity, and surface tension of HEATN are found to be significant, in agreement with an earlier study on EMIM+/NO3- (Yan, T.; Burnham, C. J.; Del Popolo, M. G.; Voth, G. A. J. Phys. Chem. B 2004, 108, 11877).     

Relaxation and short time dynamics of bulk liquids and fluids confined in spherical cavities and slit pores

The density of states for bulk and confined fluids have been modeled using a recently proposed gamma distribution (Krishnan, S. H.; Ayappa, K. G. J. Chem. Phys. 2004, 121, 3197). The gamma distribution results in a closed form analytical expression for the velocity autocorrelation function and the relaxation time of the fluid. The two parameters of the gamma distribution are related analytically to the second and fourth frequency moments of the fluid using short time expansions. The predictions by the proposed gamma model are compared with the velocity autocorrelation functions obtained using the theory of instantaneous normal modes (INMs) and from molecular dynamics simulations. The model is applied to a bulk soft sphere liquid and fluids confined in a spherical cavity and slit-shaped pores. The gamma model is able to capture the resulting changes in relaxation time due to changes in density and temperature extremely well for both the bulk liquid and confined inhomogeneous fluid situations. In all cases, the predictions by the gamma model are superior to those obtained from the INM theory. In the case of the fluid confined in a slit pore, the loadings were obtained from a grand canonical Monte Carlo simulation where the pore is equilibrated with a bulk fluid. This is similar to a confinement situation in a surface force apparatus. The predicted relaxation times vs pore widths from the gamma model are seen to accurately capture the oscillations due to formation and disruption of layers within the slit pore.     

Temperature-dependent hydration at micellar surface: activation energy barrier crossing model revisited

In recent years, the validity of the activation energy barrier crossing model at the micellar surface brings notable controversy (Sen, P.; Mukherjee, S.; Halder, A.; Bhattacharyya, K. Chem. Phys. Lett. 2004, 385, 357-361. Kumbhakar, M.; Goel, T.; Mukherjee, T.; Pal, H. J. Phys. Chem. B 2004, 108, 19246-19254.) in the literature. In order to check the validity of the model by time-resolved solvation of a probe fluorophore, a wider range of temperature must be considered. At the same time, spatial heterogeneity (solubilization) of the probe and structural perturbation of the host micelle should carefully be avoided, which was not strictly maintained in the earlier studies. We report here the solvation dynamics of 4-(dicyanomethylene)-2-methyl-6(p-dimethylamino-styryl) 4H-pyran (DCM) in the SDS micelle at 298, 323, and 348 K. The probe DCM is completely insoluble in bulk water in this wide range of temperature. The size of the micelle at different temperatures using the dynamic light scattering (DLS) technique is found to have insignificant change. The hydration number of the micelle, determined by sound velocity measurements, decreases with increasing temperature. Time-resolved fluorescence anisotropy reveals the retention of the probe in the micellar interface within the temperature range. The average solvation time decreases with increasing temperature. The result of the solvation study has been analyzed in the light of energetics of bound to free water conversion at a constant size and decreasing hydration number at the micellar surface. The solvation process at the micellar surface has been found to be the activation energy barrier crossing type, in which interfacially bound type water molecules get converted into free type molecules. We have calculated Ea to be 3.5 kcal mol-1, which is in good agreement with that obtained by molecular dynamics simulation studies.     

Enthalpy-entropy contributions to salt and osmolyte effects on molecular-scale hydrophobic hydration and interactions

Salts and additives can significantly affect the strength of water-mediated interactions in solution. We present results from molecular dynamics simulations focused on the thermodynamics of hydrophobic hydration, association, and the folding-unfolding of a hydrophobic polymer in water and in aqueous solutions of NaCl and of an osmolyte trimethylamine oxide (TMAO). It is known that addition of NaCl makes the hydration of hydrophobic solutes unfavorable and, correspondingly, strengthens their association at the pair as well as the many-body level (Ghosh, T.; Kalra, A.; Garde, S. J. Phys. Chem. B 2005, 109, 642), whereas the osmolyte TMAO has an almost negligible effect on the hydrophobic hydration and association (Athawale, M. V.; Dordick, J. S.; Garde, S. Biophys. J. 2005, 89, 858). Whether these effects are enthalpic or entropic in origin is not fully known. Here we perform temperature-dependent simulations to resolve the free energy into entropy and enthalpy contributions. We find that in TMAO solutions, there is an almost precise entropy-enthalpy compensation leading to the negligible effect of TMAO on hydrophobic phenomena. In contrast, in NaCl solutions, changes in enthalpy dominate, making the salt-induced strengthening of hydrophobic interactions enthalpic in origin. The resolution of total enthalpy into solute-solvent and solvent-solvent terms further shows that enthalpy changes originate primarily from solvent-solvent energy terms. Our results are consistent with experimental data on the hydration of small hydrophobic solutes by Ben-Naim and Yaacobi (Ben-Naim, A.; Yaacobi, M. J. Phys. Chem. 1974, 78, 170). In combination with recent work by Zangi, Hagen, and Berne (Zangi, R.; Hagen, M.; Berne, B. J. J. Am. Chem. Soc. 2007, 129, 4678) and the experimental data on surface tensions of salt solutions by Matubayasi et al. (Matubayasi, N.; Matsuo, H.; Yamamoto, K.; Yamaguchi, S.; Matuzawa, A. J. Colloid Interface Sci. 1999, 209, 398), our results highlight interesting length scale dependences of salt effects on hydrophobic phenomena. Although NaCl strengthens hydrophobic interactions at both small and large length scales, that effect is enthalpy-dominated at small length scales and entropy-dominated for large solutes and interfaces. Our results have implications for understanding of additive effects on water-mediated interactions, as well as on biocompatibility of osmolyte molecules in aqueous solutions.     

Molecular simulation of solvent-induced stokes shift in absorption/emission spectra of organic chromophores

The values of steady-state solvatochromic Stokes shifts (SS) in absorption/emission electronic spectra of organic chromophores are studied theoretically in the framework of the Hush-Marcus model. Charge distributions for chromophore solutes in their S0 and S1 states are found by means of conventional quantum-chemical methods combined with the continuum PCM approach for treating solvation effects. The solvent reorganization energies, which are expected to correlate with the solvent-induced part of 1/2 SS, are found in a molecular dynamics (MD) simulation which invokes a novel method for separation of the inertial piece of the electrostatic response (Vener, et al. J. Phys. Chem. B 2006, 110, 14950). Computations, performed in two solvents (acetonitrile and benzene), consider three organic dyes: coumarin 153 as a benchmark system and two other chromophores, for which experimental spectra are also reported. The results are found to be in reasonable agreement with the experiment. A consistent treatment of nonlinear effect in the solvent response, promoted by the polarizability of solutes and contributing to the solvent reorganization energies (Ingrosso, et al. J. Phys. Chem. B 2005, 109, 3553), improves the results of computations.     

Long-range proton transfer in aqueous Acid-base reactions

We study the mechanism of proton transfer (PT) in the aqueous acid-base reaction between the photoacid 8-hydroxy-1,3,6-pyrenetrisulfonic acid (HPTS) and acetate by probing the vibrational resonances of HPTS, acetate, and the hydrated proton with femtosecond mid-infrared laser pulses. We find that PT takes place in a distribution of hydrogen-bound reaction complexes that differ in the number of water molecules separating the acid and the base. The number of intervening water molecules ranges from 0 to 5, which, together with a strongly distance-dependent PT rate, explains the observed highly nonexponential reaction kinetics. The kinetic isotope effect for the reaction is determined to be 1.5, indicating that tunneling does not play a significant role in the transfer of the proton. Rather, the transfer mechanism is best described in terms of the adiabatic PT picture as it has been formulated by Hynes and co-workers [Staib, A.; Borgis, D.; Hynes, J. T. J. Chem. Phys. 1995, 102, 2487. Ando, K.; Hynes, J. T. J. Phys. Chem. B 1997, 101, 10464.], where solvent fluctuations play an essential role in forming the correct hydrogen-bond configuration and solvent polarization to facilitate PT.     

Accuracy of recent potential energy surfaces for the He-N2 interaction. I. Virial and bulk transport coefficients

A new exchange-Coulomb semiempirical model potential energy surface for the He-N2 interaction has been developed. Together with two recent high-level ab initio potential energy surfaces, it has been tested for the reliability of its predictions of second-virial coefficients and bulk transport phenomena in binary mixtures of He and N2. The agreement with the relevant available measurements is generally within experimental uncertainty for the exchange-Coulomb surface and the ab initio surface of Patel et al. [J. Chem. Phys. 119, 909 (2003)], but with slightly poorer agreement for the earlier ab initio surface of Hu and Thakkar [J. Chem. Phys. 104, 2541 (1996)].     

Revised self-consistent continuum solvation in electronic-structure calculations

The solvation model proposed by Fattebert and Gygi [J. Comput. Chem. 23, 662 (2002)] and Scherlis et al. [J. Chem. Phys. 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multigrid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett. 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the polarizable continuum model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond-forming compounds.     

How does trimethylamine N-oxide counteract the denaturing activity of urea?

Trimethylamine N-oxide, TMAO, stabilizes globular proteins and is able to counteract the denaturing activity of urea. The mechanism of this counteraction has remained elusive up to now. A rationalization is proposed grounded on the same theoretical model used to clarify the origin of cold denaturation, and the denaturing activity of GdmCl versus the stabilizing one of Gdm(2)SO(4) [G. Graziano, Phys. Chem. Chem. Phys., 2010, 12, 14245-14252; G. Graziano, Phys. Chem. Chem. Phys., 2011, 13, 12008-12014]. The fundamental quantities are: (a) the difference in the solvent-excluded volume on passing from the N-state to the D-state, calculated in water and in aqueous osmolyte solution; (b) the difference in energetic attractions of the N-state and the D-state with the surrounding solvent molecules, calculated in water and in aqueous osmolyte solution. In aqueous 8 M urea + 4 M TMAO solution, the first quantity is so large and positive to counteract the second one that is large and negative due to preferential binding of urea molecules to the protein surface. This happens because aqueous 8 M urea + 4 M TMAO solution has a volume packing density markedly larger than that of water, rendering the cavity creation process much more costly. The volume packing density increase reflects the strength of the attractions of water molecules with both urea and TMAO molecules. This mechanism readily explains why TMAO counteraction is operative even though urea molecules are preferentially located on the protein surface.     

Fewest-switches surface hopping and decoherence in multiple dimensions

In a recent article (Subotnik, J. E.; Shenvi, N. J. Chem. Phys.2011, 134, 24105), we introduced a new approach for incorporating decoherence into the fewest-switches surface-hopping (FSSH) algorithm, titled augmented FSSH (A-FSSH). The A-FSSH algorithm was designed to correct the well-known overcoherence problem in traditional FSSH, and thus allow wave packets on different surfaces to separate naturally subject to different forces. As presented earlier, however, the A-FSSH algorithm was restricted to two electronic states. We now extend the method to more than two electronic states and present several new model problems with multiple electronic and nuclear dimensions. Lastly, starting with the quantum Liouville equation, we rederive and implement the new phase correction suggested by Shenvi (Shenvi, N.; Subotnik, J. E.; Yang, W. J. Chem. Phys.2011, 135, 24101) and co-workers for propagating the electronic amplitude along a specified nuclear trajectory and find much improved results in certain cases.     

Hydrodynamic force on a microparticle approaching a wall in a nanoparticle dispersion: observation of a separation-dependent effective viscosity

Colloid probe atomic force microscopy was used to measure the hydrodynamic force exerted on a 30-μm-diameter silica particle being moved toward or away from a silica plate in aqueous dispersions of 22-nm-diameter silica nanoparticles (6 or 8 vol %). Upon comparing the measured force to predictions made using the well-known expression of Cox and Brenner (Cox, R. G.; Brenner, H. Chem. Eng. Sci.1967, 22, 1753-1777) assuming a constant viscosity equal to that of the bulk dispersion, the measured drag force was found to become significantly less than that predicted at smaller particle-plate separation distances (e.g., <500 nm). A recent theoretical paper by Bhattacharya and Blawzdziewicz (Bhattacharya, S.; Blawzdziewicz, J. J. Chem. Phys.2008, 128, 214704) predicted that in a solution of dispersed nanoparticles the effective viscosity characterizing the hydrodynamic force on the particle should vary from that of the solvent at contact to that of the bulk dispersion at large separations. By adjusting the viscosity in the Cox and Brenner expression to make the predicted hydrodynamic force match that measured (i.e., the effective viscosity), a curve showing these exact characteristics was obtained. The effective viscosity profile was not a function of particle speed, and changes in the effective viscosity extended to separation distances of as large as 2 μm (nearly 100 times the hard diameter of the nanoparticles). These results suggest that in the range of typical colloidal forces (on the order of 100 nm), the dynamics of particle motion in such systems are determined by the viscosity of the solvent and not that of the bulk dispersion.     

Implicit solvent models: Combining an analytical formulation of continuum electrostatics with simple models of the hydrophobic effect

The recent development of approximate analytical formulations of continuum electrostatics opens the possibility of efficient and accurate implicit solvent models for biomolecular simulations. One such formulation (ACE, Schaefer & Karplus, J. Phys. Chem., 1996, 100:1578) is used to compute the electrostatic contribution to solvation and conformational free energies of a set of small solutes and three proteins. Results are compared to finite-difference solutions of the Poisson equation (FDPB) and explicit solvent simulations and experimental data where available. Small molecule solvation free energies agree with FDPB within 1–1.5 kcal/mol, which is comparable to differences in FDPB due to different surface treatments or different force field parameterizations. Side chain conformation free energies of aspartate and asparagine are in qualitative agreement with explicit solvent simulations, while 74 conformations of a surface loop in the protein Ras are accurately ranked compared to FDPB. Preliminary results for solvation free energies of small alkane and polar solutes suggest that a recent Gaussian model could be used in combination with analytical continuum electrostatics to treat nonpolar interactions. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 322–335, 1999     

New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations

In a recent article (Lee, M. S.; Salsbury, F. R. Jr.; Brooks, C. L., III. J Chem Phys 2002, 116, 10606), we demonstrated that generalized Born (GB) theory provides a good approximation to Poisson electrostatic solvation energy calculations if one uses the same definitions of molecular volume for each. In this work, we present a new and improved analytic method for reproducing the Lee-Richards molecular volume, which is the most common volume definition for Poisson calculations. Overall, 1% errors are achieved for absolute solvation energies of a large set of proteins and relative solvation energies of protein conformations. We also introduce an accurate SASA approximation that uses the same machinery employed by our GB method and requires a small addition of computational cost. The combined methodology is shown to yield an efficient and accurate implicit solvent representation for simulations of biopolymers.     

Reaction of OH + NO2: high pressure experiments and falloff analysis

High pressure experiments on the OH + NO2 reaction are presented for 3 different temperatures. At 300 K, experiments in He (p = 2-500 bar) as well as in Ar (p = 2-4 bar) were performed. The rate constants obtained in Ar agree well with values which have been reported earlier by our group (Forster, R.; Frost, M.; Fulle, D.; Hamann, H. F.; Hippler, H.; Schlepegrell, A.; Troe, J. J. Chem. Phys. 1995, 103, 2949. Fulle, D.; Hamann, H. F.; Hippler, H.; Troe, J. J. Chem. Phys. 1998, 108, 5391). In contrast, the rate coefficients determined in He were found to be 15-25% lower than the values given in our earlier publications. Additionally, results for He as bath gas at elevated temperatures (T = 400 K, p = 3-150 bar; T = 600 K, p = 3-150 bar) are reported. The results obtained at elevated pressures are found to be in good agreement with existing literature data. The observed falloff behavior is analyzed in terms of the Troe formalism taking into account two reaction channels: one yielding HNO3 and one yielding HOONO. It is found that the extracted parameters are in agreement with rate constants for vibrational relaxation and isotopic scrambling as well as with experimentally determined branching ratios. Based on our analysis we determine falloff parameters to calculate the rate constant for atmospheric conditions.