Water models based on a single potential energy surface and different molecular degrees of freedom

Up to now it has not been possible to neatly assess whether a deficient performance of a model is due to poor parametrization of the force field or the lack of inclusion of enough molecular properties. This work compares several molecular models in the framework of the same force field, which was designed to include many-body nonadditive effects: (a) a polarizable and flexible molecule with constraints that account for the quantal nature of the vibration [B. Hess, H. Saint-Martin, and H. J. C. Berendsen, J. Chem. Phys. 116, 9602 (2002), H. Saint-Martin, B. Hess, and H. J. C. Berendsen, J. Chem. Phys. 120, 11133 (2004)], (b) a polarizable and classically flexible molecule [H. Saint-Martin, J. Hernandez-Cobos, M. I. Bernal-Uruchurtu, I. Ortega-Blake, and H. J. C. Berendsen, J. Chem. Phys. 113, 10899 (2000)], (c) a polarizable and rigid molecule, and finally (d) a nonpolarizable and rigid molecule. The goal is to determine how significant the different molecular properties are. The results indicate that all factors--nonadditivity, polarizability, and intramolecular flexibility--are important. Still, approximations can be made in order to diminish the computational cost of the simulations with a small decrease in the accuracy of the predictions, provided that those approximations are counterbalanced by the proper inclusion of an effective molecular property, that is, an average molecular geometry or an average dipole. Hence instead of building an effective force field by parametrizing it in order to reproduce the properties of a specific phase, a building approach is proposed that is based on adequately restricting the molecular flexibility and/or polarizability of a model potential fitted to unimolecular properties, pair interactions, and many-body nonadditive contributions. In this manner, the same parental model can be used to simulate the same substance under a wide range of thermodynamic conditions. An additional advantage of this approach is that, as the force field improves by the quality of the molecular calculations, all levels of modeling can be improved.     

Calculation of the effect of collisional broadening on high-resolution translational energy loss spectra

The collisional broadening of peaks in the spectra arising from translational energy spectroscopy (TES) studies is theoretically investigated. A numerical calculation, based on the TRIO matrix ion-beam transport computer programme, is used to simulate the collision event and its effects on the focussing properties of a number of ‘double-focussing’ instrument designs. The ion-optical models utilised include a commercial mass spectrometer and two novel high-resolution energy spectrometers (TESI and TESII), incorporating quadrupole and hexapole field lenses to focus the beam and reduce image aberrations. For a given design of spectrometer, peak broadening is evaluated in terms of the translational energy change suffered by the ion during collision and the angle through which it is scattered.     

Supercritical fluid effect on the rates of elementary bimolecular reactions

The effect of the supercritical fluid (SCF) present in the reaction system on the rate of a bimolecular reaction has been investigated theoretically. Calculations have been carried out in the framework of the theory of nonideal reaction rates in condensed phases. The intermolecular interactions of the nearest neighbors are described in the quasi-chemical approximation taking into account the short-order correlation effects. The competing effects of raising the reaction temperature (which increases the reaction rate) and raising the pressure by increasing the amount of SCF (which hinders the meeting of the reactants) are discussed. Increasing the proportion of SCF reduces the self-diffusion coefficient and increases the viscosity of the reaction mixture.     

Electronic excitation energies of molecules in solution within continuum solvation models: investigating the discrepancy between state-specific and linear-response methods

In a recent article [R. Cammi, S. Corni, B. Mennucci, and J. Tomasi, J. Chem. Phys. 122, 104513 (2005)], we demonstrated that the state-specific (SS) and the linear-response (LR) approaches, two different ways to calculate solute excitation energies in the framework of quantum-mechanical continuum models of solvation, give different excitation energy expressions. In particular, they differ in the terms related to the electronic response of the solvent. In the present work, we further investigate this difference by comparing the excitation energy expressions of SS and LR with those obtained through a simple model for solute-solvent systems that bypasses one of the basic assumptions of continuum solvation models, i.e., the use of a single Hartree product of a solute and a solvent wave function to describe the total solute-solvent wave function. In particular, we consider the total solute-solvent wave function as a linear combination of the four products of two solute states and two solvent electronic states. To maximize the comparability with quantum-mechanical continuum model the resulting excitation energy expression is recast in terms of response functions of the solvent and quantities proper for the solvated molecule. The comparison of the presented expressions with the LR and SS ones enlightens the physical meaning of the terms included or neglected by these approaches and shows that SS agrees with the results of the four-level model, while LR includes a term classified as dispersion in previous treatments and neglects another related to electrostatic. A discussion on the possible origin of the LR flaw is finally given.     

Electronic excitation energies of molecules in solution: state specific and linear response methods for nonequilibrium continuum solvation models

We present a formal comparison between the two different approaches to the calculation of electronic excitation energies of molecules in solution within the continuum solvation model framework, taking also into account nonequilibrium effects. These two approaches, one based on the explicit evaluation of the excited state wave function of the solute and the other based on the linear response theory, are here proven to give formally different expressions for the excitation energies even when exact eigenstates are considered. Calculations performed for some illustrative examples show that this formal difference has sensible effects on absolute solvatochromic shifts (i.e., with respect to gas phase) while it has small effects on relative (i.e., nonpolar to polar solvent) solvatochromic shifts.     

Contributions from monomolecular and bimolecular reactions to the disappearance of diphenylcarbonyl oxide in solution

It was found by flash photolysis that the overall kinetics of diphenylcarbonyl oxide disappearance in acetonitrile, benzene, and n-hexane has both a bimolecular and a monomolecular component. The monomolecular route is the isomerization of diphenylcarbonyl oxide into dioxirane. The activation parameters of this process were measured. The activation energy of the biomolecular decay of diphenylcarbonyl oxide is slightly positive for acetonitrile, is close to zero for benzene, and is negative for n-hexane. This dependence of the activation energy on the nature of the solvent is due to the fact that the reaction includes the equilibrium formation of an intermediate species.     

Substituent effect on the excess Gibbs energy of saturated solutions of phenols

Solubility and vapour-pressure data have been measured and used to evaluate excess Gibbs energies G_N^E for several phenols along the solid-liquid equilibrium curve. The effect of the structure of the solute molecule on the extremum G_N^E value is discussed.     

Transition structures and energy barriers of pericyclic reactions in the CASSCF approach

Five energy hypersurfaces of the most examined pericyclic reactions have been investigated by using ab initio SCF , CASSCF , and the semiempirical AM 1 methods. The systems are H₄, H₆, C₃H₆, C₄H₄, and C₃OH₄. Stationary points and their sets of harmonic vibrational frequencies have been calculated by means of analytical gradient techniques in the frameworks of the respective approaches. ZPE corrected energy barriers are based on single-point calculations including dynamical correlation corrections by CAS -CI (SD )+DC , CASCEPA , or MP 2.     

Predictions of hydration free energies from continuum solvent with solute polarizable models: the SAMPL2 blind challenge

This paper reports the results of our attempt to predict hydration free energies on the SAMPL2 blind challenge dataset. We mostly examine the effects of the solute electrostatic component on the accuracy of the predictions. The usefulness of electronic polarization in predicting hydration free energies is assessed by comparing the Electronic Polarization from Internal Continuum model and the self consistent reaction field IEF-PCM to standard non-polarizable charge models such as RESP and AM1-BCC. We also determine an optimal restraint weight for Dielectric-RESP atomic charges fitting. Statistical analysis of the results could not distinguish the methods from one another. The smallest average unsigned error obtained is 1.9 ± 0.6 kcal/mol (95% confidence level). A class of outliers led us to investigate the importance of the solute–solvent instantaneous induction energy, a missing term in PB continuum models. We estimated values between −1.5 and −6 kcal/mol for a series of halo-benzenes which can explain why some predicted hydration energies of non-polar molecules significantly disagreed with experiment.     

Gibbs energy calculations for the distillation of a dilute solution in a multistep separation cascade

Calculations of a decrease in Gibbs energy in the distillation of an ideal dilute solution at cascade steps are presented. A thermodynamic interpretation of the total useful work of the separation of binary mixture components is suggested.     

A note on excess Gibbs energy models,equations of state and the local composition concept

A density-dependent local composition expression for the residual energy is derived from a generalized NRTL expression for the excess energy and the van der Waals fluid theory. Integration of this expression yields a volume-dependent expression for the Helmholtz energy from which equations of state utilizing the local composition concept are derived and which in the high-density limit contain the well-known activity coefficient models.The local composition versions of the Carnahan—Starling—van der Waals, the Redlich—Kwong—Soave and the Peng—Robinson equations of state are derived. It is further shown that the group contribution versions of the NRTL, the Wilson and the UNIQUAC excess models may be derived from the generalized NRTL expression for the residual energy when applied to groups instead of molecules.It is thus demonstrated that all current local composition activity-coefficient models can be derived from a local composition version of the van der Waals equation of state using different sets of assumptions. In the same way the van Laar, the Scatchard—Hildebrand and the Flory—Huggins activity coefficient models are obtained from the van der Waals equation of state using the original mixing rules.     

Estimation of the Gibbs energy of C60 fullerene solution in organic solvents based on the additive group method

The literature data on the Gibbs energy of C₆₀ fullerene dissolution in organic solvents of different classes are analyzed. The contributions of the functional groups (-CH₃,-CH₂-, >CH-, >C<,-OH,-Ph,-Napht, etc.) of solvent molecules to the Gibbs energy of C₆₀ fullerene solution were calculated based on the additive group model. The effects of different functional groups on the solution process are discussed.     

On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy

Implicit solvent hydration free energy models are an important component of most modern computational methods aimed at protein structure prediction, binding affinity prediction, and modeling of conformational equilibria. The nonpolar component of the hydration free energy, consisting of a repulsive cavity term and an attractive van der Waals solute-solvent interaction term, is often modeled using estimators based on the solvent exposed solute surface area. In this paper, we analyze the accuracy of linear surface area models for predicting the van der Waals solute-solvent interaction energies of native and non-native protein conformations, peptides and small molecules, and the desolvation penalty of protein-protein and protein-ligand binding complexes. The target values are obtained from explicit solvent simulations and from a continuum solvent van der Waals interaction energy model. The results indicate that the standard surface area model, while useful on a coarse-grained scale, may not be accurate or transferable enough for high resolution modeling studies of protein folding and binding. The continuum model constructed in the course of this study provides one path for the development of a computationally efficient implicit solvent nonpolar hydration free energy estimator suitable for high-resolution structural and thermodynamic modeling of biological macromolecules.     

Single-molecule force spectroscopy of bimolecular reactions: system homology in the mechanical activation of ligand substitution reactions

The mechanochemistry of the bimolecular nucleophilic substitution of DMSO for substituted pyridines at a square-planar pincer Pd(II) center was investigated using single-molecule force spectroscopy (SMFS). The SMFS data are interpreted in terms of the Bell-Evans model, which gives thermal off-rates for two reactions that agree well with previous, stress-free measurements. The characteristic force dependency of the rupture rate, fbeta, is effectively constant for the two reactions examined (22 +/- 2 and 24 +/- 2 pN), and the system homology in the mechanical response is consistent with expected similarities in the reaction potential energy surfaces.     

On the role of dynamical barriers in barrierless reactions at low energies: S(1D) + H2

Reaction probabilities as a function of total angular momentum (opacity functions) and the resulting reaction cross sections for the collision of open shell S((1)D) atoms with para-hydrogen have been calculated in the kinetic energy range 0.09-10 meV (1-120 K). The quantum mechanical hyperspherical reactive scattering method and quasi-classical trajectory and statistical quasi-classical trajectory approaches were used. Two different ab initio potential energy surfaces (PESs) have been considered. The widely used reproducing kernel Hilbert space (RKHS) PES by Ho et al. [T.-S. Ho, T. Hollebeek, H. Rabitz, S. D. Chao, R. T. Skodje, A. S. Zyubin, and A. M. Mebel, J. Chem. Phys 116, 4124 (2002)] and the recently published accurate double many-body expansion (DMBE)/complete basis set (CBS) PES by Song and Varandas [Y. Z. Song and A. J. C. Varandas, J. Chem. Phys. 130, 134317 (2009)]. The calculations at low collision energies reveal very different dynamical behaviors on the two PESs. The reactivity on the RKHS PES is found to be considerably larger than that on the DMBE/CBS PES as a result of larger reaction probabilities at low total (here also orbital) angular momentum values and to opacity functions which extend to significantly larger total angular momentum values. The observed differences have their origin in two major distinct topographic features. Although both PESs are essentially barrierless for equilibrium H-H distances, when the H-H bond is compressed the DMBE/CBS PES gives rise to a dynamical barrier which limits the reactivity of the system. This barrier is completely absent in the RHKS PES. In addition, the latter PES exhibits a van der Walls well in the entrance channel which reduces the height of the centrifugal barrier and is able to support resonances. As a result, a significant larger cross section is found on this PES, with marked oscillations attributable to shape resonances and/or to the opening of partial wave contributions. The comparison of the results on both PESs is illustrative of the wealth of the dynamics at low collision energy. It is also illuminating about the difficulties encountered in modeling an all-purpose global potential energy surface.     

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