Thirty years of continuum solvation chemistry: a review,and prospects for the near future

With the recent occurrence of the 30^th anniversary of the first quantum mechanical continuum solvent code (Rinaldi D, Rivail J-L (1973) Theor Chim Acta 32:57), it seems like an appropriate moment to briefly review the variety of continuum QM models now available. This paper begins with such an overview, before shifting the discussion to a critical examination of some aspects of the basic theory, taking as the definition and evaluation of the solvation energy as an example. Advantages and disadvantages of using continuum-discrete models are examined, with particular attention paid to the evaluation of the solutes response properties. Some guidelines, and an operative definition of specific solute-solvent interactions, are presented. Then the paper moves on to examine problems regarding solutes of very large size, as well as complex systems. An example of the latter is the surface enhancing properties of large metal cluster aggregates with respect to the optical properties of a chromophore in a liquid medium. The paper ends with some extrapolations to the near future, mostly based on the material presented in the preceding sections.Proceedings of the 11th International Congress of Quantum chemistry satellite meeting in honour of Jean-Louis Rivail     

Ab initio conformational maps in the gas phase and aqueous solution for a prototype of the glycosidic linkage

Ab initio conformational maps for methoxyethoxymethane (MEM) in both the gas phase and aqueous solution have been constructed using two different approaches. The results obtained allow us to conclude that a rigid conformational map is able to predict the regions of the minima, in the potential energy surface of MEM, in full agreement with those found in the relaxed conformational map, in both phases studied. This is a good indication that ab initio rigid conformational maps may be reliably used to sort the stablest conformers of disaccharides in aqueous solution. Besides that, in the MEM case, the solvation effects do not give rise to any new local minimum in its potential energy surface, but just change the relative energies of the stablest conformers found in the gas phase. This may be an indication that even in aqueous solution the anomeric effect is still the determinant effect defining the conformation of the molecule.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Rotational cooling of Li 2 ( 1 S g + ) molecules by ultracold collisions with a helium gas buffer

The very weak interaction of Li₂ with He atoms has been obtained from accurate ab initio calculations and is here analyzed in terms of its anisotropic features. Quantum scattering calculations of the rotational inelastic de-excitation cross sections are carried out using a recently proposed multichannel treatment, the modified variable phase method, implemented by the authors and applied here to ultralow collision energies. General conclusions on the low efficiency of a He buffer gas in cooling down molecular rotations in this system are presented and analyzed.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail.This work is affectionately dedicated to Prof. Jean-Louis Rivail on the occasion of his university retirement. We wish our friend many more happy years of research and the continued opportunity of guiding young scientists.     

Electrostatic effects in enzyme catalysis: a quantum mechanics/molecular mechanics study of the nucleophilic substitution reaction in haloalkane dehalogenase

Combined quantum mechanics/molecular mechanics molecular dynamics simulations have been carried out to study the cleavage of the carbon–chlorine bond in 1,2-dichloroethane catalysed by haloalkane dehalogenase from Xanthobacter Autotrophicus GJ10. The process has been compared with an adequate counterpart in aqueous solution, the nucleophilic attack of acetate anion on 1,2-dichloroethane. Within the limitations of the model, mainly due to the use of a semiempirical Hamiltonian, our results reproduce the magnitude and characteristics of the catalytic effect. Comparisons of the enzymatic and in solution potentials of mean force reveal that, irrespective of the reference state, the enzyme shows a larger affinity for the transition state. The origin of this increased affinity is found in the differences in the electrostatic pattern created by the environment in aqueous solution and in the enzyme.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Optimized parameters for continuum solvation calculations with carbohydrates

Continuum solvent models have been shown to be an efficient method for the calculation of the energetics of biomolecules in solution. However, for these methods to produce accurate results, an appropriate set of atomic radii or volumes is needed. While these have been developed for proteins and nucleic acids, the same is not true of carbohydrates. Here, a set of optimized parameters for continuum solvation calculations of carbohydrates in conjunction with the Carbohydrate Solution Force Field are presented. Explicit solvent free-energy perturbation simulations were performed on a set of hexapyranose sugars and used to fit atomic radii for Poisson-Boltzmann and generalized-Born calculations, and to fit atomic volumes for use with the analytical continuum electrostatics model. The solvation energetics computed with the optimized radii and a Poisson-Boltzmann model show remarkable agreement with explicit solvent simulation, with a root-mean-square error of 1.19 kcal/mol over a large test set of sugars in many conformations. The generalized-Born model gives slightly poorer agreement, but still correlates very strongly, with an error of 1.69 kcal/mol. The analytical continuum electrostatics model correlates well with the explicit solvent results, but gives a larger error of 4.71 kcal/mol. The remarkable agreement between the solvation free energies computed in explicit and implicit solvent provides strong motivation for the use of implicit solvent models in the simulation of carbohydrate-containing systems.     

Solvent effects on the asymmetric Diels–Alder reaction between cyclopentadiene and (−)-menthyl acrylate revisited with the three-layer hybrid local self-consistent field/molecular mechanics/self-consistent reaction field method

The construction of the three-layer hybrid local self-consistent field/molecular mechanics/self-consistent reaction field method is detailed. This method is specifically devoted to the study of the reactivity of large chemical systems in solution. The solvent, modeled by a polarizable continuum, surrounds the whole solute molecule. Solute–solvent interactions are taken into account by means of the self-consistent reaction field approach. The solute system is treated by both quantum and molecular mechanics, the former being principally applied to the reactive part, i.e., the part undertaking bond forming or breaking, the latter being reserved for the ancillary encumbering groups. The connection between the molecular mechanics and the quantum mechanics part is accomplished by a strictly localized bond orbital that remains frozen within the local self-consistent field framework. As a test system, the asymmetric Diels–Alder reaction between cyclopentadiene and (–)-menthyl acrylate is studied for the first time with steric interactions and electrostatic solvent effects taken into account simultaneously. The results indicate that the coupling of both interactions leads to conclusions that could not have been guessed from separate calculations.Proceedings of the 11th International Congress of Quantum chemistry satellite meeting in honour of Jean-Louis Rivail     

Effects of protonation on proton-transfer processes in guanine–cytosine Watson–Crick base pairs

Intermolecular proton-transfer processes in guanine–cytosine Watson–Crick base pairs have been studied using the B3LYP density functional method. Protonation of the base pair was carried out both at the N7 and at the O6 atoms of guanine. It is found that protonation induces a strengthening of the base pair and facilitates the N1–N3 single-proton-transfer reaction. The double-proton-transfer reaction, however, turns out to be unfeasible when the system is protonated at these sites. Mutagenic implications of these proton-transfer processes are discussed.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Homolytic dissociation in hydrogen-bonding liquids: energetics of the phenol O–H bond in methanol and the water O–H bond in water

The energetics of the phenol O–H bond in methanol and the water O–H bond in liquid water were investigated by microsolvation modelling and statistical mechanics Monte Carlo simulations. The microsolvation approach was based on density functional theory calculations. Optimised structures for clusters of phenol and the phenoxy radical with one and two methanol molecules are reported. By analysing the differential solvation of phenol and the phenoxy radical in methanol, we predict that the phenol O–H homolytic bond dissociation enthalpy in solution is 24.3±11 kJ/mol above the gas-phase value. The analysis of the water O–H bond dissociation by microsolvation was based on optimised structures of OH–(H₂O)_1–6 and –(H₂O)_1–7 clusters. Microsolvation modelling and statistical mechanics simulations predict that the HO–H bond dissociation enthalpies in the gas phase and in liquid water are very similar. Our results stress the importance of estimating the differences between the solvation enthalpies of the radical species and the parent molecule and the limitations of local models based on microsolvation.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Calculating pKa values for substituted phenols and hydration energies for other compounds with the first‐order fuzzy‐border continuum solvation model

We have computed pK_a values for 11 substituted phenol compounds using the continuum Fuzzy‐Border (FB) solvation model. Hydration energies for 40 other compounds, including alkanes, alkenes, alkynes, ketones, amines, alcohols, ethers, aromatics, amides, heterocycles, thiols, sulfides, and acids have been calculated. The overall average unsigned error in the calculated acidity constant values was equal to 0.41 pH units and the average error in the solvation energies was 0.076 kcal/mol. We have also reproduced pK_a values of propanoic and butanoic acids within about 0.1 pH units from the experimental values by fitting the solvation parameters for carboxylate ion carbon and oxygen atoms. The FB model combines two distinguishing features. First, it limits the amount of noise which is common in numerical treatment of continuum solvation models by using fixed‐position grid points. Second, it uses either second‐ or first‐order approximation for the solvent polarization, depending on a particular implementation. These approximations are similar to those used for solute and explicit solvent fast polarization treatment which we developed previously. This article describes results of using the first‐order technique. This approximation places the presented methodology between the Generalized Born and Poisson‐Boltzmann continuum solvation models with respect to their accuracy of reproducing the many‐body effects in modeling a continuum solvent. © 2012 Wiley Periodicals, Inc.     

Accurate predictions of nonpolar solvation free energies require explicit consideration of binding-site hydration

Continuum solvation methods are frequently used to increase the efficiency of computational methods to estimate free energies. In this paper, we have evaluated how well such methods estimate the nonpolar solvation free-energy change when a ligand binds to a protein. Three different continuum methods at various levels of approximation were considered, viz., the polarized continuum model (PCM), a method based on cavity and dispersion terms (CD), and a method based on a linear relation to the solvent-accessible surface area (SASA). Formally rigorous double-decoupling thermodynamic integration was used as a benchmark for the continuum methods. We have studied four protein-ligand complexes with binding sites of varying solvent exposure, namely the binding of phenol to ferritin, a biotin analogue to avidin, 2-aminobenzimidazole to trypsin, and a substituted galactoside to galectin-3. For ferritin and avidin, which have relatively hidden binding sites, rather accurate nonpolar solvation free energies could be obtained with the continuum methods if the binding site is prohibited to be filled by continuum water in the unbound state, even though the simulations and experiments show that the ligand replaces several water molecules upon binding. For the more solvent exposed binding sites of trypsin and galectin-3, no accurate continuum estimates could be obtained, even if the binding site was allowed or prohibited to be filled by continuum water. This shows that continuum methods fail to give accurate free energies on a wide range of systems with varying solvent exposure because they lack a microscopic picture of binding-site hydration as well as information about the entropy of water molecules that are in the binding site before the ligand binds. Consequently, binding affinity estimates based upon continuum solvation methods will give absolute binding energies that may differ by up to 200 kJ/mol depending on the method used. Moreover, even relative energies between ligands with the same scaffold may differ by up to 75 kJ/mol. We have tried to improve the continuum solvation methods by adding information about the solvent exposure of the binding site or the hydration of the binding site, and the results are promising at least for this small set of complexes.     

Computation of pKa values of substituted aniline radical cations in dimethylsulfoxide solution

A newly developed computation strategy was used to calculate the absolute pKa values of 18 substituted aniline radical cations in dimethylsulfoxide (DMSO) solution with the error origin elucidated and deviation minimized. The B3LYP/6-311++G(2df,2p) method was applied and was found to be capable of reproducing the gas-phase proton-transfer free energies of substituted anilines with a precision of 0.83 kcal/mol. The IEF-PCM solvation model with gas-phase optimized structures was adopted in calculating the pKa values of the substituted neutral anilines in DMSO, regenerating the experimental results within a standard deviation of 0.4 pKa unit. When the IEF-PCM solvation model was applied to calculate the standard redox potentials of anilide anions, it showed that the computed values agreed well with experiment, but the redox potentials of substituted anilines were systematically overestimated by 0.304 eV. The cause of this deviation was found to be related to the inaccuracy of the calculated solvation free energies of aniline radical cations. By adjusting the size of the cavity in the IEF-PCM method, we derived a reliable procedure that can reproduce the experimental pKa values of aniline radical cations within 1.2 pKa units to those from experiment.     

Thermochemistry of arylselanyl radicals and the pertinent ions in acetonitrile

Reduction and oxidation potentials of a series of parasubstituted phenylselanyl radicals, XC(6)H(4)Se(*), have been measured using photomodulated voltammetry in acetonitrile. The thermodynamic significance of these data was substantiated through a study of the oxidation process of the pertinent selenolates in linear sweep voltammetry. Both the reduction and the oxidation potentials correlate linearly with the Hammett substituent coefficients sigma and sigma(+) leading in the latter case to slopes, rho(+), of 2.5 and 3.8, respectively. Through comparison of these slopes with those published previously for the O- and S-centered analogues, it is revealed that the pi-interaction becomes progressively smaller as the size of the radical center increases in the order O, S, and Se. Solvation energies of the pertinent selenolates and selanylium ions have been extracted from thermochemical cycles incorporating the measured electrode potentials for XC(6)H(4)Se(*) as well as electron affinities and ionization potentials obtained from theoretical calculations at the B3LYP/6-31+G(d) level. The extracted data show the expected overall substituent dependency for both kinds of ions; that is, the absolute value of the solvation energy decreases as the charge becomes more delocalized. The data have also been compared with solvation energies computed using the polarizable continuum model (PCM). Interestingly, we find that, while the model seems to work well for selenolates, it underestimates the solvation of selanylium ions in acetonitrile by as much as 25 kcal mol(-)(1). These large deviations are ascribed to the fact that the PCM method does not take specific solvent effects into account as it treats the solvent as a continuum described solely by its dielectric constant. Gas-phase calculations show that the arylselanylium ions can coordinate covalently to one or two molecules of acetonitrile in strong Ritter-type adducts. When this strong interaction is included in the solvation energy calculations by means of a combined supermolecule and PCM approach, the experimental data are reproduced within a few kcal mol(-)(1). Although the energy difference of the singlet and triplet spin states of the arylselanylium ions is small for the gas-phase structures, the singlet cation is undoubtedly the dominating species in solution because the triplet cation lacks the ability to form covalent bonds.     

Incorporation of solvent effects into density functional predictions of molecular polarizabilities and hyperpolarizabilities

A study of the effect of the field, the basis set, the functional, and the cavity size on molecular polarizabilities and hyperpolarizabilities of substituted benzenes in liquid or solution is reported. The calculations have been performed using the density functional theory (DFT) within the conductor‐like screening model (COSMO). The optimized computational parameters are adopted to calculate molecular polarizabilities and hyperpolarizabilities of substituted benzenes in liquid or solution. The results show good agreement with the experimental values. From comparison of the different theoretical results, it is found that at the same theoretical level, the selection of the different solvation models may play an important role in the calculations of molecular solvation polarizability, and using the same solvation model, the effects of the different theoretical methods are relatively small. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Solvation oscillations and excited-state dynamics of 2-amino- and 2-hydroxy-7-nitrofluorene and its 2'-deoxyriboside

Push-pull substituted fluorenes are considered for use as dynamic solvation probes in polynucleotides. Their fluorescence band is predicted (by simulations) to show weak spectral oscillations on the subpicosecond time scale depending on the nucleotide sequence. The oscillations reflect the local far-infrared spectrum of the environment around the probe molecule. A connection is provided by the continuum theory of polar solvation which, however, neglects molecular aspects. We examine the latter using acetonitrile solution as a test case. A collective librational solvent mode at 100 cm(-1) is observed with 2-amino-7-nitrofluorene, 2-dimethylamino-7-nitrofluorene, 2-hydroxy-7-nitrofluorene, and its 2'-deoxyriboside. Different strengths of the oscillation indicate that rotational friction of nearby acetonitrile molecules depends on the solute structure or that H bonding is involved in launching the librational coherence. Polar solvation in methanol is used for comparison. With hydroxynitrofluorenes, the observation window is limited by intersystem crossing for which rates are reported. A prominent excited-state absorption band of nitrofluorenes at 430 nm can be used to monitor polar solvation. Structural and electronic relaxation pathways are discussed with the help of quantum chemical calculations.     

Predicting hydration free energies of polychlorinated aromatic compounds from the SAMPL-3 data set with FiSH and LIE models

Next-generation solvation models are devised to mimic the accuracy and generality of explicit solvation models at the speed of current popular implicit solvation models. One such method is the first-shell of hydration (FiSH) continuum model that was trained on hydration energetics from LIE calculations and molecular dynamics simulations in explicit solvent. Here we tested prospectively the FiSH model on the SAMPL-3 hydration data set that zooms in the effect of chlorination on solvation. We compare these FiSH predictions with those from retrospective LIE calculations. We find that neither FiSH nor LIE can reproduce well the absolute values and the trend of hydration free energies in the biphenyl and dioxin aromatic chlorination series. Some of the hypotheses behind this performance are discussed and tested. The LIE explicit-solvent model shows some improvement relative to the FiSH continuum model, and we correct a systematic deviation in the continuum van der Waals term of FiSH associated with aromatic Cl atom type.     

Cope elimination: elucidation of solvent effects from QM/MM simulations

The Cope elimination reactions for threo- and erythro-N,N-dimethyl-3-phenyl-2-butylamine oxide have been investigated using QM/MM calculations in water, THF, and DMSO. The aprotic solvents provide up to million-fold rate accelerations. The effects of solvation on the reactants, transition structures, and rates of reaction are elucidated here using two-dimensional potentials of mean force (PMF) derived from free-energy perturbation calculations in Monte Carlo simulations (MC/FEP). The resultant free energies of activation in solution are in close agreement with experiment. Ab initio calculations at the MP2/6-311+G-(2d,p) level using the PCM continuum solvent model were also carried out; however, only the QM/MM methodology was able to reproduce the large rate increases in proceeding from water to the dipolar aprotic solvents. Solute-solvent interaction energies and radial distribution functions are also analyzed and show that poorer solvation of the reactant in the aprotic solvents is primarily responsible for the observed rate enhancements. It is found that the amine oxide oxygen is the acceptor of three hydrogen bonds from water molecules for the reactant but only one to two weaker ones at the transition state. The overall quantitative success of the computations supports the present QM/MM/MC approach, featuring PDDG/PM3 as the QM method.     

COSMO-RS: A novel view to physiological solvation and partition questions

Both, dielectric continuum solvation models as well as surface or group based methods using polarity and lipophilicity parameters have been proven to be useful tools for the analysis of solvation and partition questions. For the first time, COSMO-RS provides an integrated theory, which combines the aspects of continuum solvation and surface interactions, and which ends up with chemical potentials of molecules in almost arbitrary solvents and mixtures. Due to its sound theoretical basis, COSMO-RS does not only provide a new quantitative access to solvation and partition properties in well defined solvents, but it also opens a novel view and gives a better understanding of the general problem of solvation. Finally, this allows for a generalisation of COSMO-RS to sophisticatedphysiological partition problems involving as complex phases as blood, brain, or cell membranes. The use of COSMO-RS for drug discovery and design is demonstrated by applications to blood-brain partition coefficients, and water solubility.     

Combined quantum mechanical and molecular mechanical simulations of one- and two-electron reduction potentials of flavin cofactor in water, medium-chain acyl-CoA dehydrogenase, and cholesterol oxidase

Flavin adenine dinucleotide (FAD) is a common cofactor in redox proteins, and its reduction potentials are controlled by the protein environment. This regulation is mainly responsible for the versatile catalytic functions of flavoenzymes. In this article, we report computations of the reduction potentials of FAD in medium-chain acyl-CoA dehydrogenase (MCAD) and cholesterol oxidase (CHOX). In addition, the reduction potentials of lumiflavin in aqueous solution have also been computed. Using molecular dynamics and free-energy perturbation techniques, we obtained the free-energy changes for two-electron/two-proton as well as one-electron/one-proton addition steps. We employed a combined quantum mechanical and molecular mechanical (QM/MM) potential, in which the flavin ring was represented by the self-consistent-charge density functional tight-binding (SCC-DFTB) method, while the rest of the enzyme-solvent system was treated by classical force fields. The computed two-electron/two-proton reduction potentials for lumiflavin and the two enzyme-bound FADs are in reasonable agreement with experimental data. The calculations also yielded the pKa values for the one-electron reduced semiquinone (FH*) and the fully reduced hydroquinone (FH2) forms. The pKa of the FAD semiquinone in CHOX was found to be around 4, which is 4 units lower than that in the enzyme-free state and 2 units lower than that in MCAD; this supports the notion that oxidases have a greater ability than dehydrogenases to stabilize anionic semiquinones. In MCAD, the flavin ring interacts with four hydrophobic residues and has a significantly bent structure, even in the oxidized state. The present study shows that this bending of the flavin imparts a significant destabilization (approximately 5 kcal/mol) to the oxidized state. The reduction potential of lumiflavin was also computed using DFT (M06-L and B3LYP functionals with 6-31+G(d,p) basis set) with the SM6 continuum solvation model, and the results are in good agreement with results from explicit free-energy simulations, which supports the conclusion that the SCC-DFTB/MM computation is reasonably accurate for both 1e(-)/1H+ and 2e(-)/2H+ reduction processes. These results suggest that the first coupled electron-proton addition is stepwise for both the free and the two enzyme-bound flavins. In contrast, the second coupled electron-proton addition is also stepwise for the free flavin but is likely to be concerted when the flavin is bound to either the dehydrogenase or the oxidase enzyme.     

Microsolvated transition state models for improved insight into chemical properties and reaction mechanisms

Over the years, several methods have been developed to effectively represent the chemical behavior of solutes in solvents. The environmental effects arising due to solvation can generally be achieved either through inclusion of discrete solvent molecules or by inscribing into a cavity in a homogeneous and continuum dielectric medium. In both these approaches of computational origin, the perturbations on the solute induced by the surrounding solvent are at the focus of the problem. While the rigor and method of inclusion of solvent effects vary, such solvation models have found widespread applications, as evident from modern chemical literature. A hybrid method, commonly referred to as cluster-continuum model (CCM), brings together the key advantages of discrete and continuum models. In this perspective, we intend to highlight the latent potential of CCM toward obtaining accurate estimates on a number of properties as well as reactions of contemporary significance. The objective has generally been achieved by choosing illustrative examples from the literature, besides expending efforts to bring out the complementary advantages of CCM as compared to continuum or discrete solvation models. The majority of examples emanate from the prevalent applications of CCM to organic reactions, although a handful of interesting organometallic reactions have also been discussed. In addition, increasingly accurate computations of properties like pK(a) and solvation of ions obtained using the CCM protocol are also presented.