"Free Energies of Solvation with Surface, Volume, and Local Electrostatic Effects and Atomic Surface Tensions to Represent the First Solvation Shell," J. Liu, C. P. Kelly, A. C. Goren, A. V. Marenich, C. J. Cramer, D. G. Truhlar, C.-G. Zhan, Journal of Chemical Theory and Computations, 6, 1109-1117 (2010).
Abstract.Building on the SVPE (surface and volume polarization for electrostatics) model for electrostatic contributions to the free energy of solvation with explicit consideration of both surface and volume polarization effects, on the SMx approach to including first-solvation-shell contributions, and on the linear relationship between the electric field and short-range electrostatic contributions found by Chipman, we have developed a new method for computing absolute aqueous solvation free energies by combining the SVPE method with semiempirical terms that account for effects beyond bulk electrostatics. The new method is called SMVLE, and the elements it contains are denoted by SVPE-CDSL, where SVPE denotes accounting for bulk electrostatic interactions between solute and solvent with both surface and volume contributions, CDS denotes the inclusion of solvent cavitation, changes in dispersion energy, and possible changes in local solvent structure by a semiempirical term utilizing geometry-dependent atomic surface tensions as implemented in SMx models, and L represents the local electrostatic effect derived from the outward-directed normal electric field on the cavity surface. The semiempirical CDS and L terms together represent the deviation of short-range contributions to the free energy of solvation from those accounted for by the SVPE term based on the bulk solvent dielectric constant. A solute training set containing a broad range of molecules used previously in the development of SM6 is used here for SMVLE model calibration. The aqueous solvation free energies predicted by the parametrized SMVLE model correlate exceedingly well with experimental values. The square of the correlation coefficient is 0.9949 and the slope is 1.0079. Comparison of the final SMVLE model against the earlier SMx solvation model shows that the parametrized SMVLE model not only yields good accuracy for neutrals but also significantly increases the accuracy for ions, making it the best implicit solvation model to date for aqueous solvation free energies of ions. The semiempirical terms associated with the outward-directed electric field account in a physical way for the improvement in the predictive accuracy for ions. The SMVLE method greatly decreases the need to include explicit water molecules for accurate modeling of solvation free energies of ions.
"Sorting Out the Relative Contributions of Electrostatic Polarization, Dispersion, and Hydrogen Bonding to Solvatochromic Shifts on Vertical Electronic Excitation Energies," A. V. Marenich, C. J. Cramer, and D. G. Truhlar, Journal of Chemical Theory and Computations, 6, 2829-2844 (2010).
Abstract.Conventional polarized continuum model calculations of solvatochromic shifts on electronic excitation energies using popular quantum chemical programs (e.g., Gaussian or Turbomole) include the noninertial and inertial bulk-solvent polarization, which will be called electrostatics, but not dispersion interactions and specific effects like hydrogen bonding. For the n-pi* excitation of acetone in several solvents, we estimated the nonelectrostatic contributions in two ways: (i) the vertical excitation model (VEM) of Li et al. (Int. J. Quantum Chem. 2000, 77, 264), but updated to use TD-DFT corrected linear response with SMD atomic radii, and (ii) in the case of acetone in water, ensemble averaging over supermolecule calculations with up to 12 explicit solvent molecules selected from a molecular dynamics trajectory, with the explicit solvent surrounded by a continuum solvent. The TD-DFT VEM calculations carried out with the M06 density functional for 23 solvents result in a dispersion contribution to the red of 261-356 cm-1 and a hydrogen-bonding contribution to the blue of up to 289 cm-1.
"Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions," A. V. Marenich, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry B, 113, 6378-6396 (2009).
Abstract. We present a new continuum solvation model based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent. The model is called SMD, where the "SD" stands for "density" to denote that the full solute electron density is used without defining partial atomic charges. "Continuum" denotes that the solvent is not represented explicitly but rather as a dielectric medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where "universal" denotes its applicability to any charged or uncharged solute in any solvent or liquid medium for which a few key descriptors are known (in particular, dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the solution of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calculation are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality constants called atomic surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aqueous ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and dimethyl sulfoxide, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaqueous organic solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 organic solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic atomic Coulomb radii and atomic surface tension coefficients) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G*, M05-2X/6-31+G**, M05-2X/cc-pVTZ, B3LYP/6-31G*, and HF/6-31G*. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calculations in which the solute is represented by its electron density in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6?1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions with either Gaussian03 or GAMESS.
"Universal Solvation Model Based on the Generalized Born Approximation with Asymmetric Descreening," A. V. Marenich, C. J. Cramer, and D. G. Truhlar, Journal of Chemical Theory and Computations, 5, 2447-2464 (2009).
Abstract.We present a new self-consistent reaction field continuum solvation model based on the generalized Born (GB) approximation for the bulk electrostatic contribution to the free energy of solvation. The new model improves on the earlier SM8 model by using the asymmetric descreening algorithm of Grycuk to treat dielectric descreening effects rather than the Coulomb field approximation; it will be called Solvation Model 8 with asymmetric descreening (SM8AD). The SM8AD model is applicable to any charged or uncharged solute in any solvent or liquid medium for which a few key descriptors are known, in particular dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters. It does not require the user to assign molecular mechanics types to an atom or a group; all parameters are unique and continuous functions of geometry. This model employs a single set of parameters (solvent acidity-dependent intrinsic Coulomb radii for the treatment of bulk electrostatics and solvent description-dependent atomic surface tensions coefficients for the treatment of nonelectrostatic and short-range electrostatic effects). The SM8AD model was optimized over 26 combinations of theoretical levels including various basis sets (MIDI!, 6-31G*, 6-31+G*, 6-31+G**, 6-31G**, cc-pVDZ, DZVP, 6-31B*) and electronic structure methods (M05-2X, M05, M06-2X, M06, M06-HF, M06-L, mPW1PW, mPWPW, B3LYP, HF). It may be used with confidence with any level of electronic structure theory as long as self-consistently polarized Charge Model 4 or other self-consistently polarized charges compatible with CM4 charges are used, for example, CM4M charges can be used. With M05-2X/6-31G*, the SM8AD model achieves a mean unsigned error of 0.6 kcal/mol on average over 2560 solvation free energies of tested aqueous and nonaqueous neutral solutes and a mean unsigned error of 3.9 kcal/mol on average over 332 solvation free energies of aqueous and nonaqueous ions.
"Extension of a Temperature-Dependent Aqueous Solvation Model to Compounds Containing Nitrogen, Fluorine, Chlorine, Bromine, and Sulfur," A. C. Chamberlin, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry B, 112, 3024-3039 (2008).
Abstract. Most methods for predicting free energies of solvation have been developed or validated exclusively for room temperature. Recently, we developed a model called SM6T for predicting aqueous solvation free energies as a function of temperature for solutes composed of C, H, or O, and here we present solvation model 8 with temperature dependence (SM8T) for predicting the temperature dependence of aqueous free energies of solvation for compounds containing H, C, N, O, F, S, Cl, and Br in the range 273-373 K. We also describe the database of experimental aqueous free energies of solvation used to parametrize the model. SM8T partitions the temperature dependence of the free energy of solvation into two components: the temperature dependence of the bulk electrostatic contribution to the free energy of solvation, which is computed using the generalized Born equation, and the temperature dependence of first-solvation-shell effects, which is modeled by terms proportional to the solvent-exposed surface areas of atoms in functional groups determined entirely by geometry. SM8T predicts the temperature dependence of aqueous free energies of solvation with a mean unsigned error of 0.08 kcal/mol over a database of 4403 measurements on 348 compounds at various temperatures. We also discuss the accuracy of SM8T for predicting the temperature dependence of aqueous free energies of solvation for ions and present free energies of solvation as a function of temperature for two sample ions.
"Self-Consistent Reaction Field Model for Aqueous and Nonaqueous Solutions Based on Accurate Polarized Partial Charges," A. V. Marenich, R. M. Olson, C. P. Kelly, C. J. Cramer, and D. G. Truhlar, Journal of Chemical Theory and Computations, 3, 2011-2033 (2007).
Abstract. A new universal continuum solvation model (where "universal" denotes applicable to all solvents), called SM8, is presented. It is an implicit solvation model, also called a continuum solvation model, and it improves on earlier SMx universal solvation models by including free energies of solvation of ions in nonaqueous media in the parametrization. SM8 is applicable to any charged or uncharged solute composed of H, C, N, O, F, Si, P, S, Cl, and/or Br in any solvent or liquid medium for which a few key descriptors are known, in particular dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters. It does not require the user to assign molecular-mechanics types to an atom or group; all parameters are unique and continuous functions of geometry. It may be used with any level of electronic structure theory as long as accurate partial charges can be computed for that level of theory; we recommend using it with self-consistently polarized Charge Model 4 or other self-consistently polarized class IV charges, in which case analytic gradients are available. The model separates the observable solvation free energy into two components: the long-range bulk electrostatic contribution arising from a self-consistent reaction field treatment using the generalized Born approximation for electrostatics is augmented by the non-bulk-electrostatic contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell. The cavities for the bulk electrostatics calculation are defined by superpositions of nuclear-centered spheres whose sizes are determined by intrinsic atomic Coulomb radii. The radii used for aqueous solution are the same as parametrized previously for the SM6 aqueous solvation model, and the radii for nonaqueous solution are parametrized by a training set of 220 bare ions and 21 clustered ions in acetonitrile, methanol, and dimethyl sulfoxide. The non-bulk-electrostatic terms are proportional to the solvent-accessible surface areas of the atoms of the solute and have been parametrized using solvation free energies for a training set of 2346 solvation free energies for 318 neutral solutes in 90 nonaqueous solvents and water and 143 transfer free energies for 93 neutral solutes between water and 15 organic solvents. The model is tested with three density functionals and with four basis sets: 6-31+G(d,p), 6-31+G(d), 6-31G(d), and MIDI!6D. The SM8 model achieves mean unsigned errors of 0.5-0.8 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 2.2-7.0 kcal/mol for ions. The model outperforms the earlier SM5.43R and SM7 universal solvation models as well as the default Polarizable Continuum Model (PCM) implemented in Gaussian 98/03, the Conductor-like PCM as implemented in GAMESS, Jaguar's continuum model based on numerical solution of the Poisson equation, and the GCOSMO model implemented in NWChem.
"Predicting Aqueous Free Energies of Solvation as Functions of Temperature," A. C. Chamberlin, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry B, 110, 5665-5675 (2006).
Abstract. This work introduces a model, solvation model 6 with temperature dependence (SM6T), to predict the temperature dependence of aqueous free energies of solvation for compounds containing H, C, and O in the range 273-373 K. In particular, we extend solvation model 6 (SM6), which was previously developed (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theory Comput. 2005, 1, 1133) for predicting aqueous free energies of solvation at 298 K, to predict the variation of the free energy of solvation relative to 298 K. Also, we describe the database of experimental aqueous free energies of solvation for compounds containing H, C, and O that was used to parametrize and test the new model. SM6T partitions the temperature dependence of the free energy of solvation into two components: the temperature dependence of the bulk electrostatic contribution to the free energy of solvation, which is computed using the generalized Born equation, and the temperature dependence of first-solvation-shell effects which is modeled using a parametrized solvent-exposed surface-area-dependent term. We found that SM6T predicts the temperature dependence of aqueous free energies of solvation with a mean unsigned error of 0.08 kcal/mol over our entire database, whereas using the experimental value at 298 K produces a mean unsigned error of 0.53 kcal/mol.
"Adding Explicit Solvent Molecules to Continuum Solvent Calculations for the Calculation of Aqueous Acid Dissociation Constants,", C. P. Kelly, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry A, 110, 2493-2499 (2006).
Abstract. Aqueous acid dissociation free energies for a diverse set of 57 monoprotic acids have been calculated using a combination of experimental and calculated gas and liquid-phase free energies. For ionic species, aqueous solvation free energies were calculated using the recently developed SM6 continuum solvation model (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theory Comput. 2005, 1, 1133). This model combines a dielectric continuum with atomic surface tensions to account for bulk solvent effects. For some of the acids studied, a combined approach that involves attaching a single explicit water molecule to the conjugate base (anion), and then surrounding the resulting anion-water cluster by a dielectric continuum, significantly improves the agreement between the calculated pKa value and experiment. This suggests that for some anions, particularly those concentrating charge on a single exposed heteroatom, augmenting implicit solvent calculations with a single explicit water molecule is required, and adequate, to account for strong short-range hydrogen bonding interactions between the anion and the solvent. We also demonstrate the effect of adding several explicit waters by calculating the pKa of bicarbonate (HCO3-) using as the conjugate base carbonate (CO32-) bound by up to three explicit water molecules.
"Density Functional and Hybrid DFT SM5.43R Continuum Solvation Models for Aqueous and Organic Solvents," J. D. Thompson, C. J. Cramer, and D. G. Truhlar, Theoretical Chemistry Accounts, 113, 107-131 (2005).
Abstract. Hybrid density functional theory, which is a combined Hartree-Fock and density functional method, provides a simple but effective way to incorporate nonlocal exchange effects and static and dynamical correlation energy into an orbital-based theory with affordable computational cost for many important problems of gas-phase chemistry. The inclusion of a reaction field representing an implicit solvent in a self-consistent hybrid density functional calculation provides an effective and efficient way to extend this approach to problems of liquid-phase chemistry. In previous work, we have parameterized several models based on this approach, and in the present article, we present several new parameterizations based on implicit solvation models SM5.43 and SM5.43R. In particular, we extend the applicability of these solvation models to several combinations of the MPWX hybrid-density functional with various one-electron basis sets, where MPWX denotes a combination of Barone and Adamorsquos modified version of Perdew and Wangrsquos exchange functional, Perdew and Wangrsquos correlation functional, and a percentage X of exact Hartree-Fock exchange. SM5.43R parameter optimizations are presented for the MPWX/MIDI!, MPWX/MIDI!6D, and MPWX/6-31+G(d,p) combinations with X=0 (i.e., pure density functional theory), 25, 42.8, and 60.6, and for MPWX/6-31G(d) and MPWX/6-31+G(d), with X=0, 42.8, and 60.6; this constitutes a total of 18 new parameter sets. [Note that parameter optimizations using MPW25/6-31G(d) and MPW25/6-31+G(d) were carried out in a previous SM5.43R parameterization.] For each of the five basis sets, we found no significant loss in the accuracy of the model when parameters averaged over the four values of X are used instead of the parameters optimized for a specific value of X. Therefore for each of the five basis sets used here, the SM5.43R and SM5.43 models are defined to have a single parameter set that can be used for any value of X between 0 and 60.6. The new models yield accurate free energies of solvation for a broad range of solutes in both water and organic solvents. On the average, the mean-unsigned errors, as compared with those from experiment, of the free energies of solvation of neutral solutes range from 0.50 to 0.55 kcal/mol and those for ions range from 4.5 to 4.9 kcal/mol. Since the SM5.43R model computes the free energy of solvation as a sum of bulk-electrostatic and non-bulk-electrostatic contributions, it may be used for detailed analysis of the physical effects underlying a calculation of the free energy of solvation. Several calculations illustrating the partitioning of these contributions for a variety of solutes in n-hexadecane, 1-octanol, and water are presented.
"SM6: A Density Functional Theory Continuum Solvation Model for Calculating Aqueous Solvation Free Energies of Neutrals, Ions, and Solute-Water Clusters" C. P. Kelly, C. J. Cramer, and D. G. Truhlar, Journal of Chemical Theory and Computation, 1, 1133-1151 (2005).
A new charge model, called Charge Model 4 (CM4), and a new continuum solvent model, called Solvation Model 6 (SM6), are presented. Using a database of aqueous solvation free energies for 273 neutrals, 112 ions, and 31 ion-water clusters, parameter sets for the mPW0 hybrid density functional of Adamo and Barone (Adamo, C.; Barone, V. J. Chem. Phys. 1998, 108, 664-675) were optimized for use with the following four basis sets: MIDI!6D, 6-31G(d), 6-31+G(d), and 6-31+G(d,p). SM6 separates the observable aqueous solvation free energy into two different components: one arising from long-range bulk electrostatic effects and a second from short-range interactions between the solute and solvent molecules in the first solvation shell. This partition of the observable solvation free energy allows SM6 to effectively model a wide range of solutes. For the 273 neutral solutes in the test set, SM6 achieves an average error of ~0.50 kcal/mol in the aqueous solvation free energies. For solutes, especially ions, that have highly concentrated regions of charge density, adding an explicit water molecule to the calculation significantly improves the performance of SM6 for predicting solvation free energies. The performance of SM6 was tested against several other continuum models, including SM5.43R and several different implementations of the Polarizable Continuum Model (PCM). For both neutral and ionic solutes, SM6 outperforms all of the models against which it was tested. Also, SM6 is the only model (except for one with an average error 3.4 times larger) that improves when an explicit solvent molecule is added to solutes with concentrated charge densities. Thus, in SM6, unlike the other continuum models tested here, adding one or more explicit solvent molecules to the calculation is an effective strategy for improving the prediction of the aqueous solvation free energies of solutes with strong local solute-solvent interactions. This is important, because local solute-solvent interactions are not specifically accounted for by bulk electrostatics, but modeling these interactions correctly is important for predicting the aqueous solvation free energies of certain solutes. Finally, SM6 retains its accuracy when used in conjunction with the B3LYP and B3PW91 functionals, and in fact the solvation parameters obtained with a given basis set may be used with any good density functional or fraction of Hartree-Fock exchange.
Abstract. Vapor-phase molecules are adsorbed at air-water interfaces to a much greater extent than can be explained by air-water partition coefficients, indicating that interface adsorption can play an important role, and this can be very important for environmental phenomena. On the basis of a statistical thermodynamic analysis, we separate the observable free energy of adsorption into a dimensionality change and a coupling part so that the modeling effort is correctly focused on the coupling part. On the basis of this analysis, we present two kinds of models for predicting partitioning between the vapor phase and the macroscopic surface of liquid water. The first model, called SM5.0R-Surf, involves atomic surface tensions developed previously for bulk solvation in organic liquids and a set of four solvent descriptors that characterize the properties of the water layer at the air-water interface. The latter descriptors are treated as parameters that are determined empirically by optimization for a set of 85 solutes for which the air-water surface adsorption coefficients (Ki/a) are known experimentally. The resulting descriptors indicate that interfacial water has increased hydrogen-bond acidity and increased hydrogen-bond basicity as compared to bulk water. A second kind of model involves an empirical correlation of the interfacial-water partition coefficient Ki/w with the calculated van der Waals surface area, and this kind of model can be based either on experimental data, yielding the semiempirical surface area (SESA) model, or on theoretical data, yielding the semitheoretical surface area (STSA) model. The SM5.0R-Surf and STSA models should be especially useful for environmental modeling because neither model requires any experimental data about the solute, other than its molecular structure. As an example, we use the above models to calculate air-water adsorption coefficients for 24 different pesticides, chlorinated arenes, and polyaromatic hydrocarbons (PAHs). We also show that several models in the literature can be used successfully even if we substitute calculated instead of experimental data for the solute parameters that they originally required. In related work reported here, the SM5.0R parametrization for predicting free energies of solvation in organic solvents is extended to include solutes containing phosphorus. This extension is based on the experimental free energies of 13 solutes in 9 organic solvents (37 data points). The SM5.0R model extended in this way and the new SM5.0R-Surf model can therefore be used to predict the free energy of solvation at air-water interfaces and in bulk organic liquids for any solute composed of H, C, N, O, F, S, Cl, Br, I, and/or P, whereas the STSA model does not contain parameters that depend on atomic number and can, in principle, be used for any molecule.
"New Universal Solvation Model and Comparison of the Accuracy of Three Continuum Solvation Models, SM5.42R, SM5.43R, and C-PCM, in Aqueous Solution and Organic Solvents and for Vapor Pressures," J. D. Thompson, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry 108, 6532-6542 (2004).
Abstract.We present a new continuum solvation model, called Solvation Model 5.43R (SM5.43R). The model is based on the generalized Born approximation for electrostatics augmented by terms that are proportional to the solvent-accessible surface areas (SASAs) of the atoms of the solute, and it is parametrized to predict the free energy of solvation of solutes containing H, C, N, O, F, P, S, Cl, and Br in water and organic solvents. The new model is an improvement over our previous solvation model, SM5.42R, in that it is based on CM3 charges rather than CM2 charges, it was trained over a larger and more diverse training set, and the choice of the value of the solvent radius, which is used to compute the SASA of the atoms of the solute, was made on a different basis than was used for SM5.42R. This paper presents parametrizations of SM5.43R using HF/6-31G(d), B3LYP/6-31G(d), mPW1PW91/6-31G(d), and mPW1PW91/6-31+G(d) to describe the electronic structure of the solute. For a data set of neutral solutes with known experimental aqueous free energies of solvation containing at most H, C, N, O, F, P, S, Cl, and Br (257 data), the mean-unsigned error (MUE, in kcal/mol), as compared to experiment, calculated by SM5.43R is respectively 0.50, 0.49, 0.50, and 0.54 using these four solute wave functions. A similar MUE is obtained for SM5.42R using HF/6-31G(d). The corresponding MUEs calculated by several other generally available continuum solvation models are approximately a factor of 2 larger than those computed by SM5.43R and SM5.42R using the same electronic structure methods. For a data set of solutes with experimental free energies of solvation in 16 organic solvents (621 data), SM5.43R and SM5.42R yield MUEs 6.3 to 7.9 times smaller than the MUEs calculated by the other continuum solvation models. The SM5.43R model is, however, universal in that it can be used in any organic solvent, as well as water. Furthermore, it allows one to analyze solvation trends in terms of local properties, and this is illustrated for acetanilide in water and diethyl ether.
Abstract. The SM5.42 solvation model is extended to include compounds containing Si. The new parameters are based on a data set of 13 octanol/water partition coefficients (which we convert into 13 differential free energies of solvation), three absolute solvation energies, and one pKa. The data set includes compounds containing C, H, O, and Si. We carried out parametrizations using compounds in the data set that do not contain bonds between Si and O (i.e., eight differential free energies of solvation and three absolute free energies of solvation for nine compounds) at the HF/MIDI!, HF/MIDI!6D, HF/6-31G*, HF/6-31+G*, HF/cc-pVDZ, BPW91/MIDI!, BPW91/MIDI!6D, BPW91/DVZP, B3LYP/MIDI!, AM1, and PM3 levels of theory. The mean unsigned errors over the eight differential free energies of solvation and three absolute solvation energies for these levels of theory are in the range of 0.48-0.53 kcal/mol. We used five additional differential free energies of solvation for five compounds that do contain O-Si bonds to parametrize the BPW91/6-31G* level of theory. The resulting mean unsigned error over all 13 differential free energies of solvation and absolute free energies of solvation is 0.44 kcal/mol for this level of theory.
Abstract. Ab initio and density functional levels of electronic structure theory are applied to characterize alternative mechanisms for the reductive dechlorination of hexachloroethane (HCA) to perchloroethylene (PCE). Aqueous solvation effects are included using the SM5.42R continuum solvation model. After correction for a small systematic error in the electron affinity of the chlorine atom, theoretical predictions are accurate to within 23 mV for four aqueous reduction potentials relevant to HCA. A single pathway that proceeds via two successive single-electron transfer/barrierless chloride elimination steps, is predicted to be the dominant mechanism for reductive dechlorination. An alternative pathway predicted to be accessible involves trichloromethylchlorocarbene as a reactive intermediate. Bimolecular reactions of the carbene with other species at millimolar or higher concentrations are predicted to potentially be competitive with its unimolecular rearrangement to form PCE.
"The Thermodynamics of Solvation and the Treatment of Equilibrium and Nonequilibrium Solvation Effects by Models Based on Collective Solvent Coordinates," C. J. Cramer and D. G. Truhlar, in Free Energy Calculations in Rational Drug Design, edited by M. R. Reddy and M. D. Erion (Kluwer Academic/Plenum), to be published.
Abstract. A pedagogical overview of the thermodynamics of solvation and of simulation methods for modeling equilibrium and nonequilibrium properties of liquid-phase solutions. Topics covered include molar free energy, activities, ideal and nonideal mixtures, electrolytes, and solubility.
Abstract. The SM5.42R solvation model, which is based on SM5-type atomic surface tensions, class IV point charges based on Charge Model 2, and rigid geometries, is parameterized for the intermediate-neglect-of-differential-overlap-for-spectroscopy (INDO/S) method, both in the original (INDO/S) and more recent (INDO/S2) versions. The parameterization is based on 2184 free energies of solvation of 275 neutral solutes and 49 ions in water and 90 organic solvents.
"Two-Response-Time Model Based on CM2/INDO/S2 Electrostatic Potentials for the Dielectric Polarization Component of Solvatochromic Shifts on Vertical Excitation Energies," J. Li, C. J. Cramer, and D. G. Truhlar, International Journal of Quantum Chemistry 77, 264-280 (2000). (Festschrift in Honor of Michael C. Zerner's 60th Birthday).
Abstract. A model is presented for the electrostatic component of solvatochromic shifts on vertical electronic excitation energies. The model, called vertical electrostatic model 42 (VEM42), is based on representing the solute by a set of distributed atomic monopoles obtained by charge model 2 (CM2) and representing the solvent by its static and optical dielectric constants. The theory is applied here with intermediate neglect of differential overlap for spectroscopy-parameterization 2 (INDO/S2) configuration interaction wave functions. The model is implemented in the ZINDO electronic structure code package. We present illustrative applications to the singlet n -> pi* excitation of acetone in nine solvents. When the electrostatics are augmented by one-parameter estimates of dispersion and hydrogen-bonding contributions, the experimental solvatochromic shifts in the nine solvents are reproduced with a mean unsigned error of 65 cm-1 (0.2 kcal/mol). These calculations present a compelling picture of a quantitative origin of the solvatochromic red and blue shifts in this prototype n -> pi* excitation.
"A Universal Solvation Model Based on the Conductor-like Screening Model," D. M. Dolney, G. D. Hawkins, P. Winget, D. A. Liotard, C. J. Cramer, and D. G. Truhlar, Journal of Computational Chemistry 21, 340-366 (2000).
Abstract. Atomic surface tensions are parameterized for use with solvation models in which the electrostatic part of the calculation is based on the conductor-like screening model (COSMO) and the semiempirical molecular orbital methods AM1, PM3, and MNDO/d. First, the convergence of the calculated polarization free energies with respect to the numerical parameters of the electrostatic calculations is examined. The accuracy and precision of the calculated values are improved significantly by adjusting two parameters that control the segmentation of the solvent accessible surface that is used for the calculations. The accuracy of COSMO calculations is further improved by adopting an optimized set of empirical electrostatic atomic radii. Finally, the electrostatic calculation is combined with SM5-type atomic surface tension functionals that are used to compute the non-electrostatic portions of the solvation free energy. All parameterizations are carried out using rigid (R) gas-phase geometries; this combination (SM5-type surface tensions, COSMO electrostatics, and rigid geometries) is called SM5CR. Six air/water and 76 water/solvent partition coefficients were added to the training set of air/solvent data points previously used to parameterize the SM5 suite of solvation models, thereby bringing the total number of data points in the training set to 2266. The model yields free energies of solvation and transfer with mean unsigned errors of 0.63, 0.59, and 0.61 kcal/mol for AM1, PM3, and MNDO/d, respectively, over all 2217 data for neutral solutes in the training set and mean unsigned errors of 3.0, 2.7, and 3.1 kcal/mol, respectively, for 49 data for ions.
"Prediction of Vapor Pressures from Self-Solvation Free Energies Calculated by the SM5 Series of Universal Solvation Models," P. Winget, G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry B 104, 4726-4734 (2000).
Abstract. The SM5.4, SM5.2R, and SM5.0 solvation models are applied to calculate the vapor pressure of 156 molecules. This provides a test of the solvation models, but—even more so—it provides a useful scheme for estimating the vapor pressure at 298 K of any organic molecule for which a few standard descriptors are known or can be estimated.
"Computational Electrochemistry: Aqueous One-Electron Oxidation Potentials for Substituted Anilines," P. Winget, E. J. Weber, C. J. Cramer, and D. G. Truhlar, Physical Chemistry Chemical Physics 2, 1231-1239 (2000); erratum: 2, 1871 (2000).
Abstract. One-electron oxidation potentials are computed for aniline and 21 mono- and di-substituted anilines in aqueous solution using SM5.42R, and the calculations are used to develop linear correlations for predicting oxidation potentials. The average error in the oxidation potentials is 0.04 eV.
"Prediction of Soil Sorption Coefficients Using a Universal Solvation Model," P. Winget, C. J. Cramer, and D. G. Truhlar, Environmental Science and Technology 34, 4733-4740 (2000).
Abstract. Using a database of 440 molecules, we develop a set of effective solvent descriptors that characterize the organic carbon component of soil and thereby allow quantum mechanical SM5 universal solvation models to be applied to partitioning of solutes between soil and air. Combining this set of effective solvent descriptors with solute atomic surface tension parameters already developed for water/air and organic solvent/air partitioning allows one to predict the partitioning of any solutes composed of H, C, N, O, F, P, S, Cl, Br, and I between soil and water. We also present linear correlations of soil/water partitioning with 1-octanol/water partition coefficients using the same database. The quantum mechanical calculations have the advantages that they require no experimental input and should be robust for a wide range of solute functionality. The quantitative effective solvent descriptors can be used for a better understanding (than with previously available models) of the source of different partitioning phenomena in cases where the results exhibit significant fragment interactions. We anticipate that the model will be useful for understanding the partitioning of organic chemicals in the environment between water and soil or, more generally, between water and soil or sediments (geosorbents).
Abstract. The SMx family of quantum mechanical solvation models accounts for electric and electronic polarization via the generalized Born model and for non-electrostatic components of solvation by microscopic surface tensions. The SM5.4 model, which is the most physical, has been parameterized for water and for any organic solvent for which certain macroscopic data are available, in particular, the index of refraction, bulk surface tension, dielectric constant, and hydrogen bonding acidity and basicity as measured by the Abraham empirical a2 and b2 scales; for neutral solutes, the mean unsigned errors for aqueous and non-aqueous free energies of solvation are 0.5 kcal/mol (215 data points) and 0.4 kcal/mol (1784 data points), respectively . By adding solvation effects to gas-phase calculations, it is possible to model the effects of solvent on conformational analysis, molecular recognition, reaction kinetics, etc. The SM5.4 model is also useful for the calculation of solute partition coefficients between two solvents. Moreover, it is possible to generalize the SM5.4 model to phases that are less well characterized than homogeneous solvents—an example is presented here for the case of bilayers of phosphatidyl choline—in order to model partitioning between biophases.
"Analytical Energy Gradients of a Self-Consistent Reaction-Field Solvation Model Based on CM2 Charges," T. Zhu, J. Li, D. A. Liotard, C. J. Cramer, and D. G. Truhlar, Journal of Chemical Physics 110, 5503-5513 (1999).
Abstract. Analytical energy gradients have been derived for an SM5-type solvation model based on Hartree-Fock self-consistent-reaction-field theory and CM2 atomic charges. The method is combined with an analytic treatment of the first derivatives of non-electrostatic first-solvation-shell contributions to the free energy and implemented in the General Atomic and Molecular Electronic Structure package (GAMESS). The resulting equations allow one to use accurate class IV charges to calculate equilibrium geometries of solutes in liquid-phase solutions. The algorithm is illustrated by calculations of optimized geometries and solvation free energies for water, methanol, dimethyl disulfide, and 9-methyladenine in water and 1-octanol.
"Ethylene Polymerization by Zirconocene Catalysis," P. K. Das, D. W. Dockter, D. R. Fahey, D. E. Lauffer, G. D. Hawkins, J. Li, T. Zhu, C. J. Cramer, D. G. Truhlar, S. Dapprich, R. D. J. Froese, M. C. Holthausen, Z. Liu, K. Mogi, S. Vyboishchikov, D. G. Musaev, and K. Morokuma, in Transition State Modeling for Catalysis, edited by D. G. Truhlar and K. Morokuma (American Chemical Society Symposium Series Volume 721, Washington, DC, 1999), pp. 208-224.
Abstract. The production of polyethylene by zirconocene catalysis is a multistep process that includes initiation, propagation, and termination. Each of these steps has a number of associated equilibrium and transition state structures. These structures have been studied in the gas-phase environment using density functional and integrated methods. We have also examined the effects of solvation upon the energetics of the various polymerization steps employing continuum and explicit representations of the solvent (toluene). The reaction steps we have studied are initiation, propagation, propylene and hexene incorporation, termination by hydrogenolysis, termination by beta-H transfer to the metal, termination by beta-H transfer to the monomer, and reactivation. The solvation effect of toluene takes on special significance for the initiation, termination by hydrogenolysis and by beta-H transfer to the metal, and reactivitation steps.
"Application of a Universal Solvation Model to Nucleic Acid Bases. Comparison of Semiempirical Molecular Orbital Theory, Ab Initio Hartree-Fock Theory, and Density Functional theory," J. Li, C. J. Cramer, and D. G. Truhlar, Biophysical Chemistry 103, 3802-3803 (1999). (Special issue on Implicit Solvent Representation in Biomolecular Chemistry)
Abstract. The free energies of solvation of six nucleic acid bases (adenine, cytosine, hypoxanthine, guanine, thymine, and uracil) in water and chloroform are calculated using CM2 class IV charges and SM5.42R atomic surface tensions. Using any of three approximations to the electronic wave function, (AM1, Hartree-Fock, or DFT), we obtain good agreement with experiment for five cases where the experimental results are known for the partition coefficients between the two solvents. Decomposition of the solvation effects into bulk electrostatic contributions and first-solvation-shell effects shows that the partitioning is dominated by the former, and this illustrates the importance of using accurate partial atomic charges for modeling these molecules in aqueous solution.
"Extension of the Platform of Applicability of the SM5.42R Universal Solvation Model," J. Li, T. Zhu, G. D. Hawkins, P. Winget, D. A. Liotard, C. J. Cramer, and D. G. Truhlar, Theoretical Chemistry Accounts 103, 9-63 (1999).
Abstract. We present eight new parameterizations of the SM5.42R solvation model, in particular we present parameterizations for HF/MIDI!, HF/6-31G*, HF/6-31+G*, HF/cc-pVDZ, AM1, PM3, BPW91/MIDI!, and B3LYP/MIDI!. Two of the new cases are parameterized using the reaction field operator presented previously, and six of the new cases are parameterized with a simplified reaction field operator; results obtained by the two methods are compared for selected examples. For a training set of 2135 data for 275 neutral solutes containing H, C, N, O, F, S, P, Cl, Br, and I in 91 solvents (water and 90 nonaqueous solvents), seven of the eight new parameterizations give mean unsigned errors in the range 0.43-0.46 kcal/mol, and the eighth—for a basis set containing diffuse functions—gives a main unsigned error of 0.53 kcal/mol. The mean unsigned error for 49 ionic solutes (containing the same elements) in water is 3.5-3.9 kcal/mol for the RHF (Hartree-Fock), BPW91 (Becke-Perdew-Wang 1991), and B3LYP (Becke three-parameter Lee-Yang-Parr) cases and 4.1 and 4.0 kcal/mol for PM3 (Parameterized Model 3) and AM1 (Austin Model 1), respectively. The methods are tested for sensitivity of solvation free energies to geometry and for predicting partition coefficients of carbonates, which were not included in the training set.
"Direct Dynamics for Free Radical Kinetics in Solution: Solvent Effect on the Rate Constant for the Reaction of Methanol with Atomic Hydrogen," Y.-Y. Chuang, M. L. Radhakrishnan, P. L. Fast, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry A 103, 4893-4909 (1999).
Abstract. We calculate the rate constant for the reaction H + CH3OH -> H2 + CH2OH both in the gas phase and in aqueous solution at 298 K. To accomplish this, we apply two different methods to estimate the electronic energies along the reaction path. First, we use specific reaction parameters (SRP) to mix the exchange and correlation energies in Becke’s adiabatic connection theory (AC-SRP) to optimize the model for the specific bond-breaking, bond-making combination under consideration. Second, we obtain the potential energy using a linear combination of the Hartree-Fock method and AM1 with specific reaction parameters (HF||AM1-SRP); in this linear mixing method, eight NDDO parameters and the linear mixing parameter are simultaneously optimized by a genetic algorithm. To calculate the reaction rate constants in solution, the solute atomic charges are represented by class IV charges, the electric polarization of the solvent is determined from the electronic charge distribution of the solute self-consistently, and the solute electronic, solvent electric polarization terms are augmented by first-solvation-shell terms calculated by the SM5.42 solvation model. Reaction rate constants of the hydrogen transfer reaction and the kinetic isotope effects are studied both in the gas phase at 200-2400 K and in aqueous solution at 298 K. The AC-SRP and HF||AM1-SRP methods, although quite different, give qualitatively similar pictures of the reaction at the separable equilibrium solvation level; however, it is found that a full equilibrium solvation path (ESP) calculation, which involves optimization of structures along the reaction path in the presence of solvent, is essential to reproduce the speedup of the reaction due to solvation. The final calculation, based on the HF||AM1-SRP electronic structure calculations and ESP dynamics with variational transition state theory in curvilinear coordinates with the microcanonical optimized multidimensional tunneling approximations, agrees well with experiment not only for the speedup due to the solvation but also for the D + CH3OH and H + CD3OH kinetic isotope effects.
"New Tools for Rational Drug Design," G. D. Hawkins, J. Li, T. Zhu, C. C. Chambers, D. J. Giesen, D. A. Liotard, C. J. Cramer, and D. G. Truhlar, in Rational Drug Design: Novel Methodology and Practical Applications, edited by A. L. Parrill and M. R. Reddy (American Chemical Society Symposium Series Volume 719, Washington, DC, 1999), pp. 121-140.
Abstract. We have developed two new tools for molecular modeling that can be very useful for computer-aided drug design, namely class IV charges and the SMx series of solvation models. This contribution overviews the current status of our efforts in these areas, including the CM2 charge model and the SM5 series of solvation models. The solvation models may be used to estimate partition coefficients for phase transfer equilibria of organic solutes between water and 1-octanol, the most widely used mimic of cellular biophases, and also between water and other solvents that have been used for this purpose, e.g., hexadecane and chloroform.
"Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics," C. J. Cramer and D. G. Truhlar, Chemical Reviews 99, 2161-2200 (1999).
Abstract. A review covering continuum solvation theory, models for equilibrium solvation, dipole moments and charge and spin distributions, and solvent effects on equilibria, spectra, and dynamics.
"Nonequilibrium Solvation Effects for a Polyatomic Reaction in Solution," Y.-Y. Chuang and D. G. Truhlar, Journal of the American Chemical Society 121, 10157-10167 (1999).
Abstract. We present a general linear-response method for including nonequilibrium solvation effects (solvent friction effects) in variational transition state theory with multidimensional tunneling (VTST/MT) for calculating reaction rate constants in solution. The generalized Langevin approach is used to include a collective solvent coordinate into VTST/MT, and a general prescription is suggested for coupling this collective solvent coordinate to the solute, which is treated in its full dimensionality. The new formalism is illustrated by application to the aqueous free radical reaction H + CH3OH -> H2 + CH2OH at 298 K. This reaction is treated with a linear mixing of Hartree-Fock theory and Austin Model 1 with specific reaction parameters (HF||AM1-SRP). The results with nonequilibrium solvation (NES) are compared to those obtained earlier with the separable equilibrium solvation (SES) and the equilibrium solvation path (ESP) approximations. We focus on the speedup due to solvation and on the kinetic isotope effects. We calculate that nonequilibrium solvation decreases the rate constant by a factor of 2 but changes the kinetic isotope effects by less than 2%. We also present results that show how the nonequilibrium effect depends on the solvation time and the strength of the solute-solvent coupling.
Abstract. We present 13C dynamic NMR results for relative free energies of equilibrium structures and free energies of activation for conformational transformations of 1,3-dimethylthiourea in aqueous solution, and we compare the results to theoretical predictions. The latter are based on ab initio gas-phase electronic structure calculations of the geometries, dipole moments, and energies combined with semiempirical molecular orbital calculations of the free energies of solvation in three different solvents. The gas-phase electronic structure calculations were performed using Moller-Plesset second-order (MP2) perturbation theory with a correlation-consistent polarized valence-double-zeta basis set; we calculated relative energies for the three minima Z,Z, E,Z, and E,E and for three transition states on the potential energy surface. The solvation energy calculations were carried out using the SM5.4/A-aqueous, -chloroform, and -organic solvation models; these solvation models are based on semiempirical molecular orbital theory with class IV charges and geometry-based first-solvation-shell effects. The relative energies of the conformers and transition states are compared to experiment in water and five organic solvents.
"Modeling Free Energies of Solvation and Transfer," D. J. Giesen, C. C. Chambers, G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, in Computational Thermochemistry, edited by K. Irikura and D. J. Frurip (American Chemical Society Symposium Series Volume 677, Washington, DC, 1998), pp. 285-300 (1998).
Abstract. The free energy of transfer of a solute from one medium to another, which is the free energy of solvation if the first medium is the gas phase and the second is a liquid-phase solution, controls all solvation and partitioning phenomena. The SM5.4 quantum mechanical solvation model allows for the calculation of (i) partitioning free energies between the gas phase and a solvent (i.e., free energies of solvation) or (ii) partitioning free energies between two solvents. The model provides a framework for interpreting the factors responsible for differential solvation effects and can be used to predict solvation effects on chemical equilibria and kinetics--examples in this chapter include partitioning of the nucleic acid bases between water and chloroform, solvation effects on anomeric conformational equilibria, and solvation effects on the rate of the Claisen rearrangement.
"Universal Quantum Mechanical Model for Solvation Free Energies Based on Gas-Phase Geometries," G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry B 102, 3257-3271 (1998).
Abstract. We present a new solvation model for predicting free energies of transfer of organic solutes from the gas phase to aqueous and organic solvents. The model is based on class II charges, gas-phase geometries, a generalized Born approximation to the polarization free energy, and SM5-type atomic surface tensions. The initial parameterization of the new model was developed to utilize the MNDO/d Hamiltonian, and we also present parameters for the MNDO, AM1, and PM3 Hamiltonians. These parameterizations are based on reasonably accurate gas-phase geometries for 43 ions and 260 neutral solute molecules composed of H, C, N, O, F, S, Cl, Br, and I and containing a wide variety of functional groups. For aqueous solutions, the parameterization is based on data for 248 of the neutrals and all of the ions. For organic solvents, it is based on 1836 experimental data points for 227 of the neutral solutes in 90 organic solvents. The parameterization based on the MNDO/d Hamiltonian is called SM5.2R/MNDO/d, and it yields a mean unsigned error of 3.8 kcal/mol for the free energy of hydration of ions, and a mean unsigned error of 0.38 kcal/mol for the free energy of solvation of neutral solutes. Gas-phase geometries for all solute molecules were calculated at the Hartree-Fock level with a heteroatom-polarized valence-double-zeta basis set (HF/MIDI!), and we confirmed that the average errors increase only about 0.1 kcal/mol if we use the MNDO/d geometries.
"OMNISOL: Fast Prediction of Free Energies of Solvation and Partition Coefficients," G. D. Hawkins, D. A. Liotard, C. J. Cramer, and D. G. Truhlar, Journal of Organic Chemistry 63, 4305-4313 (1998).
Abstract. The SM5.0R model for predicting solvation energies using only geometry-dependent atomic surface tensions was developed previously for aqueous solution. Here we extend it to organic solvents. The method is based on gas-phase geometries and exposed atomic surface areas; electrostatics are treated only implicitly so a wave function or charge model is not required (which speeds up the calculations by about two orders of magnitude). The SM5.0R model has been parameterized for solvation free energies of solutes containing H, C, N, O, F, S, Cl, Br, and I. The training set for organic solvents consists of 227 neutral solutes in 90 organic solvents for a total of 1836 data points. The method achieves a mean unsigned error of 0.38 kcal/mol when applied using gas-phase geometries calculated at the Hartree-Fock level with a heteroatom-polarized valence-double-zeta basis set (HF/MIDI!) and a mean unsigned error of 0.39 kcal/mol when applied using semiempirical molecular orbital gas-phase geometries. In related work reported here, the parameterization for predicting aqueous solvation free energies is also extended to include organic solutes containing iodine. This extension is based on 8 solutes and yields a mean unsigned error of 0.25 kcal/mol. The resulting SM5.0R model for solvation energies in aqueous and organic solvents can therefore be used to predict partition coefficients for any solute containing H, C, N, O, F, S, Cl, Br, and/or I.
"Density Functional Solvation Model Based on CM2 Atomic Charges," T. Zhu, J. Li, G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Journal of Chemical Physics 109, 9117-9133 (1998).
Abstract. We extend the SM5 solvation model for calculating solvation free energies of a variety of organic solutes in both aqueous and organic solvents so that it can be employed in conjunction with high-level electronic structure calculations. The extension is illustrated by presenting three implementations based on density-functional theory (DFT). The three implementations are called SM5.42R/BPW91/MIDI!6D, SM5.42R/BPW91/DZVP, and SM5.42R/BPW91/6-31G*. They have the following features: (1) They utilize gradient-corrected DFT with polarized double zeta basis sets to describe the electronic structure of a solute. The particular exchange-correlation functional adopted is Becke’s exchange with Perdew-Wang 1991 correlation functional, usually called BPW91. The MIDI!6D, DZVP, and 6-31G* basis sets are used. (2) They employ fixed solute geometries in solvation calculations. The model is designed to predict solvation free energies based on any reasonably accurate gas-phase solute geometry. (3) The electric polarization in the solute-solvent system is described by the generalized Born approximation with self-consistent reaction-field solute partial atomic charges obtained from the CM2 charge model. (4) The solvation effects within the first solvation shell are included in the form of SM5-type atomic surface tensions. Both DFT parameterizations are developed using 275 neutral solutes and 49 ions with gas-phase Hartree-Fock/MIDI! geometries. These solutes contain a wide variety of organic functional groups which include H, C, N, O, F, P, S, Cl, Br, and I atoms. For 2135 free energies of solvation of the neutral molecules in water and 90 organic solvents, SM5.42R/BPW91/MIDI!6D, SM5.42R/BPW91/DZVP, and SM5.42R/BPW91/6-31G* yield mean unsigned errors in solvation free energies of 0.45 kcal/mol, 0.44 kcal/mol, and 0.43 kcal/mol, respectively. For 49 ions in water, SM5.42R/BPW91/MIDI!6D produces a mean unsigned error of 3.9 kcal/mol, while SM5.42R/BPW91/DZVP and SM5.42R/BPW91/6-31G* give 3.6 kcal/mol and 3.9 kcal/mol respectively.
"Universal Reaction Field Model Based on Ab Initio Hartree-Fock Theory," J. Li, G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Chemical Physics Letters 288, 293-298 (1998).
Abstract. We present a model for free energies of solvation based on Hartree-Fock self-consistent-reaction-field (SCRF) calculations for electrostatics combined with atomic surface tensions (AST) for deviations from bulk electrostatics in the first solvation shell, including cavity, dispersion, and solvent-structure contributions. The SCRF part combines an ab initio treatment of the solute with solute-solvent interactions modeled using class IV charges. The AST part is parameterized for both water and general organic solvents. Mean unsigned errors are 3.9 kcal/mol for 49 ions in water and 0.46 kcal/mol for 275 neutrals in 91 solvents.
"Factors Controlling the Relative Stability of Anomers and Hydroxymethyl Conformers of Glucopyranose," S. E. Barrows, J. W. Storer, C. J. Cramer, A. D. French, and D. G. Truhlar, Journal of Computational Chemistry 19, 1111-1129 (1998). (special issue in honor of N. L. Allinger)
Abstract. The relative energies of 11 different conformers of D-glucose, including different exo-anomeric orientations and at least one of each hydroxymethyl conformer (G?, G+, and T) for each of the two anomeric forms (a and b), were calculated at much more complete levels of quantum mechanical (QM) electronic structure theory than previously available, and relative free energies in solution were calculated by adding rotational, vibrational, and aqueous solvation effects. The gas-phase results are based on very large basis sets (up to 624 contracted basis functions) and the coupled cluster method for electron correlation. Solvation Model 5.4/AM1 was used to calculate the effects of aqueous solvation. Factors contributing to the relative energies of these conformers have been analyzed. Relative energies varied considerably (up to 4.5 kcal/mol), depending on the theoretical level, and different levels of theory disagreed as to which anomer was lower in energy. The highest-level gas-phase calculations predicted the alpha-anomer to be lower in free energy by 0.4 kcal/mol (Boltzmann average). Gas-phase energies from several different classical force fields were compared to QM results. The QM structures optimized at the MP2/cc-pVDZ level of theory compared well with experiment for three different crystal structures. In water, the beta-anomers were better solvated than the aalpha-anomers by 0.6 kcal/mol (Boltzmann average). Contributions of individual hydrophilic groups to the solvation free energies were analyzed.
"Interface of Electronic Structure and Dynamics for Reactions in Solution," Y.-Y. Chuang, C. J. Cramer, and D. G. Truhlar, International Journal of Quantum Chemistry 70, 887-896 (1998). (Sanibel issue)
Abstract. We compare two systematic approaches to the calculation
of reaction rates in liquid solutions: the separable equilibrium
(SES) approximation and the equilibrium solvation path (ESP)
These approaches are tested for two
ClCH3 + NH3 -> Cl-? + H3CNH3+ (R1)
NH4+ÖN¥H3 -> NH3 …N´H4+ (R2)
both in aqueous solution. The first reaction illustrates the importance of variational optimization of the transition state, and the second illustrates the importance of tunneling. Free energies of solvation are calculated by Solvation Model 5. All calculations are carried out by the new AMSOLRATE program, which is an interface of the AMSOL and POLYRATE programs.
General Discussion (on solvent effects on 1,3-dipolar addition reactions), D. G. Truhlar and C. J. Cramer, Faraday Discussions Chemical Society 110, 477-479 (1998).
Abstract. In these discussion remarks we compare the predictions of SM5.42R/AM1 calculations of solvent effects on 1,3-dipolar addition reactions to the prediction of explicit-solvent Monte Carlo calculations by Repaskey and Jorgensen, and we extend the calculations to larger systems. The new calculations allow us to improve and understand better the comparison of theory with experiment.
"Quantum Chemical Analysis of Para-Substitution Effects on the Electronic Structure of Phenylnitrenium Ions in the Gas Phase and Aqueous Solution," M. B. Sullivan, K. Brown, C. J. Cramer, and D. G. Truhlar, Journal of the American Chemical Society 120, 11778-11783 (1998).
Abstract. Ab initio calculations for para-substituted phenylnitrenium ions predict larger singlet-triplet splittings, shorter singlet C-N+ bond lengths, and higher singlet aromatic ring stretching frequencies for substituents with greater electron-donating character. Trends in these properties correlate linearly with para-substituent constants sR+, indicating that phenylnitrenium ions closely resemble other electron-deficient aromatic systems where resonance interactions with substituents are dominant. Sensitivity to substitution is large as judged by the slope of the correlating line for aqueous singlet-triplet splittings, r = 6.4. For 13 of 15 substituted cases, aqueous solvation preferentially stabilizes the single state by 0.9 to 4.4 kcal/mol; for the p-CO2H and p-CF3 cases, the triplet state is better solvated by less than 1 kcal/mol.
"Universal Solvation Models," G. D. Hawkins, T. Zhu, J. Li, C. C. Chambers, D. J. Giesen, D. A. Liotard, C. J. Cramer, and D. G. Truhlar, in Combined Quantum Mechanical and Molecular Mechanical Methods, edited by J. Gao and M. A. Thompson (American Chemical Society Symposium Series volume 712, Washington, DC, 1998), pp. 201-219.
Abstract. This chapter presents an overview of the SM5 suite of universal solvation models for computing free energies of solvation in water and nonaqueous solvents. After a general review of the theoretical components of all the SM5 solvation models, we specifically compare the performance of those that have been parameterized for both aqueous and organic solvents. These are called the universal solvation models, and they include models based on semiempirical neglect of diatomic differential overlap molecular orbital theory, density functional theory, and ab initio Hartree-Fock theory, and also a model with implicit electrostatics.
Abstract. Ab initio calculations predict that in 2-hydroxy- and 2-methoxy-tetrahydropyran, hyperconjugative delocalization of lone pair density on the exocyclic oxygen atom at C(1) into the sigma* orbital of the C(1)O(5) bond is maximized when the OR group at C(1) is oriented gauche to C(1)O(5). This exo-anomeric effect lengthens the C(1)O(5) bond, shortens the exocyclic C(1)O bond, and stabilizes the gauche conformers by about 4 kcal/mol over the anti. In the anti orientation, hyperconjugative interaction of the OR group at C(1) with other appropriately oriented sigma* orbitals increases, but the geometric and energetic consequences are less marked. Solvation effects reduce the energetic stabilization associated with the exo-anomeric effect in the tetrahydropyrans. This derives from a combination of changes in the overall electrostatics and also from decreased accessibility of the hydrophilic groups in the gauche conformers. For glucose or glucosides, instead of the simple tetrahydropyran model systems, the interactions of the exocyclic OR group at C(1) with the hydroxy group at C(2) can significantly affect these hyperconjugative delocalizations. In the glucose and glucoside systems, solvation effects oppose the formation of intramolecular hydrogen bonds. MM3(94) force field calculations show systematic deviations in the relative energies and structures of the various model systems with respect to the more reliable HF/cc-pVDZ predictions.
"A Solvation Model for Chloroform Based on Class IV Atomic Charges," D. J. Giesen, C. C. Chambers, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry 101, 2061-2069 (1997).
Abstract. We present a parameterization of the SM5.4 solvation model, previously applied to aqueous solutions and general organic solvents, for predicting free energies of solvation in chloroform. As in all SM5 models, the calculations are based on a set of geometry-based functional forms for parameterizing atomic surface tensions of organic solutes. In particular, the atomic surface tensions depend in some cases on distances to nearby atoms. Combining the atomic surface tensions with electrostatic effects included in a Fock operator by the generalized Born model enables one to calculate free energies of solvation. Atomic charges are obtained by both the AM1-CM1A and PM3-CM1P class IV charge models, which yield similar results, and hence the same atomic radii and similar surface tensions are used with both charge models. Experimental free energies of solvation and free energies of transfer from aqueous solution are used to parameterize the theory for chloroform. The parameterization is based on a set of 205 neutral solutes containing H, C, N, O, F, S, Cl, Br, and I that we used previously to parameterize a model for general organic solvents plus 32 additional solutes added for this study. For the present parameterization, we used free energies of solvation in chloroform for 88 solutes, free energies of solvation in other solvents for 123 solutes, and free energies of transfer from water to chloroform for 26 other solutes. We obtained a mean unsigned error in the free energies of solvation in chloroform of 0.43 kcal/mol using CM1A atomic charges and 0.34 kcal/mol using CM1P atomic charges.
"New Methods for Potential Functions for Simulating Biological Molecules," G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Journal de Chimie Physique 94, 1448-1481 (1997).
Abstract. We calculate atomic charges and solvation energies for 9-methyladenine, thymine, alanine depeptide, and N-acetylserine-N'-methanylamide using the CM1A class IV charge model and the SM5.4/A and SM5.4PD/A solvation models. The CM1A charge model provides atomic charges as accurate as or more accurate than those used in popular molecular dynamics force fields but is very economical in both computer time and the effort required to generate charges; thus it is very promising for examining effects of conformational changes, substituents, solvation, binding, and even reaction. The solvation models have been parameterized over broad functionalities and are well suited to rapid calculations on large systems.
"What Controls the Partitioning of Nucleic Acid Bases Between Chloroform and Water?," D. J. Giesen, C. C. Chambers, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry, Journal of Physical Chemistry B 101, 5084-5088 (1997)
Abstract. The free energies of partitioning between water and chloroform are predicted for six nucleic acid bases using the SM5.4/A water and chloroform solvation models. We obtain a mean unsigned accuracy of 0.2 log10 units compared to experiment. Predictions are made for an additional six unnatural nucleic acid bases. Functional group contributions to the solvent-solvent partitioning phenomenon are examined and the validity of fragment-based partitioning models is assessed
"Parameterized Model for Aqueous Free Energies of Solvation Using Geometry-Dependent Atomic Surface Tensions with Implicit Electrostatics," G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry B 101, 7147-7157 (1997).
Abstract. We present a new model for predicting aqueous solvation energies based entirely on geometry-dependent atomic surface tensions. The model is especially suited for rapid estimations on large molecules or large sets of molecules. This method is designed to be employed with gas-phase geometries to obtain solvation free energies of organic molecules containing H, C, N, O, F, S, Cl, and Br. We parameterized the model by using a training set containing 235 neutral solutes with a variety of functional groups, and we achieve a mean unsigned error of 0.55 kcal/mol when the model is applied using gas-phase geometries calculated at the Hartree-Fock level with a heteroatom-polarized valence-double-zeta basis set (HF/MIDI!) and a mean unsigned error of 0.57 kcal/mol when it is applied using gas-phase geometries from Austin Model 1 (AM1). For a smaller set of 99 solutes, we compared the new model to two previously published models based on atomic solvation parameters and we achieve a mean unsigned error of 0.56 kcal/mol as compared to 1.87 and 2.13 kcal/mol for the previous models. A simple extension is provided to allow treatment of certain kinds of charged groups. The model is expected to be especially useful for problems requiring high efficiency because of the size of the system, e. g., protein folding, or problems requiring rapid estimations because of the large number of calculations required, e. g., scoring of combinatorial libraries.
"Singlet-Triplet Splittings and 1,2-Hydrogen Shift Barriers for Methylphenylborenide, Methylphenylcarbene, and Methylphenylnitrenium in the Gas Phase and Solution. What a Difference a Charge Makes," C. J. Cramer, D. G. Truhlar, and D. E. Falvey, Journal of the American Chemical Society 119, 12338-12342 (1997).
Abstract. In the isoelectronic series methylphenylborenide, methylphenylcarbene, and methylphenylnitrenium, fundamental differences are predicted for singlet state geometries, singlet-triplet state splittings, barriers to singlet 1,2-hydrogen migration, and sensitivity of 1,2-hydrogen migration to solvent effects in n-heptane and acetonitrile. We conclude that isoelectronic analogies are dangerous for systems having different formal charges, and that the interaction of the divalent center with a conjugating substituent is very sensitive to the electron donating or withdrawing nature (and power) of the hypovalent atom. Solvent effects on the singlet-triplet splitting result from static polarity differences whereas the solvent effects on 1,2-hydrogen migration result primarily from polarizability differences. For the experimentally characterized carbene case, extensive comparison of calculated and measured results is provided.
"A Universal Solvation Model for the Quantum Mechanical Calculation of Free Energies of Solvation in Non-Aqueous Solvents," D. J. Giesen, G. D. Hawkins, D. A. Liotard, C. J. Cramer, and D. G. Truhlar, Theoretical Chemistry Accounts 98, 85-109 (1997); erratum: 101, 309 (1999).
Abstract. The SM5.4 quantum mechanical solvation model has been extended to calculate free energies of solvation in virtually any organic solvent. Electrostatics and solute-solvent polarization are included self-consistently by the generalized Born equation with class IV charges, and first-solvation-shell effects are modeled in terms of solvent-accessible surface areas that depend on solute geometries and four solvent descriptors. The inclusion of solvent properties into the first-solvation-shell term provides a model that predicts accurate solvation free energies in any solvent for which those properties are known. The model was developed using 1786 experimentally measured solvation free energies for 206 solutes in one or more of 90 solvents. Parameters have been obtained for solutes containing H, C, N, O, F, S, Cl, Br, and I, and the solutes used for parameterization span a wide range of organic functional groups. Solvents used in the parameterization contain H, C, N, O, F, P, S, Cl, Br, and I and include the most common organic solvents. Two general parameterizations are presented here, one for use with the AM1 Hamiltonian (SM5.4/A) and one for use with the PM3 Hamiltonian (SM5.4/P). In each case, one parameter is specially re-optimized for benzene and toluene to reduce systematic errors for these solvents. Chloroform is also treated with special parameters. The final mean unsigned error for both the SM5.4/A and SM5.4/P parameterizations is less than 0.5 kcal mol-1 over the entire data set of 1786 free energies of solvation in 90 organic solvents.
Abstract. This chapter reviews the theoretical background for continuum models of solvation, recent advances in their implementation, and illustrative examples of their use. Continuum models are the most efficient way to include condensed-phase effects into quantum mechanical calculations, and this is typically accomplished by the using self-consistent reaction field (SCRF) approach for the electrostatic component. This approach does not automatically include the non-electrostatic component of solvation, and we review various approaches for including that aspect. The performance of various models is compared for a number of applications, with emphasis on heterocyclic tautomeric equilibria because they have been the subject of the widest variety of studies. For nonequilibrium applications, e.g., dynamics and spectroscopy, one must consider the various time scales of the solvation process and the dynamical process under consideration, and the final section of the review discusses these issues.
Page 28, eq. (56) The sum over m' should be moved inside the parentheses in front of the P-sub-mumu term"Quantum Chemical Conformational Analysis and X-Ray Structure of 4-Methyl-3-Thiosemicarbazide," C. C. Chambers, E. Archibong, S. M. Mazhari, A. Jabalameli, J. D. Zubkowski, R. H. Sullivan, E. J. Valente, C. J. Cramer, and D. G. Truhlar, Journal of Molecular Structure: Theochem 388, 161-167 (1996).
Abstract. We present X-ray crystallographic results and gas-phase electronic structure calculations of the geometry of 4-methyl-3-thiosemicarbazide. Using Hartree- Fock theory with a 6-31G* basis set, we calculated relative energies for eight different conformations. For the lowest-energy conformations of each of the four possible combinations of rotamers about the two C-N bonds, we also included electron correlation by Møller-Plesset second-order (MP2) perturbation theory with the same basis set. From these calculations, we selected the lowest-energy structure and calculated structural parameters at the MP2 level of theory with the larger correlation-consistent cc-pVDZ basis set. The geometry of the minimum- energy gas-phase structure is in good agreement with the structure observed experimentally in the crystal.
"Factors Controlling Regioselectivity in the Reduction of Polynitroaromatics in Aqueous Solution," S. E. Barrows, C. J. Cramer, D. G. Truhlar, M. S. Elovitz, and E. J. Weber, Environmental Science and Technology 30, 3028-3038 (1996).
Abstract. Regioselectivities in the bisulfide reduction of ten polynitroaromatics to monoamine products have been determined; four of these compounds have also been reduced by anoxic sediments in heterogeneous aqueous solution, and the same regioselectivities are observed. This suggests that reduction takes place in the liquid phase and is mediated by an organic electron shuttle reagent. Analyses of Austin Model 1-Solvation Model 2 electrostatic potential surfaces for the radical anions of these polynitroaromatic compounds provides a reliable method of predicting the regioselectivity of their reduction. In particular, at their minimum-energy geometries in aqueous solution, it is the more negative nitro group that is selectively reduced. This is consistent with a mechanism where regioselection occurs upon kinetic protonation at the site of maximum negative charge in the radical anion formed after the first electron transfer to the neutral PNA . Inclusion of solvation effects is critical in order to confidently predict the electrostatic preference for the reduction of one nitro group over the others. Sterically uncongested nitroaromatic radical anions have gas-phase geometries in which the nitro group is coplanar with the aromatic ring. However, ortho substituents and solvation effects both oppose this tendency, and can lead to nitro groups that are rotated out of the ring plane and pyramidalized.
The electrostatic potential pictured for the first molecule in Figure 1, 2-amino-4,6-dinitrotoluene, is incorrect (it
corresponds to the highest energy stereostructure found in the Supporting Information). The electrostatic potential
for the lowest energy stereostructure, which IS correctly depicted in ball-and-stick form in Figure 1, shows maximum
negative potential on the nitro group ortho to methyl. All discussion of this molecule in the text remains correct,
only the printed picture was in error.
In the discussion of solvent effects on electronic polarization (p. 3034), the data for 1-bromo-2,4-dinitrobenzene
should be "gas phase, 0.17 more negative para; aqueous solution, 0.42 more negative ortho"."Model for Aqueous Solvation Based on Class IV Atomic Charges and First-Solvation Shell Effects," C. C. Chambers, G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry 100, 16385-16398 (1996).
Abstract. We present a new set of geometry-based functional forms for parameterizing effective coulomb radii and atomic surface tensions of organic solutes in water. In particular, the radii and surface tensions depend in some cases on distances to nearby atoms. Combining the surface tensions with electrostatic effects included in a Fock operator by the generalized Born model enables one to calculate free energies of solvation, and experimental free energies of solvation are used to parameterize the theory for water. Atomic charges are obtained by both the AM1-CM1A and PM3-CM1P class IV charge models, which yield similar results, and hence the same radii and surface tensions are used with both charge models. We considered 215 neutral solutes containing H, C, N, O, F, S, Cl, Br, and I and encompassing a very wide variety of organic functional groups, and we obtained a mean unsigned error in the free energy of hydration of 0.50 kcal/mol using CM1A charges and 0.48 kcal/mol using CM1P charges. The predicted solvation energies for 12 cationic and 22 anionic solutes have mean unsigned deviations from experiment of 4.6 and 4.8 kcal/mol for models based on AM1 and PM3, respectively.
Note: The errata for this paper is included as a series of .jpg pictures. Click here to view the pictures."Parameterized Models of Aqueous Free Energies of Solvation Based on Pairwise Descreening of solute Atomic charges from a
Abstract. The pairwise descreening approximation provides a rapid
computational algorithm for the evaluation of solute shape effects on
electrostatic contributions to solvation energies. In this article we show that solvation models based on this algorithm are useful for predicting
free energies of solvation across a wide range of solute functionalities, and we present six new general parameterizations of aqueous free
energies of solvation based on this approach. The first new model is based on SM2-type atomic surface tensions, the AM1 model for the solute,
and Mulliken charges. The next two new models are based on SM5-type surface tensions, either the AM1 or the PM3 model for the solute, and
Mulliken charges. The final three models are based on SM5-type atomic surface tensions and are parameterized using the AM1 or the PM3
model for the solute and CM1 charges. The parameterizations are based on experimental data for a set of 219 neutral solute molecules
containing a wide range of organic functional groups and the atom types H, C, N, O, F, P, S, Cl, Br, and I and on data for 42 ions containing the
same elements. The average errors relative to experiment are slightly better than previous methods, but--more significantly--the computational
cost is reduced for large molecules, and the methods are well suited to using analytic derivatives.
"A Universal Organic Solvation Model," D. J. Giesen, M. Z. Gu,
C. J. Cramer, and D. G. Truhlar, Journal of Organic
Chemistry 61, 8720-8721 (1996).
Abstract. A solvation model is presented for the quantum mechanical
calculation of gas-to-liquid and liquid-to-liquid transfer free
a data set spanning 90 organic solvents and 205 organic solutes, the mean unsigned error in 1784 molar transfer free energies is 0.5 kcal (0.35
log10 units at 298 K).
Abstract. We present improved algorithms for the SMx (x = 1, 1a, 2, 3) solvation models presented previously [see the overview in C. J. Cramer and D. G. Truhlar, J. Comput.-Aided Mol. Design, 6, 629 (1992)]. These models estimate the free energy of solvation by augmenting a semiempirical Hartree-Fock calculation on the solute with the generalized Born (GB) model for electric polarization of the solvent and a surface tension term based on solvent-accessible surface area. This paper presents three improvements in the algorithms used to carry out such calculations, namely (i) an analytical accessible surface area algorithm, (ii) a more efficient radial integration scheme for the dielectric screening computation in the GB model, and (iii) a damping algorithm for updating the GB contribution to the Fock update during the iterations to achieve a self-consistent field. Improvements (i) and (ii) decrease the computer time, and improvement (iii) leads to more stable convergence. Improvement (ii) removes a small systematic numerical error that was explicitly absorbed into the parameterization in the SMx models. Therefore we have adjusted the parameters for one of the previous models to yield essentially identical performance as was obtained originally while simultaneously taking advantage of improvement (ii). The resulting model is called SM2.1. The fact that we obtain similar results after removing the systematic quadrature bias attests to the robustness of the original parameterization.
p. 430. The index of summation of equation 46 should run to M, not M-1. This error is typographical only;
the code has always used the correct index."A General Semiempirical Quantum Mechanical Solvation Model for Nonpolar Solvation Energies. n-Hexadecane," D. J. Giesen, J. W. Storer, C. J. Cramer, and D. G. Truhlar, Journal of the American Chemical Society, 117, 1057-1068 (1995).
Abstract. A new solvation model has been developed that accurately predicts solvation free energies in the nonpolar solvent n-hexadecane. The model is based on AM1-CM1A and PM3-CM1P partial charges, and it is based on a single set of parameters that is applicable to both the AM1 and PM3 Hamiltonians. To take account of both short-range and long-range solvation-shell interactions, each atom has two surface tensions associated with different effective solvent radii. For hydrogen, one of these surface tensions depends on the bond orders to carbon, nitrogen, oxygen, and sulfur, although only weakly. In addition to presenting the general parameterization, the article provides an analysis of the surface tension parameterization based on data for three rare gases. The model yields an RMS error of 0.41 kcal/mol over a set of 306 data points (153 molecules, 2 Hamiltonians) that includes alkanes, alkenes, alkynes, aromatics, alcohols, ethers, aldehydes, ketones, esters, amines, nitriles, pyridines, thiols, sulfides, fluorides, chlorides, bromides, iodides, water, and ammonia.
Equation (25). q_k/gamma_kk' should be q_k gamma_kk'"Continuum Solvation Models: Classical and Quantum Mechanical Implementations," C. J. Cramer and D. G. Truhlar, in Reviews in Computational Chemistry, Vol. 6, edited by K. B. Lipkowitz and D. B. Boyd (VCH Publishers, New York, 1995), 1-72.
Abstract. A comprehensive review, this book chapter covers theory and applications of many continuum solvation models and includes comparative results for a number of systems.
"A Semiempirical Quantum Mechanical Solvation Model for Solvation Free Energies in All Alkane Solvents," D. J. Giesen, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry, 99, 7137-7146 (1995).
Abstract. Using a linear fit of the solvent-ordering part of the microscopic surface tension to experimental macroscopic surface tensions, the Generalized Born/Surface Tension solvation model presented previously for n-hexadecane (called Solvation Model 4 or SM4), is extended to include all alkanes as solvents, including normal, branched, and cyclic alkanes. The general SM4 alkane model is applicable to any alkane solvent for which the macroscopic dielectric constant and surface tension are either known or estimable. It treats electrostatic effects, including polarization of the solute by a reaction field, in terms of a continuum dielectric model of the solvent, uses element-based surface tension terms to account for first-solvation-shell effects, and uses an element-independent surface tension to account for solvent-ordering effects that extend further into solution. The electrostatic terms are based on the recently developed Charge Model 1 (CM1) for computing atomic partial charges. This charge model allows the development of a single set of parameters which is applicable to both the AM1 and PM3 Hamiltonians and also to any other electronic structure method that provides reasonably accurate geometries and partial charges.
"Relative Stability of Alternative Chair Forms and Hydroxymethyl Conformations of D-Glucopyranose," S. E. Barrows, F. J. Dulles, C. J. Cramer, D. G. Truhlar, and A. D. French, Carbohydrate Research, 276, 219-251 (1995).
Abstract. The relative energies of two hydroxymethyl conformers for each of the two chair forms (4C1 and 1C4) of beta-D-glucose were calculated at much more complete levels of quantum mechanical (QM) electronic structure theory than previously available, and relative free energies in solution were calculated by adding vibrational, rotational, and solvent effects. The gas-phase results are based on very large basis sets (up to 624 contracted basis functions), and the coupled cluster method for electron correlation. Solvation Model 4 was used to calculate the effects of hydration or nonpolar solvation. Molecular mechanics (MM) and quantum mechanical (QM) electronic structure theory have been applied to analyze the factors contributing to the relative energies of these conformers. Relative energies varied widely (up to 35 kcal/mol) depending on theoretical level, and several levels of theory predict the experimentally unobserved 1C4 ring conformation to be the lower in energy. The highest-level calculations predict the 4C1 chair to be lower in free energy by about 8 kcal/mol, and we also find that the gauche, i.e., gt, conformer of 4C1 is lower than the trans, i.e., tg. Low-energy structures optimized by either quantum mechanical or molecular mechanical methods were commonly characterized by multiple intramolecular hydrogen bonds. Superior hydrogen bonding geometries are available in the 1C4 chair, but are counteracted by increased steric repulsions between axial substituents; MM calculations also indicate increased torsional strain in the 1C4 chair. Manifestations of greater steric strain in the calculated 1C4 structures compared to the 4C1 structures include longer ring bonds, a larger bond angle at the ring oxygen atom, and smaller puckering amplitudes. The MM and QM 4C1 structures compare well with each other and with available X-ray diffraction data. The largest discrepancies between the two kinds of models occur for geometric parameters associated with the anomeric center-the QM structure agrees better with experiment. Greater differences between QM and MM structures are observed for 1C4 structures, especially in the relative orientations of hydroxyl groups serving as hydrogen bond acceptors. In water, the 4C1 chairs are better solvated than the 1C4 chairs by about 5 to 9 kcal/mol because of both larger polarization free energies and improved hydrogen bonding interactions with the first solvation shell. In (a hypothetical) n-hexadecane solution, the 4C1 chairs are better solvated by about 2 to 4 kcal/mol both because of larger polarization free energies and because the larger solvent accessible surface areas of the 4C1 conformers allow increased favorable dispersion interactions. The differential polarization free energies are associated primarily with the hydroxyl groups; the greater steric congestion in the 1C4 chairs reduces opportunities for favorable dielectric screening.
"Pairwise Solute Screening of Solute Charges from a Dielectric Medium," G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Chemical Physics Letters, 246, 122-129 (1995).
Abstract. We present an algorithm for incorporating a pairwise descreening approximation into the calculation of the electrostatic component of the polarization free energy of solvation within the generalized Born approximation. The method was tested on a set of 139 molecules containing H, C, O, and N. The complexity of the descreening calculation is greatly simplified by the pairwise approximation; nevertheless, using the pairwise descreening method to parameterize a new version of a previous generalized Born solvation model, we found that the RMS error relative to experiment increased by only 0.2 kcal/mol.
Page 124, eq. (15). U-sub-kk' = R-sub-kk' - rho-sub-k' should be replaced withU-sub-kk' = R-sub-kk' + rho-sub-k'
Abstract. Using PM3-SM3 calculations, the differential free energy of solvation between cyclic and acyclic phosphate esters is shown to result from solute screening of solute charges from the dielectric of the solvent.
Errata:Table 1. The first three numbers in the column labeled "Poisson" should be -120, -104, -224. These were typographical errors.
"Entropic Contributions to Free Energies of Solvation," D. J. Giesen, C. J. Cramer, and D. G. Truhlar, Journal of Physical Chemistry 98, 4141-4147 (1994).
Abstract. Two alternative ways to treat the entropy of solution in the molecular thermodynamics of liquid-phase solutions have proved useful under various circumstances. The first is the ideal solution theory in which the entropic effects are the same as for mixing ideal gases. The second is the theory of Flory and Huggins which is most appropriate for nondilute solutions of chain molecules in small solvents. The two theories are compared for their ability to describe solutions of alkanes, both straight-chain and branched, in aqueous solution. The alkanes provide an especially appropriate testing field because electrostatic effects are minimal, and it is reasonable to assume that the solvation free energy consists almost entirely of entropic contributions and first-hydration-shell effects. The tests show that the experimental data are better correlated by the ideal solution theory than by adding an explicit volume-dependent contribution from Flory-Huggins theory, as suggested by Sharp, Nicholls, Friedman, and Honig. We disagree with a recent recommendation that one should use Flory-Huggins theory to change the definition of the experimental free energy of transfer of a solute from the gas phase into solution and also with the suggestions that there is a general volume contribution to the free energy of solvation that is well modeled by the Flory-Huggins term.
Page 4142. In equation 13, insert ln before the integration sign. Results and conclusions are not affected."Quantum Chemical Conformational Analysis of 1,2-Ethanediol: Correlation and Solvation Effects on the Tendency to Form Internal Hydrogen Bonds in the Gas Phase and Aqueous Solution," C. J. Cramer and D. G. Truhlar, Journal of the American Chemical Society 116, 3892-3900 (1994).
Abstract. Correlated ab initio calculations with very large (correlation-consistent polarized valence triple-zeta) basis sets predict that 1,2-ethanediol adopts a gas-phase population of conformers at 298 K comprised of rotamers 98% gauche and 2% trans about the C-C bond. Gauche conformers that have internal hydrogen bonds make up 83% of the total population. Changes in relative energy of up to 0.6 kcal/mol are observed upon decreasing the size of the basis set to correlation-consistent polarized double-zeta (which is still larger than commonly used polarized double-zeta basis sets), illustrating the difficulty of even gas-phase conformational analysis in the seemingly simple molecule; the extra variational freedom and more complete polarization space in the larger basis stabilizes trans hydroxyl conformations and increases by a factor of 2 both the predicted fractional population of trans C-C rotamers and the predicted population of conformers with no internal hydrogen bond. Solvation effects were studied using the SMx series of quantum statistical aqueous solvation models. By adding calculated free energies of solvation to gas-phase free energies, it is found that the trans population increases from 2 to 12%, and the portion of conformers having no internal hydrogen bond increases from 17 to 25%. The calculated results are in reasonable agreement with experimental results both in the gas phase and in aqueous solution. The results provide a consistent picture of the competition between the various effects (electronic energies, zero point effects, thermal vibrational-rotational free energy components, and electric polarization and first hydration shell contributions to solvation free energies) that, when combined with the proper statistics, contribute to determining the populations of all possible isomers in aqueous solution. Calculated relative solvation free energies for gauche vs trans C-C torsion are also in good agreement with classical Monte Carlo and molecular dynamics simulation results.
"Solvation Modeling in Aqueous and Nonaqueous Solvents: New Techniques and a Re-examination of the Claisen Rearrangement," J. W. Storer, D. J. Giesen, G. D. Hawkins, G. C. Lynch, C. J. Cramer, D. G. Truhlar, and D. A. Liotard, in Structure and Reactivity in Aqueous Solution: Characterization of Chemical and Biological Systems, edited by C. J. Cramer and D. G. Truhlar (American Chemical Society, Washington, DC, 1994), pp. 24-49.
Abstract. This chapter presents an overview of recent improvements and extensions of the quantum mechanical generalized-Born-plus-surface-tensions (GB/ST) approach to calculating free energies of solvation, followed by a new treatment of solvation effects on the Claisen rearrangement. The general improvements include more efficient algorithms in the AMSOL computer code and the use of class IV charge models. These improvements are used with specific reaction parameters to calculate the solvation effect on the Claisen rearrangement both in alkane and in water, and the results are compared to other recent work on this reaction.
"Development and Biological Applications of Quantum Mechanical Continuum Solvation Models," C. J. Cramer and D. G. Truhlar, in Solute/Solvent Interactions (Theoretical and Computational Chemistry, Vol. 1), edited by P. Politzer and J. S. Murray (Elsevier, Amsterdam, 1994), pp. 9-54.
Abstract. This book chapter examines the various methods that include solvent effects using a dielectric continuum and discusses how the models can be applied to systems of biological interest. Dielectric continuum models can be used to gain further insight into the electronic structure and molecular conformation of compounds such a dopamine and glucose. The role of dielectric continuum models in the calculation of predictors in QSAR and LSER relationships is explored.
Page 17. Change lambda = 0.5 to lambda = 1.
Page 18. Lines 14-15: Change end of sentence to "via the factor of 0.5 by which eq. (8) differs from g in
eq. (9)." Lines 21 and 25: Change lambda = 1 to lambda = 2. Lines 26-27, replace last sentence of paragraph
by: Yet another method may be employed in which lamdba = 0.5. For any value of lambda that is used to
optimize the orbitals (and hence the dipole moment), the final energy should be calculated correctly for
the resulting orbitals, including the cost of distorting the solute and polarizing the solvent, although
only for the nonphysical choice lamdba = 0.5 is the eigenvalue E of the nonlinear Schroedinger equation
equal to the final free energy, and only for the choice lambda = 1 are the orbitals and dipole moment
optimized correctly in the environment.
Page 18, last paragraph. Lines 1-2: Change "Both" to "Two"; change lambda = 0.5 to lamdba = 1; move Refs.
57,66 to precede 71; change lambda = 1 to lambda = 0.5. Delete the last 7 lines of page 18 and the first
2 lines of page 19.
Page 20, line 4, delete "with lambda = 0.5"
Page 20, lines 9-14: Change sentence to: Tapia  has discussed the competing derivations with lambda =
0.5 and 1, but it appears that all recent implementations of the general multipole approach have used
the theoretically justified  value lambda = 1 [71,132-139].
Page 22. Lines 4-6: Change sentence to: "With regard to the last point, there has been some discussion of
taking lamdba = 0.5." Lines 9-11: Change sentence to: "Published work, however, seems to be based
exclusively on lamdba = 1 [65,74,128,169-179,182]."
Abstract. We present calculations of the absolute free energy of solvation of five nucleic acid bases and five methylated nucleic acid bases using a recently developed local-field SCF procedure in which the electronic structure and geometry are both optimized in the presence of solvent. The calculated solvation free energies are increased 23%-34% by the aqueous-phase relaxation.
"Quantum Chemical Conformational Analysis of Glucose in Aqueous Solution," C. J. Cramer and D. G. Truhlar, Journal of the American Chemical Society 115, 5745-5753 (1993).
Abstract. We have calculated the aqueous solvation effects on the anomeric and conformational equilibria of D-glucopyranose using a quantum solvation model based on a continuum treatment of dielectric polarization and solvent accessible surface area. The solvation model puts the relative ordering of the hydroxymethyl conformers in line with the experimentally determined ordering of populations. Our calculations indicate that the anomeric equilibrium is controlled primarily by effects that are also present in the gas-phase potential energy function, that the gauche/trans O-C(6)-C(5)-O hydroxymethyl conformational equilibrium is dominated by favorable solute-solvent hydrogen bonding interactions, and that other rotameric equilibria are controlled mainly by dielectric polarization of the solvent. The description of the aqueous free energy changes of the latter require at least a distributed monopole representation since they do not correlate with overall dipole moment.
"Correlation and Solvation Effects on Heterocyclic Equilibria in Aqueous Solution," C. J. Cramer and D. G. Truhlar, Journal of the American Chemical Society 115, 8810-8817 (1993).
Abstract. We report extended-basis-set electronic structure calculations with high levels of electron correlation for heterocyclic tautomerizations, augmented by a detailed analysis of the aqueous solvation free energy differences which includes both electronic and geometric relaxation in aqueous solution, according to the Austin Model 1-Solvation Model 2 (AM1-SM2). The equilibria used as test cases are the competition between the hydroxy and oxo forms of 5-hydroxyisoxazoles; these involve two oxo (keto) and two hydroxy (enol) forms. For the unsubstituted parent system, it is found that the energy differences between the two oxo forms and between oxo and hydroxy forms are both very sensitive not only to extending the basis sets and including electron correlation but also to including electron correlation at levels higher than second order, indicating the difficulty of treating sp2 and sp3 centers on an equal footing in ring systems. We also find that treatments of electrostatic components of solvation free energies based on the popular Onsager model underestimate the solvation energy of the syn-hydroxy form because local bond moments have significant effects on the bulk electric polarization even when they largely cancel in the net dipole moment. Finally, we note that there is a significant difference in first-hydration-shell effects for the oxo and hydroxy forms over and above that accounted for by electrostatic polarization. The effects of methyl substitution on the isoxazole ring are explored, and the calculated equilibrium shifts are consistent with available experimental data, which are thereby explained in terms of a combination of changes in both the gas-phase and solvation free energies.
Abstract. A model for absolute free energies of solvation of organic, small inorganic, and biological molecules in aqueous solution is described. This model has the following features: (i) the solute charge distribution is described by distributed monopoles, and solute screening of dielectric polarization is treated with no restrictions on solute shape; (ii) the energetic effects of cavity formation, dispersion interactions, and solute-induced restructuring of water are included by a semiempirical cavity surface tension; and (iii) both of these effects are included in the solute Hamiltonian operator for self-consistent field (SCF) calculations to allow solvent-induced electronic and geometric distortion of the solute. The model is parameterized for solutes composed of H, C, N, O, F, P, S, Cl, Br, and I against experimental data for 150 neutral solutes and 28 ions, with mean absolute errors of 0.7 and 2.6 kilocalories per mole, respectively.
Page 216. In line 1, -0.56 should be -0.52."PM3-SM3: A General Parameterization for Including Aqueous Solvation Effects in the PM3 Molecular Orbital Model," C. J. Cramer and D. G. Truhlar, Journal of Computational Chemistry 13, 1089-1097 (1992).
Abstract. Our recently proposed scheme for including aqueous solvation free energies in parameterized NDDO SCF models is extended to the Parameterized Model 3 semiempirical Hamiltonian. The solvation model takes accurate account of the hydrophobic effect for hydrocarbons, as well as electric polarization of the solvent, the free energy of cavitation, and dispersion interactions. Eight heteroatoms are included (along with H and C), and the new model is parameterized accurately for the water molecule itself, which allows meaningful treatments of specifically hydrogen bonded water molecules. The unphysical partial charges on nitrogen atoms predicted by the Parameterized Model 3 Hamiltonian limit the accuracy of the predicted solvation energies for some compounds containing nitrogen, but the model may be very useful for other systems, especially those for which PM3 is preferred of AM1 for the solute properties of the particular system under study.
Page 1095. Equation 5 is missing two terms because of a typographical error. The missing terms are
+0.5 Sum-over-k,k'(k.not=.k') Z_k Z_k'/r_kk' - 0.5 (1 - 1/Epsilon) Sum-over-k,k' Z_k q_k gamma_kk'
where _ denotes a subscript. Results and conclusions are not affected."AM1-SM2 and PM3-SM3 Parameterized SCF Solvation Models for Free Energies in Aqueous Solution," C. J. Cramer and D. G. Truhlar, Journal of Computer-Aided Molecular Design 6, 629-666 (1992).
Abstract. Two new continuum solvation models have been presented recently, and in the paper they are explained and reviewed in detail with further examples. Solvation Model 2 (AM1-SM2) is based on the Austin Model 1 and Solvation Model 3 (PM3-SM3) on the Parameterized Model 3 semiempirical Hamiltonian. In addition to the incorporation of phosphorus parameters, both of the new models address specific deficiencies in the original Solvation Model 1 (AM1-SM1), viz., (1) more accurate account is taken of the hydrophobic effect for hydrocarbons, (2) assignment of heavy-atom surface tensions is based on the presence or absence of bonded hydrogen atoms, and (3) the treatment of specific hydration-shell water molecules is more consistent. The new models offer considerably improved performance compared to AM1-SM1 for neutral molecules and essentially equivalent performance for ions. The solute charges within the Parameterized Model 3 Hamiltonian limit the utility of PM3-SM3 for compounds containing nitrogen and possibly phosphorus. For other systems both AM1-SM2 and PM3-SM3 give realistic results, but AM1-SM2 in general outperforms PM3-SM3. Key features of the models are discussed with respect to alternative approaches.
Page 634. Because of typographical errors, the last term of equation 19 is missing, and the second term had
"=" in the summation index instead of "does not equal". The corrected equation will be the same as the
corrected equation 5 in Ref. 4 above. Results and conclusions are not affected.
Page 644. The row for 2-pentanone in table 5 should be:
2-pentanone -2.7 0.0 -2.7 -2.6 -0.3 -2.9 -2.9 -0.7 -3.6 -3.5
Page 646. The experimental free energy of solvation values given for P(OCH3)3, P(OC2H5)3, and P(OC3H7)3 in
table 5 are actually the experimental free energies for OP(OCH3)3, OP(OC2H5)3, and OP(OC3H7)3, respectively.
Thus they should be deleted from the error calculations. The error rows requiring correction are:
SM1a SM2 SM3
Mean unsigned error for compounds with four or more kinds of atoms 0.5 0.8 0.8
Mean unsigned error of all (147) compounds 0.6 0.7 0.9
RMS error of all compounds 0.8 0.9 1.2
Page 648. The experimental free energy of solvation for MeOH2+ should read -85 kcal/mol rather than -83 kcal/mol.
Page 648. The row for HC2- in table 6 should be:
HC2- -78.6 1.8 -76.8 -78.6 0.7 -77.7 -77.7 1.2 -76.5 -73
Page 650, last paragraph. For the full set of 147 compounds in Table 5 for which experimental data are available,
SM2 and SM3 give mean unsigned errors of 0.64 (root-mean-square error: 0.87) and 0.92 (rms error: 1.27) kcal/mol,
respectively. For SM1, the set of 147 compounds gives a mean unsigned error of 1.17 (rms error: 1.52) kcal/mol.
Page 653. For 2-pentanone, q(0) is -0.37, and alpha(0) is 2.1 angstroms. Each of the comparisons of q(0) and
alpha(0) in this section are for the SM2 model.
Page 655. In Table 10 the experimental value for reaction V should be 2.4 kcal/mol, not 1.0."What Causes Aqueous Acceleration of the Claisen Rearrangement?" C. J. Cramer and D. G. Truhlar, Journal of the American Chemical Society 114, 8794-8799 (1992).
Abstract. We report the results of applying a new self-consistent-field solvation model to the Claisen rearrangement of allyl vinyl ether, all possible methoxy-substituted derivatives, two alkylated derivatives, and one carboxymethylated derivative in order to understand the effects of aqueous solvation on the reaction rates. We have employed the AM1-SM2 version of the model to calculate the changes in free energies of solvation in passing from the lowest-energy conformations of the starting materials to both chair and boat transition states. The hydrophobic effect is always accelerative but always small and not very structure sensitive. Other first-hydration-shell effects attributable to hydrophilic parts of the reagents are more sensitive to the substitution pattern. The polarization contributions to the activation energies are usually larger. A favorable polarization contribution is found to be associated with efficient sequestration of charges of opposite sign into separated regions of space. We conclude that aqueous acceleration of the Claisen rearrangement is caused by electric polarization and first-hydration-shell hydrophilic effects, with the relative magnitudes and even the signs of these effects being quite sensitive to substitution pattern.
Page 8794. The last row of Table III should read:HF/6-31G* -0.11 0.40 -0.60 0.23 0.00 0.07
Abstract. We present a new general parameterization for aqueous solvation free energies of molecules and ions in aqueous solution. It is obtained by extending a semianalytic treatment of solvation recently proposed for use with molecular mechanics and liquid simulations by Still et al. As extended here, the solvation terms are included in a Fock operator. The model incorporates reaction field polarization effects through the generalized Born functional with charges obtained by AM1 molecular orbital calculations, and it includes cavitation, dispersion, and hydrophobic effects through an empirical function of solvent-accessible-surface area. A general parameter set, including parameters for H, C, N, O, F, S, Cl, Br, and I, has been obtained by considering a data set consisting of 141 neutral molecules, 10 cations, and 17 anions. The neutral molecules include alkanes, cycloalkanes, alkenes, arenes, alkynes, ethers, heterocycles, carboxylic acids, esters, nitriles, aldehydes, ketones, alcohols, amines, nitro compounds, sulfides, thiols, halides, and polyfunctional compounds. Then general parameterization is called Solvation Model 1, and it is particularly well suited for chemical reaction dynamics and reaction intermediates. We also discuss how the model may be refined for solvation free energies for stable neutral molecules.
Page 8306. Connolly's name is misspelled in Ref. 27.
Page 8310. In Table VI, 1,2-dibromomethane should be 1,2-dibromoethane.
Supplementary material, page 1. The row for 2-pentanone should be 2-pentanone -2.7 -1.7 -4.4 -3.5 -2.7
In equation 11, the sum over mu' should be moved inside the parentheses in front of the P-sub-mu'mu' term"Molecular Orbital Theory Calculations of Aqueous Solvation Effects on Chemical Equilibria," C. J. Cramer and D. G. Truhlar, Journal of the American Chemical Society 113, 8552-8554. Erratum: 113, 9901 (1991).
Abstract. The SM1 Model is applied to reaction equilibria, in particular, acid-base proton transfers, prototropic tautomerizations, and rotameric equilibria in a Communication to the Editor.
Page 8552. In Ref. 7a, 5129 should be S129.Page 8552. In Table II the experimental value for reaction 5 should be 2.4 kcal/mol, not 1.0.