Ion solvation thermodynamics from simulation with a polarizable force field

Thermodynamic measurements of the solvation of salts and electrolytes are relatively straightforward, but it is not possible to separate total solvation free energies into distinct cation and anion contributions without reference to an additional extrathermodynamic assumption. The present work attempts to resolve this difficulty using molecular dynamics simulations with the AMOEBA polarizable force field and perturbation techniques to directly compute absolute solvation free energies for potassium, sodium, and chloride ions in liquid water and formamide. Corresponding calculations are also performed with two widely used nonpolarizable force fields. The simulations with the polarizable force field accurately reproduce in vacuo quantum mechanical results, experimental ion-cluster solvation enthalpies, and experimental solvation free energies for whole salts, while the other force fields do not. The results indicate that calculations with a polarizable force field can capture the thermodynamics of ion solvation and that the solvation free energies of the individual ions differ by several kilocalories from commonly cited values.     

Multipole electrostatics in hydration free energy calculations

Hydration free energy (HFE) is generally used for evaluating molecular solubility, which is an important property for pharmaceutical and chemical engineering processes. Accurately predicting HFE is also recognized as one fundamental capability of molecular mechanics force field. Here, we present a systematic investigation on HFE calculations with AMOEBA polarizable force field at various parameterization and simulation conditions. The HFEs of seven small organic molecules have been obtained alchemically using the Bennett Acceptance Ratio method. We have compared two approaches to derive the atomic multipoles from quantum mechanical calculations: one directly from the new distributed multipole analysis and the other involving fitting to the electrostatic potential around the molecules. Wave functions solved at the MP2 level with four basis sets (6-311G*, 6-311++G(2d,2p), cc-pVTZ, and aug-cc-pVTZ) are used to derive the atomic multipoles. HFEs from all four basis sets show a reasonable agreement with experimental data (root mean square error 0.63 kcal/mol for aug-cc-pVTZ). We conclude that aug-cc-pVTZ gives the best performance when used with AMOEBA, and 6-311++G(2d,2p) is comparable but more efficient for larger systems. The results suggest that the inclusion of diffuse basis functions is important for capturing intermolecular interactions. The effect of long-range correction to van der Waals interaction on the hydration free energies is about 0.1 kcal/mol when the cutoff is 12?, and increases linearly with the number of atoms in the solute/ligand. In addition, we also discussed the results from a hybrid approach that combines polarizable solute with fixed-charge water in the HFE calculation.     

Absolute binding free energies for the SAMPL6 cucurbit[8]uril host–guest challenge via the AMOEBA polarizable force field

As part of the SAMPL6 host–guest blind challenge, the AMOEBA force field was applied to calculate the absolute binding free energy for a cucurbit[8]uril host complexed with 14 diverse guests, ranging from small, rigid structures to drug molecules. The AMOEBA results from the initial submission prompted an investigation into aspects of the methodology and parameterization employed. Lessons learned from the blind challenge include: a double annihilation scheme (electrostatics and van der Waals) is needed to obtain proper sampling of guest conformations, annihilation of key torsion parameters of the guest are recommended for flexible guests, and a more thorough analysis of torsion parameters is warranted. When put in to practice with the AMOEBA model, the lessons learned improved the MUE from 2.63 to 1.20 kcal/mol and the RMSE from 3.62 to 1.68 kcal/mol, respectively. Overall, the AMOEBA protocol for determining absolute binding free energies benefitted from participation in the SAMPL6 host–guest blind challenge and the results suggest the implementation of the methodology in future host–guest calculations.     

Evaluation of solvation free energies for small molecules with the AMOEBA polarizable force field

The effects of electronic polarization in biomolecular interactions will differ depending on the local dielectric constant of the environment, such as in solvent, DNA, proteins, and membranes. Here the performance of the AMOEBA polarizable force field is evaluated under nonaqueous conditions by calculating the solvation free energies of small molecules in four common organic solvents. Results are compared with experimental data and equivalent simulations performed with the GAFF pairwise‐additive force field. Although AMOEBA results give mean errors close to “chemical accuracy,” GAFF performs surprisingly well, with statistically significantly more accurate results than AMOEBA in some solvents. However, for both models, free energies calculated in chloroform show worst agreement to experiment and individual solutes are consistently poor performers, suggesting non‐potential‐specific errors also contribute to inaccuracy. Scope for the improvement of both potentials remains limited by the lack of high quality experimental data across multiple solvents, particularly those of high dielectric constant. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Polarizable Atomic Multipole-based Molecular Mechanics for Organic Molecules

An empirical potential based on permanent atomic multipoles and atomic induced dipoles is reported for alkanes, alcohols, amines, sulfides, aldehydes, carboxylic acids, amides, aromatics and other small organic molecules. Permanent atomic multipole moments through quadrupole moments have been derived from gas phase ab initio molecular orbital calculations. The van der Waals parameters are obtained by fitting to gas phase homodimer QM energies and structures, as well as experimental densities and heats of vaporization of neat liquids. As a validation, the hydrogen bonding energies and structures of gas phase heterodimers with water are evaluated using the resulting potential. For 32 homo- and heterodimers, the association energy agrees with ab initio results to within 0.4 kcal/mol. The RMS deviation of hydrogen bond distance from QM optimized geometry is less than 0.06 ?. In addition, liquid self-diffusion and static dielectric constants computed from molecular dynamics simulation are consistent with experimental values. The force field is also used to compute the solvation free energy of 27 compounds not included in the parameterization process, with a RMS error of 0.69 kcal/mol. The results obtained in this study suggest the AMOEBA force field performs well across different environments and phases. The key algorithms involved in the electrostatic model and a protocol for developing parameters are detailed to facilitate extension to additional molecular systems.     

On the transferability of hydration-parametrized continuum electrostatics models to solvated binding calculations

Using molecular mechanics force field partial atomic charges, we show the nonuniqueness of the parametrization of continuum electrostatics models with respect to solute atomic radii and interior dielectric constant based on hydration (vacuum-to-water transfer) free energy data available for small molecules. Moreover, parameter sets that are optimal and equivalent for hydration free energy calculations lead to large variations of calculated absolute and relative electrostatic binding free energies. Hence, parametrization of solvation effects based on hydration data, although a necessary condition, is not sufficient to guarantee its transferability to the calculation of binding free energies in solution.     

Toward accurate solvation dynamics of lanthanides and actinides in water using polarizable force fields: from gas-phase energetics to hydration free energies

In this contribution, we focused on the use of polarizable force fields to model the structural, energetic, and thermodynamical properties of lanthanides and actinides in water. In a first part, we chose the particular case of the Th(IV) cation to demonstrate the capabilities of the AMOEBA polarizable force field to reproduce both reference ab initio gas-phase energetics and experimental data including coordination numbers and radial distribution functions. Using such model, we predicted the first polarizable force field estimate of Th(IV) solvation free energy, which accounts for −1,638 kcal/mol. In addition, we proposed in a second part of this work a full extension of the SIBFA (Sum of Interaction Between Fragments Ab initio computed) polarizable potential to lanthanides (La(III) and Lu(III)) and to actinides (Th(IV)) in water. We demonstrate its capabilities to reproduce all ab initio contributions as extracted from energy decomposition analysis computations, including many-body charge transfer and discussed its applicability to extended molecular dynamics and its parametrization on high-level post-Hartree–Fock data.     

Derivation of force field parameters for SnO2-H2O surface systems from plane-wave density functional theory calculations

Plane-wave density functional theory (DFT-PW) calculations were performed on bulk SnO2 (cassiterite) and the (100), (110), (001), and (101) surfaces with and without H2O present. A classical interatomic force field has been developed to describe bulk SnO2 and SnO2-H2O surface interactions. Periodic density functional theory calculations using the program VASP (Kresse et al., 1996) and molecular cluster calculations using Gaussian 03 (Frisch et al., 2003) were used to derive the parametrization of the force field. The program GULP (Gale, 1997) was used to optimize parameters to reproduce experimental and ab initio results. The experimental crystal structure and elastic constants of SnO2 are reproduced reasonably well with the force field. Furthermore, surface atom relaxations and structures of adsorbed H2O molecules agree well between the ab initio and force field predictions. H2O addition above that required to form a monolayer results in consistent structures between the DFT-PW and classical force field results as well.     

Molecular dynamics simulations of methane hydrate using polarizable force fields

Molecular dynamics simulations of methane hydrate have been carried out using the polarizable AMOEBA and COS/G2 force fields. Properties calculated include the temperature dependence of the lattice constant, the OC and OO radial distribution functions, and the vibrational spectra. Both the AMOEBA and COS/G2 force fields are found to successfully account for the available experimental data, with overall somewhat better agreement with experiment being found for the AMOEBA model. Comparison is made with previous results obtained using TIP4P and SPC/E effective two-body force fields and the polarizable TIP4P-FQ force field, which allows for in-plane polarization only. Significant differences are found between the properties calculated using the TIP4P-FQ model and those obtained using the other models, indicating an inadequacy of restricting explicit polarization to in-plane only.     

A valence bond model for aqueous Cu(II) and Zn(II) ions in the AMOEBA polarizable force field

A general molecular mechanics (MM) model for treating aqueous Cu²⁺ and Zn²⁺ ions was developed based on valence bond (VB) theory and incorporated into the atomic multipole optimized energetics for biomolecular applications (AMOEBA) polarizable force field. Parameters were obtained by fitting MM energies to that computed by ab initio methods for gas‐phase tetra‐ and hexa‐aqua metal complexes. Molecular dynamics (MD) simulations using the proposed AMOEBA‐VB model were performed for each transition metal ion in aqueous solution, and solvent coordination was evaluated. Results show that the AMOEBA‐VB model generates the correct square‐planar geometry for gas‐phase tetra‐aqua Cu²⁺ complex and improves the accuracy of MM model energetics for a number of ligation geometries when compared to quantum mechanical (QM) computations. On the other hand, both AMOEBA and AMOEBA‐VB generate results for Zn²⁺–water complexes in good agreement with QM calculations. Analyses of the MD trajectories revealed a six‐coordination first solvation shell for both Cu²⁺ and Zn²⁺ ions in aqueous solution, with ligation geometries falling in the range reported by previous studies. © 2012 Wiley Periodicals, Inc.     

Estimating and modeling charge transfer from the SAPT induction energy

Recent studies using quantum mechanics energy decomposition methods, for example, SAPT and ALMO, have revealed that the charge transfer energy may play an important role in short ranged inter‐molecular interactions, and have a different distance dependence comparing with the polarization energy. However, the charge transfer energy component has been ignored in most current polarizable or non‐polarizable force fields. In this work, first, we proposed an empirical decomposition of SAPT induction energy into charge transfer and polarization energy that mimics the regularized SAPT method (ED‐SAPT). This empirical decomposition is free of the divergence issue, hence providing a good reference for force field development. Then, we further extended this concept in the context of AMOEBA polarizable force field, proposed a consistent approach to treat the charge transfer phenomenon. Current results show a promising application of this charge transfer model in future force field development. © 2017 Wiley Periodicals, Inc.     

Molecular mechanics (MM2) and conformational analysis of compounds with N?C?O units. Parametrization of the force field and anomeric effect

A molecular mechanics force field was developed for systems bearing the N? C? O unit on the basis of 6-31G* and 4-21G “ab initio” calculations with full optimization of the geometry and experimental heats of formation. The parameters used, which implicitly included the anomeric effect, provided good geometric and energetic results, both for the compounds on which the parametrization was based and for others on which the validity of the predictions was checked.     

A new strategy for the evaluation of force parameters from quantum mechanical computations

A new strategy for the determination of force parameters is presented. The equilibrium values appearing in the force field equations representing the “stretching” and “bending” of bonds are directly determined from quantum mechanical calculations without geometrical restrictions. The determination of the force parameters is carried out by means of a rigorous fitting between the quantum mechanic and the molecular mechanical energy variations arising from the perturbation of the geometric variables. The strategy presented here has been incorporated into a computer program named PAPQMD, which was developed in order to provide nonquantum mechanical experts with a powerful tool for the determination of approximate force parameters. The program was developed upon the assumption that force parameters are not universal, but they strongly depend on the molecular environment. This implies that the parametrization procedure should be done in a molecular model close to the molecule or molecules to be studied by means of molecular mechanical or dynamic methods, and consequently, it is no longer supposed that the variation of one geometrical parameter does not affect the rest of the molecular geometry. PAPQMD performs the fitting between molecular mechanics and quantum mechanical energies considering all the perturbations that the modification in one geometric variable causes in all the others, enabling the parametrization even of large molecules. The ability of our method to reproduce experimentally derived force parameters is discussed and compared with the widely used Hopfinger's strategy. The study of the behavior of PAPQMD and Hopfinger's strategies for reproducing the force parameters of two complex molecules demonstrates the superiority of the methodology presented here.     

The Structure, Thermodynamics and Solubility of Organic Crystals from Simulation with a Polarizable Force Field

An important unsolved problem in materials science is prediction of the thermodynamic stability of organic crystals and their solubility from first principles. Solubility can be defined as the saturating concentration of a molecule within a liquid solvent, where the physical picture is of solvated molecules in equilibrium with their solid phase. Despite the importance of solubility in determining the oral bioavailability of pharmaceuticals, prediction tools are currently limited to quantitative structure-property relationships that are fit to experimental solubility measurements. For the first time, we describe a consistent procedure for the prediction of the structure, thermodynamic stability and solubility of organic crystals from molecular dynamics simulations using the polarizable multipole AMOEBA force field. Our approach is based on a thermodynamic cycle that decomposes standard state solubility into the sum of solid-vapor sublimation and vapor-liquid solvation free energies [Formula: see text], which are computed via the orthogonal space random walk (OSRW) sampling strategy. Application to the n-alkylamides series from aeetamide through octanamide was selected due to the dependence of their solubility on both amide hydrogen bonding and the hydrophobic effect, which are each fundamental to protein structure and solubility. On average, the calculated absolute standard state solubility free energies are accurate to within 1.1 kcal/mol. The experimental trend of decreasing solubility as a function of n-alkylamide chain length is recapitulated by the increasing stability of the crystalline state and to a lesser degree by decreasing favorability of solvation (i.e. the hydrophobic effect). Our results suggest that coupling the polarizable AMOEBA force field with an orthogonal space based free energy algorithm, as implemented in the program Force Field X, is a consistent procedure for predicting the structure, thermodynamic stability and solubility of organic crystals.     

Towards accurate solvation dynamics of divalent cations in water using the polarizable amoeba force field: From energetics to structure

Molecular dynamics simulations were performed using a modified amoeba force field to determine hydration and dynamical properties of the divalent cations Ca2+ and Mg2+. The extension of amoeba to divalent cations required the introduction of a cation specific parametrization. To accomplish this, the Thole polarization damping model parametrization was modified based on the ab initio polarization energy computed by a constrained space orbital variation energy decomposition scheme. Excellent agreement has been found with condensed phase experimental results using parameters derived from gas phase ab initio calculations. Additionally, we have observed that the coordination of the calcium cation is influenced by the size of the periodic water box, a recurrent issue in first principles molecular dynamics studies.     

Additive CHARMM force field for naturally occurring modified ribonucleotides

More than 100 naturally occurring modified nucleotides have been found in RNA molecules, in particular in tRNAs. We have determined molecular mechanics force field parameters compatible with the CHARMM36 all‐atom additive force field for all these modifications using the CHARMM force field parametrization strategy. Emphasis was placed on fine tuning of the partial atomic charges and torsion angle parameters. Quantum mechanics calculations on model compounds provided the initial set of target data, and extensive molecular dynamics simulations of nucleotides and oligonucleotides in aqueous solutions were used for further refinement against experimental data. The presented parameters will allow for computational studies of a wide range of RNAs containing modified nucleotides, including the ribosome and transfer RNAs. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.