Atomic radius and charge parameter uncertainty in biomolecular solvation energy calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parameterization problems, including those beyond continuum solvation calculations.The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters

Computational Study of Copper(II) Complexation and Hydrolysis in Aqueous Solutions Using Mixed Cluster/Continuum Models

We use density functional theory (B3LYP) and the COSMO continuum solvent model to characterize the structure and stability of the hydrated Cu(II) complexes [Cu(MeNH_2)(H_2O)_(n−1)]^(2+) and [Cu(OH)_x(H_2O)_(n−x)]^(2−x) (x = 1−3) as a function of metal coordination number (4−6) and cluster size (n = 4−8, 18). The small clusters with n = 4−8 are found to be the most stable in the nearly square-planar four-coordinate configuration, except for [Cu(OH)_3(H_2O)]^−, which is three-coordinate. In the presence of the two full hydration shells (n = 18), however, the five-coordinate square-pyramidal geometry is the most favorable for Cu(MeNH_2)^(2+) (5, 6) and Cu(OH)^+ (5, 4, 6), and the four-coordinate geometry is the most stable for Cu(OH)_2 (4, 5) and Cu(OH)_3^− (4). (Other possible coordination numbers for these complexes in the aqueous phase are shown in parentheses.) A small energetic difference between these structures (0.23−2.65 kcal/mol) suggests that complexes with different coordination numbers may coexist in solution. Using two full hydration shells around the Cu^(2+) ion (18 ligands) gives Gibbs free energies of aqueous reactions that are in excellent agreement with experiment. The mean unsigned error is 0.7 kcal/mol for the three consecutive hydrolysis steps of Cu^(2+) and the complexation of Cu^(2+) with methylamine. Conversely, calculations for the complexes with only one coordination shell (four equatorial ligands) lead to a mean unsigned error that is >6.0 kcal/mol. Thus, the explicit treatment of the first and the second shells is critical for the accurate prediction of structural and thermodynamic properties of Cu(II) species in aqueous solution

Relevance of cis- and trans-dichloride Ru intermediates in Grubbs-II olefin metathesis catalysis (H(2)IMesCl(2)Ru=CHR)

Using density functional theory with the B3LYP and M06 functionals, we show conclusively that the (H2IMes)(Cl)2Ru olefin metathesis mechanism is bottom-bound with the chlorides remaining trans throughout the reaction, thus attempts to effect diastereo- and enantioselectivity should focus on manipulations that maintain the trans-dichloro Ru geometry

Advances in Computational Solvation Thermodynamics

The aim of this thesis is to develop improved methods for calculating the free energy, entropy and enthalpy of solvation from molecular simulations. Solvation thermodynamics of model compounds provides quantitative measurements used to analyze the stability of protein conformations in aqueous milieus. Solvation free energies govern the favorability of the solvation process, while entropy and enthalpy decompositions give insight into the molecular mechanisms by which the process occurs. Computationally, a coupling parameter λ modulates solute-solvent interactions to simulate an insertion process, and multiple lengthy simulations at a fixed λ value are typically required for free energy calculations to converge; entropy and enthalpy decompositions generally take 10-100 times longer. This thesis presents three advances which accelerate the convergence of such calculations: 1) Development of entropy and enthalpy estimators which combine data from multiple simulations; 2) Optimization of λ schedules, or the set of parameter values associated with each simulation; 3) Validation of Hamiltonian replica exchange, a technique which swaps λ values between two otherwise independent simulations. Taken together, these techniques promise to increase the accuracy and precision of free energy, entropy and enthalpy calculations. Improved estimates, in turn, can be used to investigate the validity and limits of existing solvation models and refine force field parameters, with the goal of understanding better the collapse transition and aggregation behavior of polypeptides

Free-Energy Barriers and Reaction Mechanisms for the Electrochemical Reduction of CO on the Cu(100) Surface, Including Multiple Layers of Explicit Solvent at pH 0

The great interest in the photochemical reduction from CO_2 to fuels and chemicals has focused attention on Cu because of its unique ability to catalyze formation of carbon-containing fuels and chemicals. A particular goal is to learn how to modify the Cu catalysts to enhance the production selectivity while reducing the energy requirements (overpotential). To enable such developments, we report here the free-energy reaction barriers and mechanistic pathways on the Cu(100) surface, which produces only CH_4 (not C_2H_4 or CH_3OH) in acid (pH 0). We predict a threshold potential for CH_4 formation of −0.52 V, which compares well to experiments at low pH, −0.45 to −0.50 V. These quantum molecular dynamics simulations included ∼5 layers of explicit water at the water/electrode interface using enhanced sampling methodology to obtain the free energies. We find that that chemisorbed hydroxyl-methylene (CH–OH) is the key intermediate determining the selectivity for methane over methanol