Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections

Molecular Density Functional Theory (MDFT) offers an efficient implicit- solvent method to estimate molecule solvation free-energies whereas conserving a fully molecular representation of the solvent. Even within a second order ap- proximation for the free-energy functional, the so-called homogeneous reference uid approximation, we show that the hydration free-energies computed for a dataset of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by two to three orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canoni- cal to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justifcation to empirical partial molar volume corrections that have been proposed recently.Comment: Version with correct equation numbers is here: http://compchemmpi.wikispaces.com/file/view/sergiievskyi_et_al.pdf/513575848/sergiievskyi_et_al.pdf Supporting information available online at: http://compchemmpi.wikispaces.com/file/view/SuppInf_sergiievskyi_et_al_07-04-2014.pdf/513576008/SuppInf_sergiievskyi_et_al_07-04-2014.pd

Molecular Density Functional Theory for water with liquid-gas coexistence and correct pressure

The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular density functional theory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third order expansion of the functional around the bulk liquid density that imposes the right pressure and the correct second order derivatives. Although this theory is not limited to water, we apply it to study hydrophobic solvation in water at room temperature and pressure and compare the results to all-atom simulations. With this correction, molecular density functional theory gives, at a modest computational cost, quantitative hydration free energies and structures of small molecular solutes like n-alkanes, and of hard sphere solutes whose radii range from angstroms to nanometers. The macroscopic liquid-gas surface tension predicted by the theory is comparable to experiments. This theory gives an alternative to the empirical hard sphere bridge correction used so far by several authors.Comment: 18 pages, 6 figure

Fast calculation of thermodynamic and structural parameters of solutions using the 3DRISM model and the multi-grid method

In the paper a new method to solve the tree-dimensional reference interaction site model (3DRISM) integral equations is proposed. The algorithm uses the multi-grid technique which allows to decrease the computational expanses. 3DRISM calculations for aqueous solutions of four compounds (argon, water, methane, methanol) on the different grids are performed in order to determine a dependence of the computational error on the parameters of the grid. It is shown that calculations on the grid with the step 0.05\Angstr and buffer 8\Angstr give the error of solvation free energy calculations less than 0.3 kcal/mol which is comparable to the accuracy of the experimental measurements. The performance of the algorithm is tested. It is shown that the proposed algorithm is in average more than 12 times faster than the standard Picard direct iteration method.Comment: the information in this preprint is not up to date. Since the first publication of the preprint (9 Nov 2011) the algorithm was modified which allowed to achieve better results. For the new algorithm see the JCTC paper: DOI: 10.1021/ct200815v, http://pubs.acs.org/doi/abs/10.1021/ct200815

Multigrid solver for the reference interaction site model of molecular liquids theory

In this article, we propose a new multigrid-based algorithm for solving integral equations of the reference interactions site model (RISM). We also investigate the relationship between the parameters of the algorithm and the numerical accuracy of the hydration free energy calculations by RISM. For this purpose, we analyzed the performance of the method for several numerical tests with polar and nonpolar compounds. The results of this analysis provide some guidelines for choosing an optimal set of parameters to minimize computational expenses. We compared the performance of the proposed multigrid-based method with the one-grid Picard iteration and nested Picard iteration methods. We show that the proposed method is over 30 times faster than the one-grid iteration method, and in the high accuracy regime, it is almost seven times faster than the nested Picard iteration method

3DRISM Multigrid Algorithm for Fast Solvation Free Energy Calculations

In this paper we present a fast and accurate method for modeling solvation properties of organic molecules in water with a main focus on predicting solvation (hydration) free energies of small organic compounds. The method is based on a combination of (i) a molecular theory, three-dimensional reference interaction sites model (3DRISM); (ii) a fast multigrid algorithm for solving the high-dimensional 3DRISM integral equations; and (iii) a recently introduced universal correction (UC) for the 3DRISM solvation free energies by properly scaled molecular partial volume (3DRISM-UC, Palmer et al., <i>J. Phys.: Condens. Matter</i> <b>2010</b>, <i>22</i>, 492101). A fast multigrid algorithm is the core of the method because it helps to reduce the high computational costs associated with solving the 3DRISM equations. To facilitate future applications of the method, we performed benchmarking of the algorithm on a set of several model solutes in order to find optimal grid parameters and to test the performance and accuracy of the algorithm. We have shown that the proposed new multigrid algorithm is on average 24 times faster than the simple Picard method and at least 3.5 times faster than the MDIIS method which is currently actively used by the 3DRISM community (e.g., the MDIIS method has been recently implemented in a new 3DRISM implicit solvent routine in the recent release of the AmberTools 1.4 molecular modeling package (Luchko et al. <i>J. Chem. Theory Comput</i>. <b>2010</b>, <i>6</i>, 607–624). Then we have benchmarked the multigrid algorithm with chosen optimal parameters on a set of 99 organic compounds. We show that average computational time required for one 3DRISM calculation is 3.5 min per a small organic molecule (10–20 atoms) on a standard personal computer. We also benchmarked predicted solvation free energy values for all of the compounds in the set against the corresponding experimental data. We show that by using the proposed multigrid algorithm and the 3DRISM-UC model, it is possible to obtain good correlation between calculated and experimental results for solvation free energies of aqueous solutions of small organic compounds (correlation coefficient 0.97, root-mean-square deviation <1 kcal/mol)

Accurate calculations of the hydration free energies of druglike molecules using the reference interaction site model

We report on the results of testing the reference interaction site model (RISM) for the estimation of the hydration free energy of druglike molecules. The optimum model was selected after testing of different RISM free energy expressions combined with different quantum mechanics and empirical force-field methods of structure optimization and atomic partial charge calculation. The final model gave a systematic error with a standard deviation of 2.6 kcal/mol for a test set of 31 molecules selected from the SAMPL1 blind challenge set [J. P. Guthrie, J. Phys. Chem. B 113, 4501 (2009)]. After parametrization of this model to include terms for the excluded volume and the number of atoms of different types in the molecule, the root mean squared error for a test set of 19 molecules was less than 1.2 kcal/mol

Accurate calculations of the hydration free energies of druglike molecules using the reference interaction site model

We report on the results of testing the reference interaction site model (RISM) for the estimation of the hydration free energy of druglike molecules. The optimum model was selected after testing of different RISM free energy expressions combined with different quantum mechanics and empirical force-field methods of structure optimization and atomic partial charge calculation. The final model gave a systematic error with a standard deviation of 2.6 kcal/mol for a test set of 31 molecules selected from the SAMPL1 blind challenge set [J. P. Guthrie, J. Phys. Chem. B 113, 4501 (2009)]. After parametrization of this model to include terms for the excluded volume and the number of atoms of different types in the molecule, the root mean squared error for a test set of 19 molecules was less than 1.2 kcal/mol

Reference interaction site model with structural descriptors correction as an efficient tool for hydration free energy predictions

This abstract discusses reference interaction site models with structural descriptors correction as an efficient tool for hydration free energy predictions