Free Energies Of Organic Molecules Research Articles

Precision and computational efficiency of nonequilibrium alchemical methods for computing free energies of solvation. II. Unidirectional estimates.

The present paper is the second part of a series of papers aimed at assessing the accuracy of alchemical computational approaches based on nonequilibrium techniques for solvation free energy of organic molecules in the context of molecular dynamics simulations. In Paper I [Procacci, J. Chem. Phys. 151, 144113 (2019)], we dealt with bidirectional estimates of solvation free energies using nonequilibrium approaches. Here, we assess accuracy and precision of unidirectional estimates with the focus on the Gaussian and Jarzynski estimators. We present a very simple methodology to increase the statistics in the work distribution, hence boosting the accuracy and precision of the Jarzynski unidirectional estimates at no extra cost, exploiting the observed decorrelation between the random variables represented by the Lennard-Jones solute-solvent recoupling or decoupling work and by the electrostatic work due to the charging/discharging of the solute in the solvent.

Incorporation of Hydrogen Bond Angle Dependency into the Generalized Solvation Free Energy Density Model.

To describe the physically realistic solvation free energy surface of a molecule in a solvent, a generalized version of the solvation free energy density (G-SFED) calculation method has been developed. In the G-SFED model, the contribution from the hydrogen bond (HB) between a solute and a solvent to the solvation free energy was calculated as the product of the acidity of the donor and the basicity of the acceptor of an HB pair. The acidity and basicity parameters of a solute were derived using the summation of acidities and basicities of the respective acidic and basic functional groups of the solute, and that of the solvent was experimentally determined. Although the contribution of HBs to the solvation free energy could be evenly distributed to grid points on the surface of a molecule, the G-SFED model was still inadequate to describe the angle dependency of the HB of a solute with a polarizable continuum solvent. To overcome this shortcoming of the G-SFED model, the contribution of HBs was formulated using the geometric parameters of the grid points described in the HB coordinate system of the solute. We propose an HB angle dependency incorporated into the G-SFED model, i.e., the G-SFED-HB model, where the angular-dependent acidity and basicity densities are defined and parametrized with experimental data. The G-SFED-HB model was then applied to calculate the solvation free energies of organic molecules in water, various alcohols and ethers, and the log P values of diverse organic molecules, including peptides and a protein. Both the G-SFED model and the G-SFED-HB model reproduced the experimental solvation free energies with similar accuracy, whereas the distributions of the SFED on the molecular surface calculated by the G-SFED and G-SFED-HB models were quite different, especially for molecules having HB donors or acceptors. Since the angle dependency of HBs was included in the G-SFED-HB model, the SFED distribution of the G-SFED-HB model is well described as compared to that of the G-SFED model.

Calculating free energies of organic molecules on insulating substrates.

The challenges and limitations in calculating free energies and entropies of adsorption and interaction of organic molecules on an insulating substrate are discussed. The adhesion of 1,3,5-tri(4'-cyano-[1,1'-biphenyl]-4-yl)benzene (TCB) and 1,4-bis(4-cyanophenyl)-2,5-bis(decyloxy)benzene (CDB) molecules to step edges on the KCl(001) surface and the formation of molecular dimers were studied using classical molecular dynamics. Both molecules contain the same anchoring groups and benzene ring structures, yet differ in their flexibility. Therefore, the entropic contributions to their free energy differ, which affects surface processes. Using potential of mean force and thermodynamic integration techniques, free energy profiles and entropy changes were calculated for step adhesion and dimer formation of these molecules. However, converging these calculations is nontrivial and comes at large computational cost. We illustrate the difficulties as well as the possibilities of applying these methods towards understanding dynamic processes of organic molecules on insulating substrates.

Comparison of Implicit and Explicit Solvent Models for the Calculation of Solvation Free Energy in Organic Solvents.

2015, 55, 1192-1201) and experimental data. The comparison indicates that both PB and GB give poor agreement with explicit solvent calculations and even worse agreement with experiments (root-mean-square deviation ≈ 15 kJ/mol). The main problem seems to be the prediction of the apolar contribution, which should include the solvent entropy. The quantum mechanical-based SMD model gives significantly better agreement with experimental data than do PB or GB, but it is not as good as explicit solvent calculation results. The dielectric constant ε of the solvent is found to be a powerful predictor for the polar contribution to the free energy in implicit models; however, the Onsager relation may not hold for realistic solvent, as suggested by explicit solvent and SMD calculations. From the comparison, we also find that with an optimization of the apolar contribution, the PB model gives slightly better agreement with experiments than the SMD model, whereas the correlation between the optimized GB models and experiments remains poor. Further optimization of the apolar contribution is needed for GB models to be able to treat solvents other than water.

High-Throughput Calculations of Molecular Properties in the MedeA Environment: Accuracy of PM7 in Predicting Vibrational Frequencies, Ideal Gas Entropies, Heat Capacities, and Gibbs Free Energies of Organic Molecules

The atomistic and molecular simulation environment MedeA (MedeA: Materials Exploration and Design Analysis, version 2.14.6; Material Design, Inc.: Angel Fire, NM, 1998–2014; http://www.materialsdesign.com) in its functionalities and graphical user interface has been enhanced to prepare and submit on the order of 1000 simulations on different structures, and to collect and help in the analysis of the results. We illustrate this with the determination of the accuracy of the semiempirical (SE) package MOPAC2012 (Stewart, J. J. P. MOPAC2012; Stewart Computational Chemistry: Colorado Springs, CO, USA, 2012; http://OpenMOPAC.net) with the PM7 method (Stewart, J. J. P. Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and reoptimization of parameters. J. Mol. Model. 2013, 19, 1–32) to compute frequencies of vibration and thermodynamic properties, specifically the zero point energies, ideal gas heat capacity at constant pressure, entropy, and Gibbs free energy, between 200 and 1000 K for 795 organic molecules. The results were compared with experimental data and density functional theory (DFT) values (using B3LYP/TZVP and BP86/TZVP DFT methods). This comparison showed that the PM7 frequencies of vibration above 2500 cm–1 are systematically underestimated. An a posteriori correction using a linear relationship rescaling of the frequencies permitted resetting to zero the average relative deviations with respect to experimental reference values. This frequency correction also removed the bias from the zero point energies, ideal gas heat capacity, and entropy average deviations from the PM7 results. The root-mean-square deviation (RMSD) of PM7 and the DFT heat capacities of 160 organic molecules were equivalent with respect to experimental values, being about 5 %, 2.5 %, and 3 % at 300 K, 600 K, and 1000 K, respectively. The RMSD of PM7, when compared to the DFT values, became 4 %, 2 %, and 1 % for the same temperatures when the analysis was extended to a set of 795 molecules. In the case of the ideal gas entropies, the RMSD of the PM7 relative to DFT values were between 5 % and 4 % between 300 K and 1000 K, respectively. The RMSD of the Gibbs free energies of PM7 were 15 kJ mol–1 and 30 kJ mol–1 at 300 K and 1000 K, respectively. The efficiency of this semiempirical approach was tested on a set of approximately 5800 molecules. This set was processed in about a day, thus demonstrating the scalability of the approach to big data sets.

Classification study of solvation free energies of organic molecules using machine learning techniques

Classification models to predict the solvation free energies of organic molecules were developed using decision tree, random forest and support vector machine approaches and with MACCS fingerprints, MOE and PaDEL descriptors.

New solvation free energy function comprising intermolecular solvation and intramolecular self-solvation terms

Solvation free energy is a fundamental thermodynamic quantity that should be determined to estimate various physicochemical properties of a molecule and the desolvation cost for its binding to macromolecular receptors. Here, we propose a new solvation free energy function through the improvement of the solvent-contact model, and test its applicability in estimating the solvation free energies of organic molecules with varying sizes and shapes. This new solvation free energy function is constructed by combining the existing solute-solvent interaction term with the self-solvation term that reflects the effects of intramolecular interactions on solvation. Four kinds of atomic parameters should be determined in this solvation model: atomic fragmental volume, maximum atomic occupancy, atomic solvation, and atomic self-solvation parameters. All of these parameters for total 37 atom types are optimized by the operation of a standard genetic algorithm in such a way to minimize the difference between the experimental solvation free energies and those calculated by the solvation free energy function for 362 organic molecules. The solvation free energies estimated from the new solvation model compare well with the experimental results with the associated squared correlation coefficients of 0.88 and 0.85 for training and test sets, respectively. The present solvation model is thus expected to be useful for estimating the solvation free energies of organic molecules.

An Accurate Prediction of Hydration Free Energies by Combination of Molecular Integral Equations Theory with Structural Descriptors

In this work, we report a novel method for the estimation of the hydration free energy of organic molecules, the structural descriptors correction (SDC) model. The method is based on a combination of the reference interaction site model (RISM) with several empirical corrections. The model requires only a small number of chemical descriptors associated with the main features of the chemical structure of solutes: excluded volume, branch, double bond, benzene ring, hydroxyl group, halogen atom, aldehyde group, ketone group, ether group, and phenol fragment. The optimum model was selected after testing of different RISM free energy expressions on a training set of 65 molecules. We show that the correction parameters of the SDC model are transferable between different chemical classes, which allows one to cover a wide range of organic solutes. The new model substantially increases the accuracy of calculated HFEs by RISM giving the standard deviation of the error for a test set of 120 organic molecules around 1.2 kcal/mol.

“Bimolecular” QSPR: Estimation of the solvation free energy of organic molecules in different solvents

“Bimolecular” QSPR: Estimation of the solvation free energy of organic molecules in different solvents

Comparative Study on Solvation Free Energy Expressions in Reference Interaction Site Model Integral Equation Theory

The performance of the recently proposed partial wave (PW) free energy functional is compared with those of two previous expressions, Gaussian fluctuation (GF) and hypernetted chain (HNC), within the reference interaction site model framework. The applications to the calculations of ambient and supercritical water, solvation free energies of organic molecules, and partition coefficients clearly show that the PW and GF free energy expressions provide more reliable results than the HNC functional, indicating rather associative situations of geometry in ordinary liquids of medium-sized molecules.

Parametrized Model for Aqueous Free Energies of Solvation Using Geometry-Dependent Atomic Surface Tensions with Implicit Electrostatics

We present a new model for predicting aqueous free energies of solvation 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 parametrized 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.

Classical electrostatics in biology and chemistry.

A major revival in the use of classical electrostatics as an approach to the study of charged and polar molecules in aqueous solution has been made possible through the development of fast numerical and computational methods to solve the Poisson-Boltzmann equation for solute molecules that have complex shapes and charge distributions. Graphical visualization of the calculated electrostatic potentials generated by proteins and nucleic acids has revealed insights into the role of electrostatic interactions in a wide range of biological phenomena. Classical electrostatics has also proved to be successful quantitative tool yielding accurate descriptions of electrical potentials, diffusion limited processes, pH-dependent properties of proteins, ionic strength-dependent phenomena, and the solvation free energies of organic molecules.

Correction - "Relation between Structure and Free Energy of Organic Molecules"

Correction - "Relation between Structure and Free Energy of Organic Molecules"

Relation between Structure and Free Energy of Organic Molecules

Relation between Structure and Free Energy of Organic Molecules