1
|
Bursik B, Eller J, Gross J. Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State. J Phys Chem B 2024; 128:3677-3688. [PMID: 38579126 DOI: 10.1021/acs.jpcb.3c07447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/07/2024]
Abstract
We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.
Collapse
Affiliation(s)
- Benjamin Bursik
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart 70569, Germany
| | - Johannes Eller
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart 70569, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart 70569, Germany
| |
Collapse
|
2
|
Gilson MK, Kurtzman T. Free Energy Density of a Fluid and Its Role in Solvation and Binding. J Chem Theory Comput 2024; 20:2871-2887. [PMID: 38536144 PMCID: PMC11197885 DOI: 10.1021/acs.jctc.3c01173] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/10/2024]
Abstract
The concept that a fluid has a position-dependent free energy density appears in the literature but has not been fully developed or accepted. We set this concept on an unambiguous theoretical footing via the following strategy. First, we set forth four desiderata that should be satisfied by any definition of the position-dependent free energy density, f(R), in a system comprising only a fluid and a rigid solute: its volume integral, plus the fixed internal energy of the solute, should be the system free energy; it deviates from its bulk value, fbulk, near a solute but should asymptotically approach fbulk with increasing distance from the solute; it should go to zero where the solvent density goes to zero; and it should be well-defined in the most general case of a fluid made up of flexible molecules with an arbitrary interaction potential. Second, we use statistical thermodynamics to formulate a definition of the free energy density that satisfies these desiderata. Third, we show how any free energy density satisfying the desiderata may be used to analyze molecular processes in solution. In particular, because the spatial integral of f(R) equals the free energy of the system, it can be used to compute free energy changes that result from the rearrangement of solutes as well as the forces exerted on the solutes by the solvent. This enables the use of a thermodynamic analysis of water in protein binding sites to inform ligand design. Finally, we discuss related literature and address published concerns regarding the thermodynamic plausibility of a position-dependent free energy density. The theory presented here has applications in theoretical and computational chemistry and may be further generalizable beyond fluids, such as to solids and macromolecules.
Collapse
Affiliation(s)
- Michael K Gilson
- Skaggs School of Pharmacy and Pharmaceutical Sciences, and Department of Chemistry and Biochemistry, UC San Diego, La Jolla, CA, 92093, USA
| | - Tom Kurtzman
- PhD Programs in Chemistry, Biochemistry, and Biology, The Graduate Center of the City University of New York, New York, 10016, USA; Department of Chemistry, Lehman College, The City University of New York, Bronx, New York, 10468, USA
| |
Collapse
|
3
|
Sammüller F, Hermann S, de Las Heras D, Schmidt M. Noether-Constrained Correlations in Equilibrium Liquids. PHYSICAL REVIEW LETTERS 2023; 130:268203. [PMID: 37450808 DOI: 10.1103/physrevlett.130.268203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 06/12/2023] [Indexed: 07/18/2023]
Abstract
Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field Noether's theorem yields the local force balance. Three distinct two-body correlation functions emerge at second order, namely the standard two-body density, the localized force-force correlation function, and the localized force gradient. An exact Noether sum rule interrelates these correlators. Simulations of Lennard-Jones, Yukawa, soft-sphere dipolar, Stockmayer, Gay-Berne and Weeks-Chandler-Andersen liquids, of monatomic water and of a colloidal gel former demonstrate the fundamental role in the characterization of spatial structure.
Collapse
Affiliation(s)
- Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| |
Collapse
|
4
|
Cao S, Qiu Y, Unarta IC, Goonetilleke EC, Huang X. The Ion-Dipole Correction of the 3DRISM Solvation Model to Accurately Compute Water Distributions around Negatively Charged Biomolecules. J Phys Chem B 2022; 126:8632-8645. [PMID: 36282904 DOI: 10.1021/acs.jpcb.2c04431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
The 3D reference interaction site model (3DRISM) provides an efficient grid-based solvation model to compute the structural and thermodynamic properties of biomolecules in aqueous solutions. However, it remains challenging for existing 3DRISM methods to correctly predict water distributions around negatively charged solute molecules. In this paper, we first show that this challenge is mainly due to the orientation of water molecules in the first solvation shell of the negatively charged solute molecules. To properly consider this orientational preference, position-dependent two-body intramolecular correlations of solvent need to be included in the 3DRISM theory, but direct evaluations of these position-dependent two-body intramolecular correlations remain numerically intractable. To address this challenge, we introduce the Ion-Dipole Correction (IDC) to the 3DRISM theory, in which we incorporate the orientation preference of water molecules via an additional solute-solvent interaction term (i.e., the ion-dipole interaction) while keeping the formulism of the 3DRISM equation unchanged. We prove that this newly introduced IDC term is equivalent to an effective direct correlation function which can effectively consider the orientation effect that arises from position dependent two-body correlations. We first quantitatively validate our 3DRISM-IDC theory combined with the PSE3 closure on Cl-, [ClO]- (a two-site anion), and [NO2]- (a three-site anion). For all three anions, we show that our 3DRISM-IDC theory significantly outperforms the 3DRISM theory in accurately predicting the solvation structures in comparison to MD simulations, including RDFs and 3D water distributions. Furthermore, we have also demonstrated that the 3DRISM-IDC can improve the accuracy of hydration free-energy calculation for Cl-. We further demonstrate that our 3DRISM-IDC theory yields significant improvements over the 3DRISM theory when applied to compute the solvation structures for various negatively charged solute molecules, including adenosine triphosphate (ATP), a short peptide containing 19 residues, a DNA hairpin containing 24 nucleotides, and a riboswitch RNA molecule with 77 nucleotides. We expect that our 3DRISM-IDC-PSE3 solvation model holds great promise to be widely applied to study solvation properties for nucleic acids and other biomolecules containing negatively charged functional groups.
Collapse
Affiliation(s)
- Siqin Cao
- Theoretical Chemistry Institute, Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin53706, United States
| | - Yunrui Qiu
- Theoretical Chemistry Institute, Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin53706, United States
| | - Ilona C Unarta
- Theoretical Chemistry Institute, Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin53706, United States
| | - Eshani C Goonetilleke
- Theoretical Chemistry Institute, Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin53706, United States
| | - Xuhui Huang
- Theoretical Chemistry Institute, Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin53706, United States
| |
Collapse
|
5
|
Tanaka S, Yamamoto N, Kasahara K, Ishii Y, Matubayasi N. Crystal Growth of Urea and Its Modulation by Additives as Analyzed by All-Atom MD Simulation and Solution Theory. J Phys Chem B 2022; 126:5274-5290. [DOI: 10.1021/acs.jpcb.2c01764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Senri Tanaka
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Naoki Yamamoto
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kento Kasahara
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Yoshiki Ishii
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| |
Collapse
|
6
|
Yasoshima N, Ishiyama T, Matubayasi N. Adsorption Energetics of Amino Acid Analogs on Polymer/Water Interfaces Studied by All-Atom Molecular Dynamics Simulation and a Theory of Solutions. J Phys Chem B 2022; 126:4389-4400. [PMID: 35653506 DOI: 10.1021/acs.jpcb.2c01297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Energetics of adsorption was addressed with all-atom molecular dynamics simulation on the interfaces of poly(2-methoxyethyl acrylate) (PMEA), poly(methyl methacrylate) (PMMA), and poly(butyl acrylate) (PBA) with water. A wide variety of adsorbate solutes were examined, and the free energy of adsorption was computed with the method of energy representation. It was found that the adsorption free energy was favorable (negative) for all the combinations of solute and polymer, and among PMEA, PMMA, and PBA, the strongest adsorption was observed on PMMA for the hydrophobic solutes and on PMEA for the hydrophilic ones. According to the decomposition of the adsorption free energy into the contributions from polymer and water, it was seen that the polymer contribution is larger in magnitude with the solute size. The total free energy of adsorption was correlated well with the solvation free energy in bulk water only for hydrophobic solutes. The roles of the intermolecular interaction components such as electrostatic, van der Waals, and excluded-volume were further studied, and the electrostatic component was influential only in determining the polymer dependences of the adsorption propensities of hydrophilic solutes. The extent of adsorption was shown to be ranked by the van der Waals component in the solute-polymer interaction separately over the hydrophilic and hydrophobic solutes, with the excluded-volume effect from water pointed out to also drive the adsorption.
Collapse
Affiliation(s)
- Nobuhiro Yasoshima
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Tatsuya Ishiyama
- Department of Applied Chemistry, Graduate School of Science and Engineering, University of Toyama, Toyama 930-8555, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| |
Collapse
|
7
|
Matubayasi N. Solvation energetics of proteins and their aggregates analyzed by all-atom molecular dynamics simulations and the energy-representation theory of solvation. Chem Commun (Camb) 2021; 57:9968-9978. [PMID: 34505117 DOI: 10.1039/d1cc03395f] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Solvation is a controlling factor for the structure and function of proteins. This article addresses the effects of solvation from an energetic perspective for the fluctuations and cosolvent-induced changes in protein structures and the equilibrium of aggregate formation for a peptide. A theoretical framework to analyze the solvation effects with an explicit solvent is introduced by adopting the energy-representation theory of solvation, and the connection of the solvation free energy to the protein structure and the aggregation tendency is quantitatively described in combination with all-atom molecular dynamics simulations. The interaction components that govern the solvation effects on the structural variations of proteins are further identified through correlation analysis, and a computational scheme to assess the shift of an aggregation equilibrium due to the addition of a cosolvent is provided.
Collapse
Affiliation(s)
- Nobuyuki Matubayasi
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan.
| |
Collapse
|
8
|
Kojima H, Handa K, Yamada K, Matubayasi N. Water Dissolved in a Variety of Polymers Studied by Molecular Dynamics Simulation and a Theory of Solutions. J Phys Chem B 2021; 125:9357-9371. [PMID: 34351173 DOI: 10.1021/acs.jpcb.1c04818] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The performance of a polymer medium as a separation membrane is determined by the dissolution free energy ΔG and diffusion coefficient D of the permeant. In this work, ΔG and D of water are investigated with all-atom molecular dynamics simulation in a wide variety of polymer species in the amorphous state. The computed ΔG is shown to agree well with the experimental value for linear homopolymers, and the degrees of polymerization of the homopolymers do not affect ΔG when they are beyond ∼10. The copolymers of ethylene-vinylidene difluoride, ethylene-vinyl acetate, and ethylene-acrylamide are then examined by changing the repeating patterns of the constituent monomers in both the periodic and graft forms. It is found that ΔG is determined primarily by the overall compositions of the monomers and is not affected by the copolymerization topology (periodic or graft). The hydrophobicity of the copolymer is enhanced, furthermore, when the hydrophobicity and hydrophilicity of the ethylene and non-ethylene parts are well contrasted and those parts are fragmented along the polymer chain. According to the computed D, the diffusivity of water tends to be larger when the (co)polymer is more hydrophobic and ΔG is more positive. D is actually seen to vary by orders of magnitude with the polymer structures, while the effect of the polymer species on the water permeation is stronger for ΔG than for D.
Collapse
Affiliation(s)
- Hidekazu Kojima
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kazuya Handa
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kazuo Yamada
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| |
Collapse
|
9
|
Chuev GN, Fedotova MV, Valiev M. Renormalized site density functional theory for models of ion hydration. J Chem Phys 2021; 155:064501. [PMID: 34391371 DOI: 10.1063/5.0060249] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The development of accurate statistical mechanics models of molecular liquid systems is a problem of great practical and fundamental importance. Site-density functional theory (SDFT) is one of the promising directions in this area, but its success hinges upon the ability to efficiently reconcile the co-existence of two distinct intra- and inter-molecular interaction regimes in a molecular liquid. The renormalized formulation of SDFT (RSDFT), which we have recently developed, resolves this problem by introducing an additional potential field variable that decouples two interaction scales and maps the molecular liquid problem onto the effective simple liquid mixture. This work provides a critical assessment of RSDFT for the hydrated ion system-a problem that historically has always been one of the most difficult cases for SDFT applications. Using a two-site model of water, we perform a comprehensive analysis of hydrated alkali metal and halogen ions, including both structural and free energy based characteristics. The results indicate that RSDFT provides a significant improvement over conventional three-dimensional reference interaction site model implementations and may prove useful in coarse grained simulations based on two-site solvent models.
Collapse
Affiliation(s)
- Gennady N Chuev
- Institute of Theoretical and Experimental Biophysics, Russian Academy of Science, Pushchino, Moscow Region 142290, Russia
| | - Marina V Fedotova
- G. A. Krestov Institute of Solution Chemistry, Russian Academy of Sciences, Akademicheskaya St., 1, 153045 Ivanovo, Russia
| | - Marat Valiev
- Molecular Sciences Software Group, Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, USA
| |
Collapse
|
10
|
Ashbaugh HS, Vats M, Garde S. Bridging Gaussian Density Fluctuations from Microscopic to Macroscopic Volumes: Applications to Non-Polar Solute Hydration Thermodynamics. J Phys Chem B 2021; 125:8152-8164. [PMID: 34283590 PMCID: PMC8389927 DOI: 10.1021/acs.jpcb.1c04087] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
The hydration of
hydrophobic solutes is intimately related to the
spontaneous formation of cavities in water through ambient density
fluctuations. Information theory-based modeling and simulations have
shown that water density fluctuations in small volumes are approximately
Gaussian. For limiting cases of microscopic and macroscopic volumes,
water density fluctuations are known exactly and are rigorously related
to the density and isothermal compressibility of water. Here, we develop
a theory—interpolated gaussian fluctuation theory (IGFT)—that
builds an analytical bridge to describe water density fluctuations
from microscopic to molecular scales. This theory requires no detailed
information about the water structure beyond the effective size of
a water molecule and quantities that are readily obtained from water’s
equation-of-state—namely, the density and compressibility.
Using simulations, we show that IGFT provides a good description of
density fluctuations near the mean, that is, it characterizes the
variance of occupancy fluctuations over all solute sizes. Moreover,
when combined with the information theory, IGFT reproduces the well-known
signatures of hydrophobic hydration, such as entropy convergence and
solubility minima, for atomic-scale solutes smaller than the crossover
length scale beyond which the Gaussian assumption breaks down. We
further show that near hydrophobic and hydrophilic self-assembled
monolayer surfaces in contact with water, the normalized solvent density
fluctuations within observation volumes depend similarly on size as
observed in the bulk, suggesting the feasibility of a modified version
of IGFT for interfacial systems. Our work highlights the utility of
a density fluctuation-based approach toward understanding and quantifying
the solvation of non-polar solutes in water and the forces that drive
them toward surfaces with different hydrophobicities.
Collapse
Affiliation(s)
- Henry S Ashbaugh
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Mayank Vats
- Center for Biotechnology and Interdisciplinary Studies and the Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, United States
| | - Shekhar Garde
- Center for Biotechnology and Interdisciplinary Studies and the Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, United States
| |
Collapse
|
11
|
Borgis D, Luukkonen S, Belloni L, Jeanmairet G. Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional. J Chem Phys 2021; 155:024117. [PMID: 34266282 DOI: 10.1063/5.0057506] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid-gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5 kBT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes.
Collapse
Affiliation(s)
- Daniel Borgis
- Maison de la Simulation, USR 3441 CNRS-CEA-Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Sohvi Luukkonen
- Maison de la Simulation, USR 3441 CNRS-CEA-Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Luc Belloni
- Universié Paris-Saclay, CEA, CNRS, NIMBE, 91191 Gif-sur-Yvette, France
| | - Guillaume Jeanmairet
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France
| |
Collapse
|
12
|
Eller J, Matzerath T, van Westen T, Gross J. Predicting solvation free energies in non-polar solvents using classical density functional theory based on the PC-SAFT equation of state. J Chem Phys 2021; 154:244106. [PMID: 34241354 DOI: 10.1063/5.0051201] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a predictive Density Functional Theory (DFT) for the calculation of solvation free energies. Our approach is based on a Helmholtz free-energy functional that is consistent with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. This allows for a coarse-grained description of the solvent based on an inhomogeneous density of PC-SAFT segments. The solute, on the other hand, is described in full detail by atomistic Lennard-Jones interaction sites. The approach is entirely predictive as it only takes the PC-SAFT parameters of the solvent and the force-field parameters of the solute as input. No adjustable parameters or empirical corrections are involved. The framework is applied to study self-solvation of n-alkanes and to the calculation of residual chemical potentials in binary solvent mixtures. Our DFT approach accurately predicts solvation free energies of small molecular solutes in three different non-polar solvents, namely n-hexane, cyclohexane, and benzene. Additionally, we show that the calculated solvation free energies agree well with those obtained by molecular dynamics simulations and with the residual chemical potential calculated by the bulk PC-SAFT equation of state. We observe higher deviations for the solvation free energy of systems with significant solute-solvent Coulomb interactions.
Collapse
Affiliation(s)
- Johannes Eller
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Tanja Matzerath
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| |
Collapse
|
13
|
Hsu TY, Jeanmairet G. Assessing the correctness of pressure correction to solvation theories in the study of electron transfer reactions. J Chem Phys 2021; 154:131102. [PMID: 33832266 DOI: 10.1063/5.0048343] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Liquid state theories have emerged as a numerically efficient alternative to costly molecular dynamics simulations of electron transfer reactions in solution. In a recent paper [Jeanmairet et al., Chem. Sci. 10, 2130-2143 (2019)], we introduced the framework to compute the energy gap, free energy profile, and reorganization free energy using molecular density functional theory. However, this technique, as other molecular liquid state theories, overestimates the bulk pressure of the fluid. Because of the very high pressure, the predicted free energy is dramatically exaggerated. Several attempts were made to fix this issue, either based on simple a posteriori correction or by introducing bridge terms. By studying two model half reactions in water, Cl → Cl+ and Cl → Cl-, we assess the correctness of these two types of corrections to study electron transfer reactions. We found that a posteriori correction, because it violates the Variational principle, leads to an inconsistency in the definition of the reorganization free energy and should not be used to study electron transfer reactions. The bridge approach, because it is theoretically well grounded, is perfectly suitable for this type of systems.
Collapse
Affiliation(s)
- Tzu-Yao Hsu
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France
| | - Guillaume Jeanmairet
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France
| |
Collapse
|
14
|
Yadav AK, Bandyopadhyay P, Urbic T, Dill KA. Analytical 2-Dimensional Model of Nonpolar and Ionic Solvation in Water. J Phys Chem B 2021; 125:1861-1873. [PMID: 33539097 PMCID: PMC7958497 DOI: 10.1021/acs.jpcb.0c10329] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A goal in computational chemistry is computing hydration free energies of nonpolar and charged solutes accurately, but with much greater computational speeds than in today's explicit-water simulations. Here, we take one step in that direction: a simple model of solvating waters that is analytical and thus essentially instantaneous to compute. Each water molecule is a 2-dimensional dipolar hydrogen-bonding disk that interacts around small circular solutes with different nonpolar and charge interactions. The model gives good qualitative agreement with experiments. As a function of the solute radius, it gives the solvation free energy, enthalpy and entropy as a function of temperature for the inert gas series Ne, Ar, Kr, and Xe. For anions and cations, it captures relatively well the trends versus ion radius. This approach should be readily generalizable to three dimensions.
Collapse
Affiliation(s)
- Ajeet Kumar Yadav
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Pradipta Bandyopadhyay
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Večna pot 113, SI-1000, Ljubljana, Slovenia
| | - Ken A Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, New York, New York 11794, United States
- Department of Physics and Astronomy, Stony Brook University, New York, New York 11794, United States
- Department of Chemistry, Stony Brook University, New York, New York 11794, United States
| |
Collapse
|
15
|
Lutsko JF. Explicitly stable fundamental-measure-theory models for classical density functional theory. Phys Rev E 2021; 102:062137. [PMID: 33465965 DOI: 10.1103/physreve.102.062137] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 11/30/2020] [Indexed: 11/07/2022]
Abstract
The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) is reexamined in the light of the recently introduced concept of global stability of the density functional based on its boundedness [Lutsko and Lam, Phys. Rev. E 98, 012604 (2018)2470-004510.1103/PhysRevE.98.012604]. It is shown that within the present paradigm, explicit stability of the functional can be achieved only at the cost of giving up accuracy at low densities. It is argued that this is an acceptable trade-off since the main value of DFT lies in the study of dense systems. Explicit calculations for a wide variety of systems show that a proposed explicitly stable functional is competitive in all ways with the popular White Bear models while sharing some of their weaknesses when applied to non-close-packed solids.
Collapse
Affiliation(s)
- James F Lutsko
- Center for Nonlinear Phenomena and Complex Systems CP 231, Université Libre de Bruxelles, Blvd. du Triomphe, 1050 Brussels, Belgium
| |
Collapse
|
16
|
Lutsko JF, Schoonen C. Classical density-functional theory applied to the solid state. Phys Rev E 2020; 102:062136. [PMID: 33466033 DOI: 10.1103/physreve.102.062136] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
The standard model of classical density-functional theory (cDFT) for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated fundamental measure hard-sphere functionals suffer from potential numerical instabilities either due to possible instabilities in the functionals themselves or due to implementations that mix real- and Fourier-space components inconsistently. Here we present a new implementation based on a demonstrably stable hard-sphere functional that is implemented in a completely consistent manner. The present work does not depend on approximate spherical integration schemes and so is much more robust than previous algorithms. The methods are illustrated by calculating phase diagrams for the solid state using the standard Lennard-Jones potential as well as a new class of potentials recently proposed by Wang et al. [Phys. Chem. Chem. Phys. 22, 10624 (2020)PPCPFQ1463-907610.1039/C9CP05445F]. The latter span the range from potentials for small molecules to those appropriate to colloidal systems simply by varying a parameter. We verify that cDFT is able to semiquantitatively reproduce the phase diagram in all cases. We also show that for these problems computationally cheap Gaussian approximations are nearly as good as full minimization based on finite differences.
Collapse
Affiliation(s)
- James F Lutsko
- Center for Nonlinear Phenomena and Complex Systems CP 231, Université Libre de Bruxelles, 1050 Brussels, Belgium
| | - Cédric Schoonen
- Center for Nonlinear Phenomena and Complex Systems CP 231, Université Libre de Bruxelles, 1050 Brussels, Belgium
| |
Collapse
|
17
|
Jeanmairet G, Levesque M, Borgis D. Tackling Solvent Effects by Coupling Electronic and Molecular Density Functional Theory. J Chem Theory Comput 2020; 16:7123-7134. [PMID: 32894674 DOI: 10.1021/acs.jctc.0c00729] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Solvation effects can have a tremendous influence on chemical reactions. However, precise quantum chemistry calculations are most often done either in vacuum neglecting the role of the solvent or using continuum solvent model ignoring its molecular nature. We propose a new method coupling a quantum description of the solute using electronic density functional theory with a classical grand-canonical treatment of the solvent using molecular density functional theory. Unlike a previous work, both densities are minimized self-consistently, accounting for mutual polarization of the molecular solvent and the solute. The electrostatic interaction is accounted using the full electron density of the solute rather than fitted point charges. The introduced methodology represents a good compromise between the two main strategies to tackle solvation effects in quantum calculation. It is computationally more effective than a direct quantum mechanics/molecular mechanics coupling, requiring the exploration of many solvent configurations. Compared to continuum methods, it retains the full molecular-level description of the solvent. We validate this new framework onto two usual benchmark systems: a water solvated in water and the symmetrical nucleophilic substitution between chloromethane and chloride in water. The prediction for the free energy profiles are not yet fully quantitative compared to experimental data, but the most important features are qualitatively recovered. The method provides a detailed molecular picture of the evolution of the solvent structure along the reaction pathway.
Collapse
Affiliation(s)
- Guillaume Jeanmairet
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes, Interfaciaux, PHENIX, F-75005 Paris, France.,Réseau sur le Stockage Électrochimique de l'Énergie (RS2E), FR CNRS 3459, 80039 Amiens Cedex, France
| | - Maximilien Levesque
- PASTEUR, Département de chimie, École normale supérieure, PSL University, Sorbonne, Université, CNRS, 75005 Paris, France.,Aqemia, 75006 Paris, France
| | - Daniel Borgis
- PASTEUR, Département de chimie, École normale supérieure, PSL University, Sorbonne, Université, CNRS, 75005 Paris, France.,Maison de la Simulation, CEA, CNRS, Université Paris-Sud, UVSQ, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| |
Collapse
|
18
|
Borgis D, Luukkonen S, Belloni L, Jeanmairet G. Simple Parameter-Free Bridge Functionals for Molecular Density Functional Theory. Application to Hydrophobic Solvation. J Phys Chem B 2020; 124:6885-6893. [DOI: 10.1021/acs.jpcb.0c04496] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Daniel Borgis
- Maison de la Simulation, USR 3441 CNRS-CEA-Université Paris-Saclay, 91191 Gif-sur-Yvette, France
- PASTEUR, Département de Chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, Paris, 75005, France
| | - Sohvi Luukkonen
- Maison de la Simulation, USR 3441 CNRS-CEA-Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Luc Belloni
- LIONS, NIMBE, CEA, CNRS, Université Paris-Saclay, Gif-sur-Yvette, 91191, France
| | - Guillaume Jeanmairet
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, Paris, F-75005, France
- Réseau sur le Stockage Électrochimique de l’Énergie, CNRS FR3459, 33 rue Saint Leu, Amiens, Cedex 80039, France
| |
Collapse
|
19
|
Luukkonen S, Belloni L, Borgis D, Levesque M. Predicting Hydration Free Energies of the FreeSolv Database of Drug-like Molecules with Molecular Density Functional Theory. J Chem Inf Model 2020; 60:3558-3565. [DOI: 10.1021/acs.jcim.0c00526] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Sohvi Luukkonen
- Maison de la Simulation, CNRS-CEA-Université Paris-Saclay, Gif-sur-Yvette 91191, France
| | - Luc Belloni
- LIONS, NIMBE, CEA, CNRS, Université Paris-Saclay, Gif-sur-Yvette 91191 France
| | - Daniel Borgis
- Maison de la Simulation, CNRS-CEA-Université Paris-Saclay, Gif-sur-Yvette 91191, France
- PASTEUR, Département de Chimie, École normale supérieure, PSL University, Sorbonne Université, CNRS, Paris 75005, France
| | - Maximilien Levesque
- PASTEUR, Département de Chimie, École normale supérieure, PSL University, Sorbonne Université, CNRS, Paris 75005, France
- Aqemia, Paris 75001, France
| |
Collapse
|
20
|
Zhang BW, Matubayasi N, Levy RM. Cavity Particle in Aqueous Solution with a Hydrophobic Solute: Structure, Energetics, and Functionals. J Phys Chem B 2020; 124:5220-5237. [PMID: 32469519 DOI: 10.1021/acs.jpcb.0c02721] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Endpoints density functional theory (DFT) provides a framework for calculating the excess chemical potential of a solute in solution using solvent distribution functions obtained from both physical endpoints of a hypothetical charging process which transforms the solvent density from that of the pure liquid to the solution state. In this work, the endpoints DFT equations are formulated in terms of the indirect (solvent-mediated) contribution ω(x) to the solute-solvent potential of mean force, and their connections are established with the conventional DFT expressions which are based on the use of direct correlation functions. ω actually corresponds to the free-energy cost to move a cavity particle (a tagged solvent molecule which interacts with the other solvent molecules but not the solute) from the bulk to the configuration x of a solvent molecule relative to the solute and is a suitable variable to describe the solvent effects on the solute-solvent interactions. HNC and PY type approximations are then used to integrate the DFT charging integral involved in the exact expression for the excess chemical potential. With these approximations, molecular simulations are to be performed at the two endpoints of solute insertion: pure solvent without the solute and the solution system with the fully coupled solute-solvent interaction. An endpoints method thus utilizes the ensembles of intermolecular configurations of physical interest, which are often readily accessible with MD simulations given the present computational power. To illustrate properties of the formulation, we perform simulations of model systems consisting of a cavity particle in an aqueous solution containing a spherical hydrophobic solute of three different sizes from which ω(x) and the solute chemical potential can be calculated using endpoints DFT expressions. These are compared with corresponding results obtained using the approximations needed in order to evaluate the endpoints DFT charging integral when cavity particle simulation data is not available. We analyze a new approximation (two-points quadratic HNC) to the DFT charging integral which captures the correct behavior of the cavity distributions at both endpoints of the solute insertion. The behavior of the cavity particle in simple and complex liquids plays an important role in various theoretical treatments of the solute chemical potential. For pure Lennard-Jones fluids, the free energy to bring a cavity particle from the bulk to the center of a fluid particle is negative. However, for solutes of varying size, this is not generally true for Lennard-Jones fluids or the systems studied in this work. We carry out energetic and structural analyses of the cavity particle in aqueous solution with hydrophobic solutes of varying size and discuss the results in the context of the hydrophobic effect.
Collapse
Affiliation(s)
- Bin W Zhang
- Center for Biophysics and Computational Biology, and Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Ronald M Levy
- Center for Biophysics and Computational Biology, and Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| |
Collapse
|
21
|
Robert A, Luukkonen S, Levesque M. Pressure correction for solvation theories. J Chem Phys 2020; 152:191103. [DOI: 10.1063/5.0002029] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Affiliation(s)
- Anton Robert
- PASTEUR, Département de Chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France
| | - Sohvi Luukkonen
- Maison de la Simulation, CNRS-CEA-Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Maximilien Levesque
- PASTEUR, Département de Chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France
- Aqemia, Paris, France
| |
Collapse
|