Quantum-mechanical van der Waals dispersion interactions play an essential role for both intra-protein and protein-water interactions -- the two main driving forces for the structure and dynamics of proteins in aqueous solution. Typically, these interactions are only treated phenomenologically via pairwise potential terms in classical force fields. Here, we use an explicit quantum-mechanical approach based on density-functional tight-binding with the many-body dispersion formalism, which allows us to demonstrate the unexpected relevance of the many-body character of dispersion interactions for protein energetics and the protein-water interaction. In contrast to commonly employed pairwise approaches, many-body effects significantly decrease the relative stability of the native state in the absence of water. In an aqueous environment, the collective character of the protein-water van der Waals interaction counteracts this effect and stabilizes native conformations and transition states. This stabilization arises due to a high degree of delocalization and collectivity of protein-water dispersion interactions, suggesting a remarkable persistence of long-range electron correlation through aqueous environments. Our findings are exemplified on prototypical showcases of proteins forming $β$-sheets, hairpins, and helices, emphasizing the crucial role of plasmon-like solute-solvent interactions in biomolecular systems.
We theoretically study physical properties of one-dimensionally and regularly placed solutes. The solute is rigid-body, has arrow-like shape, and changes its direction up or down. If the solutes are immersed in continuum solvent, nothing happens in the system. However, the property of the directions differs in granular solvent (e.g., hard-sphere solvent). Depending on distance between the nearest-neighbor solutes, the directional property periodically changes as follows: "ferromagnetic-like" \leftrightarrow "random" \leftrightarrow "antiferromagnetic-like". Furthermore, the directional propert…
A method for study of charge-transfer interactions between solute molecules and solvent based on the comparison of the ratios of spectral shifts of different electronic transitions in solute molecules in chemically inert solvent is proposed. The method is applicable to molecules that do not change their dipole moment on excitation. As an example, a presence of charge transfer interactions in higher electronic states of aromatic hydrocarbons (benzene, phenanthrene, and naphthalene) dissolved in water and alcohols was demonstrated.
The solubility of a "heavy" alkane (solute) in a "light" alkane (solvent) is generally temperature dependent. Moreover, it is determined by the molar masses of the solute and solvent. In the current paper, published solubility data for binary normal-alkane mixtures is reviewed (solid-liquid equilibrium). A total of 43 unique solute-solvent data-sets, obtained from a total of 24 published experimental studies, are collected and presented in a systematic manner. Based on thermodynamic considerations and the experimental data, it is demonstrated that there is a log-linear relationship between the…
Coarse-grained modeling and efficient computer simulations are critical to the study of complex molecular processes with many degrees of freedom and multiple spatiotemporal scales. Variational implicit-solvent model (VISM) for biomolecular solvation is such a modeling framework, and its initial success has been demonstrated consistently. In VISM, an effective free-energy functional of solute-solvent interfaces is minimized, and the surface energy is a key component of the free energy. In this work, we extend VISM to include the solute mechanical interactions, and develop fast algorithms and GP…
A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model (Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. {\bf 104}, 527 (2006) and J. Chem.\Phys. {\bf 124}, 084905 (2006)). In the level-set method, a possible solute-solvent interface is represented by the zero level-set (i.e., the zero level surface) of a level-set function and is eventually evolved into the equilibrium solute-solvent interface. The evolution law is determined by minimization of a solvation free energy {\it…
A multi-scale framework was recently proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent, where we formulated the physical model and developed a numerical fluid dynamics integrator. In this study, we incorporated the fluid dynamics integrator with the Amber simulation engine to conduct atomistic simulations of biomolecules. At this stage of the development, only nonelectrostatic interactions, i.e., van del Waals and hydrophobic interactions are included in the mu…
Molecular excitations in the liquid-phase environment are renormalized by the surrounding solvent molecules. Herein, we employ the GW approximation to investigate the solvation effects on the ionization energy of phenol in various solvent environments. The electronic effects differ by up to 0.4 eV among the five investigated solvents. This difference depends on both the macroscopic solvent polarizability and the spatial decay of the solvation effects. The latter is probed by separating the electronic subspace and the GW correlation self-energy into fragments. The fragment correlation energy de…
We show how the Smoluchowski dynamics of a colloidal Brownian particle suspended in a molecular solvent can be reached starting from the microscopic Liouvillian evolution of the full classical model in the high friction limit. The integration of the solvent degrees of freedom goes through a multiple time scale perturbation expansion which removes the secular divergences. A simple dynamical Monte Carlo scheme is then proposed to solve the resulting evolution equation for the colloid solute particle. In particular we study the approach to the equilibrium Boltzmann distribution at late times and …
Recent studies of the hydration of micro- and nanoscale solutes have demonstrated a strong {\it coupling} between hydrophobic, dispersion and electrostatic contributions, a fact not accounted for in current implicit solvent models. We present a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy with respect to a solvent volume exclusion function. The solvent accessible surface is output of our theory. Our method is illustrated with the hydration of alkane-assembled solutes on different length scales, and captures the strong sensitivity to the particular form …
Efficient, accurate, and adaptable implicit solvent models remain a significant challenge in the field of molecular simulation. A recent implicit solvent model, IS-SPA, based on approximating the mean solvent force using the superposition approximation, provides a platform to achieve these goals. IS-SPA was originally developed to handle non-polar solutes in the TIP3P water model but can be extended to accurately treat polar solutes in other polar solvents. In this manuscript, we demonstrate how to adapt IS-SPA to include the treatment of solvent orientation and long ranged electrostatics in a…
Selectively exciting target molecules to high vibrational states is inefficient in the liquid phase, which restricts the use of IR pumping to catalyze ground-state chemical reactions. Here, we demonstrate that this inefficiency can sometimes be solved by confining the liquid to an optical cavity under vibrational strong coupling conditions. For a liquid solution of 13CO2 solute in a 12CO2 solvent, cavity molecular dynamics simulations show that exciting a polariton (hybrid light-matter state) of the solvent with an intense laser pulse, under suitable resonant conditions, may lead to a very str…
The Gibbs free energy of transferring a solute at infinite dilution between two solvents quantifies differences in solute-solvent interactions $-$ if the transfer takes place at constant molarity of the solute. Yet, many calculation formulae and measuring instructions that are commonly used to quantify solute-solvent interactions correspond to transfer processes in which not the molarity of the solute but its concentration measured in another concentration scale is constant. Here, we demonstrate that in this case, not only the change in solute-solvent interactions is quantified but also the en…
Strong quasi-adiabatic laser alignment of the indole-water-dimer clusters, an amino-acid chromophore bound to a single water molecule through a hydrogen bond, was experimentally realized. The alignment was visualized through ion and electron imaging following strong-field ionization. Molecular-frame photoelectron angular distributions showed a clear suppression of electron yield in the plane of the ionizing laser's polarization, which was analyzed as strong alignment of the molecular cluster with $\left< \cos^2θ_{2D} \right> \ge$ 0.9.
For many chemical processes the accurate description of solvent effects are vitally important. Here, we describe a hybrid ansatz for the explicit quantum mechanical description of solute-solvent and solvent-solvent interactions based on subsystem density functional theory and continuum solvation schemes. Since explicit solvent molecules may compromise scalability of the model and transferability of the predicted solvent effect, we aim to retain both, for different solutes as well as for different solvents. The key for the transferability is the consistent subsystem decomposition of solute and …
A general class of nonadditive sticky-hard-sphere binary mixtures, where small and large spheres represent the solvent and the solute, respectively, is introduced. The solute-solute and solvent-solvent interactions are of hard-sphere type, while the solute-solvent interactions are of sticky-hard-sphere type with tunable degrees of size nonadditivity and stickiness. Two particular and complementary limits are studied using analytical and semi-analytical tools. The first case is characterized by zero nonadditivity, lending itself to a Percus-Yevick approximate solution from which the impact of s…
The high-energy tail of the distribution of solute-solvent interaction energies is poorly characterized for condensed systems, but this tail region is of principal interest in determining the excess free energy of the solute. We introduce external fields centered on the solute to modulate the short-range repulsive interaction between the solute and solvent. This regularizes the binding energy distribution and makes it easy to calculate the free energy of the solute with the field. Together with the work done to apply the field in the presence and absence of the solute, we calculate the excess …
We derive an expression for the chemical potential of an associating solute in a solvent relative to the value in a reference fluid using the quasichemical organization of the potential distribution theorem. The fraction of times the solute is not associated with the solvent, the monomer fraction, is expressed in terms of (a) the statistics of occupancy of the solvent around the solute in the reference fluid and (b) the Widom factors that arise because of turning on solute-solvent association. Assuming pair-additivity, we expand the Widom factor into a product of Mayer f-functions and the resu…
Non-radiative decay channels in the L-edge fluorescence spectra from transition metal-aqueous solutions give rise to spectral dips in X-ray transmission spectra. Their origin is unraveled here using partial and inverse partial fluorescence yields on the micro-jet combined with multi-reference ab initio electronic structure calculations. Comparing Fe2+, Fe3+, and Co2+ systems we demonstrate unequivocally that spectral dips are due to a state-dependent electron delocalization within the manifold of d-orbitals.
The problem of a solute described by Quantum Chemistry within a solvent represented as a polarizable continuum model (PCM) is here reformulated in terms of the open quantum systems (OQS) theory. Using its stochastic Schrödinger Equation formulation, we are able to provide a more comprehensive picture of the electronic energies and of the coupling between solute and solvent electronic dynamics. In particular, OQS-PCM proves to be a unifying theoretical framework naturally including polarization and dispersion interactions, the effect of solvent fluctuations, and the non-Markovian solvent respon…
The presence of solvent tunes many properties of a molecule, such as its ground and excited state geometry, dipole moment, excitation energy, and absorption spectrum. Because the energy of the system will vary depending on the solvent configuration, explicit solute-solvent interactions are key to understanding solution-phase reactivity and spectroscopy, simulating accurate inhomogeneous broadening, and predicting absorption spectra. In this tutorial review, we give an overview of factors to consider when modeling excited states of molecules interacting with explicit solvent. We provide practic…
We develop an extension of the time-dependent equation-of-motion formulation of the polarizable continuum model (EOM-TDPCM) to introduce nonequilibrium cavity field effects in quantum mechanical calculations of solvated molecules subject to time-dependent electric fields. This method has been implemented in Octopus, a state-of-the-art code for real-space, real-time time-dependent density functional theory (RT-TDDFT) calculations. To show the potential of our methodology, we perform EOM-TDPCM/RT-TDDFT calculations of trans-azobenzene in water and in other model solvents with shorter relaxation …
The correct treatment of vibronic effects is vital for the modeling of absorption spectra of solvated dyes, as many prominent spectral features can often be ascribed to vibronic transitions. Vibronic spectra can be computed within the Franck-Condon approximation for small dyes in solution using an implicit solvent model. However, implicit solvent models neglect specific solute-solvent interactions and provide only an approximate treatment of solvent polarization effects. Furthermore, temperature-dependent solvent broadening effects are often only accounted for using a broadening parameter chos…
Solvent can occupy up to ~70% of macromolecular crystals and hence having models that predict solvent distributions in periodic systems could improve in the interpretation of crystallographic data. Yet there are few implicit solvent models applicable to periodic solutes while crystallographic structures are commonly solved assuming a flat solvent model. Here we present a newly-developed periodic version of the 3D-RISM integral equation method that is able to solve for efficiently and describe accurately water and ions distributions in periodic systems; the code can compute accurate gradients t…
We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density $ρ(\mathbf{r},\mathbfΩ)$ around the solute is a function of the position $\mathbf{r}\equiv(x,y,z)$ and of the three Euler angles $\mathbfΩ\equiv(θ,ϕ,ψ)$ describing the solvent orientation.…
The Menshutkin reaction is a methyl transfer reaction relevant in fields ranging from biochemistry to chemical synthesis. In the present work, energetics and solvent distributions for NH$_{3}$+MeCl and Pyr+MeBr reactions were investigated in the gas-phase, in water, methanol, acetonitrile, benzene, and in cyclohexane by means of reactive molecular dynamics simulations. For polar solvents (water, methanol, and acetonitrile) and benzene, strong to moderate catalytic effect for both reactions is found whereas apolar and bulky cyclohexane interacts weakly with the solute and does not show pronounc…
The real and imaginary parts of the susceptibility are fundamentally associated with the molecular dispersion and absorption, respectively. Measurement of the molecular dispersion has given insight into underlying molecular dynamics such as the identification of conical intersections and solute-solvent interactions. We show that when using a shaped pulse(s), it is possible to mix the real and imaginary parts of the nonlinear susceptibility into the molecular absorption. We then explain how to separate the real and imaginary parts of the nonlinear susceptibility when using a shaped pulse(s). We…
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 SAFT (PC-SAFT) equation of state. This allows 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 i…
The calculation of the solvation properties of a single water molecule in liquid water is carried out in two ways. In the first, the water molecule is placed in a cavity and the solvent is treated as a dielectric continuum. This model is analyzed by numerically solving the Poisson equation using the DelPhi program. The resulting solvation properties depend sensitively on the shape and size of the cavity. In the second method, the solvent and solute molecules are treated explicitly in molecular dynamics simulations using Ewald boundary conditions. We find a 2 kcal/mole difference in solvation f…
The mutual entropic depletion force felt by two solute "big" hard spheres immersed in a binary mixture solvent of nonadditive "small" hard spheres is calculated as a function of the surface-to-surface distance by means of canonical Monte Carlo simulations and through a recently proposed rational-function approximation [Phys. Rev. E \textbf{84}, 041201 (2011)]. Four representative scenarios are investigated: symmetric solute particles and the limit where one of the two solute spheres becomes a planar hard wall, in both cases with symmetric and asymmetric solvents. In all cases, the influence on…
The time-dependent fluorescence Stokes shifts monitors the relaxation of the polarization of a polar solvent in the surroundings of a photoexcited solute molecule, but also the structural variation of the solute following photoexcitation and the subsequent molecular charge redistribution. Here, we formulate a simple nonequilibrium quantum theory of solvation for an explicitly time-dependent continuous solvent. The time-dependent solvent induces nonequilibrium fluctuations on the solvent dynamics which are directly reflected in different time components in the time-dependent Stokes shift. We il…
Many important applications of electronic structure methods involve molecules or solid surfaces in a solvent medium. Since explicit treatment of the solvent in such methods is usually not practical, calculations often employ continuum solvation models to approximate the effect of the solvent. Previous solvation models either involve a parametrization based on atomic radii, which limits the class of applicable solutes, or based on solute electron density, which is more general but less accurate, especially for charged systems. We develop an accurate and general solvation model that includes a c…
Molecular dynamics simulation is a prominent way of analyzing the dynamic properties of a system. The molecular dynamics simulation of diffusion, an important transport property, of dilute solution of cysteine in SPCE water at five different temperatures (288 K, 293 K, 303 K, 313 K, 323 K) under the pressure of 1 bar is studied using GROMACS. OPLS AA force field parameters are used throughout the simulation. The system under study consists of 3 cysteine molecules (mole fraction 0.003) as solute and 1039 water molecules (mole fraction 0.997) as solvent. The radial distribution functions (RDFs) …
Solvation effect might 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 previous work, both densities are minimized self consistently, accounting for mutual polarization of the molecular solvent…
This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces theory, as applied to the solvent-solute boundary. In these approaches, the solvent-solute boundary is determined by a variational principle that determines the major physical observables of interest, for example, biomolecular surface area, enclosed volume, electrostatic potential, ion density, electron density, etc. Recently, differential geometry theory has b…
We propose a new model for estimating the free energy of forming a molecular cavity in a solvent, by assuming this energy is dominated by the electrostatic energy associated with creating the static (interface) potential inside the cavity. The new model approximates the cavity-formation energy as that of a shell capacitor: the inner, solute-shaped conductor is held at the static potential, and the outer conductor (at the first solvation shell) is held at zero potential. Compared to cavity energies computed using free-energy pertubation with explicit-solvent molecular dynamics, the new model ex…
Notwithstanding the long and distinguished history of studies of vibrational energy relaxation, exactly how it is that high frequency vibrations manage to relax in a liquid remains somewhat of a mystery. Both experimental and theoretical approaches seem to say that there is a natural frequency range associated with intermolecular motions in liquids, typically spanning no more than a few hundred cm^{-1}. Landau-Teller-like theories explain how a solvent can absorb any vibrational energy within this "band", but how is it that molecules can rid themselves of superfluous vibrational energies signi…
Two-photon excitation is an attractive means for controlling chemistry in both space and time. Isoenergetic one- and two-photon excitations (OPE and TPE) in non-centrosymmetric molecules are often assumed to reach the same excited state and, hence, to produce similar excited-state reactivity. We compare the solvent-to-solute excited-state proton transfer of the super photobase FR0-SB following isoenergetic OPE and TPE. We find up to 62 % increased reactivity following TPE compared to OPE. From steady-state spectroscopy, we rule out the involvement of different excited states and find that OPE …
For a distinguished water molecule, the solute water, we assess the contribution of each coordination state to its excess chemical potential, using a molecular aufbau approach. In this approach, we define a coordination sphere, the inner-shell, and separate the excess chemical potential into packing, outer-shell, and local chemical contributions; the coordination state is defined by the number of solvent water molecules within the coordination sphere. The packing term accounts for the free energy of creating a solute-free coordination sphere in the liquid. The outer-shell term accounts for the…
We describe a parallel linear-scaling computational framework developed to implement arbitrarily large multi-state empirical valence bond (MS-EVB) calculations within CHARMM. Forces are obtained using the Hellman-Feynmann relationship, giving continuous gradients, and excellent energy conservation. Utilizing multi-dimensional Gaussian coupling elements fit to CCSD(T)-F12 electronic structure theory, we built a 64-state MS-EVB model designed to study the F + CD3CN -> DF + CD2CN reaction in CD3CN solvent. This approach allows us to build a reactive potential energy surface (PES) whose balanced a…
Continuum models to handle solvent and electrolyte effects in an effective way have a long tradition in quantum-chemistry simulations and are nowadays also being introduced in computational condensed-matter and materials simulations. A key ingredient of continuum models is the choice of the solute cavity, i.e. the definition of the sharp or smooth boundary between the regions of space occupied by the quantum-mechanical (QM) system and the continuum embedding environment. Although most of the solute-based approaches developed lead to models with comparable and high accuracy when applied to smal…
The influence of hydroxyectoine on the properties of the aqueous solution in presence of DPPC lipid bilayers is studied via semi-isotropic constant pressure (NPT) Molecular Dynamics simulations. We investigate the solvent-co-solute behavior in terms of Kirkwood-Buff integrals as well as hydrogen bond life times for an increasing hydroxyectoine concentration up to 0.148 mol/L. The observed preferential exclusion mechanism identifies hydroxyectoine as a kosmotropic osmolyte. Our findings in regards to the DPPC lipid bilayer indicate an increase of the surface pressure as well as the solvent acce…
The Angular Localization Function (ALF): a practical tool to measure solvent angular order with Molecular Density Functional Theory
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX（界面电解质与纳米系统物理化学 PHENIX）；Réseau sur le Stockage Électrochimique de l’Énergie (RS2E)（电化学储能网络 RS2E）
The properties of model solutions consisting of a solute --- single curcumin molecule in water, methanol and dimethyl sulfoxide solvents have been studied using molecular dynamics (MD) computer simulations in the isobaric-isothermal ensemble. The united atom OPLS force field (OPLS-UA) model for curcumin molecule proposed by us recently [J. Mol. Liq., 2016, 223, 707] in combination with the SPC/E water, and the OPLS-UA type models for methanol and dimethyl sulfoxide have been applied. We have described changes of the internal structure of the solute molecule induced by different solvent media i…
A comparative study between Choline and Tetra-methyl ammonium bromide is presented here. Choline which is a crucial component for our dietary requirements causes many diseases if there is deficiency. We used combined approach of all-atom molecular dynamics simulation coupled with neutron scattering technique to study mainly the solvent behavior in this study. There is follow up work where we discussed about the solute dynamical behavior.
We study the solvation free energy of two different conformations (helix and extended) of two different peptides (deca-alanine and deca-glycine) in two different solvents (water and aqueous guanidinium chloride, GdmCl). The free energies are obtained using the quasichemical organization of the potential distribution theorem, an approach that naturally provides the repulsive (solvophobic or cavity) and attractive (solvophilic) contributions to solvation. The solvophilic contribution is further parsed into a chemistry contribution arising from solute interaction with the solvent in the first sol…
A classical density functional theory is applied to study solvation of solutes in water. An approx- imate form of the excess functional is proposed for water. This functional requires the knowledge of pure solvent direct correlation functions. Those functions can be computed by using molecular simulations such as molecular dynamic or Monte Carlo. It is also possible to use functions that have been determined experimentally. The functional minimization gives access to the solvation free energy and to the equilibrium solvent density. Some correction to the functional are also proposed to get the…
The hydration free energy of a macromolecule is the central property of interest for understanding its distribution over conformations and its state of aggregation. Calculating the hydration free energy of a macromolecule in all-atom simulations has long remained a challenge, necessitating the use of models wherein the effect of the solvent is captured without explicit account of solvent degrees of freedom. This situation has changed with developments in the molecular quasi-chemical theory (QCT), an approach that enables calculation of the hydration free energy of macromolecules within all-ato…
The multipole-expansion (MPE) model is an implicit solvation model used to efficiently incorporate solvent effects in quantum chemistry. Even within the recent direct approach, the multipole basis used in MPE to express the dielectric response still solves the electrostatic problem inefficiently or not at all for solutes larger than $\approx 10$ non-hydrogen atoms. In existing MPE parameterizations, the resulting systematic underestimation of the electrostatic solute-solvent interaction is presently compensated for by a systematic overestimation of non-electrostatic attractive interactions. Ev…
The dynamics of the electrons for a molecule in solution is coupled to the dynamics of its polarizable environment, i.e., the solvent. To theoretically investigate such electronic dynamics, we have recently developed equations of motion (EOM) for the apparent solvent polarization charges that generate the reaction field in the Polarizable Continuum Model (PCM) for solvation and we have coupled them to a real-time time-dependent density functional theory (RT TDDFT) description of the solute [Corni et al. J. Phys. Chem. A 119, 5405 (2014)]. Here we present an extension of the EOM-PCM approach to…
It is a promising extension of the quantum mechanical/molecular mechanical (QM/MM) approach to incorporate the solvent molecules surrounding the QM solute into the QM region to ensure the adequate description of the electronic polarization of the solute. However, the solvent molecules in the QM region inevitably diffuse into the MM bulk during the QM/MM simulation. In this article we developed a simple and efficient method, referred to as boundary constraint with correction (BCC), to prevent the diffusion of the solvent water molecules by means of a constraint po- tential. The point of the BCC…
Solubility of poorly soluble species in bulk and nanopores from grand-canonical Wang-Landau sampling
Institute for Computational Physics, University of Stuttgart（斯图加特大学计算物理研究所）；SC SimTech, Stuttgart Center for Simulation Science, University of Stuttgart（斯图加特大学斯图加特模拟科学中心）；Institute for Physics of Functional Materials, Hamburg University of Technology（汉堡工业大学功能材料物理研究所）
We address the problem of predicting the solvation free energy and equilibrium solvent density profile in fews minutes from the molecular density functional theory beyond the usual hypernetted-chain approximation. We introduce a bridge functional of a coarse-grained, weighted solvent density. In few minutes at most, for solutes of sizes ranging from small compounds to large proteins, we produce (i) an estimation of the free energy of solvation within 1 kcal/mol of the experimental data for the hydrophobic solutes presented here, and (ii) the solvent distribution around the solute. Contrary to …
