Data scarcity, bias, and experimental noise are all frequently encountered problems in the application of deep learning to chemical and material science disciplines. Transfer learning has proven effective in compensating for the lack in data. The use of quantum calculations in machine learning enables the generation of a diverse dataset and ensures that learning is less affected by noise inherent to experimental databases. In this work, we propose a transfer learning approach for the prediction of solvation free energies that combines fundamentals from quantum calculations with the higher accuracy of experimental measurements. The employed model architecture is based on the directed-message passing neural network for the molecular embedding of solvent and solute molecules. A significant advantage of models pre-trained on quantum calculations is demonstrated for small experimental datasets and for out-of-sample predictions. The improved out-of-sample performance is shown for new solvents, for new solute elements, and for the extension to higher molar mass solutes. The overall performance of the pre-trained models is limited by the noise in the experimental test data, known as the aleatoric uncertainty. On a random test split, a mean absolute error of 0.21 kcal/mol is achieved. This is a significant improvement compared to the mean absolute error of the quantum calculations (0.40 kcal/mol). The error can be further reduced to 0.09 kcal/mol if the model performance is assessed on a more accurate subset of the experimental data.
PCMSolver is an open-source library for continuum electrostatic solvation. It can be combined with any quantum chemistry code and requires a minimal interface with the host program, greatly reducing programming effort. As input, PCMSolver needs only the molecular geometry to generate the cavity and the expectation value of the molecular electrostatic potential on the cavity surface. It then returns the solvent polarization back to the host program. The design is powerful and versatile: minimal loss of performance is expected, and a standard single point self-consistent field implementation req…
This review describes the theory and implementation of implicit solvation models based on continuum electrostatics. Within quantum chemistry this formalism is sometimes synonymous with the polarizable continuum model, a particular boundary-element approach to the problem defined by the Poisson or Poisson-Boltzmann equation, but that moniker belies the diversity of available methods. This work reviews the current state-of-the art, with emphasis on theory and methods rather than applications. The basics of continuum electrostatics are described, including the nonequilibrium polarization response…
Free energies of ionic solvation calculated from computer simulations exhibit a strong system size dependence. We perform a finite-size analysis based on a dielectric-continuum model with periodic boundary conditions. That analysis results in an estimate of the Born ion size. Remarkably, the finite-size correction applies to systems with only eight water molecules hydrating a sodium ion and results in an estimate of the Born radius of sodium that agrees with the experimental value.
Continuum solvation models enable efficient first principles calculations of chemical reactions in solution, but require extensive parametrization and fitting for each solvent and class of solute systems. Here, we examine the assumptions of continuum solvation models in detail and replace empirical terms with physical models in order to construct a minimally-empirical solvation model. Specifically, we derive solvent radii from the nonlocal dielectric response of the solvent from ab initio calculations, construct a closed-form and parameter-free weighted-density approximation for the free energ…
The conductor-like polarization model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in chemical simulations. However, its application in quantum mechanical calculations of large-scale biomolecular systems can be limited by computational expense of both the gas phase electronic structure and the solvation interaction. We have previously used graphical processing units (GPUs) to accelerate the first of these steps. Here, we extend the use of GPUs to accelerate electronic structure calculations including C-PCM solvation. Implementation on the GPU …
Liquid state theories such as integral equations and classical density functional theory often overestimate the bulk pressure of fluids because they require closure relations or truncations of functionals. Consequently, the cost to create a molecular cavity in the fluid is no longer negligible and those theories predict wrong solvation free energies. We show how to correct them simply by computing an optimized Van der Walls volume of the solute and removing the undue free energy to create such volume in the fluid. Given this versatile correction, we demonstrate that state-of-the-art solvation …
We demonstrate that with two small modifications, the popular dielectric continuum model is capable of predicting, with high accuracy, ion solvation thermodynamics in numerous polar solvents, and ion solvation free energies in water--co-solvent mixtures. The first modification involves perturbing the macroscopic dielectric-flux interface condition at the solute--solvent interface with a nonlinear function of the local electric field, giving what we have called a solvation-layer interface condition (SLIC). The second modification is a simple treatment of the microscopic interface potential (sta…
We report a development of a new fast surface-based method for numerical calculations of solvation energy of biomolecules with a large number of charged groups. The procedure scales linearly with the system size both in time and memory requirements, is only a few percent wrong for any molecular configurations of arbitrary sizes, gives explicit value for the reaction field potential at any point, provides both the solvation energy and its derivatives suitable for Molecular Dynamics simulations. The method works well both for large and small molecules and thus gives stable energy differences for…
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…
Free energies govern the behavior of soft and liquid matter, and improving their predictions could have a large impact on the development of drugs, electrolytes or homogeneous catalysts. Unfortunately, it is challenging to devise an accurate description of effects governing solvation such as hydrogen-bonding, van der Waals interactions, or conformational sampling. We present a Free energy Machine Learning (FML) model applicable throughout chemical compound space and based on a representation that employs Boltzmann averages to account for an approximated sampling of configurational space. Using…
Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific…
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…
Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecul…
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…
Calculated state-of-the art results for solvation and ionization energies of thousands of organic molecules relevant to battery design
Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；University of Vienna（维也纳大学）；Uppsala University（乌普萨拉大学）；Vector Institute for Artificial Intelligence（人工智能向量研究所）；University of Toronto（多伦多大学）；Technische Universität Berlin（柏林工业大学）
A recently developed statistical mechanical Quasi-Chemical Theory (QCT) has led to significant insights into solvation phenomena for both hydrophilic and hydrophobic solutes. The QCT exactly partitions solvation free energies into three components: 1) inner-shell chemical, 2) outer-shell packing, and 3) outer-shell long-ranged contributions. In this paper, we discuss efficient methods for computing each of the three parts of the free energy. A Bayesian estimation approach is developed to compute the inner-shell chemical and outer-shell packing contributions. We derive upper and lower bounds on…
Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, …
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…
Solvation free energies are efficiently predicted by molecular density functionnal theory (MDFT) if one corrects the overpressure introduced by the usual homogeneous reference fluid approximation. Sergiievskyi et al. [Sergiievskyi et al., JPCL, 2014, 5, 1935-1942] recently derived the rigorous compensation of this excess of pressure (PC) and proposed an empirical "ideal gas" supplementary correction (PC+) that further enhances the calculated solvation free energies. In a recent paper [Misin et al, JCP, 2015, 142, 091105], those corrections were applied to solvation free energy calculations usi…
Theories of solvation free energies often involve electrostatic potentials at the position of a solute charge. Simulation calculations that apply cutoffs and periodic boundary conditions based on molecular centers result in center-dependent contributions to electrostatic energies due to a systematic sorting of charges in radial shells. This sorting of charges induces a surface-charge density at the cutoff sphere or simulation-box boundary that depends on the choice of molecular centers. We identify a simple solution that gives correct, center-independent results, namely the radial integration …
Solvation free energy is an important quantity in Computational Chemistry with a variety of applications, especially in drug discovery and design. The accurate prediction of solvation free energies of small molecules in water is still a largely unsolved problem, which is mainly due to the complex nature of the water-solute interactions. In this letter we develop a scheme for the determination of the electrostatic contribution to the solvation free energy of charged molecules based on nonlocal electrostatics involving a minimal parameter set which in particular allows to introduce atomic radii …
We present a multiwavelet-based implementation of a quantum/classical polarizable continuum model. The solvent model uses a diffuse solute-solvent boundary and a position-dependent permittivity, lifting the sharp-boundary assumption underlying many existing continuum solvation models. We are able to include both surface and volume polarization effects in the quantum/classical coupling, with guaranteed precision, due to the adaptive refinement strategies of our multiwavelet implementation. The model can account for complex solvent environments and does not need a posteriori corrections for volu…
Recent advances in machine learning and their applications have lead to the development of diverse structure-property relationship models for crucial chemical properties, and the solvation free energy is one of them. Here, we introduce a novel ML-based solvation model, which calculates the solvation energy from pairwise atomistic interactions. The novelty of the proposed model consists of a simple architecture: two encoding functions extract atomic feature vectors from the given chemical structure, while the inner product between two atomistic features calculates their interactions. The result…
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 …
Reported here are theoretical calculations on the triflic acid and water, establishing molecular scale information necessary to modeling of the structure, thermodynamics, and ionic transport of Nafion membranes. To characterize side chain flexibility and accessibility of the acid proton, free energies for rotation of both carbon-sulfur and sulfur-oxygen (hydroxyl) bonds are presented. The energetic barrier to rotation of the acid proton away from the sulfonic acid oxygen plane is substantially flattened, with barrier less than one kcal/mol, by electrostatic solvation. The activation free energ…
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory but replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [J. Phys. …
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…
Quantum chemical calculations on quantum computers have been focused mostly on simulating molecules in gas-phase. Molecules in liquid solution are however most relevant for Chemistry. Continuum solvation models represent a good compromise between computational affordability and accuracy in describing solvation effects within a quantum chemical description of solute molecules. Here we report on the extension of the Variational Quantum Eigensolver to solvated systems, using the Polarizable Continuum Model. We show that accounting for solvation effects does not impact the algorithmic efficiency. …
Alchemical free energy calculations via molecular dynamics have been widely used to obtain thermodynamic properties related to protein-ligand binding and solute-solvent interactions. Although soft-core modeling is the most common approach, the linear basis function (LBF) methodology [Naden, L. N.; et al. J. Chem. Theory Comput. 2014, 10 (3), 1128; 2015, 11 (6), 2536] has emerged as a suitable alternative. It overcomes the end-point singularity of the scaling method while maintaining essential advantages such as ease of implementation and high flexibility for postprocessing analysis. In the pre…
The current computational study investigates the changes in solvation dynamics of water when introducing hydrophobic side chains to the molecular probe N-methyl-6-oxyquinolinium betaine. High precision transient fluorescence and absorption measurements published in the companion paper revealed an influence of hydrophobic sidechain alterations on the observed solvation dynamics of a chromophore in water. As the influence of shape, size and structure of chromophores on the time-dependent Stokes shift was so far thought to play a role only in slowly rotating solvents compared to the solute or if …
Continuum solvation models enable electronic structure calculations of systems in liquid environments, but because of the large number of empirical parameters, they are limited to the class of systems in their fit set (typically organic molecules). Here, we derive a solvation model with no empirical parameters for the dielectric response by taking the linear response limit of a classical density functional for molecular liquids. This model directly incorporates the nonlocal dielectric response of the liquid using an angular momentum expansion, and with a single fit parameter for dispersion con…
Despite the modern level of development of computational chemistry methods and techno-logical progress, fast and accurate determination of solvation free energy remains a huge problem for physical chemists. In this paper, we describe two computational schemes that can potentially solve this problem. We consider systems of poorly soluble drug compounds in supercritical carbon dioxide. Considering that the biggest contribution among all inter-molecular interactions is made by van der Waals interactions, we model solute and solvent particles as coarse-grained ones interacting via the effective Le…
Charge hydration asymmetry (CHA)--a characteristic dependence of hydration free energy on the sign of the solute charge--quantifies the asymmetric response of water to electric field at microscopic level. Accurate estimates of CHA are critical for understanding hydration effects ubiquitous in chemistry and biology. However, measuring hydration energies of charged species is fraught with significant difficulties, which lead to unacceptably large (up to 300%) variation in the available estimates of the CHA effect. We circumvent these difficulties by developing a framework which allows us to extr…
Employing a classical density-functional description of liquid environments, we introduce a rigorous method for the diffusion quantum Monte Carlo calculation of free energies and thermodynamic averages of solvated systems that requires neither thermodynamic sampling nor explicit solvent electrons. We find that this method yields promising results and small convergence errors for a set of test molecules. It is implemented readily and is applicable to a range of challenges in condensed matter, including the study of transition states of molecular and surface reactions in liquid environments.
University of Michigan（密歇根大学）；Stanford University（斯坦福大学）
Deep learning based methods have been widely applied to predict various kinds of molecular properties in the pharmaceutical industry with increasingly more success. Solvation free energy is an important index in the field of organic synthesis, medicinal chemistry, drug delivery, and biological processes. However, accurate solvation free energy determination is a time-consuming experimental process. Furthermore, it could be useful to assess solvation free energy in the absence of a physical sample. In this study, we propose two novel models for the problem of free solvation energy predictions, …
For the problem of molecular solvation, formulated as a liquid submitted to the external potential field created by a molecular solute of arbitrary shape dissolved in that solvent, we draw a connection between the Gaussian field theory derived by David Chandler [Phys. Rev. E, 1993, 48, 2898] and classical density functional theory. We show that Chandler's results concerning the solvation of a hard core of arbitrary shape can be recovered by either minimising a linearised HNC functional using an auxiliary Lagrange multiplier field to impose a vanishing density inside the core, or by minimising …
We analyze deficiencies of commonly used Coulomb approximations in Generalized Born solvation energy calculation models and report a development of a new fast surface-based method (FSBE) for numerical calculations of the solvation energy of biomolecules with charged groups. The procedure is only a few percents wrong for molecular configurations of arbitrary sizes, provides explicit values for the reaction field potential at any point of the molecular interior, water polarization at the surface of the molecule, both the solvation energy value and its derivatives suitable for Molecular Dynamics …
The solvation model proposed by Fattebert and Gygi [Journal of Computational Chemistry 23, 662 (2002)] and Scherlis et al. [Journal of Chemical Physics 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region wher…
The computational modelling of reactions is simple in theory but can be quite tricky in practice. This article aims at the purpose of providing an assistance to a proper way of describing reactions theoretically and provides rough guidelines to the computational methods involved. Reactions in liquid phase chemical equilibrium can be described theoretically in terms of the Gibbs free energy of reaction. This property can be divided into a sum of three disjunct terms, namely the gas phase reaction energy, the finite temperature contribution to the Gibbs free energy, and the Gibbs free energy of …
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…
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…
Recent predictions of absolute binding free energies of host-guest complexes in aqueous solution using electronic structure theory have been encouraging for some systems, while other systems remain problematic for others. In paper I summarize some of the many factors that could easily contribute 1-3 kcal/mol errors at 298 K: three-body dispersion effects, molecular symmetry, anharmonicity, spurious imaginary frequencies, insufficient conformational sampling, wrong or changing ionization states, errors in the solvation free energy of ions, and explicit solvent (and ion) effects that are not wel…
Predicting solvation free energies with an implicit solvent machine learning potential
Faculty of Physics and Center for NanoScience, Department of Veterinary Sciences, Ludwig-Maximilians-Universität München（物理系和纳米科学中心、兽医学系，路德维希-马克西米利安大学慕尼黑）；Atomistic Modeling Center, Munich Data Science Institute, Technical University of Munich（原子模型中心、慕尼黑数据科学研究所，慕尼黑技术大学）；Multiscale Modeling of Fluid Materials, Department of Engineering Physics and Computation, TUM School of Engineering and Design, Technical University of Munich（多尺度流体材料建模，工程物理与计算系，TUM工程与设计学院，慕尼黑技术大学）
Solvation is a notoriously difficult and nagging problem for the rigorous theoretical description of chemistry in the liquid phase. Successes and failures of various approaches ranging from implicit solvation modeling through dielectric continuum embedding and microsolvated quantum chemical modeling to explicit molecular dynamics highlight this situation. Here, we focus on quantum chemical microsolvation and discuss an explicit conformational sampling ansatz to make this approach systematic. For this purpose, we introduce an algorithm for the rolling and automated microsolvation of solutes. Ou…
The PAH family of organic compounds (polycyclic aromatic hydrocarbons), involved in several fields of chemistry, has received particular attention in astrochemistry, where their vibrational spectroscopy, thermodynamic, dynamic, and fragmentation properties are now abundantly documented. This survey aims at drawing trends for low spin-multiplicity surfaces of PAHs bearing internal energies in the range 1-10 eV. It addresses some typical alternatives to the ground-state regular structures of PAHs, making explicit possible intramolecular rearrangements leading to high-lying minima. These isomeris…
