A statistical thermodynamic development is given of a new implicit solvent model that avoids the traditional system size limitations of computer simulation of macromolecular solutions with periodic boundary conditions. This implicit solvent model is based upon the quasi-chemical approach, distinct from the common integral equation trunk of the theory of liquid solutions. The physical content of this theory is the hypothesis that a small set of solvent molecules are decisive for these solvation problems. A detailed derivation of the quasi-chemical theory escorts the development of this proposal. The numerical application of the quasi-chemical treatment to Li$^+$ ion hydration in liquid water is used to motivate and exemplify the quasi-chemical theory. Those results underscore the fact that the quasi-chemical approach refines the path for utilization of ion-water cluster results for the statistical thermodynamics of solutions.
Department of Engineering Physics and Computation, TUM School of Engineering and Design, Technical University of Munich（工程物理与计算系，TUM工程与设计学院，慕尼黑技术大学）；Atomistic Modeling Center (AMC), Munich Data Science Institute (MDSI), Technical University of Munich（原子建模中心（AMC），慕尼黑数据科学研究所（MDSI），慕尼黑技术大学）
Accurate modeling of the solvent environment for biological molecules is crucial for computational biology and drug design. A popular approach to achieve long simulation time scales for large system sizes is to incorporate the effect of the solvent in a mean-field fashion with implicit solvent models. However, a challenge with existing implicit solvent models is that they often lack accuracy or certain physical properties compared to explicit solvent models, as the many-body effects of the neglected solvent molecules is difficult to model as a mean field. Here, we leverage machine learning (ML…
Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multi-method approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obt…
We present an implicit solvent model for ab initio electronic structure calculations which is fully self-consistent and is based on direct solution of the nonhomogeneous Poisson equation. The solute cavity is naturally defined in terms of an isosurface of the electronic density according to the formula of Fattebert and Gygi (J. Comp. Chem. 23, 6 (2002)). While this model depends on only two parameters, we demonstrate that by using appropriate boundary conditions and dispersion-repulsion contributions, solvation energies obtained for an extensive test set including neutral and charged molecules…
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…
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…
The properties of binary mixtures of dimethylsulfoxide and glycerol, measured by several techniques, are reported. Special attention is given to those properties contributing or affecting chemical reactions. In this respect the investigated mixture behaves as a relatively simple solvent and it is especially well suited for studies on the influence of viscosity in chemical reactivity. This is due to the relative invariance of the dielectric properties of the mixture. However, special caution must be taken with specific solvation, as the hydrogen-bonding properties of the solvent changes with th…
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…
Large scale molecular dynamics simulations are used to study drying suspensions of a binary mixture of large and small particles in explicit and implicit solvents. The solvent is first modeled explicitly and then mapped to a uniform viscous medium by matching the diffusion coefficients and the pair correlation functions of the particles. `Small-on-top' stratification of the particles, with an enrichment of the smaller ones at the receding liquid-vapor interface during drying, is observed in both models under the same drying conditions. With the implicit solvent model, we are able to model much…
A temperature (T)-dependent coarse-grained (CG) Hamiltonian of polyethylene glycol/oxide (PEG/PEO) in aqueous solution is reported to be used in implicit-solvent material models in a wide temperature (i.e., solvent quality) range. The T-dependent nonbonded CG interactions are derived from a combined "bottom-up" and "top-down" approach. The pair potentials calculated from atomistic replica-exchange molecular dynamics simulations in combination with the iterative Boltzmann inversion are post-refined by benchmarking to experimental data of the radius of gyration. For better handling and a fully c…
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 Li-Air battery is a very promising candidate for powering future mobility, but finding a suitable electrolyte solvent for this technology turned out to be a major problem. We present a systematic computational investigation of the known chemical space for possible Li-Air electrolyte solvents. It is shown that the problem of finding better Li-Air electrolyte solvents is not only - as previously suggested - about maximizing Li+ and O2- solubilities, but about finding the optimal balance of these solubilities with the viscosity of the solvent. As our results also show that trial-and-error exp…
We report results of quantum chemical calculations for the neutral and anionic species of (4,4{'})-bipyridine (44BPY), a prototypical molecule with a floppy degree of freedom, placed in vacuo and in solvents. In addition to equilibrium geometries and vibrational frequencies and spectra, we present adiabatic energy curves for the vibrational modes with significant intramolecular reorganization upon charge transfer. Special attention is paid to the floppy strongly anharmonic degree of freedom of 44BPY, which is related to the most salient structural feature, namely the twist angle $θ$ between th…
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）
An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here, we present a calculation of the electric field on the solute-solvent interface that is exact for piece-wise linear variations of the potential and analyze four different alternatives to compute the force using a boundary element method. We performed a verification exercise for two cases: the isolated and two interacting molecules. Our results suggest that the boundary element method outperforms the finite difference method, as the latter needs a mu…
Antioxidant capacity of garlic has been attributed to organic sulfur compounds such us allyl methyl disulfide. Using quantum chemical calculations at B3LYP/6-31+G (d) and G3MP2B3/6-31+G (d) levels of theory, we study three possible oxidation reactions of this compound against hydrogen peroxide, a reactive oxygen species, from a thermodynamic point of view. Because these reactions are supposed to occur in biological media, solvent effect was taken into consideration. Oxidation over the double bond that leads to the formation of an epoxide is more thermodynamically feasible, limiting the antioxi…
We have established the detailed phase diagram of the prototypical deep eutectic solvent ethaline (ethylene glycol / choline chloride 2:1) as a function of the hydration level, in the bulk state and confined in the nanochannels of mesostructured porous silica matrices MCM-41 and SBA-15, with pore radii $R_P$ = 1.8 nm and 4.15 nm. For neat and moderately hydrated DESs, freezing was avoided and glassforming solutions were formed in all cases. For mass fraction of water above a threshold value $W_g'\approx30\%$, crystallization occurred and led to the formation of a maximally-freeze concentrated …
Implicit electron-density solvation models based on joint density-functional theory offer a computationally efficient solution to the problem of calculating thermodynamic quantities of solvated systems from firstprinciples quantum mechanics. However, despite much recent interest in such models, to date the applicability of such models in the plane-wave context to non-aqueous solvents has been limited because the determination of the model parameters requires fitting to a large database of experimental solvation energies for each new solvent considered. This work presents an alternate approach …
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…
Fast and accurate simulation of complex chemical systems in environments such as solutions is a long standing challenge in theoretical chemistry. In recent years, machine learning has extended the boundaries of quantum chemistry by providing highly accurate and efficient surrogate models of electronic structure theory, which previously have been out of reach for conventional approaches. Those models have long been restricted to closed molecular systems without accounting for environmental influences, such as external electric and magnetic fields or solvent effects. Here, we introduce the deep …
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…
Theoretical Study of Reactivity Indices and Rough Potential Energy Curves for the Dissociation of 59 Fullerendiols in Gas-Phase and in Aqueous Solution with an Implicit Solvent Model
We introduce a multimodel approach to the simulation of the optical properties of molecular dyes in solution, whereby the effects of thermal fluctuations and of dielectric screening on the absorption spectra are accounted for by explicit and implicit solvation models, respectively. Thermal effects are treated by averaging the spectra of molecular configurations generated by an ab initio molecular-dynamics simulation where solvent molecules are treated explicitly. Dielectric effects are then dealt with implicitly by computing the spectra upon removal of the solvent molecules and their replaceme…
We have investigated a water-stable sol-gel method based on ethylene glycol as a solvent and bridging ligand for the synthesis of ferroelectric lead zirconate titanate in bulk and thin film forms. This method offers lower toxicity of the solvent, higher stability towards atmospheric moisture and a simplified synthetic procedure compared to traditional sol-gel methods. Ceramic pellets of Nb-doped lead zirconate titanate (PNZT) in the rhombohedral phase were produced with high density and good piezoelectric properties, comparable to those reported in the literature and those found in commercial …
We present a method to derive implicit solvent models of electrolyte solutions from all-atom descriptions; providing analytical expressions of the thermodynamic and structural properties of the ions consistent with the underlying explicit solvent representation. Effective potentials between ions in solution are calculated to perform perturbation theory calculations, in order to derive the best possible description in terms of charged hard spheres. Applying this method to NaCl solutions yields excellent agreement with the all-atom model, provided ion association is taken into account.
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…
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…
The lack of a procedure to determine equilibrium thermodynamic properties of a small system interacting with a bath is frequently seen as a weakness of conventional statistical mechanics. A typical example for such a small system is a solute surrounded by an explicit solvation shell. One way to approach this problem is to enclose the small system of interest in a large bath of explicit solvent molecules, considerably larger than the system itself. The explicit inclusion of the solvent degrees of freedom is obviously limited by the available computational resources. A potential remedy to this p…
The association of ions in electrolyte solutions at very low concentration and low temperature is studied using computer simulations and quasi-chemical ion-pairing theory. The specific case of the restricted primitive model (charged hard spheres) is considered. Specialised simulation techniques are employed that lead to efficient sampling of the arrangements and distributions of clusters and free ions, even at conditions corresponding to nanomolar solutions of simple salts in solvents with dielectric constants in the range 5-10, as used in recent experimental work on charged-colloid sus- pensi…
