Solute-solvent Interaction Energy Research Articles

Hybrid equilibrium-nonequilibrium molecular dynamics approach for two-dimensional solute-pump/solvent-probe spectroscopy.

There has been a tremendous effort in accessing liquid-phase solvation dynamics using ultrafast spectroscopies for decades. It is recently demonstrated that one can go beyond tracking the relaxation of the solute-solvent interaction energy as reported in traditional time-dependent fluorescence spectroscopy. Combining a resonant solute pump with a subsequent nonresonant 4-wave-mixing light-scattering solvent probe gives rise to two-dimensional solute-pump/solvent probe (SPSP) spectroscopy, which displays the nonequilibrium relaxation of the intermolecular vibrations after the solute gets electronically excited. However, the response function of the SPSP spectra has been challenging to calculate, even on the classical-mechanical level, due to the difficulty of evaluating the surviving Poisson bracket. In this work, a hybrid equilibrium-nonequilibrium molecular dynamics simulation approach is proposed where the Poisson bracket can be estimated using nonequilibrium molecular dynamics. Applying the resulting numerically exact formalism and the previously proposed hybrid instantaneous-normal-mode/molecular-dynamics approach to a preferential solvation model system reveals that the SPSP spectroscopy provides an alternative measure for solvation dynamics, which is more sensitive to the local solvent structures than the traditional energetic dynamics measured in the time-dependent fluorescence spectroscopy.

Energy-Representation Theory of Solutions: Its Formulation and Application to Soft, Molecular Aggregates

Abstract The energy-representation theory of solutions is developed to address the dissolution of a molecule in homogeneous fluid as well as the partitioning into such nanoscale structures as micelle and lipid membrane and the physisorption onto gas-liquid and solid-liquid interfaces in a unified manner as solvation in an extended sense. The present review describes the formulation of the solution theory with illustrative applications to the peptide configuration in lipid membrane, the water dissolution into polymer, and the physisorption on urea crystal in contact with liquid water. The solution theory in the energy representation is a density-functional scheme formulated by adopting the solute-solvent pair interaction energy as a one-dimensional coordinate for distribution functions and provides an approximate functional for the solvation free energy in terms of energy distribution functions in the reference-solvent and solution systems of interest. Each of the solute and solvent molecules is treated as a single unit as a whole, and due to this feature, a species with intramolecular flexibility and a solvent system with nano-scale inhomogeneity or interface can be analyzed in a common framework. The role of water is pointed out in determining the configuration of a peptide in lipid membrane, and the dissolution of water into polymer medium is described at chemical accuracy. Some directions of future developments are also discussed.

Accelerating the Calculation of Solute-Solvent Interaction Energies through Systematic Molecular Fragmentation.

The method of systematic molecular fragmentation by annihilation (SMFA) is modified to apply to the interaction energy between a solute and solvent, where the solute is a pair of reacting molecules. For NH3 + CH3Cl as the solute, it is shown that SMFA can estimate (to chemical accuracy) the average binding energy of the solute in large water clusters containing up to 160 water molecules, at an appropriate level of electronic structure theory. The SMFA calculation can be carried out in a computation time that makes it feasible to estimate the solvation contribution to free energies of activation and reaction by ensemble averaging.

Are Explicit Solvent Models More Accurate than Implicit Solvent Models? A Case Study on the Menschutkin Reaction.

In this work, contemporary quantum mechanical (QM) implicit solvent models (SMD, SM12, and COSMO-RS) and a molecular mechanical (MM) explicit solvent model were used to predict the aqueous free energy barrier of a simple Menschutkin reaction (NH3 + CH3Cl). Surprisingly, the explicit solvent approach performed the worst, while the implicit solvent models yielded reasonably accurate values that are in accord with available experimental data. The origin of the large error in the explicit solvent model was due to the use of a fixed set of Lennard-Jones parameters during the free energy perturbation (FEP) calculations. Further analyses indicate that M06-2X/6-31+G(d,p) yielded solute-solvent interaction energies that are in good agreement with benchmark DLPNO-CCSD(T)/CBS values. When end-state MM to M06-2X/6-31+G(d,p) corrections were added using FEP, it significantly improved the accuracy of the explicit solvent MM result and demonstrated that the accuracy of these models may be systematically improved with end-state corrections based on a validated QM level of theory.

Mutually polarizable QM/MM model with in situ optimized localized basis functions.

We extend our recently developed quantum-mechanical/molecular mechanics (QM/MM) approach [Dziedzic et al., J. Chem. Phys. 145, 124106 (2016)] to enable in situ optimization of the localized orbitals. The quantum subsystem is described with onetep linear-scaling density functional theory and the classical subsystem - with the AMOEBA polarizable force field. The two subsystems interact via multipolar electrostatics and are fully mutually polarizable. A total energy minimization scheme is employed for the Hamiltonian of the coupled QM/MM system. We demonstrate that, compared to simpler models using fixed basis sets, the additional flexibility offered by in situ optimized basis functions improves the accuracy of the QM/MM interface, but also poses new challenges, making the QM subsystem more prone to overpolarization and unphysical charge transfer due to increased charge penetration. We show how these issues can be efficiently solved by replacing the classical repulsive van der Waals term for QM/MM interactions with an interaction of the electronic density with a fixed, repulsive MM potential that mimics Pauli repulsion, together with a modest increase in the damping of QM/MM polarization. We validate our method, with particular attention paid to the hydrogen bond, in tests on water-ion pairs, the water dimer, first solvation shells of neutral and charged species, and solute-solvent interaction energies. As a proof of principle, we determine suitable repulsive potential parameters for water, K+, and Cl-. The mechanisms we employed to counteract the unphysical overpolarization of the QM subsystem are demonstrated to be adequate, and our approach is robust. We find that the inclusion of explicit polarization in the MM part of QM/MM improves agreement with fully QM calculations. Our model permits the use of minimal size QM regions and, remarkably, yields good energetics across the well-balanced QM/MM interface.

Study of the Wilcox torsion balance in solution for a Tröger's base derivative with hexyl-and heptyl substituents using a combined molecular mechanics and quantum chemistry approach.

The folding equilibrium of the Wilcox torsion balance in solution has been studied using a molecular mechanics method for sampling the conformational space and semi-empirical and density-functional quantum chemistry methods for characterizing the relative stabilities of various solute-solvent clusters extracted with the aid of the MD-quench technique from the different simulations that were performed. The role of the solvent environment has been analyzed by choosing four solvents of different polarities, namely water, acetone, tetrachloromethane, and n-hexane. In all cases, it is found that the attractive intramolecular interactions in folded conformations are strongly compensated by the increase of the solute-solvent interaction energies when the molecule unfolds. The latter can be well explained by the larger number of solvent molecules that can bind to the Wilcox molecule when in an unfolded conformation. The results of this work therefore support the experimental results of Yang et al. (Nature Chem 5:1006, 2013) that the folding free energy of the Wilcox balance is strongly reduced in solution as compared to the gas phase.

Red Moon methodology compatible with quantum mechanics/molecular mechanics framework: Application to solid electrolyte interphase film formation in lithium-ion battery system.

The Red Moon (RM) method [a hybrid Monte Carlo (MC)/molecular dynamics reaction method] is capable of realizing the practical atomistic simulation for complex chemical reaction systems beyond the range of application of the traditional molecular simulation techniques. In the RM method, the chemical reaction is treated stochastically based on the MC method. In the present study, to extend the applicability of the RM methodology, a new energy estimation method for the MC procedure has been proposed by using the quantum mechanics (QM)/molecular mechanics (MM) method. To validate its calculation reliability, we have examined it in a typical dimerization reaction in electrolytes of lithium-ion batteries (LIBs) and found that both solute internal energy and short-range solute-solvent interaction energy are significantly improved in comparison to the conventional energy estimation method using the MM method. As a practical application, we have dealt with the solid electrolyte interphase film formation in LIB, focusing on the bifurcation of dimerization reactions between the reduction products, and were able to reproduce the tendency similar to that in the experimental observations. It is concluded that the present RM methodology compatible with the QM/MM framework is expected to make a significant contribution to a variety of materials design and function development involved in various complex chemical reactions.

Prediction of solubility of etodolac in binary solvents using extended hildebrand solubility approach

The solubility of etodolac in binary solvent system i.e. methanol water system was analyzed in term of solute solvent interaction using extended Hildebrand solubility approach (EHSA).The solubility equation employs the term interaction energy (W) to replace the geometric mean (δ1δ2), where δ1 and δ2 are the cohesive energy densities for the solvent and solute, respectively. The new equation provides an accurate prediction of solubility once the interaction energy ‘W’ is obtained. In this case, the energy term is regressed against a polynomial in δ1 of the binary mixture. TisconSonicator A-72 & UV-Visibile spectrophotometer shimadzu UV-1700 were used in prediction & evaluation of solubility of Etodolac. Ideal Solubility of Etodolac was calculated by heat of fusion and absolute melting point obtained from DSC data reported in literature. Molar volume and solubility parameter of Etodolac were calculated from Fedor fragmental constant using floatation & experimentally solubility method. Results showed the solubility of Etodolac in the binary solvent, methanol-water shows a bell-shaped profile with a solubility maximum well below the ideal solubility of the drug. This is an attribute to solvation of the drug with the methanol-water mixture, and indicates that the solute-solvent interaction energy is larger than the geometric mean (δ1δ2) of regular solution. It was observed that in binary Methanol water system maximum solubility occurs at 17.17δ i.e.(30:70) & 21.6 δ (80:20) system.

Interaction-component analysis of the effects of urea and its alkylated derivatives on the structure of T4-lysozyme.

The effects of urea and its alkylated derivatives on the structure of T4-lysozyme were analyzed from the standpoint of energetics. Molecular dynamics simulations were conducted with explicit solvent, and the energy-representation method was employed to compute the free energy of transfer of the protein from pure-water solvent to the mixed solvents of water with urea, methylurea, 1,1-dimethylurea, and isopropylurea. Through the decomposition of the transfer free energy into the cosolvent and water contributions, it was observed that the former is partially cancelled by the latter and governs the total free energy of transfer. To determine the interaction component responsible for the transfer energetics, the correlations of the transfer free energy were also examined against the change in the solute-solvent interaction energy upon transfer and the corresponding changes in the electrostatic, van der Waals, and excluded-volume components. It was then found over the set of protein structures ranging from native to (partially) unfolded ones that the transfer free energy changes in parallel with the van der Waals component even when the cosolvent is alkylated. The electrostatic and excluded-volume components play minor roles in the structure modification of the protein, and the denaturing ability of alkylurea is brought by the van der Waals interaction.

Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis.

The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH3, NH4+, CN-) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The implications of these results for further refinement of this model are also discussed.

Nonpolar Solvation Free Energy from Proximal Distribution Functions.

Using precomputed near neighbor or proximal distribution functions (pDFs) that approximate solvent density about atoms in a chemically bonded context one can estimate the solvation structures around complex solutes and the corresponding solute-solvent energetics. In this contribution, we extend this technique to calculate the solvation free energies (ΔG) of a variety of solutes. In particular we use pDFs computed for small peptide molecules to estimate ΔG for larger peptide systems. We separately compute the non polar (ΔGvdW) and electrostatic (ΔGelec) components of the underlying potential model. Here we show how the former can be estimated by thermodynamic integration using pDF-reconstructed solute-solvent interaction energy. The electrostatic component can be approximated with Linear Response theory as half of the electrostatic solute-solvent interaction energy. We test the method by calculating the solvation free energies of butane, propanol, polyalanine, and polyglycine and by comparing with traditional free energy simulations. Results indicate that the pDF-reconstruction algorithm approximately reproduces ΔGvdW calculated by benchmark free energy simulations to within ∼ kcal/mol accuracy. The use of transferable pDFs for each solute atom allows for a rapid estimation of ΔG for arbitrary molecular systems.

TINKTEP: A fully self-consistent, mutually polarizable QM/MM approach based on the AMOEBA force field.

We present a novel quantum mechanical/molecular mechanics (QM/MM) approach in which a quantum subsystem is coupled to a classical subsystem described by the AMOEBA polarizable force field. Our approach permits mutual polarization between the QM and MM subsystems, effected through multipolar electrostatics. Self-consistency is achieved for both the QM and MM subsystems through a total energy minimization scheme. We provide an expression for the Hamiltonian of the coupled QM/MM system, which we minimize using gradient methods. The QM subsystem is described by the onetep linear-scaling DFT approach, which makes use of strictly localized orbitals expressed in a set of periodic sinc basis functions equivalent to plane waves. The MM subsystem is described by the multipolar, polarizable force field AMOEBA, as implemented in tinker. Distributed multipole analysis is used to obtain, on the fly, a classical representation of the QM subsystem in terms of atom-centered multipoles. This auxiliary representation is used for all polarization interactions between QM and MM, allowing us to treat them on the same footing as in AMOEBA. We validate our method in tests of solute-solvent interaction energies, for neutral and charged molecules, demonstrating the simultaneous optimization of the quantum and classical degrees of freedom. Encouragingly, we find that the inclusion of explicit polarization in the MM part of QM/MM improves the agreement with fully QM calculations.

Hydration thermodynamics beyond the linear response approximation

The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, and , with the solvent environment. Throughout the A B transformation of the solute, the solvation system is described by a Hamiltonian that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density that the dimensionless perturbational solute–solvent interaction energy has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density . The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute–solvent electrostatic interactions, or (2) the shorter-range attractive interactions are switched-on in the A B process.

Interaction-component analysis of the hydration and urea effects on cytochrome c.

Energetics was analyzed for cytochrome c in pure-water solvent and in a urea-water mixed solvent to elucidate the solvation effect in the structural variation of the protein. The solvation free energy was computed through all-atom molecular dynamics simulation combined with the solution theory in the energy representation, and its correlations were examined over sets of protein structures against the electrostatic and van der Waals components in the average interaction energy of the protein with the solvent and the excluded-volume component in the solvation free energy. It was observed in pure-water solvent that the solvation free energy varies in parallel to the electrostatic component with minor roles played by the van der Waals and excluded-volume components. The effect of urea on protein structure was then investigated in terms of the free-energy change upon transfer of the protein solute from pure-water solvent to the urea-water mixed solvent. The decomposition of the transfer free energy into the contributions from urea and water showed that the urea contribution is partially canceled by the water contribution and governs the total free energy of transfer. When correlated against the change in the solute-solvent interaction energy upon transfer and the corresponding changes in the electrostatic, van der Waals, and excluded-volume components, the transfer free energy exhibited strong correlations with the total change in the solute-solvent energy and its van der Waals component. The solute-solvent energy was decomposed into the contributions from the protein backbone and side chain, furthermore, and neither of the contributions was seen to be decisive in the correlation to the transfer free energy.

Calculations of Solvation Free Energy through Energy Reweighting from Molecular Mechanics to Quantum Mechanics.

In this work, the solvation free energies of 20 organic molecules from the 4th Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL4) have been calculated. The sampling of phase space is carried out at a molecular mechanical level, and the associated free energy changes are estimated using the Bennett Acceptance Ratio (BAR). Then the quantum mechanical (QM) corrections are computed through the indirect Non-Boltzmann Bennett's acceptance ratio (NBB) or the thermodynamics perturbation (TP) method. We show that BAR+TP gives a minimum analytic variance for the calculated solvation free energy at the Gaussian limit and performs slightly better than NBB in practice. Furthermore, the expense of the QM calculations in TP is only half of that in NBB. We also show that defining the biasing potential as the difference of the solute-solvent interaction energy, instead of the total energy, can converge the calculated solvation free energies much faster but possibly to different values. Based on the experimental solvation free energies which have been published before, it is discovered in this study that BLYP yields better results than MP2 and some other later functionals such as B3LYP, M06-2X, and ωB97X-D.

Microhydration of selenate, chromate and sulphate dianions: observation of indistinguishable IR spectra

ABSTRACTStructures, energetics and infrared (IR) spectra of the SeO42−.nH2O, CrO42−.nH2O and SO42−.nH2O clusters at ωB97X-D/aug-cc-pvtz level of theory are studied. It is observed that both the microhydrated SeO42− and CrO42− clusters are stabilised by double-hydrogen bonding (DHB), single-hydrogen bonding (SHB) and H-bonded cyclic water ring arrangements like the microhydrated SO42− cluster. It is also observed that the conformations having cyclic water network are found to be more stable in contrast to the other conformers having SHB or DHB arrangements. The calculated solute–solvent interaction energy for a particular structure is found to be nearly same (within 2%–6%) for all the hydrated clusters. The structure having at least one cyclic water ring is characterised by a peak in the range of 3450–3480 cm−1 in the IR spectra for all the systems. A single sharp peak at ∼3520 cm−1 is observed for the structure with six double-hydrogen arrangements. We do observe a near indistinguishable IR spectral pattern (within 1%) in the O–H stretching region for a particular structure in all the systems. It may be attributed to the same oxidation state of the central atom, identical geometry of the hydrated cluster and nearly same solute–solvent interaction energy.

Three-dimensional reference interaction site model self-consistent field analysis of solvent and substituent effects on the absorption spectra of Brooker's merocyanine.

Solvent and substituent effects on the absorption spectra of Brooker's merocyanine (BM) are investigated using the three-dimensional reference interaction site model self-consistent field method and time-dependent density functional theory. The π-π* excitation energies are computed for BM and its derivative 2,6-di-tert-butyl (di-t-Bu) BM. The behaviors of the computed excitation energies with increasing solvent polarity are in good agreement with those of the corresponding experimental measurements. In addition, analysis of the solute-solvent interaction energies and spatial distribution functions reveals that the effects of the solvent on the absorption spectra are reduced by the steric hindrance of the t-Bu groups. Furthermore, from the difference in the solute-solvent interaction energies of BM and di-t-Bu BM, it is shown that the effect of the t-Bu substituents on the absorption spectrum is greater in high-polarity solvents.

3D RISM theory with fast reciprocal-space electrostatics.

The calculation of electrostatic solute-solvent interactions in 3D RISM ("three-dimensional reference interaction site model") integral equation theory is recast in a form that allows for a computational treatment analogous to the "particle-mesh Ewald" formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems.

Energetic contributions from the cation and anion to the stability of carbon dioxide dissolved in imidazolium-based ionic liquids.

Cation and anion effects were investigated in the energetics of CO2 solvation in room-temperature ionic liquids. The solvation free energy in 1-n-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C4mim][NTf2]) was calculated with three types of force fields by molecular dynamics simulations combined with the energy-representation (ER) method, and the interaction responsible for the CO2 stability was examined in terms of the average sum of the solute-solvent interaction energy and its electrostatic and van der Waals components. A key role of the van der Waals component was found for the cation contribution, and the electrostatic component was seen to be minor in the anion contribution. The solvation free energy of CO2 was also investigated in ionic liquids of the form 1-n-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Cnmim][NTf2]) with varying alkyl-chain lengths of n = 4, 6, 8, and 12 by the ER method. The free energy was found to depend weakly on n, in agreement with experiments, and the cation and anion contributions and the electrostatic and van der Waals interaction components acted similarly at all values of n examined. The alkyl-chain length was found not to affect the local structure around CO2 strongly, and its effect on the interaction energy with CO2 appeared mainly through the bulk density.

Solvation effects on chemical shifts by embedded cluster integral equation theory.

The accurate computational prediction of nuclear magnetic resonance (NMR) parameters like chemical shifts represents a challenge if the species studied is immersed in strongly polarizing environments such as water. Common approaches to treating a solvent in the form of, e.g., the polarizable continuum model (PCM) ignore strong directional interactions such as H-bonds to the solvent which can have substantial impact on magnetic shieldings. We here present a computational methodology that accounts for atomic-level solvent effects on NMR parameters by extending the embedded cluster reference interaction site model (EC-RISM) integral equation theory to the prediction of chemical shifts of N-methylacetamide (NMA) in aqueous solution. We examine the influence of various so-called closure approximations of the underlying three-dimensional RISM theory as well as the impact of basis set size and different treatment of electrostatic solute-solvent interactions. We find considerable and systematic improvement over reference PCM and gas phase calculations. A smaller basis set in combination with a simple point charge model already yields good performance which can be further improved by employing exact electrostatic quantum-mechanical solute-solvent interaction energies. A larger basis set benefits more significantly from exact over point charge electrostatics, which can be related to differences of the solvent's charge distribution.