New evaluation of reconstructed spatial distribution function from radial distribution functions

Although three dimensional (3D) solvation structure is much more informative than one dimensional structure, its evaluation is difficult experimentally and theoretically. In our previous Communication [Yokogawa et al., J. Chem. Phys. 123, 211102 (2005)], we proposed a new method to present reconstructed spatial distribution function (RC-SDF) from a set of radial distribution functions (RDFs). In this article, we successfully extended the method more accurately with new basis sets. This new method was applied to two liquid solvation structures, methanol and dimethyl sulfoxide, as examples. Their RC-SDFs evaluated here clearly show that the former solvation structure is well defined while the latter one is broad, which agrees well with the SDFs calculated directly from molecular dynamics simulations. These results indicate that the method can reproduce well these 3D solvation structures in reasonable computational cost.     

Nuclear spin relaxation driven by intermolecular dipolar interactions: the role of solute-solvent pair correlations in the modeling of spectral density functions

Nuclear spin relaxation provides useful information related to the dynamics of molecular systems. When relaxation is driven by intermolecular dipolar interactions, the relevant spectral density functions (SDFs) also have significant contributions, in principle, from distant spins all over the dynamic range typically probed by NMR experiments such as NOESY. In this work, we investigate the intermolecular dipolar spin relaxation as driven by the relative diffusion of solvent and solute molecules taking place under a central force field, and we examine the relevant implications for (preferential) solvation studies. For this purpose, we evaluate the SDFs by employing a numerical approach based on spatial discretization of the time-propagation equation, and we supply an analytical solution for the simplest case of a steplike mean-field potential. Several situations related to different solute-solvent pair correlation functions are examined in terms of static/dynamic effects and relaxation modes, and some conclusions are drawn about the interpretation of NOE measurements. While we confirm previous results concerning the spoiling effect of long-range spins (Halle, B. J. Chem. Phys. 2003, 119, 12372), we also show that SDFs are sufficiently sensitive to pair correlation functions that useful, yet rather complicated, inferences can be made on the nature of the solvation shell.     

Dispersion and repulsion contributions to the solvation energy: Refinements to a simple computational model in the continuum approximation

A computational method for the evaluation of dispersion and repulsion contributions to the solvation energy is here presented in a formulation which makes use of a continuous distribution of the solvent, without introducing additional assumptions (e.g., local isotropy in the solvent distribution). The analysis is addressed to compare the relative importance of the various components of the dispersion energy (n = 6, 8, 10) and of the repulsion term, to compare several molecular indicators (molecular surface and volume, number of electrons) which may be put in relation to the dispersion-repulsion energy, and to define simplified computational strategies. The numerical examples refer to saturated hydrocarbons in water, treated with the homogeneous approximation of the distribution function which for this type of solution appears to be acceptable.     

Difference spatial distribution function analysis of aqueous solutions. II. Hydration structures of dimethyl ether, 180 degrees ethyl methyl ether and 0 degree ethyl methyl ether solutions

Monte Carlo simulations are systematically presented to demonstrate the influence of the hydrophobic group's steric bulk on hydration structure. We have simulated a dimethyl ether (DME), two conformations for ethyl methyl ether (0 degree EME and 180 degrees EME), and 0 degree ethanol solutions. Spatial distribution function (SDF), goo(x,y,z) and difference SDF (DSDF), delta goo(x,y,z), obtained from MC simulation in an infinitely dilute aqueous solution of ether show the three-dimensional probability of an atom-atom pair distribution between solute and solvent atoms. Based on the results of SDF in an infinitely dilute aqueous solution of ether, the distribution of hydration water molecules can be divided into hydrogen acceptor (HA) and hydrophobic hydration (HH), regions, and the spatial orientation of the hydrogen-bonded water in the HA region is found to form a triple-layer structure, as it does in alcohol solutions. From the results of an analysis of the DSDF delta goo(x,y,z) between the SDFs of EME and DME, it is apparent that the distribution changes of hydration water molecules in ether solutions are essentially similar to those in the alcohol solutions. Further, we show that the hydration water molecules are distributed mainly in the stable area in the binding energy's (BE) contour maps for each region.     

MLIMC: Machine Learning-Based Implicit-Solvent Monte Carlo

Monte Carlo (MC) methods are important computational tools for molecular structure optimizations and predictions. When solvent effects are explicitly considered, MC methods become very expensive due to the large degree of freedom associated with the water molecules and mobile ions. Alternatively implicit-solvent MC can largely reduce the computational cost by applying a mean field approximation to solvent effects and meanwhile maintains the atomic detail of the target molecule. The two most popular implicit-solvent models are the Poisson-Boltzmann (PB) model and the Generalized Born (GB) model in a way such that the GB model is an approximation to the PB model but is much faster in simulation time. In this work, we develop a machine learning-based implicit-solvent Monte Carlo (MLIMC) method by combining the advantages of both implicit solvent models in accuracy and efficiency. Specifically, the MLIMC method uses a fast and accurate PB-based machine learning (PBML) scheme to compute the electrostatic solvation free energy at each step. We validate our MLIMC method by using a benzene-water system and a protein-water system. We show that the proposed MLIMC method has great advantages in speed and accuracy for molecular structure optimization and prediction.     

Be2+在水、甲醇和乙醇中结构性质的从头算分子动力学模拟

采用Car-Parrinello分子动力学(CPMD)方法分别研究了Be²⁺在水、甲醇和乙醇中的溶剂结构性质, 并对Be²⁺的第一溶剂壳结构的实验及理论结果进行了比较. 所得第一溶剂壳结构与已报道的实验和理论结果较为一致. 对径向分布函数、配位数以及角度分布等进行了详细的分析. 结果表明: 在水、甲醇和乙醇中, Be²⁺第一溶剂壳为稳定理想的四面体结构. 在本文的模拟时间尺度内,没有观察到第一溶剂壳中的分子与第二溶剂壳中的分子进行交换, 进一步证明Be²⁺第一溶剂壳为稳定的四配位结构. 根据计算得到的空间分布函数, Be²⁺在溶剂分子的等高面上主要集中分布在溶剂分子接受氢键的方向. 根据氧原子在Be²⁺周围的分布, 壳层分子主要集中分布在Be²⁺周围的四个区域, 进一步证实溶剂壳为四面体对称.     

The effect of aqueous solvation upon alpha-helix formation for polyalanines

The incremental free energies of aqueous solution for acetyl(ala)NNH2 in its extended unfolded and alpha-helical conformations are compared using the SM5.2 solvation method of Cramer and Truhlar. A combination of density functional theory (DFT) at the B3LYP/D95(d,p) and AM1 has been employed using the ONIOM method. The incremental solvation energies of alpha-helical structures are very similar for both ONIOM and AM1 optimized structures as these structures do not significantly change upon solution. However, the conformations of the unfolded peptides change from extended beta-strand to polyproline II conformations upon aqueous solution. The incremental solvation free energy per residue of the polyproline II structure is about 2 kcal/mol/residue greater than that for the alpha-helix, representing an upper limit for the difference between the solvation energies. However, most of this difference disappears when the energy required to distort the optimized gas-phase extended beta-strand structure to the optimized polyproline II solution structure is included in the analysis, leaving an estimated difference in incremental solvation free energy of 0.3-0.5 kcal/mol favoring the unfolded structure. The solution structure sacrifices the stability derived from the intramolecular C5 H-bonds for more favorable interactions with the aqueous solvent.     

Theoretical study of the 1,3-hydrogen shift of triazene in water

The 1,3-hydrogen shift of triazene in aqueous solution was studied with a combination of QM/MM methods. First, the different species involved were characterized and the activation free-energies calculated with ASEP/MD, a method that makes use of the mean field approximation. Then the reaction dynamics was simulated with a QM/MM/MD method. A very strong influence of the solvent was observed, both specific, with the participation of a water molecule, and from the rest of the solvent. The effect of solvation on the geometry and electron distribution of triazene is important: N-N bond lengths tend to be more similar and the molecule acquires a planar structure. For the transition state structure, a substantial degree of ionic nature was found. Dynamic solvent effects were also analyzed.     

Difference spatial distribution function analysis of aqueous solutions. III. Hydration structures of alcohol and ether solutions having straight chain and branched alkyl groups

Spatial distribution functions (SDFs), gOO(x,y,z) and gOH(x,y,z), obtained from Monte Carlo simulations at 298 K were applied to characterize the anisotropic structure of infinitely dilute aqueous solutions of alcohols and ethers having straight chain and branched alkyl groups. In spite of the different size and shape of the hydrophobic groups, the spatial orientation of the hydrogen-bonded water molecules was found to be of linear type with a triple layer structure in the hydrogen acceptor (HA) region and a double layer structure in the hydrogen donor (HD) region. The volumes and the coordination number (CN) in the HA region were essentially identical for all alcohol and ether solutions, but the volumes for the isopropyl alcohol (IPA) and isopropyl methyl ether (IPE) solutions were greater than those for the other solutions. In the hydrophobic hydration (HH) region, these values increased with increasing size and shape of hydrophobic groups, except in the case of IPA and IPE solutions. These results indicated that the hydration structures around the isopropyl group in alcohol and ether solutions differed from those in other solutions. From the results of the difference SDF (DSDF), AgOO(x,y,z), between SDFs gOO(x,y,z) for the two states, it was apparent that the distribution of hydration water molecules in the HA region for ether solution was characterized by the increase of the distribution in the direction of lone pair electrons on the oxygen atom of the solute molecule with increasing hydrophobicity.     

Conformation of a flexible chain in explicit solvent: exact solvation potentials for short Lennard-Jones chains

The average conformation of a flexible chain molecule in solution is coupled to the local solvent structure. In a dense solvent, local chain structure often mirrors the pure solvent structure, whereas, in a dilute solvent, the chain can strongly perturb the solvent structure which, in turn, can lead to either chain expansion or compression. Here we use Monte Carlo (MC) simulation to study such solvent effects for a short Lennard-Lones (LJ) chain in monomeric LJ solvent. For an n-site chain molecule in solution these many-body solvent effects can be formally mapped to an n-body solvation potential. We have previously shown that for hard-sphere and square-well chain-in-solvent systems this n-body potential can be decomposed into a set of two-body potentials. Here, we show that this decomposition is also valid for the LJ system. Starting from high precision MC results for the n = 5 LJ chain-in-solvent system, we use a Boltzmann inversion technique to compute numerically exact sets of two-body solvation potentials which map the many-body chain-in-solvent problem to a few-body single-chain problem. We have carried out this mapping across the full solvent phase diagram including the dilute vapor, dense liquid, and supercritical regions and find that these sets of solvation potentials are able to encode the complete range of solvent effects found in the LJ chain-in-solvent system. We also show that these two-site solvation potentials can be used to obtain accurate multi-site intramolecular distribution functions and we discuss the application of these exact short chain potentials to the study of longer chains in solvent.     

The Binding Energy Distribution Analysis Method (BEDAM) for the Estimation of Protein-Ligand Binding Affinities

The Binding Energy Distribution Analysis Method (BEDAM) for the computation of receptor-ligand standard binding free energies with implicit solvation is presented. The method is based on a well established statistical mechanics theory of molecular association. It is shown that, in the context of implicit solvation, the theory is homologous to the test particle method of solvation thermodynamics with the solute-solvent potential represented by the effective binding energy of the protein-ligand complex. Accordingly, in BEDAM the binding constant is computed by means of a weighted integral of the probability distribution of the binding energy obtained in the canonical ensemble in which the ligand is positioned in the binding site but the receptor and the ligand interact only with the solvent continuum. It is shown that the binding energy distribution encodes all of the physical effects of binding. The balance between binding enthalpy and entropy is seen in our formalism as a balance between favorable and unfavorable binding modes which are coupled through the normalization of the binding energy distribution function. An efficient computational protocol for the binding energy distribution based on the AGBNP2 implicit solvent model, parallel Hamiltonian replica exchange sampling and histogram reweighting is developed. Applications of the method to a set of known binders and non-binders of the L99A and L99A/M102Q mutants of T4 lysozyme receptor are illustrated. The method is able to discriminate without error binders from non-binders, and the computed standard binding free energies of the binders are found to be in good agreement with experimental measurements. Analysis of the results reveals that the binding affinities of these systems reflect the contributions from multiple conformations spanning a wide range of binding energies.     

Efficient Calculation of Absorption Spectra in Solution: Approaches for Selecting Representative Solvent Configurations and for Reducing the Number of Explicit Solvent Molecules

Dye-sensitized solar cells(DSSCs) are one of the most promising renewable energy technologies. Charge transfer and charge transport are pivotal processes in DSSCs, which govern solar energy capture and conversion. These processes can be probed using modern electronic structure methods. Because of the heterogeneity and complexity of the local environment of a chromophore in DSSCs(such as solvatochromism and chromophore aggregation), a part of the solvation environment should be treated explicitly during the calculation. However, because of the high computational cost and unfavorable scaling with the number of electrons of high-level quantum mechanical methods, approaches to explicitly treat the local environment need careful consideration. Two problems must be tackled to reduce computational cost. First, the number of configurations representing the solvent distribution should be limited as much as possible. Second, the size of the explicit region should be kept relatively small. The purpose of this study is to develop efficient computational approaches to select representative configurations and to limit the explicit solvent region to reduce the computational cost for later(higher-level) quantum mechanical calculations. For this purpose, an ensemble of solvent configurations around a 1-methyl-8-oxyquinolinium betaine(QB) dye molecule was generated using Monte Carlo simulations and molecular mechanics force fields. Then, a fitness function was developed using data from inexpensive electronic structure calculations to reduce the number of configurations. Specific solvent molecules were also selected for explicit treatment based on a distance criterion, and those not selected were treated as background charges. The configurations and solvent molecules selected proved to be good representatives of the entire ensemble; thus, expensive electronic structure calculations need to be performed only on this subset of the system, which significantly reduces the computational cost.     

Molecular density functional theory of solvation: from polar solvents to water

A classical density functional theory approach to solvation in molecular solvent is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position and orientation-dependent free-energy density functional. In the homogeneous reference fluid approximation, limited to two-body correlations, the unknown excess term of the functional approximated by the angular-dependent direct correlation function of the pure solvent. We show that this function can be extracted from a preliminary MD simulation of the pure solvent by computing the angular-dependent pair distribution function and solving subsequently the molecular Ornstein-Zernike equation using a discrete angular representation. The corresponding functional can then be minimized in the presence of an arbitrary solute on a three-dimensional cubic grid for positions and Gauss-Legendre angular grid for orientations to provide the solvation structure and free-energy. This two-step procedure is proved to be much more efficient than direct molecular dynamics simulations combined to thermodynamic integration schemes. The approach is shown to be relevant and accurate for prototype polar solvents such as the Stockmayer solvent or acetonitrile. For water, although correct for neutral or moderately charged solute, it tends to underestimate the tetrahedral solvation structure around H-bonded solutes, such as spherical ions. This can be corrected by introducing suitable three-body correlation terms that restore both an accurate hydration structure and a satisfactory energetics.     

Site-specific solvation determined by intermolecular nuclear Overhauser effect--measurements and molecular dynamics

Site-specific solvation has been determined by intermolecular NOE measurements between solvent and solute. The experimental effect is shown on the four compounds 2-butanol, L-alanyl-L-tryptophan (Ala-Trp), adenosine and the disodium salt of adenosine 5'-monophosphate (5'-AMP) in the two solvents water and dimethyl sulfoxide (DMSO). The strength of NOE transfer correlates with the average distribution of solvent molecules around the corresponding solvation sites represented by the number of solvent molecules in a first solvation sphere, which can be obtained from molecular dynamics simulations in water. Saturation transfer between exchanging protons explains some deviations from this correlation. The NOE transfer measurements provide information on specific solute-solvent interactions and contribute to a better understanding of solvation phenomena. On the basis of a distinct relationship between steric solvation hindrance and the strength of NOE transfer, the application of such measurements for conformational analysis has been demonstrated for the first time.     

Characterization of metal ions in coordinating solvent mixtures by means of Raman spectroscopy.

Titration Raman spectroscopy has been developed for studying the solvation structure of metal ions in solution. The method affords us the solvation number, and the value thus obtained in neat solvents is in good agreement with that determined by EXAFS. The method is then applied to solvent mixtures, and the individual solvation number for each solvent is extracted. In a solvent mixture of N,N-dimethylformamide (DMF) and N,N,N',N'-tetramethylurea (TMU), the metal ion prefers DMF to TMU, which is ascribed to the solvation steric effect. The same applies also for the solvent mixture of N,N-dimethylpropionamide (DMPA) and DMF. However, unlike TMU, DMPA changes its conformation from the planar cis to non-planar staggered upon solvation to the metal ion. The enthalpy for the conformational change of DMPA is positive in the bulk, while it is significantly negative in the coordination sphere of the manganese(II) ion. Here, we briefly describe the procedure of measurements and analyses for the titration Raman spectroscopy, and review the solvation structure of the alkaline earth, first transition metal(II) and lanthanide(III) ions in some solvent mixtures in view of solvation steric effect.     

Theoretical study on ionization process in aqueous solution

Ionization potential (ionization energy) is a fundamental quantity characterizing electronic structure of a molecule. It is known that the energy in solution phase is significantly different from that in the gas phase. In this report, vertical and adiabatic ionization processes in aqueous solution are studied based on a hybrid method of quantum chemistry and statistical mechanics called reference interaction site model-SCF-spacial electron density distribution method. A role of solvation effect is elucidated through molecular level information, i.e., solvent distribution function around solute molecule. By utilizing the linear response regime, a simple expression to evaluate the spectral width from the distribution function is proposed and compared with experimental data.     

Microsolvated transition state models for improved insight into chemical properties and reaction mechanisms

Over the years, several methods have been developed to effectively represent the chemical behavior of solutes in solvents. The environmental effects arising due to solvation can generally be achieved either through inclusion of discrete solvent molecules or by inscribing into a cavity in a homogeneous and continuum dielectric medium. In both these approaches of computational origin, the perturbations on the solute induced by the surrounding solvent are at the focus of the problem. While the rigor and method of inclusion of solvent effects vary, such solvation models have found widespread applications, as evident from modern chemical literature. A hybrid method, commonly referred to as cluster-continuum model (CCM), brings together the key advantages of discrete and continuum models. In this perspective, we intend to highlight the latent potential of CCM toward obtaining accurate estimates on a number of properties as well as reactions of contemporary significance. The objective has generally been achieved by choosing illustrative examples from the literature, besides expending efforts to bring out the complementary advantages of CCM as compared to continuum or discrete solvation models. The majority of examples emanate from the prevalent applications of CCM to organic reactions, although a handful of interesting organometallic reactions have also been discussed. In addition, increasingly accurate computations of properties like pK(a) and solvation of ions obtained using the CCM protocol are also presented.