Number Of Explicit Solvent Molecules Research Articles

The Study of Molecules and Processes in Solution: An Overview of Questions, Approaches and Applications

Many industrial processes, several natural processes involving non-living matter, and all the processes occurring within living organisms take place in solution. This means that the molecules playing active roles in the processes are present within another medium, called solvent. The solute molecules are surrounded by solvent molecules and interact with them. Understanding the nature and strength of these interactions, and the way in which they modify the properties of the solute molecules, is important for a better understanding of the chemical processes occurring in solution, including possible roles of the solvent in those processes. Computational studies can provide a wealth of information on solute–solvent interactions and their effects. Two major models have been developed to this purpose: a model viewing the solvent as a polarisable continuum surrounding the solute molecule, and a model considering a certain number of explicit solvent molecules around a solute molecule. Each of them has its advantages and challenges, and one selects the model that is more suitable for the type of information desired for the specific system under consideration. These studies are important in many areas of chemistry research, from the investigation of the processes occurring within a living organism to drug design and to the design of environmentally benign solvents meant to replace less benign ones in the chemical industry, as envisaged by the green chemistry principles. The paper presents a quick overview of the modelling approaches and an overview of concrete studies, with reference to selected crucial investigation themes.

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

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

Modelling the aqueous and nonaqueous interfaces for CO2 electro-reduction over Sn catalysts

Abstract In CO2 electroreduction, Sn catalysts with a high overpotential for hydrogen evolution reaction and a high selectivity towards formic acid formation are very attractive. Many efforts have been made for improving the catalytic performance and for understanding the mechanisms. In electrochemistry, the role of solvents for surface reactions was deserved to be investigated, in particular for some nonaqueous solvents. Here, we have modeled the aqueous (water) and nonaqueous (acetonitrile and dichloromethane) for investigation of CO2 electroreduction on Sn surface, by constrained ab initio molecular dynamics simulations and thermodynamic integrations, including a number of explicit solvent molecules in computational models. It was found that CO2 reduction is initiated from formate formation and solvents, in particular, water can effectively facilitate the reaction.

A complete basis set study of the lowest n–π* and π–π* electronic transitions of acrolein in explicit water environment

The solvatochromic shift of the first n–π* and π–π* transitions of s-trans acrolein molecule in water is systematically investigated. Monte Carlo simulations are made to generate solute–solvent configurations used in CIS(D)/aug-cc-pVXZ (X = 2, 3, 4, 5, 6) calculations. Analysis of the convergence of the results with the cardinal number and the number of explicit solvent molecules is made. Our results elucidate the solvatochromic shift of the n–π* transition dominated by electrostatic interaction and the π–π* transition requiring non-electrostatic interaction.

Using EPR spectroscopy as a unique probe of molecular-scale reorganization and solvation in self-assembled gel-phase materials.

We describe the synthesis of spin-labeled bis-ureas which coassemble with bis-urea gelators and report on self-assembly as detected using electron paramagnetic resonance spectroscopy (EPR). Specifically, EPR detects the gel-sol transition and allows us to quantify how much spin-label is immobilized within the gel fibers and how much is present in mobile solvent pools-as controlled by temperature, gelator structure, and thermal history. EPR is also able to report on the initial self-assembly processes below the gelation threshold which are not macroscopically visible and appears to be more sensitive than NMR to intermediate-sized nongelating oligomeric species. By studying dilute solutions of gelator molecules and using either single or double spin-labels, EPR allows quantification of the initial steps of the hierarchical self-assembly process in terms of cooperativity and association constant. Finally, EPR enables us to estimate the degree of gel-fiber solvation by probing the distances between spin-labels. Comparison of experimental data against the predicted distances assuming the nanofibers are only composed of gelator molecules indicates a significant difference, which can be assigned to the presence of a quantifiable number of explicit solvent molecules. In summary, EPR provides unique data and yields powerful insight into how molecular-scale mobility and solvation impact on assembly of supramolecular gels.

Vertical Electronic Excitations in Solution with the EOM-CCSD Method Combined with a Polarizable Explicit/Implicit Solvent Model.

The accurate calculation of electronic transition energies and properties of isolated chromophores is not sufficient to provide a realistic simulation of their excited states in solution. In fact, the solvent influences the solute geometry, electronic structure, and response to external fields. Therefore, a proper description of the solvent effect is fundamental. This can be achieved by combining polarizable explicit and implicit representations of the solvent. The former provides a realistic description of solvent molecules around the solute, while the latter introduces the electrostatic effect of the bulk solution and reduces the need of too large a number of explicit solvent molecules. This strategy is particularly appealing when an accurate method such as equation of motion coupled cluster singles and doubles (EOM-CCSD) is employed for the treatment of the chromophore. In this contribution, we present the coupling of EOM-CCSD with a fluctuating charges (FQ) model and polarizable continuum model (PCM) of solvation for vertical excitations in a state-specific framework. The theory, implementation, and prototypical applications of the method are presented. Numerical tests on small solute-water clusters show very good agreement between full EOM-CCSD and EOM-CCSD-FQ calculations, with and without PCM, with differences ≤ 0.1 eV. Additionally, approximated schemes that further reduce the computational cost of the method are introduced and showed to perform well compared to the full method (errors ≤ 0.1 eV).

Generalized image charge solvation model for electrostatic interactions in molecular dynamics simulations of aqueous solutions

This paper extends the image charge solvation model (ICSM) [Y. Lin, A. Baumketner, S. Deng, Z. Xu, D. Jacobs, W. Cai, An image-based reaction field method for electrostatic interactions in molecular dynamics simulations of aqueous solutions, J. Chem. Phys. 131 (2009) 154103], a hybrid explicit/implicit method to treat electrostatic interactions in computer simulations of biomolecules formulated for spherical cavities, to prolate spheroidal and triaxial ellipsoidal cavities, designed to better accommodate non-spherical solutes in molecular dynamics (MD) simulations. In addition to the utilization of a general truncated octahedron as the MD simulation box, central to the proposed extension is an image approximation method to compute the reaction field for a point charge placed inside such a non-spherical cavity by using a single image charge located outside the cavity. The resulting generalized image charge solvation model (GICSM) is tested in simulations of liquid water, and the results are analyzed in comparison with those obtained from the ICSM simulations as a reference. We find that, for improved computational efficiency due to smaller simulation cells and consequently a less number of explicit solvent molecules, the generalized model can still faithfully reproduce known static and dynamic properties of liquid water at least for systems considered in the present paper, indicating its great potential to become an accurate but more efficient alternative to the ICSM when bio-macromolecules of irregular shapes are to be simulated.

Calculation of solvation free energies of Li+ and O2 − ions and neutral lithium–oxygen compounds in acetonitrile using mixed cluster/continuum models

Solvation effects play a major role in determining the cycling characteristics of the non-aqueous rechargeable Li-air battery. We use a mixed cluster/continuum solvent model with varying number of explicit solvent molecules (n = 4–10) to calculate the solvation free energies ( $$ \Updelta G_{\text{solv}}^{*} $$ ) of Li+ and O2 − ions and neutral LiO2, Li2O2, LiO, and Li2O species in acetonitrile solvent. Calculations for complexes with the full first solvation shell around Li+ (n = 4) and O2 − (n = 8) show excellent agreement with the solvation free energies obtained using the cluster pair approximation (the error is below 2.0 kcal/mol). The use of the pure continuum model fitted to reproduce the experimental values of $$ \Updelta G_{\text{solv}}^{*} $$ (Li+) and $$ \Updelta G_{\text{solv}}^{*} $$ (O2 −) gives the solvation free energies of various lithium–oxygen species (Li x O y ; x, y = 1, 2) that are in excellent agreement with the results obtained using mixed cluster/continuum models (n ≥ 8). This provides a theoretical framework for including solvent effects in the theoretical models of oxygen reduction and evolution reactions in the aprotic Li-air battery.

Computational (solute-solvent cluster + PCM) study of medium effects on the experimental 13C and 1H NMR chemical shifts of lactones and lactams

Solvent effects on the 1H and 13C NMR chemical shifts of some lactones: β-propiolactone, γ-butyrolactone, δ-valerolactone and ε-caprolactone, as well as lactams: azetidin-2-one, pyrrolidin-2-one, δ-valerolactam and ε-caprolactam have been investigated and discussed in a wide range of solvents. The experimental results were compared with density functional calculations using a large basis set. Solvent effects were computed by means of an integrated approach including the polarizable continuum model and an optimum number of explicit solvent molecules surrounding the solute. The agreement between computed and experimental chemical shifts fully validates our integrated approach. In order to quantify and elucidate the origin of the solvent effects on the 1H and 13C chemical shifts of the selected compounds, a multi-linear regression analysis has been carried out using the empirical Kamlet–Abboud–Taft solvatochromic parameters. It has been found that there is a good correlation between the solvent-induced chemical shifts of 13C and the π* scale of solvent dipolarity polarizability. 1H chemical shifts are affected mainly by the dipolarity–polarizability and the basicity of the solvent. An excellent agreement has been obtained between the calculated and the experimental data. Copyright © 2011 John Wiley & Sons, Ltd.

Electronic spectroscopy of biomolecules in solution: fluorescein dianion in water

A combined and sequential Monte Carlo–quantum mechanics methodology is used to describe the electronic absorption spectrum of the fluorescein dianion in water. Different sets of 100 statistically relevant configurations composed of the solute and several solvent molecules are sampled from the Monte Carlo simulation for a posteriori quantum mechanical calculations of the spectra. In the largest case the configurations are composed of fluorescein and 90 explicit water molecules embedded in the electrostatic field of all remaining water molecules within a distance of 11.3 Å. These configurations include 305 atoms and 842 valence electrons, justifying the use of a semi-empirical approach. The electronic spectrum is then calculated using the INDO/CIS method. The solvatochromic shift of fluorescein in water, compared with in isolation, is calculated using the discrete and explicit solvent models. The use of electrostatically embedded explicit water molecules, in INDO/CIS calculations, gives a good description of the spectral shift of the fluorescein dianion in aqueous environment. The results are verified to converge both statistically and with respect to the number of explicit solvent molecules used.

TDDFT study of absorption spectrum of ketocyanine dye complexes with metal ions: explicit solvent model

Transition energies for a ketocyanine dye and its complexes with Li+ and Mg2+ ions with an implicit solvent have been studied. Molecular Dynamics simulations have been used to prepare structures of the dye in acetonitrle solution of lithium or magnesium perchlorate. TDDFT methodology has been used to calculate the transition energies for dye and dye-ion complexes solvated by an increasing number of acetonitrile molecules. Results have been compared to the predictions of the continuous solvation model. Evolution of the spectrum with the number of explicit solvent molecules has been observed and the solvent-induced shifts have been determined. It has been found that the explicit solvation model may predict sequence of transitions and their parentage different than that resulting from implicit solvation. Effect of the perchlorate counterion for the dye-cation spectrum has been also analyzed.

Trans-Platinum anticancer drug AMD443: A detailed theoretical study by DFT–TST method on the hydrolysis mechanism

The two-step hydrolysis of trans-[PtCl2(NH3)(2 picoline)], AMD443, a novel anticancer drug has been investigated using density functional theory (DFT) with and without a number of explicit solvent molecules. Pentacoordinated trigonal–bipyramidal (TBP)-like structure transition state (TS) along with other stationary points on potential energy surface were optimized and characterized. To obtain accurate energies for the reaction surfaces, single-point energies were calculated by conductor-like polarisable calculation model (CPCM) using larger basis sets. Significant differences in the geometry and position of the TBP transition state are found between explicitly solvated and gas phase structures. The computed values of rate constant of different steps are in good agreement with the available experimental results.

Towards a first principles prediction of pK a: COSMO-RS and the cluster-continuum approach

The COSMO-RS method, a post-quantum chemistry extension of the quantum chemical dielectric continuum solvation model COSMO with a statistical thermodynamics treatment for realistic solvation simulation, has been applied to the prediction of the aqueous pK a of acids and bases. The combination of the COSMO-RS approach to pK a prediction with the cluster-continuum approach (explicit solvation of the solute compound with one or more solvent molecules) was used on three data sets consisting of 94 acids and 75 bases. Correlation of the calculated free energies of dissociation in water with the experimental aqueous pK a of the solute acids and bases in their bare state and explicitly solvated by one or two solvent molecules showed an increase of the regression slope with the number of explicit solvent molecules, thus showing a regression slope that is closer to the theoretical value than the slope found for bare solutes. It was found that the cluster-continuum approach is limited to a pK a range of strong to moderately weak acids and bases, because the optimisations of the solvent–solute complexes of the ionic species of very weak acids (such as the anion of tert-butanol) did not lead to the desired complexes, but yielded dissociation products.

Solvent Effects on Global Reactivity Properties for Neutral and Charged Systems Using the Sequential Monte Carlo Quantum Mechanics Model

The energy of the frontier molecular orbitals and reactivity indices such as chemical potential, hardness, and electrophilicity of neutral and charged molecules have been investigated in aqueous solution using explicit model for the solvent with the sequential Monte Carlo/quantum mechanics methodology. The supermolecular structures of the solute-solvent system were generated by Monte Carlo simulation. Statistically uncorrelated structures have been extracted for quantum mechanical calculations of the solute surrounded by the first solvation shell, using explicit water molecules, and the second and third shells as atomic point charges. The supermolecular calculations treating both the solute and the solvent explicitly were performed within density functional theory. The solvent dependence of the frontier molecular orbital energies was analyzed and used to calculate the reactivity indices in solution. The dependence of the results with respect to the number of explicit solvent molecules is also analyzed. It is seen that for the systems considered here, the energies of the highest occupied molecular orbital and the lowest unoccupied molecular orbital show a strong dependence with the number of solvent molecules. However, the properties derived from these are relatively stable. In particular, the results reported here for the reactivity indices obtained using the first solvation shell are similar to those obtained for the limit bulk value. For comparison, the reactivity indices were also calculated in the gas phase and using the polarizable continuum model (PCM). As frequently reported in the literature, neutral molecules do not show significant changes in the reactivity indices between gas phase and the PCM model. However, with the explicit solvent model some important changes were observed: a larger negative chemical potential, a smaller hardness, and a larger electrophilicity. The stabilization of an anion corresponding to a negative chemical potential is obtained only by using explicit solvent molecules. In general, the solvent effect was well treated by using the first solvation shell, and the calculated results are in agreement with the experimental trends. The delocalization of the solute orbitals over the solvent region is analyzed, and its consequence to the reactivity indices are discussed. The importance of including explicit solvent molecules and adopting a statistical approach for the liquid is emphasized.

77Se NMR Spectroscopic, DFT MO, and VBT Investigations of the Reversible Dissociation of Solid (Se6I2)[AsF6]2·2SO2in Liquid SO2to Solutions Containing 1,4-Se6I22+in Equilibrium with Sen2+(n= 4, 8, 10) and Seven Binary Selenium Iodine Cations: Preliminary Evidence for 1,1,4,4-Se4Br42+andcyclo-Se7Br+

The composition of a complex equilibrium mixture formed upon dissolution of (Se(6)I(2))[AsF(6)](2).2SO(2) in SO(2)(l) was studied by (77)Se NMR spectroscopy at -70 degrees C with both natural-abundance and enriched (77)Se-isotope samples (enrichment 92%). Both the natural-abundance and enriched NMR spectra showed the presence of previously known cations 1,4-Se(6)I(2)(2+), SeI(3)(+), 1,1,4,4-Se(4)I(4)(2+), Se(10)(2+), Se(8)(2+), and Se(4)(2+). The structure and bonding in 1,4-Se(6)I(2)(2+) and 1,1,4,4-Se(4)I(4)(2+) were explored using DFT calculations. It was shown that the observed Se-Se bond alternation and presence of thermodynamically stable 4ppi-4ppi Se-Se and 4ppi-5ppi Se-I bonds arise from positive charge delocalization from the formally positively charged tricoordinate Se(+). The (77)Se chemical shifts for cations were calculated using the relativistic zeroth-order regular approximation (ZORA). In addition, calculations adding a small number of explicit solvent molecules and an implicit conductor-like screening model were conducted to include the effect that solvent has on the chemical shifts. The calculations yielded reasonable agreement with experimental chemical shifts, and inclusion of solvent effects was shown to improve the agreement over vacuum values. The (77)Se NMR spectrum of the equilibrium solution showed 22 additional resonances. These were assigned on the basis of (77)Se-(77)Se correlation spectroscopy, selective irradiation experiments, and spectral simulation. By combining this information with the trends in the chemical shifts, with iodine, selenium, and charge balances, as well as with ZORA chemical shift predictions, these resonances were assigned to acyclic 1,1,2-Se(2)I(3)(+), 1,1,6,6-Se(6)I(4)(2+), and 1,1,6-Se(6)I(3)(+), as well as to cyclic Se(7)I(+) and (4-Se(7)I)(2)I(3+). A preliminary natural-abundance (77)Se NMR study of the soluble products of the reaction of (Se(4))[AsF(6)](2) and bromine in liquid SO(2) included resonances attributable to 1,1,4,4-Se(4)Br(4)(2+)(.) These assignments are supported by the agreement of the observed and calculated (77)Se chemical shifts. Resonances attributable to cyclic Se(7)Br(+) were also observed. The thermal stability of (Se(6)I(2))[AsF(6)](2).2SO(2)(s) was consistent with estimates of thermodynamic values obtained using volume-based thermodynamics (VBT) and the first application of the thermodynamic solvate difference rule for nonaqueous solvates. (Se(6)I(2))[AsF(6)](2).2SO(2)(s) is the first example of a SO(2) solvate for which the nonsolvated parent salt, (Se(6)I(2))[AsF(6)](2)(s), is not thermodynamically stable, disproportionating to Se(4)I(4)(AsF(6))(2)(s) and Se(8)(AsF(6))(2)(s) (DeltaG degrees for the disproportion reaction is estimated to be -17 +/- 15 kJ mol(-1) at 298 K from VBT theory).

A Coupled Car-Parrinello Molecular Dynamics and EXAFS Data Analysis Investigation of Aqueous Co2+

We have studied the microscopic solvation structure of Co(2+) in liquid water by means of density functional theory (DFT)-based Car-Parrinello molecular dynamics (CPMD) simulations and extended X-ray absorption fine structure (EXAFS) data analysis. The effect of the number of explicit water molecules in the simulation box on the first and second hydration shell structures has been considered. Classical molecular dynamics simulations, using an effective two-body potential for Co(2+)-water interactions, were also performed to show box size effects in a larger range. We have found that the number of explicit solvent molecules has a marginal role on the first solvation shell structural parameters, whereas larger boxes may be necessary to provide a better description of the second solvation shell. Car-Parrinello simulations were determined to provide a reliable description of structural and dynamical properties of Co(2+) in liquid water. In particular, they seem to describe both the first and second hydration shells correctly. The EXAFS signal was reconstructed from Car-Parrinello simulations. Good agreement between the theoretical and experimental signals was observed, thus strengthening the microscopic picture of the Co(2+) solvation properties obtained using first-principle simulations.

Quantum Chemical Investigation of the Koch Carbonylation of Methyl tert-Butyl Ether (MTBE)

Methyl tert-butyl ether (MTBE) is a widely used additive in oxygenated gasoline that has recently come under environmental pressure. Consequently, the demand for MTBE is likely to decrease in the future, and new uses for MTBE need to be explored. Production of methyl 2,2-dimethylpropanoate (methyl pivalate) via Koch carbonylation chemistry is an attractive option because methyl pivalate has been shown to be a fluid with a much lower ozone-forming potential than many other oxygenated solvents. Semiempirical, Hartree-Fock, MP2, and density functional theory calculations, believed to be the first on this system, indicated that the most energetically difficult step in this chemistry is the decomposition of MTBE to tert-butyl cation and methanol. Specific solvation effects were included in these calculations by inclusion of a small number of explicit solvent molecules, and nonspecific solvation effects were taken into account using a dielectric continuum model.

Combining Microsolvation and Polarizable Continuum Studies: New Insights in the Rotation Mechanism of Amides in Water

We present a quantum mechanical investigation of the rotation mechanisms of N,N-dimethylformamide (DMF) and N,N-dimethylacetamide (DMA) in water. This rotation can happen through two distinct transition states known as TS1 and TS2, where the nitrogen lone pair is on the opposite side of the oxygen atom or on the same side, respectively. The analysis is focused on complementary descriptions of the solvent, either represented by a limited number of explicit solvent molecules (microsolvation), by an implicit (or continuum) solvation, or by combinations of these two approaches. The combined approach (microsolvation + continuum) can provide quantitative agreement with the experimental results for the gas to solution shift of the rotational barrier. For both amides, continuum effects alone are sufficient to select the correct channels. However, hydrogen-bond effects (via the explicit solvent molecules) are necessary to obtain quantitative agreement with experiment, provided this is combined with a continuum description. In the rotation in DMF, it seems that a single water molecule is directly involved, while the other solvent molecules act as a “mean field” (the bulk), which is well reproduced by a polarizable continuum medium. The mechanism in DMA is less clear. In gas phase the steric repulsive interactions between methyl groups make TS1 clearly favored with respect to TS2. In water, the larger dipole moment of TS2 produces an opposite effect with respect to the repulsion interactions, making the corresponding channel less disfavored than in gas phase. The results are compared with previous Monte Carlo simulations, and this comparison is used to draw a more general picture about how different descriptions of the solvent can take into account long-range and mediated effects on one side and shorter-range and dynamic effects on the other side.

A charge-scaling method to treat solvent in QM/MM simulations

We present a method to treat the solvent efficiently in hybrid quantum mechanical/molecular mechanical simulations of chemical reactions in enzymes. The method is an adaptation of an approach developed for molecular-mechanical free-energy simulations. The charges of each of the exposed ionizable groups are scaled, and the system is simulated in the presence of a limited number of explicit solvent molecules to obtain a reasonable set of structures. Continuum electrostatics methods are then used to correct the energies. Variations in the procedure are discussed with an emphasis on modifications from the original protocol. We illustrate the method by applying it to the study of a hydrolysis reaction in a highly charged system comprising a complex between the base excision repair enzyme uracil-DNA glycosylase and double-stranded DNA. The resulting adiabatic reaction profile is in good agreement with experiment, in contrast to that obtained without scaling the charges.

Electrostatic free energy calculations using the generalized solvent boundary potential method

Free energy perturbation (FEP) calculations using all-atom molecular dynamics simulations with a large number of explicit solvent molecules are a powerful approach to study ligand–macromolecule association processes at the atomic level. One strategy to carry out FEP calculations efficiently and reduce computational time is to consider the explicit dynamics of only a small number of atoms in a localized region around the ligand. Such an approximation is motivated by the observation that the factors governing binding specificity are dominated by interactions in the vicinity of the ligand. However, a straightforward truncation of the system may yield inaccurate results as the influence exerted by the remote regions of the macromolecule and the surrounding solvent through long-range electrostatic effects may be significant. To obtain meaningful results, it is important to incorporate the influence of the remote regions of the ligand–macromolecule complex implicitly using some effective potential. The generalized solvent boundary potential (GSBP) that was developed recently [W. Im, S. Bernèche, and B. Roux, J. Chem. Phys. 114, 2924 (2001)] is an efficient computational method to represent the long-range electrostatic interactions arising from remote (outer) regions in simulations of a localized (inner) region with a small number of explicit atoms. In the present work, FEP calculations combined with GSBP are used to illustrate the importance of these long-range electrostatic factors in estimation of the charging free energy of an aspartate ligand bound to the aspartyl-tRNA synthetase. Calculations with explicit spherical simulation inner regions of different radii are used to test the accuracy of the GSBP method and also illustrate the importance of explicit protein and solvent dynamics in the free energy estimation. The influence of the represented outer region is tested using separate simulations in which the reaction field and/or the protein static field are excluded. Both components are shown to be essential to obtain quantitatively meaningful results. The ability of implicitly treating the influence of protein fluctuations in the outer region using a protein dielectric constant is examined. It is shown that accurate charging free energy calculations can be performed for this system with a spherical region of 15 to 20 Å radius, which roughly corresponds to 1500–3500 moving atoms. The results indicate that GSBP in combination with FEP calculations is a precise and efficient approach to include long-range electrostatic effects in the study of ligand binding to large macromolecules.