Hydration Free Energy Difference Research Articles

Quasi-chemical theory for anion hydration and specific ion effects: [formula omitted](aq) vs.[formula omitted](aq)

Anion hydration is complicated by H-bond between neighboring water molecules in addition to H-bond donation to the anion. This situation leads to competing structures and anharmonic vibrations for simple clusters like (H2O)nCl-. This study applies quasi-chemical theory to study anion hydration and exploits dynamics calculations on isolated clusters to account for anharmonicity. Comparing singly hydrated halide clusters, classic H-bond donation to the anion occurs for F- , while Cl- clusters exhibit flexible dipole-dominated interactions. The predicted Cl- – F- hydration free energy difference agrees with experiment, a significant theoretical step for addressing issues like Hofmeister ranking and selectivity in ion channels.

Calculation of the properties of the S3− radical anion and its complexes with Cu+ in aqueous solution

A species observed in aqueous sulfidic solutions at high T and P has recently been identified as the anion radical S3−, based on the Raman spectrum obtained in a hydrothermal diamond–anvil cell (Pokrovski and Dubrovinsky, 2011, Science, 331, 1052–1054).Such a species had not been expected to occur in such environments, although S3− as an component of lapis lazuli, other solids and even albite melt has been well studied (Winther et al., 1998; Reinen and Lindner, 1999; Arieli et al., 2004; Shnitko et al., 2008; Bacci et al., 2009).We have calculated the structures, energetics, vibrational and UV–visible spectra of S3− and several other similar species and confirm the species identification of Pokrovski and Dubrovinsky, although we are still somewhat concerned about the apparent lack of a third peak which we calculate to be present in the Raman spectrum of S3−.Our calculations indicate that the reaction:S6-2⇒2S3-in aqueous solution has a free energy change of +3kcal/mol at 298K and 1atm pressure but −13kcal/mol at 723K and 1atm pressure, consistent with the disappearance of disulfide species and the appearance of S3−at high T. Likewise, the free energy for the reaction:2H2S+SO4-2+H+⇒S3-+.75O2+2.5H2Odecreases from 44.1 to 19.0kcal/mol between 298 and 723K (again at 1atm). This is consistent with the decrease in concentrations of SH− and SO4−2 and the formation of S3− observed by Pokrovski and Dubrovinski over this temperature range. The corresponding log K values are in semiquantitative agreement with those found by Pokrovski and Dubrovinsky.The main contribution to these changes in reaction free energy with temperature come from the VRT (vibrational–rotational–translational) contribution to the gas-phase free energy, while the hydration free energy difference changes little.Calculation of 34S–32S isotopic fractionations for S3− at 298K give δ values of around +4.3% relative to H2S, a value intermediate between that of S3 and S3−2.Calculated free energies for exchange reactions between S3− and SH− establish that S3− forms complexes with Cu+ which are similar in stability to its complexes with SH−. The S3Cu(OH2) complex shows two coordination at Cu and a nearly linear <S–Cu–O while the (S3−)2Cu complex is planar and 4-coordinate at Cu.

Theoretical analysis of the gas-phase hydration of common atmospheric pre-nucleation [formula omitted] and (H3O+)(H2SO4)(H2O)n cluster ions

Small atmospheric ions are always hydrated. The hydration affects their mobility, stability, and lifetime, which are critically important for the determination of nucleation rates. The gas-phase hydration of anions and cations of the atmospheric nucleation precursor H2SO4 has been studied using the Density Functional Theory (DFT). We found that the interaction between the common atmospheric ions and polar water molecules lead to the formation of the strongly hydrogen bonded hydrate complexes, whose thermodynamic stability is much higher than that of neutral atmospheric hydrates (H2SO4)(H2O)n. Both negatively and positively charged hydrates are much more stable than the aforementioned neutral form; however, the hydration of cations is much stronger than that of anions. The difference in hydration free energies is very large (∼10kcalmol−1); however, it decreases quickly when the cluster is growing. The observed positive hydration sign preference is consistent with previous studies for pure water.

Hydration free energy difference of acetone, acetamide, and urea

The hydration free energy and hydration entropy difference of urea and acetone, and of acetamide and acetone have been calculated both by free energy perturbation and by the method of thermodynamic integration. The obtained results show a striking asymmetry between the thermodynamic changes accompanying the replacement of the first and second CH(3) group of acetone by NH(2). Thus, the first CH(3)NH(2) exchange is found to lead to an about 10 kJmol decrease in the energy, 8 kJmol decrease in the Helmholtz free energy, and 5-10 Jmol K decrease in the entropy of hydration, while similar values accompanying the second CH(3)NH(2) exchange are found to be about -65 kJmol, -35 kJmol and -100 Jmol K, respectively. These results indicate that the two NH(2) groups of the urea molecule have a strong synergetic effect on the thermodynamics of the hydration of urea. The fact that the replacement of the two CH(3) groups of acetone by NH(2) leads to a strong decrease in the hydration entropy indicates that urea clearly has an ordering effect on nearby water.

Role of fluctuations in a snug-fit mechanism of KcsA channel selectivity

The thermodynamic exclusion of Na+ relative to K+ in potassium channels is examined by calculating the distribution of binding energies for Na+ and K+ in a model of the selectivity filter of the KcsA potassium channel. These distributions are observed to take a surprisingly simple form: Gaussian with a slight positive skewness that is insignificant in the present context. Complications that might be anticipated from these distributions are not problematic here. Na+ occupies the filter with a mean binding energy substantially lower than that of K+. The difference is comparable to the difference in hydration free energies of Na+ and K+ in bulk aqueous solution. Thus, the average energies of binding to the filter do not discriminate Na+ from K+ when measured from a baseline of the difference in bulk hydration free energies. The strong binding of Na+ constricts the filter, consistent with a negative partial molar volume of Na+ in water in contrast with a positive partial molar volume of K+ in water. Discrimination in favor of K+)can be attributed to the scarcity of favorable binding configurations for Na+ compared to K+. That relative scarcity is quantified as enhanced binding energy fluctuations, which reflects both the energetically stronger binding of Na+ and the constriction of the filter induced by Na+ binding.

Calculation of the Hydration Free Energy Difference between Pyridine and Its Methyl-Substituted Derivatives by Computer Simulation Methods

The difference of the hydration free energy of pyridine and its methyl- and symmetrically dimethyl-substituted derivatives has been calculated by the method of free energy perturbation. To check the precision of the results obtained, we have repeated the calculations using thermodynamic integration over different paths. Besides the hydration free energy, the difference in the energy and entropy of hydration between pyridine and monomethyl- and dimethylpyridines has also been determined. The obtained results clearly show that the hydration free energy of the pyridine derivatives becomes more negative with each additional methyl group. However, the accuracy of the calculation does not allow us to draw any conclusion about the dependence of the hydration free energy on the location of the methyl group. The analysis of the Coulomb and Lennard-Jones contributions to the hydration free energy differences has shown the dominance of the latter term. The comparison of the hydration energy and free energy values has shown that there is a strong compensation effect between the energetic and entropic terms of the free energy. The hydration energy of the solute becomes considerably more negative with each additional methyl group due to the dispersion attraction between the methyl group and the surrounding water molecules. The introduction of a methyl group results in an approximately 30 J/(mol K) decrease of the entropy of hydration, and hence, at 300 K, the entropic contribution to the hydration free energy increases by about 9 kJ/mol. Due to their opposite signs, the entropic and energetic contributions largely cancel each other, resulting in approximately an order of magnitude smaller value for the free energy.

Improved precision and efficiency of free energy calculations for small systems using lambda-scaled atomic masses and separating conformational and transformational sampling.

We present results showing the importance of appropriate treatment of atomic masses in molecular dynamics (MD)-based single topology free-energy perturbations (FEPs) on small molecule systems. The reversibility of gas phase simulations is significantly improved by scaling the atomic mass of mutated atoms with the lambda variable normally used for the scaling of energy terms. Because this effect is less pronounced for solvated systems, it will not cancel in estimates of the relative hydration free energy difference. The advantage of mass scaling is demonstrated by a null mutation of ethane to ethane and the calculation of the relative hydration free energy difference between ethane and n-propane. Furthermore, it is found that the simulation time necessary for converged MD/FEPs is prohibitively large for relative hydration free energy calculations on cyclic alkanes. Therefore, we explore an alternative free energy pathway including strongly constrained conformations to improve convergence in FEP simulations of flexible molecules.

Factors determining the relative stability of anionic tetrahedral complexes in serine protease catalysis and inhibition.

Quantum mechanical ab initio (RHF/6-31+G*//RHF/3-21G) calculations were used to simulate the formation of the tetrahedral complex intermediate (TC) in serine protease active site by substrates and transition-state analog inhibitors. The enzyme active site was simulated by an assembly of the amino acids participating in catalysis, whereas the substrates and inhibitors were simulated by small ligands, acetamide (1) and trifluoroacetone (2), respectively. For the first time, the principal factors determining the relative stability of the TC in serine proteases are arranged according to their energy contributions. These include (a) formation of the new covalent bond between Ser195 O(gamma) and the electrophilic center of a ligand; (b) stabilization of the oxyanion in the oxyanion hole; (c) basic catalysis by His57; and (d) hydrogen bond between Asp102 carboxylate and N(delta) of the protonated His57. We have directly calculated the gas-phase relative free energy of formation of TC(AS)(2) and TC(AS)(1), the value of DeltaDeltaG(g)[TC(AS)(2,1)]. It is DeltaE(cov), the relative energy of the new covalent bond between the enzyme and the ligand formed in a TC that determines the experimentally observed large difference in the stability of TCs formed by substrates and TS-analog inhibitors of serine proteases. We demonstrated that the relative stability of TCs formed by a series of mono- and dipeptide amides and TFKs, derived from experimental kinetic data, can be rather well approximated by the sum of the theoretically calculated value of DeltaDeltaG(g)[TC(AS)(2, 1)] and the difference in hydration free energies of isolated ligands.

New Effective Potentials Extraction Method for the Interaction between Cations and Water

A very simple method for the extraction of effective interaction potentials from ab initio calculations was proposed (Periole et al. J. Phys. Chem. 1997, 101, 5018), and simple two-body cation−water interaction potentials were derived for several cations, Li+, Na+, K+, Be2+, Mg2+, and Ca2+, using two facts: first, water molecules in the close vicinity of cations are strongly structured and present a constrained orientation towards the ion; second, at larger distances the ion-water interaction is mainly electrostatic. In the present work, an extension to Rb+ and Sr2+ and some refinements of this method are presented. In particular, we explore the most adequate way of including the nonadditivity and polarization effects that arise from the ion-water-water and water-water interactions. The potentials obtained with the new extraction methods are compared with the empirical potentials of Åqvist (Åqvist, J. J. Phys. Chem. 1990, 94, 8021) that were adjusted to reproduce experimental data. Those obtained with the exploration−TIE method are also tested by performing molecular dynamics simulations of the various cation−water systems and the results are found to be in good agreement with experimental data. In particular, they yield cation hydration free energy differences (ΔG values) that are, in general, in good accordance with experimental figures. This latter method is ideally suited and easy to apply to obtain effective interaction potentials for molecular systems with restricted geometric conditions that appear in numerical simulations, either Monte Carlo or molecular dynamics.

Calculation of Relative Hydration Free Energy Differences for Heteroaromatic Compounds: Use in the Design of Adenosine Deaminase and Cytidine Deaminase Inhibitors

Heteroaromatic compounds frequently undergo reversible covalent hydration in aqueous solution with the extent of hydration dependent on the heterocycle and its substituents. Using a combined quantu...

Simple Two-Body Cation−Water Interaction Potentials Derived from ab Initio Calculations. Comparison to Results Obtained with an Empirical Approach

Ab initio calculations were performed on M(H2O)n systems, M being Li+, Na+, K+, Be2+, Mg2+, or Ca2+, with n = 1, 2, 4, or 6. For the most hydrated systems, parameters for the effective Lennard-Jones interaction between the cation and the water molecules were determined, so as to reproduce ab initio results. In order to compare our results to those obtained previously by J. Åqvist with a purely empirical approach, water−water interactions were assumed to be given by the TIP3P model. Different forms for the effective two-body interaction potential were tested. The best fits of ab initio data were obtained with a smooth r-7 repulsive and a classical r-4 attractive term, in addition to standard Coulombic interactions. Though better fits were obtained for alkaline cations than for alkaline-earth ones, only Be2+ obviously requires a more complicated form of the potential energy function.The corresponding parameters were tested with molecular dynamics simulations of cations in water solutions and with hydration free energy difference calculations, using the thermodynamic perturbation approach. Radial distribution functions consistent with experimental data were obtained for all cations. Free energy differences are obviously much more challenging. The most accurately reproduced value is the difference between the hydration free energies of Na+ and K+. This result is likely to be significant since effective interaction energies between Na+ or K+ and water molecules as obtained in Åqvist's and in the present work are found to be very similar, despite the fact that the corresponding sets of parameters were determined with completely different approaches.

Calculated One-Electron Reduction Potentials and Solvation Structures for Selected p-Benzoquinones in Water

The one-electron reduction of quinones is important not only in electrochemistry but also in biochemical energy storage, energy utilization, and organic chemcial reactions. Thermodynamic cycles are investigated to estimate aqueous one-electron reduction potentials for the redox indicators p-benzoquinone and p-duroquinone, as well as chloro-substituted p-benzoquinones. Gas-phase reduction free energy differences are approximated from electron affinities calculated by using the hybrid Hartree−Fock/density-functional B3LYP method, a semiempirical quantum chemical method that expresses a molecule's exchange-correlation energy as a weighted sum of Hartree−Fock, local, and gradient-corrected density-functional energies. Free energy perturbation theory was used with molecular dynamics simulations (at constant temperature, pressure, and number of atoms) to estimate hydration free energy differences. Calculated one-electron reduction potentials for the quinones are within 10−190 meV of experimental values. An exce...

Calculation of relative free energy differences for the covalent hydration of organic compounds: A combined quantum mechanical and free energy perturbation study

AbstractThe relative free energy difference (ΔΔGhyd) for the reversible addition of water to two unsaturated molecules is accurately computed using a combination of ab initio quantum mechanical calculations and free energy perturbation methods. Initial attempts to calculate the absolute hydration free energy difference (ΔGhyd) for formaldehyde and trichloroacetaldehyde gave values that differed substantially from experimental results even after inclusion of electron correlation energy contributions using third‐order (MP3) and fourth‐order (MP4) Møller‐Plesset perturbation theory and QCISD(T) correlation methods at the 6‐31G** basis set level. Inaccuracies in ΔGhyd were attributed to errors in the calculation of both ΔGgas and ΔΔGsol. Gas phase quantum mechanical free energies (ΔGgas) varied significantly (2–3 kcal/mol) depending on the level of theory. Errors in ΔΔGsol were attributed to slow convergence of the calculations using the thermodynamic cycle perturbation (TCP) method with explicit solvent. These errors were minimized or canceled, however, when relative hydration free energy differences (ΔΔGhyd) were calculated using a combination of ab initio quantum mechanical calculations and free energy perturbation methods. Calculated values for a variety of aldehydes and ketones were consistent with experimental data. © 1995 John Wiley &amp; Sons, Inc.

Quantitative analysis of DNA secondary structure from solvent-accessible surfaces: the B- to Z-DNA transition as a model.

Solvent structure and its interactions have been suggested to play a critical role in defining the conformation of polynucleotides and other macromolecules. In this work, we attempt to quantitate solvent effects on the well-studied conformational transition between right-handed B- and left-handed Z-DNA. The solvent-accessible surfaces of the hexamer sequences d(m5CG)3, d(CG)3, d(CA)3, and d(TA)3 were calculated in their B- and Z-DNA conformations. The difference in hydration free energies between the Z and the B conformations (delta delta GH(Z-B] was determined from these surfaces to be -0.494 kcal/mol for C-5 methylated d(CG), 0.228 kcal/mol for unmethylated d(CG), 0.756 kcal/mol for d(CA)-d(TG), and 0.896 kcal/mol for d(TA) dinucleotides. These delta delta GH(Z-B) values were compared to the experimental B- to Z-DNA transition energies of -0.56 kcal/mol that we measured for C-5 methylated d(CG), 0.69-1.30 kcal/mol reported for unmethylated d(CG), 1.32-1.48 kcal/mol reported for d(CA)-d(TG), and 2.3-2.4 kcal/mol for d(TA) dinucleotides. From this comparison, we found that the calculated delta delta GH(Z-B) of these dinucleotides could account for the previous observation that the dinucleotides were ordered as d(m5CG) greater than d(CG) greater than d(CA)-d(TG) greater than d(TA) in stability as Z-DNA. Furthermore, we predicted that one of the primary reasons for the inability of d(TA) sequences to form Z-DNA results from a decrease in exposed hydrophilic surfaces of adjacent base pairs due to the C-5 methyl group of thymine; thus, d(UA) dinucleotides should be more stable as Z-DNA than the analogous d(TA) dinucleotides.(ABSTRACT TRUNCATED AT 250 WORDS)

Evaluation of the Adaptive Umbrella Sampling Method

Abstract The adaptive umbrella sampling technique, introduced recently to improve the probability ratio method and found to perform more reliably than the customary harmonic umbrella sampling, is tested and compared with other free energy methods. One of the tests applies the method to a transition involving a chemical change: calculation of the hydration free energy difference between acetone and dimethylamine and the other test calculates the conformational free energy difference between the C 7 and αR conformations of the alanide dipeptide. The dipeptide problem is also treated by two types of thermodynamic integrations and by the perturbation method. The result for the acetone-dimethylamine problem is compared with previous calculations on the same system using the perturbation method, overlap ratio method and finite difference thermodynamic integration. Enhancements to the adaptive umbrella sampling method are also presented.

Calculation of the Thermodynamic Solvent Isotope Effect for Ferrousand FerricIons in Water

Molecular dynamics simulations of molecular models of Fe2+ and Fe3+ in water (L2O = H2O or D2O) are used to generate various correlation functions that characterize the respective hexaaquo hydration complexes. The static Fe2+-oxygen and Fe2+-hydrogen correlation functions are compared in detail with the first difference neutron diffraction results of Enderby et al. for Ni2+ . Velocity autocorrelation functions and corresponding power spectra are generated and analyzed for those modes of hydration shell water molecules whose reduced masses are most sensitive to the changes from H2O to D2O. Various approximations are applied to these data to calculate the solvent isotope effect on the difference in hydration free energies for Fe2+ and Fe3+ . These different approximations all lead to the qualitative conclusion that the net solvent isotope effect reflects a large degree of cancellation between the OL stretching modes and the librational modes. The simulation results generally agree with the results of earlier quantum chemical calculations applied to the same system, but in some respects the new results are not as realistic as the earlier ones. It is proposed that the agreement with experiment would be improved by changes in the model potential which are motivated by other, independent considerations.

Test of the overlap ratio method on the calculation of the aqueous hydration free energy difference between acetone and dimethylamine

The overlap ratio method, used previously for relatively simple systems only, has been tested successfully in an aqueous system: the calculation of the hydration free energy difference between acetone and dimethylamine. The results are compared with previous calculations on the same system using the perturbation method and the finite difference thermodynamic integration method.

The finite difference thermodynamic integration, tested on calculating the hydration free energy difference between acetone and dimethylamine in water

A new technique is proposed to compute by Monte Carlo (or molecular dynamics) computer simulation the hydration free energy differences. The method, called finite difference thermodynamic integration, is a combination of the thermodynamic integration and the perturbation method. It was compared with thermodynamic integration over two different paths and the perturbation method on computing the solvation free-energy difference between the dilute aqueous solution of acetone and dimethyl amine. Finite difference thermodynamic integration was found to have the best convergence characteristics among the methods tested.

Hydrogen bonding solvent effect on the basicity of primary amines CH3NH2, C2H5NH2, and CF3CH2NH2

The equilibria RNH3+(H2O)n−1 + H2O = RNH3+(H2O)n were measured for R = CH3, C2H5, and CF3CH2 from n = 1 to n = 3 with a pulsed electron beam high ion source pressure mass spectrometer. The proton and hydrate transfer equilibria CH3NH3+(H2O)n + C2H5NH2 = CH3NH2 + C2H5NH3+(H2O)n were measured for n = 0 to n = 3. These data allow the evaluation of ΔH0 and ΔG0 for the reactions: R0NH3+(H2O)n + RNH3+ = R0NH3+ + RNH3+(H2O)n. ΔH0 = δΔH00,n(RNH3+), ΔG = δΔG00,n(RNH3+). These data are compared with δΔE0,3 (STO-3G) evaluated by Hehre and Taft. In general good agreement is observed at n = 3. The δΔH00,3(RNH3+) ≈ δΔE0,3(RNH3+) are also found close to the ion hydration free energy difference in aqueous solutions.