Local measures of intermolecular free energies in solution

Proton spin-lattice relaxation rate changes induced by freely diffusing oxygen in aqueous and mixed solvents are reported for representative amino acids and glucose. The local oxygen concentration at each spectrally resolved proton was deduced from the paramagnetic contribution to the relaxation rate. The measured relaxation increment is compared to that of the force-free diffusion relaxation model, and the differences are related to a free energy for the oxygen association with different portions of the solute molecules. The free energy differences are small, on the order of -800 to -2000 J/mol, but are uniformly negative for all proton positions measured on the amino acids in water and reflect the energetic benefit of weak association of hydrophobic cosolutes. For glucose, CH proton positions report negative free energies for oxygen association, the magnitude of which depends on the solvent; however, the hydroxyl positions report positive free energy differences relative to the force-free diffusion model, which is consistent with partial occupancy in the OH region by a solvent hydrogen bond.     

Anomalous reorganization free energies in optical electron transfer in solution

Autoionization bands are observed in the photoelectron emission spectroscopy of aqueous solutions of cyanometalate complexes (Mn, Fe, W, Mo), anions (NO₃, CIO⁻₄ and cations (Ag⁺ TI⁺. Reorganization free energies for autoionization bands are anomalously low in absolute value (by≈1 eV) in comparison with direct transitions to the continuum. Interpretation is based on potential energy profiles and model calculations for the reorganization free energy.     

A polarovoltric method for halogen ion determination in dilute solution

The application of polarovoltric titration to halogen ion determination with silver nitrate solution has been described and the results quoted show that analysis of even highly dilute halide solutions is possible with an accuracy of about ±0.2%.     

Solute-solute-solvent interactions in dilute aqueous solutions of aliphatic diols. Excess enthalpies and gibbs free energies

The heats of dilution and the osmotic coefficients for some aliphatic diols (1,3-propanediol; 1,2-butanediol; 1,3-butanediol; 1,4-butanediol; 2,3-butanediol; 1,5-pentanediol; 1,6-hexanediol) in water at 25°C are reported. The experimental free energy and enthalpy pairwise interaction coefficients were evaluated and are discussed in terms of the hydrophobic-hydrophilic properties of the solutes. The effect of the mutual position of the polar hydrophilic groups in the molecule on the experimental interaction coefficients transposed to the McMillan-Mayer (MM) state is emphasized. The Sawage-Wood additivity of groups (SWAG) approach has been used and critically discussed.Paper presented at J.C.A.T. '86-Ferrara 27–30 Ottobre 1986.     

Cluster free energies and nucleation: a density functional approach

Density functional methods of statistical mechanics are applied to calculate the average density profiles and free energies of small (50–500 particles) liquid clusters in unstable or metastable equilibrium with respect to the vapor. The results are compared with those obtained from experiments on homogeneous nucleation of liquids from the vapor.     

Precision of free energies calculated by molecular dynamics simulations of peptides in solution

Errors in free energies for molecular replacement and for conformation change of a small model peptide have been determined empirically by repeated simulations from different starting points. All calculations have been done using thermodynamic integration, in which the system's potential energy is coupled to a parameter λ, that is increased or decreased by a small amount at each step of the simulation. The effects of several factors that may alter the precision are evaluated. These factors include: the length of the simulation, the dependence of the potential energy on λ, the use of conformational restraints, and their magnitude and form. The methods used for restraint and conformational forcing are described in detail. The free energy change, calculated as the mean from several successive simulations with alternately increasing and decreasing λ, is found to be independent of the length of the simulations. As expected, longer simulations produce more precise results. The variation of the calculated free energies is found to consist of two parts, a random error and a systematic hysteresis, i.e., a dependence on the direction in which λ changes. The hysteresis varies as the inverse of the length of the simulation and the random error as the inverse square root The advantage of the use of a different (nonlinear) dependence of the attractive and repulsive parts of the nonbonded potential energy on the coupling parameter when “creating” particles in solution is found to be very large. This nonlinear coupling was found to be superior to the use of linear coupling and a nonlinear change of the coupling parameter with the simulation time. The hysteresis in conformational free energy calculations is found to increase markedly if too weak a forcing restraint is chosen. It is shown how to deconvolute the contribution of a torsional restraint from the dependence of the free energy on a torsion angle.     

Extended solvent-contact model approach to SAMPL4 blind prediction challenge for hydration free energies

Extended solvent-contact model was applied to the blind prediction of the hydration free energies of 47 organic molecules included in the SAMPL4 data set. To obtain a suitable prediction tool, we constructed a hydration free energy function involving three kinds of atomic parameters. With respect to total 34 atom types introduced to describe all SAMPL4 molecules, 102 atomic parameters were defined and optimized with a standard genetic algorithm in such a way to minimize the difference between the experimental hydration free energies and those calculated with the hydration free energy function. In this parameterization, we used a training set comprising 77 organic molecules with varying sizes and shapes. The estimated hydration free energies for the SAMPL4 molecules compared reasonably well with the experimental results with the associated squared correlation coefficient and root mean square deviation of 0.89 and 1.46 kcal/mol, respectively. Based on the comparative analysis of experimental and computational hydration free energies of the SAMPL4 molecules, the methods for further improvement of the present hydration model are suggested.     

A microsolvation approach to the prediction of the relative enthalpies and free energies of hydration for ammonium ions

Hartree–Fock (HF) and second-order Møller–Plesset (MP2) calculations were used to investigate the structures and thermochemistry of methylammonium–water clusters (Me_4-m NH _m ⁺ (H₂O) _n , m=1–4, n=1–4). Water molecules were treated ab initio and with effective fragment potentials (EFP). In addition to a thorough phase-space search, the importance of basis set, electron correlation, and thermodynamic effects was systematically examined. Cluster structures resulted from hydrogen bond formation between the ammonium group and water molecules; upon saturation of the hydrogen bonding sites of the ammonium group, water molecules entered the second hydration shell. With only four water molecules, the experimental relative enthalpies of hydration were well reproduced at the HF level, while the MP2 relative free energies were in best agreement with experiment. Absolute energies of hydration were calculated using an empirical correction. These results strongly suggest that a HF-based microsolvation approach employing a small number of water molecules can be used to compute relative enthalpies of hydration.     

Estimating relative free energies from a single ensemble: Hydration free energies

The ability to determine the free energy of solvation for a number of small organic molecules with varying sizes and properties from the coordinate trajectory of a single simulation of a given reference state was investigated. The relative free energies were estimated from a single step perturbation using the perturbation formula. The reference state consisted of a cavity surrounded by solvent. To enhance sampling a soft-core interaction was used for the cavity. The effect of the size of the cavity, the effective core height, and the length of simulation on the ability to reproduce results obtained from thermodynamic integration calculations was considered. The results using a single step perturbation from an appropriately chosen initial state were comparable to results from thermodynamic integration calculations for a wide range of compounds. Using a large number of compounds the computational efficiency was potentially increased by 2–3 orders of magnitude over traditional free energy approaches. Factors determining the efficiency of the approach are discussed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1604–1617, 1999     

A classical point charge model study of system size dependence of oxidation and reorganization free energies in aqueous solution

The response of water to a change of charge of a solvated ion is, to a good approximation, linear for the type of iron-like ions frequently used as a model system in classical force field studies of electron transfer. Free energies for such systems can be directly calculated from average vertical energy gaps. Exploiting this feature, we have computed the free energy and the reorganization energy of the M2+/M3+ and M1+/M2+ oxidations in a series of model systems all containing a single Mn+ ion and an increasing number of simple point charge water molecules. Long-range interactions are taken into account by Ewald summation methods. Our calculations confirm the observation made by Hummer, Pratt, and Garcia (J. Phys. Chem. 1996, 100, 1206) that the finite size correction to the estimate of solvation energy (and hence oxidation free energy) in such a setup is effectively proportional to the inverse third power (1/L3) of the length L of the periodic cell. The finite size correction to the reorganization energy is found to scale with 1/L. These simulation results are analyzed using a periodic generalization of the Born cavity model for solvation, yielding three different estimates of the cavity radius, namely, from the infinite system size extrapolation of oxidation free energy and reorganization energy, and from the slope of the linear dependence of oxidation free energy on 1/L3. The cavity radius for the reorganization energy is found to be significantly larger compared to the radius for the oxidation (solvation) free energy. The radius controlling the 1/L3 dependence of oxidation free energy is found to be comparable to the radius for reorganization. The implication of these results for density functional theory-based ab initio molecular dynamics calculation of redox potentials is discussed.     

A simple theoretical approach to bond energies

The linear combination of fragment configurations (LCFC) method is used to study factors which control the relative strengths of bonds. Trends in bond strengths and the relative stability of structural isomers are predicted for a variety of organic molecules. It is argued that complex interactions within large organic molecules can be simplified to the interaction of the two electrons of a single bond. A compilation of experimental data is presented to support the proposed theoretical model.     

Simple estimation of absolute free energies for biomolecules

One reason that free energy difference calculations are notoriously difficult in molecular systems is due to insufficient conformational overlap, or similarity, between the two states or systems of interest. The degree of overlap is irrelevant, however, if the absolute free energy of each state can be computed. We present a method for calculating the absolute free energy that employs a simple construction of an exactly computable reference system which possesses high overlap with the state of interest. The approach requires only a physical ensemble of conformations generated via simulation and an auxiliary calculation of approximately equal central-processing-unit cost. Moreover, the calculations can converge to the correct free energy value even when the physical ensemble is incomplete or improperly distributed. As a "proof of principle," we use the approach to correctly predict free energies for test systems where the absolute values can be calculated exactly and also to predict the conformational equilibrium for leucine dipeptide in implicit solvent.     

Alchemical prediction of hydration free energies for SAMPL

Hydration free energy calculations have become important tests of force fields. Alchemical free energy calculations based on molecular dynamics simulations provide a rigorous way to calculate these free energies for a particular force field, given sufficient sampling. Here, we report results of alchemical hydration free energy calculations for the set of small molecules comprising the 2011 Statistical Assessment of Modeling of Proteins and Ligands challenge. Our calculations are largely based on the Generalized Amber Force Field with several different charge models, and we achieved RMS errors in the 1.4-2.2 kcal/mol range depending on charge model, marginally higher than what we typically observed in previous studies (Mobley et al. in J Phys Chem B 111(9):2242-2254, 2007, J Chem Theory Comput 5(2):350-358, 2009, J Phys Chem B 115:1329-1332, 2011; Nicholls et al. in J Med Chem 51:769-779, 2008; Klimovich and Mobley in J Comput Aided Mol Design 24(4):307-316, 2010). The test set consists of ethane, biphenyl, and a dibenzyl dioxin, as well as a series of chlorinated derivatives of each. We found that, for this set, using high-quality partial charges from MP2/cc-PVTZ SCRF RESP fits provided marginally improved agreement with experiment over using AM1-BCC partial charges as we have more typically done, in keeping with our recent findings (Mobley et al. in J Phys Chem B 115:1329-1332, 2011). Switching to OPLS Lennard-Jones parameters with AM1-BCC charges also improves agreement with experiment. We also find a number of chemical trends within each molecular series which we can explain, but there are also some surprises, including some that are captured by the calculations and some that are not.     

计算受体和配体结合自由能的新方法

利用ABEEMσπ浮动电荷力场与连续介质模型相结合的方法,计算了受体和配体的结合自由能.将结合自由能分解为真空中的力场作用项、溶剂化能量以及熵效应.由于ABEEMσπ/MM方法充分考虑了外界环境发生变化引起的体系中各个位点之间的电荷极化,因而极大地提高了结合自由能的计算精度.利用该方法计算的2个复合物的结合自由能与实验值的偏差均小于0.5kJ/mol.     

An empirical equation-of-state for solid-fluid interfacial free energies

The contact angle,, formed by a liquid on a solid surface in air depends on the solid-air ( _S ), liquid-air ( _L ) and solid-liquid ( _SL ) interfacial free energies, as described by Young's equation. Critical examination of reported contact angles for numerous liquids and solids leads to an empirical correlation between _sL and both _Y and _S . Combination of this correlation with Young's equation gives an empirical relation allowing calculation of _S from _L and Calculations made with these empirical relations agree well with estimations of _S obtained by the method of critical spreading, and are consistent with Young's equation.Founded and supported by F. Hoffmann-La Roche and Co., Limited Company, Basel, Switzerland.     

AM1-SM2 and PM3-SM3 parameterized SCF solvation models for free energies in aqueous solution

Summary Two new continuum solvation models have been presented recently, and in this paper they are explained and reviewed in detail with further examples. Solvation Model 2 (AM1-SM2) is based on the Austin Model 1 and Solvation Model 3 (PM3-SM3) on the Parameterized Model 3 semiempirical Hamiltonian. In addition to the incorporation of phosphorus parameters, both of these new models address specific deficiencies in the original Solvation Model 1 (AM1-SM1), viz., (1) more accurate account is taken of the hydrophobic effect of hydrocarbons, (2) assignment of heavy-atom surface tensions is based on the presence or absence of bonded hydrogen atoms, and (3) the treatment of specific hydration-shell water molecules is more consistent. The new models offer considerably improved performance compared to AM1-SM1 for neutral molecules and essentially equivalent performance for ions. The solute charges within the Parameterized Model 3 Hamiltonian limit the utility of PM3-SM3 for compounds containing nitrogen and possibly phosphorus. For other systems both AM1-SM2 and PM3-SM3 give realistic results, but AM1-SM2 in general outperforms PM3-SM3. Key features of the models are discussed with respect to alternative approaches.