Water coordination structures and the excess free energy of the liquid

We assess the contribution of each coordination state to the hydration free energy of a distinguished water molecule, the solute water. We define a coordination sphere, the inner-shell, and separate the hydration free energy into packing, outer-shell, and local, solute-specific (chemical) contributions. The coordination state is defined by the number of solvent water molecules within the coordination sphere. The packing term accounts for the free energy of creating a solute-free coordination sphere in the liquid. The outer-shell contribution accounts for the interaction of the solute with the fluid outside the coordination sphere and it is accurately described by a Gaussian model of hydration for coordination radii greater than the minimum of the oxygen-oxygen pair-correlation function: theory helps identify the length scale to parse chemical contributions from bulk, nonspecific contributions. The chemical contribution is recast as a sum over coordination states. The nth term in this sum is given by the probability p(n) of observing n water molecules inside the coordination sphere in the absence of the solute water times a factor accounting for the free energy, W(n), of forming an n-water cluster around the solute. The p(n) factors thus reflect the intrinsic properties of the solvent while W(n) accounts for the interaction between the solute and inner-shell solvent ligands. We monitor the chemical contribution to the hydration free energy by progressively adding solvent ligands to the inner-shell and find that four-water molecules are needed to fully account for the chemical term. For a chemically meaningful coordination radius, we find that W(4) ≈ W(1) and thus the interaction contribution is principally accounted for by the free energy for forming a one-water cluster, and intrinsic occupancy factors alone account for over half of the chemical contribution. Our study emphasizes the need to acknowledge the intrinsic solvent properties in interpreting the hydration structure of any solute, with particular care in cases where the solute-solvent interaction strength is similar to that between the solvent molecules.     

Symmetrization of excess Gibbs free energy: A simple model for binary liquid mixtures

A symmetric expression for the excess Gibbs free energy of liquid binary mixtures is obtained using an appropriate definition for the effective contact fraction. We have identified a mechanism of local segregation as the main cause of the contact fraction variation with the concentration. Starting from this mechanism we develop a simple model for describing binary liquid mixtures. In this model two parameters appear: one adjustable, and the other parameter depending on the first one. Following this procedure we reproduce the experimental data of (liquid + vapor) equilibrium with a degree of accuracy comparable to well-known more elaborated models. The way in which we take into account the effective contacts between molecules allows identifying the compound which may be considered to induce one of the following processes: segregation, anti-segregation and dispersion of the components in the liquid mixture. Finally, the simplicity of the model allows one to obtain only one resulting interaction energy parameter, which makes easier the physical interpretation of the results.     

A quasi lattice-local composition model for the excess Gibbs free energy of liquid mixtures

Two new expressions for the excess Gibbs energy of liquid mixtures are derived from Guggenheim's quasi-lattice model and Wilson's local composition concept. These are called the Local Surface Guggenheim equation (LSG) and the Local Composition Guggenheim equation (LCG). The LSG equation is similar, but not identical to UNIQUAC. The new equations require only two adjustable parameters per binary, and no higher-order parameters for extension to multicomponent systems.A critical discussion is given of Guggenheim's quasi-lattice expression for the excess Gibbs energy of athermal mixtures. This expression gives the combinatorial contribution to the new equations.A new method is proposed in the evaluation of the pure component structural parameters, independent of particular assumptions about the lattice parameters.The application of the LSG and the LCG equations to practical problems of phase-equilibria is considered in detail.     

An efficient method for computing steady state solutions with Gillespie's direct method

Gillespie's direct method is a stochastic simulation algorithm that may be used to calculate the steady state solution of a chemically reacting system. Recently the all possible states method was introduced as a way of accelerating the convergence of the simulations. We demonstrate that while the all possible states (APS) method does reduce the number of required trajectories, it is actually much slower than the original algorithm for most problems. We introduce the elapsed time method, which reformulates the process of recording the species populations. The resulting algorithm yields the same results as the original method, but is more efficient, particularly for large models. In implementing the elapsed time method, we present robust methods for recording statistics and empirical probability distributions. We demonstrate how to use the histogram distance to estimate the error in steady state solutions.     

A highly efficient hybrid method for calculating the hydration free energy of a protein

We develop a new method for calculating the hydration free energy (HFE) of a protein with any net charge. The polar part of the energetic component in the HFE is expressed as a linear combination of four geometric measures (GMs) of the protein structure and the generalized Born (GB) energy plus a constant. The other constituents in the HFE are expressed as linear combinations of the four GMs. The coefficients (including the constant) in the linear combinations are determined using the three‐dimensional reference interaction site model (3D‐RISM) theory applied to sufficiently many protein structures. Once the coefficients are determined, the HFE and its constituents of any other protein structure are obtained simply by calculating the four GMs and GB energy. Our method and the 3D‐RISM theory give perfectly correlated results. Nevertheless, the computation time required in our method is over four orders of magnitude shorter.     

An efficient newton-like method for molecular mechanics energy minimization of large molecules

Techniques from numerical analysis and crystallographic refinement have been combined to produce a variant of the Truncated Newton nonlinear optimization procedure. The new algorithm shows particular promise for potential energy minimization of large molecular systems. Usual implementations of Newton's method require storage space proportional to the number of atoms squared (i.e., O(N²)) and computer time of O(N³). Our suggested implementation of the Truncated Newton technique requires storage of less than O(N^1.5) and CPU time of less than O(N²) for structures containing several hundred to a few thousand atoms. The algorithm exhibits quadratic convergence near the minimum and is also very tolerant of poor initial structures. A comparison with existing optimization procedures is detailed for cyclohexane, arachidonic acid, and the small protein crambin. In particular, a structure for crambin (662 atoms) has been refined to an RMS gradient of 3.6 × 10^?6 kcal/mol/Å per atom on the MM2 potential energy surface. Several suggestions are made which may lead to further improvement of the new method.     

Application of barycentric method for determination of free energy of liquid monodisperse system accomplishing diffusion

The barycentric method has been applied to determining the thermodynamic potential (the free energy) of a liquid rarefied monodisperse colloid system in which free unstationary diffusion under constant external conditions has been accomplished. Free energy at an arbitrary moment of time has been obtained as a function of horizontal mass center shift toward the cuvette cavity geometrical center of the liquid disperse system investigated. A very good coincidence between the numerical results from the proposed barycentric method and another classical thermodynamic method has been observed.     

An efficient method for the calculation of quantum mechanics/molecular mechanics free energies

The combination of quantum mechanics (QM) with molecular mechanics (MM) offers a route to improved accuracy in the study of biological systems, and there is now significant research effort being spent to develop QM/MM methods that can be applied to the calculation of relative free energies. Currently, the computational expense of the QM part of the calculation means that there is no single method that achieves both efficiency and rigor; either the QM/MM free energy method is rigorous and computationally expensive, or the method introduces efficiency-led assumptions that can lead to errors in the result, or a lack of generality of application. In this paper we demonstrate a combined approach to form a single, efficient, and, in principle, exact QM/MM free energy method. We demonstrate the application of this method by using it to explore the difference in hydration of water and methane. We demonstrate that it is possible to calculate highly converged QM/MM relative free energies at the MP2/aug-cc-pVDZ/OPLS level within just two days of computation, using commodity processors, and show how the method allows consistent, high-quality sampling of complex solvent configurational change, both when perturbing hydrophilic water into hydrophobic methane, and also when moving from a MM Hamiltonian to a QM/MM Hamiltonian. The results demonstrate the validity and power of this methodology, and raise important questions regarding the compatibility of MM and QM/MM forcefields, and offer a potential route to improved compatibility.     

An approximate but efficient method to calculate free energy trends by computer simulation: Application to dihydrofolate reductase-inhibitor complexes

Summary Derivatives of free energy differences have been calculated by molecular dynamics techniques. The systems under study were ternary complexes of Trimethoprim (TMP) with dihydrofolate reductases of E. coli and chicken liver, containing the cofactor NADPH. Derivatives are taken with respect to modification of TMP, with emphasis on altering the 3-, 4- and 5-substituents of the phenyl ring. A linear approximation allows the encompassing of a whole set of modifications in a single simulation, as opposed to a full perturbation calculation, which requires a separate simulation for each modification. In the case considered here, the proposed technique requires a factor of 1000 less computing effort than a full free energy perturbation calculation. For the linear approximation to yield a significant result, one has to find ways of choosing the perturbation evolution, such that the initial trend mirrors the full calculation. The generation of new atoms requires a careful treatment of the singular terms in the non-bonded interaction. The result can be represented by maps of the changed molecule, which indicate whether complex formation is favoured under movement of partial charges and change in atom polarizabilities. Comparison with experimental measurements of inhibition constants reveals fair agreement in the range of values covered. However, detailed comparison fails to show a significant correlation. Possible reasons for the most pronounced deviations are given.     

An efficient method for computing the QTAIM topology of a scalar field: The electron density case

An efficient method for computing the quantum theory of atoms in molecules (QTAIM) topology of the electron density (or other scalar field) is presented. A modified Newton–Raphson algorithm was implemented for finding the critical points (CP) of the electron density. Bond paths were constructed with the second‐order Runge–Kutta method. Vectorization of the present algorithm makes it to scale linearly with the system size. The parallel efficiency decreases with the number of processors (from 70% to 50%) with an average of 54%. The accuracy and performance of the method are demonstrated by computing the QTAIM topology of the electron density of a series of representative molecules. Our results show that our algorithm might allow to apply QTAIM analysis to large systems (carbon nanotubes, polymers, fullerenes) considered unreachable until now. © 2012 Wiley Periodicals, Inc.     

A new apparatus for measuring the vapour pressure of liquid mixtures excess Gibbs free energy of octamethylcyclotetrasiloxane + cyclohexane at 308.15 K

A new apparatus for measuring the vapour pressure of liquid mixtures is described. In conjunction with an automatic pressure controller, a capacitance manometer is used as a null device to isolate the liquid and vapour. The vapour pressure is measured with a precision mercury manometer. The continuous-dilution technique for sample introduction has been incorporated in the new apparatus, so that the composition range of a mixture can be covered in two runs. The accuracy of each measured quantity is: pressure, 3 Pa; temperature (IPTS-68), 0.002 K; volume, 0.002 cm³. G^E for cyclohexane + octamethylcyclotetrasiloxane (abbreviated throughout this paper as omcts) at 308.15 K has been determined: the minimum value of ?68 J mol^?1 occurs near x₂(omcts) = 0.5.     

An analytic model for the excess properties of binary liquid mixtures

A model has been devised to analyse excess property data for binary liquid mixtures. The model embodies the concept of the segmentation of the total composition range into three distinct regions. Results are given for the analyses of Δ$\text{V}$, Δ$\text{H}$ and Δν for the acetonitrile-water and dimethylsulfoxide-water systems.     

The geometric minimum action method for computing minimum energy paths

An algorithm is proposed to calculate the minimum energy path (MEP). The algorithm is based on a variational formulation in which the MEP is characterized as the curve minimizing a certain functional. The algorithm performs this minimization using a preconditioned steepest-descent scheme with a reparametrization step to enforce a constraint on the curve parametrization.     

Incorporating the excluded solvent volume and surface charges for computing solvation free energy

Gauss's law or Poisson's equation is conventionally used to calculate solvation free energy. However, the near‐solute dielectric polarization from Gauss's law or Poisson's equation differs from that obtained from molecular dynamics (MD) simulations. To mimic the near‐solute dielectric polarization from MD simulations, the first‐shell water was treated as two layers of surface charges, the densities of which are proportional to the electric field at the solvent molecule that is modeled as a hard sphere. The intermediate water was treated as a bulk solvent. An equation describing the solvation free energy of ions using this solvent scheme was derived using the TIP3P water model. © 2013 Wiley Periodicals, Inc.     

Sorption of binary liquid mixtures on polymer networks Part I. Determination of surface excess isotherms and free energy functions

Two groups of polymer networks (polymer resins) are investigated by selective liquid sorption fromn-propanol-water mixtures. Group 1 consists of gel polymerized polar (hydrophilic) ion exchangers which swell in the binary liquid mixture. Group 2 consists of non-polar, non-swelling, macroporous resins. The free energy isotherms accompanying the sorption processes are calculated from the excess isotherms and the bulk activities. The adsorption excess free energies reveal the differences in polarity of the polymer network.     

Thermodynamics of associated solutions: New expressions for the excess Gibbs free energy and excess enthalpy of mixing of alcohol-solvent systems

This article presents new equations based on a continuous linear association model used by Kretschmer and Wiebe. The new equations are used to reduce experimental vapor-liquid equilibrium and excess enthalpy of mixing data for solutions of alcohols and active solvents. The new equations give an excellent representation of the experimental results and are able to predict equilibrium data for ternary alcohol-solvent systems with good accuracy.     

Nonrandom factor model for the excess Gibbs free energy of weak electrolytes including phosphoric acid

The Electrolyte Nonrandom Two Liquid-Nonrandom Factor (NRTL-NRF) model of Haghtalab and Vera was modified to determine the excess Gibbs free energy of weak electrolyte systems. The model was applied to the phosphoric acid solution as a weak and complex electrolyte. Its thermodynamic behavior was investigated in a wide range of concentration by choosing an appropriate equilibrium reaction between molecular and ionic species. The model contains four adjustable parameters which were determined using osmotic experimental data. The results of dissociation and of activity coefficients are presented separately.     

An efficient catalytic method for fulvene synthesis

The effects of the nature and amount of base, substrate structure, amount of added water and solvent on the condensation of carbonyl compounds with cyclopentadiene in the presence of secondary amines were investigated. Based on these studies, a new efficient and green synthesis of fulvenes was developed.     

An efficient method for the preparation of glycosides with a free C-2 hydroxyl group from thioglycosides

A new and efficient method to produce glycosides with a free C-2 hydroxyl group through 1,2-acyl group migration which occurs during the hydrolysis of 4,6-benzylidene protected thioglycosides has been developed. The acyl transfer products allow for further elaboration.     

A new method for computing surface tension using a drop of liquid

In the simulation of a liquid drop it is expensive to calculate the excess pressure and obtain the surface tension by the Laplace formula. We use the Kelvin formula which only requires the vapour density, or at most the virial pressure. Some results are given for a Lennard-Jones 12-6 fluid.