Effect of the integration method on the accuracy and computational efficiency of free energy calculations using thermodynamic integration

Although calculations of free energy using molecular dynamics simulations have gained significant importance in the chemical and biochemical fields, they still remain quite computationally intensive. Furthermore, when using thermodynamic integration, numerical evaluation of the integral of the Hamiltonian with respect to the coupling parameter may introduce unwanted errors in the free energy. In this paper, we compare the performance of two numerical integration techniques-the trapezoidal and Simpson's rules and propose a new method, based on the analytic integration of physically based fitting functions that are able to accurately describe the behavior of the data. We develop and test our methodology by performing detailed studies on two prototype systems, hydrated methane and hydrated methanol, and treat Lennard-Jones and electrostatic contributions separately. We conclude that the widely used trapezoidal rule may introduce systematic errors in the calculation, but these errors are reduced if Simpson's rule is employed, at least for the electrostatic component. Furthermore, by fitting thermodynamic integration data, we are able to obtain precise free energy estimates using significantly fewer data points (5 intermediate states for the electrostatic component and 11 for the Lennard-Jones term), thus significantly decreasing the associated computational cost. Our method and improved protocol were successfully validated by computing the free energy of more complex systems hydration of 2-methylbutanol and of 4-nitrophenol-thus paving the way for widespread use in solvation free energy calculations of drug molecules

Enthalpy of solvation correlations for organic solutes and gases dissolved in 1-propanol and tetrahydrofuran

This article discusses the enthalpy of solvation correlations for organic solutes and gases dissolved in 1-propanol and tetrahydrofuran

Heat capacity changes in proton addition to the nitrogen of saturated organic molecules in water. Effects of solvation

The \u394Cpo values for proton addition to some aminoalcohols, aminoethers and diamines in aqueous solution have been determined at 25 and 40\ub0C, using partial molal heat capacity data for the neutral molecules and their hydrochlorides. A comparison is made between \u394C po, \u394So and \u394Vo values and the corresponding values for monofunctional amines, and the following features emerge for proton addition to the nitrogen atom of saturated amines in water: (1) Either in mono- or in bifunctional amines the thermodynamic reaction parameters, \u394Cpo and \u394So, change systematically in going from primary, to secondary, to tertiary amines; the same is observed for \u394Vo, but only in the case of monofunctional amines. (2) The \u394Cpo and \u394So values of protonation of bifunctional amines are higher than those of monofunctional amines of the same type. Interpretation of this behaviour is made in terms of two concurrent solvation effects: (i) the charged nitrogen-water interaction which is strongly dependent on the number of N-bonded hydrogens; (ii) the hydration of alkyl residues which is less extensive when they are bound to a charged nitrogen than when the nitrogen is neutral

Compressibility changes in protonation of some organic aliphatic nitrogen compounds in aqueous solution

Density and sound velocity of aq. solns. contg. monofunctional primary, secondary and tertiary amines, as well as bifunctional primary and secondary amines (B), and their corresponding hydrochlorides, (BHCl), were measured; the apparent molar compressibilities were calculated.  From the limiting apparent molar compressibilities of B, BHCl and HCl in aq. soln. the changes in compressibilities, Δϕ°K,S, for protonation of B was obtained.  The pattern shown by the Δϕ°K,S values was similar to that presented by the changes, ΔX°r, of other thermodn. properties, such as Cp and V, for the formation of BHCl species from B and HCl.  The different values of Δϕ°K,S obsd. for amines having the same no. of hydrogens bonded to N but differing in the presence of a second hydrophilic group was attributed to the removal of the hydrophobic hydration of the alkyl groups brought about by this center

Volumetric properties of amphionic molecules in water. Part 2. Thermal expansibility and compressibility related to the formation of zwitterionic structures

The dependence of the partial molar volumes of a number of α-amino acids, ω-amino acids, dipeptides and diketopiperazines on temperature has been determined at various concentrations and for the temperature range 0-55°C using an automatic dilatometer; the limiting partial molar expansibilities, Φ°E, have been calculated. Measurements of the sound velocity at 15 MHz and at various concentrations allowed us to determine the compressibility of the solutions at 25°C and to calculate the limiting partial compressibilities, Φ°K,S, for some of the above mentioned compounds. Finally, by using the known values Φ°E and Φ°K,S together with the partial molar heat capacity of the solute and some physical properties of pure water, the limiting isothermal partial molar compressibilities, Φ°K,T, have been obtained. The values of Φ°E and Φ°K,S and the trends they show when the structure of the amphionic molecule is changed have been analysed by taking into account the features exhibited by Φ°E and Φ°K,S of related charged and non-charged compounds. The dependence on temperature and pressure of the internal and external proton-exchange reaction between a carboxyl and an amino group have been evaluated and compared

Volumetric properties of amphionic molecules in water. Part 1. Volume changes in the formation of zwitterionic structures

The values of the limiting partial molar volumes, Φ°v, at 25°C of some typical amphionic molecules (α-amino acids, ω-amino acids and polypeptides) are reported. The methods followed to obtain the values of the volume change, ΔVzw, in the reaction for the formation of an amphionic molecule from the corresponding neutral molecule are critically reviewed and two ways of calculating these quantities are proposed. In both these methods the values of the neutral forms are calculated using group-contribution values obtained by two different procedures. In the first one, a criterion of best fitting is used between the experimental and calculated Φ°v values of a large number (220) of hydrocarbons and monofunctional compounds; in the second one, a model is used in which the Φ°v values in water are correlated with the van der Waals volumes, Vw, and the volumetric effects connected with the substitution of a hydrocarbon part of the molecule by a hydrophilic part are evaluated. The ΔVzw values are compared with the volume change associated with the reaction of proton exchange between primary amines and carboxylic acids; the correlation of the ΔVzw values with the distance between the NH+3 and COO- groups and with the nature of the chain separating them is also discussed