Quasi-chemical theories of associated liquids

Abstract

It is shown how traditional development of theories of fluids based upon the concept of physical clustering can be adapted to an alternative local clustering definition. The alternative clustering definition can preserve a detailed valence description of the interactions between a solution species and its nearneighbors, i.e., cooperativity and saturation of coordination for strong association. These clusters remain finite even for condensed phases. The simplest theory to which these developments lead is analogous to quasi-chemical theories of cooperative phenomena. The present quasi-chemical theories require additional consideration of packing issues because they don't impose lattice discretizations on the continuous problem. These quasi-chemical theories do not require pair decomposable interaction potential energy models. Since calculations may be required only for moderately sized clusters, we suggest that these quasi-chemical theories could be implemented with computational tools of current molecular electronic structure theory. This can avoid an intermediate step of approximate force field generation.

Assessing the accuracy of approximate treatments of ion hydration based on primitive quasichemical theory

“…6,7 QCT gets its name because the factors K i ͑n͒ in Eq. ͑11͒ assume the form of equilibrium constants for pseudochemical binding reactions for one ion and n solvent molecules.…”

“…͑11͒ and ͑13͒ differs somewhat from the standard QCT literature. 6,7 Here, our starting point with Eq. ͑6͒ consists of inserting ␦ n,n Ј in the configurational integral to sort out the number of solvent molecules in the inner-shell region, which is treated as a small open system in equilibrium with a bath of solvent molecules.…”

“…Thermodynamic solvation properties can then be expressed in an expanded form as a finite sum over configurational integrals of clusters comprising the ion and the n inner solvent molecules under the average influence of the surrounding bulk. 6,7 When the radius of the inner region is chosen sufficiently small to correspond to the first coordination shell of the ion, the contribution from the clusters with a small number of solvent molecules dominates and the sum converges rapidly. This theoretical construct provides a rich framework to analyze and interpret the results from experimental measurements in the gas phase, 9 as well as from computer simulations.…”

“…[1][2][3][4][5] More recently, QCT was further developed and extended by Pratt and co-workers in studies of the hydrophobic effect and ion solvation. [6][7][8] In the case of ion solvation, QCT typically consists of defining a spherical inner shell region of radius R based on a distance criterion between the ion and the solvent molecule. Introducing step functions into the Boltzmann configurational integral to enforce this criterion, QCT then proceeds to carry out a strict book-keeping of the configurations with exactly n solvent molecules lying inside the inner shell region.…”

Structure and thermodynamics of colloidal protein cluster formation: Comparison of square-well and simple dipolar models

“…17 The present report employs coarse-grained models of colloidal protein-protein interactions to solve for the free energy and structure of clusters using a cell-based, quasichemical ͑QC͒ theory. [18][19][20][21][22][23][24][25] Previous work showed that the QC theory was quantitatively accurate for predicting cluster free energies in simple lattice systems up to typical experimental volume fractions ͑ϳ10 −2 ͒ for protein solutions. 26 The osmotic second virial coefficient ͑B 22 ͒ has been used as a tool to quantify the average magnitude and sign of interactions between protein molecules in dilute solution, [27][28][29][30] although it is not, per se, a direct predictor of standard free energies of association.…”