Spatially Resolved Thermodynamic Integration: An Efficient Method To Compute Chemical Potentials of Dense Fluids

Abstract

Many popular methods for the calculation of chemical potentials rely on the insertion of test particles into the target system. In the case of liquids and liquid mixtures, this procedure increases in difficulty upon increasing density or concentration, and the use of sophisticated enhanced sampling techniques becomes inevitable. In this work, we propose an alternative strategy, spatially resolved thermodynamic integration, or SPARTIAN for short. Here, molecules are described with atomistic resolution in a simulation subregion and as ideal gas particles in a larger reservoir. All molecules are free to diffuse between subdomains adapting their resolution on the fly. To enforce a uniform density profile across the simulation box, a single-molecule external potential is computed, applied, and identified with the difference in chemical potential between the two resolutions. Since the reservoir is represented as an ideal gas bath, this difference exactly amounts to the excess chemical potential of the target system. The present approach surpasses the high density/concentration limitation of particle insertion methods because the ideal gas molecules entering the target system region spontaneously adapt to the local environment. The ideal gas representation contributes negligibly to the computational cost of the simulation, thus allowing one to make use of large reservoirs at minimal expenses. The method has been validated by computing excess chemical potentials for pure Lennard-Jones liquids and mixtures, SPC and SPC/E liquid water, and aqueous solutions of sodium chloride. The reported results well reproduce literature data for these systems.

Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method

“…For that purpose, any computational method aiming at calculating chemical potentials could be used. In particular, we use the spatially-resolved thermodynamic integration (SPARTIAN) method [ 36 ], recently implemented by us. In SPARTIAN, the target system, described with atomistic resolution, is embedded in a reservoir of ideal gas particles.…”

“…We compare the results obtained using Equations ( 30 ) and ( 31 ) with the results obtained with the SPARTIAN method [ 36 ] and use the excess chemical potential result from to find the reference value. We present the results in Figure 12 where a good agreement between the two datasets is apparent.…”

“… Excess chemical potential at as a function of the density for systems described by a TSLJ potential with . Red squares indicate the data obtained with the spatially-resolved thermodynamic integration (SPARTIAN) method [ 36 ], and the blue triangles are the data points obtained with the method outlined in the text. …”

Ligand‐protein interactions in lysozyme investigated through a dual‐resolution model

“…8 Other approaches maintain the highresolution description for the solute while employing a simplified model for the solvent, with varying degrees of detail depending on the specific systems and applications [33][34][35][36][37][38] ; among these, some treat the solvent with an adaptive resolution approach, that is, solvent molecules are AT in proximity of the solute and smoothly blend in a CG representation away from it. [39][40][41][42][43][44][45][46][47] Recently, we have proposed a dual-resolution model 12 where, in the CG part, only the C α carbons of the protein chain are retained and connected one with the other by harmonic bonds. This model has been employed in the present work with the aim of assessing the accuracy of a hybrid AT/CG description of a protein for binding free energy calculations.…”

Concurrent coupling of realistic and ideal models of liquids and solids in Hamiltonian adaptive resolution simulations

“…To attain the same density in all parts of the simulation one has to impose a single-molecule potential that can be traced back to the difference in Gibbs free energy between the two models concurrently employed to represent the same system [30,31]. Hence, in the process of parametrising the setup so as to have a uniform density profile, one quantifies the liquid's chemical potential difference between the simple and the accurate representation [32]. This procedure is similar in spirit to a thermodynamic integration [19], however it does not require the time-dependent switch of the Hamiltonian between two models, rather a single run concurrently contains the information about the two end states and all those in between.…”