Free volume hypothetical scanning molecular dynamics method for the absolute free energy of liquids

Abstract

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy, S, and free energy, F, by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics (MD) techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). With our recent version of HS, called HSMC-EV, each TP is calculated from MC simulations, where the simulated particles are excluded from the volume reconstructed in previous steps. In this paper we remove the excluded volume (EV) restriction, replacing it by a "free volume" (FV) approach. For liquid argon, HSMC-FV leads to an improvement in efficiency over HSMC-EV by a factor of 2-3. Importantly, the FV treatment greatly simplifies the HS implementation for liquids, allowing a much more natural application of the method for MD simulations. Given the success and popularity of MD, the present development of the HSMD method for liquids is an important advancement for HS methodology. Results for the HSMD-FV approach presented here agree well with our HSMC and thermodynamic integration results. The efficiency of HSMD-FV is equivalent to HSMC-EV. The potential use of HSMC(MD)-FV in protein systems with explicit water is discussed.

Absolute Free-Energy Calculations of Liquids Using a Harmonic Reference State

“…For consistency and comparison with previous studies, 27,29,47 the results are presented in the form of configurational free energy, A c .…”

“…27,29,47 Instead of a sharp cutoff, we used a switching function to taper out the van der Waals interactions from 6.0 to 7.15 Å, and we did not add any long-range corrections. Long-range corrections (E LRC ) can be added by analytically integrating the potential to an infinite distance, 48 where N is the number of particles, F is the particle density, S(r) is the switching function, and E vdw (r) is the usual van der Waals pair energy function with parameters for argon.…”

Molecular interpretation of Trouton’s and Hildebrand’s rules for the entropy of vaporization of a liquid

“…An indirect route to liquid-phase entropy is to subtract the entropy of vaporization from the entropy of an ideal gas obtained either from experiment [19][20][21][22], distribution functions [23][24][25][26][27] or perturbation calculations [28]. White and Meirovitch use another approach based on the probabilities to insert solvent molecules, one at a time, into a system [29]. However, these approaches give relative rather than explicit information on the liquid phase.…”

Relative stability of the open and closed conformations of the active site loop of streptavidin

“…45,46,[20][21][22] Because HSMC(D) provides an approximation for ρ B ([α k ], x N ), one can, in principle, estimate the free energy of the system from any single structure. [20][21][22] This is the reason why in practice reliable HSMC(D) results for F (but not necessarily for S and E) can be obtained from a relatively small sample.…”

“…Notice, however, that carrying out such calculations with thermodynamic integration (TI) would be practically unfeasible if the structural variance between m and n were significant. Therefore, alternatively (and as in previous work) we use our HSMD method mentioned earlier, [20][21][22][23][24][25] which enables one to calculate the absolute S and F. Thus, only two (separate) local MD simulations of the loop in m and n are carried out, from which F m , F n , and F mn = F m -F n (and S mn = S m -S n ) are obtained directly and the integration process is avoided. (Other methods for calculating the absolute F and S are reviewed, for example, in Ref.…”