Entropy of Simulated Liquids Using Multiscale Cell Correlation

Abstract

Accurately calculating the entropy of liquids is an important goal, given that many processes take place in the liquid phase. Of almost equal importance is understanding the values obtained. However, there are few methods that can calculate the entropy of such systems, and fewer still to make sense of the values obtained. We present our multiscale cell correlation (MCC) method to calculate the entropy of liquids from molecular dynamics simulations. The method uses forces and torques at the molecule and united-atom levels and probability distributions of molecular coordinations and conformations. The main differences with previous work are the consistent treatment of the mean-field cell approximation to the approriate degrees of freedom, the separation of the force and torque covariance matrices, and the inclusion of conformation correlation for molecules with multiple dihedrals. MCC is applied to a broader set of 56 important industrial liquids modeled using the Generalized AMBER Force Field (GAFF) and Optimized Potentials for Liquid Simulations (OPLS) force fields with 1.14*CM1A charges. Unsigned errors versus experimental entropies are 8.7 J K − 1 mol − 1 for GAFF and 9.8 J K − 1 mol − 1 for OPLS. This is significantly better than the 2-Phase Thermodynamics method for the subset of molecules in common, which is the only other method that has been applied to such systems. MCC makes clear why the entropy has the value it does by providing a decomposition in terms of translational and rotational vibrational entropy and topographical entropy at the molecular and united-atom levels.

Energy-entropy prediction of octanol–water logP of SAMPL7 N-acyl sulfonamide bioisosters

“…Vibrational entropy of each kind of motion and unit is calculated in the harmonic approximation for a quantum harmonic oscillator where h is Planck's constant, N vib is the number of vibrations, and v i are the vibrational frequencies, which are derived using where i are the eigenvalues of the N transvib × N transvib massweighted force covariance matrix for translational vibration or N rovib × N rovib moment-of-inertia-weighted torque covariance matrix for rotational vibration. Forces and torques are halved in the mean-field approximation except for the UA force covariance matrix [26,27,43,46] because UA correlations are directly accounted for in the molecule reference frame. The six lowest-frequency vibrations for the UA force covariance matrix are removed to avoid double-counting entropy at the molecule level.…”

“…Positional entropy for a dilute solute in a solvent is calculated by discretising the volume V • available to the molecule at its concentration by the volume of a solvent molecule V solvent , giving [30,31,47] V solvent is taken as the volume of a simulation box of pure solvent divided by the number of solvent molecules, and V • is taken as the same in both solvents and so cancels for the partition coefficient. Orientational entropy is calculated by discretising the rotational volume of the molecule about its three rotational axes according to the number of molecules in the molecule's first solvation shell N c [26,27], weighted by the probability p(N c ) of each N c using (4)…”

“…We have developed a general method to evaluate free energy directly from an MD simulation for all molecules in the system, both solvent and solute alike, and over a large range of length scales [26][27][28]. Called Energy-Entropy Multiscale Cell Correlation (EE-MCC), it takes the energy from the simulation energy and evaluates the entropy over a series of units at multiple length scales, either correlated if covalently bonded, or in a mean-field cell if otherwise.…”

“…Notably, entropy is calculated from the probability distribution over all quantum states of the system relating to all degrees of freedom of all molecules. MCC has been progressively developed for liquids [26,27,29], solutions [30][31][32][33], chemical reactions [34], and proteins [28,35,36]. As well as being general, MCC has the advantage of providing a detailed breakdown of entropy over all degrees of freedom of the system.…”

Thermodynamic Origin of Differential Excipient-Lysozyme Interactions

“…Energy is calculated directly from the system Hamiltonian by summing over per-atom energies. Entropy is calculated for all molecules in the system from forces and coordinates at multiple length scales using MCC, which has been applied to liquids (Higham et al, 2018;Ali et al, 2019), chemical reactions (Ali et al, 2020), and proteins (Chakravorty et al, 2020). The three length scales employed here from smallest to largest are 1) water and monatomic ions, 2) excipients and residues, and 3) the whole protein, which are classified here as united-atom, monomer, and polymer levels, respectively.…”