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

Green, James; Irudayam, Sheeba Jem; Henchman, Richard H.

doi:10.1016/j.jct.2011.01.003

Cited by 12 publications

(10 citation statements)

References 58 publications

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“…The use by QHA of a single broad harmonic potential makes it sensitive to conformational changes, slower in convergence, and prone to predicting a much larger entropy increase. The excessive nature of the QHA spread is highlighted by being larger than the entropy change for the vaporization of a liquid to a gas of ∼85 J K −1 mol −1 by Trouton's rule, 81 and yet conformational change in solution involves a much smaller gain in flexibility. Two reasons for the better performance of MCC are the use of rotational coordinates and the closely Gaussian distribution of forces to which is fitted a single harmonic potential averaged over all energy wells with a separate term to account for the multimodal dihedral distribution.…”

Section: Discussionmentioning

confidence: 99%

Entropy of Proteins Using Multiscale Cell Correlation

Chakravorty

Higham

Henchman

2020

J. Chem. Inf. Model.

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A new multiscale method is presented to calculate the entropy of proteins from molecular dynamics simulations. Termed Multiscale Cell Correlation (MCC), the method decomposes the protein into sets of rigid-body units based on their covalent-bond connectivity at three levels of hierarchy: molecule, residue and united atom. It evaluates the vibrational and topographical entropy from forces, torques and dihedrals at each level, taking into account correlations between sets of constituent units that together make up a larger unit at the coarser length scale. MCC gives entropies in close agreement with normal mode analysis and smaller than those using quasiharmonic analysis as well as providing much faster convergence. Moreover, MCC provides an insightful 1 decomposition of entropy at each length scale and for each type of amino acid according to their solvent exposure and whether they are terminal residues. While the residue entropy depends weakly on solvent exposure, there is greater variation in entropy components for larger, more polar amino acids, which have increasing conformational entropy but reduced vibrational entropy with greater solvent exposure.

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Section: Discussionmentioning

confidence: 99%

Entropy of Proteins Using Multiscale Cell Correlation

Chakravorty

Higham

Henchman

2020

J. Chem. Inf. Model.

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“…Another viable method for liquid-phase entropy is the cell approximation which maps regions of the potential energy surface into single, representative energy wells, whose entropy is determined from the force [ 34 ] plus an entropy term for the probability distribution of the energy wells [ 35 ]. This is the method we have been working to generalise, progressing from liquid argon [ 34 ] to liquid water with its rotational vibration and orientational degrees of freedom [ 35 , 36 , 37 ], organic liquids with an internal one-dimensional dihedral entropy [ 38 ], single molecules with internal entropy based on force correlation [ 39 ], and molecular liquids in a multiscale framework from atom to united atom to molecule to system [ 40 ]. This development has been supported by extensive parallel studies on the entropy of aqueous solutions [ 41 , 42 , 43 , 44 , 45 , 46 , 47 ].…”

Section: Introductionmentioning

confidence: 99%

Entropy of Simulated Liquids Using Multiscale Cell Correlation

Ali

Higham

Henchman

2019

Entropy

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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.

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“…The philosophy of our approach is that it should be simple, fast, scalable, general, treats all molecules equivalently, gives a decomposition of entropy over all degrees of freedom of the system to explain the entropy obtained, and achieves comparable accuracy to that of the force-field used. The method builds on our earlier work for liquid water, 27,37 organic liquids 71 and single flexible molecules of united atoms. 29 Previously for water, vibrational frequencies had been extracted from force and torque magnitudes 27 or squared forces and squared torques 37 and the number of energy wells had been calculated using a generalized Pauling model [52][53][54][55]72 originally developed for the residual entropy of ice.…”

Section: Introductionmentioning

confidence: 99%

“…Vibrational Entropy The size of each energy well is determined from the forces and torques on the particle and thermal de Broglie wavelengths and waveangles from the integrals over translational and rotational momenta. 53,71,75 Correlations between the forces and torques of different particles are accounted for in a covariance matrix. One immediate assumption made is that the vibrational entropy of the atoms within each united atom is small and can be ignored.…”

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confidence: 99%

Entropy of flexible liquids from hierarchical force–torque covariance and coordination

et al. 2018

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New theory is presented to calculate the entropy of a liquid of flexible molecules from a molecular dynamics simulation. Entropy is expressed in two terms: a vibrational term, representing the average number of configurations and momentum states in an energy well, and a topographical term, representing the effective number of energy wells. The vibrational term is derived in a hierarchical manner from two force-torque covariance matrices, one at the molecular level and one at the united-atom level. The topographical term comprises conformations and orientations, which are derived from the dihedral distributions and 1 coordination numbers, respectively. The method is tested on fourteen liquids, ranging from argon to cyclohexane. For most molecules our results lie within the experimental range, and are slightly higher than those by the 2PT method, the only other method currently capable of directly calculating entropy for such systems. As well as providing an efficient and practical way to calculate entropy, the theory serves to give a comprehensive characterization and quantification of molecular structure.

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

Cited by 12 publications

References 58 publications

Entropy of Proteins Using Multiscale Cell Correlation

Entropy of Proteins Using Multiscale Cell Correlation

Entropy of Simulated Liquids Using Multiscale Cell Correlation

Entropy of flexible liquids from hierarchical force–torque covariance and coordination

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