Partial molar properties from molecular simulation using multiple linear regression

Tyler R. Josephson, Ramanish Singh, Mona S. Minkara, Evgenii O. Fetisov, J. Ilja Siepmann

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11 Scopus citations


Partial molar volumes, energies, and enthalpies can be computed from NpT-Gibbs ensemble simulations through a post-processing procedure that leverages fluctuations in composition, total volume, and total energy of a simulation box. By recording the instantaneous box volumes V and instantaneous number of molecules (Formula presented.) of each of n species for M frames, a large (Formula presented.) matrix (Formula presented.) is constructed, as well as the (Formula presented.) vector (Formula presented.). The (Formula presented.) vector of partial molar volumes (Formula presented.) may then be solved using (Formula presented.). A similar construction permits calculation of partial molar energies using M instantaneous measurements of the total energy of the simulation box, and (Formula presented.). Partial molar enthalpies may be derived from (Formula presented.), (Formula presented.), and pressure p. These properties may be used to calculate enthalpy and entropy of transfer (absorption, extraction, and adsorption) for species in complex mixtures. The method is demonstrated on three systems in the NpT-Gibbs ensemble: a highly compressible natural gas condensate of methane, n-butane, and n-decane, the liquid-phase adsorption of 1,5-pentanediol and ethanol onto the MFI zeolite, and a relatively incompressible mixture of ethanol, n-dodecane, and water at liquid-liquid equilibrium. Property predictions are compared to those from numerical differentiation of simulation data sequentially changing the composition and from equations of state. The method can also be extended to reaction equilibria in a closed system and is applied to a reactive first-principles Monte Carlo simulation of compressed nitrogen/oxygen.

Original languageEnglish (US)
Pages (from-to)3589-3602
Number of pages14
JournalMolecular Physics
Issue number23-24
StatePublished - Dec 17 2019

Bibliographical note

Funding Information:
This research was primarily supported by the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under Award DE-FG02-17ER16362 (development and testing of the MLR approach and simulations of adsorption equilibria). This research was also supported by the Abu Dhabi Petroleum Institute Research Center, Project Code LTR14009 (simulations of ethanol/n-dodecane/water and natural gas mixtures). Simulations of reactive equilibria of compressed NO were supported by the National Science Foundation (CHE-1265849) and used resources of the Argonne Leadership Computing Facility (Argonne National Laboratory), which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. A portion of the computer resources were provided by the Minnesota Supercomputing Institute at the University of Minnesota. The University of Minnesota Disability Resource Center also supported this work through providing access assistants to MSM. We thank Yangzesheng Sun for helpful conversations about correlations.

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • Monte Carlo simulation
  • phase equilibria
  • reaction equilibria
  • thermodynamics


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