TY - JOUR
T1 - Multiple linear regression and thermodynamic fluctuations are equivalent for computing thermodynamic derivatives from molecular simulation
AU - Rahbari, Ahmadreza
AU - Josephson, Tyler R.
AU - Sun, Yangzesheng
AU - Moultos, Othonas A.
AU - Dubbeldam, David
AU - Siepmann, J. Ilja
AU - Vlugt, Thijs J.H.
PY - 2020
Y1 - 2020
N2 - Partial molar properties are of fundamental importance for understanding properties of non-ideal mixtures. Josephson and co-workers (Mol. Phys. 2019, 117, 3589–3602) used least squares multiple linear regression to obtain partial molar properties in open constant-pressure ensembles. Assuming composition-independent partial molar properties for the narrow composition range encountered throughout simulation trajectories, we rigorously prove the equivalence of two approaches for computing thermodynamic derivatives in open ensembles of an n-component system: (1) multiple linear regression, and (2) thermodynamic fluctuations. Multiple linear regression provides a conceptually simple and computationally efficient way of computing thermodynamic derivatives for multicomponent systems. We show that in the reaction ensemble, the reaction enthalpy can be computed directly by simple multiple linear regression of the enthalpy as a function of the number of reactant molecules. Non-linear regression and a Gaussian process model taking into account the compositional dependence of partial molar properties further support that multiple linear regression captures the correct physics.
AB - Partial molar properties are of fundamental importance for understanding properties of non-ideal mixtures. Josephson and co-workers (Mol. Phys. 2019, 117, 3589–3602) used least squares multiple linear regression to obtain partial molar properties in open constant-pressure ensembles. Assuming composition-independent partial molar properties for the narrow composition range encountered throughout simulation trajectories, we rigorously prove the equivalence of two approaches for computing thermodynamic derivatives in open ensembles of an n-component system: (1) multiple linear regression, and (2) thermodynamic fluctuations. Multiple linear regression provides a conceptually simple and computationally efficient way of computing thermodynamic derivatives for multicomponent systems. We show that in the reaction ensemble, the reaction enthalpy can be computed directly by simple multiple linear regression of the enthalpy as a function of the number of reactant molecules. Non-linear regression and a Gaussian process model taking into account the compositional dependence of partial molar properties further support that multiple linear regression captures the correct physics.
KW - Linear regression
KW - Molecular simulation
KW - Open ensembles thermodynamic fluctuations
KW - Partial molar properties
UR - http://www.scopus.com/inward/record.url?scp=85089584515&partnerID=8YFLogxK
U2 - 10.1016/j.fluid.2020.112785
DO - 10.1016/j.fluid.2020.112785
M3 - Article
AN - SCOPUS:85089584515
SN - 0378-3812
VL - 523
JO - Fluid Phase Equilibria
JF - Fluid Phase Equilibria
M1 - 112785
ER -