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Abstract
The free energy is central to statistical mechanics and thermodynamics, and its accurate calculation via. computational modeling is important for a large number of applications, especially when its experimental value is hard to obtain. Several established and general methods for calculating the Helmholtz free energy across different length scales, including continuum, atomistic and quantum mechanical, are compared and analyzed. A computational approach is then proposed to calculate the temperature dependences of internal energy and absolute Helmholtz free energy for solid and liquid phases with the coupling of thermodynamic integration (TI) and harmonic approximation calculations from both classical molecular dynamics (MD) and density functional theory (DFT). We use the LennardJones system as an example (i.e. argon) for the demonstration of the approach. It is observed that the free energy transits smoothly from being describable by the harmonic approximation to including anharmonic effects at a transition temperature around 0.56 Tm; below this temperature, the quantum behavior of atoms is important. At higher temperatures (T > 0.56 Tm), the TI and harmonic approximation results for the Helmholtz free energy functions become increasingly divergent with the increase of temperature. This work demonstrates that a multiscale approach employing TI, MD, and DFT can provide accurate calculations of the temperature dependence of absolute Helmholtz free energy for both solid and liquid phases.
Original language  English 

Journal  Computational Materials Science 
Early online date  11 Dec 2017 
DOIs  
Publication status  Published  Mar 2018 
Keywords
 Thermodynamic integration
 Harmonic approximation
 Molecular dynamics
 Quantum mechanics
 Helmholtz free energy
 Argon
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 1 Finished

Structural Evolution across multiple time and length scales
Withers, P. (PI), Cartmell, S. (CoI), Cernik, R. (CoI), Derby, B. (CoI), Eichhorn, S. (CoI), Freemont, A. (CoI), Hollis, C. (CoI), Mummery, P. (CoI), Sherratt, M. (CoI), Thompson, G. (CoI) & Watts, D. (CoI)
1/06/11 → 31/05/16
Project: Research