Two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), are applied to study hot, dense helium in the density–temperature range of 0.387 ... 5.35 gcm-3 and 500 K ... 1.28×108 K. One coherent equation of state (EOS) is derived by combining DFT-MD data at lower temperatures with PIMC results at higher temperatures. Good agreement between both techniques is found in an intermediate temperature range. For the highest temperatures, the PIMC results converge to the Debye–Hückel limiting law. In order to derive the entropy, a thermodynamically consistent free energy fit is introduced that reproduces the internal energies and pressure derived from the first-principles simulations. The equation of state is presented in the form of a table as well as a fit.
This code derives the equation of hot, dense helium. Using a 2D spline interpolation as function of temperature and density, the code computes pressure (P), internal energy (E), Helmholtz free energy (F), and entropy (S).
There are no copyright restrictions for this material but we would appreciate citations to these two articles:
- B. Militzer, Path Integral Monte Carlo and Density Functional Molecular Dynamics Simulations of Hot, Dense Helium, Phys. Rev. B 79 (2009) 155105, cond-mat/08050317.
- B. Militzer, First Principles Calculations of Shock Compressed Fluid Helium, Phys. Rev. Lett. 97 (2006) 175501.
1. Download the code
| Date | File Description | Download Link |
|---|---|---|
| 2022-11-04 | Standard code | Download eoshe_11-04-22.tar.gz |
2. Installation
To install our helium EOS code:
cd ~/Downloads
tar -xzf eoshe_11-04-22.tar.gz
gfortran eoshe.f log55.f spline.f -o eoshe
If compilation fails, try another compiler or adjust compiler flags.
3. Files included
| eoshe.f | Main code: computes P, E, F, S from T and ρ; outputs a test table. |
| log55.f | 2D free energy interpolation. |
| spline.f | Simple 1D spline interpolation. |
| eoshe.out | Example output file for comparison. |
4. Execution and tests
./eoshe > my_eoshe.out
diff eoshe.out my_eoshe.out
5. Units and conventions
rs= 2.400000 rhoHe(g/cc)= 0.387289 T(K)= 500.000 E(Ha/e)= -1.431865 ...
...
rs= 0.800000 rhoHe(g/cc)= 10.456811 T(K)= 128000000.000 E(Ha/e)= 902.363130 ...
All quantities are in atomic units; see our hydrogen-helium EOS table for details.
6. Limitations
Temperature range: 500 to 1.28×108 K.
Density range: 0.387289 to 5.35 g/cm³.
If you have feedback, please email militzer@berkeley.edu.
The work was supported in part by NASA and NSF.