A Neural Network Potential for Sodium
Lehrstuhl für Theoretische Chemie, RuhrUniversität Bochum
The Neural Network potential for sodium has been constructed using about 18000 DFT calculations (PBE functional, PWSCF code) as a reference.
The training set consists of crystalline and amorphous bulk structures, about 8% of the structures have been used as independent test set to check the generalization properties of the potential. The accuracy in reproducing the total energies from DFT is better than 1 meV per atom for both the training and the test set. For energy differences the error is even smaller and the relative stabilities of the investigated phases of sodium are in excellent agreement with the underlying DFT calculations.

structures 
RMSE (eV/atom) 
Training Set 
16500 
0.72 
Test Set 
1500 
0.91 
In the table below the lattice constants and bulk moduli obtained by DFT and the Neural Network potential are compared.

bcc 
fcc 

DFT 
NN 
DFT 
NN 

lattice constant (Ang) 
4.201 
4.202 
5.297 
5.297 
bulk modulus (GPa) 
7.63 
7.59 
7.624 
7.613 



In the following figure the Neural Network and DFT energies for several structures extracted from a NPT MD simulation of liquid sodium at 600 K and 100 GPa (64 atom cell) are compared. Further details and tests of the potential can be found in the reference given below.
Comparison of the Neural Network and DFT energies for some bulk Na structures extracted from a molecular dynamics simulation
Related publications:
H. Eshet, R.Z. Khaliullin, T.D. Kühne, J. Behler, and M. Parrinello, Phys. Rev. B 81, 184107 (2010).
H. Eshet, R.Z. Khaliullin, T.D. Kühne, J. Behler, and M. Parrinello, Phys. Rev. Lett. 108, 115701 (2012).
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