# Total energy

The GAP total energy is usually understood as 1) the expectation value of the electronic Hamiltonian plus 2) the classical electrostatic interaction between the electrons and nuclei plus 3) the electrostatic interaction between the nuclei. That is, we usually work in the Born-Oppenheimer approximation. The kinetic energy of the nuclei is what we call the kinetic energy in molecular dynamics (which is used to compute the instantaneous temperature), whereas the total energy is what we call the potential energy.

The total energy in GAP is usually (but not necessarily) obtained from a fit to reference density functional theory (DFT) data, and it may or may not contain van der Waals corrections or some other corrections on top of DFT. While it is technically possible to train a GAP from classical force field reference data, under most normal circumstances is does not make sense to do it (since a GAP is generally computationally slower).

In GAP theory^{[1]}^{[2]}, the total energy is always obtained as a sum over local energies, which are defined per atom:

[math]\displaystyle{ E = \sum_{i=1}^{N_\text{atoms}} \epsilon_i. }[/math]

## Reference list

- ↑
**A.P. Bartók, M.C. Payne, R. Kondor, and G. Csányi**.*Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons*. Phys. Rev. Lett.**104**, 136403 (2010). - ↑
**A.P. Bartók and G. Csányi**.*Gaussian Approximation Potentials: a brief tutorial introduction*. Int. J. Quantum Chem.**115**, 1051 (2015).