Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons

We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, as derived from quantum mechanical calculations. The models do not have a fixed functional form and hence are capable of modeling complex potential energy landscapes. They are systematically improvable with more data. We apply the method to bulk crystals, and test it by calculating properties at high temperatures. Using the interatomic potential to generate the long molecular dynamics trajectories required for such calculations saves orders of magnitude in computational cost.

Figure 1

Deviation of atomic forces between DFT and various models: the Brenner [18] and Tersoff [19] potentials and different GAP models for different semiconductors. In the bottom row the horizontal lines correspond to the smallest standard deviation of the error theoretically attainable given the range of the potential (see text). The configurations are taken from molecular dynamics runs at 1000 K.

Figure 2

(a) Phonon dispersion curves for diamond using the GAP model (lines), Tersoff (dotted lines), DFT (triangles), and experiment (squares) [20]. (b) Temperature dependence of the ${\Gamma }_{{25}^{\prime }}$ mode from MD using GAP (circles, 250 atoms, 20 ps) and experiment (squares) [21]. In accordance with common practice [22] the calculated points have been shifted by a constant to agree with experiment at zero temperature to account for the anharmonic effects of zero-point motion and a quantum correction to the kinetic temperature is also applied [23]. (c) Phonon dispersion of iron using GAP (solid), Finnis-Sinclair potential [24] (dotted), and DFT (triangles).

Figure 3

Linear thermal expansion coefficient of diamond in the GAP model (dashed line) and DFT (dash-dotted line) using the quasiharmonic approximation [25], and derived from MD (216 atoms, 40 ps) with GAP (solid) and the Brenner potential (dotted). Experimental results are shown with squares [26].

Figure 4

The energetics of the linear transition path for a migrating vacancy (top) and for the rhombohedral graphite to diamond transformation (bottom).