Table 2.

Unit-cell volumes and energies (relative to black P) for relevant allotropes, comparing DFT + MBD and GAP + R6 results.

	Volume (Å3/atom)				ΔEnergy (eV/atom)
	Expt.	DFT + MBD	GAP + R6	Error versus DFT (%)	DFT + MBD	GAP + R6
White P (β-P4, $P\overline{1}$)	25.99a	25.76	25.72	−0.2	+0.178	+0.154
Fibrous P ($P\overline{1}$)	21.7b	21.77	22.09	+1.4	+0.001	+0.003
Hittorf’s P (P2/c)	21.8c	21.82	22.01	+0.9	−0.001	±0.000
Black P (Cmce)	19.03d	18.83	18.74	−0.5	±0 (reference)
As-type P ($R\overline{3}m$)	–e	15.48	15.44	−0.2	−0.011	−0.009

^aFrom ref. ²; XRD at 88 K.

^bFrom ref. ¹⁰; XRD at 293(2) K.

^cCalc. from lattice parameters in ref. ⁹; XRD at room temperature.

^dFrom ref. ⁸⁰; XRD at 293 K.

^eHigh-pressure allotrope⁶⁷, here studied in a hypothetical form without external pressure. A recent experimental study reports 14.6 ų/atom at 6.05 GPa⁷².