Atoms: P₄

Structure info
Layer group	pman
Layer group number	42
Structure origin	original03-18
COD id of parent bulk structure	COD 9012486
ICSD id of parent bulk structure	ICSD 36434
Mono/few-layer report(s)	10.1038/nnano.2014.35

Stability
Energy above convex hull [eV/atom]	0.039
Heat of formation [eV/atom]	0.039
Dynamically stable	Yes

Basic properties
Magnetic state	NM
Band gap [eV]	0.903
Band gap (HSE06) [eV]	1.511
Band gap (G₀W₀) [eV]	2.025

Repeat: 1234   Download: XYZ CIF JSON

Axis	x [Å]	y [Å]	z [Å]	Periodic
1	4.631	0.000	0.000	Yes
2	0.000	3.306	0.000	Yes
3	0.000	0.000	17.110	No

Lengths [Å]	4.631	3.306	17.110
Angles [°]	90.000	90.000	90.000

Convex hull

P4 (4P-1)
Heat of formation [eV/atom]	0.04
Energy above convex hull [eV/atom]	0.04

Monolayers from C2DB
P4, (4P-1)	0.04 eV/atom
P2, (2P-1)	0.04 eV/atom

Bulk crystals from OQMD123
P42	0.00 eV/atom

Stiffness tensor

Cij (N/m)	xx	yy	xy
xx	23.59	17.00	-0.00
yy	16.92	101.96	0.00
xy	0.00	0.00	44.68

Stiffness tensor eigenvalues
Eigenvalue 0	20.08 N/m
Eigenvalue 1	44.68 N/m
Eigenvalue 2	105.47 N/m

Phonons

Property	Value
Minimum eigenvalue of Hessian [eV/Ų]	-0.00

Deformation potentials

DVB (eV)	xx	yy	xy
Γ	-2.69	0.06	-0.00
X	-7.80	1.41	-0.00
S	-2.44	0.04	-1.44
Y	-0.23	-2.79	-0.00
kVBM	-2.69	0.06	-0.00

	xx	yy	xy
Band Gap	4.25	4.88	0.00

DCB (eV)	xx	yy	xy
Γ	1.56	4.94	0.00
X	-1.21	-12.64	-0.00
S	-2.71	0.56	3.07
Y	1.34	3.66	-0.00
kCBM	1.56	4.94	0.00

Electronic band structure and density of states

Effective masses (PBE)

Property (VBM)	Value
Min eff. mass	0.13 m0
Max eff. mass	8.16 m0
DOS eff. mass	1.03 m0
Crystal coordinates	[0.000, -0.029]
Warping parameter	-0.000
Barrier height	0.4 meV
Distance to barrier	0.0063 Å-1

Property (CBM)	Value
Min eff. mass	0.13 m0
Max eff. mass	1.24 m0
DOS eff. mass	0.41 m0
Crystal coordinates	[-0.000, -0.000]
Warping parameter	0.005
Barrier height	> 43.3 meV
Distance to barrier	> 0.0189 Å-1

Electronic band structure (HSE06@PBE)

Property	Value
KVP: Band gap (HSE06) [eV]	1.51
KVP: Direct band gap (HSE06) [eV]	1.51
Valence band maximum wrt. vacuum level (HSE06)	-5.40 eV
Conduction band minimum wrt. vacuum level (HSE06)	-3.89 eV

Electronic band structure (G₀W₀@PBE)

Property	Value
Band gap (G₀W₀) [eV]	2.03
Direct band gap (G₀W₀) [eV]	2.03
Valence band maximum wrt. vacuum level (G₀W₀)	-5.96 eV
Conduction band minimum wrt. vacuum level (G₀W₀)	-3.93 eV

Born charges

ZPij	ux	uy	uz
Px	-0.00	-0.00	-0.35
Py	0.00	0.00	-0.00
Pz	-0.01	0.00	-0.00

ZPij	ux	uy	uz
Px	0.00	0.00	0.35
Py	-0.00	0.00	-0.00
Pz	0.01	0.00	0.00

ZPij	ux	uy	uz
Px	0.00	0.00	-0.35
Py	-0.00	0.00	0.00
Pz	-0.01	-0.00	0.00

ZPij	ux	uy	uz
Px	-0.00	-0.00	0.35
Py	0.00	0.00	0.00
Pz	0.01	-0.00	-0.00

Optical polarizability

Properties
Static interband polarizability at (x) [Å]	6.055
Static interband polarizability at (y) [Å]	4.533
Static interband polarizability at (z) [Å]	0.343
Plasma frequency (x) [Å0.5]	0.000
Plasma frequency (y) [Å0.5]	0.000

Infrared polarizability

Static polarizability	[Å]
Phonons only (x)	0.23
Phonons only (y)	0.00
Phonons only (z)	0.00
Total (phonons + electrons) (x)	6.29
Total (phonons + electrons) (y)	4.53
Total (phonons + electrons) (z)	0.34

Raman spectrum

Mode	Frequency (1/cm)	Degeneracy
Mode 1	0.4	3
Mode 2	128.4	1
Mode 3	187.7	1
Mode 4	225.3	1
Mode 5	350.9	1
Mode 6	426.6	1
Mode 7	433.4	1
Mode 8	437.7	1
Mode 9	465.2	1
Mode 10	468.	1

Optical absorption (BSE and RPA)

Property	Value
The exciton binding energy from the Bethe–Salpeter equation (BSE) [eV].	0.62

Bader-charge analysis

#	Chemical symbol	Charges [|e|]
0	P	-0.00
1	P	0.00
2	P	-0.00
3	P	0.00

Miscellaneous

Miscellaneous details
Unique ID	4P-1
Number of atoms	4
Number of species	1
Formula	P4
Reduced formula	P
Stoichiometry	A
Unit cell area [Å2]	15.312
Original file-system folder	/home/niflheim2/cmr/C2DB-ASR/tree/A/P/P4-276f0a298324
Magnetic state	NM
Spin axis	z
Old uid	P4-276f0a298324
Inversion symmetry	Yes
Layer group	pman
Layer group number	42
Structure origin	original03-18
Band gap [eV]	0.903
gap_dir	0.903
gap_dir_nosoc	0.903
Vacuum level [eV]	3.233
Fermi level [eV]	-1.369
minhessianeig	-0.000
Dynamically stable	Yes
Band gap (HSE06) [eV]	1.511
gap_dir_hse	1.511

Miscellaneous details
vbm_hse	-2.168
cbm_hse	-0.656
Band gap (G₀W₀) [eV]	2.025
gap_dir_gw	2.025
vbm_gw	-2.723
cbm_gw	-0.698
E_B	0.624
Static interband polarizability at (x) [Å]	6.055
Static interband polarizability at (y) [Å]	4.533
Static interband polarizability at (z) [Å]	0.343
Static polarizability (phonons) (x) [Å]	0.232
Static polarizability (phonons + electrons) (x) [Å]	6.287
Static polarizability (phonons) (y) [Å]	0.000
Static polarizability (phonons + electrons) (y) [Å]	4.533
Static polarizability (phonons) (z) [Å]	0.000
Static polarizability (phonons + electrons) (z) [Å]	0.343
Plasma frequency (x) [Å0.5]	0.000
Plasma frequency (y) [Å0.5]	0.000
Energy [eV]	-21.301
ICSD id of parent bulk structure	ICSD 36434
COD id of parent bulk structure	COD 9012486
Mono/few-layer report(s)	10.1038/nnano.2014.35
Energy above convex hull [eV/atom]	0.039
Heat of formation [eV/atom]	0.039