Table 1 Summary of calculated defect properties in diamond, hBN, and TMDs

Hosts	E_g (eV)	Defects	Point groups	Defect levels (eV)						E_ZPL (eV)	S	DW	D (GHz)	τ_R (μs)
				Spin up			Spin down
				e_x	e_y	a₁	e_x	e_y	a₁
Diamond	5.47	N_CV_C⁻¹	C_3v	1.87	1.87	0.69	4.64	4.64	1.62	2.10	2.93	0.05	2.86	0.014
hBN	5.62	C_BV_N	C_2v	1.53	3.00	5.30	4.76	5.05	5.77	1.71	2.21	0.11	10.77	0.032
MoS₂	2.37 (1.98)	Mo_S	C_3v	0.40 (0.18)	0.40 (0.22)	1.80 (1.59)	2.34 (2.10)	2.34 (2.10)	2.35 (2.12)	1.11 (1.09)	0.74	0.48	20.51	37.7
		W_S	C_3v	0.84 (0.48)	0.84 (0.71)	1.98 (1.89)	2.33 (2.04)	2.33 (2.06)	2.35 (2.09)	0.91 (0.94)	1.47	0.23	13.44	20.5
WS₂	2.46 (1.85)	W_S	C_3v	0.81 (0.44)	0.81 (0.48)	2.04 (1.70)	2.44 (1.94)	2.44 (1.94)	2.46 (1.97)	1.03 (1.01)	1.01	0.36	14.44	14.1
		Mo_S	C_3v	0.38 (0.04)	0.38 (0.06)	1.92 (1.55)	2.44 (1.95)	2.44 (1.96)	2.44 (1.97)	1.22 (1.18)	0.45	0.64	21.65	54.2
MoSe₂	2.07 (1.72)	Mo_Se	C_3v	0.27 (0.04)	0.27 (0.06)	1.63 (1.42)	2.04 (1.79)	2.04 (1.79)	2.08 (1.81)	1.08 (1.08)	0.75	0.47	19.13	5.6
		W_Se	C_3v	0.71 (0.29)	0.71 (0.52)	1.81 (1.57)	2.03 (1.75)	2.03 (1.78)	2.08 (1.80)	0.79 (0.74)	1.95	0.14	12.43	4.2
WSe₂	2.15 (1.58)	W_Se	C_3v	0.69 (0.34)	0.69 (0.35)	1.84 (1.47)	2.10 (1.61)	2.10 (1.62)	2.16 (1.66)	0.88 (0.84)	1.63	0.20	12.88	3.2
		Mo_Se	C_3v	0.25 (−0.03)	0.25 (−0.02)	1.74 (1.35)	2.12 (1.63)	2.12 (1.65)	2.17 (1.66)	1.19 (1.08)	0.50	0.60	19.82	4.7
MoTe₂	1.71 (1.39)	Mo_Te	C_3v	0.19 (−0.09)	0.39 (0.01)	1.26 (0.85)	1.66 (1.06)	1.70 (1.23)	1.73 (1.30)	0.49 (0.36)	4.51	0.01	0.47	7.8
		W_Te	C_3v	1.51 (1.24)	1.51 (1.27)	0.86 (0.60)	1.51 (1.24)	1.51 (1.27)	0.86 (0.60)

Note: Bold numbers indicate occupied states.
All the values in the table were theoretically estimated in this work, and the numbers between parentheses correspond to results with SOC. Defect levels are relative to the VBM. Majority (minority) spin is referred to as spin up (down). The e_x, e_y, and a₁ columns indicate a₁, b₂, and \({b}_{2}^{ \&\#x00027;}\) for C_BV_N in hBN, respectively⁸⁹. Note that the notations, e_x, e_y, and a₁, are not valid anymore within SOC.

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