Table 1. MADs (all energies in eV) for various level of theory for the extended G2 set.

	G2(MAD)
Method	ΔHf	IP	EA	PA	H-Ne, Etot	TM ΔE	He2, ΔE(Re)	Ne2, ΔE(Re)	(H2O)2, De(RO...O)
HF	6.47	1.036	1.158	0.15	4.49	1.09	Unbound	Unbound	0.161 (3.048)
G2 or best ab initio	0.07a	0.053b	0.057b	0.05b	1.59c	0.19d	0.0011 (2.993)e	0.0043 (3.125)e	0.218 (2.912)f
LDA (SVWN)	3.94a	0.665	0.749	0.27	6.67	0.54g	0.0109 (2.377)	0.0231 (2.595)	0.391 (2.710)
GGA
BP86	0.88a	0.175	0.212	0.05	0.19	0.46	Unbound	Unbound	0.194 (2.889)
BLYP	0.31a	0.187	0.106	0.08	0.19	0.37g	Unbound	Unbound	0.181 (2.952)
BPW91	0.34a	0.163	0.094	0.05	0.16	0.60	Unbound	Unbound	0.156 (2.946)
PW91PW91	0.77	0.164	0.141	0.06	0.35	0.52	0.0100 (2.645)	0.0137 (3.016)	0.235 (2.886)
mPWPWh	0.65	0.161	0.122	0.05	0.16	0.38	0.0052 (2.823)	0.0076 (3.178)	0.194 (2.911)
PBEPBEi	0.74i	0.156	0.101	0.06	1.25	0.34	0.0032 (2.752)	0.0048 (3.097)	0.222 (2.899)
XLYPj	0.33	0.186	0.117	0.09	0.95	0.24	0.0010 (2.805)	0.0030 (3.126)	0.192 (2.953)
Hybrid methods
BH & HLYPk	0.94	0.207	0.247	0.07	0.08	0.72	Unbound	Unbound	0.214 (2.905)
B3P86l	0.78a	0.636	0.593	0.03	2.80	0.34	Unbound	Unbound	0.206 (2.878)
B3LYPm	0.13a	0.168	0.103	0.06	0.38	0.25g	Unbound	Unbound	0.198 (2.926)
B3PW91n	0.15a	0.161	0.100	0.03	0.24	0.38	Unbound	Unbound	0.175 (2.923)
PW1PWo	0.23	0.160	0.114	0.04	0.30	0.30	0.0066 (2.660)	0.0095 (3.003)	0.227 (2.884)
mPW1PWp	0.17	0.160	0.118	0.04	0.16	0.31	0.0020 (3.052)	0.0023 (3.254)	0.199 (2.898)
PBE1PBEq	0.21i	0.162	0.126	0.04	1.09	0.30	0.0018 (2.818)	0.0026 (3.118)	0.216 (2.896)
O3LYPr	0.18	0.139	0.107	0.05	0.06	0.49	0.0031 (2.860)	0.0047 (3.225)	0.139 (3.095)
X3LYPs	0.12	0.154	0.087	0.07	0.11	0.22	0.0010 (2.726)	0.0028 (2.904)	0.216 (2.908)
Experimental	—	—	—	—	—	—	0.0010 (2.970)t	0.0036 (3.091)t	0.236u (2.948)v

ΔH_f, heat of formation at 298 K; PA, proton affinity; E_tot, total energies (H-Ne); TM ΔE, s to d excitation energy of nine first-row transition metal atoms and nine positive ions. Bonding properties [ΔE or D_e in eV and (R_e) in Å] are given for He₂, Ne₂, and (H₂O)₂. The best DFT results are in boldface, as are the most accurate answers [experiment except for (H₂O)₂].

^aRef. 5

^bRef. 19

^cRef. 4

^dRef. 35

^eRef. 38

^fRef. 34

^gRef. 37

^hRef. 7

ⁱRef. 10

^j1.0 E_x (Slater) + 0.722 ΔE_x (B88) + 0.347 ΔE_x (PW91) + 1.0 E_c (LYP)

^k0.5 E_x (HF) + 0.5 E_x (Slater) + 0.5 ΔE_x (B88) + 1.0 E_c (LYP)

^l0.20 E_x (HF) + 0.80 E_x (Slater) + 0.72 ΔE_x (B88) + 1.0 E_c (VWN) + 0.81 ΔE_c (P86)

^m0.20 E_x (HF) + 0.80 E_x (Slater) + 0.72 ΔE_x (B88) + 0.19 E_c (VWN) + 0.81 E_c (LYP)

ⁿ0.20 E_x (HF) + 0.80 E_x (Slater) + 0.72 ΔE_x (B88) + 1.0 E_c (PW91, local) + 0.81 ΔE_c (PW91, nonlocal)

^o0.25 E_x (HF) + 0.75 E_x (Slater) + 0.75 ΔE_x (PW91) + 1.0 E_c (PW91)

^p0.25 E_x (HF) + 0.75 E_x (Slater) + 0.75 ΔE_x (mPW) + 1.0 E_c (PW91)

^q0.25 E_x (HF) + 0.75 E_x (Slater) + 0.75 ΔE_x (PBE) + 1.0 E_c (PW91, local) + 1.0 ΔE_c (PBE, nonlocal)

^r0.1161 E_x (HF) + 0.9262 E_x (Slater) + 0.8133 ΔE_x (OPTX) + 0.19 E_c (VWNS) + 0.81 E_c (LYP)

^s0.218 E_x (HF) + 0.782 E_x (Slater) + 0.542 ΔE_x (B88) + 0.167 ΔE_x (PW91) + 0.129 E_c (VWN) + 0.871 E_c (LYP)

^tRef. 27

^uRef. 33

^vRef. 32