Functional | MAD | Max (+) | Max (−) |
---|---|---|---|
DFT | |||
XYG3^{*} | 1.81 | 16.67 (SF_{6}) | −6.28 (BCl_{3}) |
M06-2X^{*} | 2.93 | 20.77 (O_{3}) | −17.39 (P_{4}) |
M06^{*} | 4.17 | 11.25 (O_{3}) | −25.89 (C_{2}F_{6}) |
B2PLYP^{*} | 4.63 | 20.37 (n-octane) | −8.01 (C_{2}F_{4}) |
B3LYP^{*} | 4.74 | 19.22 (SF_{6}) | −8.03 (BeH) |
M06-L^{*} | 5.82 | 14.75 (PF_{5}) | −27.13 (C_{2}Cl_{4}) |
BLYP^{†} | 9.49 | 41.0 (C_{8}H_{18}) | −28.1 (NO_{2}) |
PBE^{†} | 22.22 | 10.8 (Si_{2}H_{6}) | −79.7 (azulene) |
LDA^{†} | 121.85 | 0.4 (Li_{2}) | −347.5 (azulene) |
Ab initio | |||
HF^{*} | 211.48 | 582.72 (n-octane) | −0.46 (BeH) |
MP2^{*} | 10.93 | 29.21 (Si(CH_{3})_{4}) | −48.34 (C_{2}F_{6}) |
QCISD(T)^{‡} | 15.22 | 42.78 (n-octane) | −1.44 (Na_{2}) |
G2^{‡} | 1.88 | 7.2 (SiF_{4}) | −9.4 (C_{2}F_{6}) |
G3^{‡} | 1.05 | 7.1 (PF_{5}) | −4.9 (C_{2}F_{4}) |
MADs, in kcal/mol, with the largest positive error (Max(+) energy too high) and the largest negative error (Max(−) energy too low).
↵*The geometries were optimized by using B3LYP with the 6-311+G(d,p) basis set. Analytical vibrational frequencies were calculated at the same level and scaled by 0.9877 to estimate zero-point energies. Spin-orbit corrections are included. Single point calculations are performed with the 6-311+G(3df,2p) basis set.
↵^{†}Data are from ref. 28 and computed by using B3LYP/6-311+G(3df,3pd). The geometries were optimized by using B3LYP/6-31G(2df,p). Analytical vibrational frequencies were calculated at the same level and scaled by 0.9854 to estimate zero-point energies.
↵^{‡}Data are from ref. 29. The QCISD(T) results were obtained by removing the empirical ″high-level corrections″ from the G3 theory to approximate the results of QCISD(full,T)/6-311+G (3d2f,2df,2p) by a series of extrapolations in both the 1-particle and many-particle spaces.