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Table 3 The mean values of the NCIs in four types of complexes and the RMSEs of DFT calculations and GRNN corrections relative to the CCSD(T)/CBS benchmark NCIs (Unit: kcal/mol)

From: A machine learning correction for DFT non-covalent interactions based on the S22, S66 and X40 benchmark databases

Methods

Mean (RMSE/RMSE1c)

H-bonded

Dispersion

Mixed

Halogen

CCSD(T)/CBS

−10.33 (−/−)

−3.94 (−/−)

−3.70 (−/−)

−3.43 (−/−)

M062X/6-31G*(vac) (DFT1)

−12.23 (2.12/0.59)

−4.84 (1.11/0.45)

−4.86 (1.31/0.43)

−4.39 (1.85/0.53)

M062X/6-31G*a (DFT2)

−9.23 (3.13/0.54)

−3.84 (1.01/0.47)

3.79 (0.65/0.53)

−3.81 (1.31/0.52)

M062X/6-31G*b (DFT3)

−9.96 (2.37/0.37)

4.07 (0.78/0.47)

−4.05 (0.68/0.49)

3.82 (1.22/0.49)

M062X/6-31+G*a (DFT4)

−7.24 (4.78/0.76)

−3.22 (1.25/0.45)

−2.80 (1.18/0.43)

−2.91 (1.33/0.47)

ωB97XD/6-31G*(vac) (DFT5)

−12.46 (2.20/0.42)

−5.37 (1.52/0.42)

−5.20 (1.58/0.51)

−3.98 (1.72/0.53)

ωB97XD/6-31G*a (DFT6)

−9.37 (2.88/0.50)

−4.30 (1.38/0.64)

−4.01 (0.74/0.41)

−3.43 (1.25/0.55)

ωB97XD/6-31G*b (DFT7)

10.24 (2.06/0.34)

−4.61 (1.28/0.46)

−4.34 (0.86/0.40)

−3.53 (1.35/0.56)

B3LYP/6-31G*a (DFT8)

−6.76 (5.10/0.57)

0.23 (5.06/0.64)

−0.85 (3.09/0.60)

−2.23 (2.04/0.65)

B3LYP-D3/6-31G*a (DFT9)

−8.94 (3.30/0.58)

−3.88 (1.32/0.42)

−3.74 (0.67/0.66)

−4.16 (1.24/0.57)

PBE/6-31G*a (DFT10)

−8.27 (3.94/0.59)

−0.68 (4.08/0.55)

−1.72 (2.27/0.79)

−3.22 (1.80/0.56)

PBE-D3/6-31G*a (DFT11)

−9.75 (2.99/0.59)

−3.54 (1.76/0.57)

−3.74 (0.70/0.58)

−4.45 (1.66/0.60)

  1. The best results are shown in italics
  2. vacThe calculations are performed in vacuum
  3. aThe solvent is set as water (ε = 78.35)
  4. bThe solvent is set as pentylamine (ε = 4.20), which possess a similar dielectric constant as the protein environment (ε ~4.0)
  5. cThe RMSE after the GRNN correction