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Table 1 Stacking energy (in kcal mol−1) of the benzene-benzene complex as a function of the vertical separation Rvert (in Å), computed with various density functionalsa and CCSD(T)/aug-cc-pVQZ*b

From: π-π stacking tackled with density functional theory

Rvert CCSD(T)b LDA KT1 KT2 BHandH PW91 BLYP BP86 OLYP B3LYP X3LYP
2.9   13.53 14.59 14.08 17.08 24.41 31.63 27.46 38.67 30.13 28.92
3.0   8.60 9.29 9.04 11.27 17.98 24.20 20.84 30.93 22.78 21.65
3.1   5.11 5.52 5.47 7.13 13.18 18.53 15.87 24.85 17.23 16.17
3.2 3.71 2.70 2.90 2.98 4.23 9.60 14.22 12.14 20.05 13.04 12.06
3.3 1.68 1.06 1.10 1.29 2.24 6.93 10.94 9.34 16.22 9.89 8.98
3.4 0.30 −0.01 −0.09 0.17 0.92 4.95 8.45 7.25 13.14 7.52 6.68
3.5 −0.62 −0.68 −0.83 −0.54 0.06 3.48 6.55 5.68 10.65 5.73 4.96
3.6 −1.19 −1.07 −1.27 −0.96 −0.45 2.40 5.10 4.50 8.63 4.40 3.69
3.7 −1.51 −1.27 −1.50 −1.17 −0.74 1.59 3.99 3.62 6.98 3.39 2.74
3.8 −1.66 −1.33 −1.58 −1.25 −0.86 1.00 3.15 2.94 5.62 2.63 2.04
3.9 −1.70 −1.31 −1.56 −1.25 −0.89 0.57 2.50 2.43 4.51 2.06 1.52
4.0 −1.67 −1.24 −1.48 −1.18 −0.85 0.25 2.00 2.03 3.60 1.63 1.14
4.1 −1.58 −1.13 −1.37 −1.09 −0.78 0.02 1.61 1.72 2.85 1.30 0.85
4.2 −1.46 −1.02 −1.24 −0.98 −0.68 −0.15 1.31 1.47 2.24 1.05 0.64
4.3   −0.90 −1.11 −0.86 −0.58 −0.27 1.07 1.27 1.75 0.86 0.49
4.4   −0.78 −0.97 −0.75 −0.48 −0.36 0.88 1.11 1.35 0.71 0.37
4.5 −1.08 −0.67 −0.85 −0.64 −0.39 −0.42 0.73 0.97 1.03 0.59 0.28
5.0 −0.58 −0.28 −0.39 −0.26 −0.06 −0.45 0.30 0.52 0.20 0.26 0.09
5.5 −0.27 −0.09 −0.15 −0.07 0.08 −0.31 0.13 0.28 0.00 0.14 0.04
6.0 −0.11 −0.01 −0.05 0.00 0.12 −0.16 0.05 0.15 −0.03 0.08 0.03
6.5 −0.04 0.02 0.00 0.03 0.12 −0.06 0.02 0.08 −0.03 0.05 0.03
7.0   0.03 0.02 0.04 0.11 −0.01 0.00 0.05 −0.01 0.04 0.03
7.5   0.03 0.02 0.04 0.09 0.02 0.00 0.03 −0.01 0.03 0.03
8.0   0.03 0.02 0.09 0.08 0.01 −0.01 0.02 0.00 0.02 0.02
  1. aPost-SCF using LDA/TZ2P orbitals and densities, see Computational details
  2. bFrom supporting information of [51]