Introduction opposite within 1 3 σ 1 2 4 16 17 22 17 22 22 −1 −1 23 27 28 29 30 potential 30 4 31 32 12 33 2 3 34 35 36 37 Methods Computational details 38 49 40 p d d f s p d f g 42 43 44 41 45 1 3 post-SCF −1 46 Stacking distances (vertical separation) and orientations (twist angle) were explored with the various density functionals through scans of the potential energy surface (PES) in which the BP86 geometries of the monomers (e.g., DNA bases or Watson–Crick base pairs) were kept frozen. PES scans as a function of the twist angle (see below) were done using steps of 30° in case of homo-base stacks, 60° in the case of hetero-base stacks and 36° for stacks of Watson–Crick base pairs. PES scans as a function of the vertical separation (see below) were done in steps of 0.1 Å. 1 Scheme 1 TW  In the stacked DNA systems, the twist angle of 0° is defined as that twist angle at which the respective “glycosidic” N-H bonds (more precisely, the N-H bonds that replace the glycosidic N-C bonds to the sugar in the backbone) are oriented in parallel. Bond-energy decomposition E 36 1 1 \documentclass[12pt]{minimal}
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\begin{document}$$\Delta E = \Delta E_{{{\text{prep}}}}  + \Delta E_{{\operatorname{int} }} $$\end{document} E prep E int 47 2 2 \documentclass[12pt]{minimal}
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\begin{document}$$\Delta E_{{\operatorname{int} }}  = \Delta V_{{{\text{elstat}}}}  + \Delta E_{{{\text{Pauli}}}}  + \Delta E_{{{\text{oi}}}} $$\end{document} V elstat E Pauli E oi i.e. 3 48 49 3 \documentclass[12pt]{minimal}
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\begin{document}$$\Delta E_{{{\text{oi}}}}  = \sum _{\Gamma } {\text{ }}\Delta E_{\Gamma } $$\end{document} Results and discussion 50 6 5 2 3 2 2 21 3 14 17 19 22 4 Scheme 2 Stack of substituted benzene and pyridine  Scheme 3 21 bold black dot  Scheme 4 bold black dot  6h 51 1 −1 1 −1 1 −1 −1 1 Table 1 −1 vert a *b vert 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 a Computational details b [51 Reference data from Mignon and co-workers 2 50 2 43 −1 52 53 −1 2 −1 2 12 −1 2 −1 Table 2 −1 2 a b X= b LDA KT1 KT2 BHandH PW91 BLYP BP86 OLYP B3LYP X3LYP H −2.8 −3.4 −3.4 −3.2 −2.7 2.3 6.1 4.6 11.1 5.0 4.1 F −2.9 −3.4 −3.3 −3.2 −2.8 2.5 6.4 4.9 11.5 5.1 4.2 2 −3.2 −3.6 −3.6 −3.3 −3.0 2.2 6.1 4.7 11.2 4.9 3.9 Cl −3.4 −3.4 −3.4 −3.2 −2.8 2.6 6.7 5.1 11.9 5.4 4.4 3 −3.3 −3.3 −3.4 −3.2 −2.8 1.2 4.5 3.5 8.7 3.5 2.7 OH −2.7 −3.2 −3.1 −3.0 −2.5 2.8 6.8 5.2 11.9 5.5 4.6 CN −4.1 −3.9 −3.9 −3.7 −3.5 0.9 4.2 3.1 8.4 3.1 2.3 COOH −3.5 −3.6 −3.6 −3.4 −3.0 2.4 6.4 4.8 11.5 5.1 4.2 CHO −3.9 −3.8 −3.8 −3.6 −3.3 0.9 4.2 3.2 8.4 3.2 2.4 2 −3.8 −3.8 −3.7 −3.6 −3.3 2.0 5.8 4.3 10.8 4.6 3.7 MAD c  0.26 0.25 0.24 0.39 5.33 9.07 7.68 13.90 7.89 6.99 a Computational details b 50 c −1 Reference data from Jurecka and co-workers 3 21 3 −1 3 −1 −1 3 Table 3 −1 3 a,b orientation b,c b,d LDA KT1 KT2 BHandH PW91 BLYP BP86 OLYP B3LYP X3LYP 1 2.2 2.5 2.7 2.3 2.7 3.9 8.0 11.7 10.9 16.5 10.9 9.9 2 −3.1 −3.8 −3.7 −3.9 −3.5 −3.3 2.6 6.5 5.4 12.3 5.2 4.1 3 −7.2 −8.9 −8.8 −8.7 −8.3 −9.0 −2.1 1.7 0.7 8.0 0.2 −1.0 4 −8.3 −9.9 −9.4 −9.2 −8.9 −10.1 −2.9 0.8 −0.1 6.9 −0.9 −2.1 5 0.2 0.3 0.6 0.1 0.6 1.5 6.4 10.3 9.3 15.7 9.3 8.3 6 0.5 0.6 0.8 0.4 0.8 1.8 6.8 10.8 9.7 16.3 9.8 8.8 7 −0.5 −1.0 −0.7 −0.9 −0.6 0.2 2.8 5.5 5.2 8.7 5.0 4.2 8 −7.3 −9.1 −8.4 −8.3 −7.9 −8.8 −3.0 0.2 −0.2 5.6 −1.2 −2.2 9 −7.6 −9.1 −8.7 −8.5 −8.2 −9.4 −2.3 1.5 0.5 7.3 −0.2 −1.4 10 −6.6 −8.3 −7.9 −7.7 −7.5 −8.3 −1.8 1.8 0.9 7.6 0.3 −0.8 11 −7.6 −9.4 −8.8 −8.5 −8.3 −9.5 −2.8 0.6 −0.1 6.2 −1.0 −2.1 12 −5.5 −7.4 −6.7 −6.6 −6.2 −7.0 −3.6 −1.6 −1.4 1.5 −2.4 −3.1 13 −7.4 −8.8 −8.3 −8.1 −7.9 −8.6 −3.0 0.4 −0.4 5.2 −1.0 −2.0 14 −7.0 −9.1 −8.8 −8.7 −8.4 −9.4 −2.1 1.6 0.7 8.0 −0.1 −1.3  MAD1 e  0.94 0.81 0.60 1.49 4.87 8.35 7.58 13.63 7.06 6.03  MAD2 f  0.38 0.47 0.72 0.52 6.04 9.52 8.75 14.80 8.24 7.21 a Computational details b 21 c d e −1 f −1 Reference data from Wu and Yang 14 1 22 4 19 1 2 3 1 Supporting Information trends and qualitative features Fig. 1 −1 thick lines with filled circles, triangles, squares and diamonds dashed lines open squares, triangles and diamonds bold line with crosses  2 2 Fig. 2 −1 red, blue  green lines bold line with crosses  3 −1 Fig. 3 −1 thick lines with filled triangles, squares and diamonds dashed lines with open squares, triangles and diamonds red, blue, green and orange lines black line with crosses  Decomposition of interaction energy E int V elstat E Pauli E oi Methods 4 −1 −1 −1 −1 E Pauli E oi V elstat E Pauli V elstat −1 4 Table 4 a −1   A-A C-C G-G T-T U-U Twist angle 0 (TW, R vert ) (0 , 3.3 Å) (0 , 3.4 Å) (0 , 3.4 Å) (0 , 3.3 Å) (0 , 3.3 Å) E Pauli 5.35 2.43 2.13 11.00 3.72 V elstat −3.31 1.80 1.97 −2.48 −0.07 E oi −2.30 −1.88 −2.49 −5.66 −2.11 E int −0.26 2.35 1.61 2.86 1.54 Lowest energy conformation (TW, R vert ) (180 , 3.2 Å) (180 , 3.1 Å) (180 , 3.2 Å) (180 , 3.3 Å) (180 , 3.1 Å) E Pauli 5.86 7.01 4.52 4.28 6.13 V elstat −8.72 −11.32 −8.33 −9.04 −8.38 E oi −4.17 −5.12 −4.80 −3.58 −4.12 E int −7.02 −9.44 −8.61 −8.34 −6.36 a Computational details Additivity of interaction energies of stacked base pair dimers stacked dimers of hydrogen-bonded base pairs 5 54 55 5 Scheme 5 dot 54  E int 6 E add 4a b 4a \documentclass[12pt]{minimal}
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\begin{document}$$\Delta E_{{{\text{add}}}}  = \Delta E_{{{\text{AC}}}}  + \Delta E_{{{\text{BD}}}}  + \Delta E_{{{\text{AD}}}}  + \Delta E_{{{\text{BD}}}} $$\end{document} 4b \documentclass[12pt]{minimal}
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\begin{document}$$\Delta E_{{\operatorname{int} }}  = \Delta E_{{{\text{add}}}}  + \Delta E_{{{\text{coop}}}} $$\end{document} Scheme 6 Additivity approximation for the π-π interaction between two stacked Watson-Crick base pairs in terms of pairwise interactions between individual bases  E coop E add E int 5 E add E int E coop E add E int E coop E int E coop −1 E int −1 5 E coop −1 changes E coop E int Table 5 −1 a,b System TW E AC E BD E AD E BC E add E coop E int AT-AT 0 −1.23 +1.26 −1.24 −1.24 −2.45 +1.04 −1.41 AT-AT 36 −5.27 −3.93 −1.11 −0.93 −11.24 +1.11 −10.13 AT-AT 180 −1.84 +0.39 −5.44 −5.44 −12.33 +1.62 −10.71 AU-AU 0 −1.23 +0.94 −1.37 −1.37 −3.03 +1.17 −1.86 AU-AU 36 −5.27 −3.00 −1.20 −1.08 −10.55 +1.20 −9.35 AU-AU 180 −1.84 +0.28 −4.67 −4.67 −10.90 +1.73 −9.17 GC-GC 0 +2.15 +2.83 −4.90 −4.90 −4.82 +4.42 −0.40 GC-GC 36 −2.08 −1.32 −3.44 −4.71 −11.55 +3.92 −7.63 GC-GC 180 −7.59 −2.60 −1.52 −1.52 −13.23 +1.98 −11.25 a 6 \documentclass[12pt]{minimal}
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\begin{document}$$\Delta E_{{{\text{add}}}}  = \Delta E_{{{\text{A:C}}}}  + \Delta E_{{{\text{B:D}}}}  + \Delta E_{{{\text{A:D}}}}  + \Delta E_{{{\text{B:C}}}} ,\,\Delta E_{{{\text{coop}}}}  = {\text{ }}\Delta E_{{\operatorname{int} }}  - \Delta E_{{{\text{add}}}} .$$\end{document} b −1 add −1 −1 −1 −1 −1 −1 −1 −1 5 Significance of the observed trends for the structure of DNA 3 classical electrostatic component Conclusions We have analyzed π-π stacking interactions between two benzenes or benzene analogs, between two DNA bases, and between two Watson-Crick base pairs using Density Functional Theory (DFT) in combination with large basis sets. The interaction energies for a large number of density functionals have been compared with ab initio reference data. In line with previous studies, most standard density functionals recover, at best, only part of the favorable stacking interactions. 33 To gain insight into the origin of π-π stacking interactions, we have decomposed the interaction energies into the classical electrostatic attraction, Pauli repulsion and orbital interactions. Interestingly, the electrostatic interactions appear to be the most important factor that determines the shape and depth of the PES. In the case of two stacked Watson-Crick base pairs, this classical electrostatic attraction causes a minimum to occur along the energy profile at a twist angle of 36°. Furthermore, the stabilizing contributions to the stacking interaction between two Watson-Crick base pairs is shown to originate from the inter-strand stacking terms, that is, from the interaction between two bases that are in different Watson-Crick pairs and also not directly stacked on top of each other. 56 Electronic supplementary material Below is the link to the electronic supplementary material.
 Supporting Information Energy profiles for various π-π stacked systems as a function of the twist angle and the vertical separation computed with MP2 and various density functionals (PDF 1.90 mb)