Double Pancake Bonds: Pushing the Limits of Strong π–π Stacking Interactions

The concept of a double-bonded pancake bonding mechanism is introduced to explain the extremely short π–π stacking contacts in dimers of dithiatriazines. While ordinary single pancake bonds occur between radicals and already display significantly shorter interatomic distances in comparison to van der Waals (vdW) contacts, the double-bonded pancake dimer is based on diradicaloid or antiaromatic molecules and exhibits even shorter and stronger intermolecular bonds that breach into the range of extremely stretched single bonds in terms of bond distances and binding energies. These properties give rise to promising possibilities in the design of new materials with high electrical conductivity and for the field of spintronics. The analysis of the double pancake bond is based on cutting edge electron correlation theory combining multireference (nondynamical) effects and dispersion (dynamical) contributions in a balanced way providing accurate interaction energies and distributions of unpaired spins. It is also shown that the present examples do not stand isolated but that similar mechanisms operate in several analogous nonradical molecular systems to form double-bonded π-stacking pancake dimers. We report on the amazing properties of a new type of stacking interaction mechanism between π conjugated molecules in the form of a “double pancake bond” which breaks the record for short intermolecular distances and provides formidable strength for some π–π stacking interactions.


S. I. Computational Methods
All CASSCF and MR-AQCC calculations were carried out with the COLUMBUS program package 1 with analytic MR-AQCC energy gradients computed using the procedures developed in refs. 2 The 6-311++G(2d,2p) basis set 3 has been used in the geometrical and potential energy surface (PES) calculations in this work except were indicated otherwise. In addition to single state CASSCF approach, state averaged (SA) CASSCF (4,4) calculations have been performed on the triplet state which was dominated by two main configurations Φ 1 =|…a 1 2 b 1 1 a 2 1 b 2 0 | and Φ 2 =|…b 1 2 a 1 1 b 2 1 a 2 0 |. The atomic orbital (AO) integrals and AO gradient integrals have been computed with program modules taken from DALTON. 4 Full geometry optimizations were performed within given molecular symmetries in natural internal coordinates using the GDIIS method. 5

S2
The unrestricted density functional theory (UDFT) calculations (UB3LYP with GD3BJ 6 under all circumstances in this work and UM06-2X) based on the broken symmetry (BS) 7 approach were performed using the Gaussian 09 package. 8

S. II. Validation and convergency of computational modeling
MR-AQCC theory is not exactly size consistent. We performed a test, accordingly: E(monomer)*2 -E(dimer, D=10 Å) = 0.42 kcal/mol. This difference is acceptable for the purposes of this work.
The geometries of the π dimers of 1,3,2,4,6-dithiatriazine (4 2 ) and phenyl-substituted dithiatriazine (5 2 ) have been fully optimized by UM06-2X and UB3LYP methods using the 6-311++G(2d,2p) basis set. All vibrational frequencies are real at the minimum. As shown in Table   S1, the structural predictions of the UM06-2X and UB3LYP levels are in good agreement with the experimental crystal structures for the phenyl-substituted π dimer. The intermolecular distances are slightly shorter in 4 2 relative to 5 2 because the phenyl groups are repelling each other in 5 2 . These geometry differences are minor and validate the use of 4 2 as a reasonable model for the phenyl-dithiatriazine π dimer.
S3 Table S1. Comparison of the structures of 4 2 and 5 2 π dimers as obtained at the UB3LYP and UM06-2X level with 6-311++G(2d,2p) basis set and X-ray diffraction. N′ represents the terminal N atom in each monomer.

Methods System
Intermolecular Distances (Å) Further tests to the effects of basis sets on the binding energy are shown in Table S2. The binding energy increases significantly along with increasing the number of polarization functions. In summary, a double d polarization set is necessary for sulfur in these pancake bonded π-stacking dimers. Table S2. Computed binding energy values for the dithiatriazine (HCN 3 S 2 ) 2 π-dimers with C 2v symmetry. The interaction energy (E int ) was obtained by equation (S1). All data correspond to optimized geometries at the basis set level given except for those indicated.
The optimized geometries of the singlet and triplet states of 4 were obtained at the MR-AQCC(2,2)/6-311++G(d,p) level. Key data are summarized in Figure S2 and Table S3.
Both singlet and triplet states have C s symmetry with a planar structure for singlet and nonplanar structure for triplet where the mirror plane includes the CH group and the para nitrogen. The system being antiaromatic, the singlet has an unsymmetrical distribution of bond distances. The monomer in the π dimer is similar to the triplet aromatic-type geometry as shown in Table S3. The monomer has not been isolated so far. We define the interaction energy based on equation (S1). This equation will overestimate the interaction energy compared to the one based on a relaxed scan. However, this approach permits the decomposition of the interaction