Structure and Bonding in π-Stacked Perylenes: The Impact of Charge on Pancake Bonding

Perylene (PER) is a prototype of polycyclic aromatic hydrocarbons (PAHs), which play a pivotal role in various functional and electronic materials due to favorable molecule-to-molecule overlaps, which enhance electronic transport. This study provides guidelines regarding the impact of molecular charge on pancake bonding, a form of strong π-stacking interaction. Pancake bonding significantly boosts interaction energies within the monopositive dimer ([(C20H12)2]•+ or PER2+), crucial for stabilizing aggregation and crystal formation. We discovered energetically feasible sliding and rotation pathways within the [(C20H12)2]•+ dimer, connecting different configurations found in the Cambridge Structural Database (CSD). The dimer’s charge profoundly influences the pancake bond order (PBO) and the strength and structural preferences of pancake bonding. The most stable configuration is found in the monocationic state (PER2+), featuring a pancake bond order of 1/2 with one-electron multicenter bonding (1e/mc) with similar characteristics for charge −1. Increasing the total charge of the dimer to +2 or −2 leads to an unstable local minimum. Diverse distribution of pancake bonding types present in crystal structures is interpreted with modeling based on dimer computations with varying charges.


Selection of the DFT method
There is a wide selection of high-level quantum chemical methods and DFTs available for describing pancake bonded aggregates.In this work we opted for M05-2X/6-311G(d), a method that includes some dispersion effects. 1 This choice is based on a previous in-depth analysis of four pancake-bonded π-dimers. 2The results of this study consistently demonstrated that the M05-2X outperformed other modern DFT functional when compared to the highly accurate multi reference average quadratic coupled cluster MR-AQCC method. 3This evaluation of more than 50 contemporary DFT functionals, including those incorporating dispersion correction, for the pancake-bonded dimers consistently confirmed that M05-2X exhibited the lowest error in terms of optimized geometry, interaction energy, and a few other parameters.
In response to a reviewer's suggestion, we are presenting the impact of including D3 dispersion terms 4 on our results, particularly on binding energies and optimized geometries.Upon comparing the interaction energies for different types of charged dimers, we observed that the additional D3 correction led to larger (more negative) interaction energies by approximately 6.0 kcal/mol for most dimers as listed below.The relatively large interaction energy for the uncharged (vdW) dimers at ~20 kcal/mol is exaggerated further justifying the theory without the D3 terms in this application.
Concerning the optimized geometries, the differences between the two methods (without and with the D3 terms) are small and are slightly longer with the D3 terms included, in agreement with Ref. 1 .These data are summarized in the two tables below.None of the conclusions are affected by the inclusion of the D3 term.
Table S3: Optimized intermolecular carbon-carbon (CC) short contacts in angstroms (Å) for Atype perylene dimers obtained using M05-2X/6-311G(d) and M05-2X-D3/6-311G(d). , Z Avg : average of overlapping carbons) Z O : an alternative measure of the characteristic interlayer distance was determined based on Scheme 3 in the main text.We used Mercury (part of the CSD program package) to determine a centroid of the center ring of one perylene to act as the origin and measured the distance between that and the neighboring perylene.

3D reaction path
The full reaction path is shown Figure S5 3.Only structures with an R-factor of less than 4% are included in this graph.The charge assignment of ¼ and ¾ in ECINAF (2(C 20 H 12 + ), 3(C 20 H 12 ), Mo 6 O 19 2 ) has been replaced by a charge assignment of ½ and ½ compared to the data in Figure 9 and Table 3.

Charge effects on the number of unpaired electrons
An alternative assessment of the strength of pancake bonding in charged perylene dimers was considering for explaining the reduced interaction energy in the q=-1 dimers compared to the q=+1 dimers based on the fractional occupation number weighted electron density (FOD) values. 25These were computed using the ORCA software package 26 with B3LYP/def2-TZVP.Computations were based on the geometries reported at the end of this ESI document.There is a good correlation between the N_FOD index and other measures of the number of unpaired electrons. 27type  1) dimer] There is a systematic increase of the N_FOD values, measuring the number of unpaired electrons for the q=-1 dimers compared to the q=+1 dimers.An increase in the number of unpaired electrons implies a weaker pancake bonding, and this is indeed in line with the computed pancake bond strengths.It is difficult, however, to translate the number of unpaired electrons into a strength of interaction, and for this reason, the FOD based observations should be considered only as a qualitative trend.

Periodic boundary condition computations
In order to further validate our dimer-based modeling, at the suggestion of a reviewer, we performed periodic boundary condition computations.Such full computations for crystals are very expensive in terms of computational resources when the unit cells are as large as many of the perylene structures analyzed in this work.However, a few examples are presented below complementing the previously presented results.
For XIWQON (Formula: [(C 20 H 12 ) 2 ] + (SbCl 6 )  ), the crystal serves as an ideal comparison to the isolated dimer modeling.The unit cell contains an isolated perylene dimer with a total formal charge (q) of +1.Through periodic boundary condition calculations 28 using the PBE functional with kinetic energy cut-off of 70 Ry and norm-conserving pseudopotentials, we have verified that the HOMO-1 orbital exhibits intermolecular orbital overlap, playing a key role in the formation of the pancake bond, (see Figure S15) akin to the isolated dimer presented in the manuscript.Additionally, we conducted Bader charge computations 29 for the perylenes, reinforcing our conclusion of an equal charge share between the two perylenes in the dimer.
Conversely, the unit cell for ECINEJ is more intricate, comprising five perylenes and one metaloxo cluster as the counter anion.Direct comparison with the isolated dimer is challenging.Nevertheless, the orbitals exhibit distinct pancake bonding in the occupied orbital.Specifically, HOMO-2, HOMO-3, and HOMO-4 orbitals clearly reveal characteristic intermolecular overlaps of different types of pancake interactions ( Type A, C) within the unit cell (see Figure S16).Bader charge computations for each perylene indicate that two perylenes carry approximately +0.75e each, two perylenes possess approximately +0.5e charge each, and one perylene has approximately +0.2e charge (Figure S17).These charge distributions align well with our assigned values as shown in the small tables below.Given the highly approximate nature of any charge definition, the agreement is excellent for both crystals between the quantum mechanically computed Bader charges, and the charges assigned in the main text based on the BLA-charge correlation represented in Figure 2. It is clear that in a crystal computation some of the charges are assigned to the intermolecular space that is assigned fully to the molecules and counterions in the molecular model.

Assessment of aromaticity by HOMA
As suggested by a reviewer, we also calculated the Harmonic Oscillator Measure of Aromaticity (HOMA) index to assess aromaticity changes in the charged dimers. 30,31 s shown in Table S7, the HOMA index is slightly higher in the mono-cationic dimers, contributing to their enhanced stability.We observe the same trend such that pancake bonding enhances the overall aromaticity as measured by the HOMA index.

QTAIM analysis
In response to a reviewers recommendations, we have undertaken QTAIM analysis 32 for A-type dimers with total charges of +1, 0, and -1 to discern any trends.These are listed in Tables S9, S10, and S11 using the Multiwfn code. 33Due to the multicenter nature of pancake bonding, each individual bond listed in the table contributes to the overall interaction.Each contribution is small as expected, given the relatively large (compared to covalent bonds) distances and small electron densities.However, it is worth noting that QTAIM analysis does not contribute significantly to distinguishing the nature of the pancake bonding interaction in our systems.

Local vibrational mode force constant analysis
Following the reviewer's recommendation, we employed a local vibrational mode force constant analysis using the LMode-nano code 34,35 to calculate Local Stretching Force Constants (LSFC).In this analysis, we computed the local force constants for all CC short contacts of and , as detailed in Table S12 below.The table reveals that the [ 20  12 ] +1/ -1  [ 20  12 ] +1/ -1  CC force constants for negatively charged dimers are slightly larger compared to positive dimers.Consequently, the higher interaction energies in mono-cationic dimers stem from other contributing factors.
free energy of interaction (G Int ), interaction enthalpy (H Int ), and entropy change for the dimerization (S Int ) of the dimers.

Figure
Figure S4.a) Molecular orbital diagram in for [(C 20 H 12 ) 2 ] D + , an intermediate characterized in the potential energy surface in the Figures 5 in the main text and Figure S5.b) HOMO-1 and HOMO orbitals for the same.
incorporates all three parameters ΔX, ΔY, and θ together.The gray line and gray points illustrate the change in the relative orientation of perylene molecules, passing through the unique orange points representing the TSs.Throughout the transition from A to B, the path stays on the XY plane.However, when transitioning from an Atype dimer to a C-type dimer, the process becomes more intricate as θ starts to deviate from zero.This transformation necessitates both the translation and rotation of one perylene molecule over another.The journey begins from [(C 20 H 12 ) 2 ] A + (X=0.31Å,Y=1.15Å,=0.0) to [(C 20 H 12 ) 2 ] C + (X=0.0Å, Y=0.0Å,  =41.7) via an intermediate D((X=0.5 Å, Y=0.0Å,  =12.1).The most notable changes in θ occur during the transformation from D to C, where the θ value ultimately reaches 41.7° in the resulting C-type dimer.A movie depicting the complete transformation along the reaction path is provided in the supporting information.

Figure S5 .
Figure S5.Optimized X, Y, and θ values of +1 charged perylene dimers.Grey points and the grey connecting line indicate the transformation pathway from the optimized structure of [(C 20 H 12 ) 2 ] A + (A) to that of [(C 20 H 12 ) 2 ] B + (B) and [(C 20 H 12 ) 2 ] C + (C) through the three transition structures and one intermediated (D).

Figure S6 .
Figure S6.Spin density plot of transition states, discussed in connection with Figure 5 in the main text.

Figure
Figure S7.a) Optimized X and Y values of monocationic dimers and compared with those from the crystal structures by McCormack et al. 5 and Rosokha et al. 11 and after the DFT optimization for perylene dimers, with q=+1 total charge on the dimer.Grey points and the grey connecting line indicate the transformation pathway from the optimized structure of [(C 20 H 12 ) 2 ] A + (A) to that of [(C 20 H 12 ) 2 ] B + (B) through the transition structure, [TS] AB + .b) Optimized X and Y values for perylene dimers possessing total charges other than +1.The black points correspond to optimizations initiated from [(C 20 H 12 ) 2 ] A q whereas the red points represent optimized structures initiated from [(C 20 H 12 ) 2 ] B q .The green markers represent the XRD structure of neutral perylene dimers (CSD refcode PERLEN05) by Botoshansky et al.24

Figure S13 .
Figure S13.Correlation between assigned charges (Q) and experimentally determined BLA from the literature, as listed in Table3.Only structures with an R-factor of less than 4% are included in this graph.The charge assignment of ¼ and ¾ in ECINAF (2(C 20 H 12 + ), 3(C 20 H 12 ), Mo 6 O 19 2 ) has been replaced by a charge assignment of ½ and ½ compared to the data in Figure9and Table3.
a PCB parameters (if several, only the shortest are shown) X, Y, and Z.

Table S5 .
BLA values and assigned cationic perylene charges from six crystal structures from the Cambridge Structural Database (CSD) with large disorder.

Table S6 .
BLA values and assigned charges for nine anionic perylene crystal structures from the

Table S8 :
Harmonic Oscillator Measure of Aromaticity (HOMA) index of dimers at various charges.

Table S12 :
Local mode force constants, of CC bonds involved in pancake bonding.
() Optimized Coordinates (in Å) are provided as a separate XYZ file.