Bond orders for intermolecular interactions in crystals: charge transfer, ionicity and the effect on intramolecular bonds

Roby–Gould bond orders for intermolecular interactions such as hydrogen bonds, halogen bonds and chalcogen bonds in molecular crystals have been explored. Bond-order values place these interactions on a scale representing their relative strengths, in conjunction with a chemist’s notion of bonds.

: Atom· · · atom and molecule· · · molecule Roby-Gould bond indices, covalent index (c), ionic index (i), and total bond index (τ ), for hydrogen bonds (D−H · · · A, D= C, N, O, A= N, O). The distances d and the inter-penetration of van der Waals spheres (∆d) are given in Angstrom (Å). The single and multipliable contact interactions in dimers are marked with superscript s and m ( and m * for two identical interactions within one dimer). S2 Atom· · · atom ionic index versus molecule· · · molecule ionic index

S3 Hirshfeld atom charges
In this section we present the values of Hirshfeld atom charges in atomic unit (a.u.), which represents the partial charges of atoms in monomers and dimers. Charges are given for atoms X and A involved in in the hydrogen bonds (Table S3), halogen bonds (Table S4), and chalcogen bonds (Table S5). The difference in Hirshfeld charges for atoms X and A from monomer upon dimer formation are given as ∆q.  Table S4: Hirshfeld charges of atoms involved in halogen bonds and the charge transfer due to intermolecular interactions. Table S5: Hirshfeld charges of atoms involved in chalcogen bonds and the charge transfer due to intermolecular interactions.

S4 Interaction energies for hydrogen bonds, halogen bonds and chalcogen bonds
In this section we present the values of interaction energies in kcal/mol for the hydrogen bonds (Table S6), halogen bonds (Table S7), and chalcogen bonds (Table S8). Interaction energies were calculated at M062x/Def2TZVP level. The atomic and molecular Roby-Gould bond indices are also given.   S5 Testing the conservation of Roby-Gould bond bond order Table S9: Total (D−X) and (A · · · X) atom· · · atom Roby-Gould bond indices (τ ) for 15 selected dimers and corresponding monomers (τ (D−X) and τ (A · · · X) respectively). The sum of the D−X and A · · · X bond indices in dimers (τ (D−A + A · · · X) Dimer ) and the differences in D−X bond index between dimers and monomers (τ (∆ D−X )) are also given. Wavefunctions optimized at the M062x/Def2SVP level.

S6 The angle dependence of RGBI values
Two angles are most important in the discussion of the angle dependence of bond orders of a D−X · · · A intermolecular interaction, (i) D−X · · · A angle (ii) X · · · A−C angle. Among these, D−X · · · A angle is more significant as a nearly 180 D−X · · · A angle is directly linked to the effective n → σ * interaction. To test these we calculated and plotted the bond indices, total, covalent and ionic bond indices along with the AIM topological parameters at the bond critical points for a selected subset of interactions with N atom as the lone pair donor or bond acceptor (Table S10 and Figure S1). We find that these results are insufficient to show the directional sensitivity of RGBIs as compared to AIM topology. We have plotted total, covalent and ionic RGBIs for a subset of halogen and chalcogen bonded complexes versus D−X · · · A angle ( Figure  S1). No clear correlation could be found between these descriptors and the D−X · · · A angle. It may also be noted that more complicated interaction angles around atom A and its hybridization state (as it is related to lone pair directionality) can also affect bond orders. The wide range of bond order values for interaction types such as XBs and YBs may be due to a variety of reasons and the bond angle directionality is only one of them. Chemical environment around the X and A atoms involved in the interaction, the partial charges of atoms A and X (even in monomer state) etc can influence the bond order values. However, we performed similar analysis on the hypothetical geometries for molecular dimers varying the interaction angles for the linear structures N C C C Br and N C C C Cl (CSD codes: BCACEN, and CCACEN respectively) which exhibit Br · · · N and Cl · · · N interactions. This analysis clearly brings out the differences in angle dependent trends in RGBIs vs AIM topological parameters.
Table S10: The angle dependence of total (τ ), covalent (c), and ionic (i) Roby-Gould bond indices, and AIM topological parameters of a D−X · · · A intermolecular interaction with respect to D−X · · · A angle for a selected set of halogen and chalcogen bonded dimers. The distance (inÅ) and EML interaction energy (in kJ/mol) are also given.  Figure S1: The angle dependence of total (τ ), covalent (c), and ionic (i) Roby-Gould bond indices and AIM topological parameters of a D−X · · · A intermolecular interaction with respect to D−X · · · A angle for a selected set of halogen and chalcogen bonded dimers given in the Table S10.
S7 Percentage of covalency Figure S2 shows bond order-weighted average covalency percentages (%c W ) for atom· · · atom (light blue) and molecul· · · molecule bond indices (dark blue) for hydrogen, halogen and chalcogen bonds. For each interaction type, the average weighted covalency percentages were calculate using the formula: where τ i and %c i are the bond orders and percentage covalency of each interaction under XB, YB and HB. Figure S2: Bond order-weighted average covalency percentages (%c W ) for atom· · · atom (light blue) and molecul· · · molecule bond indices (dark blue) for hydrogen, halogen and chalcogen bonds. Number of interactions and molecular dimers studied for each type are given in parentheses.

S8 Molecular structures of selected dimers
In this section we present the molecular structures of all dimers considered in this study with the hydrogen bonds, halogen bonds and chalcogen bonds. The distances in Angstrom are given for only those interactions concerned in this study.
These figures were generated from the crystallographic information files (CIF) in the Cambridge Crystallographic Structure Database (CSD) using CrystalExplorer program.
Please note that the molecular structures of all dimers are listed according to the same order where their CSD codes are listed in the Tables 2, 3 and S1.
The atoms of each dimer are labeled with different colored spheres. as follows: • Hydrogen atom: yellow (small ball).

S8.1 Hydrogen bonds
S8.1.1 C−H · · · N interaction Figure S3: The molecular structure of CYACHZ01 s . Figure S4: The molecular structure of DMSDIM01 s . Figure S5: The molecular structure of MEADEN02 s . Figure S6: The molecular structure of TRAZOL02 s . Figure S7: The molecular structure of BUGKIX01 s . Figure S8: The molecular structure of BUGKIX01 s . Figure S9: The molecular structure of CYACHZ01 m . Figure S10: The molecular structure of NURWOM02 m * . Figure S11: The molecular structure of NURWOM02 m . Figure S12: The molecular structure of TEPNIT04 m * . Figure S13: The molecular structure of XEHMOM01 m . Figure S14: The molecular structure of XEHMOM01 m . Figure S15: The molecular structure of XEHMOM01 m .
S8.1.2 N−H · · · N interactions Figure S16: The molecular structure of BAZGOY05 s . Figure S17: The molecular structure of DMSDIM01 s . Figure S18: The molecular structure of FORAMO01 s . Figure S19: The molecular structure of IMAZOL06 s . Figure S20: The molecular structure of TRAZOL02 s . Figure S21: The molecular structure of FORAMO01 s . Figure S22: The molecular structure of GLOXIM11 s . Figure S23: The molecular structure of MAMPOL02 s . Figure S24: The molecular structure of LOLSUA m . Figure S25: The molecular structure of ULAWAF05 m .

S8.1.3 O−H · · · N interactions
S8.1.4 C−H · · · O interactions Figure S26: The molecular structure of ABINOR04 s . Figure S27: The molecular structure of NBONAN01 s . Figure S28: The molecular structure of POKKAD01 s . Figure S29: The molecular structure of CYACHZ01 m * . Figure S30: The molecular structure of FACETA01 m * . Figure S31: The molecular structure of GLYGLY04 m .        Figure S41: The molecular structure of CUKCAM18 m * . Figure S42: The molecular structure of SALIAC12 m * . Figure S43: The molecular structure of SUCACB03 m * . Figure S44: The molecular structure of ZZZEEU05 m * .

S8.2 Halogen bonds
S8.2.1 Cl · · · N interactions Figure S45: The molecular structure of CCACENN s . Figure S46: The molecular structure of DESKER01 s . Figure S47: The molecular structure of NABZAS s . Figure S48: The molecular structure of PCLPYR s . Figure S49: The molecular structure of VUGSIZ s . Figure S50: The molecular structure of PALPAV m . Figure S51: The molecular structure of XIZPON s . Figure S52: The molecular structure of BEDMON s . Figure S53: The molecular structure of BZQDCL11 s . Figure S54: The molecular structure of CORDUI s . Figure S55: The molecular structure of DCLBZQ20 s . Figure S56: The molecular structure of IRUFEH01 s . Figure S57: The molecular structure of JOJTIL s . Figure S58: The molecular structure of RUBSUD s . Figure S59: The molecular structure of TCACAD01 s . Figure S60: The molecular structure of GEXWUB s . Figure S61: The molecular structure of PEPFUL s . Figure S62: The molecular structure of BCACENN s . Figure S63: The molecular structure of BONFIT s . Figure S64: The molecular structure of QONHUX s . Figure S65: The molecular structure of RIRFOON s . Figure S66: The molecular structure of KUYCUD s . Figure S67: The molecular structure of BMLTAAN s . Figure S68: The molecular structure of CIRSONN s . Figure S69: The molecular structure of JEVVOW s . Figure S70: The molecular structure of VAQXUG s . Figure S71: The molecular structure of VEWTAU s . Figure S72: The molecular structure of VEWTEY s . Figure S73: The molecular structure of VITVEZ s . Figure S74: The molecular structure of WADFIR s . Figure S75: The molecular structure of ACETBR02 s .

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S8.3 Chalcogen bonds S8.3.1 S · · · N interactions Figure S76: The molecular structure of CEBYUD s . Figure S77: The molecular structure of QOBFUI s . Figure S78: The molecular structure of SAZCEC s . Figure S79: The molecular structure of GEDHAY m . Figure S80: The molecular structure of GEDHAY m . Figure S81: The molecular structure of IFULUQ04 m . Figure S82: The molecular structure of WASHEE m . Figure S83: The molecular structure of WASHEE m . Figure S84: The molecular structure of WUXPAG m . Figure S85: The molecular structure of WUXPAG m .
S8.3.2 S · · · O interactions Figure S86: The molecular structure of PAFVEY s . Figure S87: The molecular structure of WOCQEK s . Figure S88: The molecular structure of ADOFEF m * . Figure S89: The molecular structure of ADOFEF m * . Figure S90: The molecular structure of MAVRAD m . Figure S91: The molecular structure of MEHNIY m . Figure S92: The molecular structure of NAHMUE m . Figure S93: The molecular structure of NAHMUE m . Figure S94: The molecular structure of PUDMUW m .
54 Figure S95: The molecular structure of PUDMUW m . Figure S96: The molecular structure of QELQEE m . Figure S97: The molecular structure of QELQEE m . Figure S98: The molecular structure of ZAVHEJ m * .
S8.3.3 Se · · · N interactions Figure S99: The molecular structure of BESEAZ01 s . Figure S100: The molecular structure of FENFION s . Figure S101: The molecular structure of WERYAT s . Figure S102: The molecular structure of NECZUQ m * . Figure S103: The molecular structure of SECNBZ m .

S8.3.4 Se · · · O interactions
Figure S104: The molecular structure of BOJCOS m * . Figure S105: The molecular structure of LEDGAD m . Figure S106: The molecular structure of LEDGAD m . Figure S107: The molecular structure of LEVJOM m . Figure S108: The molecular structure of MUSCIM m .