Highs and Lows of Bond Lengths: Is There Any Limit?

Abstract

Two distinct points on the potential energy curve (PEC) of a pairwise interaction, the zero-energy crossing point and the point where the stretching force constant vanishes, allow us to anticipate the range of possible distances between two atoms in diatomic, molecular moieties and crystalline systems. We show that these bond-stability boundaries are unambiguously defined and correlate with topological descriptors of electron-density-based scalar fields, and can be calculated using generic PECs. Chemical databases and quantum-mechanical calculations are used to analyze a full set of diatomic bonds of atoms from the s-p main block. Emphasis is placed on the effect of substituents in C-C covalent bonds, concluding that distances shorter than 1.14 Å or longer than 2.0 Å are unlikely to be achieved, in agreement with ultra-high-pressure data and transition-state distances, respectively. Presumed exceptions are used to place our model in the correct framework and to formulate a conjecture for chained interactions, which offers an explanation for the multimodal histogram of O-H distances reported for hundreds of chemical systems.

Keywords: ELF (electron localization function); bond length; carbon-carbon bonds; hydrogen bonds; potential energy curve.

Figure 1

Potential energy curve of a generic A–B diatomic bond. Hard sphere (r _hs) and spinodal (r _sp) points are represented by red and green dots, respectively, whereas the equilibrium distance (r _e) is represented with a blue point. The stability region of the bond is displayed by the blue shaded area.

Figure 2

Difference between spinodal (r _sp) and the hard‐sphere distances (r _hs) against the (D _e/k _e)^1/2 scaling parameter of the UBER potential for several diatomic molecules: Al₂, AlCl, AlF, AlH, AlO, AlS, B₂, BCl, BeCl, BeF, BeH, BeO, BeS, BF, BH, BN, BO, BS, C₂, CCl, CF, CH, Cl₂, ClF, ClH, ClLi, ClO, ClSi, CN, CO, CP, CS, F₂, FH, FLi, FMg, FN, FNa, FO, P₂, FS, FSi, H₂, HLi, HMg, HN, HNa, HO, HP, HS, LiNa, Mg₂, MgO, MgS, Na₂, N₂, NO, NP, NS, NSi, O₂, OP, OS, OSi, P₂, Si₂, S₂, and SSi. The straight line corresponds to the equation (r _sp−r _hs)=(2.06±0.03) (D _e/k _e)^1/2. Colored symbols highlight diatomic molecules with rupture distances closer to their equilibrium values and are displayed in the inset.

Figure 3

ELF isosurfaces in beige for CH₃OH (ELF isovalue 0.78) along with bond attractors represented as small purple spheres identified by arrows at C−O distances of a) 1.45 Å and b) 0.95 Å. White, grey, and red balls stand for H, C, and O, respectively.

Scheme 1

Molecules and C−C bonds (marked in green) studied in this work.

Figure 4

Diagram comparing the hard‐sphere (red line) and the spinodal (green line) distances of the O₂ molecule with equilibrium distances found in different σ(O−O) bonds (vertical arrows).

Figure 5

(Top panel) Schematic representation of the chained interaction conjecture. In black, the covalent bonding, blue and green represents the electrostatic and van der Waals interaction regimes, respectively. Notice how the spinodal limit corresponds to the hard‐sphere distance of the next interaction. (Bottom panel) Distance histogram for the O−H interaction, bin width=0.05 Å. Covalent, H‐Bond, and van der Waals contacts have been represented as black, blue, and green bins, respectively. Dash‐dotted lines correspond to r _sp,covalent=r _hs,_H‐bond=1.36 Å and r _sp,H‐bond=r _hs,vdW=2.14 Å.