Nature and stability of the chemical bond in H₃C–XH_n (XH_n = CH₃, NH₂, OH, F, Cl, Br, I)

The chemical bond is a cornerstone of chemistry.¹ Its length, stability, and electronic structure play a decisive role in determining molecular structure, stability, and reactivity. Therefore, a thorough understanding of trends in chemical bond strengths is quintessential for advancing chemical theory and the rational design of novel molecular systems.^2,3 One notable trend is that polar covalent bonds are stronger when the polarity of the bond increases. Until recently, this phenomenon was ascribed to the increasing difference in electronegativity between the elements that constitute this polar covalent bond.⁴ For example, upon going down group 17, from H₃C–F to H₃C–I, the chemical bond weakens, which is generally explained by the decreasing electronegativity difference between carbon and the consistently heavier halogen.¹ 

Recently, we have shown, by studying the homolytic bond dissociation of various polar covalent bonds, that the correlation between polar covalent bond strength and differences in electronegativity of the elements involved in bonding is not in all situations causal.⁵ Indeed, along period 2, from H₃C–CH₃ to H₃C–F, the chemical bond strengthens because the electron-pair bonding orbital interactions become more stabilizing as the electronegativity difference across the bond is larger. However, going up group 17, from H₃C–I to H₃C–F, the carbon–halogen bond strengthens due to decreasing carbon–halogen Pauli repulsion and not due to the commonly assumed strengthening in the carbon–halogen electron-pair bonding orbital interaction. Interestingly, along this series, the bond, in fact, becomes weaker if one compares the bonds at consistent bond distances. The decreasing carbon–halogen Pauli repulsion going up group 17 arises from the smaller effective size of the lighter halogen atoms. In addition to stabilizing the carbon–halogen bond, the reduction in Pauli repulsion also allows it to assume a shorter equilibrium bond distance. At that shorter equilibrium bond distance, all interactions, including the electron-pair bonding orbital interactions, are stronger. This leads to a correlation between the carbon–halogen electron-pair bond strength and the decreasing electronegativity difference, which is erroneously invoked as a causal correlation in most textbooks.^1(b),4

Herein, we extend our previous work on the C–X bond strength in H₃C–XH_n from homolytic bond dissociation into H₃C^∙ + ^∙XH_n to two alternative, heterolytic bond dissociation pathways, namely, (i) into H₃C⁺ + ⁻XH_n (“hetero 1” in Scheme 1) and (ii) into H₃C⁻ + ⁺XH_n (“hetero 2” in Scheme 1). Our model systems cover the variation of XH_n along period 2 (XH_n = CH₃, NH₂, OH, F) and going up group 17 (XH_n = I, Br, Cl, F). All dissociation pathways were explored using the same level of relativistic, dispersion-corrected density functional theory at ZORA-BLYP-D3(BJ)/TZ2P, including the homolytic pathway to guarantee a set of consistent data.

Our purpose is to understand how H₃C–XH_n bond strengths, and trends therein, depend on the actual bond dissociation pathway.⁶ Interestingly, we find that the H₃C–XH_n bond dissociation enthalpies (BDE) differ pronouncedly for the three pathways, not only quantitatively but, in some cases, also in terms of opposite trends upon varying XH_n. Our analyses using the activation strain model (ASM)⁷ in conjunction with quantitative Kohn–Sham molecular orbital theory (KS-MO)⁸ and a matching energy decomposition analysis (EDA)⁹ reveal how these differences are caused by the profoundly different electronic structures of, and thus bonding mechanisms between, the resulting fragments in the three different dissociation pathways.^3(c),5 Our findings illustrate that it is essential for fully understanding a chemical bond to consider both (i) the molecule in which the bond exists and (ii) the fragments from which it forms or into which it dissociates.

All calculations were carried out using the Amsterdam Density Functional (ADF) program.¹⁰ The geometries and energies were calculated at the BLYP level of the generalized gradient approximation (GGA): the exchange functional developed by Becke (B) and the GGA correlation functional developed by Lee, Yang, and Parr (LYP).¹¹ The DFT-D3(BJ) method developed by Grimme and co-workers,¹² which contains the damping function proposed by Becke and Johnson,¹³ is used to describe non-local dispersion interactions. Scalar relativistic effects are accounted for using the zeroth-order regular approximation (ZORA).¹⁴ A large, uncontracted, optimized TZ2P Slater-type orbitals (STOs) basis set containing diffuse functions was used. The TZ2P all-electron basis set,¹⁵ with no frozen-core approximation, is of triple-ζ quality for all atoms and has been augmented with two sets of polarization functions. This level is referred to as ZORA-BLYP-D3(BJ)/TZ2P and provides bond dissociation enthalpies that are in close agreement with the experimentally determined values (vide infra). The accuracies of the integration grid (Becke grid) and the fit scheme (Zlm fit) were set to VERYGOOD.¹⁶ The potential energy surfaces are obtained by performing a relaxed potential energy surface scan, whereby the H₃C–XH_n bond distance is elongated from 1.10 to 2.70 Å in 33 equidistant steps. The computed potential energy surfaces were analyzed using the PyFrag 2019 program.¹⁷ Optimized structures were illustrated using CYLview.¹⁸ 

The activation strain and energy decomposition analyses, as well as the Kohn–Sham molecular orbital analysis, were performed on all 34 points acquired from the relaxed potential energy surface scan as a function of the H_nC–XH_n bond distance that defines the bond formation or dissociation process (vide supra).

Table I shows the homolytic and heterolytic bond dissociation enthalpies (BDE or ΔH_BDE) of the H₃C–XH_n bonds for XH_n = CH₃, NH₂, OH, F, Cl, Br, and I, along the three dissociation pathways defined in Scheme 1. Three key observations can be made: First, not surprisingly, the H₃C–XH_n BDE increases from homolytic dissociation (H₃C^∙ + ^∙XH_n) to heterolytic dissociation with the negative charge on the more electronegative fragment (H₃C⁺ + ⁻XH_n) to heterolytic dissociation with the negative charge on the less electronegative fragment (H₃C⁻ + ⁺XH_n). For example, the H₃C–XH_n BDE increases from 111.3 to 263.8 to 605.1 kcal mol⁻¹ when dissociating into H₃C^∙ + F^∙, H₃C⁺ + F⁻, and H₃C⁻ + F⁺, respectively (see Table I). Note that our computed homolytic BDEs, that is, the lowest energy dissociation pathway, are in close agreement with the experimentally determined BDEs. Second, the BDE values along each of the two series of bonds, i.e., along period 2 and up group 17, span a larger range if we go along these three respective dissociation pathways. For example, while the homolytic BDE along C–C to C–F changes by 26 kcal mol⁻¹ (from 85.2 to 111.3 kcal mol⁻¹), this range stretches over nearly 300 kcal mol⁻¹ (from 315.5 to 605.1 kcal mol⁻¹) for heterolytic dissociation into H₃C⁻ + ⁺F. Third, most interestingly, the BDE increases, with one exception, for all three dissociation pathways along period 2, from C–C to C–F, and up group 17, from C–I to C–F. For example, the homolytic BDE from C–C to C–F increases from 85.2 to 111.3 kcal mol⁻¹, and from C–I to C–F it strengthens from 61.0 to 111.3 kcal mol⁻¹. The exception occurs for the more favorable of the two heterolytic dissociation pathways, that is, H₃C–XH_n → H₃C⁺ + ⁻XH_n, and only for the series along period 2, from C–C to C–F, for which the heterolytic BDE decreases, not increases, from 315.5 (H₃C⁺ + ⁻CH₃) to 263.8 kcal mol⁻¹ (H₃C⁺ + ⁻F).

Next, we unveil the physical mechanisms behind the predominant trend that BDEs, in nearly all cases, become stronger from H₃C–CH₃ to H₃C–F and from H₃C–I to H₃C–F. Furthermore, we uncover the mechanism behind the exception for the heterolytic dissociation of the H₃C–XH_n bond into H₃C⁻ + ⁺XH_n, where the BDE is weaker from H₃C–CH₃ to H₃C–F.

In this section, we examine the origin of the trends in homolytic BDE (“homo” in Scheme 1), which show a pronounced strengthening along both series, from C–C to C–F and from C–I to C–F. The reasons for these similar trends are, however, quite different for the two series, as has been reported recently.⁵ On one hand, from C–C to C–F, the bond becomes stronger (with an anomaly from C–C to C–N)²¹ because of the larger electronegativity difference across the bond, that is, due to stronger electron-pair bond interactions. From a molecular orbital perspective (Scheme 2), this can be ascribed to an increasingly larger SOMO–SOMO orbital energy gap (Δε), which results in a deeper drop in the energy of the radical electron stemming from the higher-energy SOMO and, hence, in stronger electron-pair bonding orbital interaction. On the other hand, from C–I to C–F, a different mechanism is at play because the bond is stronger due to the decreasing steric repulsion with the smaller halogen atom. Upon going up in group 17, the occupied valence orbitals of XH_n are spatially less extended and bear fewer electrons in a reduced number of closed-shell AOs. This leads to a decrease in repulsive occupied–occupied orbital overlap (S²), making the C–X bond effectively stronger and shorter. This happens despite a weaker electron-pair bonding orbital interaction caused by a smaller bond overlap along the series.

In the following sections, we analyze the two heterolytic dissociation pathways and compare the two extremes, along period 2 and going up group 17, that is, H₃C–CH₃ vs H₃C–F and H₃C–I vs H₃C–F. We can do this due to the fragment-based approach of our analysis methods, i.e., the activation strain model and energy decomposition analysis (see Sec. II C). This approach gives us the freedom to select our fragments, which allows us to accurately analyze how a chemical bond arises along different association pathways (i.e., from different fragments) and, vice versa, how it fades out when it is broken along different dissociation pathways (i.e., into different fragments).²² Table S2 shows that the trends in bond dissociation enthalpies ΔH_BDE are set by the electronic bond dissociation energies ΔE_BDE, allowing us to further analyze the electronic bond energy ΔE (ΔE = −ΔE_BDE) of the bond formation process of H₃C–XH_n between ionic fragments along the bond-forming axis in more detail. The analysis of the complete set of systems along period 2 and down group 17 can be found in Figs. S1–S4 of the supplementary material.

First, we study the heterolytic dissociation pathway of the H₃C–CH₃ and H₃C–F bonds into the methyl cation H₃C⁺ and the respective anionic species ⁻CH₃ and ⁻F (“hetero 1” in Scheme 1), using the activation strain model (ASM) [Fig. 1(a)].⁷ In contrast to the situation for the homolytic dissociation pathway (“homo” in Scheme 1), we find that, along this heterolytic dissociation pathway (“hetero 1” in Scheme 1), the bond becomes weaker, not stronger, from C–C to C–F because of a less stabilizing (i.e., less negative) interaction energy ΔE_int. The strain energy ΔE_strain is not responsible for the overall trend in ∆E. It runs counter to the trend in ΔE_int, namely, it is slightly less destabilizing (i.e., less positive) from the stronger C–C to the weaker C–F bond. The reason is that the ⁻XH_n = ⁻CH₃ fragment has a small deformation energy upon C–C bond formation (associated with a slight modification in the extent of pyramidalization of the methyl anion fragment), whereas the ⁻XH_n = ⁻F cannot undergo any geometrical deformation. By means of energy decomposition analyses (EDAs),⁹ we find that the difference in interaction energy predominantly originates from the orbital interactions ∆E_oi, which are significantly less stabilizing if we go from C–C to C–F [Fig. 1(b)]. The electrostatic interaction shows the same trend, although less pronounced so, and is slightly less stabilizing from C–C to C–F. The Pauli repulsion is not responsible for the overall trend in ∆E; it runs counter and is less destabilizing from C–C to C–F.

By performing a Kohn–Sham molecular orbital (KS-MO) analysis as a function of the C–X bond distance,⁸ we find that it is both the less favorable HOMO–LUMO orbital energy gap (which becomes larger from C–C to C–F) and the less favorable HOMO–LUMO overlap (which becomes smaller from C–C to C–F) that makes the orbital interactions less stabilizing from C–C to C–F. Figure 1(c) shows the progression of the donor orbital energy and the stabilizing donor–acceptor orbital overlap along the bond-forming process between ⟨3A1_H3C⁺|3A1–_CH3⟩ and ⟨3A1_H3C⁺|2p_–F⟩, where 3A1_H3C⁺ is the accepting 2p_σ-derived LUMO of H₃C⁺, 3A1_–CH3 is the donating 2p_σ-derived HOMO of ⁻CH₃, and 2p_–F is the donating valence atomic 2p_σ-HOMO of ⁻F. The donating 2p_–F orbital is lower in energy than the 3A1–_CH3 orbital, leading to a larger and, hence, less stabilizing HOMO–LUMO orbital energy gap for the former. In addition, the orbital overlap is also smaller and, therefore, less favorable for C–F compared to C–C. The difference in orbital overlap can be traced back to the spatial extent of the occupied, donating orbital of ⁻XH_n. In Fig. 1(d), we have visualized the occupied orbitals of ⁻CH₃ and ⁻F, i.e., 3A1–_CH3 and 2p_–F, that engage in the donor–acceptor interaction with H₃C⁺. It becomes clear that, going from 3A1–_CH3 to 2p_–F, the HOMO is more contracted to the nucleus, and hence, extends less toward the incoming H₃C⁺.²³ 

Next, we examine why the chemical bond is stronger from H₃C–I to H₃C–F when heterolytically dissociating into H₃C⁺ and anionic species ⁻I and ⁻F, respectively. Figure 2(a) shows that the bond becomes stronger from C–I to C–F because of a more stabilizing interaction energy ΔE_int and a less destabilizing strain energy. The difference in strain energy originates from the deformation of the intrinsically planar H₃C⁺ fragment, which needs to pyrimidalize to accommodate the chemical bond formation with the ⁻XH_n fragment. The extent of pyramidalization, and hence the magnitude of the strain energy, stems from the effective size of the ⁻XH_n fragment. A large ⁻XH_n, such as ⁻I, engages in a more steric repulsion with the hydrogen atoms of H₃C⁺ and, therefore, forces this fragment to pyrimidalize to a larger extent than the small ⁻F. The more stabilizing interaction energy for C–F, on the other hand, originates from a less steep rise of destabilizing Pauli repulsion compared to C–I [Fig. 2(b)]. The orbital interactions show an opposite trend, namely, they are less stabilizing from the weaker C–I to the stronger C–F bond.

By analyzing the KS-MOs, we find that upon bond formation, C–F builds up significantly less repulsive occupied–occupied orbital overlap between the two approaching fragments than H₃C–I. Figure 2(c) shows the evolution of the repulsive occupied–occupied orbital overlap between ⟨2A1_H3C⁺|2p_–F⟩ for C–F and ⟨2A1_H3C⁺|5p_–I⟩ for C–I, where 2A1_H3C⁺ is the occupied all in-phase σ-orbital of H₃C⁺ and 2p_–F and 5p_–I are the valence atomic np_σ-HOMO of ⁻F and ⁻I, respectively. A small and, hence, less destabilizing orbital overlap is found for C–F, whereas a large and, therefore, more destabilizing orbital overlap is found for C–I. The reduction of repulsive orbital overlap can be explained by the difference in spatial extent of the occupied valence atomic orbitals of ⁻XH_n, that is, 2p_–F and 5p_–I. The occupied 2p_–F of C–F points, due to the intrinsic nature of this valence atomic orbital, less toward the approaching H₃C⁺ fragment than the large 5p_–I. This difference in spatial extent can be graphically illustrated by visualizing these occupied orbitals [Fig. 2(d)]. Where 2p_–F spans until the black vertical line, 5p_–I expands far beyond this line, making the latter have a better spatial match with the 2A1_H3C⁺, which amplifies the repulsive orbital overlap even further [Fig. 2(e)]. In addition, the heavier halogen also has more subvalence shells, which further raise the number of repulsive occupied–occupied orbital interactions [see also Ref. 5(a)].

Now, we move to the second heterolytic dissociation pathway, where, along period 2, the H₃C–CH₃ and H₃C–F bonds are dissociated into the methyl anion H₃C⁻ and the respective cationic species ⁺CH₃ and ⁺F (“hetero 2” in Scheme 1). In this case, the bond becomes stronger, i.e., it has a more stabilizing ΔE, from C–C to C–F, thus paralleling the same trend along the homolytic dissociation pathway for C–X bonds. This trend for pathway “hetero 2” originates from a more stabilizing interaction energy ΔE_int [Fig. 3(a)]. The strain energy ΔE_strain plays only a minor role, and the difference stems from the deformation of the ⁺CH₃ fragment, which needs to pyrimidalize upon forming the C–X bond. The trend in interaction energy, and hence bond energy, is dictated by the orbital interactions, which are significantly more stabilizing from C–C to C–F. In contrast, the electrostatic interaction and Pauli repulsion are less important for the trend; they differ hardly from C–C to C–F, with nearly superimposed curves.

To understand the origin of the difference in orbital interactions, we perform a KS-MO analysis as a function of the bond distance. This analysis reveals that the extremely low energy of the 2p_+F LUMO causes the more favorable orbital interaction ∆E_oi and, therefore, a stronger C–F bond. Figure 3(c) shows the relevant HOMO–LUMO overlap integrals and LUMO orbital energies as a function of the bond distance, that is, the overlap ⟨3A1_H3C^–|3A1_⁺CH3⟩ for C–C and ⟨3A1_H3C^–|2p_+F ⟩ for C–F, where 3A1_H3C^– is the carbon 2p_σ-derived HOMO of H₃C⁻, 3A1_⁺CH3 is the carbon 2p_σ-derived LUMO of H₃C⁺, and 2p_+F is the 2p_σ-LUMO of ⁺F. The very compact 2p_+F LUMO of the ⁺F fragment is significantly lower in energy than the less compact 3A1_⁺CH3 LUMO of the ⁺CH₃ fragment. Already the neutral parent radical ^∙F has a lower lying SOMO than ^∙CH₃, due to the larger effective nuclear charge that binds the electrons more closely to the nucleus, i.e., a larger ionization energy. The drop in orbital energy going from a neutral radical to a cationic species is, as a result, larger for ^∙F than for ^∙CH₃, due to a larger reduction of Coulomb repulsion in the very compact fluorine system.

Interestingly, the 2p_+F LUMO is effectively even lower in energy than the 3A1_H3C^– HOMO. This is also reflected by the fact that the 3A1_⁺CH3 + 2p_+F bonding MO in the C–F bond has a larger contribution from the ⁺F LUMO than from the H₃C⁻ HOMO, resulting in a gross Mulliken population of 1.5 electrons in the 2p_+F. Thus, the electrons of the 3A1_H3C^– HOMO of the methyl anion drop into the (bonding combination with the) 2p_+F LUMO of ⁺F in a way that is reminiscent of the corresponding C–F electron-pair bond in which the electron of the higher-energy methyl 3A1_CH3· SOMO drops into the (bonding combination with the) fluorine 2p_σ SOMO. This type of HOMO–LUMO interaction gains stabilization not only from the energy-lowering of the bonding MO relative to the lower-energy fragment molecular orbital (FMO) (∝S²/∆ε) but also from the energy gap between the two FMOs involved (∝∆ε). This is qualitatively illustrated in Scheme 2, which shows how the HOMO–LUMO interaction of path “hetero 2” (H₃C⁻ + ⁺XH_n) leads to more stabilization than that of path “hetero 1” (H₃C⁺ + ⁻XH_n). For a quantitative comparison of the more stabilizing ∆E_oi values of path “hetero 2” than those of path “hetero 1,” see Table S3.

The HOMO–LUMO orbital overlap shows the opposite trend, namely, it becomes significantly less favorable, i.e., smaller, from C–C to C–F [see Fig. 3(c)]. The reason for this is the spatial mismatch between the relatively diffuse H₃C⁻ HOMO and the very compact ⁺F LUMO [see Fig. 3(d)]. Therefore, the orbital overlap is not responsible for the weakening of the HOMO–LUMO orbital interactions from C–C to C–F.

Finally, we study the trend in bonding upon heterolytically dissociating H₃C–I and H₃C–F into the methyl anion H₃C⁻ and the respective cationic species ⁺I and ⁺F (“hetero 2” in Scheme 1). Figure 4(a) shows that the bond strengthens from C–I to C–F because of a more favorable interaction energy ΔE_int. The strain energy ΔE_strain, on the other hand, plays essentially no role: It is small, nearly negligible, and the strain curves for C–I and C–F are nearly superimposed. The reason is that, for both systems, the interacting fragments need to deform only very slightly (the methyl anion is already pyramidal, and the halogen fragment is monoatomic). The interaction ∆E_int is significantly more stabilizing from C–I to C–F because the trend in orbital interactions ∆E_oi and ∆E_Pauli work in the same direction: the former is more stabilizing and the latter less repulsive [Fig. 4(b)]. The electrostatic interaction shows the opposite trend, that is, it is less stabilizing from C–I to C–F.

The more stabilizing orbital interactions, from C–I to C–F, are the direct result of the significant lowering of the halogen-cation's LUMO, from ⁺I to ⁺F, as emerges from our analysis of the MO interaction mechanism [see Fig. 4(c)]. In this HOMO–LUMO interaction, the electrons of the carbon 2p_σ-derived 3A1 HOMO in the methyl anion CH₃⁻ swap into the valence np_σ of the halogen cation, as illustrated by the gross Mulliken population of 1.5 electrons in 2p_+F and 1.1 electrons in 5p_+Iσ. Thus, from C–I to C–F, these electrons are significantly more stabilized as the LUMO energy drops, from the 5p_+Iσ LUMO of ⁺I to the 2p_+Fσ LUMO of ⁺F.²⁴ Note that the trend in LUMO orbital energy overrules the trend in HOMO–LUMO overlap, which runs counter. Thus, the overlap integral decreases from ⟨3A1_H3C^–|5p_+Iσ⟩ to ⟨3A1_H3C^–|2p_+Fσ⟩, i.e., from C–I to C–F, as shown in Fig. 4(c). The reason is the better spatial match of the rather diffuse 3A1_H3C^– HOMO of the methyl anion with the likewise relatively diffuse 5p_⁺Iσ LUMO of the large iodine cation than with the more compact 2p_+Fσ LUMO of the significantly smaller fluorine cation [see Figs. 4(d) and 4(e)].

The trend in Pauli repulsion stems from the reduction in occupied–occupied orbital overlap upon going from the formation of the C–I bond to the C–F bond, also found for the “homo” and “hetero 1” dissociation pathways. The occupied–occupied overlap integrals as a function of the bond distance, ⟨1E1_H3C^–|5p_⁺Iπ⟩ for H₃C–I and ⟨1E1_H3C^–|2p_+Fπ⟩ for H₃C–F, are shown in Fig. 4(e); herein, 1E1_H3C^– represents C–H bonding orbitals of H₃C⁻ and 5p_⁺Iπ and 2p_+Fπ are the π-symmetric valence np-atomic orbitals of ⁺I and ⁺F. The repulsive orbital overlap starts at a longer bond distance and is larger for C–I than for C–F. As discussed earlier, all 5p-atomic orbitals of I⁺ are larger than the analogous 2p-atomic orbitals of F⁺ [see Fig. 4(f)]. Due to this difference in spatial extent, the former will start to overlap with the occupied 1E1_H3C^– earlier, and this overlap will rise more steeply than the latter. Furthermore, the heavier halogen also has more subvalence shells, which increases the number of repulsive occupied–occupied orbital interactions, leading to effectively more destabilizing Pauli repulsion [see also Ref. 5(a)]. This, together with the strengthening of the orbital interactions, leads to a contraction and a strengthening of the bond going from C–I to C–F.

The carbon–element bond strength in covalent H₃C–XH_n single bonds, and trends therein, along various XH_n (XH_n = CH₃, NH₂, OH, F, Cl, Br, I) depend profoundly on which homolytic or heterolytic dissociation pathway is considered. As expected, the heterolytic bond dissociation goes, in all cases, with a substantially higher bond dissociation enthalpy (BDE) than homolytic dissociation. Interestingly, heterolytic dissociation into H₃C⁺ + ⁻XH_n shows along one of the series the opposite trend (weakening from C–C to C–F but still strengthening from C–I to C–F) compared to both homolytic dissociation and heterolytic dissociation into H₃C⁻ + ⁺XH_n (strengthening from C–C to C–F and from C–I to C–F). This follows from our quantum chemical activation strain model (ASM) and quantitative molecular orbital (MO) analyses based on relativistic, dispersion-corrected density functional theory at ZORA-BLYP-D3(BJ)/TZ2P.

Our bonding analyses reveal that, upon homolytic dissociation (“homo” in Scheme 1), the H₃C–XH_n bond is stronger along period 2, from C–C to C–F, due to an increasingly more favorable electron-pair bond associated with the increased electronegativity difference across the bond. Up group 17, from C–I to C–F, the bond is also stronger but for a different reason, namely, due to decreasing steric repulsion and not due to the generally assumed strengthening of the electron-pair bonding orbital interaction. For the heterolytic dissociation into H₃C⁻ + ⁺XH_n (“hetero 2” in Scheme 1), we observe the same trends for related reasons. Thus, along period 2, from C–C to C–F, the C–X bond becomes stronger because of a strengthening in the HOMO–LUMO orbital interaction, i.e., because the ⁺XH_n LUMO drops, and up group 17, from C–I to C–F, the C–X bond strengthens due, again, to the reduction of steric repulsion as X becomes smaller. However, a different trend emerges in the case of heterolytic dissociation into H₃C⁺ + ⁻XH_n (“hetero 1” in Scheme 1). The C–X bond still strengthens up group 17, from C–I to C–F, due to the decreasing steric repulsion when X is smaller. However, now it weakens instead of strengthening along period 2, from C–C to C–F, because of a weakening in the HOMO–LUMO orbital interactions as the ⁻XH_n HOMO drops in energy, which increases the HOMO–LUMO orbital energy gap.

The present work highlights what is often overlooked: The nature and strength of a chemical bond are completely defined only if both are considered: (i) the molecule in which the bond features and (ii) the fragments into which it dissociates or from which it forms. A model of the chemical bond that does not account for this is, therefore, incomplete.

The supplementary material contains additional theoretical data and Cartesian coordinates of all structures.

We thank the Netherlands Organization for Scientific Research (NWO) for the financial support. This work was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative and VU BAZIS.

The authors have no conflicts to disclose.

Pascal Vermeeren: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). F. Matthias Bickelhaupt: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material. Cartesian coordinates can be downloaded from Yoda VU; see Ref. 25.