“Hydridic Hydrogen-Bond Donors” Are Not Hydrogen-Bond Donors

Herein, we dismiss a recent proposal by Civiš, Hobza, and co-workers to modify the IUPAC definition of hydrogen bonds in order to expand the scope from protonic Y–Hδ+ to hydridic Y–Hδ− hydrogen-bond donor fragments [J. Am. Chem. Soc.2023, 145, 8550]. Based on accurate Kohn–Sham molecular orbital (KS-MO) analyses, we falsify the conclusion that interactions involving protonic and hydridic hydrogens are both hydrogen bonds; they are not. Instead, our quantitative KS-MO, energy decomposition, and Voronoi deformation density analyses reveal two fundamentally different bonding mechanisms for protonic Y–Hδ+ and hydridic Y–Hδ− fragments which go with charge transfer in opposite directions. On one hand, we confirm the IUPAC definition for regular hydrogen bonds in the case of protonic Y–Hδ+ fragments. On the other hand, complexes involving Y–Hδ− fragments are, in fact, acceptors in other well-known families of Lewis-acid/base interactions, such as halogen bonds, chalcogen bonds, and pnictogen bonds. These mechanisms lead to the same spectroscopic phenomenon in both the Y–Hδ+ and Y–Hδ− fragments, that is, the redshift in the Y–H stretching frequency, which is, thus, not an exclusive indicator for hydrogen bonding.


■ INTRODUCTION
The hydrogen bond is a key chemical interaction in biological, supramolecular, and organic chemistry. 1IUPAC defines the hydrogen bond (HB) as an attractive interaction between a hydrogen atom from a molecule or a molecular fragment Y−H, in which Y is more electronegative than H, and an atom or group of atoms (Z), in which there is evidence of bond formation (i.e., a Y−H•••Z hydrogen-bonded complex). 2ccording to molecular orbital (MO) theory, the reason behind the stability of the HB is twofold: (i) the electrostatic attraction between the protonic hydrogen in the Y−H δ+ fragment and Z; and (ii) the covalent donor−acceptor interaction stemming from the charge transfer from the HOMO of Z into the empty σ* Y−H antibonding orbital. 3he covalency of HB is manifested in the characteristic Y−H bond elongation and a decrease, i.e., redshift, in the vibrational frequency associated with the Y−H bond stretching mode.3b,4 Hydridic hydrogens are also known to engage in intramolecular interactions that do not fit the IUPAC definition of the HB.For example, in the case of the charge inverted hydrogen bonds (CIHB), 5 a designation coined by Jabłonśki to cover systems of the type Y−H δ− •••Z, in which Y is less electronegative than H and Z is an electron-deficient fragment.In this point of view, hydrogen bonding refers to all interactions involving a hydrogen atom that can either be protonic, forming a regular HB, or hydridic, forming a CIHB.Recently, Civis, Hobza, and co-workers proposed a generalization of the IUPAC definition of HB in order to cover both the protonic and hydridic forms within the same definition. 6ccording to the authors, CIHBs still hold many important features of the HB, such as the donation of charge into the σ* Y−H δ− antibonding orbital and the elongation, i.e., redshift, of the Y−H δ− bond.This implies that, in CIHB, hydridic hydrogens behave as Lewis acids and the electron-deficient Z fragment behaves as a Lewis base; thus, the bonding mechanism of HB and CIHB would be the same.
In this work, we challenge the idea that hydridic hydrogen bonds involve only an inversely polarized H-bond donor but otherwise are, in essence, electronically similar to protonic hydrogen bonds.To this end, we analyze the bonding mechanism of a series of Me m YH•••NH 3 , Me m YH•••NCI, and Me m YH•••ICN complexes (Y = C, Si, Ge, N, P, As, O, S, Se; m = 3, 2, 1), using Kohn−Sham molecular orbital (KS-MO) theory (Scheme 1).Our model systems feature Y−H groups with protonic and hydridic hydrogens and allow for a systematic and quantitative comparison of how bonding mechanisms change in nature along the series.We show that true hydrogen bonds, i.e., in which the H-bond acts as a Lewis acid accepting charge in its σ* Y−H LUMO, can only be formed with protonic hydrogens.On the contrary, complexes involving hydridic hydrogens lead to a completely different bonding mechanism in which the molecular fragment containing the hydrogen atom acts as a Lewis base, not as a Lewis acid. 7Thus, CIHB is not a correct designation for interactions involving hydridic hydrogens, and hence, there is no need to change the IUPAC definition of the hydrogen bond.

■ RESULTS AND DISCUSSION
The Me m YH Fragments.We start by analyzing the protonic or hydridic character of the H atom of the studied model Me m YH fragments, in which Y is an element belonging to groups 14, 15, and 16 and periods 2, 3, and 4 of the periodic table (Y = C, Si, Ge, N, P, As, O, S, Se, and m = 3, 2, and 1).
For this purpose, we analyze the Voronoi deformation density (VDD) charge on the H atom (Q H ) directly bound to atom Y (see Theoretical Methods).In general, we find that Y atoms with an electronegativity higher than H (χ H = 2.20) 8 cause a charge depletion on H, i.e., a positive VDD charge on H, whereas Y atoms with an electronegativity lower than H result in an accumulation of charge on H, i.e., a negative VDD charge on H.For example, Q H is +154 milli-electrons for MeOH and −92 milli-electrons for Me 3 SiH, where the electronegativity of O and Si are χ O = 3.44 and χ Si = 1.90, respectively (Figure 1).Thus, the nature of atom Y greatly influences the charge of the H atom in the Me m YH monomer, making them either protonic or hydridic.
We recall that, according to the IUPAC definition, 2 a hydrogen bond is only formed when the Y atom is more electronegative than H.In other words, the Me 3 SiH, Me 3 GeH, Me 2 PH, and Me 2 AsH fragments with hydridic H should be unable to engage in a hydrogen bond with an electron-rich fragment, i.e., a Lewis base (Figure 1).In the following section, we quantify this statement and explain why hydrogen bonds involving a hydric hydrogen can indeed not be formed.
On the Nonexistence of Hydridic Hydrogen Bonds.To evaluate the ability of protonic and hydridic hydrogens to engage in hydrogen bonding, we study the interaction between the Me m YH fragments and NH 3 , a well-known Lewis base and hydrogen-bond acceptor, to form complexes of the type Me m YH•••NH 3 (see Scheme 1a).The equilibrium geometries, electronic bond energies ΔE, and the charge depletion on the NH 3 fragment are reported in Figure 2 (see Table S1 for additional data).We find that Me m YH  2).The charge transfer mechanism from NH 3 to Me m YH is the characteristic covalent component of the hydrogen bond, where the lone pair orbital of NH 3 (LP N ) donates charge into the empty σ* Y−H antibonding orbital of Me m YH (σ* Y−H ; see Scheme 2). 3 As the σ* Y−H becomes more populated, the Y−H bond elongates (see Table S1), resulting in the characteristic redshift in the vibrational frequency associated with the Y−H bond stretching mode.In contrast, there is no charge transfer in the Me m YH•••HNH 2 bonding motif involving a hydridic hydrogen, that is, there is no charge depletion or accumulation on NH 3 and, hence, no hydrogen bond in these complexes (see Figure 2).Next, we explain why hydridic fragments cannot form Me m YH•••NH 3 hydrogenbonded complexes.
Stable hydrogen-bonded complexes are formed because the electrostatic attraction between Y−H δ+ and the electron-rich bond acceptor, together with the covalent, charge transfer interaction, overcomes the destabilizing Pauli repulsion between the occupied σ Y−H bonding orbital (σ Y−H ) and the occupied orbitals of the bond acceptor (see Scheme 2). 3 Protonic hydrogens are depleted of electron density, which exposes their positively charged nucleus to the electron density of an incoming electron-rich fragment, resulting in a stronger electrostatic attraction.On the other hand, hydridic hydrogens have an excess of electron density that: (i) screens their positively charged nucleus, causing a weaker electrostatic attraction between Y−H δ− and the hydrogen-bond acceptor; and (ii) increases the size of σ Y−H on the H atom, resulting in a more destabilizing Pauli repulsion between σ Y−H and the occupied orbitals of the bond acceptor.As a result, hydrogen-   Hydridic Hydrogens as Bond Acceptors.We have shown that hydridic hydrogens are unable to engage in hydrogen bonds with electron-rich molecules like NH 3 .In this section, we address the question: can hydrogen bonding be the most dominant interaction when a hydridic hydrogen engages in an intermolecular interaction with electron-poor halogenbond donors as proposed by Civis, Hobza, and co-workers? 6o answer this question, we study the bonding mechanism for the interaction between Me m YH and ICN, where ICN can form a hydrogen bond with the nitrogen side and a halogen bond with the iodine side, 10 according to the IUPAC definitions of hydrogen bonds 2 and halogen bonds 10a (see Scheme 1).The equilibrium geometries, electronic bond energies ΔE, and the charge rearrangement in the ICN fragment are reported in Figure 5.    5).Note that the hydrogenbonding and halogen bonding mechanisms go with charge transfer in opposite directions; that is, ΔQ ICN is positive for the former and negative for the latter.Therefore, the negative ΔQ ICN is clear evidence that there is no hydrogen-bonding mechanism that is able to overcome the halogen bond in the Me m YH•••ICN complexes.This is because ICN is a poor hydrogen-bond acceptor, i.e., weak Lewis base, on the I side due to its very low-lying I lone-pair (LP I ) orbital (see Scheme 3).
The magnitude of the various pairwise donor−acceptor orbital interactions is approximately proportional to their orbital overlap squared (S 2 ) divided by the orbital energy gap (Δε).For Me 3 SiH•••ICN, the S and Δε for the σ Y−H → σ* I−C halogen-bond interaction are 0.19 and 4.0 eV, respectively, and its associated S 2 /Δε is 9.4 × 10 3 (see Figure 6 and Table S5 for all the Me m YH•••ICN complexes).The LP I orbital of ICN has a large amplitude on the I side and overlaps with the empty σ* Y−H of Me 3 SiH, in which S is 0.15 (Figure 6).However, this σ* Y−H ← LP I hydrogen-bond interaction is significantly weaker due to a large Δε of 13.3 eV, leading to an S 2 /Δε of only 1.7 × 10 3 , which is about five times weaker than that of the σ Y−H → σ* I−C halogen-bond interaction (Figure 6).Therefore, the  1).However, since the hydrogenbonding mechanism is negligible in the Me m YH•••ICN complexes (vide supra), the population in the empty σ* Y−H orbital does not significantly change and, therefore, cannot be responsible for the Y−H bond elongation in these complexes (Table 1).In fact, the redshift in the Me m YH halogen-bond acceptors is a consequence of their Lewis basicity.In the previous section, we showed that the halogen-  1).Consequently, the Y−H bond becomes longer and, thus, redshifts, as the σ Y−H bonding orbital loses electrons due to the halogen bond.Therefore, the redshift in the Y−H bond stretching frequency should also be expected in situations when hydridic Y−H δ− fragments behave as a Lewis base and hence is not an exclusive feature of hydrogen-bond donors.
A similar phenomenon is found when the hydridic hydrogen of Me 3 SiH engages in a stabilizing intermolecular interaction with the different electron-poor molecules studied by Civis, Hobza, and co-workers, 6 that is, ICF 3 , BrCN, S(CN) 2 , P(CN) 3 , and K + .In all these complexes, the Si−H bond elongates and redshifts upon complex formation.However, this is not because Me 3 SiH behaves a hydrogen-bond donor, but as a bond acceptor.We find that there is charge transfer from Me 3 SiH into the electron-poor fragments and the population in the filled σ Si−H bonding orbital is reduced, which, in fact, characterizes different intermolecular interactions, e.g., halogen bonds, chalcogen bonds, and pnictogen-bonds 11 (see Table S6; see addition analyses on palladium hydride, boron hydride, beryllium hydride, and lithium hydride in Tables S7 and S8).A bonding motif in which a hydridic hydrogen acts as the acceptor of a hydrogen bond exists in the particular form of dihydrogen bonds (DHB); this has been described elsewhere. 7Thus, we have presented clear evidence that the interaction between the hydridic hydrogen of Me 3 YH and an electronpoor molecule should not be seen as any kind of hydrogen bonding but instead as a different intermolecular interaction named after the nature of the electron-poor bond donor.■ THEORETICAL METHODS Computational Details.All calculations were carried out using the Amsterdam Density Functional (ADF) 2023.101program. 12All stationary points and energies were obtained using relativistic, dispersion-corrected density functional theory at ZORA-BLYP-D3(BJ)/TZ2P (see Tables S9, S10, and S11 in the Supporting Information for the Cartesian coordinates).This approach comprises 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). 13he empirical DFT-D3(BJ) correction developed by Grimme and coworkers, 14 which contains the damping function proposed by Becke and Johnson, 15 is used to account for nonlocal dispersion interactions.Scalar relativistic effects are accounted for using the zeroth-order regular approximation (ZORA). 16This level has been proven to accurately describe weak interactions. 17Molecular orbitals (MO) were expanded into a large, uncontracted set of Slater-type orbitals (STOs) containing diffuse functions: TZ2P. 18The basis set is of triple-ζ quality augmented with polarization functions, i.e., one 2p and one 3d set on H; one 3d and one 4f set on C, N, O, Si, P, S; one 4d and one 4f set on Ge, As, Se; one 5d and one 4f set on I.All electrons were included in the variational process; i.e., no frozen core approximation was applied.The accuracies of both the Zlm fitting scheme 19a and the Becke integration grid 19b were set to 'EXCELLENT'.
Bond Analyses.Insight into the bonding mechanism is obtained by analyzing the intermolecular interaction between Me m YH (Y = C, Si, Ge, N, P, As, O, S, Se) and the NH 3 or ICN fragments using the activation strain model, 9 which is a fragment-based approach to understanding the energy profile associated with a chemical process in terms of the original reactants.Thus, the total bond energy ΔE is decomposed into the strain energy ΔE strain , which is associated with the geometrical deformation of the individual reactants as the process takes place, plus the actual interaction energy ΔE int between the deformed reactants (eq 4).

E E E
The interaction energy ΔE int between the deformed reactants is further analyzed in the conceptual framework provided by the quantitative Kohn−Sham MO model. 9To this end, it is decomposed into physically meaningful terms, using a quantitative energy decomposition analysis (EDA) as implemented in ADF (eq 5). 9 The analyses are done as a function of the H bond distances along the range of 1.5 to 3.5 Å.Since ΔE strain is negligible (see Tables S1 and S3), we performed the analyses starting from the equilibrium geometry of the complex while keeping all other geometrical parameters frozen.Values in the equilibrium geometries are shown in Tables S2 and S4.
ΔV elstat is the classical Coulomb interaction between the unperturbed charge distributions of the deformed reactants which is usually stabilizing and comprises four components: (i) the electron−electron electrostatic repulsion between the electron densities of fragments 1 and 2, ΔV elstat,ρd 1 ρd 2 ; (ii) the nuclei−electron electrostatic attraction between the nuclei of fragment 1 and the electron density of fragment 2, ΔV elstat,nd 1 ρd 2 ; (iii) the electron−nuclei electrostatic attraction between the electron density of fragment 1 and the nuclei of fragment 2, ΔV elstat,ρd 1 nd 2 ; and (iv) the nuclei−nuclei electrostatic repulsion between the nuclei of fragments 1 and 2, ΔV elstat,nd 1 nd 2 .
The Pauli repulsion energy (ΔE Pauli ) comprises the destabilizing interactions between occupied orbitals on either fragment (more precisely, between same-spin occupied spinorbitals on either fragment) and arises from the antisymmetrization of the Hartree wave function due to the Pauli principle.The orbital-interaction energy (ΔE oi ) accounts for charge transfer, that is, the interaction between occupied orbitals of one fragment with unoccupied orbitals of the other fragment, including the interactions of the highest occupied and lowest unoccupied MOs (HOMO−LUMO), and polarization, that is, empty−occupied orbital mixing on one fragment, due to the presence of another fragment.ΔE disp accounts for the empirical dispersion corrections as introduced by Grimme et al. 14 To facilitate the analyses, the ASM and EDA were performed using the PyFrag 2019 program. 20oronoi Deformation Density (VDD) Charge Analysis.The Voronoi Deformation Density (VDD) charge analysis allows for the quantification of the flow of electronic charge as a consequence of chemical-bond formation. 21In our model Me m YH fragments, the VDD atomic charge of atom H directly bound to Y (Q H ) is computed by the spatial integration of the deformation density over the Voronoi cell of atom H, which is the space defined by the bond midplanes on and perpendicular to all bond axes between atom H and its neighboring atoms (eq 1).
Herein, the deformation density Δρ(r) = [ρ(r) − ∑ i ρ i (r)] is density change going from a superposition of the original atomic densities at the positions of the molecule to the actual density of that molecule.This atomic or so-called promolecular density is defined as the sum of the (spherically averaged) ground-state atomic densities ∑ i ρ i (r).This is the fictitious state in which the charge density has not been affected by chemical bonding and in which all atoms have zero charge.Then, Q H represents the amount of charge that, due to chemical bonding, flows from a position closer to another nucleus to a position closer to the nucleus of H (Q H < 0), or from a position closer to the nucleus of H to a position closer to another nucleus (Q H > 0).Besides the above regular VDD atomic charges relative to noninteracting neutral atoms, the VDD method allows for the analysis of changes in atomic charges (ΔQ), i.e., charge-density rearrangements, caused by interactions between molecular fragments (eq 2).

Journal of the American Chemical Society
Equation 2 defines the charge rearrangements in an atom A of a fragment i (ΔQ A ) in the final density of the overall complex ρ complex (r) relative to the sum of the initial molecular fragment densities ∑ fragment,i ρ i (r) i .This reveals how the interactions between the molecular fragments affect the electron density distribution in atom A of fragment i.The sum of the ΔQ A of all atoms in a fragment i gives the amount of charge transfer into (ΔQ fragment,i < 0) or out of (ΔQ fragment,i > 0) the Voronoi cell of a fragment i due to the interaction between the molecular fragments (eq 3).
■ ASSOCIATED CONTENT * sı Supporting Information

Figure 2 .
Figure 2. Equilibrium geometries (in Å), electronic bond energies (in kcal mol −1 ; in brackets), and the charge depletion on the NH 3 fragment (ΔQ NH3 ; in milli-electrons; in blue) of the Me m YH•••NH 3 hydrogen-bonded complexes (Y = C, N, O, S, Se) and the Me m YH•••HNH 2 complexes (Y = C, Si, Ge, P, As).Computed at ZORA-BLYP-D3(BJ)/TZ2P.Scheme 2. Schematic Molecular Orbital Diagram for the Attractive (Green) and Repulsive (Red) Orbital Interactions in Me m YH•••NH 3 (Y = C, N, O, S, Se) Similar to Me m YH•••NH 3 , the Me m YH fragments involving protonic and close to neutral hydrogens (Y = C, N, O, S, Se) form regular Y−H δ+ •••N δ− hydrogen bonds, in which charge flows into the hydrogen-bond donor Me m Y−H, i.e., positive ΔQ ICN (Figure 5).This bond has a strength of up to 4.6 kcal mol −1 for MeOH•••NCI (Figure 5).On the other hand, the Me m YH fragments involving a hydridic hydrogen (Y = Si, Ge, P, As) form regular H δ− •••I δ+ −C halogen bonds, in which charge flows out of the halogen-bond acceptor Me m Y−H into the halogen-bond donor I−CN, i.e., negative ΔQ ICN (Figure 5).There is one intermediate situation, namely, the Me 3 CH fragment, which shows both Me 3 CH•••NCI and Me 3 CH•••ICN bonding modes.As will become clear, this change in bonding mode occurs because we go from protonic Me m YH•••NCI
bond donor− acceptor mechanism in the Me m YH•••ICN complexes is the donation of charge from the filled σ Y−H orbital of Me m YH into the empty σ* I−C orbital of ICN.For example, in the series of Me 3 CH•••ICN, Me 3 SiH•••ICN, and Me 3 GeH•••ICN, the population in the filled σ Y−H orbital is reduced to 1.99 electrons, 1.94 electrons, and 1.94 electrons respectively, while there is charge accumulation in the ICN fragment, i.e., negative ΔQ ICN (Table

■
CONCLUSIONSWe have quantum chemically analyzed the bonding mechanism of a series of Me m YH•••NH 3 and Me m YH•••ICN complexes, in which Y = C, Si, Ge, N, P, As, O, S, Se and m = 3, 2, 1, using quantitative Kohn−Sham molecular orbital (KS-MO) theory.We showed that Me m Y−H δ+ fragments involving protonic hydrogens (i.e., Y = C, N, O, S, Se) form regular Y−H δ+ •••N δ− hydrogen bonds, whose stability is due to the H δ+ •••N δ− electrostatic attraction and the charge transfer from the hydrogen-bond acceptor NH 3 into the hydrogenbond donor Me m Y−H δ+ .The Me m Y−H δ− fragments involving hydridic hydrogens (i.e., Y = Si, Ge, P, As) are unable to act as hydrogen-bond donors and, instead, behave as Lewis bases, donating charge into electron-poor fragments, such as ICN, forming a H δ− •••I δ+ −C halogen bond.Therefore, our findings do not support the proposal to change the IUPAC definition of hydrogen bonds to include molecules with partially negatively charged H as hydrogen-bond donors. 6
Journal of the American Chemical Society Regular hydrogen bonds, as in Me m Y−H δ+ •••NH 3 , involve charge transfer into the empty σ* Y−H antibonding orbital of the hydrogen-bond donor fragment.This hydrogen-bond donor−acceptor interaction is negligible in the Me m Y−H δ− ••• ICN complexes, and the charge transfer goes in the opposite direction from the occupied σ Y−H bonding orbital into the ICN fragment.This is because ICN is a poor electron donor on the I side, which leads to a weaker hydrogen-bond donor− acceptor interaction in Me m Y−H δ− •••ICN.In turn, the covalent component in Me m Y−H δ− •••ICN is dominated by the halogenbond donor−acceptor interaction between the occupied σ Y− H bonding orbital and the empty σ* I−C antibonding orbital of ICN.Therefore, the Me m Y−H δ− fragments are halogenbond acceptors, not hydrogen-bond donors.The accumulation of charge in the empty σ* Y−H antibonding orbital causes the Y−H bond elongation and, thus, the typical redshift in the of the Y−H stretching frequency for regular Me m Y−H δ+ •••NH 3 hydrogen bonds.However, the elongation the Y−H bond can also be caused by other factors, e.g., the depletion of charge in the occupied σ Y−H bonding orbital in halogen-bonded Me m Y−H δ− •••ICN complexes.Therefore, the redshift in the Y−H stretching frequency should not be used as the unique but as one of the diagnostics to characterize hydrogen bonds.