The dihydrogen bond in X3C–H⋯H–M complexes (X = F, Cl, Br; M = Li, Na, K). A correlated quantum chemical ab initio and density functional theory study

Quantum chemical calculations were performed on nine dihydrogen-bonded complexes with haloform (F3CH, Cl3CH and Br3CH) as a proton donor and alkali metal hydride (HLi, HNa and HK) as a proton acceptor.

MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) results show that the stabilization energies of these complexes are large and comparable to the stabilization energies of standard H-bonded complexes.

Elongation and weakening (red shift) of the CH, HNa and HK bonds upon complexation were found while contraction and strengthening (blue shift) was observed in HLi.

The H⋯H bond was found to be ionic and its ionicity is larger than that of the H⋯Y bond in standard and improper H-bonds.

The calculated free energy (ΔG) revealed that only potassium hydride complexes (F3CH⋯HK, Cl3CH⋯HK and Br3CH⋯HK) are stable under standard conditions (T = 298.150 K and p = 101.325 N m−2) in the gas phase.

To elucidate the role of the electrostatic contribution, the optimization of the proton donor and proton acceptor molecules in the electric field of a partner was performed.

The HLi bond is contracted in the electric field of the haloform while the HM (M = Na, K) bonds are elongated and the electrostatic field itself is sufficient explanation of these phenomena.

Natural bond order (NBO) and natural resonance theory (NRT) analyses were performed.

The NBO analysis revealed that significant electron density was transferred from the σ bonding orbital of a proton acceptor to the antibonding σ*(CH) orbital of the proton donor.

Symmetry adapted perturbation theory (SAPT) was utilized to decompose the total interaction energy into physically correct contributions.


The first examples of a new type of bonding realized between two hydrogens (X–H⋯H–Y), currently called a dihydrogen bond (DHB) were published in the late 1960s by M. P. Brown and coworkers,1,2 but the concept of this bond was introduced by Richardson3 in 1995.

Typically, the DHB occurs between positively and negatively charged hydrogens.

This takes place when the first hydrogen is covalently bound to an element which is more electronegative than hydrogen and, simultaneously, the second hydrogen is bound to an element more electropositive than hydrogen.

Usually, X = O, N, S, halogen or C, and Y = Ir, Mo, Re, Li, Na, K, B. Since the second hydrogen atom acts as a proton acceptor this kind of interaction is considered an unconventional hydrogen bond.

The DHB is analogous to a classical hydrogen bond.

The distance between the two hydrogen atoms is shorter than 2.4 Å (the sum of the van der Waals radii) and the strength of the DHB is normally between 4 and 6 kcal mol−1, which corresponds to the average strength of a standard hydrogen bond.4–6

In recent years, much attention has been paid to understanding DHBs.7–16

The nature of classical H-bonding is well understood.

In classical H-bonding the electron density (ED) is transferred from the proton acceptor (lone electron pairs or π-electrons) to the σ* antibonding orbital of the X–H bond of the proton donor which causes weakening of this bond, its elongation, and a concomitant decrease in the X–H stretching frequency.17

In 1980, Sandorfy et al18. when measuring the association of fluoroparaffins with various proton acceptors, reported a shift in the C–H stretching frequency to higher values (so called blue shift).

Further experimental evidence of the blue shift in the C–H stretching frequency appeared in 198919 and .199720

Because the most important features (shortening of the C–H bond and blue shift of the respective stretching vibration frequency) were opposite to the characteristics of a standard H-bond, we called this bonding type improper, blue-shifting H-bonding.21

As mentioned before, the DHB of the X–H⋯H–Y type is considered to be an unconventional hydrogen bond analogous to a standard hydrogen bond.

This means that, regarding a proton donor (X–H) we should observe analogous features to those found in the case of a classical H-bond (elongation and weakening of the X–H bond and a red shift of the respective stretching frequency).

The question remains however, what happens to the vibration characteristics of the proton acceptor upon formation of the DHB?

McDowell and Forde22 studied isotope effects in the BeH2⋯HCN complex and they found that proton acceptor (BeH2) harmonic vibrational frequencies (symmetrical as well asymmetrical stretching) are blue-shifted upon complexation.

Grabowski14,23 investigated complexes of HF as a proton donor with different proton acceptors.

He showed that in the cases of HLi, HNa, H2Be and H2Mg the H–X (X = Li, Na, Be, Mg) bond involved in the DHB becomes shorter upon complexation.

Berski, Lundell and Latajka24 have studied the XeH2⋯H2O complex and have shown that the stretching frequencies of the proton acceptor are shifted to higher values (blue shift) upon complexation.

The aim of this paper is to study the DHB in complexes formed by haloforms (F3CH, Cl3CH and Br3CH) as a proton donor, and alkali metal hydrides (HLi, HNa and HK) as a proton acceptor.

Haloforms possess a negative gradient in their dipole moment, which means that upon contraction of the C–H bond, the dipole moment of the molecule increases.

Let us mention here that in the majority of systems this gradient is positive which indicates that the dipole moment of a system increases when the X–H bond increases.

Consequently, when haloforms are bound to proton acceptors, they mostly form improper blue-shifting H-bonds.

Thus the question arises: what will happen when these proton donors are bound to an alkali metal hydride which most often exhibits a contraction of the Y–H bond?

The other goal of the paper is to explain the nature of improper blue-shifting hydrogen bonds in complexes with HLi as a proton acceptor.

Theoretical methods

Calculations were performed at the second-order Møller–Plesset perturbation theory (MP2) and density functional method (B3LYP)24,25 levels using the 6-31G(d,p) and 6-311++G(d,p) basis sets.26,27

The DFT method is known to yield reliable characteristics for H-bonding (contrary to stacking where it fails) and its advantage over the MP2 procedure is the fact that it possesses a well-defined one-electron density matrix (like in the Hartree–Fock method) as required for NBO analysis.

The equilibrium structures of the molecules and complexes studied were determined at the B3LYP and MP2 levels.

Natural bond orbital (NBO) analysis28 was performed using the B3LYP electron densities.

In the case of the MP2 method the NBO analysis is less reliable.29,30

The bond orders in the considered systems were obtained from natural resonance theory (NRT) analysis implemented in an NBO version 5.0 program.31

To elucidate the role of the electrostatic contribution, optimization was performed on the proton donor and proton acceptor molecules in an electric field generated by point charges of the proton acceptor or proton donor placed where the atoms were in the complex.

The point charges were calculated using the Merz–Kollman32,33 fitting procedure at the MP2/6-311++G(d,p) level.

The stabilization energy of all complexes was calculated at the MP2/6-311++G(d,p) level and was corrected for basis set superposition error (using the Boys–Bernardi counterpoise correction34) as well as for deformation energy.

Decomposition of the total intermolecular interaction energy into physically correct contributions was made by using the symmetry adapted perturbation theory (SAPT).35–45

This approach, implemented in the SAPT program package,46,47 is based on the standard Rayleigh–Schrödinger perturbation theory supplemented by a technique called symmetrized Rayleigh–Schrödinger (SRS) perturbation for treating the antisymmetry property of the wave function of the complex with respect to the monomers.

All computations, except SAPT decomposition, were carried out with the Gaussian 03 package48.

Results and discussion


Fig. 1 shows the optimized structures of the complexes investigated.

Their geometrical and vibrational parameters obtained at the MP2 and B3LYP levels of theory are presented in Table 1 (“Full complex” column).

As seen from the figure, the CHHM atoms in all of the studied complexes are collinear.

From the data summarized in Table 1 it becomes evident that all C–H bonds in the proton donors (F3CH, Cl3CH, Br3CH) were systematically elongated upon complexation.

Both theoretical methods used predict geometrical changes in the same direction.

The elongation of these bonds given by the B3LYP method was, in all cases, larger than that predicted by MP2.

Shifts in the C–H stretching frequency upon formation of the DHB are presented in Table 1, and, evidently, the red shift of these stretching frequencies is systematically observed.

Table 1 further shows that the intermolecular H⋯H distances were shorter than 2.4 Å (the sum of the van der Waals radii) and systematically decreased in the order F3CH > Cl3CH > Br3CH as well as in the order HLi > HNa > HK.

Thus, the longest H⋯H distance (1.965 Å) was observed in F3CH⋯HLi, while the shortest one (1.565 Å) was in the Br3CH⋯HK complex.

Both methods exhibit the same trends: for chloroform and bromoform complexes the H⋯H distances calculated with the B3LYP method were larger than those calculated with the MP2 method, while in the case of the fluoroform complexes, the opposite situation was found.

We were not able to interpret these changes and trends.

The H–M (M = Li, Na, K) bond in a proton acceptor can be contracted (HLi) or elongated (HK) upon complexation.

In complexes of these two molecules (HLi and HK) both theoretical methods exhibited changes in the same direction.

A different situation was found in the case of HNa molecules, where the MP2 method predicted elongation (0.0014, 0.0007 and 0.0028 Å) while the B3LYP method predicts contraction (−0.0009, −0.0022 and −0.0022 Å) upon complexation with F3CH, Cl3CH and Br3CH, respectively.

It is obvious that contraction or elongation of the X–H bond is concomitant with an increase or decrease in the X–H stretching frequency (blue or red shift).

It must be stressed here that this relationship is valid for a large number of H-bonded and improper H-bonded complexes and up to now we are not aware of any exceptions.

Role of the electrostatic field

The change in geometrical parameters induced by the electric field are presented in Table 1 in the “Electric field” column.

Optimizing the structure of the proton donor in the electric field of a proton acceptor the electrostatic plus polarization effects are considered and the resulting geometry changes originate from the purely electrostatic (Coulombic) and polarization interactions between the proton donor and an electric field.

Both theoretical methods predicted changes in the same direction, except for the C–H bond in bromoform complexes where the MP2 method predicted contraction while the B3LYP method predicted small elongation.

The electric field produced by a proton acceptor yielded, in all complexes, contraction of the C–H bond (MP2 results).

This bond was systematically elongated in full complex calculations which indicates that non-electrostatic effects played a dominant role.

A similar situation was previously found49 in the F3CH⋯Cl complex, where the electric field caused a C–H bond contraction while full complex calculations yielded C–H bond elongation.

Complexes studied thus represent another example where the standard H-bonding behavior (elongation of the C–H bond and a red shift of the C–H stretching vibration) could not be explained by the interaction of a molecule with the electric field and other effects should be considered.

According to the data presented in Table 1, the X–C (X = F, Cl, Br) bonds were elongated in the electric field while these bonds were contracted in the full complex calculations.

The H–M bond (M = Li, Na, K), like the C–H bond, was contracted in an applied electric field.

However, when performing full complex calculations this bond was either contracted (HLi) or elongated (HNa, HK) upon complexation.

Thus it is again evident, that the electric field alone cannot explain the behavior of the HM bond in the complexes studied.

In the case of the HNa and HK systems, non-electrostatic effects evidently play an important role and should be considered.

The last column in Table 1 (Full-electric) shows the changes in the bonds caused by non-electrostatic effects.

Evidently, the changes are opposite to those caused by electrostatic effects.

In the case of the C–H as well as the H–M (M = Li, Na, K) bonds, the electrostatic effects caused contraction while non-electrostatic effects caused elongation.

The opposite situation was found for X–C (X = F, Cl, Br) bonds, where electrostatic effects yielded elongation while non-electrostatic effects caused contraction.

Non-electrostatic effects

Electrostatic effects cause contraction of the C–H and H–M bonds while non-electrostatic effects caused their elongation.

It is now necessary to answer two questions.

First, what kind of non-electrostatic effects are responsible for this elongation?

And, second, are these non-electrostatic effects similar for C–H and H–M bonds?

According to the concept proposed by Alabugin et al.,50 the change of the X–H bond length in the X–H⋯Y complexes is due to two main effects acting in opposite directions.

The hyperconjugative interaction is responsible for bond elongation while an increase in the s-character of the X atom hybrid orbital (known as Bent’s rule) and polarization of the X–H bond is responsible for bond contraction.

When the former effect dominates the X–H bond becomes longer and weaker (standard H-bonding), while when the latter effect is more significant, the bond becomes shorter and stronger.

Improper H-bonding is observed only when the hyperconjugative n(Y) → σ*(X–H) interaction is relatively weak and the respective NBO second-order charge-transfer energy is smaller than 3–5 kcal mol−1.

Table 2 summarizes the calculated second-order interaction energies between the donor–acceptor orbitals (E2(σ(HM) → σ*(CH)).

Since the E2 energy was considerably larger than the mentioned limit (3–5 kcal mol−1), hyperconjugative interaction was responsible for the C–H bond elongation in all of the complexes considered.

It should be stressed here that it was not a typical hyperconjugative interaction since electron density in these complexes was not transferred from a lone-pair orbital but from a σ(HM) orbital.

Investigating the ED changes in the HM subsystems, we found an insignificant ED increase in the antibonding σ*(HM) orbital and a much larger decrease of ED in the bonding σ(HM) orbitals (see above).

Both effects, but mainly the latter one, were responsible for the elongation and weakening of the HM bond.

Let us mention here that a completely opposite situation was found for the σ(CH) and σ*(CH) orbitals.

Figs. 2 and 3 show changes in electron density (ED) in particular orbitals of the proton acceptor HLi (Fig. 2) and the proton donor F3CH (Fig. 3) caused by complexation.

In the case of HLi, the dominant change in electron density (decrease) occurs in the σ bonding orbital, while, with respect to the CHF3, it is the CH σ* antibonding orbital which is characterised by the largest change (increase).

From these figures it is also evident that electron density is transferred from HLi to the CHF3.

To determine which type of non-electrostatic effect plays a role in the change of the C–H bond length, we compared the bond length changes with the ED changes in antibonding Δσ*(CH) orbitals.

A linear relationship (value of the correlation coefficient of the linear regression R2 equals 0.994) between the elongation of this bond and an increase of ED in the σ*(C–H) orbital was found.

This close correlation gives evidence that an increase in ED in the antibonding orbital of the C–H bond is responsible for elongation and weakening of this bond and, further, that it is a dominant non-electrostatic effect.

Concerning the HM (M = Li, Na, K) bond there is no doubt that the decrease in ED in the σ bonding orbital represents the main non-electrostatic effect responsible for the elongation and weakening of this bond that was observed.

Berski et al23. studied the xenon dihydride⋯water complex using DFT theory and concluded that there was no ED transfer (EDT) between subunits, and further, stabilization was mostly due to electrostatic interactions of the dipole–induced dipole type.

Table 2 shows that the EDT between the proton acceptor and the proton donor is comparable to that in standard hydrogen bonding complexes and is much larger than in the case of improper blue-shifting hydrogen bonded complexes.

The NRT analysis allowed us to calculate the bond order and its character.

Table 3 presents the total bond order and its covalent contribution.

The difference between these values (“total” and “covalent”) gives an ionic contribution to the total bond order.

As seen from this table the character of the H⋯H “bond” is ionic (the covalent contribution is negligible, less than 6%) and its value is between 0.015 and 0.057.

For the sake of comparison we performed NRT analysis for the standard (HOH⋯OH2, H3CH⋯Cl, F3CH⋯Cl) and improper blue-shifting hydrogen bonded complexes (H3CH⋯FH, F3CH⋯OH2, CH3CH3⋯OH2).

These calculations show that in both complex types the character of the hydrogen bond is purely ionic and is systematically smaller than 0.005.

The DHBs studied thus have the same character as standard or improper blue-shifting hydrogen bonds, but their ionicity is considerably higher.

A negative value of the Δ(c − m) term indicates that all bond orders in the proton donor as well as in the proton acceptor decrease under complexation.

Charges on atoms

Atomic charges on the monomers and the studied complexes are presented in Table 4.

Charges were determined with NBO analysis, MK (Merz–Kollman) and APT51 (atomic polar tensor) methods at the MP2/6-311++G(d,p) or B3LYP/6-311++G(d,p) levels.

Hydrogen in the proton donor of the DHB complexes possessed a small negative (or positive) charge on the hydrogen atom (F3C–H (−0.02 e), Cl3CH (−0.04 e), Cl3CH (−0.06 e)), while hydrogen in the proton acceptor had a large negative charge on the hydrogen atom: HLi (−0.63 e), HNa (−0.60 e), HK (−0.69 e).

The values presented refer to APT charges.

The differences between the charges on the hydrogen atoms Δq(H⋯H) lies between 0.7 and 1.0 e.

The smallest Δq(H⋯H) was found in the sodium hydride with fluoroform complex (0.71 e), while the largest one was present in the potassium hydride with bromoform complex (0.97 e).

By investigating the Δq(C–H) values, we found that they decreased upon complexation.

Complexation made the charge on the H atoms more positive while the charge on the C atoms became less positive.

An opposite situation was found in the proton acceptor subunit, where the value of Δq(H–M) increased.

The charge on the H atom became more negative upon complexation, while the charge on the M atom became more positive.

When considering only the Δq changes induced by complexation the following conclusions can be drawn:

• In the proton donor subunit, a decrease in Δq(C–H) yields a weaker Coulombic attraction between the carbon and hydrogen atoms, which should cause elongation and weakening of the C–H bond.

These effects were found in all investigated complexes.

• In the proton acceptor subunit, an increase in Δq(H–M) causes a stronger Coulombic attraction between the hydrogen and alkali metal atoms, which should yield contraction and strengthening of the H–M bond.

This was found only in the lithium hydride complexes.

We conclude this paragraph by stating that the behavior of the C–H and H–M bonds in the DHB complexes studied could not be explained only by changes in atomic charges.

Interaction energy terms

Symmetry adapted perturbation theory was utilized for decomposition of the total intermolecular interaction energy into physically meaningful energy contributions.

Table 5 shows the total SAPT interaction energy EintSAPT, the HF (EintHF) and correlation (Ecorr, ΣEcorr) corrections to the interaction energy, as well as the stabilization energy (Eint) determined by the variation method.

The latter values are corrected for the basis set superposition error using the Boys–Bernardi counterpoise correction12 and also for the deformation energy.

Perturbation and variation stabilization energies are similar.

The stabilization energies of the considered complexes (5–10 kcal mol−1) are similar to those of standard hydrogen bonded complexes.

As seen from Table 5, the absolute values of the Eint increase in the order: F3CH < Cl3CH < Br3CH and HLi < HNa < HK.

The largest stabilization energy (9.52 kcal mol−1) was found for the Br3CH⋯HK complex, with the smallest one (5.59 kcal mol−1) for the F3CH⋯HLi complex.

In the fluoroform containing complexes and in the Cl3CH⋯HLi complex, the absolute value of the polarization (electrostatic) term is larger than that for exchange–repulsion.

In our recent paper,49 we showed that the ratio of induction and dispersion energies (I/D index, presented in the last column of Table 5) represented a valuable tool for discriminating between standard and blue-shifted H-bonded complexes.

For standard H-bonded complexes this index is mostly higher than 1.0, while for blue-shifted H-bonded complexes it is mostly less than 1.0.

The I/D index for the DHB complexes studied (cf. Table 5) is much larger than 1.0 which indicates that dispersion energy does not play as important a role in these complexes as in blue-shifted H-bonded complexes.

It should be mentioned that the values of the I/D ratio correlates with the size of the stabilization energy.

Thermodynamic properties

Wei-Liang Zhu et al52. calculated the thermodynamic characteristics of the DHB complex formed by silicane and ammonium.

The calculations were performed using the MP2 and B3LYP methods with different AO basis sets.

The authors concluded that diffusion and polarization functions had a significant effect on the calculated changes in the free energy (ΔG) and suggested that the basis set 6-311++G(d,p) should be used when the B3LYP method is employed.

The thermodynamic characteristics (enthalpy, Gibbs free energy, entropy and reaction rate constant) of the present DHB complexes were evaluated at the recommended level52 (B3LYP/6-311++G(d,p)).

The calculated Gibbs free energies of formation (ΔG) corrected by thermal and zero-point vibrational energies, range from −2.17 to 1.44 kcal mol−1.

Only for potassium hydride complexes does the ΔG have negative values.

This means that only the F3CH⋯HK, Cl3CH⋯HK and Br3CH⋯HK complexes are stable under standard conditions (T = 298.150 K and p = 101.325 N m−2) in the gas phase.

The calculated enthalpy (ΔH) of formation, corrected by thermal energy, ranges from −5.12 to −8.62 kcal mol−1.

The absolute value of ΔH increases in the following order: HLi < HNa < HK and F3CH < Br3CH < Cl3CH (with the exception of the potassium hydride complexes, where ΔH is largest for the Br3CH⋯HK complex).


1) The stabilization energies of the complexes considered range from −5.59 to −9.52 kcal mol−1 and are similar to those in standard hydrogen bonded complexes.

2) The calculated Gibbs free energy (ΔG) is negative only for the potassium hydride complexes (F3CH⋯HK, Cl3CH⋯HK and Br3CH⋯HK), which means that only these complexes are stable under standard conditions in the gas phase (T = 298.150 K and p = 101.325 N m−2).

3) According to NRT analysis the character of the H⋯H “bond” is 94% ionic and its total value ranges from 0.015 to 0.057.

This ionicity is larger than in standard and improper H-bonded complexes.

4) Concerning the C–H and H–M (M = Li, Na, K) bonds in the DHB complexes investigated, electrostatic effects cause contraction while non-electrostatic effects cause elongation.

The non-electroststic effects responsible for the elongation of the C–H and H–M bonds are completely different.

Increasing the electron density in the antibonding orbital of the C–H bond causes elongation and weakening of this bond, evidently the dominant non-electrostatic effect.

A decrease of the ED in the σ(HM) orbital represents the main non-electrostatic effect responsible for elongation and weakening of the HM bond.

5) In the case of the H–Li bond, the contraction of the bond upon complexation is explained by the electrostatic field.

6) The behavior of the C–H and H–M bonds in the DHB complexes studied can not be explained by the changes in atomic charge.

7) The ratio of induction and dispersion energies (I/D) is much larger than one and indicates standard hydrogen bonded character when the proton donor is considered.

8) MP2 and B3LYP yield similar results and an advantage of the latter procedure is the fact that it yields a reliable one-electron density matrix.