O–Li⋯O and C–Li⋯C lithium bonds in small closed shell and open shell systems as analogues of hydrogen bonds

From H-bonding to Li-bonding – Li-bond as an analogue of the “classical” H-bond

Structures of representative hydrogen and analogous lithium-bonded complexes with oxygen as an electronegative atom are summarized in Fig. 1 for several closed shell and open shell systems. Binding energies and Hirshfeld charge and spin analyses data are collected in Tables 1 and 2, respectively.

Fig. 1:

Selected DFT geometrical parameters of the investigated structures. Distances are given in Angströms, and angles in degrees. In cases where symmetry results in equal values, only one representative value is provided. All geometries were optimized without using symmetry constraints. Symbols C ₁, C ₂ and C _s indicates possible symmetry of structures. Complete information about structures is available in Section S2 of SI.

A textbook example of a typical hydrogen-bonded system is the Zundel H₃O⁺⋯H₂O cation. ⁶⁹ This system, at its minimum energy, takes on the C₂ symmetrical structure (in accord with high level calculations of Xie et al. ⁶¹ ) with the H-bonded hydrogen lying in the central position between two water molecules of (H₂O–H–OH₂)⁺. The O–H distance in water molecules is 0.966 Å, the distance between oxygen and central hydrogen is longer, 1.196 Å, as expected for a “classical” hydrogen bond. The O–O distance is 2.390 Å, the OHO angle is 174.81°, i. e. the hydrogen bond is almost linear. This all is well known; see, e. g. Ref.  ⁶¹ .

Upon optimizing the lithium analogue of this system, (H₂O–Li–OH₂)⁺, we obtained slightly different arrangement compared to (H₂O–H–OH₂)⁺: the water molecules are further apart – the O–O distance is 3.683 Å (O–Li and Li–O bonds have a length of 1.844 Å), and the lithium atom carries a charge 0.56, much higher than that of hydrogen (0.17) in (H₂O–H–OH₂)⁺. As with (H₂O–H–OH₂)⁺, the Li-bond is almost linear, the OLiO angle being 173.44°. Our finding that both O–H–O and O–Li–O bonds in (H₂O–H–OH₂)⁺ and (H₂O–Li–OH₂)⁺ are slightly bent agrees with data from Ref.  ⁶¹ , while Duan and Scheiner report the D_2d structures. ⁶³

Similar analysis for the anionic system HO⁻⋯H₂O shows that the length of the O–H bond for hydrogen atoms not involved in H-bonding is 0.959 Å, while being 1.225 and 1.217 Å, respectively, for the hydrogen atom involved in H-bonding. Therefore, this structure is slightly asymmetric. The angle OHO is 177.48°. For the lithium analogue, the pattern is similar: the O–Li and Li–O distances are 1.694 Å and 1.717 Å, respectively, so again, the (HO–Li–OH)⁻ structure is slightly asymmetric. The angle OLiO is 178.68°.

The binding energies of positive H- and Li-bonded systems with the DFT method agree very well with our high-level CCSD(T) data and data from the literature, as presented in Table 1. With both DFT and CCSD(T) methods, the binding energy is lower for the (H₂O–Li–OH₂)⁺ cation than for (H₂O–H–OH₂)⁺, by 13 and 7 %, respectively.

Less satisfactory agreement between our binding energies and published data holds for the negatively charged (HO–H–OH)⁻ complex. All data in Table 1 spread in the interval of 112 (our CCSD(T) value) to 151 kJ/mol (our DFT value). For CCSD(T) calculations, we also performed corrections for the basis set superposition error (BSSE), which have only a small effect on the binding energies. Details are given in Section S1 of the Supplementary information (SI).

We were unable to find published data for the Li-bonded analogue (HO–Li–OH)⁻ of the (HO–H–OH)⁻ complex. Regardless of the spread of the results with the DFT and CCSD(T) methods, our data indicate that the binding energy for (HO–Li–OH)⁻ is more than by 153 kJ/mol higher than for the (HO–H–OH)⁻ anion. The Hirshfeld charge analysis in Table 2 shows that the lithium atom in the O–Li–O bond carries much higher positive charge than hydrogen in the O–H–O bonds for positively and negatively charged complexes. This is related to the much lower electronegativity of the Li atom than that of the H atom. The dominant negative charge resides on oxygen atoms in (H₂O–Li–OH₂)⁺ and (HO–H–OH)⁻ complexes, as expected. This indicates substantial charge transfer within both H- and Li-bonds in all closed shell complexes.

The last two species presented in Fig. 1 and Tables 1 and 2 are neutral H₂O–Li–OH₂ and HO–Li–OH molecules, both doublets. The H₂O–Li–OH₂ complex is treated in the literature as a hydrated metal radical, not as a H-bonded system. ^{67 , 70} Nonetheless, these complexes are relevant for comparison with the properties of the neutral doublet C₃–Li–C₃ Li–bonded complexes, the topic of the next Section “C₃–H–C₃ and C₃–Li–C₃ ”.

Geometric data of the H₂O–Li–OH₂ radical are inserted in Fig. 1 and are similar to those in Ref.  ⁶⁷ . The O–Li distances in the O–Li–O bond are 1.878 Å and 1.879 Å, respectively, only 0.03 Å larger than for the cationic Li-bonded complex and the O–Li bond is stretched by 0.020 Å in comparison with the O–Li bond in its LiOH₂ fragment. Notable differences are the O–Li–O bond angles in the cationic and neutral complexes. The O–Li–O bond in the cation (H₂O–Li–OH₂)⁺ is nearly linear, while in its neutral radical complex it is bent with the O–Li–O bond angle of 117.0°.

The Hirshfeld charge density in the Li atom of the H₂O–Li–OH₂ radical is negative, −0.13, in contrast to all other species presented in Table 2. This is somewhat unexpected considering the low electronegativity of the Li atom. We note, however, that the severe delocalization of the unpaired electron onto surrounded water molecules was reported by other authors for Li and Na complexes. ^{70 , 71} Alternative charge density analysis from DFT results shows that the Mulliken gross atomic charge on Li is still slightly negative, −0.06, while from the Hartree–Fock wave function it is positive, 0.14 el. The NBO analysis also indicates a positive charge, 0.05. The highest negative charge, −0.25 to −0.38 obtained using various charge density analyses is on the oxygen atoms of water molecules. The dominant Hirshfeld spin density is on the Li atom. Some analogy with the charge and spin density in C₃–Li–C₃ bonded complexes will be discussed in the last part.

The binding energy of H₂O–Li–OH₂ with respect to Li–OH₂ and H₂O is moderate, −61.5 kJ/mol with the CCSD(T) method and similarly with DFT. It is slightly larger than the one from the results of Hashimoto and Kamimoto ⁶⁷ for their C₁ H₂O–Li–OH₂ complex. Their second order perturbation theory (MP2) binding energy with respect to Li + 2H₂O products used for estimating binding energy for a single O–Li bond cleavage is −54.8 kJ/mol.

The neutral HO–Li–OH doublet resembles the adduct of lithium to hydrogen peroxide with a very high binding energy with respect to the dissociation channel of Li + two OH radicals, which is more than 550 kJ/mol with both CCSD(T) and DFT methods. With respect to Li + hydrogen peroxide or to LiOH + OH radical, DFT binding energies of 337 and 125 kJ/mol, respectively, were obtained. The length of the two equivalent O–Li bonds is 1.740 Å with a short O–O distance of only 2.214 Å and very sharp O–Li–O angle, 79°. We do not consider the neutral HO–Li–OH doublet species as a Li-bonded system. Nevertheless, both doublet radicals allow us to estimate some of their important properties. To be more specific, the adiabatic ionization energy of H₂O–Li–OH₂ is 3.7 eV and the adiabatic electron affinity of the radical HO–Li–OH is 3.5 eV, as obtained using the CCSD (T) method and DFT-optimized geometries. Let us note that, e. g., (HO–Li–OH)⁻ belongs among the negative secondary ion species considered in the research of lithium air batteries. ⁷²

Finally, we compare potential energy curves corresponding to transfer of H or Li atom in between two fixed oxygen atoms in complexes with (almost) linear H- and Li-bonds. We restrict ourselves to two model species, (HO–H–OH)⁻ and (HO–Li–OH)⁻ anions. In both cases, we fix the O–O distance at 5 Å which is sufficiently large to develop the double-well potentials in the potential energy curves. This is really the case, as shown for the H- and Li-bonded species in Figs. 2a and b. The energy curves resulting from DFT, MP2, and CCSD(T) single-point calculations are close to parallel for (HO–H–OH)⁻ as well as for the (HO–Li–OH)⁻ anion. The CCSD(T) barrier height for (HO–H–OH)⁻ is 429 kJ/mol. The order of magnitude lower barrier, 17 kJ/mol, for the fixed O–O distance of 5 Å is obtained for the movement of the Li atom in the (HO–Li–OH)⁻ anion. This is in part due to our selection of the O–O distance, 5 Å, which is by 2.6 Å larger than the optimized value for (HO–H–OH)⁻, but only by 1.6 Å for (HO–Li–OH)⁻. The potential energy curves for the H- and Li-bonded anions (HO–H–OH)⁻ and (HO–Li–OH)⁻ at their optimized O–O interatomic distance as shown in Figs. 2c and d, respectively, reveal only a single minimum in both cases (very flop for (HO–H–OH)⁻), again demonstrating the qualitative analogy for hydrogen and lithium bonds.

Fig. 2:

Potential energy curves for transfer of H and Li atoms, respectively, along the O–O bond line. Energy curves are shifted to zero at their respective minima. At the presented scale, the curves in Figs. (c) and (d) are nearly indistinguishable due to their considerable overlap. (a) Transfer of H atom from (HO–H–OH)⁻ to (HO–H–OH)⁻. O–O distance is fixed at 5 Å. (b) Transfer of Li atom from (HO–Li–OH)⁻ to (HO–Li–OH)⁻. O–O distance is fixed at 5 Å. (c) Transfer of H atom from (HO–H–OH)⁻ to (HO–H–OH)⁻. O–O distance is fixed at DFT-optimal value (2.44154 Å). (d) Transfer of Li atom from (HO–Li–OH)⁻ to (HO–Li–OH)⁻. O–O distance is fixed at DFT-optimal value (3.41106 Å).

C₃–H–C₃ and C₃–Li–C₃

To study the C–Li–C bond, we chose the (H₃C)₂–CH–Li–CH–(CH₃)₂ (diisopropyllithium) model (Fig. 3). We use the shorthand notation C₃–Li–C₃ which indicates that each of the two isopropyl molecules interacting through the lithium bond contains three carbon atoms. Its H-bonded analogue would be the C₃–H–C₃ complex (interaction of isopropyl radical, hereinafter referred as i-Pr^• with propane). The binding energy of C₃–H–C₃ with respect to i-Pr^• and propane is −8.34 kJ/mol. With its Li counterpart, C₃–Li–C₃, the binding energy with respect to i-Pr^• and i-Pr–Li fragments is much higher, −44.78 kJ/mol. An important part of these interactions arises from dispersion forces. Their importance can be estimated by omitting D3(BJ) and E⁽³⁾ corrections that supplement the DFT CAM-B3LYP functional. In doing so, the energy for the hydrogen binding would be only −0.17 kJ/mol, and the energy for the lithium binding would be −33.94 kJ/mol. A significant part of the dispersion interaction in the binding energy means that the C₃–H–C₃ complex should not be considered as a H-bonded system as defined by the IUPAC panel. Actually, this complex is thermochemically unstable under ambient conditions (T = 298.15 K, p = 1 atm), with ΔH = −3.01 kJ/mol and ΔG = 33.87 kJ/mol. The complex with the lithium bond is also thermochemically unstable, with ΔH = −38.84 kJ/mol and ΔG = 5.34 kJ/mol, but in this case stability can be reached at just slightly lower temperatures (below about 265 K). For the sake of comparison, a low binding energy was also found for the H-bond in the anion (CH₃–H–CH₃)⁻, but upon substitution of one or two hydrogen atoms by halogens in the CH₃ group it increased significantly. ⁷³

Fig. 3:

DFT-optimized structures corresponding to C ₃–H–C₃ and C₃–Li–C₃. For the structure on the left, the angle C₁C _α C₂ is 112.6°, the angle C₃C _β C₄ is 120.6°, and for the structure with lithium on the right, the angle C₁C _α C₂ is 109.1° and the angle C₃C _β C₄ is 119.8°. Complete information about structures is available in Section S3 of SI.

Although the neutral C₃–H–C₃ complex is not considered as a hydrogen-bonded species, we will continue to talk about some analogies between C₃–Li–C₃ and C₃–H–C₃ structures. The important geometry parameters of the C₃–Li–C₃ complex in its optimized structure (Fig. 3) are as follows: C _α –Li and Li–C _β distances are 2.00 Å and 2.30 Å, respectively. The angle C _α –Li–C _β is 131.2°. For comparison, C _α –H and H–C _β distances are 1.09 Å and 2.76 Å, respectively. Thus, hydrogen is significantly shifted towards C _α , so the C₃–H–C₃ structure represents only a weak adduct i-Pr^• with propane.

The C _α –C _β distance between carbon atoms is 3.76 Å for the structure C₃–H–C₃ and 3.92 Å for the structure with the lithium atom. Clearly, there is a noticeable similarity between the C₃–Li–C₃ and C₃–H–C₃ structures irrespective of the low stability of the C₃–H–C₃ complex. An important difference is seen by the comparison of the length of the C _α –Li bond in the C₃–Li–C₃ complex, 2.000 Å and in its fragment (for definitions, see the footnote in Table 3), 1.992 Å, the difference of 0.008 Å. In contrast, the C–H bond length of the H-bonded hydrogen in C₃–H–C₃ and its propane fragment is within the optimization precision the same, 1.092 Å. This is in line with the low H-binding energy in this species. Summarizing, C₃–Li–C₃ can be well qualified as a lithium-bonded complex, as an analogue of H-bonding considering its binding energy (in terms of the Gibbs energy, particularly at lower temperatures) and the geometry characteristics including the C _α –Li–C _β bond angle 131°. We note that according to the IUPAC definition, ¹ the hydrogen-bond angle C _α –H–C _β (and similarly the lithium-bond angle) approaches in most cases 180° and should be at least higher than 110°.

The shape of the single- or double-well potential energy curve of the H (or Li) atom motion within the H- or Li-bond, its symmetric or asymmetric form, belongs among the important characteristics of the hydrogen (or lithium) bonded species. The existence of single- and double-well potentials in bridged carbanions with linear C–H–C hydrogen bonds was analyzed by Wang and Yu. ²⁰ To proceed with the C₃–H–C₃ H-bond and C₃–Li–C₃ lithium bond in a similar manner as for the O–H–O and O–Li–O potential energy curves is not straightforward, since the C–H–C and C–Li–C bonds in C₃–H–C₃ and C₃–Li–C₃ complexes are bent. This makes it more challenging to identify properly the reaction path connecting both equivalent minima on the potential energy surface. Focusing on the C₃–Li–C₃ complex we have identified a transition state (TS) with the imaginary frequency of −239 cm⁻¹, which corresponds to movement of lithium between C _α and C _β atoms. It is accompanied by simultaneous reorganization of geometries of both isopropyl radicals, as will be discussed in Section “Analysis of C _α –Li–C _β bond properties”. In this TS, the lithium atom is not located exactly in the central position between C _α and C _β carbon atoms, but it takes the distance of 2.02 Å to C _α and 1.96 Å to C _β . Although we have successfully localized the TS and one of the minima, we failed to create a reaction path between these two stationary points using the intrinsic reaction coordinate (IRC) approach, ⁷⁴ which otherwise represents an effective tool for this purpose. The eventual reason may lie in the complexity of the overall atomic motion involved in this process.

A simple alternative to demonstrate at least approximately the double-well character of the potential energy surface is to follow the vector of amplitudes that correspond to the imaginary vibration frequency in the TS and to perform a series of single-point calculations along this vibration. The result of this approach for C₃–H–C₃ and C₃–Li–C₃ complexes is presented in Figs. 4a and b, respectively. Although TS is not completely symmetric, both minima projected in this way are energetically identical – the difference for C₃–Li–C₃ in Fig. 4b is within the numerical accuracy. For the hydrogen-bonded C₃–H–C₃ complex, with the TS with imaginary frequency of −1881 cm⁻¹, we applied the same procedure.

Fig. 4:

Energy dependence for the displacement of the hydrogen (a) and the lithium atom (b), respectively, along the transition state vibrational mode. Energy curves are shifted to zero at their respective minima. (a) C₃–H–C₃, transition state frequency −1881 cm⁻¹. (b) C₃–Li–C₃, transition state frequency −239 cm⁻¹.

The approach described above is only approximate. Although it gives double-well minima at potential energy curves, it is not suitable to find the reaction trajectory. Minima on the energetic profile, projected in this way, correspond to the points, that might be far from the positions of real potential energy surface minima. In our case, the energy barrier for the displacement of the central H or Li atom along the TS decomposition vibration (see Fig. 4a and b) is 16.7 kJ/mol and 0.3 kJ/mol for C₃–H–C₃ and C₃–Li–C₃ complexes, respectively. In fact, the real energy difference between the optimized minimum (Fig. 3) and the TS is 70.6 kJ/mol for C₃–H–C₃ and 11.0 kJ/mol for C₃–Li–C₃, respectively. We can see that the real barrier, mainly for Li atom movement, is quite low, but still much higher than the one following from above described approximate treatment. This also indicates that the real atomic motion along the reaction coordinate is considerably more complex than the movement along the decomposition mode of the TS.

As we were unable to apply the IRC approach, a second (equivalent) minimum of C₃–Li–C₃ was found using a dummy atom (DA) located in the middle between C _α and C _β and scanning the angle C _α –DA–Li (see Fig. 5). The scan of the angle C _α –DA–Li from 70° to 110° was performed with the following distances fixed: C _α –C _β is 3.93 Å; DA–Li is 0.88 Å; C _α –DA is 1.97 Å and DA–C _β is 1.97 Å. All other structural parameters were optimized for each C _α –DA–Li angle. Using this approach, we were able to optimize the second minimum. Its energy and nuclear repulsion are identical to those of the first minimum.

Fig. 5:

Schematic view of scanning the C _α –DA–Li angle in search for the second minimum. “DA” indicates dummy atom.

Once the TS and both minima were localized, we tried to estimate the isomerization reaction trajectory by connecting these structures using the NEB approach (Nudged Elastic Band), ⁷⁵ implemented in the ORCA package, as an alternative to the IRC method. Within this method, we are searching for MEP (Minimum Energy Path), connecting two structures. The atomic motion along the pathway linking our minima is quite complex. The estimation of MEP, obtained from NEB calculation with 100 intermediate images, employing also previously localized TS, still predicts maximum that is energetically higher than the energy of our TS. This maximum was localized between the first minimum and TS. Deeper inspection of this part of the reaction hypersurface allows us to find a continuous path between our two minima with the maximum corresponding to our TS. This energy profile of the isomerization is shown in lower part of Fig. 6. Obviously, the potential energy surface in wider transition region may contain several stationary points. We were able to identify other local minimum and TS in this region, but these do not play any significant role in the estimate of isomerization barrier. The minimum was too shallow to represent a stable intermediate, and the local TS was energetically slightly lower than TS, described above. Once we found minima connecting path with a maximum at our TS, there was no need to investigate the character of the hypersurface in greater details since this would not modify the activation barrier for the Li transfer within the C _α –Li–C _β  bond.

Fig. 6:

Energy (lower) and selected geometry parameters (upper) profiles for possible NEB reaction path of isomerization of C₃–Li–C₃ complex, connecting both localized minima. Geometrical parameters, selected to characterize intermediate structures are C _α –Li, C _β –Li and C _α –C _β internuclear distances and C _α –Li–C _β angle. In upper image, the scale for distances is on the left and the angle’s scale on the right.

In summary, the isomerization process resembles a bayonet lock mechanism: for the lithium atom moving from C _α to the C _β side, the entire structure must first rotate. Then, the lithium atom “slots” into the new position, and the structure is closed by reversing the rotation (illustrated in the video, available in Supplementary information).

In the upper part of Fig. 6, we present profiles for C _α –Li, C _β –Li and C _α –C _β distances, as well as C _α –Li–C _β angle. We stress, that the crossing point of the C _α –Li and C _β –Li distances corresponding to the Li transfer within the C _α –Li–C _β bond fall into the area of TS. We also note, that in the area around TS the C–Li–C angle tends to be more linear than in both minima.

Analysis of C _α –Li–C _β bond properties

The motivation to investigate and analyze the properties of C–Li–C bonds arises from our previous research on cross-linked polyethylene chains with a group of metal (M) atoms. ³⁸ In the cited work we reported the structural asymmetry of the C–M–C bond in polyethylene chains cross-linked by open shell ns¹ Li, Ag, and Au atoms. Asymmetry is observed in internuclear distances as well as in Hirshfeld charge or spin densities on carbon atoms participating in the C–M–C bonds (see Tables 5 and 6 in Ref. 38]). This phenomenon occurs in complexes of all three investigated open shell metals, but it significantly decreases in the series of Li, Ag, and Au. Cross-linking closed shell atoms, Be, Mg, and Zn, were located exactly in the middle of the C–C bond.

For polyethylene chains cross-linked by the Li atom the difference between the lengths of the two Li–C bonds was about 0.23 Å depending on the length of the polyethylene chain. In the present C₃–Li–C₃ complex, it is slightly larger, 0.30 Å. However, the asymmetry manifests itself not only in the length of C–Li bonds, but also in the directional arrangement of the bonds on both the C _α and C _β carbon atoms (using the notation of Fig. 3). The deviation from the tendency towards planar arrangement in these carbons is best illustrated by the angle of deviation of the C–H bond from the plane defined by C _α (or C _β ) and its two neighboring carbons (i. e. out-of-plane angle; in the following we will refer to it as “deviations from planarity”). As discussed further, it is an informative parameter correlating with the bonding character.

For a carbon radical in a hydrocarbon chain planar arrangement of atoms bound to the pertinent atom (sp ² hybridization) is typical, with the unpaired electron in a p orbital being perpendicular to this plane. In case of non-equivalent substituents deviation from planarity is often more pronounced. To the extent the p _z unpaired electron participates in formation of a covalent bond the affected carbon undergoes a transformation from a planar to a tetrahedral arrangement (sp ³ hybridization). Indeed, we observed strong correlation between the Hirshfeld spin density and the deviation from planarity in these carbons for open shell complexes containing C–M–C bonds. ³⁸

Let us apply these general considerations to the C₃–Li–C₃ complex. In our previous work, ³⁸ we demonstrated that the charge and the spin are concentrated on the C _α –Li–C _β moiety. Therefore, in Table 3 we present spin densities for C _α , C _β , and Li atoms, evaluated using three different types of diagnostics, namely Hirshfeld, Mulliken, and NBO spin population analysis. All of them predict consistently almost no spin density on C _α , marginal on Li, while the dominant portion of spin density is localized on the C _β atom. Hirshfeld spin distribution on C _β is 0.64.

This is in line with the nearly tetrahedral configuration sp ³ at C _α (deviation from the planarity being 60°) and the slightly distorted quasi-planar configuration sp ² at C _β (deviation from the planarity being 21°). This can also be illustrated on molecular orbitals, involved in the C _α –Li–C _β bond displayed in Fig. 7. Orbital on Fig. 7a approximates a typical sp ³ σ orbital of the C _α –Li bond, while orbital on Fig. 7b is close to the p _z orbital on C _β (slight asymmetry is caused by non-ideal planarity on C _β ).

Fig. 7:

Relevant orbitals involved in the Li-bonding, (a) and (b), and spin density (c) in C₃–Li–C₃ complex, obtained using unrestricted Kohn-Sham DFT (UKS) calculation. (a) Molecular orbital representing polar C _α (sp ³)–Li σ bond in C₃–Li–C₃ complex. UKS orbital from (α) orbital set. Conture = 0.09. (b) Molecular orbital of p _z -like type on C _β (sp ²) in C₃–Li–C₃ complex (containing unpaired electron). UKS orbital from (α) orbital set. Conture = 0.09. (c) Spin density distribution in C₃–Li–C₃ complex. Conture = 0.01.

Orbitals discussed in this section were obtained using the Unrestricted Kohn-Sham DFT (UKS) approach and were taken from the α-set. The σ (C _α –Li) orbital is doubly occupied in the C₃–Li–C₃ complex, and the spin polarization effect for this orbital is very small. Thus, the corresponding counterpart of this orbital from the β-set has an almost identical spatial part (the difference in orbital energies is 0.001 a.u.). Orbital on Fig. 7b contains an unpaired α electron, so it’s β-counterpart is unoccupied. The total UKS spin density for C₃–Li–C₃ complex, as shown in Fig. 7c, reflects the shape of a p _z -like orbital for the unpaired electron. This is in agreement with results from the spin diagnostics, as the density is dominantly located on the C _β atom. Furthermore, complex structures in Fig. 7 once again demonstrate the tetrahedral and quasi-planar configuration on C _α and C _β , respectively.

Can bonding properties in C _α –Li–C _β be qualified as a lithium analogue of an H-bond?

Lithium typically forms a single bond, and its ability to form additional bonds with, e. g. the C _β carbon atom of the second C₃ group has no support in its electronic structure. In the i-Pr–Li fragment of the C₃–Li–C₃ complex there is a strong polar C _α –Li bond with the dissociation energy of i-Pr–Li to Li + i-Pr^• products −133.44 kJ/mol as calculated using the DFT method.

Our calculations indicate an attractive interaction of the i-Pr–Li molecule and the isopropyl radical i-Pr^• due to the positive charge on lithium from the C _α –Li bond with the localized unpaired electron on the C _β carbon atom of the i-Pr^• radical. To qualify the C₃–Li–C₃ bonding as a lithium analogue to H-bond in terms of the IUPAC definition, we need to analyze which terms involved in the formation of the C₃–Li–C₃ bond are of “an electrostatic origin, which are those arising from charge transfer between the donor and acceptor leading to partial covalent bond formation between atoms participating in the (in our case) C–Li–C bond and those originating from dispersion”.

The last requirement, i. e. the contribution of the dispersion interactions, is estimated from the DFT results obtained by omitting the dispersion D3(BJ) and E⁽³⁾ terms, as mentioned in Section “C₃–H–C₃ and C₃–Li–C₃ ”. These terms contribute by about 25 % to the total binding energy of the C₃–Li–C₃ complex. In contrast, upon omitting the dispersion contributions in C₃–H–C₃, the binding energy in this complex is practically zero.

Because the electronegativity of the lithium atom is significantly lower than that of carbon, the C⁻Li⁺ bond is strongly polar. As presented in Table 3, the Hirshfeld charges on atoms involved in the C _α –Li bond are −0.29 and 0.30 for C _α and Li, respectively. This high polarity of the bond is supported also by Mulliken and NBO charge population analysis. The electrostatic contribution to binding energy can thus be related to the interaction of the positively charged Li atom from the polar C α − Li⁺ bond with the electron density distribution around the C _β carbon atom of the isopropyl radical. Fig. 8a and b depict the electrostatic potentials of individual i-Pr–Li and i-Pr^• molecules. Isopropyllithium has a very polar C–Li bond, with Hirshfeld charges −0.28 on the central carbon atom (i. e. C _α ) and 0.48 on Li atom indicating that the positive charge on Li in i-Pr–Li is higher than in the C₃–Li–C₃ complex. In the isolated isopropyl radical, we can also identify a small negative charge on the central carbon (i. e. C _β ), on which the unpaired electron is located. Hirshfeld charge and spin density for this carbon is −0.02 and 0.70, respectively. As can also be deduced from Fig. 8b, this charge is located in the p _z orbital. In fact, in organic chemistry, carbradicals, such as i-Pr^•, are attributed a certain degree of the nucleophilic character. Qualitatively, the decrease of the positive Li atom charge upon formation of the C₃–Li–C₃ complex is in line with a slight decrease of the Li charge in several Li–bonded complexes. Examples include CH₃Li–NCH, CH₃Li–N₂ complexes and their fluoride and other analogues, ³¹ and also H₂O–LiF, H₂CO–LiF and other oxygen or sulphur containing molecules. ³⁰ A much lower decrease is observed in their H–bonded counterparts.

Fig. 8:

Electrostatic potential calculated on the surface around molecule. Separated i-Pr–Li (a) and i-Pr^• (b) molecules and the C₃–Li–C₃ complex (c). Charge distributions are based on DFT calculations. (a) i-Pr–Li. (b) i-Pr^•. (c) C₃–Li–C₃. We provide view from two sides.

Summarizing these observations we can assume that the interaction between i-Pr–Li and i-Pr^• is initiated by electrostatic attraction accompanied by charge transfer upon formation of the C₃–Li–C₃ complex. As demonstrated in Fig. 8c, the electron density from the “incoming” i-Pr^• fragment is transferred to the i-Pr-Li fragment, so the isopropyl radical serves as the electron donor and the C₃–Li part as an electron acceptor. Although the magnitude of the charge transfer is rather low, we observe that the electrostatic potential around the shorter C _α –Li bond is completely negative, while around the longer Li–C _β bond it is altogether positive. As expected, most of the negative electrostatic potential remains around the C _α atom, increasing only marginally compared to isolated systems (from −0.28 to −0.29), measured by Hirshfeld charges. Furthermore, most of the positive electrostatic potential area is still located around the Li atom, but its positive charge in the complex is noticeably reduced in comparison with the free i-Pr–Li (from 0.48 to 0.30, according to Hirshfeld charges). This is the consequence of the charge-shifts through the whole complex. For the same reason, negative charge from C _β is completely drained according to Hirshfeld analysis. It is worth noting that the Mulliken and NBO charge analysis suggest certain amount of residual negative charge on C _β in the complex (see Table 3). However, we consider Hirshfeld analysis to be more reliable in this case, as the other two approaches predict rather overestimated charges for other complexes and/or atoms as well shown in Table 3. All the aforementioned factors collectively contribute to the formation of the asymmetric C _α –Li–C _β  bond.

To conclude this part, we return to the C₃–H–C₃ complex. In contrast to the C α − Li⁺ bond, the C _α –H bond in propane is significantly less polar. Consequently, the electrostatic contribution is small. Also, as presented in Table 3, only small charge transfer is observed in the C₃–H–C₃ complex. All this leads to a low binding energy of −8.3 kJ/mol, almost exclusively due to the dispersion interaction. Thus, the C₃–H–C₃ complex represents only a sizably asymmetric adduct of the isopropyl radical to propane, having a significantly weaker bond compared to C₃–Li–C₃, not compliant with the definition of H-bond.

With their positive induction effect (+I), both hydrocarbon ends of the secondary C _β carbon contribute importantly to the stability of the free radical on the C _β carbon. In the case of dimethyllithium (Me–Li–Me), both C–Li bonds are of the same length, however, in case of non identical ligands, such as ethylmethyllithium (Me–Li–Et) or isopropylmethyllithium (Me–Li–i-Pr), it is not the case. From the discussion so far it is clear that asymmetry of the C–Li–C occurs also for identical ligands, although we failed to optimize an asymmetric Me–Li–Me complex. If the carbon radical is located on ethyl (or secondary isopropyl) carbon it is stabilized by the +I effect of one (or two) methyl groups, which causes the asymmetric arrangement to be energetically preferred. This conclusion was also reached by Zhi-Feng et al. ⁷⁶ Stabilization through +I effects increases with the chain size, which could be one of the factors that leads to the slight asymmetry with increasing chain length in PE cross-linked with Ag and Au atoms as well. ³⁸

We recall that the interaction of lithium with electron-donating atoms/groups, i.e. Li-bonding as an analogue of hydrogen H-bonding, was already reported in several works; see e. g. Refs. 21], [23]. An Li-bond with participation of two carbon atoms is not treated in these works, but its theoretical description and the characterization of the nature of C-Li bonding ⁷⁷ can be valuable to understand complex molecular systems, such as Li atoms confined within nanotubes, or similar structures. ^{38 , 78}