**2. Computational Details**

In order to ensure the reliability of the theoretical characterization of the IMHB stabilizing the compounds under investigation, we have decided to use the Gaussian-4 (G4) theory [56]. The G4 theory is a high-level ab initio composite method based on DFT optimized geometries and thermochemical corrections obtained at the B3LYP/6-31G(2df,p) level [56]. Correlation effects are accounted for by using the Moller–Plesset perturbation theory up to the fourth-order and CCSD(T) coupled cluster theory. A further correction, to account for the Hartree–Fock basis set limit, is added using a linear two-point extrapolation scheme and quadruple-zeta and quintuple-zeta basis sets.

However, it would be impossible to apply the G4 scheme to characterize all possible conformers associated with these two series of substituted amino-alcohols HOCHX(CH2)n CH2NH2 and HOCH2(CH2)nCHXNH2 (*n* = 0–5, X = H, F, Cl, Br) under scrutiny because this number is huge in particular when n ≥ 3, and it would be applied only to the most stable ones. In order to make the selection of the most stable conformers, we first located the ensemble of them by using the conformer–rotamer ensemble sampling tool (CREST) recently developed by Grimme [57,58]. This method is based on the semiempirical tightbinding based quantum chemistry method GFN2-xTB [59] in the framework of metadynamics (MTD). Once the conformers ensemble is obtained, the script ENSO (Energetic Sorting of Crest ensembles) [60] is applied to classify them in a three-step process. The first one consists of a single point calculation at pbeh-3c/Def2-SVP [61] level of theory of the different structures of the ensemble. In a second step, the conformers in the range of 25 kJ/mol are selected for optimization at the same level of theory. In the last step, the range of energy is reduced to about 8 kJ/mol, the final energy, and the percentage of Boltzmann distribution being obtained from a single point wb97x/Def2-TZVPP calculations [62]. The conformers with a percentage higher than 1% were chosen to carry out the G4 calculations. It should also be mentioned that, for all the complexes including Beryllium bonds, final energies were also calculated at the G4 level, but, in these cases, instead of using the standard geometry optimization procedure within the G4 formalism, the structures were optimized using a larger basis set expansion, aug-cc-pVTZ, that includes diffuse functions, very often critical to correctly describe non-covalent interactions.

The bonding in all the systems investigated was analyzed through the use of four different approaches, namely the quantum theory of atoms in molecules (QTAIM) [63,64], the electron localization function (ELF) [65], the natural bond orbital (NBO) analysis [66], and the non-covalent interaction (NCI) formalism [67]. In the QTAIM approach, a topological analysis of the electron density of the systems permits the location of its critical points and the paths of minimum gradients connecting them, which leads to an unambiguous definition of chemical bonds, and/or ring and cage structures. The ELF procedure allows a partition of the molecular space in monosynaptic and disynaptic (or polysynaptic) basins in which the electrons of the system are distributed. The monosynaptic ones are associated with core electrons and/or lone pairs, whereas the disynaptic (or polysynaptic) correspond to bonding regions. The NBO method is based on the generation of localized hybrid orbitals which would correspond to Lewis-type representations of the molecular structures. The calculation of second-order orbital interaction energies between occupied and empty orbitals permit quantitatively characterizing donations and backdonations among occupied and empty localized molecular orbitals involved in inter and/or intramolecular interactions. The NCI formalism is an alternative analysis of the electron density, based on the fact that regions of small reduced-density gradient at low electronic densities are associated with the presence of non-covalent interactions. This analysis leads to rather visual representations if a colored scale is used to plot the isosurfaces of the reduced density, in both two- and three-dimensional spaces.

## **3. Results and Discussion**

In our theoretical survey, we have investigated, for each one of the species under consideration, the possibility of having O–H···N or N–H···O IMHBs, though, in almost all cases, the former are stronger than the latter, and, therefore, in most of the cases, the global minima are characterized by the existence of an O–H···N IMHB.

The number of stable conformers of HOCHX(CH2)nCH2NH2 and HOCH2(CH2)nCHXNH2 (*n* = 0–5, X = H, F, Cl, Br) compounds obviously increases as the number of carbon atoms increases along the series, reaching for the larger values of *n* several hundred. In what follows, we will analyze the six more stable unsubstituted HOCH2(CH2)nCH2NH2 (*n* = 0–5) amino-alcohols first, and, after that, we will pay attention to the effect of the X substituent at the α-position with respect to the CH2OH group and with respect to the CH2NH2 group.

#### *3.1. HOCH2(CH2)nCH2NH2 (n = 0–5) Compounds*

We will start our analysis by looking at the effect that the length of the carbon chain has on the strength of the IMHB between the alcohol and the amino functional groups. As expected, the conformer stabilized by the formation of a O–H···N IMHB is more stable (see Figure S1) than that exhibiting a N–H···O IMHB because the hydroxy group is a better proton donor but a weaker base than the amino group, so, in what follows, we will discuss only the systems exhibiting a O–H···N IMHB.

The structures corresponding to the most stable conformer for each value of *n* are shown in Figure 1. It can be seen that the longest O–H···N IMHB corresponds to the first member of family, 2-amino ethanol (*n* = 0) which should be the amino-alcohol with the weakest bond along the series. This bond length reaches its minimum for *n* = 2, which in principle should be the member of the series with the strongest O–H···N IMHB, its strength decreasing for larger values of *n* (*n* = 0–5).

**Figure 1.** G4 optimized structures for HOCH2(CH2)nCH2NH2 (*n* = 0–5) amino alcohols, showing the IMHB length in Å.

Unfortunately, although the calculation of the energy of an intermolecular hydrogen bond is straightforward, this is not so when dealing with IMHBs, though some procedures to estimate it have been proposed [68]. We propose, however, the use of the isodesmic reaction [69] (1) as a suitable method to have, at least, a reasonably good estimate of the relative stabilization gained in these compounds when the IMHB is formed. The isodesmic process we have used corresponds to the first reaction shown in Scheme 1.

**Scheme 1.** Isodesmic reactions to estimate the stabilization produced by the IMHB (reaction (**1**)) and the repulsive interaction between the terminal methyl groups (reaction (**2**)).

Reaction (2) in Scheme 1, in which the carbon chain is fully deployed, was used just to check whether, in the isodesmic reactions proposed, the repulsive interaction between the terminal methyl groups may significantly affect the isodesmic energy obtained with the first reaction. The ideal situation should correspond to that in which the second reaction is thermoneutral. The results obtained for these two reactions at the G4 level of theory are summarized in Table 1. It can be observed that, indeed, the reactions (2) for the set of derivatives investigated are nearly thermoneutral, which is an indication of the reliability of our isodesmic reaction (1) to provide a good estimation of the stabilization energy associated with each IMHB. Not surprisingly, the largest deviation for thermoneutrality of reaction (2) is obtained for the first member of the series, as a consequence of its higher rigidity. Nevertheless, it should be taken into account that, in these isodesmic reactions, and, mainly, when the carbon chain is sufficiently large and very flexible, the number of possible conformers for the three compounds that do not have IMHB is very large, and, in many cases, the energy difference between them is very small, even smaller than 1 kJ·mol−1.


**Table 1.** G4 calculated enthalpies (kJ·mol−1) for the isodesmic reactions included in Scheme 1.

The values in Table 1 show, in agreemen<sup>t</sup> with the IMHB length reported in Figure 1, that the strongest isodesmic stabilization interaction energy corresponds to *n* = 2, being the weakest one corresponding to *n* = 0. These energetic trends are also consistent with the characteristics of the corresponding molecular graphs drawn in Figure 2a, showing that, in all cases, the electron density at the BCP located between the H atom of the hydroxyl group and the N atom of the amino group goes through a maximum for *n* = 2.

**Figure 2.** (**a**) Molecular graphs for HOCH2(CH2)nCH2NH2 (*n* = 0–5) amino alcohols showing the electron density at the BCPs (green dots) and at the RCPs (red dots); (**b**) 3D-NCI plots for the same compounds showing the isosurfaces associated with the different intramolecular interactions.

The 3D-NCI plots included in Figure 2b also show the existence of an isosurface between the OH and the NH2 groups, which denotes the existence of a NCI whose strength increases from *n* = 0 (greenish) up to *n* = 2 (blueish). It is also worth noting that, already for *n*= 1, a second greenish lobe appears attached to the blueish one associated to the van der Waals interactions range involving the chain of carbon atoms. Indeed, for *n* = 2, the two isosurfaces are now independent and, for the remaining systems (*n* = 3–5), the extension of these secondary interactions increases with the length of the chain of carbons.

The evolution of the characteristics of the IMHB along the series is nicely reflected in the IR spectra of the different species. As shown in Figure 3, the absorption band associated with the O–H stretching of the alcoholic function, which, for the first compound (*n* = 0), is predicted to appear at 3715 cm<sup>−</sup>1, is clearly redshifted when moving to larger compounds. This red-shifting is maximum (233 cm<sup>−</sup>1) for *n* = 2, but even for *n* = 5 the red-shifting with respect to *n* = 0 is significant (141 cm<sup>−</sup>1), indicating, in agreemen<sup>t</sup> with the other indices that the IMHB for *n* = 5, though weaker than that for *n* = 2 is still stronger than for *n* = 0.

**Figure 3.** Calculated IR spectra for the HOCH2(CH2)nCH2NH2 (*n* = 0–5) amino alcohols.

*3.2. HOCHX(CH2)nCH2NH2 and HOCH2(CH2)nCHXNH2 (n = 0–5, X = F, Cl, Br) Derivatives*

Let us look now at the effects of halogen substituents at the α-position of both the -CH2OH and the -CH2NH2 functional groups. As indicated above, the number of possible conformers is huge, so, in Figures S2 and S3 of the Supplementary Materials, we present only the optimized geometries of the most stable conformers stabilized by an O–H···N or a N–H···O IMHB. As it was also the case for the unsubstituted amino alcohols, and regardless of whether the halogen substituent is at the α-position of the CH2OH group or the CH2NH2 group, the conformers with a N–H···O IMHB are less stable than those with a O–H···N IMHB, with the only exception being the HOCH2CHXNH2 (X = F, Cl, Br) derivatives (see the first row of Figure S3), where the conformer with a N–H···O IMHB is predicted to be, at the G4-level of theory, slightly more stable than the conformer exhibiting a O–H···N IMHB regardless of the nature of the substituent X.

Focusing our attention then on the compounds stabilized by O–H···N IMHB, it can be observed that, as it was the case for the unsubstituted amino-alcohols, when the halogen substituent (F, Cl or Br) is at the α-position of the CH2OH group, the IMHB length decreases from *n* = 0 to *n* = 2, where it reaches its minimum value. An NBO analysis of these compounds not only indicates (see Figure 4a) that, as expected, the most significant orbital interactions involve the occupied lone pair of the amino group and the empty antibonding σ\*O–H orbital, which necessarily results in a weakening of the O–H bond, but also (see Figure 4b) that this interaction reaches its maximum, regardless of the nature of the substituent (F, Cl or Br) for *n* = 2. It is also very important to note that the same picture shows that this effect increases following the sequence: H < F < Cl < Br, parallel to the energy of the antibonding σ\*O–H orbital decreases, favoring the charge donation from the nitrogen lone-pair. Consistently, the electron densities at the O–H BCP decrease, but those at the IMHB BCP (See Figure 4c) increase following the sequence H < F < Cl < Br (see Figure 4c).

**Figure 4.** (**a**) Dominant orbital interactions associated with the formation of O–H···N IMHBs when the substituents are at the α-position with respect to the CH2OH group (first row) and with respect to the CH2NH2 group (second row); (**b**) variation of the energy involved in these orbital interactions as a function of n for the different substituents considered; (**c**) variation of the electron density at the IMHB BCP as a function of *n* for the different substituents considered.

The effects on the IMHB characteristics by introducing the halogen substituent (F, Cl or Br) at the α-position of the CH2NH2 group are just the opposite as those just discussed for α-substitution with respect to the CH2OH group. Indeed, the presence of an electronegative atom at α-position of the CH2NH2 group results in a reduction of the intrinsic basicity of the amino group, which accordingly becomes a poorer donor towards the σ\*O–H orbital, leading to O–H···N IMHB weaker than in the unsubstituted compounds. Accordingly, this IMHB becomes about 10% longer. Again, the substituent effect increases as H < F < Cl < Br, and, therefore, whereas for substituents α to the CH2OH group the strongest O–H···N IMHB is observed for the Br derivative, when the substituent is α to the CH2NH2 group, the Br derivative exhibits the weaker IMHB. This behavior is in perfect agreemen<sup>t</sup> with the

values of the electron densities at the BCP associated with the IMHB, as shown in Table 2 for the particular case *n* = 2 being taken as a suitable example.

**Table 2.** Electron densities (a.u.) at the O–H···N IMHB BCP in HOCHX(CH2)2CH2NH2 and HOCH2(CH2)2CHXNH2 (X = H, F, Cl, Br).


These different trends are also nicely reflected in the characteristics of the corresponding IR spectra. We are going to illustrate this point again using the case *n* = 2 as a suitable example. As shown in Figure 5a, for the case in which the substitution takes place at the α-position with respect to the CH2OH group, the absorption band associated with the O–H stretching frequency is clearly red shifted upon F, Cl, and Br substitution. If the substitution takes place at the α-position with respect to the CH2NH2 group (see Figure 5b), the O–H stretching band is now blue shifted when H is replaced by F, Cl, Br.

**Figure 5.** Calculated IR spectra for HOCH2(CH2)2CH2NH2 and for compounds: (**a**) HOCHX(CH2)2CH2NH2 (X = H, F, Cl, Br) and (**b**) HOCH2(CH2)2CHXNH2 (X = F, Cl, Br).

#### *3.3. Complexes between HOCH2(CH2)nCH2NH2 (n = 0–3) and BeF2*

In this section, we will examine the effect that the interaction of the amino-alcohols HOCH2(CH2)nCH2NH2 (*n* = 0–3) with a strong Lewis acid as BeF2 will have on the IMHBs stabilizing these compounds and characterized in Section 3.1. However, the presence of the beryllium derivative opens up new scenarios in which new IMHBs enter into play as well as the possibility of having beryllium bonds replacing the IMHBs which characterize the isolated amino-alcohols.

Indeed, the association of BeF2 to the alcohol functional group (see the first column of Figure 6) leads to the amino-alcohols moiety structures being very similar to those exhibited by the isolated amino-alcohol, though the bond length of the OH···N IMHB is much shorter than the one found in Section 3.1 for the isolated system.

**Figure 6.** B3LYP/aug-cc-pVTZ optimized structures for the complexes between HOCH2(CH2)nCH2NH2 (*n* = 0–3) aminoalcohols with BeF2 stabilized through OH···N IMHBs (first column), NH···O IMHBs (second column), NH···O and OH···F IMHBs, simultaneously (third column) and through the beryllium bonds involving both the OH and the NH2 groups (fourth column). The length of all these non-covalent interactions is in Å.

This reinforcement of the OH···N IMHB is the obvious consequence of the significant electron density transfer from the oxygen atom of the hydroxy group to the empty orbitals of the Be atom to form the corresponding beryllium bond, which necessarily increases the proton donor character of the OH group. Indeed, the second-order orbital interaction energies between the nitrogen lone-pair and the σ \*O–H antibonding orbital, responsible for the formation of the O–H···N IMHB, are about four times larger for the BeF2 complexes than for the isolated amino-alcohol as shown in Table S1 of the Supplementary Materials. The effect is qualitatively similar when BeF2 interacts with the amino group (second column of Figure 6), which, upon beryllium association, also becomes a stronger proton donor, reinforcing the N–H···O IMHB, but necessarily to a lesser extent than when the group involved in the alcohol function, with the only exception of the amino-ethanol, in which case the conformer with a N–H···O IMHB is predicted to be 9 kJ·mol−<sup>1</sup> more stable than the one stabilized by the formation of a O–H···N IMHB (see Table 3).

**Table 3.** Relative stability (kJ·mol−1) of the complexes between HOCH2(CH2)nCH2NH2 (*n* = 0–3) amino-alcohols and BeF2, stabilized by the different IMHBs indicated in the first row, or through the bridge resulting from the simultaneous interaction of the Be atom with the O and N atoms of the amino-alcohol.


It is also worth noting that, when the complex is stabilized through the formation of a N–H···O IMHB, the possible formation of a second IMHB by the interaction of the O–H group with one of the fluorine atoms attached to beryllium is open, and, indeed, as shown in Table 3, this new conformer is systematically (from 6 to 11 kJ·mol−1) more stable (compare the third and the fourth column of Table 3). Nevertheless, the most important finding is that, in all cases, the global minimum (fifth column of Table 3) corresponds to a complex in which no IMHBs are formed because the interaction of the O and N atoms of the amino-alcohol with beryllium atom of BeF2 molecule forming the corresponding beryllium bonds is energetically more favorable. The propensity of Be to exhibit a tetrahedral coordination has been previously reported in the literature when competing with intermolecular hydrogen bonds [47,70]. Here, we find that this tendency of Be to behave like a "tetrahedral proton" [47,70] is also observed when competing with IMHBs. In addition, importantly, the enthalpy gap between these bridged structures and the most stable conformers exhibiting a O–H···N IMHB is big enough (8.7 to 22.2 kJ·mol−1) as to conclude, using a Boltzmann distribution function, that, at room temperature, practically 100% of the complexes are those stabilized through the formation of beryllium bonds.

An inspection of the molecular graphs of these complexes (see Figure 7) confirms the tendency of Be to be tetracoordinated, the electron density at the N–Be beryllium bond being systematically larger than that at the O–Be beryllium bond, since the amino group is a better electron donor than the hydroxyl one. On the other hand, the intrinsic stability of the complex, measured by the corresponding binding energy, increases from the amino-ethanol to the amino-pentanol, but, for the amino-butanol, goes through a little sinkhole that is consistent with the fact that, as we have discussed before, the stabilization produced in the isolated compound by the O–H···N IMHB is maximum for amino-butanol.

**Figure 7.** Molecular graphs for the HOCH2(CH2)nCH2NH2–BeF2 (n = 0–3) bridged conformers showing the electron densities (a.u.) at the BCPs between Be and the two basic sites of the amino-alcohol. The values in red correspond to the binding energies (kJ·mol−1) defined as the energy for the reaction: HOCH2(CH2)nCH2NH2–BeF2 → HOCH2(CH2)nCH2NH2 + BeF2.

Finally, it is interesting to highlight some of the peculiarities of the IR spectra of these complexes, showed in Figure 8.

**Figure 8.** Calculated IR spectra for the bridged HOCH2(CH2)nCH2NH2-BeF2 (*n* = 0–3).

The first conspicuous fact is that the stretching O–H absorption band appears significantly blue-shifted with respect to those in Figure 5a, as it corresponds to a free OH group that, in these systems, does not participate in hydrogen bonding. Indeed, the OH stretching frequency calculated for the bridge complexes in Figure 8 go from 3767 to 3832 cm<sup>−</sup>1, values rather similar to that obtained for methanol (3831 cm<sup>−</sup>1) at the same level of theory. However, for the amino-ethanol, the blue-shifting, with respect to the isomer in Figure 5a, is only 200 cm<sup>−</sup><sup>1</sup> because of the rather weak O–H···N IMHB in the isomer of Figure 5a. For amino-butanol and amino-pentanol, the shifting is greater than 1100 cm<sup>−</sup>1. Another common finger-print of the IR spectra of these complexes is the presence of a rather intense band always around 800 cm<sup>−</sup><sup>1</sup> corresponding to the symmetric stretching of the BeF2 moiety.
