**2. Results and Discussion**

In order to simplify the discussion of the equilibrium and the transition structures on the 1-oxo-3-hydroxy-2-propene:acid potential energy surfaces, we refer to the hydrogenbonded molecule 1-oxo-3-hydroxy-2-propene as **1** and name the complexes **1**:LiH(OH), **1**:LiH(ts), and **1**:LiH(CO), where **1**:LiH(OH) indicates that the acid LiH interacts with the hydroxyl oxygen, **1**:LiH(CO) indicates that the interaction with the acid occurs at the carbonyl oxygen, and **1**:LiH(ts) identifies the transition structure. These complexes are illustrated in Scheme 1.

**Scheme 1.** Some representative complexes.

#### *2.1. Ground State Structures and Binding Energies*

Table S1 of the Supporting Information provides the structures, total energies, and molecular graphs of the complexes of 1-oxo-3-hydroxy-2-propene with the Lewis acids LiH, LiF, BeH2, and BeF2. The binding energies, selected distances, and the H–O–O angles in these complexes are reported in Table 1. For the equilibrium complexes, the binding energies range from 65 kJ·mol−<sup>1</sup> for the complex **1**:LiH(OH) to 100 kJ·mol−<sup>1</sup> for **1**:BeF2(CO). For each acid, the binding energies decrease in the following order:


**Table 1.** Binding energies ( −ΔE, kJ·mol−1), distances R (Å), and H–O–O angles (<, o) for complexes of C3H4O2 with acids.

a The transition structure is 11.6 kJ·mol−<sup>1</sup> less stable than the equilibrium C3H4O2 structure. **1**:acid(CO) > **1**:acid (OH) > **1**:acid(ts).

When the interaction with the acid occurs at the carbonyl oxygen, the order of decreasing binding energy with respect to the acid is:

BeF2 > BeH2 ≈ LiF > LiH

However, when the interaction occurs at the hydroxyl oxygen, the order is:

BeF2 > LiF > BeH2 > LiH.

The differences among the binding energies of the equilibrium complexes with the acid at C=O versus O–H range from 9 kJ·mol−<sup>1</sup> for the complexes with LiF as the acid to 19 kJ·mol−<sup>1</sup> when BeF2 is the acid. Figure 1 provides a representation of the binding energies versus the O–O distance for these complexes and transition structures as a function of the acid. It is interesting to note that the binding energies of the transition structures are very similar to those of the complexes with the acid at the O–H group. Moreover, the binding energies of **1**:LiF(CO) and **1**:BeH2(CO) differ by only 0.5 kJ·mol−1.

**Figure 1.** Binding energies versus the O–O distance for **1**:acid (OH), **1**:acid (ts), and **1**:acid (CO) complexes as a function of the acid.

There are many approaches to representing the binding energies of a series of complexes. One of the most interesting and informative can be found in Figure 2, which provides a diagram illustrating the binding energies and the relative binding energies of complexes and transition structures **1**:acid(CO), **1**:acid(ts), and **1**:acid(OH). The transition structures present the barriers that separate the equilibrium structures with the acid at C=O from the structures with the acid at O–H. This barrier is 12 kJ·mol−<sup>1</sup> for the isolated parent molecule **1**. Interaction of the acid with the C=O group increases the barrier to between 15 and 21 kJ·mol−1, while interaction at the O–H group decreases the barrier to between 2 and 6 kJ·mol−1. These latter barriers and the energy differences indicate that the population of the isomer with the acid at the carbonyl group would be the greater than 98% at room temperature.

The O–O distances across the hydrogen bond in the complexes **1**:acid with hydrogen bond formation at the C=O group increase slightly relative to isolated **1**, which has an O–O distance of 2.56 Å. However, when hydrogen bond formation occurs at the O–H group, the O–O distance decreases to between 2.46 to 2.50 Å. As expected, the shortest O–O distances are found in the transition structures for proton transfer, where they decrease to 2.36 Å. An excellent second-order relationship can be obtained when the sum of the O–H distances (R1 + R2) in each system is compared to the difference (R1 − R2) using the Steiner–Limbach relationship [45,46]. The points with the largest (R1 + R2) values in Figure 3 correspond to the **1**:acid(OH) complexes, the intermediate ones to the **1**:acid(CO) complexes, and the shortest to the **1**:acid(TS) complexes. This figure illustrates that the hydrogen-bonded H atom tends to be centered between the two oxygen atoms as they approach each other. The correlation coefficient of the second-order trending in Figure 3 is 0.9996.

**Figure 2.** Binding energies of equilibrium and transition structures as a function of the nature of the complex. From these data, the barriers to interconverting the two equilibrium complexes can be readily obtained.

**Figure 3.** (R1 + R2) vs. (R1 − R2) from the Steiner–Limbach relationship.

The hydrogen bonds in all complexes are nonlinear. The deviation from linearity is 20◦ in isolated **1** and ranges from 17◦ to 22◦ in the complexes. The hydrogen bond approaches closer to linearity in the transition structures, where the deviation decreases to between 11◦ and 13◦.

#### *2.2. Orbital Description of the O–H* ... *O Hydrogen Bond*

There are two canonical lone pair (lp) orbitals associated with the carbonyl oxygen, both in the isolated base (**1**) and in the **1**:acid complexes, and these are illustrated in Figure 4. The orbital lp1 isolated is a lone-pair orbital on O, which has local σ-type symmetry relative to the C=O bond, extending from the carbonyl oxygen in a direction corresponding to a continuation of the O–H bond. Interaction of the O–H group with this orbital leads to a side-wise overlap of a *p*-type orbital on the O–H group with the C=O lp1 orbital. The orbital lp2 is a local π-type orbital on **1,** which is perpendicular to the C=O bond and directed toward the O–H group of **1** with which it interacts. This orbital extends on both sides of the C=O group, where it may also interact with an acid through the lobe of the *p*-type orbital which extends in this direction. This observation is consistent with the greater binding energies of complexes with the base interacting with **1** at the C=O group compared to those with the base interacting at the O–H group.

**Figure 4.** Representations of the lone pair (lp) orbitals of **1** isolated and interacting with the O–H group based on the NBO analysis.
