Perturbing the O–H…O Hydrogen Bond in 1-oxo-3-hydroxy-2-propene

Ab initio MP2/aug’-cc-pVTZ calculations have been carried out to identify and characterize equilibrium structures and transition structures on the 1-oxo-3-hydroxy-2-propene: Lewis acid potential energy surfaces, with the acids LiH, LiF, BeH2, and BeF2. Two equilibrium structures, one with the acid interacting with the C=O group and the other with the interaction occurring at the O–H group, exist on all surfaces. These structures are separated by transition structures that present the barriers to the interconversion of the two equilibrium structures. The structures with the acid interacting at the C=O group have the greater binding energies. Since the barriers to convert the structures with interaction occurring at the O–H group are small, only the isomers with interaction occurring at the C=O group could be experimentally observed, even at low temperatures. Charge-transfer energies were computed for equilibrium structures, and EOM-CCSD spin–spin coupling constants 2hJ(O–O), 1hJ(H–O), and 1J(O–H) were computed for equilibrium and transition structures. These coupling constants exhibit a second-order dependence on the corresponding distances, with very high correlation coefficients.

A useful property for obtaining structural information about complexes linked by noncovalent interactions and, in particular by hydrogen bonds, is spin-spin coupling constants (SSCC). SSCC are related to the electronic structure of molecules and complexes through geometry, bond order, polarization, and electron densities. As Cremer and Gräfenstein wrote [35], "The analysis of NMR spin-spin coupling leads to a unique insight into the electronic structure of closed-shell molecules". This was known for molecules from the beginning of the use of NMR spectroscopy [36][37][38] but was extended to complexes by Limbach [39,40] and Del Bene [41,42]. Through relationships between SSCC and geometry, the problem of the localization of the hydrogen-bonded proton could be solved [43].

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.
Molecules 2021, 26, x FOR PEER REVIEW 2 of 13 from the beginning of the use of NMR spectroscopy [36][37][38] but was extended to complexes by Limbach [39,40] and Del Bene [41,42]. Through relationships between SSCC and geometry, the problem of the localization of the hydrogen-bonded proton could be solved [43].
In the present paper, we report the results of an investigation of 1-oxo-3-hydroxy-2propene in a series of binary complexes with the acids LiH, LiF, BeH2, and BeF2. These complexes contain intramolecular O-H···O hydrogen bonds and lithium (alkali) and beryllium (alkaline earth) intermolecular bonds [44]. Specifically, we have determined the structures and binding energies of these complexes; the proton transfer barriers; the complex stabilization by charge-transfer interactions; and the spin-spin coupling constants 2h J(O-O), 1h J(H-O), and 1 J(O-H) across the O-H … O hydrogen bond. It is the purpose of this paper to present and discuss the results of this study.

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.

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 −1 for the complex 1:LiH(OH) to 100 kJ . mol −1 for 1:BeF2(CO). For each acid, the binding energies decrease in the following order: 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 −1 for the complexes with LiF as the acid to 19 kJ . mol −1 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 . Scheme 1. Some representative complexes.

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, BeH 2 , and BeF 2 . 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 −1 for the complex 1:LiH(OH) to 100 kJ·mol −1 for 1:BeF 2 (CO). For each acid, the binding energies decrease in the following order:

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: BeF 2 > BeH 2 ≈ LiF > LiH However, when the interaction occurs at the hydroxyl oxygen, the order is: BeF 2 > LiF > BeH 2 > 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 −1 for the complexes with LiF as the acid to 19 kJ·mol −1 when BeF 2 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:BeH 2 (CO) differ by only 0.5 kJ·mol −1 . a The transition structure is 11.6 kJ . mol −1 less stable than the equilibrium C3H4O2 structure. 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 −1 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. 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 −1 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 (R 1 + R 2 ) in each system is compared to the difference (R 1 − R 2 ) using the Steiner-Limbach relationship [45,46]. The points with the largest (R 1 + R 2 ) values in Figure  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 hydrogenbonded 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. 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°. 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 • .

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. 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°.

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 ptype 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. lp1 isolated lp1 interacting lp2 isolated lp2 interacting

Charge-Transfer Energies
The complexes 1:acid are stabilized by charge-transfer interactions. The nature of charge transfer and the associated charge-transfer energies are reported in Table 2. Given

Charge-Transfer Energies
The complexes 1:acid are stabilized by charge-transfer interactions. The nature of charge transfer and the associated charge-transfer energies are reported in Table 2. Given the nature of the lone-pair orbitals illustrated in Figure 4, it is not surprising that charge transfer from lp2 is the dominant charge-transfer interaction, with energies ranging from 158 kJ·mol −1 in 1:LiF(OH) to 189 kJ·mol −1 1:BeF 2 (OH). The charge-transfer energies involving lp1 are much less, with values between 15 and 31 kJ·mol −1 . The total charge-transfer energies vary from 100 to 213 kJ·mol −1 . It is interesting to note that the strongest complexes occur in 1:acid(CO) ( Table 1 and Figure 2), while the strongest intramolecular hydrogen bond can be seen in 1:acid(OH). Figure 5 illustrates a linear dependence of these energies on the O-O distance, with a correlation coefficient of 0.965.

Electron Density Analyses
The electron densities of the equilibrium and transition structures were analyzed using the quantum theory of atoms in molecules (QTAIM) methodology.

Electron Density Analyses
The electron densities of the equilibrium and transition structures were analyzed using the quantum theory of atoms in molecules (QTAIM) methodology.  [47,48]. Excellent exponential correlations are obtained between ρ BCP and H BCP versus the interatomic distance, as illustrated in Figure S1, in agreement with other reports of these parameters as descriptors of intermolecular interactions [49][50][51].

Spin-Spin Coupling Constants
The total spin-spin coupling constants 2h J(O-O), 1h J(H-O), and 1 J(O-H) are given in Table 3, and the paramagnetic spin-orbit (PSO), diamagnetic spin-orbit (DSO), Fermi contact (FC), and spin-dipole (SD) components are reported in Table S2 of

1h J(H-O)
The values of the second coupling constant 1h J(H-O) across the hydrogen bond are also reported in Table 3. Its value of 7.9 Hz in 1 changes minimally upon complex formation, ranging from 7.

1h J(H-O)
The values of the second coupling constant 1h J(H-O) across the hydrogen bond are also reported in Table 3. Its value of 7.9 Hz in 1 changes minimally upon complex formation, ranging from 7.

Methods
The structures of the isolated monomer 1-oxo-3-hydroxy-2-propene; the acids LiH, LiF, BeH2, and BeF2; and the complexes of 1-oxo-3-hydroxy-2-propene with the acids were optimized at second-order Møller-Plesset perturbation theory (MP2) [52][53][54][55] with the aug'-cc-pVTZ basis set [56]. This basis set was derived from the Dunning aug-cc-pVTZ basis set [57,58] by removing diffuse functions from H atoms. Searches were made of the 1-oxo-3-hydroxy-2-propene:acid potential surfaces for equilibrium structures and transition structures. Frequencies were computed to confirm that the optimized structures are indeed equilibrium structures with no imaginary frequencies and that the transition structures have one imaginary frequency along the path that connects two equilibrium structures. Optimization and frequency calculations were performed using the Gaussian 16

Methods
The structures of the isolated monomer 1-oxo-3-hydroxy-2-propene; the acids LiH, LiF, BeH 2 , and BeF 2 ; and the complexes of 1-oxo-3-hydroxy-2-propene with the acids were optimized at second-order Møller-Plesset perturbation theory (MP2) [52][53][54][55] with the aug'-cc-pVTZ basis set [56]. This basis set was derived from the Dunning aug-cc-pVTZ basis set [57,58] by removing diffuse functions from H atoms. Searches were made of the 1-oxo-3-hydroxy-2-propene:acid potential surfaces for equilibrium structures and transition structures. Frequencies were computed to confirm that the optimized structures are indeed equilibrium structures with no imaginary frequencies and that the transition structures have one imaginary frequency along the path that connects two equilibrium structures. Optimization and frequency calculations were performed using the Gaussian 16 program [59]. The binding energies of the equilibrium complexes were computed as −∆E for the reaction that forms these complexes from the isolated monomers.
The natural bond orbital (NBO) method [60] was used to obtain the stabilizing chargetransfer interactions using the NBO-6 program [61]. Since MP2 orbitals are nonexistent, the charge-transfer interactions were computed using the B3LYP functional with the aug'-cc-pVTZ basis set at the MP2/aug'-cc-pVTZ geometries so that at least some electron correlation effects could be included. The atoms in molecules (AIM) methodology [62][63][64][65] was used to produce the molecular graphs of the complexes, employing the AIMAll program [66]. The molecular graph identifies the location of electron density features of interest, including the electron density (ρ) maxima associated with the various nuclei and saddle points that correspond to bond critical points (BCPs). The zero gradient line that connects a BCP with two nuclei is the bond path.
Spin-spin coupling constants were evaluated using the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method in the CI (configuration interaction)-like approximation [67,68] with all electrons correlated. For these calculations, the Ahlrichs [69] qzp basis set was placed on 13 C, 17 O, and 19 F atoms, the hybrid basis set developed previously on 7 Li and 9 Be [70], and the qz2p basis set on the hydrogen-bonded 1 H atom. The Dunning cc-pVDZ basis was placed on the remaining 1 H atoms. All terms that contribute to the total coupling constant, namely, the paramagnetic spin-orbit (PSO), diamagnetic spin-orbit (DSO), Fermi contact (FC), and spin-dipole (SD) were evaluated. The EOM-CCSD calculations were performed using ACES II [71] on the HPC cluster Owens at the Ohio Supercomputer Center.

Conclusions
Ab initio MP2/aug'-cc-pVTZ calculations were carried out to identify and characterize hydrogen-bonded equilibrium structures and transition structures on the 1-oxo-3-hydroxy-2-propene:acid (1:acid) potential energy surfaces, with the acids LiH, LiF, BeH 2 , and BeF 2 . The results of these calculations support the following statements:

1.
Two equilibrium structures, one with the acid interacting with the C=O group and the other with the interaction occurring at the O-H group, exist on all surfaces. These structures are separated by transition structures that present the barriers to the interconversion of the two equilibrium structures.

2.
The binding energies of these complexes vary between 65 and 100 kJ·mol −1 , with binding at the C=O group preferred by 10 to 20 kJ·mol −1 .

3.
The barrier to interconverting the equilibrium structures with the acid at the C=O group to the structure with the acid at the O-H group is 12 kJ·mol −1 in isolated 1 and increases to between 15 and 21 kJ·mol −1 in the complexes. The reverse barriers range from 2 to 6 kJ·mol −1 . Thus, only structures with the acid interacting at the C=O group would be experimentally observed, even at low temperatures.

4.
Charge-transfer stabilizes the 1:acid complexes. The greater charge-transfer interactions involve electron donation from an oxygen lone pair orbital on the C=O group to an antibonding pi-type orbital on the O-H group.  Table S1: Structures (Å), total energies (au), and molecular graphs of 1-oxo-3-hydroxy-2-propene:acid complexes; Figure S1: Relationship between electron densities at the O-H hydrogen bonds and interatomic distances; Table S2