2.1.2. Ortho-Para Method (opM)

The *ortho*–*para* method (opM) was most likely used for the first time by Estácio et al. [38] for estimating the energy of intramolecular hydrogen bonds in four 1,2-disubstituted benzene derivatives: 1,2-dihydroxybenzene (catechol), 1,2-benzenedithiol, benzene-1,2-diamine, and 2-methoxyphenol (guaiacol). To describe opM, it is enough to refer to the O-H··· O hydrogen bond in 1,2-dihydroxybenzene, i.e., catechol (Figure 8).

The use of the open form that was simply obtained by rotating the hydroxyl group around the C-O bond resulted in hydrogen bond energy estimates of −3.7 or −4.0 kcal/mol at the MPW1PW91/aug-cc-pVDZ and CBS-QMPW1 levels of theory, respectively. These values were considered to be unreliable and significantly overestimated as a result of the presence of new repulsive interactions between oxygen atoms as well as the O-H dipole–dipole interactions [38]. As a consequence, it was concluded that the energetic difference between the open and closed forms cannot be regarded as the energy of the O-H··· O hydrogen bond in the latter form. However, in this and similar cases, the *para* form is a very reliable reference form. The comparison of total energy of this form with the total energy of the closed form of the *ortho* configuration gives opM, which can be seen as a variant of OCM. Based on this approach, the respective hydrogen bond energies were −2.1 and −2.3 kcal/mol [38].

**Figure 8.** Various forms of catechol (the subfigures (**a**) and (**b**) represent different forms of *para*-catechol).

It is worth emphasizing here that the high reliability of the estimate obtained by means of opM results from the high stiffness of the main part of the molecule, i.e., the benzene ring and, hence, the significant transferability of the related geometric parameter values. In other words, the stiffness of the molecular framework and its high preservation when going to the *para*-substituted reference system allowed for avoiding the typical problems that are faced by the standard version of OCM which were mentioned earlier. On the other hand, it should be noted that this method assumes that the substituent electronic effects in the *ortho* and *para* forms are similar. However, this is in line with the general knowledge on substituent effects [56–59]. Nevertheless, another question, which is completely not addressed by Estácio et al., is which form of the *para* conformer (see (a) and (b) in Figure 8) to use. While this rather purely theoretical issue seems to be insignificant for catechol due to the negligible difference in total energies between the two forms (e.g., 0.1 kcal/mol at the B3LYP/aug-cc-pVTZ level of theory), the difference may become slightly larger for other substituents or molecular frameworks.

It should be mentioned that Estácio et al. described the O-H··· O hydrogen bond in the closed form of catechol by means of a simple model that is based on the description of interacting dipoles of the O-H bonds. This model resulted in the following formula

$$E\_{\rm IIB} = -[E\_{\rm LJ}^{\rm O\cdots O} + E\_{\rm dd}] \tag{7}$$

where *E*O···<sup>O</sup> LJ is the Lennard–Jones interaction energy for the relevant pair of oxygen atoms and *E*dd is the dipole-dipole interaction energy for the closed form [38]. The energy value that was determined using this formula was −2.0 kcal/mol (MPW1PW91/aug-cc-pVDZ) and it was very closed to the one determined while using opM (−2.1 kcal/mol). Estácio et al. considered this result to be significant, because it shows that opM correctly describes both interactions, i.e., the O··· O repulsion and the interaction between the dipoles of both O-H bonds in the closed form of catechol.

#### 2.1.3. Related Rotamers Method (RRM)

As we have seen, the choice of a reasonable open form in OCM is often problematic and even sometimes impossible. This is due to the requirement that this form should be as close to the closed form as possible. This means that the conformer change should not lead to significant changes in the values of geometric parameters. In order to overcome any inaccuracies, another approach is to use more than just two conformers of a given molecule [47,60–63]. This idea will be shown on the example of 3-aminopropenal (3-aminoacrolein), which has four conformers. The N-H··· O hydrogen bond energy in the ZZ conformer of 3-aminoacrolein was quite often estimated [47,61,63–65], but the methods used did not take into account changes in the values of geometric parameters when switching from the bound system (ZZ-3-aminoacrolein) to reference forms (in particular, to ZE-3-aminoacrolein) [64,65]. The specific system of conjugated double bonds and, hence, the presence of four conformers

(see Figure 9), allowed for proposing a method that was derived from the analysis of the mutual energy relations between the four conformers of 3-aminoacrolein (Figure 9) [47].

**Figure 9.** Four conformers of 3-aminoacrolein and energetic relationships between them.

This method takes use of approximations

$$E\_{\rm HB} + R\_1 = E^{\rm ZZ} - E^{\rm ZE}, \quad R\_1 \approx E^{\rm EZ} - E^{\rm EE} \tag{8}$$

$$E\_{\rm IIB} + R\_2 = E^{\rm ZZ} - E^{\rm EZ}, \quad R\_2 \approx E^{\rm ZE} - E^{\rm EE} \tag{9}$$

that lead to the following formula for the hydrogen bond energy in the ZZ form of 3-aminoacrolein

$$E\_{\rm IIB}^{\rm RRM} = (E^{ZZ} - E^{\rm ZE}) + (E^{\rm EE} - E^{\rm EZ}) \tag{10}$$

Calculations that are based on MP2(Full)/6-31G\*\* and MP2(FC)/6-311+G\*\* level of theory gave values of −8.2 and −7.5 kcal/mol, respectively [47]. Later, B3LYP/6-311++G\*\* (however, most likely Nowroozi et al. [61] used a smaller 6-31G\*\* basis set, as evidenced by the number of 100 basis functions mentioned by them and the obtained value of −8.4 kcal/mol, which is close enough to the value of −8.2 kcal/mol obtained [47] at the MP2(Full)/6-31G\*\* level of theory) computation by Nowroozi et al. [61] gave value of −8.4 kcal/mol.

The term in the first bracket of Equation (10) is equivalent to the energy that is obtained from the most commonly used variant of OCM in which the open reference form is obtained by the rotation of the proton-acceptor group. Hence, the relationship between RRM and OCM can be expressed by the following relationship between the total energies of the conformers EE and EZ [44]:

$$E\_{\rm HB}^{\rm RRM} - E\_{\rm HB}^{\rm OCM} = E^{\rm EE} - E^{\rm EZ} \tag{11}$$

Because, in most cases, the extended EE conformer is more stable than the EZ conformer, the difference defined by the above equation is negative. For this reason, as compared to OCM, RRM gives greater stabilizations of interactions. It may even happen that interactions that are weakly destabilizing based on OCM are weakly stabilizing if RRM is considered instead, and this result is only due to "different zeros" in both of these methods [44].

It should be mentioned that RRM [47,60] has been readily adopted by Nowroozi et al. [61–63], who called it the Related Rotamers Method (RRM) and in this review it functions under that name. However, even a little earlier, practically the same method was used by Lipkowski et al. [60] to estimate the energy of O-H··· N intramolecular hydrogen bonds in some chloro-derivatives of 2-(N-dimethylaminomethyl)-phenols, but they used the term "thermodynamic cycle". Therefore, as one can see, not only are different methods used, but even the same method can function under different names [47,60–63].
