**1. Introduction**

Undoubtedly, intermolecular hydrogen bonds [1–16] occupy the main place among various intermolecular interactions. This is largely due to their intermediate strength, between weaker van der Waals interactions [7,11] and much stronger chemical bonds [1,17]. It is this intermediate strength of intermolecular hydrogen bonds that allows for them to act as a glue that binds various molecules into dimers or larger molecular aggregates. On the other hand, their relative weakness allows for the full dynamics of the bonding motif; the hydrogen bond can be broken relatively easily and a new one can be formed in its place.

It is already visible at this point that the knowledge of the strength of intermolecular hydrogen bonding is a very important element in the full description of the characteristics of this bond. Such knowledge would allow, for example, to classify them according to the strength found and study the impact of various internal and external factors on it. Because of the fact that the total energy of a molecule is a fundamental quantity available to quantum mechanics [18], the appropriate balance of total energies can be successfully used to write a strict definition of the energy of interaction (i.e., the interaction energy) between A and B systems in AB dimer:

$$E\_{\rm int} = E(\rm AB) - \left[ E(\rm A) + E(\rm B) \right] \tag{1}$$

Therefore, it is clear that the reference system for the bound AB dimer is that of the isolated monomers A and B. Another thing that I will leave behind is that these monomers may have their own, i.e., fully optimized geometries or geometries taken from the dimer. Anyway, the energy that is described by Equation (1) is strictly defined. Not quite rightly, *E*int obtained by Equation (1) is commonly taken as the interaction energy associated with the closest contact between A and B, e.g., an intermolecular hydrogen bond. Therefore, this equation has also become the main source of information regarding the strength of intermolecular hydrogen bonds in the so-called supermolecular method.

It is quite natural that one would like to have such an important quantity also in the case of intramolecular interactions, including intramolecular hydrogen bonds. However, there is a fundamental problem here. Namely, unlike in its intermolecular counterpart, breaking the intramolecular interaction is impossible without disturbing the structure of the molecule. Because of this fact, not only it is impossible to find a strict definition of the intramolecular interaction energy, but what is more, this energy is not even strictly definable (see, however, the further discussion on the QTAIM-based methods).

Nevertheless, one can try to introduce a method that results in a number that is treated (in this method) as the energy of a given intramolecular interaction. It is obvious that, in the general case, the energies obtained will differ (perhaps even significantly) among the adopted methods. For this reason, an important aspect of the proposed method is the evaluation of the reliability of the energy obtained. It would rather be a worthless result to obtain for intramolecular hydrogen bond of e.g., the OH··· O type an energy of the order of, say −50 kcal/mol, if the intermolecular equivalent in the case of a similar configuration of O and H atoms gives energy from about −4 to about −8 kcal/mol. One of the possible ways of assessing the reliability of the obtained energy value is thus comparing it to the appropriate intermolecular interaction, in which not only the type of X and Y atoms (from the XH··· Y contact), but also their spatial configuration (e.g., the key distance H··· Y) is largely preserved. Another sensible possibility is to check the fulfillment of various correlations between the found energy values and other parameters describing the strength of the H··· Y bond. One should also compare the obtained estimates for structurally closely related molecules.

This article reviews the current theoretical methods introducing the concept of the XH··· Y intramolecular hydrogen bond interaction energy (or more generally the intramolecular X··· Y interaction) and allowing for the computational generation of these energies. The main emphasis will be on the problems associated with these methods, which may naturally lead to their different, more or less reliable, variants. On the other hand, due to the multitude of numerical data concerning the interaction energy values that were determined with these methods, this issue will necessarily be of minor importance. Rather, I will limit myself to a few examples that illustrate how a given method works.

#### **2. Theoretical Methods of Estimating the Energy of Intramolecular Interactions**


**4. Conclusions**

The paper presents the synthesis of 2-[(E)-(phenylimino)methyl]phenol (**SA**) and its two deutero-derivatives (**SA-OD** and **SA-C6D5**). The bands corresponding to hydrogen bond vibrational modes (see Scheme 1) were assigned in experimental IR, IINS and Raman spectra. The analysis of the obtained spectral results proved that in a crystal state, **SA** exists in enol-imine form with a so-called quasi-aromatic intramolecular OH···N hydrogen bond of medium strength. The measured IINS spectra **SA** and **SA-C6D5** made it possible to show the influence of deuteron replacement in the remote group (aldimine ring) on the hydrogen bridge stretching vibrations νσ(OHN). The calculations of structure and vibrational spectra of two polymorphs (earlier studied by X-ray method [27]) performed by static periodic (solid state) DFT method showed a good agreement between the measured and calculated spectra, allowing for spectroscopic distinction between polymorphs α2 and β, as well as confirming the applicability of DFPT calculations for characterization of polymorphic states. Based on analysis of IR spectra, the **SA** in the studied samples was shown to exist in α-form. However, the XPD measurements carried out for **SA** and **SA-C6D5** showed dual signals

for several reflexes and did not show a phase transition in the temperature range from 20 to 295 K. On the basis of these measurements two quasi-isostructural polymorphs of **SA** (most probably, so-called α1 and α2 forms) were assumed to co-exist in the mentioned temperature range.

**Supplementary Materials:** The following are available online, Figure S1: Normalized experimental Raman and IR spectra of **SA** and its deuterated derivative **SA-OD**. Figure S2: Temperature behaviour of XRD patterns for **SA** and **SA-C6D5**. Figure S3: Temperature dependence of X-ray powder diffraction patterns of **SA** and **SA-C6D5.** Table S1: Definitions of the internal coordinates used in the potential energy distribution (PED) analysis for the assignments of the vibrational spectra, Table S2: Experimental IR, Raman, IINS and calculated (B3LYP/6-311+G(d,p)) spectral data of **SA**, Table S3: Experimental IR, Raman and calculated (B3LYP/6-311+G(d,p)) spectral data of **SA-OD**, Table S4: Experimental IINS and calculated (B3LYP/6-311+G(d,p)) spectral data of **SA-C6D5** for the region 0–1200 cm–1.

**Author Contributions:** Conceptualization, A.F.; methodology, A.F.; validation, all authors; formal analysis, A.F. and P.M.T.; investigation, Ł.H., E.A.G., J.W., M.V.V., P.L., P.M.T. and A.F.; resources, A.F. and P.M.T.; data curation, Ł.H., E.A.G., J.W., M.V.V., P.L., P.M.T. and A.F.; writing—original draft preparation, A.F.; writing—review and editing, A.F. and P.M.T.; visualization, Ł.H., E.A.G., J.W., M.V.V., P.L., P.M.T. and A.F.; supervision, A.F.; project administration, A.F.; funding acquisition, P.M.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Russian Science Foundation (RFBR, grant no 18-13-00050) and Polish Government Plenipotentiary for JINR in Dubna (PWB/168-19/2021; data 11.03.2021).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data are available within the article or Supplementary Materials.

**Acknowledgments:** A.F. acknowledges the Wrocław Centre for Networking and Supercomputing Centres (WCSS) for providing computational time and facilities.

**Conflicts of Interest:** The authors declare no conflict of interest.

**Sample Availability:** Samples of the studied compounds are not available from the authors.