Revealing the Reasons for Degeneration of Resonance-Assisted Hydrogen Bond on the Aromatic Platform: Calculations of Ortho-, Meta-, Para-Disubstituted Benzenes, and (Z)-(E)-Olefins

The energies of the O−H∙∙∙O=C intramolecular hydrogen bonds were compared quantitatively for the series of ortho-disubstituted benzenes and Z-isomers of olefins via a molecular tailoring approach. It was established that the hydrogen bond energy in the former series is significantly less than that in the latter one. The reason for lowering the hydrogen bond energy in the ortho-disubstituted benzenes compared to the Z-isomers of olefins is the decrease in the π-contribution to the total energy of the complex interaction, in which the hydrogen bond per se is enhanced by the resonance effect. By the example of the para- and meta-disubstituted benzenes, as well as E-isomers of olefins, it was explicitly shown that the aromatic ring is a much poorer conductor of the resonance effect compared to the double bond. The hydrogen bond in the ortho-disubstituted benzenes has a lower energy than a typical resonance-assisted hydrogen bond because the aromatic moiety cannot properly assist the hydrogen bond with a resonance effect. Thus, a hydrogen bond on an aromatic platform should fall into a special category, namely an aromaticity-assisted hydrogen bond, which is closer by nature to a simple hydrogen bond rather than to a resonance-assisted one.

RAHBs belong to the category of especially strong H-bonds and are identified by their specific spectral and structural features. The IR and 1 H NMR spectra of the O−H···O=C RAHB-containing substances reveal an extraordinary decrease in the ν O-H vibration frequency to 2550-2675 cm −1 and a large downfield shift of the bridging hydrogen resonance to 15-17 ppm, respectively [2,30]. In addition, the HRD data show a shortening in the O···O distance to 2.4-2.6 Å [1][2][3]. According to the RAHB concept, the strength of the hydrogen where E(D•A) is the total energy of the complex D•A, E(D), and E(A) are the energy of donor molecule D and acceptor molecule A, respectively. When using Equation (1a), the basis set superposition error (BSSE correction) should be taken into account. However, this approach is not suitable for the quantification of the intramolecular RAHB energy, since this would require the division of a whole molecule into parts. The energy of an intramolecular hydrogen bond (IMHB) is an inseparable contribution to the total energy of a molecule [35][36][37]. Essentially, the IMHB energy is a virtual quantity that can neither be measured experimentally nor calculated directly [35][36][37]. Nevertheless, two methods have been developed to indirectly estimate the IMHB energy. The first one can be designated as the function-based approach (FBA), which uses the functional dependence (2a) of the IMHB energy [E(IMHB)] on the H-bond descriptor (denotes as P parameter) [37,38] E(IMHB) = f (P) (2a) The ρ BCP (electron density at the H-bond critical points), V BCP (potential energy density at the H-bond critical point), r O···H (H-bond distance), ∆ν (shift of the X-H bond vibration due to X-H···Y H-bond) and ∆δ (change in the chemical shift of a bridging hydrogen atom in the 1 H NMR spectra due to H-bond) parameters are conventionally used as the H-bond descriptors [39][40][41][42][43][44][45][46][47].
RAHB is a complex interaction, consisting of σand π-components, which are responsible for the H-bond per se and resonance assistance, respectively. Application of the FBA method allows the energy of the RAHB σ-component to be estimated since this method is based on the properties of the σ-skeleton of molecules [37,38,60]. The MTA method estimates the total energy of intramolecular RAHB [38,60]. The difference between the RAHB energies, quantified by the FBA and MTA methods, gives an estimation of the π-contribution to the total RAHB energy [38,60]. In this way, the separation of the total RAHB energy into σand π-components was successfully carried out for classical RAHB structures such as β-diketones [38].
At the same time, the RAHB interaction is assumed to be homogeneous in its essence, i.e., independent of the nature of the unsaturated fragment connecting the H-bond donor and acceptor atoms (whether this fragment is a double bond or an aromatic ring). In the papers dealing with the study of IMHB on an aromatic platform, such IMHB is considered from the same positions as classical RAHBs in β-diketones [7,16,[61][62][63][64][65][66]. However, the MTA assessment of the total RAHB energy in compounds with aromatic moiety evidence that it is significantly lower than in those with a double bond [58,59]. The relationship between various structural parameters, as well as bond indices and the intramolecular RAHB energy in compounds on an aromatic platform, was studied by the MTA method [59]. The lengths of covalent bonds within the chelate ring and the qHOMA (quasi-Harmonic Oscillator Model of Aromaticity) index [67] were used as structural parameters, while the Wiberg's bond index [68] and the index obtained from the DDEC (Density Derived Electrostatic and Chemical) approach [69] were employed as bond indices [59]. It was concluded [59] that the IMHB in compounds on an aromatic platform should be distinguished from classical RAHBs and referred to as aromaticity-assisted hydrogen bonds (arom-AHB). However, in this work, the separation of the total arom-AHB energy into σand π-components was not made. Hence, the reasons for the decrease in the total arom-AHB energy with respect to the classical RAHB remained unclear. In order to understand why arom-AHB and classical intramolecular RAHB differ significantly in energy, in the present paper, the total arom-AHB energy was separated into σand π-components using the FBA and MTA methods. In addition, the σand π-components of arom-AHB were compared with those of RAHB.
To quantify how arom-AHB differs from the conventional RAHB, the following methodology was applied. On the one hand, a very large series of the hydroxycarbonyl aliphatic compounds as non-conjugated structures were studied in detail and their O−H···O=C IMHB energies were estimated using the MTA method [56]. For simplicity, these non-conjugated structures were referred to as the non-RAHB structures throughout the article. On the other hand, an equally extensive series of the β-diketones and related compounds (RAHB structure) were thoroughly studied and their O−H···O=C IMHB energies were also evaluated by the same MTA method [57]. Finally, the O−H···O=C IMHB energies were assessed by the MTA method for representative series of the orthohydroxybenzaldehydes, phenones, and quinones, in which the arom-AHB is realized [58]. Thus, a vast number of data on the quantitative IMHB energies was obtained for three different series of compounds representing the non-RAHB-, RAHB-, and arom-AHB structures. The former two series are two diametrically opposite poles of compounds carrying IMHB of different natures, which can serve as a benchmark for comparison and establishing the character of the H-bonds (whether the H-bond is RAHB or not) in other compounds. The latter series of compounds, placed between the above two poles, allows one to accurately determine the degree of similarity (or dissimilarity) of the arom-AHB interaction with the RAHB one (see Figure 1) MTA assessment of the total RAHB energy in compounds with aromatic moiety evidence that it is significantly lower than in those with a double bond [58,59]. The relationship between various structural parameters, as well as bond indices and the intramolecular RAHB energy in compounds on an aromatic platform, was studied by the MTA method [59]. The lengths of covalent bonds within the chelate ring and the qHOMA (quasi-Harmonic Oscillator Model of Aromaticity) index [67] were used as structural parameters, while the Wiberg's bond index [68] and the index obtained from the DDEC (Density Derived Electrostatic and Chemical) approach [69] were employed as bond indices [59]. It was concluded [59] that the IMHB in compounds on an aromatic platform should be distinguished from classical RAHBs and referred to as aromaticity-assisted hydrogen bonds (arom-AHB). However, in this work, the separation of the total arom-AHB energy into σ-and π-components was not made. Hence, the reasons for the decrease in the total arom-AHB energy with respect to the classical RAHB remained unclear. In order to understand why arom-AHB and classical intramolecular RAHB differ significantly in energy, in the present paper, the total arom-AHB energy was separated into σ-and πcomponents using the FBA and MTA methods. In addition, the σ-and π-components of arom-AHB were compared with those of RAHB.
To quantify how arom-AHB differs from the conventional RAHB, the following methodology was applied. On the one hand, a very large series of the hydroxycarbonyl aliphatic compounds as non-conjugated structures were studied in detail and their O−H···O=C IMHB energies were estimated using the MTA method [56]. For simplicity, these non-conjugated structures were referred to as the non-RAHB structures throughout the article. On the other hand, an equally extensive series of the β-diketones and related compounds (RAHB structure) were thoroughly studied and their O−H···O=C IMHB energies were also evaluated by the same MTA method [57]. Finally, the O−H···O=C IMHB energies were assessed by the MTA method for representative series of the orthohydroxybenzaldehydes, phenones, and quinones, in which the arom-AHB is realized [58]. Thus, a vast number of data on the quantitative IMHB energies was obtained for three different series of compounds representing the non-RAHB-, RAHB-, and arom-AHB structures. The former two series are two diametrically opposite poles of compounds carrying IMHB of different natures, which can serve as a benchmark for comparison and establishing the character of the H-bonds (whether the H-bond is RAHB or not) in other compounds. The latter series of compounds, placed between the above two poles, allows one to accurately determine the degree of similarity (or dissimilarity) of the arom-AHB interaction with the RAHB one (see Figure 1 The aim of the work is not only to reveal the difference between the arom-AHB and conventional RAHB interactions, but also to explain the reasons for this difference, if it is significant. The MTA method permits both to divide the total energy of the RAHB interaction into σ-and π-contributions and to quantify the pure resonance π-component using isomeric compounds without an H-bond in form of push-pull effect (PPE) energy The aim of the work is not only to reveal the difference between the arom-AHB and conventional RAHB interactions, but also to explain the reasons for this difference, if it is significant. The MTA method permits both to divide the total energy of the RAHB interaction into σand π-contributions and to quantify the pure resonance π-component using isomeric compounds without an H-bond in form of push-pull effect (PPE) energy [70,71]. The compounds with the arom-AHB studied in this article are mainly ortho-disubstituted benzenes, while the compounds with the RAHB are mainly the Z-isomers of olefins. To visually trace the differences between the π-components for the arom-AHB and RAHB, we examined the pure resonance π-contribution in the form of PPE in the isomeric para-and meta-disubstituted benzenes, as well as in the E-isomers of olefins.

Specifications of the Studied Compounds
In total, 576 different compounds were studied in this work. Some compounds with the O−H···O=C IMHB were already investigated individually, but they were not considered in aggregate, and general patterns of the changes in the IMHB strength depending on the molecular structure were not established. Other compounds exhibiting PPE were studied in this paper for the first time. Taking into account the wide variety of compounds under investigation, we have carried out their detailed specification.

Previously Studied Compounds with the O−H···O=C Intramolecular Hydrogen Bonding
In total, 153 Aliphatic hydroxy carbonyl compounds with the O−H···O=C IMHB (non-RAHB structures), 232 β-diketones as well as related compounds with the O−H···O=C IMHB (RAHB structures), and 137 ortho-hydroxybenzaldehydes, phenones, and quinones with the O−H···O=C IMHB (arom-AHB structures), studied in [56][57][58], were not considered in this paper as individual substances. Hence, they were not numbered and were integrated into the non-RAHB, RAHB, and arom-AHB clusters, respectively. Typical compounds from the non-RAHB, RAHB, and arom-AHB clusters are presented in Schemes 1-3, respectively. substituted benzenes, while the compounds with the RAHB are mainly the Z-isomers of olefins. To visually trace the differences between the π-components for the arom-AHB and RAHB, we examined the pure resonance π-contribution in the form of PPE in the isomeric para-and meta-disubstituted benzenes, as well as in the E-isomers of olefins.

Specifications of the Studied Compounds
In total, 576 different compounds were studied in this work. Some compounds with the O−H···O=C IMHB were already investigated individually, but they were not considered in aggregate, and general patterns of the changes in the IMHB strength depending on the molecular structure were not established. Other compounds exhibiting PPE were studied in this paper for the first time. Taking into account the wide variety of compounds under investigation, we have carried out their detailed specification.

Scheme 2.
The structure of the typical compounds from the RAHB cluster. Nevertheless, some clarification regarding compounds from non-RAHB, RAHB, and arom-AHB clusters needs to be made. As noted in [56,57], the compounds with a bifurcated H-bond (second compounds from left to right in Schemes 1 and 2), exhibit an anticooperative effect. However, the magnitude of the anticooperative effect is insignificant, so they can be considered in the common range of non-RAHB or RAHB structures [56,57]. For the compounds with a bifurcated H-bond, the fragmentation scheme includes six fragments to account for both H-bonds (see Scheme S1, Supplementary Materials, p. S2). It was recognized that the RAHB is implemented only if the 4n + 2 Hückel aromaticity rule Scheme 1. The structure of the typical compounds from the non-RAHB cluster.
olefins. To visually trace the differences between the π-components for the arom-AHB and RAHB, we examined the pure resonance π-contribution in the form of PPE in the isomeric para-and meta-disubstituted benzenes, as well as in the E-isomers of olefins.

Specifications of the Studied Compounds
In total, 576 different compounds were studied in this work. Some compounds with the O−H···O=C IMHB were already investigated individually, but they were not considered in aggregate, and general patterns of the changes in the IMHB strength depending on the molecular structure were not established. Other compounds exhibiting PPE were studied in this paper for the first time. Taking into account the wide variety of compounds under investigation, we have carried out their detailed specification.

Previously Studied Compounds with the O−H•••O=C Intramolecular Hydrogen Bonding
In total, 153 Aliphatic hydroxy carbonyl compounds with the O−H···O=C IMHB (non-RAHB structures), 232 β-diketones as well as related compounds with the O−H···O=C IMHB (RAHB structures), and 137 ortho-hydroxybenzaldehydes, phenones, and quinones with the O−H···O=C IMHB (arom-AHB structures), studied in [56][57][58], were not considered in this paper as individual substances. Hence, they were not numbered and were integrated into the non-RAHB, RAHB, and arom-AHB clusters, respectively. Typical compounds from the non-RAHB, RAHB, and arom-AHB clusters are presented in Schemes 1-3, respectively.   Nevertheless, some clarification regarding compounds from non-RAHB, RAHB, and arom-AHB clusters needs to be made. As noted in [56,57], the compounds with a bifurcated H-bond (second compounds from left to right in Schemes 1 and 2), exhibit an anticooperative effect. However, the magnitude of the anticooperative effect is insignificant, so they can be considered in the common range of non-RAHB or RAHB structures [56,57]. For the compounds with a bifurcated H-bond, the fragmentation scheme includes six fragments to account for both H-bonds (see Scheme S1, Supplementary Materials, p. S2). It was recognized that the RAHB is implemented only if the 4n + 2 Hückel aromaticity rule olefins. To visually trace the differences between the π-components for the arom-AHB and RAHB, we examined the pure resonance π-contribution in the form of PPE in the isomeric para-and meta-disubstituted benzenes, as well as in the E-isomers of olefins.

Specifications of the Studied Compounds
In total, 576 different compounds were studied in this work. Some compounds with the O−H···O=C IMHB were already investigated individually, but they were not considered in aggregate, and general patterns of the changes in the IMHB strength depending on the molecular structure were not established. Other compounds exhibiting PPE were studied in this paper for the first time. Taking into account the wide variety of compounds under investigation, we have carried out their detailed specification.

Previously Studied Compounds with the O−H•••O=C Intramolecular Hydrogen Bonding
In total, 153 Aliphatic hydroxy carbonyl compounds with the O−H···O=C IMHB (non-RAHB structures), 232 β-diketones as well as related compounds with the O−H···O=C IMHB (RAHB structures), and 137 ortho-hydroxybenzaldehydes, phenones, and quinones with the O−H···O=C IMHB (arom-AHB structures), studied in [56][57][58], were not considered in this paper as individual substances. Hence, they were not numbered and were integrated into the non-RAHB, RAHB, and arom-AHB clusters, respectively. Typical compounds from the non-RAHB, RAHB, and arom-AHB clusters are presented in Schemes 1-3, respectively.   Nevertheless, some clarification regarding compounds from non-RAHB, RAHB, and arom-AHB clusters needs to be made. As noted in [56,57], the compounds with a bifurcated H-bond (second compounds from left to right in Schemes 1 and 2), exhibit an anticooperative effect. However, the magnitude of the anticooperative effect is insignificant, so they can be considered in the common range of non-RAHB or RAHB structures [56,57]. For the compounds with a bifurcated H-bond, the fragmentation scheme includes six fragments to account for both H-bonds (see Scheme S1, Supplementary Materials, p. S2). It was recognized that the RAHB is implemented only if the 4n + 2 Hückel aromaticity rule Nevertheless, some clarification regarding compounds from non-RAHB, RAHB, and arom-AHB clusters needs to be made. As noted in [56,57], the compounds with a bifurcated H-bond (second compounds from left to right in Schemes 1 and 2), exhibit an anticooperative effect. However, the magnitude of the anticooperative effect is insignificant, so they can be considered in the common range of non-RAHB or RAHB structures [56,57]. For the compounds with a bifurcated H-bond, the fragmentation scheme includes six fragments to account for both H-bonds (see Scheme S1, Supplementary Materials, p. S2). It was recognized that the RAHB is implemented only if the 4n + 2 Hückel aromaticity rule is fulfilled for π-conjugated chain [60]. In the rightmost compound in Scheme 1, the eight electrons take part in π-conjugation, so this compound is of the non-RAHB type. The dependences of the IMHB energy quantified by the MTA on the ν O-H frequency and the chemical shift of the hydrogen-bonded proton were previously considered for non-RAHB, RAHB, and arom-RAHB structures [56][57][58]. In addition, the IMHB energies estimated by the MTA method were compared with the IMHB energies estimated by the difference in the energies of conformers with and without an H-bond for the RAHB and arom-AHB structures [57,58].

Newly Studied Compounds Exhibiting Push-Pull Effect
Studied compounds 1-54 exhibiting the push-pull effect are the R 1 -Don-π-Acc-R 2 systems where the Don unit is the pyrrole ring, the Acc unit is the carbonyl group and the π-linker is the ethenyl or phenyl moiety. The R 1 and R 2 substituents at the ends of the Donπ-Acc system tune the PPE strength. Depending on the nature of the π-linker, compounds 1-54 are divided into three subseries. Compounds 1-18 where the π-linker is a double bond form subseries I. Compounds 19-36 and 37-54, where the π-linker is the para-and meta-disubstituted phenyl ring, constitute subseries II and III, respectively. In turn, each subseries has parts a and b, depending on which substituent R 1 or R 2 varies or fixes.  Table 1 together with the −E π (PPE) values. The bond length, vibration frequency, HOMO and LUMO energy, and HOMO-LUMO energy gap for calculated compounds 1-54 are collected in Tables S19-S23 (Supplementary Materials, pp. S31-S33). The atom coordinates of compounds 1-54 are given in Supplementary Materials (pp. S77-S104). Table 1. Studied subseries Ia,b-IIIa,b of compounds 1-54 and −E π (PPE) values for them (in kcal/mol). electrons take part in π-conjugation, so this compound is of the non-RAHB type. The dependences of the IMHB energy quantified by the MTA on the νO-H frequency and the chemical shift of the hydrogen-bonded proton were previously considered for non-RAHB, RAHB, and arom-RAHB structures [56][57][58]. In addition, the IMHB energies estimated by the MTA method were compared with the IMHB energies estimated by the difference in the energies of conformers with and without an H-bond for the RAHB and arom-AHB structures [57,58].

Newly Studied Compounds Exhibiting Push-Pull Effect
Studied compounds 1-54 exhibiting the push-pull effect are the R1-Don-π-Acc-R2 systems where the Don unit is the pyrrole ring, the Acc unit is the carbonyl group and the π-linker is the ethenyl or phenyl moiety. The R1 and R2 substituents at the ends of the Donπ-Acc system tune the PPE strength. Depending on the nature of the π-linker, compounds 1-54 are divided into three subseries. Compounds 1-18 where the π-linker is a double bond form subseries I. Compounds 19-36 and 37-54, where the π-linker is the para-and meta-disubstituted phenyl ring, constitute subseries II and III, respectively. In turn, each subseries has parts a and b, depending on which substituent R1 or R2 varies or fixes. Compounds 1-18, 19-36, and 37-54 from subseries Ia,b, IIa,b, and IIIa,b are presented in Table  1 together with the −Eπ(PPE) values. The bond length, vibration frequency, HOMO and LUMO energy, and HOMO-LUMO energy gap for calculated compounds 1-54 are collected in Tables S19-S23 (Supplementary Materials, p. S31-S33). The atom coordinates of compounds 1-54 are given in Supplementary Materials (p. S77-S104). is fulfilled for π-conjugated chain [60]. In the rightmost compound in Scheme 1, the eight electrons take part in π-conjugation, so this compound is of the non-RAHB type. The dependences of the IMHB energy quantified by the MTA on the νO-H frequency and the chemical shift of the hydrogen-bonded proton were previously considered for non-RAHB, RAHB, and arom-RAHB structures [56][57][58]. In addition, the IMHB energies estimated by the MTA method were compared with the IMHB energies estimated by the difference in the energies of conformers with and without an H-bond for the RAHB and arom-AHB structures [57,58]. The compounds belonging to the non-RAHB, RAHB, and arom-AHB clusters are fully decoded in Tables S1-S7, S8-S10, and S11-S15, respectively (see Supplementary Materials, p.S3-S20). The −EHB(MTA) values and characteristics of the O−H···O=C IMHB for the compounds from the non-RAHB, RAHB, and arom-AHB clusters are collected in Tables S16, S17, and S18, respectively, (Supplementary Materials, p.S21-S31).

Newly Studied Compounds Exhibiting Push-Pull Effect
Studied compounds 1-54 exhibiting the push-pull effect are the R1-Don-π-Acc-R2 systems where the Don unit is the pyrrole ring, the Acc unit is the carbonyl group and the π-linker is the ethenyl or phenyl moiety. The R1 and R2 substituents at the ends of the Donπ-Acc system tune the PPE strength. Depending on the nature of the π-linker, compounds 1-54 are divided into three subseries. Compounds 1-18 where the π-linker is a double bond form subseries I. Compounds 19-36 and 37-54, where the π-linker is the para-and meta-disubstituted phenyl ring, constitute subseries II and III, respectively. In turn, each subseries has parts a and b, depending on which substituent R1 or R2 varies or fixes. Compounds 1-18, 19-36, and 37-54 from subseries Ia,b, IIa,b, and IIIa,b are presented in Table  1 together with the −Eπ(PPE) values. The bond length, vibration frequency, HOMO and LUMO energy, and HOMO-LUMO energy gap for calculated compounds 1-54 are collected in Tables S19-S23 (Supplementary Materials, p. S31-S33). The atom coordinates of compounds 1-54 are given in Supplementary Materials (p. S77-S104). is fulfilled for π-conjugated chain [60]. In the rightmost compound in Scheme 1, the eight electrons take part in π-conjugation, so this compound is of the non-RAHB type. The dependences of the IMHB energy quantified by the MTA on the νO-H frequency and the chemical shift of the hydrogen-bonded proton were previously considered for non-RAHB, RAHB, and arom-RAHB structures [56][57][58]. In addition, the IMHB energies estimated by the MTA method were compared with the IMHB energies estimated by the difference in the energies of conformers with and without an H-bond for the RAHB and arom-AHB structures [57,58]. The compounds belonging to the non-RAHB, RAHB, and arom-AHB clusters are fully decoded in Tables S1-S7, S8-S10, and S11-S15, respectively (see Supplementary Materials, p.S3-S20). The −EHB(MTA) values and characteristics of the O−H···O=C IMHB for the compounds from the non-RAHB, RAHB, and arom-AHB clusters are collected in Tables S16, S17, and S18, respectively, (Supplementary Materials, p.S21-S31).

Newly Studied Compounds Exhibiting Push-Pull Effect
Studied compounds 1-54 exhibiting the push-pull effect are the R1-Don-π-Acc-R2 systems where the Don unit is the pyrrole ring, the Acc unit is the carbonyl group and the π-linker is the ethenyl or phenyl moiety. The R1 and R2 substituents at the ends of the Donπ-Acc system tune the PPE strength. Depending on the nature of the π-linker, compounds 1-54 are divided into three subseries. Compounds 1-18 where the π-linker is a double bond form subseries I. Compounds 19-36 and 37-54, where the π-linker is the para-and meta-disubstituted phenyl ring, constitute subseries II and III, respectively. In turn, each subseries has parts a and b, depending on which substituent R1 or R2 varies or fixes. Compounds 1-18, 19-36, and 37-54 from subseries Ia,b, IIa,b, and IIIa,b are presented in Table  1 together with the −Eπ(PPE) values. The bond length, vibration frequency, HOMO and LUMO energy, and HOMO-LUMO energy gap for calculated compounds 1-54 are collected in Tables S19-S23 (Supplementary Materials, p. S31-S33). The atom coordinates of compounds 1-54 are given in Supplementary Materials (p. S77-S104).

Dependences of Hydrogen Bond Energy on Magnitudes of Potential Energy Density at Hydrogen Bond Critical Point for the Non-RAHB, RAHB, and Arom-AHB Clusters
The value of the potential energy density at the (3,−3) critical point of an H-bond (VBCP) is the most important descriptor of an H-bond, since it is widely used to estimate the energy of an H-bond due to the Espinosa-Molins-Lecomte equation and its modified versions [40,[45][46][47]. The −EHB(MTA) values taken from Tables S1-S15 (Supplementary Materials, p. S3-S20) correlate with the VBCP values for compounds from the non-RAHB, RAHB, and arom-AHB clusters (see Equations (1)   In order to interpret these findings, it is necessary to recall that the non-RAHB interaction is a simple H-bond consisting of only σ-component (H-bond per se). The RAHB interaction is complex interaction comprising σ-(H-bond per se) and π-components (resonance effect). Thus, the appearance of an additional contribution of 7.5(±1) kcal/mol to the −E HB (MTA) value for compounds from the RAHB cluster can be considered as the presence of a π-contribution to the total RAHB energy. At the same time, this π-contribution reduces to 3(±1) kcal/mol on going to compounds from the arom-AHB cluster. Therefore, the π-contribution to the arom-AHB should be significantly lower compared with the RAHB. This assumption is more fully substantiated in the next section using a wider set of H-bond descriptors, the values of which are divided into subranges. The difference between the <-E HB (MTA)> values for compounds of the arom-AHB and non-RAHB clusters is 0.5-3.0 kcal/mol, while the <-E HB (MTA)> values for compounds of the arom-AHB clusters are less compared with those for compounds of the RAHB clusters by 3.7-5.6 kcal/mol. At the same time, the <-E HB (MTA)> values for compounds of the RAHB cluster are much higher (by 5.9-7.6 kcal/mol) than those for compounds of the non-RAHB cluster (Figure 3a-c). The <-E HB (MTA)> values for compounds of the RAHB cluster are significantly larger than that for compounds of the non-RAHB cluster, since the O-H···O=C RAHB interaction in the former includes the σand π-contributions, while the O-H···O=C IMHB in the latter has only the σ-contribution [37,38,60]. The closer similarity of the <-E HB (MTA)> values for compounds of the arom-AHB cluster with those for compounds of the non-RAHB cluster rather than with the RAHB cluster suggests that the resonance contribution in the arom-AHB interaction is noticeably smaller compared with the RAHB interaction.

Comparison of Hydrogen Bond Energy Values for Compounds of the Non-RAHB, RAHB, and Arom-AHB Clusters Assessed via Molecular Tailoring and Function-Based Approaches
The estimation and comparison of the π-contribution to the O-H···O=C arom-AHB and RAHB in compounds of the arom-AHB and RAHB clusters can be implemented in an explicit form using the FBA method which relies on the values of the ρ BCP , V BCP , and r O···H parameters as the H-bond descriptors and evaluate a pure σ-component of the total RAHB energy (see Introduction). The use of the FBA method for estimating the σ-contribution to the total energy of the RAHB interaction has the following grounds. The critical point for the O-H···O=C H-bond of (3,-3) character is located on the pathway between the oxygen of the C=O group and hydrogen atoms, where the π-cloud of the molecule has a node. For this reason, the ρ BCP electron density and the V BCP potential energy density, calculated at the (3,-3) H-bond critical point, are determined by the properties of the σ-orbitals. To demonstrate the relationship between the ρ BCP and V BCP values and the σ-properties of molecules, we performed the Natural Bond Order (NBO) analysis [72] of a sample of 21 compounds in total from the non-RAHB, RAHB, and arom-AHB clusters. The NBO analysis data for compounds 1, 8a, 11, 33a, 43, 62, 88b, and 94 from the non-RAHB cluster, compounds 6, 17, 36, 42, 50, 78, and 107 from the RAHB cluster,  and compounds 13, 14, 50, 62, 70, and 104 from the arom-AHB cluster are presented in Table S67 (Supplementary Materials, p. S74).
RAHB, RAHB, and arom-AHB cluster, the −EHB(MTA) values for each of the clusters were compared with the values of the ρBCP, VBCP, and rO···H parameters as the most widely used H-bond descriptors [40,[42][43][44][45][46][47]. The total intersecting ranges of change in the ρBCP, VBCP, and rO···H parameters in the compounds of clusters under investigation are 0.030-0.051 a.u. for both the former and 1.60-1.80 Å for the latter parameter (see Tables S16-S18, Supplementary Materials, p. S21-S31). In order to more accurately compare the −EHB(MTA) values with the ρBCP, VBCP, and rO···H parameters, these parameters were divided into four subranges (0.030-0.035, 0.035-0.040, 0.040-0.046, and 0.046-0.051 a.u. for both the former and 1.60-1.65, 1.65-1.70, 1.70-1.75, and 1.75-1.80 Å for the latter parameter). The comparison was carried out in such a way that the -EHB(MTA) energy values would average for all subranges and the total ρBCP, VBCP, and rO···H ranges. The results of the comparison are given in Tables S22-S66   The Equations (14a)-(16a) show the same relationship between the r O···H values and the σ-interaction parameters derived from the NBO analysis, as shown above for the ρ BCP and V BCP values.
Thus, the findings above indicate that the ρ BCP , V BCP values, and r O···H distance used in the FBA method can serve as descriptors for estimating the energy of the σ-component in the total RAHB interaction. The π-component of the RAHB interaction is related to the resonance interaction in the π-system of molecules, which arises due to the charge transfer from the π-type lone pair of the donor oxygen atom of the O-H group to the C=O double bond through the π-system of the unsaturated fragment. The presence of the π-component of the RAHB interaction is detected using the MTA method as an additional increase in the H-bond energy compared to that estimated by the FBA method [38,60].
Within the framework of the FBA method, a family of Equations (15a)-(17a) was generated: where ρ BCP is in a.u., but V BCP is in kcal/mol. Equations (15a)-(17a) were presented in [45,56], respectively. Equation (17a) is a modified version of the well-known Espinosa-Molins-Lecomte equation [40]. The slope of the linear dependence (17a) is 0.277 instead of 0.5 as in the original equation. Preference was given to the modified version of the Espinosa-Molins-Lecomte equation due to its better agreement with the IMHB energies evaluated by the MTA method [58]. Equation (18a) was used to average the FBA method energies from Equations (15a)-(17a) and to obtain a more reliable value of −E HB (FBA) IMHB energy [37,38,45,46]: The difference between the <−E HB (FBA)> and <−E HB (MTA)> values for compounds of the non-RAHB cluster randomly varies within 1 kcal/mol. However, the <−E HB (FBA)> values for compounds of the arom-AHB and RAHB clusters are smaller than the <−E HB (MTA)> values by 0.6-3.1 and 5.9-8.0 kcal/mol, respectively, revealing the presence of π-contribution in the arom-AHB and RAHB interactions. At the same time, these data indicate that the π-contribution to the arom-AHB interaction is much lower than that to the RAHB interaction.
The emergence of the π-contribution of 2-3 kcal/mol to the total energy of IMHB on going from non-RAHB structures to arom-AHB ones agrees with the higher energy of the intermolecular H-bond for dimers of the aromatic heterocycles compared with the saturated analogues [29,[31][32][33]. <−EHB(MTA)> values for compounds of the non-RAHB cluster randomly varies within 1 kcal/mol. However, the <−EHB(FBA)> values for compounds of the arom-AHB and RAHB clusters are smaller than the <−EHB(MTA)> values by 0.6-3.1 and 5.9-8.0 kcal/mol, respectively, revealing the presence of π-contribution in the arom-AHB and RAHB interactions. At the same time, these data indicate that the π-contribution to the arom-AHB interaction is much lower than that to the RAHB interaction.

Comparison of π-Contributions to the Total Energy of Arom-AHB and RAHB Interactions
The π-contribution to the arom-AHB and RAHB interactions can be estimated as the difference between the <−E HB (MTA)> and <−E HB (FBA)> values [38]. The values of the π-contribution for compounds of the arom-AHB and RAHB clusters within the considered range of the ρ BCP , V BCP , and r O···H parameters are shown in Figure 5a-c and Tables S37-S66 (Supplementary Materials, pp. S40-S73). As follows from Figure 5a-c, the values of the π-contribution for the arom-AHB interaction are much lower compared with those of the RAHB interaction. The average value of the π-contribution for the arom-AHB interaction is 2.0 kcal/mol, while for the RAHB one it is 6.6 kcal/mol. Thus, the value of the π-contribution increases by almost three and a half times on going from the arom-AHB to RAHB interaction.
The emergence of the π-contribution of 2-3 kcal/mol to the total energy of IMHB on going from non-RAHB structures to arom-AHB ones agrees with the higher energy of the intermolecular H-bond for dimers of the aromatic heterocycles compared with the saturated analogues [29,[31][32][33].

Comparison of π-Contributions to the Total Energy of Arom-AHB and RAHB Interactions
The π-contribution to the arom-AHB and RAHB interactions can be estimated as the difference between the <−EHB(MTA)> and <−EHB(FBA)> values [38]. The values of the πcontribution for compounds of the arom-AHB and RAHB clusters within the considered range of the ρBCP, VBCP, and rO···H parameters are shown in Figure 5a-c and Tables S37-S66 (Supplementary Materials, p. S40-S73). As follows from Figure 5a-c, the values of the πcontribution for the arom-AHB interaction are much lower compared with those of the RAHB interaction. The average value of the π-contribution for the arom-AHB interaction is 2.0 kcal/mol, while for the RAHB one it is 6.6 kcal/mol. Thus, the value of the π-contribution increases by almost three and a half times on going from the arom-AHB to RAHB interaction. The main difference between the arom-AHB and RAHB interactions is that the resonance effect is transmitted through the aromatic moiety in the former case, while this effect is transmited across the olefinic bridge in the latter case. Hence, the most likely reason The main difference between the arom-AHB and RAHB interactions is that the resonance effect is transmitted through the aromatic moiety in the former case, while this effect is transmited across the olefinic bridge in the latter case. Hence, the most likely reason for the sharp decrease in the π-contribution to the arom-AHB interaction compared to the RAHB one can be the poor transfer of the resonance effect across the aromatic ring compared to the olefinic fragment. In order to explicitly compare the ability of an aromatic ring and a double bond to transmit a resonance effect, it is necessary to use the para-, meta-disubstituted benzenes and E-isomers of olefinic compounds.

Testing the Ability of the Aromatic Ring and the Double Bond to Conduct the Resonance Effect
To test and compare the ability of the aromatic ring and the olefin moiety to conduct the resonance effect, the Don-π-Acc systems were used, where the Don unit is the pyrrole ring, the Acc unit is the C=O group and the π-bridge is the phenyl ring or double bond. It is shown that the PPE arising from the addition of electron-donating and electronwithdrawing substituents to conjugated molecules significantly changes their properties in the ground and excited states [75][76][77]. The PPE energy, which is quantified using the MTA method [70,71], can serve as a measure of the conductivity of the resonance effect. The PPE strength can be varied by attaching the R 1 substituent to the Don unit and the R 2 substituent to the Acc unit. To test the conductivity of the resonance effect, compounds 1-54 were divided into three subseries, each of which consists of parts a and b (see Table 1). The double bond serves as the π-bridge in subseries Ia and b, while the para-and metadisubstituted phenyl ring acts as the π-bridge in subseries IIa,b and IIIa,b, respectively. The R 1 substituent varies, and the R 2 one is fixed in part a in subseries I, II, and III. The R 1 substituent is fixed, and the R 2 one varies in part b of these subseries.
A quantitative criterion for the PPE strength is the −E π (PPE) value, and the higher the −E π (PPE) value, the stronger the PPE and vice versa [70,71]. The PPE strength was controlled by varying the R 1 and R 2 substituents with known σ p Hammett constants [78]. The R 1 and R 2 substituents are given in Table 1 and their σ p Hammett constants are shown in Table S68 (Supplementary Materials, p. S75). The −E π (PPE) values are known to reflect the structural and spectral properties of molecules, as well as their reactivity. The double bonds of the π-spacer between the Don and Acc units lengthen, while the single bonds shorten, and the frequency of the C=O vibration decreases with increasing the −E π (PPE) value [70,71]. The HOMO and LUMO energies lower, and the HOMO-LUMO energy gap narrows as the −E π (PPE) value enhances [71]. Figure 6 shows the total ranges of changes in the −E π (PPE) values for subseries Ia,b-IIIa,b of compounds 1-54. As follows from Figure 6, the ranges of change in the −E π (PPE) values for subseries Ia,b shift significantly towards larger magnitudes with respect to those of IIa,b and IIIa,b (3.0-12.1, 3.6-12.1 vs. -0.5 ÷ 3.3, 0.4-3.6 and -1.5 ÷ 2.1, and 0.4-2.1 kcal/mol, respectively). It suggests that the phenyl ring as a π-bridge conducts the push-pull effect much worse compared to the double bond. value [70,71]. The HOMO and LUMO energies lower, and the HOMO-LUMO energy gap narrows as the −Eπ(PPE) value enhances [71]. Figure 6 shows the total ranges of changes in the −Eπ(PPE) values for subseries Ia,b-IIIa,b of compounds 1-54. As follows from Figure 6, the ranges of change in the −Eπ(PPE) values for subseries Ia,b shift significantly towards larger magnitudes with respect to those of IIa,b and IIIa,b (3.0-12.1, 3.6-12.1 vs. -0.5 ÷ 3.3, 0.4-3.6 and -1.5 ÷ 2.1, and 0.4-2.1 kcal/mol, respectively). It suggests that the phenyl ring as a π-bridge conducts the pushpull effect much worse compared to the double bond.  Figure 6. Ranges of changes for the −E π (PPE) values: subseries Ia,b; IIa,b, and IIIa,b-double bond, para-phenyl ring, and meta-phenyl ring, respectively, as the π-bridge. The R 1 substituent is fixed and the R 2 substituent varies in part a of the subseries, the R 2 substituent is fixed and the R 1 substituent varies in part b of the subseries. The −E π (PPE) values were shown [70,71] to be linearly dependent on the σ p values. The −E π (PPE) values in subseries Ia,b-IIIa,b of compounds 1-54 also reveal reliable linear dependence on the σ p Hammett constants in form (19a): where the A slope coefficients characterize the sensitivity of the PPE strength to the σ p Hammett constants, and the larger the A value, the higher the sensitivity; the B intersection points reveal the PPE strength for this subseries at zero value of the σ p Hammett constant. Equations (4)-(9) given in Figure 7a-c show the linear dependence of the -E π (PPE) values on the σ p Hammett constants for subseries Ia,b-IIIa,b of compounds 1-54. Equations (4), (6), and (8) indicate that the -E π (PPE) energy decreases with an increase in the electron-withdrawing property of the R 1 substituent attached to the Don unit of the Don-π-Acc system. Equations (5), (7), and (9) reveal that the -E π (PPE) energy augments with an increase in the electron-withdrawing property of the R 2 substituent attached to the Acc unit of the Don-π-Acc system. Analysis of the A and B coefficients in Equations (4)-(9) shown in Figure 8a,b, respectively, allows one to compare the conductivity of PPE between the phenyl ring and the double bond as the π-bridges in the Don-π-Acc system. Figure 8a demonstrates that the absolute value of A coefficient in Equations (4) and (5) for subseries Ia,b is significantly higher compared to that of Equations (6)-(9) for subseries IIa,b and IIIa,b, respectively, (5.3 and 5.4 vs. 1.9, 2.5 and 0.9, 2.1, respectively). This means that the sensitivity of the PFE strength towards the substituent electronic effect, which is defined by the value of the σ p Hammett constant, is by several times higher for the double bond as a π-bridge compared to the phenyl ring. Figure 8b displays that the B coefficient in Equations (4) and (5) for subseries Ia,b is also much larger in comparison with that of Equations (6)-(9) for subseries IIa,b and IIIa,b, respectively, (7.0 and 7.1 vs. 1.7, 1.4 and 1.2, 0.7, respectively). It follows that the PPE strength in the Don-π-Acc system, without taking into account the influence of the electronic effect of substituents at the Don and Acc units, is much higher again by several times, when the π-bridge is a double bond rather than a phenyl ring.
The above findings indicate that the phenyl ring is a poor PPE conductor with respect to the double bond. Therefore, the transmission of the resonance effect through the phenyl ring is a hindrance. This implies that the phenyl ring does not exert the same pronounced resonance effect assisting the hydrogen bond as the double bond. This explains the decrease in the π-contribution to the total energy on going from the arom-AHB to RAHB interaction by three and a half times. Additionally, this confirms the need to include the arom-AHBs into a separate class of hydrogen bonds, which differ conspicuously from a usual RAHBs and are closer to ordinary hydrogen bonds without resonance assistance.   The above findings indicate that the phenyl ring is a poor PPE conductor with respect to the double bond. Therefore, the transmission of the resonance effect through the phenyl ring is a hindrance. This implies that the phenyl ring does not exert the same pronounced resonance effect assisting the hydrogen bond as the double bond. This explains the decrease in the π-contribution to the total energy on going from the arom-AHB to RAHB interaction by three and a half times. Additionally, this confirms the need to include the arom-AHBs into a separate class of hydrogen bonds, which differ conspicuously from a usual RAHBs and are closer to ordinary hydrogen bonds without resonance assistance.

Relationship of −Eπ(PPE) Values with Structural and Spectral Parameters and Frontier Orbitals Energy
This section shows that the PPE strength reflects real structural changes in the studied molecules, as well as changes in their spectral characteristics and reactivity. The πspacer bonds lengths (double bond or phenyl ring) between the pyrrole ring and C=O group, the C=O vibrational frequency, the HOMO and LUMO energies [E(HOMO) and E(LUMO)], and the HOMO-LUMO energy gap [ΔE(HOMO-LUMO)] were chosen as the P parameter characterizing the molecular properties. The dependence of the P parameter on the −Eπ(PPE) values was established in the form of the linear relation (20a): where P is listed above bond lengths, vibrational frequency, and molecular orbital energy. The A and B coefficients of dependence (20a) of the π-spacer bond lengths, νC=O vibration frequency, and the molecular orbital energies on the −Eπ(PPE) values are given in Tables S69-S71,   , para-phenyl ring, and meta-phenyl ring, respectively, as the π-bridge. The R 1 substituent is fixed and the R 2 substituent varies in part a of the subseries, the R 2 substituent is fixed and the R 1 substituent varies in part b of the subseries.

Relationship of −E π (PPE) Values with Structural and Spectral Parameters and Frontier Orbitals Energy
This section shows that the PPE strength reflects real structural changes in the studied molecules, as well as changes in their spectral characteristics and reactivity. The π-spacer bonds lengths (double bond or phenyl ring) between the pyrrole ring and C=O group, the C=O vibrational frequency, the HOMO and LUMO energies [E(HOMO) and E(LUMO)], and the HOMO-LUMO energy gap [∆E(HOMO-LUMO)] were chosen as the P parameter characterizing the molecular properties. The dependence of the P parameter on the −E π (PPE) values was established in the form of the linear relation (20a): where P is listed above bond lengths, vibrational frequency, and molecular orbital energy. The A and B coefficients of dependence (20a) of the π-spacer bond lengths, ν C=O vibration frequency, and the molecular orbital energies on the −E π (PPE) values are given in Tables S69-S71,  The positive coefficient A in Equation (20a) means an elongation of the corresponding covalent bond, while the negative one means its shortening. One can anticipate that an increase in the −E π (PPE) values for the studied compounds, reflecting an enhancement in the strength of conjugation, is accompanied by the contraction of the single bonds and the elongation of the double bonds [79]. Indeed, the C 2 -C 6 and C 7 -C 8 single bonds are shortened, whereas the C 6 =C 7 and C 8 =O 9 double bonds are lengthened with the −E π (PPE) increasing in subseries Ia and b of studied compounds (see structure A in Scheme 4). The positive coefficient A in Equation (20a) means an elongation of the corresponding covalent bond, while the negative one means its shortening. One can anticipate that an increase in the −Eπ(PPE) values for the studied compounds, reflecting an enhancement in the strength of conjugation, is accompanied by the contraction of the single bonds and the elongation of the double bonds [79]. Indeed, the C2-C6 and C7-C8 single bonds are shortened, whereas the C6=C7 and C8=O9 double bonds are lengthened with the −Eπ(PPE) increasing in subseries Ia and b of studied compounds (see structure A in Scheme 4).  Table S69). The lengths of the C8=O9 double bond do not correlate with the −Eπ(PPE) for subseries IIa. This can be the case due to through-space interaction between the C8=O9 bond orbitals with orbitals of the neighboring R2 substituent [70]. These trends are reliably displayed by the dependencies (10)-(13) on Figure 9a,b, dependencies (S1) and (S3) of l(C 2 -C 6 ) and l(C 7 -C 8 ) on −E π (PPE) from Table S69, in which the A slope is negative, and the dependency (S2) of l(C 6 =C 7 ) on −E π (PPE) with the positive A (see Table S69). The lengths of the C 8 =O 9 double bond do not correlate with the −E π (PPE) for subseries IIa. This can be the case due to through-space interaction between the C 8 =O 9 bond orbitals with orbitals of the neighboring R 2 substituent [70].

Dependence of C=O Vibration Frequency on −E π (PPE) Value
Strengthening conjugation within the molecules under study should cause the re shift of the ν C=O vibration frequency [79]. The decrease in the ν C=O values with the −E π (PPE) enhancement takes place in subseries Ia, IIa, and IIIa of the studies compounds. This regularity is shown by Equation (14) in Figure 10 and dependencies (S31) and (S32) of ν C=O on −E π (PPE) from Strengthening conjugation within the molecules under study should cause the re shift of the νC=O vibration frequency [79]. The decrease in the νC=O values with the −Eπ(PPE) enhancement takes place in subseries Ia, IIa, and IIIa of the studies compounds. This regularity is shown by Equation (14) in Figure 10 and dependencies (S31) and (S32) of νC=O on −Eπ(PPE) from Table S70, in which the A slope is negative. The E(HOMO) and E(LUMO) energies of frontier molecular orbitals are an important characteristic of the orbital structure, since they reflect the ability of a molecule to donate Similarly to the C=O bond length, the ν C=O values do not show a correlation with the −E π (PPE) values in the subseries Ib, IIb, and IIIb of the studies compounds for the same reason.

Dependence of HOMO and LUMO Energy on −E π (PPE) Value
The E(HOMO) and E(LUMO) energies of frontier molecular orbitals are an important characteristic of the orbital structure, since they reflect the ability of a molecule to donate and accept electrons. The data obtained recognize that the E(HOMO) and E(LUMO) values vary in a regular manner with a change in the −E π (PPE). The E(HOMO) and E(LUMO) energies rise with the −E π (PPE) growth in subseries Ia, IIa, and IIIa while the E(HOMO) and E(LUMO) energies lower with the −E π (PPE) increase in subseries Ib, IIb, and IIIb. These tendencies are shown by Equations (15) (Table S71). However, the ∆E(HOMO-LUMO) energy gap narrows in all studied subseries Ia,b-IIIa,b. It follows from Equations (19) and (20) on Figure 11c and Equations (S35), (S38), (S41), and (S44) from Table S71 having negative A slope. This result is of special importance since the optical (absorption, fluorescent, phosphorescent) properties of molecules depend on the ∆E(HOMO-LUMO) energy gap value. Similarly to the C=O bond length, the νC=O values do not show a correlation with the −Eπ(PPE) values in the subseries Ib, IIb, and IIIb of the studies compounds for the same reason.

Dependence of HOMO and LUMO Energy on −Eπ(PPE) Value
The E(HOMO) and E(LUMO) energies of frontier molecular orbitals are an important characteristic of the orbital structure, since they reflect the ability of a molecule to donate and accept electrons. The data obtained recognize that the E(HOMO) and E(LUMO) values vary in a regular manner with a change in the −Eπ(PPE). The E(HOMO) and E(LUMO) energies rise with the −Eπ(PPE) growth in subseries Ia, IIa, and IIIa while the E(HOMO) and E(LUMO) energies lower with the −Eπ(PPE) increase in subseries Ib, IIb, and IIIb. These tendencies are shown by Equations (15) (Table S71). However, the ΔE(HOMO-LUMO) energy gap narrows in all studied subseries Ia,b-IIIa,b. It follows from Equations (19) and (20) on Figure 11c and Equations (S35), (S38), (S41), and (S44) from Table S71 having negative A slope. This result is of special importance since the optical (absorption, fluorescent, phosphorescent) properties of molecules depend on the ΔE(HOMO-LUMO) energy gap value.

Methods and Computational Details
The energy of the O−H···O=C IMHB and PPE in the studied compounds was estimated in accordance with the following fragmentation schemes. For both cases, the entire M molecule is the main "fragment". The M1 fragment presents the M molecule without the H-bond donor, while the M2 fragment is the M molecule without the H-bond acceptor. As the excess atoms appear when the M1 and M2 fragments are superimposed, an additional M3 fragment is introduced to compensate for them (see Scheme 5a-c for compounds with the non-RAHB, RAHB, and arom-AHB, respectively). At the cutting site of the entire M molecule, the hydrogen atoms are placed at a distance of 1.1 Å from the corresponding carbon atom (see [48,56]  the entire M molecule, the hydrogen atoms are placed at a distance of 1.1 Å from the corresponding carbon atom (see [48,56] for more details). The When calculating the PPE energy, the fragmentation scheme looks similar. The entire molecule exhibiting the PPE phenomena is the Don-π-Acc system, in which intramolecular charge transfer from the Don unit to the Acc unit via the π-linker takes place (more details in [70,71]). The M molecule without the Don unit forms the M1 fragment, whereas the M molecule without the Acc unit creates the M2 fragment. To compensate for excess atoms due to the overlap of the M1 and M2 fragments, an additional M3 fragment is again introduced (see Scheme 6a,b for a compound with the double bond as π-bridge and the phenyl ring as π-bridge, respectively. Similarly to the IMHB calculating, at the cutting site of the entire M molecule, the hydrogen atoms are placed at the distance of 1.1 Å from the corresponding carbon atom. By analogy with the calculation of the IMHB energy, the Eπ(PPE) values of the PPE energy are calculated by Equation (22a): When calculating the PPE energy, the fragmentation scheme looks similar. The entire molecule exhibiting the PPE phenomena is the Don-π-Acc system, in which intramolecular charge transfer from the Don unit to the Acc unit via the π-linker takes place (more details in [70,71]). The M molecule without the Don unit forms the M1 fragment, whereas the M molecule without the Acc unit creates the M2 fragment. To compensate for excess atoms due to the overlap of the M1 and M2 fragments, an additional M3 fragment is again introduced (see Scheme 6a,b for a compound with the double bond as π-bridge and the phenyl ring as π-bridge, respectively. pounds with the non-RAHB, RAHB, and arom-AHB, respectively). At the cutting site of the entire M molecule, the hydrogen atoms are placed at a distance of 1.1 Å from the corresponding carbon atom (see [48,56]  When calculating the PPE energy, the fragmentation scheme looks similar. The entire molecule exhibiting the PPE phenomena is the Don-π-Acc system, in which intramolecular charge transfer from the Don unit to the Acc unit via the π-linker takes place (more details in [70,71]). The M molecule without the Don unit forms the M1 fragment, whereas the M molecule without the Acc unit creates the M2 fragment. To compensate for excess atoms due to the overlap of the M1 and M2 fragments, an additional M3 fragment is again introduced (see Scheme 6a,b for a compound with the double bond as π-bridge and the phenyl ring as π-bridge, respectively. Similarly to the IMHB calculating, at the cutting site of the entire M molecule, the hydrogen atoms are placed at the distance of 1.1 Å from the corresponding carbon atom. By analogy with the calculation of the IMHB energy, the Eπ(PPE) values of the PPE energy are calculated by Equation (22a): Scheme 6. Fragmentation scheme for the E π (PPE) value calculation for compound with the double bond as π-bridge (a) and the phenyl ring as π-bridge (b).
Similarly to the IMHB calculating, at the cutting site of the entire M molecule, the hydrogen atoms are placed at the distance of 1.1 Å from the corresponding carbon atom. By analogy with the calculation of the IMHB energy, the E π (PPE) values of the PPE energy are calculated by Equation (22a): As both the IMHB and PPE interactions make a negative contribution to the total energy of the molecule, the E HB (MTA) and E π (PPE) values are always negative. For the sake of simplifying the discussion of the results, we use the inverse value of the E HB (MTA) and E π (PPE) parameters from Equations (21a) and (22a), respectively, throughout the article, i.e., −E HB (MTA) and −E π (PPE) values. Thus, an increase in the −E HB (MTA) and −E π (PPE) values corresponds to the IMHB and PPE strengthening and vice versa.
The Gaussian 09 program package [80] (Revision B.01; Gaussian Inc., Wallingford, CT, USA) was used to carry out the calculations. Initially, the geometries of the M molecules were optimized at the B3LYP/6-311++G(d,p) level. After that, the M molecules were cut into M1, M2, and M3 fragments without changing the optimized geometry of the entire M molecules. As the last step, the single-point energy calculations at the level MP2(full)/6-311++G(2d,2p) of the entire M molecule and M1, M2, and M3 fragments were used for the energy correction of geometries optimized at the B3LYP level. In order to make sure that a local minimum of energy was found, the vibrational frequencies were checked for the absence of imaginary ones. The ρ BCP and V BCP topological properties from Bader quantum theory "Atoms in Molecules" (OTAIM) [81] were calculated using the AIMAll program package [82]. NBO characteristics were obtained through the NBO program implemented in the Gaussian 09 at MP2/6-311++G(2d,2p) level. All calculations were carried out for the gas phase.

Conclusions
Using the molecular tailoring approach, intramolecular hydrogen bonds energy has been quantitatively compared between the ortho-disubstituted benzenes, where the hydrogen bond donor and hydrogen bond acceptor are separated by an aromatic moiety (arom-AHB interaction), and the Z-olefins, where the hydrogen bond donor and hydrogen bond acceptor are separated by a double bond (RAHB interaction). The energy of the arom-AHB interaction is shown to be significantly less than the energy of RAHB interaction. The total energy of these interactions is divided into the σand π-components using molecular tailoring and function-based approaches. Although the σ-components of the arom-AHB and RAHB interactions are the same, the π-component of the former is almost three and a half times smaller than that of the latter. The reason for the sharp decrease in the π-contribution to the arom-AHB interaction is the poor conductivity of the resonance effect by the aromatic ring compared to the double bond. The molecular tailoring approach suggests that the push-pull effect as part of the resonance effect is poorly conducted in the para-and meta-disubstituted benzenes as compared with the E-olefins. The energy of the push-pull effect is several times lower for the Don-π-Acc systems, where the π-bridge is the aromatic ring instead of the double bond. The sensitivity of the push-pull energy to the electronic effect of substituents at the Don and Acc units is also lower by several times in the case of the aromatic ring as the π-bridge than that of the double bond. These data reveal that the aromatic ring cannot provide the effective transfer of the resonance effect, which results in a sharp decrease in the π-component of the arom-AHB interaction and a reduction in the total energy of the arom-AHB interaction relative to the RAHB one. It makes the arom-AHB interaction more similar to a conventional hydrogen bond than to the RAHB interaction.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/molecules28020536/s1, Scheme S1: Fragmentation scheme for the E HB (MTA) value calculation in compounds with bifurcated H-bond; Tables S1-S7: Structure of compounds from the non-RAHB cluster; Tables S8-S10: Structure of compounds from the RAHB cluster; Table S11-S15: Structure of compounds from the arom-AHB cluster; Table S16-S18: Characteristics of the O-H···O=C hydrogen bond for studied compounds from the non-RAHB, RAHB and arom-AHB clusters; Tables S19-S21: The calculated E π (PPE) energy, bond length, vibration frequency, HOMO and LUMO energy, HOMO-LUMO energy gap for studied compounds; Tables S22-S36: The E HB (MTA) and E HB (FBA) hydrogen bond energy assessed via molecular tailoring and function-based approaches for compounds from non-RAHB cluster within the different ranges of r O···H , ρ BCP and V BCP parameters; Tables S37-S51: The E HB (MTA) and E HB (FBA) hydrogen bond energy assessed via molecular tailoring and function-based approaches for compounds from RAHB cluster within the different ranges of r O···H , ρ BCP and V BCP parameters; Tables S52-S66: The E HB (MTA) and E HB (FBA) hydrogen bond energy assessed via molecular tailoring and function-based approaches for compounds from arom-AHB cluster within the different ranges of r O···H , ρ BCP and V BCP parameters; Table S67: NBO characteristics for studied compounds; Table S68: The R 1 and R 2 substituents and their Hammett constants for the studied compounds; Tables S69-S71: Parameters of linear dependencies of bond length, vibrational frequency, HOMO and LUMO energy on E π (PPE) values; Atoms coordinates for newly calculated compounds.