Nearest-Neighbour and Non-Nearest-Neighbour Non-Covalent Interactions between Substituents in the Aromatic Systems: Experimental and Theoretical Investigation of Functionally Substituted Benzophenones

Benzophenone derivatives exhibit not only biological activity but also act as photo initiator and UV blocker. We carried out experimental and theoretical thermochemical studies of hydroxy- and methoxy-substituted benzophenones. Standard molar enthalpies of vaporisation were obtained from the temperature dependence of vapour pressures measured by the transpiration method. The thermodynamic data on phase transitions available in the literature (crystal–gas, crystal–liquid, and liquid–gas) were also collected and evaluated. High-level quantum chemical methods G3MP2 and G4 were used to estimate the standard molar enthalpies of formation of substituted benzophenones in the gas phase and establish agreement between experimental and theoretical results. The application of the “centrepiece” group-contribution approach to hydroxy- and methoxy-substituted benzophenones was demonstrated. A quantitative assessment of the hydrogen bond was carried out using various approaches based on experimental data and quantum chemical calculations.


Introduction
Hydroxy-and methoxy-benzophenones represent an important class of biologically active compounds. They exhibit important pharmaceutical properties such as cytotoxic effects against various cancer cells [1]. The attractive features of these compounds are commercial availability and their UV absorbing power. The benzophenones are used as cosmetics and medicine for their ability to harmlessly absorb and scatter UV radiation, protecting products and human skin from the harmful effects of UV radiation. One of the most important areas of application for benzophenones is polymers. The polymers are often exposed to ultraviolet radiation and the absorption of this energy causes the macromolecular chains to break. In order to slow down this process for outdoor use, these materials must be protected with an appropriate UV absorber, e.g., a suitable benzophenone. In order to select an appropriate stabiliser, it is necessary to evaluate the efficiency of a particular compound in terms of the potential for loss from the polymer through evaporation. The evaporation rate is controlled by the vapor pressure of the compound, so it is important to know this parameter at any temperature of application [2]. The benzophenones are low-volatile compounds and accurate vapour pressure measurement is a challenging task. In this work, the experimental focus was on the investigation of the phase transition thermodynamics of hydroxy-and methoxy-substituted benzophenones.
Here we present results on vapour pressures, enthalpies of phase transitions, and enthalpies of formation of a series of substituted benzophenones of general formulas given in Figures 1 and 2. The data available in the literature and new experimental results were evaluated and checked for internal consistency. The consistent thermochemical data sets for substituted benzophenones were used for the design and development of a "centrepiece" group-contribution approach necessary for assessing the enthalpies of vaporisation and enthalpies of formation of compounds that are important for process engineering calculations.
Molecules 2022, 27, x FOR PEER REVIEW 2 of 29 nones are low-volatile compounds and accurate vapour pressure measurement is a challenging task. In this work, the experimental focus was on the investigation of the phase transition thermodynamics of hydroxy-and methoxy-substituted benzophenones.
Here we present results on vapour pressures, enthalpies of phase transitions, and enthalpies of formation of a series of substituted benzophenones of general formulas given in Figures 1 and 2. The data available in the literature and new experimental results were evaluated and checked for internal consistency. The consistent thermochemical data sets for substituted benzophenones were used for the design and development of a "centrepiece" group-contribution approach necessary for assessing the enthalpies of vaporisation and enthalpies of formation of compounds that are important for process engineering calculations.

2-hydroxy-benzophenone
3-hydroxy-benzophenone 4-hydroxy-benzophenone 2,2'-dihydroxy-benzophenone 2,4-dihydroxy-benzophenone 2-hydroxy-4-methoxy-benzophenone 2,2′-hydroxy-4-methoxybenzophenone 2,2′,4,4′-tetrahydroxy-benzophenone 2,2′-dihydroxy-4,4′-dimethoxybenzophenone In the course of the thermochemical measurements, another aspect of the properties of benzophenones attracted our attention. This aspect is not related to our research field but has inspired a deeper interpretation of our thermochemical results. It was found [3] that by absorbing the UV light, benzophenones transform into an excited state, but harmlessly dissipate the absorbed energy and return to the ground state, i.e., they convert the absorbed photons to heat without being chemically affected. The UV stabilization process most likely occurs due to the scavenging of free radicals [4,5]. It has turned out that a mechanism of this process involves intra-molecular hydrogen bonding (intra-HB), specific for ortho-substituted benzophenones since the radical product is no longer capable of forming the intra-HB [5]. Most benzophenones shown in Figures 1 and 2 bear one or two intra-HB. Qualitative evidence for the presence of these intra-HBs in 2-hydroxy-substituted benzophenones can be found in sufficient detail in the literature. However, quantitative data on the strength of the intra-HB in such molecules is limited [6]. Therefore, we used the thermochemical datasets evaluated in this work for the proper quantification of the intra-HB strength using thermodynamic and quantum chemical methods. nones are low-volatile compounds and accurate vapour pressure measurement is a challenging task. In this work, the experimental focus was on the investigation of the phase transition thermodynamics of hydroxy-and methoxy-substituted benzophenones.
Here we present results on vapour pressures, enthalpies of phase transitions, and enthalpies of formation of a series of substituted benzophenones of general formulas given in Figures 1 and 2. The data available in the literature and new experimental results were evaluated and checked for internal consistency. The consistent thermochemical data sets for substituted benzophenones were used for the design and development of a "centrepiece" group-contribution approach necessary for assessing the enthalpies of vaporisation and enthalpies of formation of compounds that are important for process engineering calculations.

2-hydroxy-benzophenone
3-hydroxy-benzophenone 4-hydroxy-benzophenone 2,2'-dihydroxy-benzophenone 2,4-dihydroxy-benzophenone 2-hydroxy-4-methoxy-benzophenone 2,2′-hydroxy-4-methoxybenzophenone 2,2′,4,4′-tetrahydroxy-benzophenone 2,2′-dihydroxy-4,4′-dimethoxybenzophenone In the course of the thermochemical measurements, another aspect of the properties of benzophenones attracted our attention. This aspect is not related to our research field but has inspired a deeper interpretation of our thermochemical results. It was found [3] that by absorbing the UV light, benzophenones transform into an excited state, but harmlessly dissipate the absorbed energy and return to the ground state, i.e., they convert the absorbed photons to heat without being chemically affected. The UV stabilization process most likely occurs due to the scavenging of free radicals [4,5]. It has turned out that a mechanism of this process involves intra-molecular hydrogen bonding (intra-HB), specific for ortho-substituted benzophenones since the radical product is no longer capable of forming the intra-HB [5]. Most benzophenones shown in Figures 1 and 2 bear one or two intra-HB. Qualitative evidence for the presence of these intra-HBs in 2-hydroxy-substituted benzophenones can be found in sufficient detail in the literature. However, quantitative data on the strength of the intra-HB in such molecules is limited [6]. Therefore, we used the thermochemical datasets evaluated in this work for the proper quantification of the intra-HB strength using thermodynamic and quantum chemical methods. In the course of the thermochemical measurements, another aspect of the properties of benzophenones attracted our attention. This aspect is not related to our research field but has inspired a deeper interpretation of our thermochemical results. It was found [3] that by absorbing the UV light, benzophenones transform into an excited state, but harmlessly dissipate the absorbed energy and return to the ground state, i.e., they convert the absorbed photons to heat without being chemically affected. The UV stabilization process most likely occurs due to the scavenging of free radicals [4,5]. It has turned out that a mechanism of this process involves intra-molecular hydrogen bonding (intra-HB), specific for orthosubstituted benzophenones since the radical product is no longer capable of forming the intra-HB [5]. Most benzophenones shown in Figures 1 and 2 bear one or two intra-HB. Qualitative evidence for the presence of these intra-HBs in 2-hydroxy-substituted benzophenones can be found in sufficient detail in the literature. However, quantitative data on the strength of the intra-HB in such molecules is limited [6]. Therefore, we used the thermochemical datasets evaluated in this work for the proper quantification of the intra-HB strength using thermodynamic and quantum chemical methods.

Absolute Vapour Pressures and Thermodynamics of Vaporisation/Sublimation
The vapour pressures, p i , for the substituted benzophenones and their temperature dependences measured by the transpiration method are given in Table 1. Uncertainties of the sublimation/vaporisation enthalpies are expressed as the expanded uncertainty (0.95 level of confidence, k = 2). They were calculated according to a procedure described elsewhere [13,14]. They include uncertainties from transpiration experimental conditions, uncertainties of vapour pressure, uncertainties from the fitting equation, and uncertainties from temperature adjustment to T = 298.15 K.
The vapour pressures, p i , for 2,4-di-hydroxy-benzophenone and 2,2 4,4 -tetra-hydroxybenzophenone were too low to be measured within a reasonable time using the transpiration method. Their temperature dependences were measured using the Knudsen effusion method. The results of the Knudsen method are given in Table 2.  [13,14]. Uncertainties include uncertainties from the experimental conditions and the fitting equation, vapour pressures, and uncertainties from adjustment of vaporisation enthalpies to the reference temperature T = 298.15 K.
Vapour pressure results for the substituted benzophenones were fit to the following equation [7,8]: where R = 8.31446 J·K −1 ·mol −1 is the molar gas constant, the reference pressure, p re f = 1 Pa, and a and b are adjustable parameters; the arbitrary temperature T 0 applied in Equation (1) was chosen to be T 0 = 298.15 K and ∆ g l,cr C o p,m is the difference of the molar heat capacities of the gas and the liquid/crystal phases, respectively. The isobaric heat capacity differences ∆ g l,cr C o p,m required for temperature adjustments of vaporisation/sublimation enthalpies are given in Table 3. The vapour pressures at different temperatures, T, measured in this work, as well as those available from the literature, were used to derive the enthalpies of sublimation/vaporisation using the following equation:  Tables 1 and 2. The method for calculating the combined uncertainties of the vaporisation/sublimation enthalpies involves uncertainties from the experimental conditions of transpiration, uncertainties from the vapour pressure, and uncertainties due to the temperature adjustment to T = 298.15 K, as described elsewhere [13,14]. The compilation of available standard molar vaporisation/sublimation enthalpies for the compounds shown in Figures 1 and 2 is given in Table 4. The original absolute vapour pressures available in the literature were also treated using Equations (2) and (3) to evaluate the enthalpies of vaporisation/sublimation at 298.15 K (see Table 4) in the same way as our own results. The uncertainties of the literature results were also re-assessed in the same way [13,14], as for our own experimental results.
The ∆ g cr,l C o p,m -values used in Equations (1) and (2) are usually derived from empirical equations developed by Chickos and Acree [19,20]: where C o p,m (cr, 298.15 K) or C o p,m (liq, 298.15 K) values are of the experimental origin or can also be estimated using the group-additivity method [17].
The vaporisation/sublimation at 298.15 K measured in this work (see Tables 1 and 2) and those available in the literature and derived using Equation (2) are compiled in Table 4.    (2) and (3) with help of heat capacity differences from Table 3 to evaluate the enthalpy of vaporisation/sublimation at 298.15 K in the same way as our own results in Tables 1 and 2. Uncertainty of the vaporisation/sublimation enthalpy U(∆ g l,cr H o m ) is the expanded uncertainty (0.95 level of confidence) calculated according to procedure described elsewhere [13,14]. c Assessed based on vaporisation enthalpy of 3-methoxy-benzophenone (this table) and the difference between vaporisation enthalpy of 2-methoxy-and 3methoxy-acetophenone [27]. d Weighted mean value. Values in parenthesis were excluded from the calculation of the mean. Values in bold are recommended for further thermochemical calculations.
The data on vaporisation/sublimation enthalpies compiled In Table 4 are of different quality. Schmitt and Hirt [24] studied the volatility of benzophenones by measuring their rate of evaporation in a vacuum from a free surface which was monitored spectrophotometrically (UVS method). The latter method is not commonly used for vapor pressure measurements. Most likely, this method was not sufficiently developed for the measurement of low pressures and for this reason, the temperature dependencies of the vapour pressure showed an incorrect slope and the significantly lower vaporisation enthalpies compared to other established methods. Price and Hawkins [26] used a thermogravimetric method to measure the vapour pressures of a series of hydroxy-benzophenones. Enthalpies of vaporisation determined from the slope of a plot of the logarithm of the vapour pressure against reciprocal absolute temperature agreed reasonably well (see 2,2 -dihydroxy-4methoxy-benzophenone and 2,2 -dihydroxy-4,4 -dimethoxy-benzophenone in Table 4) with results from other methods (except for 2,2 ,4,4 -tetra-hydroxy-benzophenone). Only single experimental results were found in the literature for the hydroxy-benzophenones. However, the sublimation enthalpies for these compounds were measured using the established methods and in the laboratory with very good experience [15] and are considered to be reliable.

Kovats Retention Indices for Validation of Experimental Vaporisation Enthalpies
In the situation of insufficient experimental data of the ∆ g l H o m (298.15 K)-values or their inconsistency, correlation with chromatographic retention indices available for substituted benzophenones [28] can be a useful tool for verification of available data [29]. It is established that the ∆ g l H o m (298.15 K)-values correlate linearly with Kovats indices [30] in various homologous series of alkanes, alkylbenzenes, aliphatic ethers, alcohols, or in a series of structurally similar compounds [29]. We apply this approach to a set of molecules (see Table 5), where J x -values and the ∆ g l H o m (298.15 K)-values were available from the literature.
The relationship according to Equation (6) allowed estimation of the unknown vaporisation enthalpy for 4 -methoxy-benzophenone (see Table 5). This "theoretical" result, derived from correlation with the Kovats indices, is denoted J x and is used in Table 4 for comparison with another result for this compound obtained from correlation with normal boiling temperatures, as shown in the next section.

Normal Boiling Temperatures for Validation of Experimental Vaporisation Enthalpies
Another way to determine the consistency of the experimental results on vaporisation enthalpies for substituted benzophenones is also to correlate vaporisation enthalpies with normal boiling temperatures [35]. For a set of structurally similar compounds (see Table 6) with well-established ∆ g l H o m (298.15 K)-values and known normal boiling temperatures, T b , we derived the following linear correlation: The relationship according to Equation (7) allowed estimation of the unknown enthalpies of vaporisation for 3 -methoxy-benzophenone and 4 -methoxy-benzophenone (see Table 6). These "theoretical" results, derived from correlation with normal boiling temperatures, are denoted in Table 4 as T b -values. As can be seen in Table 4, the vaporisation enthalpies of 4 -methoxy-benzophenone derived from the T b and J x correlations agree well within the uncertainties attributed to them.
p,m were taken from Table 3. Uncertainties in the temperature adjustment of fusion enthalpies from T fus to the reference temperature are estimated to account with 30% to the total adjustment [18]. c Experimental values of sublimation enthalpies (see Table 4). d Calculated as the difference between columns 5 and 4 in this table. e Calculated as the sum columns 6 and 4 in this table. f Experimental values of vaporisation enthalpies (see Table 4).
From Table 4, it can be seen now that for many compounds agreement among ∆ g l,cr H o m (298.15 K)-values, which were derived in different ways, all lie within the assigned error bars. To get more confidence and reliability, we calculated the weighted average (the uncertainty was used as a weighing factor) for the substituted benzophenones given in Table 4. These values are highlighted in bold and are recommended for thermochemical calculations.

Gas-Phase Standard Molar Enthalpies of Formation
Information on the enthalpies of formation of substituted benzophenones is limited in the literature. The recent development of high-level quantum chemistry methods, especially composite methods, makes it promising to calculate enthalpies of formation ∆ f H o m (g) at the level of "chemical accuracy" [39,40].
This trend has made the G-family of composite methods a valuable tool for mutual validation of experimental and computational thermochemistry. A discrepancy or agreement between the experimental and theoretical ∆ f H o m (g, 298.15 K)-values could provide a criterion for mutual validation of both results. In addition, this valuable information helps in evaluating the quality of the thermochemical data for compounds under study. In order to compensate for the lack of enthalpy data and to validate the present results, the gas phase formation enthalpies for substituted benzophenones were estimated using the quantum chemical method G4 [11]. The experimental data on the ∆ f H o m (298.15 K)-values available in the literature and results of calculations are presented in Table 8.  [15] −245.7 ± 3.8 97.9 ± 1.9 −147.8 ± 4.3 −150.5 −149.9 −150.2 ± 2.5 3-hydroxy-benzophenone (cr) [15] −247.3 ± 4.0 131.7 ± 0.9 −115.6 ± 3.9 −125.1 −124.5 −124.8 ± 2.5 4-hydroxy-benzophenone(cr) [15] −252. 4 [11]. d Calculated by the G4 method using atomisation reactions. The expanded uncertainty assessed to be ± 3.5 kJ·mol −1 [11]. e Weighted mean value. The uncertainties were taken as the weighing factor. f Calculated by the G4 method using reaction: benzophenone + butane = acetone+ 2× toluene and using experimental ∆ f H o m (g)-values for the reaction participants [42]. g Results evaluated and recommended in our recent work [36]. Stable conformers were found by using a computer code named CREST (conformerrotamer ensemble sampling tool) [43] and optimised with the B3LYP/6-31g(d,p) method [44]. The energies E 0 and the enthalpies H 298 of the most stable conformers were finally calculated by using the G4 method (see Figures 3 and S1).  [11]. d Calculated by the G4 method using atomisation reactions. The expanded uncertainty assessed to be ± 3.5 kJ•mol −1 [11]. e Weighted mean value. The uncertainties were taken as the weighing factor. f Calculated by the G4 method using reaction: benzophenone + butane = acetone+ 2× toluene and using experimental ∆ m o (g)-values for the reaction participants [42]. g Results evaluated and recommended in our recent work [36]. Stable conformers were found by using a computer code named CREST (conformerrotamer ensemble sampling tool) [43] and optimised with the B3LYP/6-31g(d,p) method [44]. The energies E0 and the enthalpies H298 of the most stable conformers were finally calculated by using the G4 method (see Figures 3 and S1).    The conformations of 3-hydroxy-, 4-hydroxy-benzophenones, as well as of 2methoxy-, 3-methoxy, and 4-methoxy-benzophenones are generally flat and substituents are in-plane to the backbone of the benzophenone ring (see Figure S1). The conformations of 2-hydroxy substituted benzophenones are more diverse and interesting since all these molecules feature the intra-molecular hydrogen bonding (intra-HB) between the carbonyl group and the hydroxyl substituent. The most stable conformations of 2-hydroxy substituted benzophenones are given in Figure 3 (left). To assess the strength of the intra-HB as an energy difference between the hydrogen-bonded and the open form (OH group rotated 180° around the C-O axis), we also calculated the open conformers (see Figure 3, right). The discussion of these differences can be found in Section 4.
The H298 enthalpies of the most stable conformers were converted into the gas-phase standard molar enthalpies of formation, ∆ m o (g), using the experimental gas phase standard molar enthalpies of formation ∆ m o (g, 298.15 K) of auxiliary compounds (see Table  S1) using the following well-balanced reactions (WBR): The conformations of 3-hydroxy-, 4-hydroxy-benzophenones, as well as of 2-methoxy-, 3-methoxy, and 4-methoxy-benzophenones are generally flat and substituents are in-plane to the backbone of the benzophenone ring (see Figure S1). The conformations of 2-hydroxy substituted benzophenones are more diverse and interesting since all these molecules feature the intra-molecular hydrogen bonding (intra-HB) between the carbonyl group and the hydroxyl substituent. The most stable conformations of 2-hydroxy substituted benzophenones are given in Figure 3 (left). To assess the strength of the intra-HB as an energy difference between the hydrogen-bonded and the open form (OH group rotated 180 • around the C-O axis), we also calculated the open conformers (see Figure 3, right). The discussion of these differences can be found in Section 4.
The theoretical enthalpies of formation of substituted benzophenones calculated using the G4 method agree only sufficiently with the experiment (within the boundaries of their combined uncertainties). However, it should be mentioned that the combustion experiments had some deficiency as follows. The three samples of hydroxy-benzophenones studied by Davalos et al. [15] were only 99.2% pure according to DSC. A possible residual amount of water traces in samples was not characterised either. Moreover, the commercial sample of 3-hydroxy-benzopenone was measured without additional purification. The commercial sample of 2-hydroxy-4-methoxy-benzopenone was measured by Lago et al. [25] also without additional purification and attestation of traces of water. Finally, no details on the sample purity of 2,4-di-hydroxybenzophenone and on the experimental conditions can be found in the publication by Contineanu and Marchidan [41], therefore the significant deviation from the quantum chemical result shown in Table 8 should be regarded as an indicator for the need for additional combustion experiments with this compound. Considering the shortcomings of the experimental ∆ f H o m (g)-data compiled in Table 8, we decided to use the consistent set of theoretical enthalpies of formation for substituted benzophenones for the development of a "centrepiece" group-contribution approach as follows.

Construction of a Theoretical Framework
The "centrepiece" approach has been described in detail in our previous papers [27,36,45]. The basic idea of the "centrepiece approach" approach is to select a relatively large "centrepiece molecule" (rather than the traditional summation of group contributions) with wellknown thermodynamic properties that structurally most closely resembles the molecule of interest. Related to the compounds discussed in this paper, the benzophenone itself is the most suitable "centrepiece" molecule. Various substituents (hydroxyl and methoxy in this work) can be attached to the "centrepiece" at different positions on the benzene rings of the benzophenone (see Figure 4).  The enthalpic contributions for these substituents can be easily derived (see Figure  5) from the differences between the enthalpy of the substituted benzene and the enthalpy of the benzene itself. Using this scheme, the required for this work contributions ΔH(H → OH) and ΔH(H → CH3O) were derived (see Table 9) using the reliable thermochemical data for benzene, methoxybenzene, and hydroxybenzene compiled in Table S1. We postulate that these contributions are applicable to any aromatic ring system. Hence, the enthalpic contributions ΔH(H → OH) and ΔH(H → CH3O) can now be applied to construct a framework of any hydroxy-and methoxy-substituted benzophenone, starting with the benzophenone as the "centrepiece" (see Figure 4). Table 9. Parameters and pairwise nearest and non-nearest neighbour interactions of substituents on the "centrepieces" for calculation of thermodynamic properties of substituted benzenes and benzophenones at 298.15 K (in kJ•mol −1 ).  The enthalpic contributions for these substituents can be easily derived (see Figure 5) from the differences between the enthalpy of the substituted benzene and the enthalpy of the benzene itself.  The enthalpic contributions for these substituents can be easily derived (see Figure  5) from the differences between the enthalpy of the substituted benzene and the enthalpy of the benzene itself. Using this scheme, the required for this work contributions ΔH(H → OH) and ΔH(H → CH3O) were derived (see Table 9) using the reliable thermochemical data for benzene, methoxybenzene, and hydroxybenzene compiled in Table S1. We postulate that these contributions are applicable to any aromatic ring system. Hence, the enthalpic contributions ΔH(H → OH) and ΔH(H → CH3O) can now be applied to construct a framework of any hydroxy-and methoxy-substituted benzophenone, starting with the benzophenone as the "centrepiece" (see Figure 4). Table 9. Parameters and pairwise nearest and non-nearest neighbour interactions of substituents on the "centrepieces" for calculation of thermodynamic properties of substituted benzenes and benzophenones at 298.15 K (in kJ•mol −1 ).  Using this scheme, the required for this work contributions ∆H(H → OH) and ∆H(H → CH 3 O) were derived (see Table 9) using the reliable thermochemical data for benzene, methoxybenzene, and hydroxybenzene compiled in Table S1. We postulate that these contributions are applicable to any aromatic ring system. Hence, the enthalpic contributions ∆H(H → OH) and ∆H(H → CH 3 O) can now be applied to construct a framework of any hydroxy-and methoxy-substituted benzophenone, starting with the benzophenone as the "centrepiece" (see Figure 4).

Centrepiece
a The contributions were derived from the differences between the experimental enthalpy of the substituted benzene (or benzophenone) and the experimental enthalpy of benzene (or benzophenone) itself (see text). b The pairwise interactions between carbonyl and substituent were derived from the experimental enthalpies of substituted benzene (or benzophenone) and the corresponding enthalpy of the framework as shown in Figure 6. c From H298 values of the reverse reactions 9-10 participants calculated by using the G4 method. As a rule, this framework can energetically predict at a rough level the vaporisation or formation enthalpies. However, this framework is not perfect since it lacks the energetics of the interactions between the carbonyl and the substituents attached to the phenyl a The contributions were derived from the differences between the experimental enthalpy of the substituted benzene (or benzophenone) and the experimental enthalpy of benzene (or benzophenone) itself (see text). b The pairwise interactions between carbonyl and substituent were derived from the experimental enthalpies of substituted benzene (or benzophenone) and the corresponding enthalpy of the framework as shown in Figure 6. c From H 298 values of the reverse reactions 9-10 participants calculated by using the G4 method.
As a rule, this framework can energetically predict at a rough level the vaporisation or formation enthalpies. However, this framework is not perfect since it lacks the energetics of the interactions between the carbonyl and the substituents attached to the phenyl rings of benzophenone. For a more accurate assessment, the pairwise nearest and non-nearest neighbour interactions of substituents on the "centrepiece" framework should also be considered as follows.

Pairwise Interactions of Substituents on the Benzene Ring
The non-nearest neighbour (e.g., metaor parainteractions) or nearest neighbour (e.g., ortho-interactions) interactions of substituents on the benzene ring are an indispensable part of the energetics of aromatic molecules. However, quantitatively they are dependent on the type and position of the substituent. As a rule, metaor parapairwise interactions are weak, and orthointeractions are powerful. How the pairwise interactions were derived is shown in Figure 6.
For example, to quantify the enthalpic contribution "meta C = O(C 6 H 5 ) − OH" responsible for the non-bonded interaction of the carbonyl and OH-group in the meta-position on benzophenone (taken as the "centrepiece"), we must first construct the "theoretical framework" of 3-hydroxy-benzophenone (see Figure 6). To do that, we simply add the contribution ∆H(H → OH) from Table 9 to the experimental enthalpy (enthalpy of vaporisation or enthalpy of formation) of the benzophenone (as a "centrepiece") also given in Table 9. This "theoretical framework" of 3-hydroxy-benzophenone does not contain the "meta C = O(C 6 H 5 ) − OH" interaction. However, this interaction is present in the real 3-hydroxy-benzophenone (it is symbolised in Figure 6 with a red arrow). The arithmetic difference between the experimental enthalpy of 3-hydroxy-benzophenone and the enthalpy of the "theoretical framework" therefore provides the quantitative size of the pairwise interaction "meta C = O(C 6 H 5 ) − OH" directly (see Table 9). Using the same logic, the enthalpic contributions for the "ortho C = O(C 6 H 5 ) − OH" and "para C = O(C 6 H 5 ) − OH" were derived from data for 2-hydroxy-and 4-hydroxy-benzophenone. In the same way, the required enthalpy contributions for pairwise interactions of carbonyl and methoxy substituent were estimated and summarised in Table 9.

Practical Application of the Centerpiece Approach for Prediction of Enthalpies of Substituted Benzophenones
As can be seen from Table 9, the magnitudes of the pairwise interactions in terms of ∆ g l H o m are mostly not negligible. However, meaningful discussion of these magnitudes is rather limited since these contributions reflect the tightness of molecular packing in the liquid. They must be considered as empirical constants for the correct prediction of the vaporisation energetics. Does it work? We demonstrate the principle applicability of the "centrepiece" approach in the case that at least two substituents are attached to the benzophenone as a "centrepiece". In Figure 7, the algorithm for calculating the vaporisation enthalpy of the 2,4-dihydroxy-benzophenone using the "centrepiece" approach with the numerical values from Table 9 is shown. Table 9. This "theoretical framework" of 3-hydroxy-benzophenone does not contain the "meta C = O(C6H5) − OH" interaction. However, this interaction is present in the real 3hydroxy-benzophenone (it is symbolised in Figure 6 with a red arrow). The arithmetic difference between the experimental enthalpy of 3-hydroxy-benzophenone and the enthalpy of the "theoretical framework" therefore provides the quantitative size of the pairwise interaction "meta C = O(C6H5) − OH" directly (see Table 9). Using the same logic, the enthalpic contributions for the "ortho C = O(C6H5) − OH" and "para C = O(C6H5) − OH" were derived from data for 2-hydroxy-and 4-hydroxy-benzophenone. In the same way, the required enthalpy contributions for pairwise interactions of carbonyl and methoxy substituent were estimated and summarised in Table 9.

Practical Application of the Centerpiece Approach for Prediction of Enthalpies of Substituted Benzophenones
As can be seen from Table 9, the magnitudes of the pairwise interactions in terms of ∆ are mostly not negligible. However, meaningful discussion of these magnitudes is rather limited since these contributions reflect the tightness of molecular packing in the liquid. They must be considered as empirical constants for the correct prediction of the vaporisation energetics. Does it work? We demonstrate the principle applicability of the "centrepiece" approach in the case that at least two substituents are attached to the benzophenone as a "centrepiece". In Figure 7, the algorithm for calculating the vaporisation enthalpy of the 2,4-dihydroxy-benzophenone using the "centrepiece" approach with the numerical values from Table 9 is shown.  Table 4. Therefore, the "centrepiece" approach can be successfully applied to predict the vaporisation enthalpies of sub-  Table 9. All numbers are given in kJ·mol −1 .
It was found that the empirical enthalpy of vaporisation of 2,4-dihydroxy-benzophenone, ∆  Table 4. Therefore, the "centrepiece" approach can be successfully applied to predict the vaporisation enthalpies of substituted benzophenones and other aromatic systems with the contributions derived in Table 9. We now apply the "centrepiece" approach to predicting the gas-phase enthalpies of formation of substituted benzophenones. It makes more sense to discuss the magnitudes of the pairwise interactions with respect to ∆ f H o m (g) given in Table 9, since these non-covalent interactions are generally responsible for the distribution of electron density in the molecule. Moreover, they can be used to derive the strength of the intra-molecular hydrogen bonding present in the 2-hydroxy-substituted benzophenones (see Section 5).
Quantitatively, the intensity of the non-covalent interactions depends strongly on the nature of the ortho-, meta-, or para-pairs. It can be seen from Table 9 that in terms of ∆ f H o m (g) the ortho-hydroxy-benzophenone shows a strong stabilization of −24.5 kJ·mol −1 due to intra-molecular hydrogen bonding. In contrast, the ortho-dihydroxy-benzene shows a destabilization of 2.5 kJ·mol −1 despite the stabilizing intra-molecular hydrogen bonding present in this molecule. The ortho-dimethoxy-benzene also shows a destabilization of 17.5 kJ·mol −1 due to the sterical repulsion of bulky methoxy groups. In our experience, the metaand para-interactions of substituents on the benzene ring are less profound compared to ortho-interactions [39,40]. Indeed, the metaand para-interactions of the OH and CH 3 O substituents with the carbonyl group can be considered as weak, being below 4 kJ·mol −1 (see Table 9). In contrast, the strong destabilization of 11.4 kJ·mol −1 is observed for the para-isomer of methoxy-phenol. Moreover, a significant destabilization of 7.3 kJ·mol −1 is observed for the para-isomer of dimethoxy-benzene. These noticeable destabilizing effects can be explained by the specific electron density distribution within the substituted benzene ring.
Since some of the pairwise non-covalent interactions in terms of ∆ f H o m (g) have been derived using substituted benzenes (see Table 9), their applicability to benzophenone derivatives needs to be checked. We calculated the enthalpy of formation of the 2-hydroxy-4-methoxy-benzophenone using the "centrepiece" approach with the numerical values from Table 9. The calculation algorithm is given in Figure 8. stituted benzophenones and other aromatic systems with the contributions derived in Table 9. We now apply the "centrepiece" approach to predicting the gas-phase enthalpies of formation of substituted benzophenones.
It makes more sense to discuss the magnitudes of the pairwise interactions with respect to ∆ m o (g) given in Table 9, since these non-covalent interactions are generally responsible for the distribution of electron density in the molecule. Moreover, they can be used to derive the strength of the intra-molecular hydrogen bonding present in the 2-hydroxy-substituted benzophenones (see Section 5).
Quantitatively, the intensity of the non-covalent interactions depends strongly on the nature of the ortho-, meta-, or para-pairs. It can be seen from Table 9 that in terms of ∆ m o (g) the ortho-hydroxy-benzophenone shows a strong stabilization of −24.5 kJ . mol −1 due to intra-molecular hydrogen bonding. In contrast, the ortho-dihydroxy-benzene shows a destabilization of 2.5 kJ . mol −1 despite the stabilizing intra-molecular hydrogen bonding present in this molecule. The ortho-dimethoxy-benzene also shows a destabilization of 17.5 kJ . mol −1 due to the sterical repulsion of bulky methoxy groups. In our experience, the metaand para-interactions of substituents on the benzene ring are less profound compared to ortho-interactions [39,40]. Indeed, the meta-and para-interactions of the OH and CH3O substituents with the carbonyl group can be considered as weak, being below 4 kJ•mol −1 (see Table 9). In contrast, the strong destabilization of 11.4 kJ•mol −1 is observed for the paraisomer of methoxy-phenol. Moreover, a significant destabilization of 7.3 kJ•mol −1 is observed for the para-isomer of dimethoxy-benzene. These noticeable destabilizing effects can be explained by the specific electron density distribution within the substituted benzene ring.
Since some of the pairwise non-covalent interactions in terms of ∆ m o (g) have been derived using substituted benzenes (see Table 9), their applicability to benzophenone derivatives needs to be checked. We calculated the enthalpy of formation of the 2-hydroxy-4-methoxy-benzophenone using the "centrepiece" approach with the numerical values from Table 9. The calculation algorithm is given in Figure 8.
.  [25]. Therefore, the "centrepiece" approach can also be used successfully to predict the enthalpies of formation of substituted benzophenones and other aromatic systems with the contributions derived in Table 9.

Strength of Intra-Molecular Hydrogen Bonding in Ortho-Substituted Benzophenones
In this section, we consider the intra-molecular hydrogen bonded 2-hydroxy substituted benzophenones. It is known from XRD data that the distance between the carbonyl oxygen O(1) and the hydrogen of OH group (see Figure 9, left) in 2-hydroxy-benzophenone is 1.810 Å in the crystal state [15,47], and 1.678 Å in the gas state, as calculated at the B3LYP/6-311++G(3df,2p) level [15], and 1.75 Å as calculated with G3MP2 in this work. methoxy-benzophenone using the "centrepiece" approach with the numerical values from Table 9. All numbers are given in kJ•mol −−1 .
It was found that the empirical enthalpy of formation of 2-hydroxy-4-methoxy-benzophenone, ∆ m o (g, 298.15 K) = −306.2 kJ•mol −1 , agrees with the experimental value, ∆ m o (g, 298.15 K) = −297.4 ± 4.7 kJ•mol −1 [25]. Therefore, the "centrepiece" approach can also be used successfully to predict the enthalpies of formation of substituted benzophenones and other aromatic systems with the contributions derived in Table 9.

Strength of Intra-Molecular Hydrogen Bonding in Ortho-Substituted Benzophenones
In this section, we consider the intra-molecular hydrogen bonded 2-hydroxy substituted benzophenones. It is known from XRD data that the distance between the carbonyl oxygen O(1) and the hydrogen of OH group (see Figure 9, left) in 2-hydroxy-benzophenone is 1.810 Å in the crystal state [15,47], and 1.678 Å in the gas state, as calculated at the B3LYP/6-311++G(3df,2p) level [15], and 1.75 Å as calculated with G3MP2 in this work. Figure 9. Intra-molecular hydrogen bonding in 2-hydroxy-benzophenone (left) and 2,2'-di-hydroxy-benzophenone (right).
In 2,2'-di-hydroxy-benzophenone both hydroxyl groups act as intramolecular hydrogen-bond donors to the O(1) carbonyl atom (see Figure 9, right). From XRD data in the crystal state, the distance between the carbonyl oxygen O(1) and the hydrogen of H-O(2) group is 1.873 Å and between the carbonyl oxygen O(1) and the hydrogen of H-O(3) group is 1.772 Å [48]. The reason for the difference in the two intra-molecular hydrogen bonds in 2,2'-di-hydroxy-benzophenone is not evident. In the shorter one, O(1)…H-O(3), the hydroxyl group is also involved in a bifurcated inter-molecular interaction [48]. The other hydroxyl group H-O(2) therefore appears to be somewhat deficient in hydrogen bonding [48]. In the gas phase, however, the distances between the carbonyl oxygen O(1) and both hydroxyl groups become indistinguishable: 1.729 Å and 1.728 Å as calculated at the B3LYP-6-311++G** level [49]. In this work, the distances of 1.79 Å and 1.79 Å were calculated with G3MP2.
In a qualitative way, intra-HB strength can be assessed in terms of OH chemical shifts [50], double-bond deuterium isotope effects on 13 C chemical shifts [51], OH stretch frequencies [52], or O…O distances [53]. The quantitative way to determine intra-HB strength is a challenging task because, as shown below, the choice of an appropriate "nonbonded" reference system is thwarted with complications.

Strength of Intra-Molecular Hydrogen Bonding from the "Ortho-Para" Method
Determination of the intra-molecular hydrogen bonding strength in 2-hydroxy-benzophenone using the "ortho-para" method is illustrated in Figure 10. In 2,2'-di-hydroxy-benzophenone both hydroxyl groups act as intramolecular hydrogenbond donors to the O(1) carbonyl atom (see Figure 9, right). From XRD data in the crystal state, the distance between the carbonyl oxygen O(1) and the hydrogen of H-O(2) group is 1.873 Å and between the carbonyl oxygen O(1) and the hydrogen of H-O(3) group is 1.772 Å [48]. The reason for the difference in the two intra-molecular hydrogen bonds in 2,2'-di-hydroxy-benzophenone is not evident. In the shorter one, O(1) . . . H-O(3), the hydroxyl group is also involved in a bifurcated inter-molecular interaction [48]. The other hydroxyl group H-O(2) therefore appears to be somewhat deficient in hydrogen bonding [48]. In the gas phase, however, the distances between the carbonyl oxygen O(1) and both hydroxyl groups become indistinguishable: 1.729 Å and 1.728 Å as calculated at the B3LYP-6-311++G** level [49]. In this work, the distances of 1.79 Å and 1.79 Å were calculated with G3MP2.
In a qualitative way, intra-HB strength can be assessed in terms of OH chemical shifts [50], double-bond deuterium isotope effects on 13 C chemical shifts [51], OH stretch frequencies [52], or O . . . O distances [53]. The quantitative way to determine intra-HB strength is a challenging task because, as shown below, the choice of an appropriate "non-bonded" reference system is thwarted with complications.

Strength of Intra-Molecular Hydrogen Bonding from the "Ortho-Para" Method
Determination of the intra-molecular hydrogen bonding strength in 2-hydroxybenzophenone using the "ortho-para" method is illustrated in Figure 10.
This approach was suggested by Minas da Piedade [54]. The idea behind it is to use a simple "ortho-para" isomerization reaction, provided that experimental ∆ f H o m (g)-values for the reaction participants are known. It is obvious that the intra-HB is present on the left side of the reaction and absent on the right side. Therefore, the enthalpy of this reaction should represent the intra-HB strength. Using the experimental ∆ f H o m (g)-values for 2-hydroxy-benzophenone and 4-hydroxy-benzophenone given in Table 8, the intra-HB strength was calculated to be (−147.8 − 122.1) = −25.7 ± 5.7 kJ·mol −1 . However, this result should be corrected with the additional interaction between the OH and carbonyl group, as para C = O(C 6 H 5 ) − OH = −3.4 kJ·mol −1 (see Table 9, column 2), present in 4-hydroxy-benzophenone. Only now the result (−25.7 + 3.4) = −22.3 ± 5.7 kJ·mol −1 could be considered as the strength of the intra-HB in 2-hydroxy-benzophenone. Unfortunately, this "corrected" ortho-para method can only be used to determine intra-HB strength in 2-hydroxybenzophenone. The structures of other ortho-substituted benzophenones (see Figure 2) are too complex to find a suitable reference molecule. This approach was suggested by Minas da Piedade [54]. The idea behind it is to use a simple "ortho-para" isomerization reaction, provided that experimental ∆ m o (g)-values for the reaction participants are known. It is obvious that the intra-HB is present on the left side of the reaction and absent on the right side. Therefore, the enthalpy of this reaction should represent the intra-HB strength. Using the experimental ∆ m o (g)-values for 2-hydroxy-benzophenone and 4-hydroxy-benzophenone given in Table 8 Table 9, column 2), present in 4-hydroxybenzophenone. Only now the result (−25.7 + 3.4) = −22.3 ± 5.7 kJ . mol −1 could be considered as the strength of the intra-HB in 2-hydroxy-benzophenone. Unfortunately, this "corrected" ortho-para method can only be used to determine intra-HB strength in 2-hydroxybenzophenone. The structures of other ortho-substituted benzophenones (see Figure 2) are too complex to find a suitable reference molecule.

Strength of Intra-Molecular Hydrogen Bonding from the Well-Balanced Reactions
In our recent work, we developed thermodynamically based tools to quantify HB strength in aliphatic [50] and aromatic systems [55]. One of them is based on the enthalpies of well-balanced reactions (9 to 14) as it was already shown in Section 4. The idea behind this is shown in Figure 11, where reaction (9) is written in reverse. Figure 11. Determination of the intra-molecular hydrogen bonding strength in 2-hydroxy-benzophenone using the "well-balanced reaction" method. The reaction enthalpy ∆ m o (WBR) = −24.5 kJ•mol −1 (see Table 10, column 2). The intra-HB-strength ΔHWBR = −24.5 kJ•mol −1 (see Table 10, column 3).
The enthalpies of well-balanced reactions (9 to 14) are given in Table 10, column 2.

Strength of Intra-Molecular Hydrogen Bonding from the Well-Balanced Reactions
In our recent work, we developed thermodynamically based tools to quantify HB strength in aliphatic [50] and aromatic systems [55]. One of them is based on the enthalpies of well-balanced reactions (9 to 14) as it was already shown in Section 4. The idea behind this is shown in Figure 11, where reaction (9) is written in reverse. Figure 10. Determination of the intra-molecular hydrogen bonding strength in 2-hydroxy-benzophenone using the "ortho-para" method. The blue arrow represents the additional para C = O(C6H5) − OH = −3.4 kJ . mol −1 , that should be subtracted from the enthalpy of this reaction to attribute the corrected result to intra-HB strength.
This approach was suggested by Minas da Piedade [54]. The idea behind it is to use a simple "ortho-para" isomerization reaction, provided that experimental ∆ m o (g)-values for the reaction participants are known. It is obvious that the intra-HB is present on the left side of the reaction and absent on the right side. Therefore, the enthalpy of this reaction should represent the intra-HB strength. Using the experimental ∆ m o (g)-values for 2-hydroxy-benzophenone and 4-hydroxy-benzophenone given in Table 8, the intra-HB strength was calculated to be (−147.8 − 122.1) = −25.7 ± 5.7 kJ . mol −1 . However, this result should be corrected with the additional interaction between the OH and carbonyl group, Table 9, column 2), present in 4-hydroxybenzophenone. Only now the result (−25.7 + 3.4) = −22.3 ± 5.7 kJ . mol −1 could be considered as the strength of the intra-HB in 2-hydroxy-benzophenone. Unfortunately, this "corrected" ortho-para method can only be used to determine intra-HB strength in 2-hydroxybenzophenone. The structures of other ortho-substituted benzophenones (see Figure 2) are too complex to find a suitable reference molecule.

Strength of Intra-Molecular Hydrogen Bonding from the Well-Balanced Reactions
In our recent work, we developed thermodynamically based tools to quantify HB strength in aliphatic [50] and aromatic systems [55]. One of them is based on the enthalpies of well-balanced reactions (9 to 14) as it was already shown in Section 4. The idea behind this is shown in Figure 11, where reaction (9) is written in reverse. Figure 11. Determination of the intra-molecular hydrogen bonding strength in 2-hydroxy-benzophenone using the "well-balanced reaction" method. The reaction enthalpy ∆ m o (WBR) = −24.5 kJ•mol −1 (see Table 10, column 2). The intra-HB-strength ΔHWBR = −24.5 kJ•mol −1 (see Table 10, column 3).
The enthalpies of well-balanced reactions (9 to 14) are given in Table 10, column 2.  Figure 11. Determination of the intra-molecular hydrogen bonding strength in 2-hydroxy-benzophenone using the "well-balanced reaction" method. The reaction enthalpy ∆ r H o m(WBR) = −24.5 kJ·mol −1 (see Table 10, column 2). The intra-HB-strength ∆H WBR = −24.5 kJ·mol −1 (see Table 10, column 3). Table 10. Strength of intra-molecular hydrogen bonding (intra-HB) in ortho-substituted benzophenones at T = 298.15 K (p • = 0.1 MPa, in kJ·mol −1 ). 3.5 --a Reaction enthalpies calculated using the G4 method and the WBR reactions 9-14 (in reverse notation). b Intra-HB strength derived from the enthalpies of WBR reactions 9-14 (column 2) after corrections for pairwise interactions of substituents were performed as shown in Figure S2. c Intra-HB strength is calculated using the G3MP2 and the "HB and Out" method. d Difference between columns 3 and 4. e Intra-HB strength calculated per single bond.

Ortho-Substituted Benzophenones
The enthalpies of well-balanced reactions (9 to 14) are given in Table 10, column 2. In contrast to the "ortho-para" method, the reference molecules for this method do not contain any additional substituent interactions that would have to be corrected. Indeed, in the case of 2-hydroxy-benzophenone shown in Figure 11, the enthalpy of this reaction is equivalent to the pairwise interaction of carbonyl and hydroxyl groups, defined as ortho C = O(C 6 H 5 ) − OH = −24.5 kJ·mol −1 in Section 4 (see Table 9, column 2). The latter interaction could be considered as the strength of the intra-HB in 2-hydroxy-benzopenone and agrees well with those −22.3 ± 5.7 kJ·mol −1 , derived from the "ortho-para" method.
Also, for 2,2'-di-hydroxy-benzophenone, the enthalpy of the well-balanced reaction is directly related to the intra-HB-strength ∆H WBR = −20.4 kJ·mol −1 per single bond (see Figure 12). tion). b Intra-HB strength derived from the enthalpies of WBR reactions 9-14 (column 2) after corrections for pairwise interactions of substituents were performed as shown in Figure S2. c Intra-HB strength is calculated using the G3MP2 and the "HB and Out" method. d Difference between columns 3 and 4. e Intra-HB strength calculated per single bond.
In contrast to the "ortho-para" method, the reference molecules for this method do not contain any additional substituent interactions that would have to be corrected. Indeed, in the case of 2-hydroxy-benzophenone shown in Figure 11, the enthalpy of this reaction is equivalent to the pairwise interaction of carbonyl and hydroxyl groups, defined as ortho C = O(C6H5) − OH = −24.5 kJ . mol −1 in Section 4 (see Table 9, column 2). The latter interaction could be considered as the strength of the intra-HB in 2-hydroxy-benzopenone and agrees well with those −22.3 ± 5.7 kJ . mol −1 , derived from the "ortho-para" method.
For other di-hydroxy-and tetra-hydroxy-substituted benzophenones given in Table  10, the enthalpies of the well-balanced reactions require some correction before being related to the intra-HB strength. For example, as shown in Figure 13, in 2,4-dihydroxybenzophenone we need to subtract the para C = O(C6H5) − OH and meta OH-OH interactions given in Table 9. The resulting intra-HB-strength ΔHWBR = −24.3 kJ•mol −1 (see Table 10, column 3) can hardly be distinguished from those in 2-hydroxybenzophenone. Similarly, we "corrected" the well-balanced reaction enthalpies (see Figure S2) and the resulting strengths are shown in Table 10, column 3.  Table 10, column 2). The intra-HB-strength ∆H WBR = −40.8/2 = −20.4 kJ·mol −1 per single bond.
The intra-HB strength in 2,2'-dihydroxybenzophenone is slightly less than in 2hydroxy-benzophenone, although the distances between the O(1) and hydroxy groups are shorter in 2,2'-di-hydroxy-benzophenone (as calculated using G3MP2 in this work).
For other di-hydroxy-and tetra-hydroxy-substituted benzophenones given in Table 10, the enthalpies of the well-balanced reactions require some correction before being related to the intra-HB strength. For example, as shown in Figure 13, in 2,4-dihydroxybenzophenone we need to subtract the para C = O(C 6 H 5 ) − OH and meta OH-OH interactions given in Table 9. The resulting intra-HB-strength ∆H WBR = −24.3 kJ·mol −1 (see Table 10, column 3) can hardly be distinguished from those in 2-hydroxybenzophenone. Similarly, we "corrected" the well-balanced reaction enthalpies (see Figure S2) and the resulting strengths are shown in Table 10, column 3.  Table 9). The intra-HB-strength ΔHWBR = (−32.2 + 3.4 + 4.5) = −24.3 kJ•mol −1 (see Table 10, column 3).
It has turned out that the intra-HB strength in mono-, di-, tri-, and tetra-substituted benzophenones is generally at a similar level of −24 kJ•mol −1 and the influence of the nearest neighbour substituents is about 5 kJ•mol −1 irregular decrease or increase in intra-HB strength.

Strength of Intra-Molecular Hydrogen Bonding from the "HB and Out" Method
With the modern development of quantum chemical (QC) methods, the quantitative "theoretical" measure of intra-HB strength is commonly defined as the energy difference between the hydrogen-bonded and open conformer (OH group rotated 180 °C around the C-O axis). This method is referred to as "HB and Out" [56] but requires that the OH group of the open conformer is not involved in steric or other interfering interactions [57].
It has turned out that the intra-HB strength in mono-, di-, tri-, and tetra-substituted benzophenones is generally at a similar level of −24 kJ·mol −1 and the influence of the nearest neighbour substituents is about 5 kJ·mol −1 irregular decrease or increase in intra-HB strength.

Strength of Intra-Molecular Hydrogen Bonding from the "HB and Out" Method
With the modern development of quantum chemical (QC) methods, the quantitative "theoretical" measure of intra-HB strength is commonly defined as the energy difference between the hydrogen-bonded and open conformer (OH group rotated 180 • C around the C-O axis). This method is referred to as "HB and Out" [56] but requires that the OH group of the open conformer is not involved in steric or other interfering interactions [57].
2-Hydroxy-substituted benzophenones are very suitable molecules for studying of hydrogen bond energies estimated by the "HB and Out" method as the OH proton has no noticeable interactions in the open "Out" conformations.
The magnitudes of the intra-HB strength of 2-hydroxy-and 2,2'-dihydroxy-substituted benzophenones were estimated by subtracting the QC computed energies of the nonhydrogen-bonded conformer from the energies of the hydrogen-bonded conformer, shown in Figure 3. These values are referred to as ∆H conf and are summarised in Table 10 for comparison. For 2-hydroxy-benzophenone ∆H conf values were calculated using both the G4 and the G3MP2 methods (see Figure 3). It has turned out that the results are practically indistinguishable. Taking into account that the G3MP2 method is significantly less timeconsuming compared to the G4 method, all ∆H conf -values in Table 10 were calculated using the G3MP2.
The strength of intra-HB in 2-hydroxy-benzophenone calculated by the G3MP2 method is −35.7 kJ·mol −1 . The strength of two intra-HBs in 2,2'-di-hydroxy-benzophenone calculated by the G3MP2 method is −68.6 kJ·mol −1 , but the strength related to a single HB is −34.3 kJ·mol −1 and is equal to that in 2-hydroxy-benzophenone. These results differ significantly from the intra-HB strength in 2-hydroxy-benzophenone, −24.5 kJ·mol −1 , and in 2,2'di-hydroxy-benzophenone, −40.8 kJ·mol −1 , as derived from the "ortho-para" method and from WBR. Moreover, for other substituted benzophenones the strength estimated with "HB and Out" is systematically more negative with the differences shown in Table 10, last column.
Which values are correct? Apparently, it is the coinciding values derived with the "ortho-para" and WBR methods! This is because the consistency of the experimental and quantum chemical results for substituted benzophenones has been convincingly demonstrated in the previous sections. Moreover, the hydrogen bonded conformations of the ortho-hydroxy-substituted benzophenones were involved in calculations by the WBR method, confirming the level of the intra-HB strength evaluated by these methods. From these facts, it can be concluded that the reason for the observed discrepancy could therefore rather lie in the definition of the intra-HB strength by the "HB and Out" method.
Does the intra-HB strength, defined as the energy difference between the hydrogenbonded and open forms (OH group rotated 180 • around the C-O axis), really represent a correct "non-H-bonded" reference? Perhaps an alternative to the "HB and Out" procedure, the phenyl group can be rotated 180 • about the C-C axis (see Figure 14). these facts, it can be concluded that the reason for the observed discrepancy could therefore rather lie in the definition of the intra-HB strength by the "HB and Out" method. Does the intra-HB strength, defined as the energy difference between the hydrogenbonded and open forms (OH group rotated 180° around the C-O axis), really represent a correct "non-H-bonded" reference? Perhaps an alternative to the "HB and Out" procedure, the phenyl group can be rotated 180° about the C-C axis (see Figure 14). Figure 14. Determination of the intra-molecular hydrogen bonding strength in 2-hydroxy-benzophenone using the "HB and Out" method and an alternative phenyl group rotated 180° around the C-C axis. (All values in kJ•mol −1 ).
We calculated the energy of the later conformation using G3MP2 and the destabilisation of 38.1 kJ•mol −1 is clear evidence that in both non-H-bonded "reference" conformations there is a significant amount of sterical repulsions of the OH-group and the phenyl ring is incorporated, and these conformations are hardly suitable to be used as references for determining the strength of the intra-HB strength in hydroxy-substituted benzophenones. Consequently, only the "ortho-para" and WBR methods should be applied for quantification of intra-HB strength in similarly shaped molecules.

Conclusions
The consistent sets of standard molar thermodynamic properties of formation and Figure 14. Determination of the intra-molecular hydrogen bonding strength in 2-hydroxybenzophenone using the "HB and Out" method and an alternative phenyl group rotated 180 • around the C-C axis. (All values in kJ·mol −1 ).
We calculated the energy of the later conformation using G3MP2 and the destabilisation of 38.1 kJ·mol −1 is clear evidence that in both non-H-bonded "reference" conformations there is a significant amount of sterical repulsions of the OH-group and the phenyl ring is incorporated, and these conformations are hardly suitable to be used as references for determining the strength of the intra-HB strength in hydroxy-substituted benzophenones.
Consequently, only the "ortho-para" and WBR methods should be applied for quantification of intra-HB strength in similarly shaped molecules.

Conclusions
The consistent sets of standard molar thermodynamic properties of formation and phase transitions for substituted benzophenones were evaluated in this work with help of complementary measurements of vapour pressures, sublimation/vaporisation, and fusion enthalpies, as well as with help of empirical and high-level quantum chemical calculations. Thermodynamic properties of substituted benzophenones were recommended as reliable benchmark properties for thermochemical calculations. The evaluated vaporisation and formation enthalpies were used to design and develop the "centrepiece" approach for prediction of thermodynamic properties of the aromatic systems. The strength of intra-molecular hydrogen bonding was evaluated using quantum chemical and thermochemical methods.