Prediction of thermodynamic properties: centerpiece approach—how do we avoid confusion and get reliable results?

The absolute vapor pressures of three amino-alcohols were measured using the transpiration method. The consistent set of standard molar enthalpies of vaporization for eighteen amino-alcohols was evaluated using empirical and structure–property correlations. The averaged values of vaporization enthalpies were recommended as reliable benchmark properties for the heat management of CO2 capture technologies. Centerpiece approach based on the group-additivity principles was developed toward amino-alcohols.


Introduction
The group-additivity (GA) approach offers an excellent way of assessing the thermodynamic properties of molecules whose properties have not been measured. One of the most popular GA approaches was developed by Sydney W. Benson [1]. A group is defined by Benson as "a polyvalent atom (ligancy ≥ 2) in a molecule together with all of its ligands." The sum of the groups that constitute a molecule of interest provides a quick appraisal of a thermodynamic property. The GA works well for the gas-phase standard molar enthalpies of formation Δ f H o m (g, 298.15 K). The GA performance for the liquid-phase enthalpies of formation, Δ f H o m (liq, 298.15 K), is less successful because the intermolecular interactions between the molecules are randomly distributed among the groups. This fact aggravates the accuracy of the prediction considerably. In contrast, the standard molar enthalpies of vaporization, Δ f H o m (298.15 K), obey sufficiently well to the additivity rules. An important step in this direction was made by Ducros and co-workers [2] who showed that group additivity can be used to estimate the Δ f H o m (298.15 K)-values of organic and organometallic compounds with good precision. In his later work [3], Sydney W. Benson also expanded the GA method for calculating enthalpy of vaporization. We endorsed and followed Benson [4]. The crucial advantage of the Benson's method is that the energetics of a molecule of interest can be collected from scratch. However, many interactions between nearest and non-nearest neighbor groups, between substituents, and between fragments of the molecule are not taken into account by this procedure [5]. In the original Benson's scheme, such interactions are included as a list of individual "non-additive" contributions. However, the variety of possible structures of organic compounds is countless, so that the list of individual "non-additive" contributions can be endless.
In our most recent work [6,7], we develop a "centerpiece" approach that is closely related to the conventional group-contribution methods [3,4]. In the latter methods, the molecule of interest is collected completely from welldefined group contributions. In contrast, the idea of this "centerpiece" approach is to select a "core" molecule that may possibly close to mimic the structure of the molecule of interest, but the selected "centerpiece" molecule has the well-established thermodynamic properties. Different substituents can be attached (or subtracted) to this "centerpiece" in different positions. The visualization of the "centerpiece" approach is given in Fig. 1.
For the prediction, e.g., the enthalpy of vaporization of 2-(phenyl-amino)-ethanol, a similarly shaped 2-(methylamino)-ethanol, can be seen as a well-suited "centerpiece." Indeed, the latter molecule already bears the energetic contribution due to the inherent intra-molecular hydrogen bond (intra-HB), which is the most significant feature of aminoethanols. Such a contribution is unique to the "centerpiece" molecule and cannot be captured by any other method. This special feature of the "centerpiece" approach increases the reliability of the property prediction for the similarly shaped molecules significantly. The experimental vaporization enthalpy of 2-(methyl-amino)-ethanol is well established in the literature [8,9]. Using this value as the "centerpiece," we can therefore exchange the methyl-group CH 3 with the phenyl-group C 6 H 5 and estimate the desired Δ g l H o m (298.15 K)value for of 2-(phenyl-amino)-ethanol. It should be noted that the conventional GA method to such predictions will not work because intra-HB is not parameterized at all. To validate the "centerpiece" approach to amino-alcohols, we examined the series of amino-alcohols shown in Fig. 2.
The focus of this work was on vapor pressure measurements and the standard molar vaporization enthalpies,Δ

Materials
All samples of amino-alcohols with purities of 0.96-0.99 mass fraction according to specification by manufacturer were of commercial origin (see Table S1). Samples were purified by repeated distillation at reduced pressures. Purities of samples were measured by a gas chromatograph equipped with FID and a HP-5 capillary column. No impurities (greater than the mass fraction 0.0004) were found in the compounds studied by the transpiration.

Experimental thermochemical methods
Vapor pressures of 1-(dimethylamino)-2-propanol, 2-(phenyl-amino)-ethanol, and 2-(benzyl-amino)-ethanol at different temperatures were measured by using the transpiration method with a self-made setup [10,11]. Vapor pressures derived from the transpiration method are reliable within (1 to 3) % [10,11]. The standard molar enthalpies of vaporization, Δ g l H o m , were derived from the temperature dependence of vapor pressure. The error in the enthalpies of vaporization is assumed to be within ± (0.3 to 0.5) kJ·mol −1 [10,11]. For more details on the experimental procedure, see the Supporting Information.

Absolute vapor pressures and thermodynamics of vaporization
The experimental absolute vapor pressures, p i , and temperature dependences measured with the help of the transpiration method for amino-alcohols were fitted with the following equation [10]: where a and b are adjustable parameters, the reference pressure p ref = 1Pa , and R = 8.31446 J . K −1. mol −1 . The Δ g l C o p,m is the difference of the molar heat capacities of the gas and the liquid phases, respectively (see Table S2). The arbitrary temperature T 0 applied in Eq. (1) was chosen to be T 0 = 298.15 K.
The vapor pressures for DL-2-amino-1-butanol and 1-(dimethylamino)-2-propanol were measured for the first time. The vapor pressures at different temperatures for 2-(phenyl-amino)-ethanol are reported by Stull [47]. These data correspond to the significantly higher temperature range, and a comparison is not possible. The vapor pressure temperature dependence for 2-(benzyl-amino)-ethanol was measured by Razzouk et al. [15] using the static method. The comparison of the available data is given in Fig. S1. Our transpiration results are significantly lower compared to those of the static technique. It has turned out that the purity of the sample used by Razzouk et al. [15] was only 97.7% according to gas chromatography as determined after vapor pressure measurements. The information of the remaining 2.3% impurities is absent in the paper. In our experience with the static method, however, these impurities should be the decomposition product with higher volatility and could significantly increase the vapor pressure. Nevertheless, this apparent disagreement led us to look for additional data that would help resolve the observed contradictions. As a matter of fact, the SciFinder [16] compiles experimental boiling temperatures at various pressures. The accuracy of this data is questionable as it comes from the distillation of a compound after its synthesis and not from special physicochemical studies. However, the numerous data on boiling temperatures at standard pressure, as well as at reduced pressures, provide at least a reliable level of the experimental vapor pressures and a reliable trend of the dependence of the vapor pressure temperature. As can be seen in Fig. S1, the boiling points taken from SciFinder agree fair with our transpiration results, but not with those from the static method.
After we have resolved the contradictions observed in this way for 2-(benzyl-amino)-ethanol, we have systematically (see Table S3) collected the data available in SciFinder for aminoalcohols (see Fig. 2). These data were used to derive vaporization enthalpies of amino-alcohols (see Table 2). The "empirical" results derived in this way are designated in Table 2 as SF values.
Vapor pressure temperature dependences measured in this work (and those taken from the literature) were used to derive vaporization enthalpies according to the following equation: The entropies of vaporization were also obtained from vapor pressures temperature dependences according to Eq. (3): Table 1. The procedure for calculating the combined uncertainties of enthalpy of vaporization has been described elsewhere [12,13]. The uncertainties include uncertainties in vapor pressure, uncertainties due to the experimental conditions of transpiration, and uncertainties in adjustment to T = 298.15 K. The compilation of the Δ  Table 2.

Correlation of enthalpies of vaporization of amino-alcohols with their boiling temperatures
The relation of vaporization enthalpy to boiling point is a well-established phenomenon, and Trouton's rule is the    best evidence of this. According to our experience, the aminoalcohols are thermally stable compounds, which boil between 400 and 560 K [17][18][19], depending on their size and structure. In our previous paper [20], we have established a linear correlations of Δ The results calculated from this correlation were in agreement with those derived from other methods within of ± 1.5 kJ·mol −1 . We used Eq. (4) to calculate vaporization enthalpies of 1-(dimethylamino)-2-propanol, 2-(dimethylamino)-1-propanol, 2-(phenyl-amino)-ethanol,  Table 2, and designated as the T b -values.

Kovats retention indices for validation of experimental vaporization enthalpies
In homologous series (e.g., alcohols, alkylbenzenes, alkanes, etc.), the vaporization enthalpies Δ  Table 3: Table 2 The standard molar vaporization enthalpies, Δ g l H o m , of substituted amino-alcohols a Techniques: T = transpiration method; S = static method; n/a = method is not available; SF-from experimental boiling temperatures reported at different pressures compiled by the SciFinder [16] (see text); J xresults obtained from Kovats indices (see text); Add = calculated according to the "centerpiece" approach b Uncertainties are the standard uncertainty. They include uncertainties from the vapor pressure fitting equation and uncertainties from adjustment to the reference temperature T = 298. 15  The "theoretical" results derived from this correlation are given in Table 2 and designated as J x . The vaporization enthalpies derived from the correlations with Kovats indices (see Table 3, column 5) are in a good agreement with those obtained by the transpiration method (see Table 2).
Such good agreement can be seen as an additional validation of the experimental data measured in this work by using the transpiration method (see Table 2). It can be seen from Table 3

Evaluation of available vaporization enthalpies
As can be seen from Table 2 Table 2 was conducted with the correlation Δ other methods, especially in cases where data are scarce. The experimental and "theoretical" vaporization enthalpies derived for each amino-alcohol are given in Table 2. From this table, it can be seen that for every compound agreement among Δ g l 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 of amino-alcohols given in Table 2. These values are highlighted in bold and are recommended for thermochemical calculations performed in the following section.

Prediction of vaporization enthalpies of amino-alcohols with the "centerpiece" approach.
The general idea of the "centerpiece" approach is already shown in Fig. 1. Now we apply this idea for predicting the Δ  Table 2.
First of all, let us complete the prediction shown in Fig Table 2. According to the idea, the vaporization enthalpy of 2-(phenyl-amino)-ethanol is derived by cutting the CH 3 group (with its contribution to vaporization enthalpy of 6.33 kJ·mol −1 , given in Table S4) and attaching the C 6 H 5 group (with its contribution to vaporization enthalpy of 31.7 kJ·mol −1 , given in Table S4) instead. The resulting "additive" value Δ  Table 2).
Another option for predicting the vaporization enthalpy of 2-(phenyl-amino)-ethanol is to start (see Fig. 3) from the experimental vaporization enthalpy of 2-(ethylamino)-ethanol Δ g l H o m (298.15 K) = 60.8 ± 0.2 kJ·mol −1 given in Table 2. In this case, in order to derive the desired value, we need to cut off the CH 3 and CH 2 groups and append the C 6 H 5 group instead. The resulting "additive" value Δ   Kovats indices, Jx, on the standard non-polar column OV-1 [23] b Experimental data from Table 2 c Calculated using Eq. (5) with the assessed standard uncertainty of ± 1.0 kJ·mol −1 d Difference between columns 4 and 5 in this table e Experimental data measured by using the transpiration method (see Table 2)  Table 2). It is even easier to predict the vaporization enthalpy of 2-(benzyl-amino)-ethanol starting from the same "centerpiece" 2-(ethyl-amino)ethanol as it is shown in Fig. 3. The resulting "additive" value Δ  Table 2).
The examples of the "centerpiece" approach application given in Figs. 1 and 3 show a generally possible way to obtain a reliable prediction even starting from different species. However, this method cannot be considered as universal, as the selection of the starting "centerpiece" requires some preliminary knowledge of effects that arise when substituents are placed in close proximity in the germinal or vicinal position on the alkane skeleton. This idea is demonstrated in Fig. 4. Using the "centerpiece" approach, the vaporization enthalpy of DL-2-amino-1-butanol can be estimated starting from 2-amino-ethanol, 2-amino-1-propanol and from 2-amino-1-pentanol. Experimental vaporization enthalpies for these amino-alcohols are given in Table S5.
The four steps required to construct DL-2-amino-1-butanol from 2-amino-ethanol are shown in Fig. 4 (left). The resulting "additive" value Δ  Table 2). Maybe there are too many construction steps to get a correct result? Starting with 2-amino-1-propanol, the number of steps is considerably lower (see Fig. 4, middle). But even in this case the "additive" value Δ  Table 2). What is wrong with the centerpiece approach? Starting with 2-amino-1-pentanol, we also need only one step to construct DL-2-amino-1-butanol (see Fig. 4, right). We can finally get the "additive" result Δ At first glance, none of the three starting molecules, namely 2-amino-ethanol, 2-amino-1-propanol, and 2-amino-1-pentanol, are very different. But it is not correct. It is known that the energetics of aminoalcohols and 1,2-alkanediols are determined by the intra-molecular hydrogen bonding [24,25]. Let us first consider 1,2-alkanediols, for which a plausible explanation was given in our previous work [25]. With the 1,2-alkanediols, an unusual sequence of the Δ As can be seen in Fig. 5, the trend similar to that of 1,2-alkanediols applies to aminoalcohols: the strongest intra-HB is in 2-amino-ethanol. However, already in 2-amino-1-propanol, the CH 3 group, which is located in the close proximity of the amino-group, reduces the strength of the intra-HB for steric reasons. Similar to 1,2-alkanediols, an attachment of the next alkyl fragments to 2-amino-ethanol does not have the same effect as with the first substitution. As a consequence, the vaporization enthalpies of 2-amino-ethanol and 2-amino-1-propanol are out of the linear correlation shown in Fig. 5. The linearity of the chain-length dependence of the enthalpy of vaporization begins with 2-amino-1-butanol. Such a peculiar energetic behavior that has been observed in aminoalcohols can now explain the trial and error observed with three "centerpieces" shown in Fig. 4. Indeed, using 2-amino-ethanol and 2-amino-1-propanol to predict the enthalpy of vaporization of 2-amino-1-butanol could be considered as a typical "error," as both molecules have much more individual characteristics than is applicable for group additivity. In contrast, using the 2-amino-1-pentanol as the "centerpieces" is optimal for the prediction, since according to Fig. 5, this molecule is already out of perturbation specific for the smaller homologues.
Another important factor for the selection of the "centerpiece" molecule is illustrated in Fig. 6. Let us try to predict vaporization enthalpies of two branched aminoalcohols: enthalpies of 2-(dimethyl-amino)-1-propanol and 1-(dimethyl-amino)-2-propanol starting from Δ g l H o m (298. 15 K) = 47.1 ± 0.1 kJ·mol −1 [26] of 2-(dimethyl-amino)ethanol as the "centerpiece" molecule. In both cases, we just need to replace the CH 2 group with the CH group and add the contribution for the CH 3 group as it is shown in Fig. 6. In both cases, however, the "additive" results do not agree with the experimental values evaluated in Table 2.
The obvious reason for the observed disagreement is the appearance of steric repulsions between substituents, since they occur in close proximity on the small skeleton. Due to these repulsions, the tightness of the packaging of the molecules in the liquid is unique for each type of branching. Therefore, the correct selection of the "centerpiece" molecule is hardly possible.
The consequence for proper use of the "centerpiece" approach is that the small branched molecules and molecules with strong steric interactions (e.g., 2-amino-2-methyl-1-propanol) must be excluded from application. Nonetheless, we are systematically testing the "centerpiece" approach with different types of organic and metal-organic compounds. The reliable results have been already obtained for aldehydes and esters [27], for substituted benzenes [6,7], and for tris(beta-diketonato)iron complexes [28] In summary, the compilation of experimental results evaluated in Table 2 made it possible to validate three