Group Contribution Revisited: The Enthalpy of Formation of Organic Compounds with “Chemical Accuracy” Part VI

Abstract

In this paper we provide the reader with a ready to use Group Contribution (GC) method for the heat of formation (gaseous state) of organics in the form of an Excel spreadsheet with all data, enabling further predictions, and an accompanying manual on how to use the GC model for predicting the heat of formation for organics. In addition, in order to widen the applicability of the method whilst retaining chemical accuracy compared to our previous publications on this topic, we include further chemical groups including acetals, benzyl ethers, bicyclic hydrocarbons, alkanediols and glycerol, polycyclic aromatic hydrocarbons, aromatic fluoro compounds, and finally several species which we include to illustrate how the GC model can be successfully applied to species we did not consider during the parameterization of the GC model parameters.

1. Introduction

The heat of formation is a crucial parameter with respect to the stability of molecules and chemical transformations as well as in chemical process design. Due to the lack of experimental data (the space of organic molecules comprises many billions of different molecules), predictive models are highly desired. This work is the continuation of work that resulted in five earlier papers [1,2,3,4,5] on a Group Contribution (GC) method. In order to avoid a lot of text repetition we refer to these earlier papers (all are open access) for all necessary references to previous GC work by a variety of authors and differences in approaches taken including achieved accuracy and reliability. Our aim is to have a method available which allows accurate predictions to be obtained for the heat of formation of organic molecules, i.e., with chemical accuracy, previously unprecedented. Peterson et al. [6] formulated this as “in the thermochemistry literature this is almost universally interpreted as 1 kcal/mol or about 4 kJ/mol”, i.e., the aim is to have the difference between experimental and model values less than 1 kcal/mol, i.e., 4.2 kJ/mol. In the five earlier papers the Group Contribution (GC) method was re-evaluated and, despite the method being old [7] it was demonstrated that it is possible to establish a GC parametrization for organic molecules achieving unprecedented chemical accuracy. It is important to mention that we are not fostering a method with an averaged absolute deviation within chemical accuracy but each individual result is within chemical accuracy. Apart from being accurate and reliable (very few if any outliers, and certainly not with large deviation), values for the property are to be obtained at one’s fingertips. For the process developer or the experimental chemist, it is more than useful to have a method with such qualities, especially when multiple process routes are to be compared.

In a recent paper Aouichaoui c.s. [8] included a table (their Table 6) revealing that our Group Contribution (GC) model performs by far the best for the heat of formation of organic molecules out of a total of nine methods. In our previous papers we have explained why our approach can be understood to be more successful. Unfortunately, these authors did not mention that our method [1,2,3,4,5], next to having the smallest Mean Absolute Error (MAE), also reveals chemical accuracy for almost all individual species. Based on the papers referred to, our work was based on 458 entries which is less than most other methods. Meanwhile, however, our more accurate (within chemical accuracy) results are based on more than twice that number ([1,2,3,4,5] + current paper). For the understanding of our approach it is important to realize that the designation that our method is GC-MLR [8] is not correct as we did not apply any form of (computer-assisted) multi-linear regression (see our previous publications for reasons and details).

On the methodology applied, for the purpose of the evaluation of the enthalpy of formation ΔHf of organic molecules from their molecular structure, the Group Contribution (GC) approach is one of the most important and widely applied methods [1,2,3,4,5,7,9,10,11,12,13,14,15,16,17]. The original GC method is based on the assumption that a molecule can be decomposed into molecular fragments which are in essence mutually independent, and the molecular property of interest is the sum of the individual properties of the molecular fragments. The GC method is a so-called data-driven model with experimental data being used to parametrize the model; for the heat of formation ΔHf the essential equation reads

ΔHf = Σ Nj.ΔHf(j)
j = 1,N

(1)

In Equation (1), Nj represents the number of times Group j occurs in the molecule of interest, whereas ΔHf(j) is the group contribution of the chemical Group j to the heat of formation. In this work, the ΔHf (in this paper, also indicated as dHf) is the enthalpy of formation for the ideal gas species at the reference temperature of 298.15 K and 101,325 Pascal (1 atm.).

The G4 quantum method (which has previously been demonstrated to provide generally very reliable heats of formation) has been applied to provide further independent information when an experimental and a GC-predicted value do not agree. It is being used as a source of information to address the problem when disagreement is observed. When such a difference is observed we need to be sure which is the cause, for when it is the GC value we have a reason to introduce additional GC parameters. When the G4 value and the GC model values agree, the experimental value might be in error. A larger number of G4-calculated heats of formation was calculated to obtain further support for the good performance of this method as observed in earlier studies. When the G4 method works well for a closely related set of molecules, it will also for an additional member. This is not a priori the case for experimental or GC model values. In some cases we arrive at still unexplainable differences, and subsequently invoke Density Functional Theory (DFT)-based calculations as a further independent source of information. Examples will be found in the present paper.

In order to widen the applicability of the method developed previously, in the present work we include further chemical groups including acetals, benzyl ethers, bicyclic hydrocarbons, alkanediols and glycerol, polycyclic aromatic hydrocarbons, aromatic fluoro compounds, and finally several species which we include to illustrate how the GC model can be successfully applied to species we did not consider before during the parameterization of the GC model parameters. To enable other researchers’ easy access to the method we provide an Excel spreadsheet containing all our data thus far. First of all, it makes it very easy to add other compounds and compute the heat of formation according to the GC model. Secondly, by comparing to similar compounds in the table the user will easily see which group parameters should be used in describing the new molecule appropriately. A brief manual is provided (see Section 3.1).

2. Materials and Methods

2.1. Experimental Data

As the GC method is a data-driven method we need reliable and accurate data to parametrize the model, i.e., determine the numerical values for the group parameters ΔHf(j) in Equation (1). As the amount of reliable and accurate experimental values is limited (compared to the large number of classes of molecules), we may also need quantum computational tools to compute sufficiently reliable heats of formation. It has been discussed and demonstrated by various authors that the G4 method (see Section 2.2) is such a method [4,5,18,19,20,21,22,23,24].

2.2. Computational Methods

The most common and generally applicable method for deriving the heat of formation from electronic structure calculations is by way of computing the atomization energy. The atomization energy is simply the energy required to break the molecule into its constituent atoms, as illustrated for hydrocarbons by the following formula:

C_mH_n = mC + nH

(2)

This is thus simply a calculation based on the standard definition of the heat of formation of a compound being the sum of the enthalpy change of the reaction by which the compound is formed from the elements. Following on from our previous work [4,5] we continue applying ab initio type calculations based on the G4 method [25,26,27] in the present work, or alternatively refer to G4 computed results reported by other authors. G4 is a procedure that approximates the energy of a CCSD(T)/6-311++G(3df,2p) single-point calculation at the B3LYP/6-31G(2df,p) optimized geometry by using a series of somewhat less expensive calculations. Further details about this so-called composite method can be found in the original references [25,26,27]. We have been employing Gaussian 16 (G16) [25,26,27] (including the GaussView visualization tool) for geometry optimization, force constants were calculated analytically, and tight convergence criteria were used (fopt = (calcfc, tight)). Structures were verified as minima on the potential energy surface via the calculation of second derivatives (frequency calculation). For structures with multiple low-energy conformations, conformational searching was performed, and subsequently Boltzmann averaged enthalpies were obtained. In cases with ~50 or fewer conformations, the conformational search was performed manually; in more complex cases, the GMMX conformational search tool in GaussView was utilized. In a small number of cases, the potential number of conformations was so large (more than a few hundred) that only the presumed lowest energy conformation was considered. In S1 (Supplementary Materials) we provide the optimized G4 structures (XYZ coordinates) of the lowest energy conformations of all the species studied. Along with the structures, we list the G4 energies, ZPEs, and thermodynamic corrections for 298.15 K. In a separate table (also in Supplementary Materials S1), we summarize the G4 enthalpies and Gibbs free energies at 298 K that were used for conformational averaging. The G4 data were converted into the enthalpies of formation in the way described by Wiberg and Rablen [20], which, in essence, follows the correction scheme proposed earlier by Saeys et al. [28]. This procedure aims to correct for systematic deviation in the calculation of the atomization energies of the elements. The enthalpy of formation is obtained using the formula

dHf(C_mH_nN_pO_w; 298 K) = dH_G4(C_mH_nN_pO_w; 298 K) − mX − nY − pZ − qW

(3)

The term on the left is the computed enthalpy of formation, whereas the first term on the right-hand side is the direct G4 result. X, Y, Z, and W are the empirically corrected per-atom G4 enthalpies of C, H, N, and O in their standard states. However, here we have used the numerical values of X, Y, Z, and W recommended by van der Spoel [18] rather than the ones developed by Wiberg and Rablen (the differences are relatively small, but the former appear to yield somewhat better agreement with experiment). At the researcher’s convenience, Equation (3) can be extended to include other atoms. This approach overcomes the problem of the systematic increase in the deviation in ab initio and DFT-based methods in terms of the number of atoms because the atomic energies, which are the reference for the evaluation of the heat of formation from the elements, are not perfect. As the contributions X, Y, and Z are determined empirically using a set of experimental data, we may observe some differences between G4 results from different publications. These are generally in the kJ/mol range but can incidentally be higher. We adopted the atom-specific corrections, so the values for X, Y, … in Equation (3), from van der Spoel c.s. [18], who have reported the results of all their calculations in the Supplementary Materials to their paper and in a database which is freely accessible on the Virtual Chemistry website.

Contrary to other works in which the G4 method was used to evaluate the heat of formation, in the current work, whenever possible, we computed the averaged value for the heat of formation over different accessible conformations. It is formally more correct and has an impact compared to minimum energy structure evaluation only when flexible units are present. In a previous paper [4], we observed, from calculations on substituted cycloalkanes, that the contribution due to conformational averaging is typically of the order of 1–2 kJ/mol depending on the structure and therewith the accessible conformations.

In addition to G4 calculations we incidentally invoked B3LYP calculations with a 6-311+G** basis set to evaluate relative energies within a series of molecules. This is an older density functional, being a mix of density functional character and the traditional Hartree–Fock character, which turned out to give good relative energies for organic molecules [29]. These Density Functional Theory (DFT) type quantum calculations were performed using the Spartan program [30]. This type of calculation was only and specifically applied to evaluate relative energies between different configurations of the same molecule and subsequently employed to determine whether certain differences in heat of formation between specific molecules can be rationalized before introducing additional group contribution parameters. Even though the B3LYP method has always been considered an appropriate method to evaluate energy differences between organic species, we emphasize that, as some readers may argue that another method may lead to more accurate results, we only use the results in an indicative way whereas the numerical values of the group contribution parameters were always based on either experimental results, preferably, or on G4-calculated results.

3. Results

3.1. The Group Contribution Method with Chemical Accuracy

Supplementary Materials S2 is the Excel spreadsheet comprising all data we have reported about in the previous five papers and the current paper. Evidently the interested reader can also find all group parameters in the publications, but in the Excel file they are all collected (at the top, both individual group parameters as well as group–group interaction parameters) and by comparing with a molecule similar to the one of interest it is more evident which group parameters are involved, which reduces errors and therewith the risk of erroneous prediction. The latter particularly applies to the interaction parameters defined, e.g., the alkyl–phenyl interaction or the F–F interaction in terminal CF₂H. The Word document, Supplementary Materials S3, is to be seen as a brief manual for those who wish to apply our GC model.

3.2. Further Classes of Molecules

3.2.1. Acetals

Table 1. Experimental heats of formation [13], GC model and G4 values for a series of acetals. The G4 values in column 6 are conformationally averaged values, except for those values printed in italic. All values in kJ/mol.

Acetals	Exp [13] Verevkin	GC Model	GC Model-G4	ABS (GC Model-Exp)	G4	ABS (GC Model-G4)	G4-Exp
dimethoxymethane	−348.2	−350.0	3.1	1.8	−353.1	3.1	−4.9
diethoxymethane	−414.8	−420.7	−2.1	5.9	−418.6	2.1	−3.8
dibutoxymethane	−492.2	−503.2	0.5	11.0	−503.7	0.5	−11.5
1,1-dimethoxyethane	−389.7	−392.4	0.2	2.7	−392.6	0.2	−2.9
1,2-dimethoxyethane		−350.0	−5.4		−344.6	5.4
1,1-diethoxyethane	−454	−463.1	−4.4	9.1	−458.7	4.4	−4.7
1,2-diethoxyethane		−420.7	−9.4		−411.3	9.4
2,2-dimethoxypropane	−423.1	−434.7	−0.8	11.6	−433.9	0.8	−10.8
2,2-diethoxypropane	−495.3	−505.4	−5.0	10.1	−500.4	5.0	−5.1
1,3-diethoxypropane		−441.4	−3.2		−438.2	3.2
1,1-dimethoxybutane	−425.7	−433.6	0.9	7.9	−434.5	0.9	−8.8
1-ethoxy-1-methoxyethane		−427.7	−2.1		−425.6	2.1
1-ethoxy-2-methoxyethane		−385.4	−7.0		−378.4	7.0
trimethoxymethane	−530.8	−529.0	8.2	1.8	−537.2	8.2	−6.4
triethoxymethane	−630.6	−635.1	1.6	4.5	−636.7	1.6	−6.1
1,1,1-trimethoxyethane		−567.4	9.0		−576.4	9.0
averaged absolute difference				6.65		3.93	6.50

comprises experimental [13], (our current) GC model, and quantum G4 results for the heat of formation of a series of acetals. We notice a larger difference between the model and the experimental values. The GC model would, by its nature, be expected to be the weakest of all three (experimental, GC model, G4), but when the differences between two molecules are only straightforward CH₂ increments the relative difference between the heats of formation should be represented reliably. Whereas the experimental and GC values agree within chemical accuracy for dimethoxymethane and diethoxymethane, for dibutoxybutane the difference is as high as 11 kJ/mol. The G4 value for this molecule is very close to the GC model value, and the experimental value given by Pedley c.s. [31] reads −501 kJ/mol. The consistency between the effect of simple CH₂ increments and GC model and G4 values makes us conclude that Verevkin’s experimental value [13] must be off the true value by significantly more than chemical accuracy. An identical reasoning can be applied to 2,2-di-methoxy-propane, where Pedley c.s. [31] have reported a value of −429.6 kJ/mol, also much closer to the G4 and GC model values than Verevkin’s experimental value. As in the previous case, it also agrees with physico-chemical understanding (differences between structures are CH₂ increments only).

A further larger deviation is revealed for 1,1-dimethoxybutane. No value from Pedley c.s. [31] is available, and the value in the NIST database [32] from Wiberg must be erroneous: −309 kJ/mol. The G4 and GC model values are, again, very close.

Overall, the absolute averaged difference reads 6.65 kJ/mol for the difference between Verevkin’s experimental values [13] and GC model values, but 3.93 kJ/mol for the pair GC model and G4. When we adopt the available experimental data from Pedley c.s. [31] the AAD with the GC model is evaluated as 4.8 kJ/mol.

For the reasons already formulated we conclude that the GC model provides good values, mostly within chemical accuracy.

3.2.2. Benzyl Ethers

For the benzyl ethers (

Table 2. Experimental heats of formation [13], GC model and G4 values for a series of benzyl ethers. The G4 values in column 6 are conformationally averaged values. All values in kJ/mol.

Benzyl Ethers	Exp [13]	GC Model	GC Model-G4	ABS (GC Model-Exp)	G4	ABS (GC Model-G4)	G4-Exp
methyl benzyl ether	−82.1	−83.5	−4.2	1.4	−79.3	4.2	2.8
ethyl benzyl ether	−114.3	−119.9	−6.6	5.6	−113.3	6.6	1.0
t-butyl benzyl ether	−183.4	−188.6	−6.8	5.2	−181.8	6.8	1.6
t-amylbenzyl ether	−202	−192.2	9.0	9.8	−201.2	9.0	0.8
(1-methoxyethyl) benzene	−112.4	−125.9	−3.2	13.5	−122.7	3.2	−10.3
(1-ethoxyethyl) benzene	−143.6	−140.2	16.6	3.4	−156.8	16.6	−13.2
(1-propoxyethyl) benzene	−165.6	−160.9	17.3	4.8	−178.1	17.3	−12.5
(1-butoxyethyl) benzene	−190	−181.5	17.3	8.5	−198.8	17.3	−8.8
(1-isopropoxyethyl)-benzene	−177.9	−191.6	0.9	13.7	−192.5	0.9	−14.6
1-sec-butoxyethylbenzene (RR/SS diastereomer)	−199	−206.2	5.4	7.2	−211.6	5.4	−12.6
1-sec-butoxyethylbenzene (RS/SR diastereomer)	−201.1	−206.2	8.1	5.1	−214.3	8.1	−13.2
methyl cumyl ether	−140.5	−162.2	−9.1	21.7	−153.1	9.1	−12.6
ethyl cumyl ether	−175.5	−182.6	3.7	7.1	−186.3	3.7	−10.8
propyl cumyl ether	−198.1	−203.2	6.6	5.1	−209.8	6.6	−11.7
butyl cumyl ether	−218.5	−223.8	6.8	5.3	−230.6	6.8	−12.1

) we see similar behavior as for the acetals, but with a number of larger differences between experimental [13] and GC model values.

3.2.3. Bicyclic Hydrocarbons

When we want to establish a useful group contribution method we also need to account for more complex molecules like norbornane and other bicyclic hydrocarbons. These species were already discussed along with the G4-calculated heats of formation by Wiberg and Rablen [20]. In our previous paper [5] we concluded that the values for the atomization energies of the elements as determined by van der Spoel c.s. [18] are the better choice compared to those used in Ref. [20]. Therefore, the values in

Table 3. Experimental heats of formation [33] and G4 values for a series of bicyclic hydrocarbons. The G4 values in column 3 are based on the lowest-energy conformation. All values in kJ/mol.

Bicyclic Hydrocarbons	Experiment [33]	G4	Exp-G4	ABS (Exp-G4)	Other Exp
bicyclo[2.1.0]pent-2-ene	333	327.8	5.2	5.2
bicyclo[2.1.0]pentane	158	156.1	1.9	1.9
cis-bicyclo[2.2.0]hexane	125	129.6	−4.6	4.6
bicyclo[2.2.0]hex-2-ene		259.5
bicyclo[2.2.0]hex-1(4)-ene		381.0
bicyclo[2.1.1]hexane		57.7
bicyclo[2.1.1]hex-2-ene	251	228.2	22.8
norbornene	85.4	79.5	5.9	5.9	82.6 ± 2.1 [34]
norbornane		−56.1	1.4	1.4	−54.7 ± 4.7 [31]
norbornadiene	244	237.3	6.7	6.7	245.3 ± 2.7 [31]
quadracyclane (tetracyclo[3.2.0.0(2,7).0(4,6)]heptane)	336	332.1	3.9	3.9
bicyclo[3.2.0]hept-6-ene	139.7	138.7	0.9	0.9
bicyclo[3.2.0]heptane		7.1
bicyclo[3.2.0]hept-1(5)-ene		181.9
bicyclo[2.2.2]octene		21.1
bicyclo[2.2.2]octane		−95.7	−3.3	3.3	−99.0 [35]
averaged absolute difference				3.76

are new and deviate from those in Ref. [20]. In Table 3 we also provide experimental values with most of those from Roth c.s. [33]. Even though we do not have solid evidence about their reliability, not much else is available, and it is gratifying to see that agreement with G4 values is actually quite good: an averaged absolute deviation of 3.8 kJ/mol when we disregard bicyclo[2.1.1]hex-2-ene which reveals a very large deviation of over 22 kJ/mol. For norbornene a more recent value of −82.6 kJ/mol by Steel c.s. [34] provides a somewhat more close agreement with the G4 result. With a GC method not being appropriate to account for this kind of structure (ring strain as in the cyclic alkanes and more) we conclude the G4 data illustrate a valuable alternative to experimental data for similar species. The molecules with their associated heats of formation can subsequently be used as groups in the GC approach.

3.2.4. Alkanediols and Glycerol

In the context of our work this class is problematic in the sense that we find few experimental values which we can regard as accurate and highly reliable (as we will see below), and we also do not know beforehand to what extent hydroxyl–hydroxyl interactions will require additional caution and action (additional parameters). We will initially adopt the critically reviewed values presented by Pedley c.s. [31]. Please note that the GC parameters we are using here have been previously established for species with a single hydroxyl group only and therefore are not specifically tuned to accommodate diols. For the α-ω-alkanediols, entries 1–5 in

Table 4. Experimental heats of formation [31], GC model and G4 values [18] for a series of diols and glycerol. All values in kJ/mol.

Diols	Experiment [31]	GC Model	GC Model-Exp	ABS (GC Model-Exp)	G4 [18]	ABS (Model-G4)
1,2-ethanediol	−387.5	−383.26	4.24	4.24	−379.3	3.96
1,3-propanediol	−392.1	−403.89	−11.79	11.79	−399.7	4.19
1,4-butanediol	−426.7	−424.52	2.18	2.18	−424.9	0.38
1,5-pentanediol	−449.1	−445.15	3.95	3.95	−441.9	3.25
1,6-hexanediol	−461.2	−465.78	−4.58	4.58
1,2-propanediol	−421.3	−421.49	−0.19	0.19	−426.8	5.31
1,3-butanediol	−433.2	−442.12	−8.92	8.92	−440.2	1.92
2,3-butanediol	−482.3	−459.72	22.58	22.58	−457.6	2.12
2,4-pentanediol	−474.1	−480.35	−6.25	6.25	−477.7	2.65
glycerol	−577.4	−570.76	6.64	6.64
averaged absolute difference				7.13		2.97

, we observe reasonable agreement (not always within chemical accuracy) between experimental and GC model values. Therefore, unexpectedly for 1,3-propanediol the difference is significant, 11.8 kJ/mol. However, for 1,3-propanediol there is also a value of −408.4 kJ/mol from Knauth and Sabbah [36] which is in better agreement with the GC model value. It could be questioned whether this value is truly reliable when we take into consideration the values reported by Knauth and Sabbah for the longer alkanediols (see below). It may also be noted that the error in the experimental values is typically given as 3 kJ/mol. For 1,3-propanediol yet another value was reported by Emel’yanenko and Verevkin [37], namely −410.6 ± 2.2 kJ/mol. However, the GC model values agree within chemical accuracy with G4-calculated values due to van der Spoel c.s. [18]. This agreement as well as the fact that the series only involves a subsequent CH₂ increment between consecutive species must lead to the conclusion that the (available) experimental values, which also differ clearly between authors, are not always sufficiently accurate.

Further experimental data on α-ω-alkanediols, 1,6-hexanediol up to 1,10-decanediol, are available from a publication from Knauth and Sabbah [38]. The differences between the experimental and the GC model values vary from 9 to 25 kJ/mol and with very irregular CH₂ increment values. Even when considering the ring sizes, hydroxyl–hydroxy interactions would be potentially possible, which does not seem to agree with the observed irregular behavior.

The next four entries have hydroxyl groups which are not both at terminal positions. Only for 1,2-propanediol is the agreement between the experimental value given by Pedley c.s. [31] within chemical accuracy from the GC model value. For the other three species the difference is clearly beyond chemical accuracy and, especially for 2,3-butanediol, the difference is as large as 22.6 kJ/mol. Ordinary chemical knowledge cannot rationalize the difference between this result and the other diols. When we consider the G4 results we observe agreement with GC model values within or nearly within (1,2-propanediol) chemical accuracy.

Finally, for glycerol we observe reasonable agreement between the experimental value and the GC model value. It illustrates that, when we compare glycerol with the entire series, no additional GC parameter is needed to account for potential hydroxyl–hydroxyl interactions.

3.2.5. Polycyclic Aromatic Hydrocarbons

In Table 5 we have collected experimental data [39] and data from our GC model for a series of polycyclic aromatic hydrocarbons. This series, contrary to the series in Table 6 that we will discuss later, contains molecules with groups that could at least in principle be more or less adequately accounted for by the GC model parameters we have established thus far [1,2,3,4,5]. The results reveal agreement within chemical accuracy for all but tri- and tetraphenylmethane with the larger deviation for the latter species. When taking into account all species the averaged absolute difference reads 7.98 kJ/mol and thus is almost within chemical accuracy. However, we aim for chemical accuracy for each individual species. For both tri- and tetraphenylmethane we can expect steric hindrance (interaction between phenyl groups) to be the reason for the larger difference between experimental and GC model values which is consistent with the effect for tetraphenylmethane being larger than for triphenylmethane and the fact that for both the experimental value is more positive compared to the model value. When we exclude these two, we find that the averaged absolute difference reduces to 3.73 kJ/mol. Roux c.s. [39] have reported on a larger series of polycyclic aromatics (see also discussion on Table 6), and the current results suggest (as our GC model was previously established on well-established experimental data) that their results are accurate and reliable. For some cases these authors have noted, “There are insufficient literature values to properly evaluate the data” and this also applies to the experimental value associated with p-tetraphenyl and therefore this value was associated with a larger error (±11 kJ/mol). There is also another value from Balepin c.s. [40] which reads 382 kJ/mol which is close to the GC model value.

We conclude that with the exception for crowded species for which we may expect steric hindrance to be present, the GC model provides reliable and relatively accurate values for the heat of formation of this class of species.

Table 5. Experimental heats of formation [39] and GC model values for the heat of formation of a series of polycyclic aromatic hydrocarbons. All values in kJ/mol. The averaged absolute deviation whilst disregarding the congested tetraphenyl species is well within chemical accuracy.

Polycyclic Aromatic Hydrocarbons	Experiment	GC Model	GC Model-Exp	ABS (GC Model-Exp)
biphenyl	180.3 ± 3.3	181	0.70	0.7
diphenylmethane	165	160.4	−4.63	4.6
triphenylmethane	276.1	267.5	−8.60	8.6
tetraphenylmethane	398.1 ± 6.9	361	−37.10	37.1
p-terphenyl	284.4 ± 3.8	284	−0.40	0.4
o-terphenyl	282.8 ± 3.2	284	1.20	1.2
m-terphenyl	280. ± 3.9	284	4.00	4.0
1,3,5-triphenylbenzene	371.8 ± 3.8	374	2.20	2.2
p-tetraphenyl	400. ± 11	387	−13.00	13.0
averaged absolute difference				7.98
averaged absolute difference with two tetraphenyl-containing species disregarded				3.10

Table 5. Experimental heats of formation [39] and GC model values for the heat of formation of a series of polycyclic aromatic hydrocarbons. All values in kJ/mol. The averaged absolute deviation whilst disregarding the congested tetraphenyl species is well within chemical accuracy.

Polycyclic Aromatic Hydrocarbons	Experiment	GC Model	GC Model-Exp	ABS (GC Model-Exp)
biphenyl	180.3 ± 3.3	181	0.70	0.7
diphenylmethane	165	160.4	−4.63	4.6
triphenylmethane	276.1	267.5	−8.60	8.6
tetraphenylmethane	398.1 ± 6.9	361	−37.10	37.1
p-terphenyl	284.4 ± 3.8	284	−0.40	0.4
o-terphenyl	282.8 ± 3.2	284	1.20	1.2
m-terphenyl	280. ± 3.9	284	4.00	4.0
1,3,5-triphenylbenzene	371.8 ± 3.8	374	2.20	2.2
p-tetraphenyl	400. ± 11	387	−13.00	13.0
averaged absolute difference				7.98
averaged absolute difference with two tetraphenyl-containing species disregarded				3.10

Table 6 comprises data on polycyclic aromatic hydrocarbons with interconnected ring systems, mostly with strong aromatic character. For this reason, and similar to the approach we adopted in previous publications for benzene and naphthalene, we adopt these molecules as a group each to account for the overall conjugated structure and thereby reliable heats of formation. As we saw in Table 5 there is a larger set from Roux c.s. which appears to be very consistent. For the values in Table 6 we have no values like GC model values to compare, for reasons just explained. But for most of the species we have G4-calculated values [18]. For anthracene there are various experimental values, e.g., 230.8 ± 4.6 from Coleman and Pilcher [41], which are relatively close and the value seems therefore reliable; the G4 value is in reasonable agreement considering experimental error. The available G4 values are in relatively good agreement with the experimental values except for pyrene and triphenylene. Possibly, the G4 method has some deficiency for these more highly interconnected aromatic molecules.

We have shown a single GC model result, namely for bianthracene. When we adopt the experimental value for anthracene and take anthracene as a group, we find the value 470.8 kJ/mol for bianthracene which just agrees within chemical accuracy with the corresponding experimental result.

Thus, by adopting each of the molecules in Table 6 as a group we may use the experimental values as the GC parameter for the heat of formation of those groups.

Table 6. Experimental heats of formation [39] and G4 quantum values [18] for the heat of formation of a series of polycyclic aromatic hydrocarbons. The second experimental value for fluorene originates from Rakus c.s. [42]. For the single GC model, see the text. All values in kJ/mol.

Polycyclic Aromatic Hydrocarbons	Experiment [39]	G4 [18]	GC Model
Indene	161.2 ± 2.3	158.2
Anthracene	229.4 ± 2.9	221
naphthacene	342.6 ± 5.9
phenanthrene	202.2 ± 2.3	197.9
Fluorene	176.7 ± 3.1	180.6
	175.0 ± 1.5 [42]
pyrene	225.5 ± 2.5	213.9
perylene	318.3 ± 3.7
triphenylene	270.1 ± 4.4	255.8
bianthracene	475		470.8

Table 6. Experimental heats of formation [39] and G4 quantum values [18] for the heat of formation of a series of polycyclic aromatic hydrocarbons. The second experimental value for fluorene originates from Rakus c.s. [42]. For the single GC model, see the text. All values in kJ/mol.

Polycyclic Aromatic Hydrocarbons	Experiment [39]	G4 [18]	GC Model
Indene	161.2 ± 2.3	158.2
Anthracene	229.4 ± 2.9	221
naphthacene	342.6 ± 5.9
phenanthrene	202.2 ± 2.3	197.9
Fluorene	176.7 ± 3.1	180.6
	175.0 ± 1.5 [42]
pyrene	225.5 ± 2.5	213.9
perylene	318.3 ± 3.7
triphenylene	270.1 ± 4.4	255.8
bianthracene	475		470.8

3.2.6. Aromatic Fluoro Compounds

Fluorine is an element having a significant effect on the rest of an organic molecule, i.e., the neighboring carbon atoms. The effect is even significant on the 1s core electrons of both the nearest and even the next-nearest neighbor carbon atom [43]. In one of our earlier papers [3] we were able to describe fluoroalkanes well, but aromatic fluoro compounds turned out to be problematic. In the present work we attempt to develop the GC model further with respect to aromatic fluoro compounds while now also taking G4-calculated values as reference.

Before we start with the somewhat more complex fluoroaromatics, we will first attempt to describe fluorobenzenes which is a prerequisite to the successful description of the more complex species at a later stage.

Table 7. Experimental (for references, see column 2), GC model, and G4 values from van der Spoel c.s. [18]. All values in kJ/mol.

Fluorobenzenes	Experiment	GC Model	ABS (Exp-G4)	ABS (GC Model-Exp)	G4	ABS (GC Model-G4)
hexafluorobenzene	−956 [44]	−959.5	2.5	−3.5	−953.5	6.0
1,2,3,4,5-pentafluorobenzene	−806 [44]	−806.0	2.8	0.0	−803.2	2.8
1,2,3,4-tetrafluorobenzene	n.a.	−634.5			−635.7	1.2
1,2,4,5-tetrafluorobenzene	−646.8 [45]	−652.5	1.0	5.7	−647.8	4.7
1,3,5-trifluorobenzene	n.a.	−491.5			−495.6	4.1
1,2,4-trifluorobenzene	n.a.	−478.5			−477.9	0.6
1,2-difluorobenzene	−283.0 [46]	−286.5	7.1	3.5	−290.1	3.6
1,3-difluorobenzene	−309.2 [46]	−302.0	3.3	7.2	−305.9	3.9
1,4-difluorobenzene	−306.7 [46]	−304.5	4.2	2.2	−302.5	2.0
benzene, 1-fluoro-4-methyl-	−147.5 [46]	−146.4		1.1
averaged absolute difference			2.78	2.32		3.21

n.a.: not available.

comprises a series of multiple F-substituted fluorobenzenes. This series was very useful as we could establish additional interaction parameters enabling us to account well for the heats of formation. These include a correction for an F connected to a phenyl ring: +38 kJ/mol, a nearest neighbor F–F interaction (1,2-interaction) of +18 kJ/mol, and finally a correction for the 1,3-F–F interaction of magnitude +2.5 kJ/mol. The G4-calculated values agree very well with and are within chemical accuracy from the experimental values with the exception of 1,2-difluorobenzene. The G4 value for this species and the GC model value are very close, however, differing only by 3.6 kJ/mol. As in 1,2-difluorobenzene there are no types of interactions other than those present in all the other species, which therefore casts doubt on the accuracy of the experimental value. Overall, the absolute differences are well within chemical accuracy for exp-G4, model-exp, as well as model-G4. Overall, we thus observe good agreement between experimental values, the GC model (with additional interaction parameters), and the G4 values.

Table 8. Experimental heats of formation [47], GC model and G4 values for a series of aromatic fluoro compounds. The G4 values in column 6 are conformationally averaged values, except for those values printed in italic (column 6). All values in kJ/mol. Numbering as in [48] and in Scheme 1.

Aromatic Fluoro Compounds (in Brackets Numbering as in Ref. [47] and Scheme 1)		Exp [47]	GC Model	GC Model-Exp	ABS (GC Model-Exp)	G4	Exp-G4
1-fluorononane	(1)	−423.5	−425.9	−2.4	2.4	−417.2	−6.3
1-fluorododecane	(2)	−489.2	−487.8	1.4	1.4	−481.3	−7.9
1-fluorotetradecane	(3)	−533.0	−529.1	4.0	4.0	−523.8	−9.2
triphenyl(3-fluoropropane)	(4)	57.5	10.7	−46.8	46.8	42.6	14.9
fluoromethylbenzene	(5)	−126.3	−148.6	−22.4	22.4	−125.0	−1.3
fluorocyclohexane	(6)	−336.6	−339.1	−2.4	2.4	−327.0	−9.6
fluorodiphenylmethane	(7)	−42.6	−55.5	−12.90	12.9	−28.7	−13.9
2-fluoro-2-methyl-1,3-diphenylpropane	(8)	−136.7	−136.1	0.58	0.58	−133.0	−3.7
1,3-diphenyl-(2-methylphenyl)2-fluoropropane	(9)	−14.1	−23.9	−9.8	9.8	−22.5	8.4
1,3-diphenyl-2-phenyl-2-fluoropropane	(10)	15.0	−3.3	−18.3	18.3	1.0	14.0
1,1-difluoro-3-phenylpropane	(11)	−414.4	−405.8	8.6	8.6	−407.1	−7.3
1,1,1-triphenyl-3,3-difluoropropane	(12)	−157.6	−205.1	−47.5	47.5	−179.5	21.9
1,2-diphenyl-1,1-difluoroethane	(13)	−260.5	−319.6	−59.1	59.1	−294.4	33.9
2,2-difluorononane	(14)	−671.5	−674.5	−3.0	3.0	−675.9	4.4
trifluoroethylbenzene	(15)	−623.9	−628.6	−4.8	4.8	−629.6	5.8
(1,1,1-trifluoro-2-phenylethane)
1,1,1-trifluoro-2,2-diphenylethane	(16)	−516.1	−521.5	−5.4	5.4	−515.5	−0.6
1,1,1-triphenyl-2,2,2-trifluoroethane	(17)	−364.9	−428.0	−63.1	63.1	−393.9	29.0
1,2-diphenyl-1,1,2-trifluoroethane	(18)	−462.2	−521.5	−59.3	59.3	−473.5	11.3
1,2-diphenyl-1,1,2,2-tetrafluoroethane	(19)	−689.0	−751.0	−62.0	62.0	−691.2	2.2

comprises experimental [47], GC model, and G4 heat of formation values for a series of mostly, but not exclusively, aromatic fluoro compounds. We have kept the order as in the table of the paper by Schaffer c.s. [47]. The structures are shown in Scheme 1. For the readers who are not necessarily interested in the details for each individual molecule, we first summarize our findings. The 19 molecular structures can be divided into three groups. The first group are those structures that do not reveal any additional steric or other strain effects and the GC model values agree well with the experimental and the G4 values. A second group is formed by those structures which have clear steric hindrance issues, and therefore the experimental and the GC model values do not agree. A third group consists of molecules that have, at first sight, no steric interactions, preventing good agreement between the experimental and the GC model values, but still these values do not agree. We have performed additional density-functional-theory-based quantum calculations and the results clarify the situation for molecules from both the second and the third group, which does mean, however, that a number of species cannot be appropriately described by the GC model due to steric interaction, something we have discussed before with regard to other molecules with steric effects [2].

For the first three entries (structures 1–3) the GC model and experimental values agree very well, within chemical accuracy, whereas the G4 values deviate from the experimental values by more than chemical accuracy. The G4 values for these species do not include conformational averaging. For all species this would involve a positive correction of several kJ/mol (see discussion in Ref. [4]), thus leading to a somewhat less negative heat of formation. For 2,2-difluorononane this brings the experimental and G4 values really very close. For structures 1–3 the gap between the experimental and the G4 values increases by a few kJ/mol.

For 1,1-difluoro-3-phenylpropane, structure 11, we observe reasonably good agreement though slightly beyond chemical accuracy, but the G4 value agrees with the GC model value very much within chemical accuracy. We applied the additional parameter related to the 1,1-difluoro group representing the specific F–F interaction in this configuration (magnitude −17.5 kJ/mol) as established previously [3]. C–F bonds are known to considerably strengthen each other when situated on a single carbon, an effect probably best attributed to cooperative electrostatic stabilization [48]. We note that we found an error for 1,1-difluoro-3-phenyl-propane in Ref. [3] in the calculation of the GC model value. It is, however, the model value, all GC parameter values were quoted correctly, and also the now correct GC model value is within chemical accuracy from the experimental value.

The former also implies that for CF₃ we have three such interactions involved. It will turn out to be a crucial parameter in accounting for, e.g., the heat of formation of 1,1,1-trifluoro-2-phenylethane (structure 15) and we subsequently observe pretty good agreement between the experimental and the G4 value and a difference between the model and the G4 value of about 10 kJ/mol. We observe a somewhat similar result for 1,1,1-trifluoro-2,2-diphenylethane, structure 16, with the experimental and the G4 values being very close and the GC model value being off these values by about 15 kJ/mol. The exact choice for the parameter associated with the 1,1,1-trifluoro group very much influences the difference between the experimental and the GC model values. More data would be required to arrive at a more detailed picture.

A seemingly sincere problem for the GC model concerns fluoromethylbenzene, structure 5. This is no peculiar molecule as no steric interactions are expected anywhere and therefore this molecule should be well accounted for by our GC model. However, whereas the experimental and G4 values agree very well, our GC value deviated by 22.4 kJ/mol from the experimental value with the GC value suggesting higher stability. We have performed B3LYP density functional theory type (B3LYP/6-311+G**) calculations on the hypothetical reaction

octane + fluoromethylbenzene → 3-fluorooctane + methylbenzene (toluene)

which revealed a higher stability in favor of the left-hand side of 25.3 kJ/mol which is to be compared to the 22.4 kJ/mol quoted before. Thus, all three values, experimental, GC model, and G4, are now in good agreement within chemical accuracy. It remains elusive why this molecule shows this additional contribution, as the structure does not give any straightforward indication. For a GC model it is problematic as it is not unlikely one would believe a, in the end, de facto incorrect prediction by such a model. Schaffer c.s. [47] also indicated what they called a “strain enthalpy”, the difference between the experimental and GC-based method they applied. For structure 5 its value was determined as 14.4 kJ/mol (this value could be compared to our value 22.4 kJ/mol, a difference due to the fact that the GC approaches are different). Schaffer c.s. attributed the difference to dipolar repulsion between the fluorine and the phenyl ring. Our DFT quantum calculations provided a direct independent quantitative correction accounting for the difference between our model and the experimental value.

From the structure we would not expect a serious problem for structure 8, 2-fluoro-2-methyl-1,3-diphenylpropane, and indeed we see almost perfect agreement between the experimental value, the GC model value, and the G4 quantum result. Structure 6, fluorocyclohexane, is also expected to be non-problematic and indeed the difference between the experimental and the GC model values is 2.4 kJ/mol and therewith within chemical accuracy. What we cannot explain is the relatively large, and unexpected, difference of 10 kJ/mol between the experimental and the G4 values.

For species structure 4, triphenyl(3-fluoropropane), we find a significant difference between the experimental and the GC model values, but when we compare it to triphenylmethane (Table 5) we must conclude that steric hindrance is the origin and we cannot account for this by a GC model in an appropriate way. Invoking density functional type quantum calculations to obtain relative energies between appropriate isomers could give a reasonably good estimate for the magnitude, leading to a better estimate of the heat of formation, an approach we reported before [4]. Because of the similarity of the structures, we can conclude the same for the structures 12 and 17. A similar problem is observed for 1,2-diphenyl-1,1-difluoroethane, structure 13, where we may expect some steric hindrance but the experimental and G4 values for the heat of formation differ by as much as 34 kJ/mol, a result we currently cannot rationalize.

A true problem concerns fluorodiphenylmethane (structure 7) which, regarding its structure, is highly similar to diphenylmethane which could be described well by our GC model (Table 5). However, for fluorodiphenylmethane we observe a difference of 12.9 kJ/mol between the experimental and the GC model values. Also unexpected is the larger difference between the experimental and the G4 values: 13.9 kJ/mol. The GC model value and the G4 value differ by, however, 26.8 kJ/mol. We do consider this unexpected as we have the evidence that diphenylmethane-related species can be sufficiently described by our GC model (Table 5). For diphenylmethane the experimental value of 165.0 ± 2.2 kJ/mol [39] is to be compared to the GC model value of 160.4 kJ/mol, and another comparison is for diphenylamine where we found a GC model value of 221.0 kJ/mol to be compared to an experimental value of 219.3 kJ/mol and a G4 value of 214.3 kJ/mol [5]. When we now consider B3LYP/6-311+G** density functional type calculations for (structure 7 related),

octane + fluorodiphenylmethane → 3-fluorooctane + diphenylmethane

the calculated energy change in this hypothetical reaction was calculated as −17 kJ/mol with the left-hand side with fluorodiphenylmethane being the less stable one. This result accounts semi-quantitatively (as one cannot expect a highly accurate result from our B3LYP calculations) for the difference between the experimental and the GC model values of −12.9 kJ/mol. As for structure 5, Schaffer c.s. [47] attributed the difference to dipolar repulsion between the fluorine and the phenyl ring. Thus, our DFT quantum calculations provided a direct independent quantitative correction accounting for the difference between our model and the experimental value but we cannot explain the issue with the G4 value.

A similar problem is observed for 1,2-diphenyl-1,1-difluoroethane, structure 13, where we may expect steric hindrance but we also find that the experimental and G4 values for the heat of formation differ by 34 kJ/mol. For 1,2-diphenyl-1,1-difluoroethane, structure 13, we considered the hypothetical reaction

octane + 1,1-difluoro-1,2-diphenylethane → 2,2-difluorooctane + diphenylethane

and found a B3LYP-calculated energy difference of 22.7 kJ/mol to be compared to the difference between the experimental and the GC model values of 62.6 kJ/mol. The B3LYP energy difference is very much off the other value, but here it is worthwhile to note that by correcting the GC model using the B3LYP-calculated energy difference we arrive at −296.9 kJ/mol which agrees very well with the G4 value of −294.4 kJ/mol. This puts some doubt on the correctness of the experimental value of −260.5 kJ/mol. Moreover, when we look at the structures 7, 8, and 13, structure 8 is the most free from steric effects and therefore the lowest strain energy is expected. In that respect, structure 13 looks, at least at first sight, intermediate to structures 7 and 8. This is more in line with our results than those from Schaffer c.s. [47] who reported 40 kJ/mol for the strain energy in structure 13. Schaffer c.s. reported a value of 36.7 kJ/mol for the strain energy for the highly congested structure 4 but a higher value (40 kJ/mol) for structure 13. In our view all these observations together suggest the experimental value from Schaffer et al. is not correct, and the G4 value is clearly preferred.

When we look at the geometries of structures 9 and 10, 1,3-diphenyl-(2-methylphenyl)2-fluoropropane and 1,3-diphenyl-(2-methylphenyl)2-fluoropropane, we may expect some steric hindrance but less than in structures 4, 12, and 17, which is indeed the case and exactly in the expected order when we look at the 3-D chemical structures. For both structures 9 and 10, however, we find good agreement between the GC model and the conformationally averaged G4 values, whereas the differences with the experimental values are much greater, 8 kJ/mol and 14 kJ/mol.

For the last two structures in Table 8, 1,2-diphenyl-1,1,2-trifluoroethane (structure 18) and 1,2-diphenyl-1,1,2,2-tetrafluoroethane (structure 19), we observe reasonable (11 kJ/mol difference) to good agreement (2.1 kJ/mol) between the experimental and the G4 values. For a quantum method which accounts very well for structure 19 there is no reason whatsoever why it would not for structure 18, and this therefore puts some doubt on the absolute accuracy of the experimental value for structure 18. The GC model values are much off, around 60 kJ/mol, and suggest higher stability than reality (experimental and G4 values). As it is not a priori obvious that the cause here is also steric hindrance we performed density functional type quantum calculations (B3LYP/6-311+G**) on the following hypothetical reactions:

octane + 4,4,5-trifluorodiphenylethane → 4,4,5-trifluorooctane + diphenylethane + 31 kJ/mol

octane + 4,4,5,5-tetrafluorodiphenylethane → 4,4,5,5-tetrafluorooctane + diphenylethane + 35 kJ/mol

In both cases the fluorosubstituted diphenylethane-involved side turned out to be less stable than the diphenylethane side. Whereas we cannot expect the B3LYP approach to give very precise results, the energy differences have the correct sign and reveal the correct order of magnitude.

Even though the procedure we followed using the B3LYP calculations is thought to be fully correct, to check we performed a similar set of calculations related to 2-fluoro-2-methyl-1,3-diphenylpropane, structure 8, as that compound has a GC model heat of formation value which differs by only 0.58 kJ/mol from the experimental value (structure 8 in Table 8). We thus consider the hypothetical reaction

octane + 2-fluoro-2-methyl-1,3-diphenylpropane → 3-fluoro-3-methyl-octane + 1,3-diphenylpropane

and the calculated energy difference was found as −3.8 kJ/mol. Because we have not checked whether we have the conformation with the lowest energy for 2-fluoro-2-methyl-1,3-diphenylpropane, the value −3.8 kJ/mol is an upper limit and the correct value is possibly (somewhat) closer to 0. This small value confirms that structure 8 is indeed strain-free and therefore the GC model accounts well for the heat of formation in agreement with the experimental value as well as excellent agreement with the G4 value of −133 kJ/mol. Thus, are B3LYP calculations reveal useful and correct information on energy differences not accounted for by the additive GC model, with particular quantitatively good estimates for smaller energy differences (structures 5 and 8).

In summary, our GC model could account well for about 50% of the heats of formation of the fluoro hydrocarbons when we compare to the available experimental data, viz. Table 8. In a number of other cases steric hindrance was very important and consequently the GC approach cannot be applied. Still, in a variety of cases (see discussion above) for molecules which did suffer from steric hindrance, we could rationalize the results by B3LYP DFT calculations. Obviously, for the latter class our GC model could not be applied (achieving a good performance) without such additional DFT work. A few unresolved issues remain. For fluorocyclohexane, structure 6, we cannot explain the relatively large, and unexpected, difference of 10 kJ/mol between the experimental and GC model values on the one hand and the G4 values on the other hand. The same applies to fluorotetradecane. One might suggest that the correction to the atomization energy is the origin, but for 2,2,-difluorononane we find very good agreement between the experimental and G4 values. We have clearly formulated arguments why the experimental value for 1,2-diphenyl-1,1-difluoroethane, structure 13, must be in error.

What is very peculiar is that for structures 4, 6, 7, 10, 13, 17, and 18 the difference between the experimental and the G4 values is more than 10 kJ/mol. In some cases we see good agreement between experiment and GC model, in other cases not. Now the question arises whether the problem is with the experimental values or with the G4 values. For fluorocyclohexane, structure 6, the relatively large and unexpected (no steric or dedicated electronic effects are expected) difference of 10 kJ/mol between the experimental and GC model values on the one hand and the G4 values on the other hand remains unexplained, with the G4 value more suspicious although we have no explanation why this would happen for this structure. For structure 4, triphenyl(3-fluoropropane), where we have clear strong steric effects, the case is less clear. For structure 13 we have already seen evidence that there is an issue with the experimental value. For 1,3-diphenyl-2-phenyl-2-fluoropropane, structure 10, we have very good agreement between the GC model and G4, suggesting a problem with the experimental value. Comparing structures 18 and 19, 1,2-diphenyl-1,1,2-trifluoroethane and 1,2-diphenyl-1,1,2,2-tetrafluoroethane, is very interesting. For structure 19 we see close G4 and experimental values, so why not for structure 18? The G4 method is well defined, and there is no argument to believe it works for one and not for the other of these two structures. The experimental determination of the heat of formation is all but direct, and it involves a number of steps and also issues like purity. The likelihood of an error in the experimental value is therefore larger, but in some cases (fluoroalkanes) the performance of the G4 method cannot be understood well.

3.3. Further Examples

Here we present several cases of molecules that were not involved in the parametrization before, so we purely use the established GC parameters to evaluate the heat of formation following our GC model. These examples are incorporated to illustrate that we have established a group contribution parametrization which produces reliable and accurate heats of formation, generally within chemical accuracy, of organic molecules.

3.3.1. Benzylalcohol

Our GC approach for benzylalcohol (below chemical structure) involves a phenyl group (+84.5), a CH₂ group (−20.63), a terminal OH group (−171), and the interaction term between a phenyl and an alkyl (+6), leading to −101.1 kJ/mol which is to be compared to the experimental value −100.4±1.3 kJ/mol given by Pedley c.s. [31].

3.3.2. β-Alanine

For β-alanine we do not expect any additional issues as the functional groups are clearly separated.

The experimental value of −421.2 ± 1.9 kJ/mol (quoted by Dorofeeva and Ryzhova [21]) is to be compared to the GC model value which is established by one carboxylic group, two methylene groups, and a terminal amino group: −391 – 2 × (20.63) + 13 = −419.3 kJ/mol. The GC model and experimental values are less than 2 kJ/mol apart.

3.3.3. Glycine

Here we may expect a potential interaction between the amino group and (one of) the oxygens. For the GC heat of formation we have a carboxylic group, one methylene group, and a terminal amino group which adds up to −391 −20.63 +13 (these numerical values can be found in the Excel file) = −398.6 kJ/mol which differs by 6.5 kJ/mol from the experimental value −392.1 ± 0.6 kJ/mol given by Pedley c.s. [31] and 4.9 kJ/mol from the experimental value −393.7 ± 1.5 kJ/mol recommended by Dorofeeva and Rhyzova [21].

3.3.4. Glutamic Acid (Amino Pentanedioic Acid)

The GC computed heat of formation reads 2 × (−391) [COOH] + 2 × (−20.63) [CH₂] + (−4) [CH]+ 3 [non-terminal NH₂] = −816.3 kJ/mol which is to be compared to the experimental value of −819.4 ± 4.0 (recommended by Dorofeeva and Rhyzova [21]).

3.3.5. Tyrosine

−391 [COOH] + 84.5 [phenyl] + 3 [non-terminal NH2] + (−4) [CH] + (−20.63) [CH2] + (−183.5) [OH] + 7 [phenol correction) + 6 [phenyl mono-alkyl subsitution] = −498.6 kJ/mol to be compared to the G4 value −497.4 kJ/mol reported by van der Spoel c.s. [18].

3.3.6. Alkyl Benzoates

Table 9. Experimental heats of formation [49,50] and GC model values for a series of benzoates. All values in kJ/mol.

Alkyl Benzoates	Experiment [49]	GC Model	GC Model-Exp
Methylbenzoate	−274.5	−271.9	2.6
Ethylbenzoate	−305.3	−305.5	−0.2
n-propylbenzoate	−331.3 ± 5.1	−326.1	5.2
methyl-2-methylbenzoate	−301.5 [50]	−308.2	−6.7
methyl-3-methylbenzoate	−309.6 [50]	−308.2	1.4
methyl 4-methylbenzoate	−308.7 [50]	−308.2	0.5
phenylbenzoate	−142.6	−145	−2.4

contains experimental [49] and GC model values for the heat of formation of a series of alkyl benzoates. The GC model values were simply calculated using previously established GC parameters [1,2,3,4,5]. We observe excellent agreement between experimental and GC model values that are within chemical accuracy except for when considering the much higher experimental error for n-propylbenzoate and the fact that for methyl-2-methylbenzoate steric hindrance is to be expected (as for similar species, see Ref. [5]) which would imply the experimental value is less negative than the model value which is indeed the case.

4. Discussion and Conclusions

In this work we extended the range of applicability of the GC approach we developed in five earlier publications [1,2,3,4,5]. We added further chemical groups including acetals, benzyl ethers, bicyclic hydrocarbons, alkanediols and glycerol, polycyclic aromatic hydrocarbons, aromatic fluoro compounds, and finally several species which we include to illustrate how the GC model can be successfully applied to species we did not consider during the parameterization of the GC model parameters. As before, the goal of chemical accuracy was achieved with exceptions, in particular when steric effects were significant. As in the previous publications we heavily refer to G4 quantum calculations which turned out to be a good reference in case experimental values are not available. Still, it had to be acknowledged that in some cases a significant difference between the experimental and G4 values was observed. In cases in which the GC model and G4 values agree well this puts doubt on the experimental value, but we also found cases in which the G4 value seems disputable although we did not find an explanation.

Overall, our studies [1,2,3,4,5] and the present paper have shown it is possible to arrive at a GC model to account for the heat of formation of organic molecules whilst, unprecedentedly, achieving chemical accuracy. Next to experimental data we relied on G4-calculated results which have been shown, by others as well as by ourselves, to provide very good values for the heats of formation. Steric hindrance may hamper the application of the GC model whilst still achieving good performance. However, as in previous publications we have demonstrated that when steric effects have a significant effect we can apply B3LYP type density-functional-theory-based quantum calculations to obtain a relatively good estimate of the effect and eventually arrive at a reasonably good value for the heat of formation. As long as one considers molecules which comprise the types of groups we have been discussing, good performance, largely within chemical accuracy, can be expected.

Attached to this paper are a manual and an Excel file enabling other researchers to readily apply the GC model developed in the five studies [1,2,3,4,5] and the current one.