A Database of Formation Enthalpies of Nitrogen Species by

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A Database of Formation Enthalpies of Nitrogen Species by Compound Methods (CBS-QB3, CBS-APNO, G3, G4) John M Simmie J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 30 Sep 2015 Downloaded from http://pubs.acs.org on October 3, 2015

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The Journal of Physical Chemistry

A Database of Formation Enthalpies of Nitrogen Species by Compound Methods (CBS-QB3, CBS-APNO, G3, G4) John M. Simmie∗ Combustion Chemistry Centre & School of Chemistry, National University of Ireland, Galway H91 TK33, Ireland E-mail: [email protected]

Abstract Accurate thermochemical data for compounds containing C/H/N/O are required to underpin kinetic simulation and modelling of the reactions of these species in different environments. There is a dearth of experimental data so computational quantum chemistry has stepped in to fill this breach and to verify whether particular experiments are in need of revision. A number of composite model chemistries (CBS-QB3, CBSAPNO, G3 and G4) are used to compute theoretical atomization energies and hence enthalpies of formation at 0 K and 298.15 K and these are benchmarked against the best available compendium of values, the Active Thermochemical Tables or ATcT. In general the agreement is very good for some 28 species with the only discrepancy being for hydrazine. It is shown that, although individually the methods do not perform that well, collectively the mean unsigned error is < 1.7 kJ mol−1 ; hence, this approach provides a useful tool to screen published values and validate new experimental results. ∗

To whom correspondence should be addressed

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Using multiple model chemistries does have some drawbacks but can produce good results even for challenging molecules like HOON and CN2 O2 . The results for these smaller validated molecules are then used as anchors for determining the formation enthalpies of larger species such as methylated hydrazines and diazenes, five and six membered heterocyclics via carefully chosen isodesmic working reactions with the aim of resolving some discrepancies in the literature and establishing a properly validated database. This expanded database could be useful in testing the performance of computationally less-demanding density function methods with newer functionals which have the capacity to treat much larger systems than those tested here.

Introduction The determination of basic thermochemical data by theoretical methods for molecules and transient species has now become de facto the main method of approach 1,2 given that classical experiments are no longer fashionable. Hence the increasing importance of theoretical methods which can be availed of by non-expert users but which nevertheless employ highlevel theories. The most stringent methods are currently approaches such as high-accuracy extrapolated ab initio thermochemistry or HEAT procedure, 3–5 focal point analysis, 6 the Wx family, 7–9 the Feller-Peterson-Dixon 10,11 or FPD approach, the ATOMIC protocol of Bakowies, 12 etc. Although these ‘exquisitely accurate’ methods 13 are being properly so described, they are somewhat restricted in their application to very small species and/or to expert users. At a lower level of theory model chemistries or compound methods such as the CBSx and G-n families have been extensively used because they provide a useful compromise between theoretical exactitude and computational expense. So, for example, CBS-APNO, G3 and G3B3 have been used by da Silva et al. 14 to characterize five-membered nitrogen heterocyclics highlighting a discrepancy in the experimental enthalpy of formation of the six-membered pyrimidine of up to 12 kJ mol−1 . 2 ACS Paragon Plus Environment

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Ashcraft and Green 15 carried out CBS-QB3 calculations of 105 non-cyclic C/H/N/O molecules to determine formation enthalpies, entropies and heat capacities — using these to construct group values for future application in automatic mechanism generation. Nitrile, nitro, nitroso, nitrite, nitrate, amine, imino and azo functional groups are to be found in their selection. He, Zhang and Gao 16 have examined the performance of 7 composite methods in computing the enthalpies of formation of 63 nitrogen-containing species via an atomization procedure; they showed that G4 performs best achieving a mean absolute deviation of 2.6 kJ mol−1 . More strikingly 98% of their species showed deviations of less than 6 kJ mol−1 from the experimental values. Dorofeeva et al. have also used G4 theory in both atomization and isodesmic incarnations to predict the formation enthalpies of some 29 azides basing their results on hydrazoic acid or hydrogen azide HN3 as the anchor. 17 Recently we 18,19 compared the results computed from five composite model chemistries of molecular and radical formation enthalpies of C/H/O species obtained by an atomization procedure against the values listed in the Active Thermochemical Tables (ATcT). 20–22 A comprehensive discussion of the statistical merits of employing methods singly or in pairs, etc was given there. It is important in expanding current databases that the ‘anchoring’ values be comprehensively validated so that results based on them can be relied on. For example, Notario and co-workers 23 have recently shown that the thermochemistry of alkyl-substituted hydrazines and amines requires further study — given that, it is crucial to ensure that the values for the parent molecules, in this case hydrazine and ammonia, should be well-established. Suntsova and Dorofeeva 24 have shown that the experimental gas-phase enthalpies of formation of many aliphatic nitro and nitramines are incompatible with quantum chemical computations. In this work the focus of attention is on a selection of C/H/N/O compounds using the same protocols as previously, firstly, to check that the methodology employed is in good agreement with the ATcT, secondly, where it is not to identify these outliers and verify by



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independent means the reasons for the disagreement, and, thirdly, to use these now validated species as chaperons in the construction of isodesmic working reactions to tackle much larger molecules whose experimental values may be conflicted.

Computational Methodology Four compound methods have been chosen for benchmarking as part of this work ; CBSQB3, 25 CBS-APNO, 26 G3 27 and G4 28 as expressed in the application Gaussian. 29 For the computation of 0 K enthalpies of formation, ∆f H0 , the theoretical atomization energy, TAE0 , for the reaction: Cm Hn Np Oq → m C(3 P0 ) + n H(2 S1/2 ) + p N(4 S3/2 ) + q O(3 P2 )

must be calculated; this is given by:

TAE0 = m H0 (3 C) + n H0 (2 H) + p (4 N)q H0 (3 O) − H0 (Cm Hn Np Oq )

where H0 is the 0 K enthalpy of an atom or molecule, and is the sum of the electronic and zero-point energies. Zero-point energies are automatically computed, adjusted by a built-in scale factor and added to the 0 K electronic energy by each compound method as part of its pre-defined series of computations. The ∆f H0 of the molecule then follows knowing the theoretical atomization energy and the experimentally known formation enthalpies of the gaseous component atoms, Table 1: [ ] ∆f H0 (Cm Hm Np Oq ) = m ∆f H0 (3 C) + n ∆f H0 (2 H) + p ∆f H0 (4 N) + q ∆f H0 (3 O) − TAE0

It is to be noted that the four methods use a variety of approaches to compute the optimized geometry and consequently the vibrational frequencies; these range from Hartree-Fock


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Table 1: Gaseous atomic formation enthalpies 30 / kJ mol−1 T /K 0 298.15

C (3 P ) H (2 S1/2 ) N (4 S3/2 ) O (3 P2 ) 711.38 216.034 470.573 246.844 716.87 217.998 472.435 249.229

Uncertainty C ±0.057, H ±0.000, N ±0.024, O ±0.002

to B3LYP with unique basis sets. Two of the methods apply a second optimization after the frequency calculation, whilst subsequently 3 to 6 single point corrections are included, along with some empirical corrections, using a variety of methods such as CCSD(T), QCISD(T), MP2 and MP4 as well as basis set extrapolations. The very diversity of approaches, each of which is subject to unique systematic errors, renders the final result, the averaged atomization energy, TAE0 , somewhat less reliant on the precise nature of each methodology because of the variety of theoretical approaches and corrections employed. It must be emphasized that each model chemistry employs unique recipes to arrive at a result for the structure, energies, enthalpies, etc of a particular species. Needless to say these composite methods lack the rigor of the current best theories such as CCSDTQ 31 or even the thermochemical methodologies discussed earlier but they are affordable for the species under consideration here. All of the compound methods employed here are based on single-determinantal wave functions which either neglect or give an incomplete treatment of electron correlation — one of the main sources of error in ab initio molecular electronic calculations. A quantitative measure of their need is given by the T1 diagnostic of Lee and Taylor; 32 values larger than 0.02 indicating that they are required. Thus the interesting molecule nitrosyl-O-hydroxide, 33 HOON, has a T1 of 0.032 and does not give satisfactory results with the methods in use here and neither does CH3 OON. In appropriate cases some vibrational modes were treated as hindered rotors and the reported Gaussian-09 298.15 K enthalpies and Gibbs free energies corrected. Hindered rotor corrections, 34–38 computed via Gaussian-09, applied to the determination of reaction enthalpies in the isodemic examples are quite small and do not exceed 0.1 kJ mol−1 gen5 ACS Paragon Plus Environment


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erally and are thus ignored. For the more direct atomization calculation the correction for tetramethylhydrazine, for example, amounts to only 0.6 kJ mol−1 .

Results and Discussion The results of the calculations are shown in Tables 2 and 3; the first Table only compares the ATcT value to the mean over the four composite methods or ‘all methods average’, ∆f H ◦ , and the associated uncertainty defined here as the standard deviation, ± σ. The second Table compares the computed formation enthalpies at 298.15 K to the ATCT value and its associated uncertainty.

0K In general terms the agreement between the computed mean values and the ATcT Tables is extremely good as with previous conclusions 18,19 on the ability of the composite methods taken as a whole to approach ‘chemical accuracy’, that is, a mean unsigned error of −0.59 and a population standard deviation of 5.40, both in kJ mol−1 . Hydrazine (diazane), H2 N−NH2 , appears as an outlier for which all four methods consistently predict higher values of the formation enthalpy at 0 K of 4.2 to 8.6 kJ mol−1 . The average formation enthalpy of 115.4 ± 2.0 kJ mol−1 corresponds to a mean total atomization energy, TAE0 , of 1, 689.9 ± 2.0 kJ mol−1 in very good agreement with coupled-cluster computations combined with interference-corrected explicitly correlated second-order perturbation theory 39 of 1,691.5 kJ mol−1 . These are to be compared with the ATcT equivalent of 1, 695.6 ± 0.2 kJ mol−1 . Most recently Chan and Radom 40 have developed a cost-effective method, W3X-L, which builds on an accurate approximation to the all-electron scalar-relativistic CCSD(T)/CBS energy (W2X) together with additional post-CCSD(T) treatment. Geometry optimization and frequency calculations are undertaken at B3LYP/cc-pVTZ+d with differing scaling factors


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Table 2: Formation enthalpies at 0 K / kJ mol−1 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 †

Species QB3 APNO G3 G4 ATcT ∆f H ◦ Hydrogen azide HNNN 297.2 296.4 303.0 294.5 298.13 297.8 ± 3.6 Nitrosyl hydride HNO 105.6 112.0 113.3 107.8 109.89 109.7 ± 3.6 Peroxy nitrous acid −2.1 7.4 12.5 7.3 7.57 6.2 ± 6.1 Nitrous acid trans −78.4 −72.2 −68.8 −73.5 −73.044 −73.2 ± 4.0 Nitrous acid cis −76.6 −70.0 −66.1 −70.8 −71.25 −70.9 ± 4.3 Hydroxylamine trans −36.4 −31.1 −29.4 −31.1 −33.12 −32.0 ± 3.0 Hydroxylamine cis −18.3 −13.7 −11.2 −13.5 −14.7 −14.2 ± 3.0 Ammonia oxide 66.9 73.3 76.9 72.8 72.3 72.5 ± 4.1 Ammonia −37.1 −38.4 −35.7 −35.7 −38.565 −36.7 ± 1.3 Nitric acid −137.7 −128.1 −122.7 −127.7 −124.45 −129.0 ± 6.3 Diazene trans E 208.2 212.0 212.8 206.9 207.36 210.0 ± 2.9 Diazene cis Z 229.7 233.8 235.0 228.4 229.60 231.7 ± 3.2 Isodiazene 305.9 311.2 312.8 306.0 308.00 309.0 ± 3.5 Hydrazine 113.8 114.6 118.2 114.8 109.66 115.4 ± 2.0 Hydrogen cyanide 133.0 134.2 131.6 128.6 129.675 131.8 ± 2.4 Hydrogen isocyanide 191.9 194.2 192.0 190.5 191.58 192.1 ± 1.5 † Isofulminic acid HONC 230.2 234.3 234.8 230.6 234.68 232.5 ± 2.4 Fulminic acid HCNO† 164.1 170.4 169.7 167.0 170.8 167.8 ± 2.9 Isocyanic acid HNCO −118.7 −117.5 −117.6 −116.0 −116.06 −117.6 ± 0.8 Cyanic acid HOCN −14.5 −9.9 −12.1 −13.8 −12.25 −12.6 ± 2.0 Methylenimine 97.5 97.9 97.8 95.3 96.61 97.1 ± 1.2 Methylamine −4.9 −8.3 −3.8 −4.7 −5.83 −5.4 ± 2.0 Dimethylamine 6.4 0.7 7.3 6.1 6.02 5.1 ± 3.0 Cyanogen NCCN 310.6 311.8 306.3 302.5 308.16 307.8 ± 4.2 Isocyanogen CNCN 409.0 414.9 409.1 405.6 410.7 409.6 ± 3.9 Diisocyanogen CNNC 608.5 613.8 610.7 602.8 610.1 609.0 ± 4.6 Nitrosobenzene 216.9 208.9 219.5 214.3 215.6 214.9 ± 4.5 Trimethylamine 3.4 −4.8 4.0 3.4 4.54 1.5 ± 4.2

The chemical structures shown in ATcT v1.112 are incorrect.



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for the zero-point energy, the entropy and the enthalpy function. They claim that W3X-L provides the highest-level theoretical values now available for the thermochemical quantities in the G2/97 test set. 41 Interestingly their formation enthalpy at 0 K of 112.1 kJ mol−1 lies some 2.5 kJ mol−1 higher than the ATcT value and 3.3 kJ mol−1 lower than the value obtained in this work. An ‘unusually large discrepancy’ had been flagged by Karton et al. 42 in a series of W4 calculations 9 which found a TAE0 of 1,693.5 kJ mol−1 . Their results were close to an earlier attempt by the Karlsruhe group 43 of 1,694.0 kJ mol−1 and an FPD calculation 10 of 1, 693.9± 1.7 kJ mol−1 . Earlier Matus et al. 44 used the FPD approach of coupled cluster theory CCSD(T) and augmented correlation consistent basis sets, aug-cc-pVnZ, up to quintupleζ including core-valence, scalar relativistic corrections and scaled zero point energies to compute ∆f H ◦ (0K) of 111.3 (TAE0 = 1, 694.0) and ∆f H ◦ (298.15K) of 96.6 kJ mol−1 . Thus the high-level results are somewhat at odds, although they all unanimously predict higher ∆f H’s than the ATcT recommendation, and further work would be desirable to clarify the situation particularly as, to be shown later, the experimental picture is not clearcut. Difficulties were encountered for peroxynitrous acid, HOON−O, which exists in three conformational forms in which the OONO dihedral is either trans or cis and the H-atom is in plane or perpendicular to the plane. The two lowest energy forms did not converge and only the results for the least stable ‘trans/perp’, with dihedrals of OONO ∼ 176◦ and NOOH ∼ 100◦ , are shown; these difficulties were previously reported by McGrath and Rowland. 45 At both CBS-QB3 and W1BD 46 level the relative energies are in excellent quantitative agreement with their conclusions that ‘cis/cis’ < ‘cis/perp’ < ‘trans/perp’. Amongst the 28 species listed there are 6 clusters which bear further examination. For example, for the cyanogens, C2 N2 ,the difference between the ATcT value and the mean value computed here is a consistent +0.4 → +1.1 kJ mol−1 which given the 300 → 600 kJ mol−1 range in formation enthalpies is encouraging agreement. However for the cyanic/fulminic acids and their isomers the difference increases to as much as 3.0 kJ mol−1 for fulminic acid


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HNCO whereas the difference is only 0.3 kJ mol−1 for cyanic acid HOCN. As noted above only hydrazine appears to be the exception to the generally good agreement and a visual illustration of the Table 2 data can be seen in a Bland Altman 47 or Tukey ∑ mean-difference plot, Figure 1. The mean difference or bias, defined as ni (ATcT−∆f H ◦ )/n, and the associated 95% confidence intervals, ∼ 1.96 σ, where σ is the standard deviation, are also shown together with the standard errors in the bias and the limits of agreement.

Figure 1: Average formation enthalpy at 0 K, (ATcT + mean)/2, versus difference between ATcT and the mean of the four model chemistries, (ATcT – mean); — bias, - - - 95% limits of agreement (kJ mol−1 ).



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Table 3: Formation enthalpies at 298.15 K / kJ mol−1 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Species QB3 APNO G3 G4 ATcT This work Hydrogen azide 291.0 290.1 296.7 288.2 291.83 ± 0.58 291.5 ± 3.7 Nitrosyl hydride 103.2 109.6 110.8 105.4 106.92 ± 0.11 107.2 ± 3.6 Peroxynitrous acid −7.8 1.1 6.3 1.6 0.49 ± 0.42 0.3 ± 5.9 Nitrous acid trans −83.6 −77.6 −74.1 −78.7 −78.701 ± 0.08 −78.5 ± 3.9 Nitrous acid cis −82.1 −75.6 −71.7 −76.3 −77.61 ± 0.39 −76.4 ± 4.3 Hydroxylamine trans −46.4 −41.0 −39.4 −40.9 −43.50 ± 0.49 −41.9 ± 3.1 Hydroxylamine cis −28.4 −23.8 −21.3 −23.6 −25.20 ± 1.5 −24.2 ± 3.0 Ammonia oxide 56.2 62.7 66.3 62.1 61.1 ± 1.7 61.8 ± 4.2 Ammonia −44.1 −45.4 −42.7 −42.8 −45.558 ± 0.03 −43.7 ± 1.3 Nitric acid −146.0 −136.6 −131.2 −136.0 −134.16 ± 0.18 −137.4 ± 6.2 Diazene trans E 201.0 204.9 205.6 199.7 200.22 ± 0.56 202.8 ± 2.9 Diazene cis Z 222.6 226.7 227.8 221.2 222.47 ± 0.83 224.6 ± 3.2 Isodiazene 298.9 304.1 305.8 298.9 300.94 ± 0.81 301.9 ± 3.6 Hydrazine 99.3 100.0 103.7 100.3 95.51 ± 0.19 100.8 ± 2.0 Hydrogen cyanide 132.9 134.0 131.4 128.5 129.292 ± 0.10 131.7 ± 2.4 Hydrogen isocyanide 192.5 194.7 192.7 191.0 191.96 ± 0.57 192.7 ± 1.5 Isofulminic acid 229.4 233.5 234.1 229.7 233.15 ± 1.02 231.7 ± 2.4 Fulminic acid 163.5 167.8 168.0 166.7 169.3 ± 1.2 166.5 ± 2.1 Isocyanic acid −120.8 −119.6 −119.6 −118.8 −119.05 ± 0.37 −119.7 ± 0.8 Cyanic acid −16.3 −11.8 −13.9 −15.6 −14.86 ± 1.01 −14.4 ± 2.0 Methylenimine 89.9 90.3 90.2 87.7 88.70 ± 0.98 89.5 ± 1.2 Methylamine −19.7 −23.0 −18.5 −19.4 −20.91 ± 0.53 −20.2 ± 2.0 Dimethylamine −14.9 −20.5 −13.8 −15.1 −15.89 ± 0.69 −16.1 ± 3.0 Cyanogen 312.8 313.9 308.7 304.7 310.10 ± 0.43 310.0 ± 4.2 Isocyanogen 411.7 417.6 411.9 408.2 413.0 ± 1.6 412.3 ± 3.9 Diisocyanogen 612.0 617.3 614.4 605.9 613.0 ± 1.7 612.4 ± 4.9 Nitrosobenzene 202.1 194.1 205.0 199.7 198.6 ± 1.5 200.2 ± 4.6 Trimethylamine −24.3 −32.4 −23.4 −24.2 −24.02 ± 0.64 −26.1 ± 4.3


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298.15 K Discussion of agreement at 298 K Hydrazine has been somewhat problematic with experimental values 48,49 for ∆f H ◦ (298.15 K) ranging from 50.42 to 150 kJ mol−1 before a 1998 review by Chase 50 settled on 95.35 kJ mol−1 based in essence on work by Hughes et al. 51 Note that values for the methylsubstituted hydrazines 52,53 are anchored on that for hydrazine and that practical devices, such as hydrazine thrusters whose output ranges from 1 to 400 N, are in common usage for attitude control in satellites, spacecraft, space probes and launch vehicles. Calculation of the useful output energy derived from using hydrazine does depend upon accurate knowledge of √ its thermochemical properties since the specific impulse is approximately ∝ (Q/M ) where Q is the energy release and M the molecular masses of the exhaust gases. 54 Hydrazine is a major industrial commodity and an experimental re-determination of its heat of combustion or other relevant thermochemical datum would be most useful in resolving the issue. Nitric acid is possibly somewhat on the high side at −134.16 ± 0.18 kJ mol−1 since an atomization value of −137.4 ± 6.2 kJ mol−1 indicates otherwise as do isodesmic reactions involving the chaperons HNC/HONO/HONC and HCN/HONO/HOCN both of which indicate a value nearer −135.8 kJ mol−1 but not the working reaction with HCN/HONO/HCNO which results in −132.5 kJ mol−1 . This is an indication that the tabulated value for fulminic acid HCNO is not consistent as adverted to earlier. Paradoxically the computed reaction enthalpy change for the reaction:

HCNO + HOCN −→ HNCO + HONC of −40.11 ± 1.49 is almost identical to that calculated directly from the ATcT recommended enthalpies of formation of −40.34 kJ mol−1 but this agreement is somewhat fortuitous because the large positive difference, (ATcT – ∆f H ◦ ), encountered for HCNO of 2.79 is counterbalanced by the smaller positive differences for HNCO and HONC of 0.63 and 1.49 re11 ACS Paragon Plus Environment


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spectively and the small negative difference for HOCN of −0.44 which result in a difference of the reaction enthalpies of 0.63 + 1.49 − (−0.44) − 2.79 = −0.23, all in kJ mol−1 . The literature is somewhat ambiguous with Dorofeeva et al. 55 settling on −134.3 ± 0.5 kJ mol−1 which in essence was the average of a number of previous experimental values and by an ab initio isodesmic calculation — the latter however was obtained at a low level of theory. Although the literature generally refers to a review by Chase 50 which is itself based on a weighted average of a number of results dating back to the 1930s. Suntsova and Dorofeeva 24 have shown, in calculations of a series of some 57 aliphatic nitro and nitramines, that the G4 model chemistry tends to underestimate formation enthalpies when the atomization method is employed. This observation is not inconsistent with the results in Table 3, for those compounds with ∆f H ◦ > 0, and hydrazine is again exceptional.

Methylated hydrazines In a G4 series of calculations Notario et al. 23 pointed out a number of discrepancies and fundamental problems with some early experimental determinations of ∆f H ◦ (298.15 K) for methylated hydrazines and amines. Their results, and, associated values 53,56,57 for the hydrazines are shown in Table 4. In general there is good agreement with the G4 values computed in this work, normally within 0.5 kJ mol−1 which probably arises from different choices for the formation enthalpies of the C/H/N atoms. The glaring exception is that for monomethylhydrazine, CH3 NHNH2 , which differs by ≈ 10 kJ mol−1 . Monomethylhydrazine or MMH is conformationally diverse with ‘trans’ and ‘cis’ forms most usefully visualised by inserting a dummy atom at the midpoint of the two H-atoms bonded to nitrogen to generate XNNC dihedrals of 142.4 and 25.7◦ respectively at B3LYP/631G(2df,p), the combination used in G4 geometry optimisations. Inspection of both forms reveals that in essence inversion is occurring at both nitrogen centers. The ‘cis’ form is the more stable by some 3 kJ mol−1 ; the full relaxed potential energy scan is quite complex in contrast to the well-behaved 3-fold symmetric methyl rotor. The trimethylhydrazine can 12 ACS Paragon Plus Environment

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also be categorised in this fashion with notional ‘cis’ and ‘trans’ conformers; but the ‘trans’ is now more stable by ≈ 10 kJ mol−1 . Similarly, 1,2-dimethylhydrazine (unsymmetrical dimethylhydrazine or UDMH) exists with trans and cis CNNC dihedrals of −164.9 and −44.1◦ respectively with the former being some 5.8 kJ mol−1 more stable. The tetra-substituted hydrazine, like hydrazine and 1,1dimethylhydrazine (symmetrical dimethylhydrazine or SDMH), is conformationally unique. In Table 4 it is assumed that the literature values from theoretical studies pertain to the lowest energy conformer in the absence of this distinction having been explicitly made by previous workers. Table 4: Methylated hydrazines, ∆f H ◦ (298.15 K) / kJ mol−1 Species monomethyl ‘trans’ ‘cis’ monomethyl 1,1-dimethyl 1,2-dimethyl trans cis 1,2-dimethyl trimethyl ‘cis’ ‘trans’ trimethyl tetramethyl

QB3 98.6 95.8 96.5 83.8 97.0 103.3 97.3 93.9 83.8 84.0 82.8

APNO 97.7 94.1 94.9 80.3 94.0 98.9 94.4 87.7 78.3 78.5 74.4

G3 103.1 100.1 100.8 87.9 101.2 106.8 101.6 97.0 87.3 87.5 85.2

G4 98.8 95.8 96.7 83.9 96.3 102.5 96.7 93.6 83.4 83.6 82.6

∆f H ◦ 99.5 ± 2.4 96.4 ± 2.6 97.2 ± 5.3 84.0 ± 3.1 97.1 ± 3.0 102.9 ± 3.3 97.5 ± 4.9 93.0 ± 3.9 83.2 ± 3.7 83.4 ± 3.9 81.3 ± 4.7

Literature 90.7 53 108.2 23 94.6 ± 0.6 56 83.9 ± 3.2 56 79.7 53 83.4 23 92.7 53 95.8 23 92.0 ± 4.2 56 78.6 53 82.4 23 76.4 53 80.7 23

In order to compare results with those in the compendium, “Thermochemical Data of Organic Compounds”, 56 the computed values have been weighted according to the population distributions of each conformer derived from Gibbs free energies; the species names are shown highlighted in Table 4.



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Isodesmic validation Independently of the atomization calculations it is possible to check that the results obtained are self-consistent. For example:

NH3 + (CH3 )3 N −→ (CH3 )NH2 + (CH3 )2 NH should result in an enthalpy change, ∆r H(298.15 K) of 32.78±1.08 kJ mol−1 on adopting the ATcT values. The mean computed enthalpy change is 33.55±0.78 kJ mol−1 thus establishing a degree of confidence in the tabulated values. A different, more piecemeal, approach is to compute the formation enthalpy of a target compound by employing isodesmic working reactions with well-known chaperons in which the cancellation of error plays a big part. In the following Sections this approach is used to double-check values for some of the more obscure species and to extend the database by considering slight changes in the molecular framework, for example, H2 NNH2 ⇒ CH3 NHNH2 , and, later, more profound changes.

Nitrogen hydride oxide or ammonia oxide Ammonia oxide, H3 NO, ‘a small elusive molecule’ as described by Wang and Mannan 58 is an isomer of hydroyxlamine, NH2 OH. They recommended a value of 55.7 ± 2.9 kJ mol−1 based on working reaction {1}, Table 5, and averaged over six composite methods, only one of which, namely G3, is used here. Their value for ammonia, which they employed as a chaperon, lies some 1.6 kJ mol−1 lower than the recommended value so in turn that means that their ammonia oxide value is also too low and should be closer to 57.3 kJ mol−1 . A grand weighted-average of 60.3 ± 1.1 kJ mol−1 is indicated here from reactions {1}–{3} in agreement with the atomization value of 61.8 ± 4.2 kJ mol−1 and the ATcT of 61.1 ± 1.7 kJ mol−1 . Note that reaction {2} in Table 5 leads to an anomalously high value for the target molecule; a reflection of our earlier finding that fulminic acid HNCO is more stable


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by about 3 kJ mol−1 than the ATcT value. Fortunately this has little effect on the final computed number that emerges because the most uncertain values contribute least to the overall result. The mean total atomization energy at 0 K of 1, 293.1±4.1 compares very favourably with that calculated by Vogiatzis et al. 39 of 1,292.1 kJ mol−1 if somewhat less so with Klopper et al. 43 of 1,290.5 kJ mol−1 using different versions of coupled-cluster explicitly-correlated perturbation theory. Table 5: Isodesmic reactions to determine ammonia oxide / kJ mol−1 {1} ∆f H ◦ u {2} ∆f H ◦ u {3} ∆f H ◦ u

H3 NO + H2 O = H2 O2 + NH3 ∆r H 59.01 −241.822 −135.442 −45.558 1.81 1.52 0.027 0.064 0.03 1.52 H3 NO + HCN = HCNO + NH3 ∆r H 65.14 129.291 169.3 −45.558 −70.69 3.56 0.10 1.2 0.03 3.35 H3 NO = NH2 OH ∆r H 60.85 −25.20 −86.05 1.97 1.5 1.27

Methyl amines To determine monomethylamine, isodesmic reactions can be based on well-known anchors, all of whose values are taken from the ATcT: Table 6: Isodesmic reactions to determine methylamine / kJ mol−1 {4} ∆f H ◦ u {5} ∆f H ◦ u {6} ∆f H ◦ u

CH3 NH2 + C6 H6 = NH3 + C6 H5 CH3 ∆r H −21.72 83.18 −45.558 50.41 −56.61 1.00 0.26 0.03 0.37 0.89 CH3 NH2 + C2 H6 = NH3 + C3 H8 ∆r H −22.11 −83.78 −45.558 −104.39 −44.06 1.03 0.17 0.03 0.29 0.98 CH3 NH2 + CH3 OH = NH3 + CH3 OCH3 ∆r H −20.52 −200.71 −45.558 −184.02 −8.34 1.21 0.18 0.03 0.44 1.11

The computed reaction enthalpies range from −56.6 kJ mol−1 for reaction {4} to −8.3 kJ mol−1 for reaction {6} but the absolute uncertainties are small in each case, Table 6. 15 ACS Paragon Plus Environment


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The final grand weighted value for methylamine is thus −21.6 ± 0.6 kJ mol−1 which is in satisfactory agreement with ATcT’s −20.91±0.53 and the atomization number of −20.2±2.0 kJ mol−1 , Table 3. Dimethylamine now follows from (CH3 )2 NH + NH3 = 2 CH3 NH2 to yield −15.8 ± 0.8 versus −16.1 ± 3.0 kJ mol−1 from atomization and trimethylamine similarly −24.8 ± 1.2 kJ mol−1 (atomization −26.1 ± 4.3 kJ mol−1 ). In summary a consistent set of values for these multiply-substituted amines.

Methyl hydrazines An exactly similar series of calculations for cis monomethylhydrazine together with the inclusion of another isodesmic involving NH3 and CH3 NH2 , and based on the ATcT value for hydrazine of 95.51±0.19 kJ mol−1 (which replaces ammonia in the sequence of reactions {4}– {6} above), results in a final value of 91.53 ± 0.44 kJ mol−1 . This is at variance with the atomization-derived value of 96.43 ± 2.55 kJ mol−1 . Adoption of a ∆f H ◦ (298.15 K) value of 100.8 ± 2.0 kJ mol−1 for hydrazine, the atomization derived value shown in Table 3, implies an isodesmic value of 96.9 ± 1.1 kJ mol−1 for cis monomethylhydrazine which is now in excellent agreement with the atomization-derived enthalpy of 96.4 ± 2.6 kJ mol−1 . In turn that implies a ∆f H ◦ (298.15K) of 97.7 kJ mol−1 for monomethylhydrazine since the trans/cis difference amounts to 3.11 ± 0.32 kJ mol−1 and the ratio cis:trans=0.75:0.25. Kanno et al. 59 showed from explicitly correlated RHF-UCCSD(T)-F12 calculations with VDZ-F12 basis sets at a ωB97X-D/6-311++G(d,p) geometry that an enthalpy of formation of 109.85 kJ mol−1 is indicated for the ‘cis’ conformer of methylhydrazine; this was estimated from the enthalpy difference from H2 , N2 , and C. This could be interpreted as an indication that a higher value is most likely for the monomethyl derivative and thus supporting a higher value for the parent hydrazine. Values for the so-called unsymmetrical dimethylhydrazine UDMH or (CH3 )2 NNH2 , can


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be derived via two isodesmic reactions:

(CH3 )2 NNH2 + NH3 −→ CH3 NHNH2 + CH3 NH2 (CH3 )2 NNH2 + 2 C6 H6 −→ N2 H4 + 2 C6 H5 CH3 for which reaction enthalpies of 36.03 ± 0.55 and −49.20 ± 1.76 kJ mol−1 respectively result leading to a grand weighted average of 85.3 ± 1.2 kJ mol−1 as against an atomization value of 84.0 ± 3.1 kJ mol−1 . The symmetrical compound trans SDMH, CH3 NHNHCH3 , follows from a direct comparison where ∆f H ◦ (SDMH) = ∆f H ◦ (SDMH) + (13.12 ± 0.51) = 98.5 kJ mol−1 cf. 97.1 ± 3.0 kJ mol−1 . The more stable trans conformer of trimethylhydrazine averages at 86.1±1.2 (atomization 83.2 ± 3.7) kJ mol−1 with the cis conformer less stable by 9.83 ± 0.37 kJ mol−1 . Finally for the tetra compound a value of 84.5 ± 1.5 is obtained in only moderate agreement with the atomization 81.3 ± 4.7 kJ mol−1 . The values obtained from isodesmic reactions and from atomization calculations for the methyl-substituted hydrazines cannot be easily reconciled by employing the ATcT of 95.5 kJ mol−1 for hydrazine nor with using the atomization value from this work of 100.8 kJ mol−1 ; however a compromise value, based on the isodesmic procedure shown below, of 99.43 ± 0.94 kJ mol−1 can do so. In the absence of reliable calorimetric data — the study of Aston and co-workers 60 on 1,2-dimethylhydrazine exemplifies the considerable difficulties faced by experimentalists dealing with these compounds with 14 out of 15 runs failing to combust properly — the compromise value for hydrazine is used as an anchor, Table 7. The conclusion from the above analysis is that an anchor value for hydrazine of ∼ 100 kJ mol−1 is required in order to rationalize the thermochemistry of the methylhydrazines. An independent evaluation of hydrazine itself is possible by utilising working reactions involving the conformers of diazene, NH−NH: ethene/trans diazene/ethane, ethene/cis diazene/ethane and cyclopropene/trans diazene/cyclopropane. The reaction enthalpies of



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Table 7: Methylated hydrazines, ∆f H ◦ (298.15 K) / kJ mol−1 molecule hydrazine monomethyl ‘cis’ ‘trans’ 1,1-dimethyl 1,2-dimethyl trans cis trimethyl ‘trans’ ‘cis’ tetramethyl

isodesmic atomization 99.4 ± 1.0 100.8 ± 2.0 95.5 ± 1.1 96.4 ± 2.6 98.6 ± 1.1 99.6 ± 2.4 83.9 ± 1.2 84.0 ± 3.1 97.3 ± 1.8 97.1 ± 3.0 103.0 ± 1.8 102.9 ± 3.3 84.9 ± 1.2 83.2 ± 3.7 94.1 ± 1.2 93.0 ± 3.7 83.6 ± 1.3 81.3 ± 4.7

−36.20 ± 0.90,−14.45 ± 1.08 and −128.52 ± 1.06 kJ mol−1 feed through to ∆f H(0 K) for hydrazine of 114.4, 114.8 and 114.0 kJ mol−1 , respectively, leading to a final value of 114.4±0.8 kJ mol−1 in excellent agreement with the atomization value presented earlier of 115.4 ± 2.0 kJ mol−1 . Similarly at 298.15 K the same systems give rise to reaction enthalpies of −36.06 ± 0.90, −14.31 ± 1.09 and −129.39 ± 1.04 kJ mol−1 , respectively, which result in ∆f H ◦ (298.15 K) of 99.9, 100.4 and 99.3 kJ mol−1 leading to a final value of 99.9 ± 0.8 kJ mol−1 emerges which is consistent with the atomization value of 100.8 ± 2.0 kJ mol−1 . Whilst it might be argued that the over reliance on the diazenes compromises these computations high-level CCSD(T)/CBS calculations by Matus et al., 44 Martin and Taylor 61 and by Chan and Radom 62 for diazenes agree both with ATcT and with the values computed here.

Other methyl derivatives For each of the other species present in Table 3 the substitution of a methyl group for hydrogen was attempted where feasible using exactly the same methodologies as outlined above. The results are presented in Table 8. There are very few previous values in the literature with which one could compare but Pasinszki and Westwood 71 have shown from CCSD(T) calculations that the relative energies


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Table 8: Methylated species, ∆f H ◦ (298.15 K) / kJ mol−1 molecule CH3 CN CH3 NC CH3 NCO CH3 OCN CH3 CNO CH3 ONC CH3 N3 CH3 ONO2 CH3 NNH cis CH3 NNH trans CH3 (H)NN CH3 NNCH3 cis CH3 NNCH3 trans (CH3 )2 NN CH3 NO CH3 NO2 CH3 ONH2 cis CH3 ONH2 trans

isodesmic 74.4 ± 1.6 175.0 ± 1.1 −108.9 ± 1.6 2.2 ± 1.3 127.7 ± 1.7 240.7 ± 1.3 296.3 ± 0.7 −124.9 ± 1.2 194.5 ± 1.1 177.9 ± 1.1 275.6 ± 1.0 193.8 ± 2.0 155.2 ± 1.9 254.7 ± 1.2 72.7 ± 1.1 −76.4 ± 0.7 −18.7 ± 1.9 −28.9 ± 1.0

atomization 75.3 ± 1.9 175.9 ± 1.7 −108.4 ± 1.1 2.8 ± 0.9 125.0 ± 2.5 239.3 ± 1.8 295.5 ± 4.2 −128.1 ± 6.1 195.3 ± 2.9 178.6 ± 2.8 276.7 ± 3.0 194.7 ± 2.9 156.1 ± 2.8 255.9 ± 2.8 71.3 ± 2.9 −77.5 ± 3.9 −17.5 ± 3.3 −27.7 ± 2.7

literature 74.04 ± 0.37 63 65.86 64 73.6 65 80.3 15 163.5 ± 7.2 56 172.9 ± 1.0 66 174.9 65 4.60 15 2.9 65

296.5 67 297.9 17 −122.2 ± 1.3 68 −130.5 15 −119.2 65 173.6–182.0 44

147.7–160.7 44 62.15 69 72.8 65 −74.1 ± 1.1 70 −78.1 24 −71.5 ± 0.4 91

of the isomers CH3 NCO, CH3 OCN, CH3 CNO and CH3 ONC are as 0:105:240:343 whereas here it is found that 0:111:237:351 kJ mol−1 . The case of methyl azide, CH3 −N−N⊖ −N⊕ , is particularly interesting; Dorofeeva and colleagues 17 employed 50 isodesmic reactions and averaged the resultant values to obtain 297.9 kJ mol−1 all at a G4 level of theory. Although one could compute the standard deviation in a straightforward manner the correct, if more laborious approach, would be to weight each of their individual values via the uncertainties of each chaperon and an assumed generalised uncertainty of the G4 method. Here we compare just two examples present in their scheme, reactions {23} and {31} in the nomenclature of their supporting information documentation:

CH3 N3 + CH3 OH −→ HN3 + CH3 OCH3 CH3 N3 + C2 H6 −→ HN3 + C3 H8



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where the G4 results for reaction enthalpy are in perfect agreement at −25.4 and +11.0 kJ mol−1 respectively and close to the averaged reaction enthalpies of −24.44 ± 0.64 and 11.27 ± 0.87 kJ mol−1 . In this work the individual formation enthalpies of {23} 295.7 ± 0.9 and {31} 297.3 ± 1.2 kJ mol−1 leads to a final result of ∆f H ◦ of 296.3 ± 0.72 kJ mol−1 . Although both approaches have merit it is considered that using multiple model chemistries accompanied by two or more independent working reactions, as here, is probably more advantageous. Matus and co-workers 44 utilised isodesmic reactions and G3(MP2) atomization methods to calculate methyldiazene and 1,2-dimethyldiazene; their isodesmic results, were based on the working reactions:

CH3 NNH + NH3 −→ CH3 NH2 + N2 H2 CH3 NNCH3 + 2 NH3 −→ 2 CH3 NH2 + N2 H2

On the assumption that they have chosen the lowest energy conformer in each case then their results bracket those reported here. Conformers of nitrosomethane, H3 CNO, such as the formaldehyde oxime, H2 C−NOH, which exists in trans and cis forms and N-oxide methanimine, H2 C−NH(O), more commonly formaldonitrone, can now be derived directly. The nitrone follows from three isodesmic reactions:

CH2 NH(O) + CH3 NO −→ CH2 NH + CH3 NO2 CH2 NH(O) + NO −→ CH2 NH + NO2 CH2 NH(O) + HNO −→ CH2 NH + HNO2 yielding 66.4 ± 1.3 kJ mol−1 (atomization 66.9 ± 2.6) from computed reaction enthalpies of −126.16±1.61, −37.84±3.01 and −163.10±1.90 kJ mol−1 ; the first two of these were utilised


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by Polá˘sek and Ture˘cek who initially prepared ‘the elusive formaldonitrone’ by femtosecond collisional neutralisation of its cationic radical 72 and determined ∆f H ◦ (298.15 K) of 58 ± 0.3 kJ mol−1 from G2(MP2) calculations. The first working reaction requires values for nitrosomethane and nitromethane both of which were determined here as 72.7 ± 1.1 (atomization 71.3 ± 2.9) and −76.4 ± 0.7 (atomization −78.1 ± 3.9) kJ mol−1 . The working reactions used to determine nitromethane are shown later below. Those for nitrosomethane were:

CH3 NO + C6 H6 −→ C6 H5 NO + CH4 CH3 NO + CH3 OCH3 −→ CH3 NO2 + C2 H6 and had reaction enthalpies of −32.42 ± 1.23 and −46.76 ± 2.21 kJ mol−1 . Based on this value for the nitrone direct comparisons with the other isomers yields 19.7 ± 2.0 (atomization 20.3 ± 2.2) for the trans oxime and 40.2 ± 2.1 (atomization 40.7 ± 2.1) for the cis oxime. These conclusions are qualitatively similar to those reported by Long et al. 73 from G2 calculations. DePrince and Mazziotti 74 have studied the isomerisation of nitrosomethane to formaldoxime with a parametric variational two-electron reduced-density-matrix method and have predicted formaldonitrone to be very slightly more stable than nitrosomethane by 0.2 kJ mol−1 with their CCSD(T)/cc-pV∞Z calculations showing a much larger difference of 6.2 kJ mol−1 . Comparable 0 K figures obtained here have the nitrone more stable by 3.1 kJ mol−1 .

Beyond ATcT The previous Sections dealt with tabulated values and simple extensions such substitution of methyl into hydrazine, etc. More radical changes to the molecular framework are possible but always with the aim of rooting the results back to the ATcT or to well-established 21 ACS Paragon Plus Environment


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values. For example, 2-nitrofuran can be computed via a pair of working reactions involv˙ ing H2 O/furan/HNO3 and H/furan/NO 2 whose reaction enthalpies of 109.19 ± 2.13 and −182.56 ± 3.90 kJ mol−1 lead to −36.2 ± 2.3 and −36.1 ± 4.0 kJ mol−1 for the target 2nitrofuran in good agreement with the atomization value of −36.2 ± 5.3 kJ mol−1 . The results are in good agreement with DFT atomization calculations by Li et al. 75 with B3LYP, B3PW91 and MPW1PW91 all predicting ∼ −37.5 but PBEPBE is the exception at −45 kJ mol−1 ; the experimental value 76 is considerably higher at −29 ± 3 kJ mol−1 . Both aniline and N-methyl aniline can be derived from the set of working reactions:

C6 H5 NH2 + CH4 −→ C6 H5 CH3 + NH3 C6 H5 NH2 + CH3 OH −→ C6 H5 CH3 + NH2 OH(cis) C6 H5 NH(CH3 ) + NH3 −→ C6 H5 NH2 + CH3 NH2 C6 H5 NH(CH3 ) + HNO −→ C6 H5 NO + CH3 NH2 for which the reaction enthalpies are −5.49±0.52, 140.35±0.81, 17.86±0.66 and −22.91±0.54 kJ mol−1 respectively. These lead then to ∆f H ◦ (298.15 K) of 85.0 ± 0.6 kJ mol−1 for aniline (atomization 90.0±6.8) and 93.8±1.1 kJ mol−1 for N-methylaniline (atomization 95.8±7.8); the latter is in reasonable agreement with a recent combustion calorimetric determination of 90.9 ± 2.1 kJ mol−1 by Emel’yanenko et al. 77 In the case of aniline there are a number of values near 82 kJ mol−1 and one near 87 kJ mol−1 ; this latter was largely adopted by Pedley et al. 56 at 87.1 ± 1. kJ mol−1 . It is to be expected that the reaction: C6 H5 NH2 + C6 H5 N(CH3 )2 −→ 2 C6 H5 NH(CH3 ) would be nearly thermoneutral and the computed reaction enthalpy change of 1.12 ± 0.41 kJ mol−1 confirms this. Hence, a value of 101.5 ± 1.7 kJ mol−1 emerges for N,N′ -dimethylaniline which is in very good agreement with the literature value 78 of 100.5 ± 3.4 kJ mol−1 . In


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summary, the published results for aniline, N-methyl and N,N′ -dimethyl derivatives are not consistent because they predict a reaction enthalpy of some −5.8 kJ mol−1 as against that indicated above. In the case of simple species, like urea, this can be computed from the sets of reactions:

(NH2 )2 CO + H2 O −→ CO2 + 2 NH3 (NH2 )2 CO + 2 CH4 −→ (CH3 )2 CO + 2 NH3 (NH2 )2 CO + C2 H6 −→ (CH3 )2 CO + N2 H4 reaction enthalpies of −10.72 ± 1.70, 78.82 ± 2.09 and 200.66 ± 1.12 kJ mol−1 yield a final weighted value of −233.8 ± 1.0 kJ mol−1 (atomization −232.4 ± 2.6) as against the −235.7 ± 1.4 kJ mol−1 measured by Bodi et al. in dissociative vacuum-ultraviolet photoionisation experiments. 79 The simplest amide, formamide, can be computed from:

HCONH2 + H2 O −→ syn HCOOH + NH3 to yield −189.8 ± 0.5 kJ mol−1 (atomization −189.1 ± 2.0) in very good agreement with the calorimetric experiments of Emel’yanenko et al. 80 of −188.6 ± 0.4 kJ mol−1 and the Bakowies 81 ATOMIC/A value of −188.7 kJ mol−1 . In turn acetamide, CH3 CONH2 , follows from a reaction with urea and acetone: 2 CH3 CONH2 −→ (NH2 )2 CO + (CH3 )2 CO to yield −234.6±1.4 kJ mol−1 (atomization −234.5±2.5) or from methane/formamide/ethane: CH3 CONH2 + CH4 −→ HCONH2 + C2 H6



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for which a reaction enthalpy of 36.33 ± 0.07 yields −235.4 ± 0.5 and a final average of −235.3 ± 0.5 kJ mol−1 — this is in only moderate agreement with a much earlier Barnes and Pilcher calorimetric result 82 of −238.3 ± 0.8 kJ mol−1 but in excellent agreement with a W3X-L calculation 40 of −236.5 kJ mol−1 . The isomeric N-methylformamide, HCONHCH3 , exists in two rotameric forms with the cis, ∠HNCH = 0◦ , being more stable than the trans by some 5.38 ± 0.08 kJ mol−1 . Individually ∆f H ◦ = −188.6±0.8 kJ mol−1 (atomization −188.9±2.5) for the cis; in conjunction with a 91.7% abundance for the cis, the formation enthalpy of N-methylformamide is −188.2 ± 1.0 kJ mol−1 . This is to be compared with a literature value of −191.2 ± 2.0 kJ mol−1 due to Ushakov et al. 83 Benzamide, C6 H5 CONH2 , results from a working reaction involving methane, formamide and toluene to yield −100.1 ± 1.1 kJ mol−1 (atomization −97.3 ± 6.5) which is excellent agreement with a calorimetric value of −100.9 ± 1.2 kJ mol−1 due to Gomez and Sabbah. 84 The isomeric trans and cis formanilides, C6 H5 NHCHO, are thus −64.3 ± 1.2 and −61.2 ± 1.3 kJ mol−1 (atomizations of −61.4 ± 6.1 and −58.4 ± 6.3). All of the above amides and a good deal more have been the subject of G4 calculations by Marochkin and Dorofeeva 85 with the primary aim of seeing what effect substitution has on the N C bond dissociation enthalpy. Incidentally they have tabulated the molecular atomization values for many amides which are in nearly complete agreement with those found here. For nitramide, H2 NNO2 , two working reactions can be framed: H2 NNO2 + CH4 −→ CH3 NH2 + HNO2 H2 NNO2 + CH4 −→ CH3 NO2 + NH3

for which a value for nitromethane, CH3 NO2 , would be advantageous. Although this was recently determined by Asatryan et al. 70 at −74.1 ± 1.12 kJ mol−1 , via CBS-QB3, CBS-


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APNO and G3 calculations, the working reactions:

CH3 NO2 + CH3 OH −→ C2 H6 + HONO2 CH3 NO2 + CH3 OH −→ CH3 OCH3 + HONO were used to re-determine ∆f H ◦ = −76.4 ± 1.2 kJ mol−1 (atomization −78.1 ± 3.9) using updated ATcT values for the chaperons. These results are in reasonable agreement with the experiments of Miroshnichenko et al. 87 whose −74.5 ± 0.8 kJ mol−1 neatly brackets earlier values. 56 The final value for nitramide is thus 0.48±1.09 kJ mol−1 (atomization 2.4±5.5); coupledcluster calculations by Szakács and co-workers 88 up to CCSDT(Q) indicate a value of 4.9±2.4 kJ mol−1 . Their paper summarises other results which range wildly from −26 to +10 kJ mol−1 . Values for cis and trans methyl nitrites, CH3 ONO, isomers of nitromethane, were determined from methanol/nitrous acid/dimethyl ether working reactions to yield −68.5 ± 1.0 kJ mol−1 (atomization −68.7 ± 4.1) and −63.3 ± 0.83 kJ mol−1 (atomization −64.6 ± 3.9) respectively. These are in very good agreement with very recent additions to version 1.122 of the ATcT of −67.24 ± 0.46 and −64.30 ± 0.46 kJ mol−1 . These and a ∆f H ◦ of −74.77 ± 0.50 for nitromethane were established during a combined experimental and theoretical paper on thermal isomerisation reactions of nitromethane. 89 Once a satisfactory value for nitromethane has been obtained then this can be used to derive a result for nitrobenzene via a CH4 /CH3 NO2 /C6 H6 working reaction together with a purely ATcT-based isodesmic reaction HNO/C6 H5 NO/HNO2 to yield 56.8 ± 1.4 kJ mol−1 (atomization 58.5 ± 5.2) which differs considerably from the experimental values 90,91 of 68.5±0.67 and 65.6±1.6 kJ mol−1 . Earlier G3X calculations by Dorofeeva and Moiseeva 92 had obtained 56 kJ mol−1 and they pointed out that this cast doubt on the older experimental value. 90 The more recent experimental value of Verevkin et al. 91 was accompanied by some



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20 G4 isodesmic calculations yielding 64.8 kJ mol−1 , each of which however relied on a value for nitromethane of −71.5 ± 0.4 kJ mol−1 . The contentious acrylonitrile or vinyl cyanide, whose industrial importance is matched by the disparate spread in the experimental values for formation enthalpies as highlighted by Notario et al., 93 can be computed from the now established value for methyl cyanide via: CH2 −CHCN + CH4 −→ CH3 CN + CH2 −CH2 ∆r H ◦ of 14.04 ± 0.50 kJ mol−1 which leads to 187.4 ± 1.7 kJ mol−1 (atomization 190.2 ± 3.4) in some disagreement with the 197.0 kJ mol−1 from an ATOMIC/A calculation 12 but in accord with the recommended 188 ± 7 kJ mol−1 by Notario and colleagues and with a very recent 40 W3X-L computation of 188.3 kJ mol−1 .

N-heterocycles Apart from nitrosobenzene there are no ring systems in the ATcT which contain nitrogen and specifically no N-heterocyclics. So expanding the database is difficult if one attempts always to route the results back to ATcT. However given the success of the procedures used here one can continue this approach choosing if possible working reactions which are approximately thermoneutral, ensuring maximum cancellation of error, for example, furazan + furan = 2 isoxazole:

The computed reaction enthalpy change of −1.77±0.88 kJ mol−1 leads to ∆f H ◦ (298.15 K) of 193.6 ± 1.4 kJ mol−1 for furazan if the McCormick and Hamilton 94 value for isoxazole of 78.58 ± 0.54 kJ mol−1 is accepted. However the furazan isodesmic result is more than 5 kJ mol−1 away from the atomization value of 198.9±4.7 from this work. A more recent isoxazole result by Steele et al. 95 of 82.0 ± 0.6 kJ mol−1 gives 200.5 ± 1.4 kJ mol−1 for furazan which 26 ACS Paragon Plus Environment

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is now in good agreement with the atomization value. The isomeric oxazole can also be determined, via direct comparison with isoxazole, as −14.7 ± 0.8 (atomization −14.5 ± 2.5) kJ mol−1 which does agree with the −15.5 ± 0.54 kJ mol−1 of McCormick and Hamilton. 94 A similar approach can be used to determine pyrimidine based on values for pyridine: 96,97

the reaction enthalpy of 8.77 ± 0.38 kJ mol−1 feeds through to generate 188.9 ± 2.2 (atomization 188.2±1.8) kJ mol−1 . da Silva et al. 14 had recommended a value of 187.4±4.2 kJ mol−1 from CBS-APNO/G3B3/G3 calculations and maintained that the experimental value 98 of 195.8 ± 1.5 kJ mol−1 was some 4–12 kJ mol−1 too high. Verevkin et al. 99 have since shown from calorimetric experiments that ∆f H ◦ (298.15 K) = 189.7 ± 0.7 kJ mol−1 validating the earlier work of da Silva et al.; in parallel they conducted atomization computations with CBS-APNO, G3, G4 and W1 composite methods and showed that G4 works best. Furthermore they proposed method-specific empirical corrections to the atomization procedure to improve agreement between theory and experiment. Partly the reason for this was that they found a large scatter in the reaction enthalpy for the abovementioned working reaction, in complete contrast to the value found here in which CBS-QB3 substitutes for W1(RO) and the resultant uncertainty is dominated by the uncertainty in the chaperon pyridine of ±1.5 kJ mol−1 and not by the reaction enthalpy uncertainty which is very small. Bakowies 12 has also showed that the experimental value for pyrimidine is incorrect, computing an ATOMIC/A value of 188.7 kJ mol−1 ; his work shows the need for proper validation databases since the experimental value had found its way into popular, but not critically and often revised, databases. The isomeric pyrazine, C4 H4 N2 , of D2h symmetry can be calculated directly from the enthalpy difference of −16.85±2.04 kJ mol−1 as 205.7±3.0 kJ mol−1 (atomization 205.1±3.2). This conflicts with the only experimental value of 196.1 ± 1.5 due to Tjebbes 100 but agrees 27 ACS Paragon Plus Environment


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with the ATOMIC/A calculation of 207.1 kJ mol−1 and the experimental re-determination of Verevkin et al. 99 of 203.2 ± 1.5 kJ mol−1 . Finally the remaining isomer, pyridazine, is similarly determined as 281.5 ± 3.1 (atomization 280.9 ± 3.4) kJ mol−1 and is to be compared with the experimental 99 280.2 ± 0.7 and the calculated, 99 via G4 and W1 corrected atomization values, of 280.1 kJ mol−1 . As regards the saturated and unsaturated five- and six-membered parent N-heterocycles Table 9 summarises the position as regards experimental values and comparisons with both isodesmic and atomization calculations. From which it can be seen that the second literature value for pyrrole is clearly incorrect but otherwise there is good agreement. Table 9: N-ring systems, ∆f H ◦ (298.15 K) / kJ mol−1 heterocycle pyrrole pyrrolidine pyridine piperidine

isodesmic 109.2 ± 2.3 −4.7 ± 1.5 138.5 ± 1.2 −47.6 ± 1.5

atom. 110.9 −1.0 141.4 −46.7

literature 108.3 ± 0.50 101 143.2 102 −3.4 ± 0.96 103 −3.6 ± 0.92 104 140.2 105 140.6 ± 1.5 96 140.7 ± 1.5 97 −47.15 ± 0.63 106 −48.83 ± 2.25 107

Pyrrole The compounds in Table 9 represent key structures and it is important to have confidence in their base values. The absence of suitable chaperons makes verification more difficult but for pyrrole working reactions involving propane/dimethylamine/cyclopentadiene and benzene/pyridine/cylopentadiene results in ∆f H ◦ of 109.2 ± 2.3 kJ mol−1 (atomization −110.9 ± 4.6) where a non-ATcT value has perforce been used for 1,3-cyclopentadiene. 18 Irrespective the indications are that the Scott et al. 101 result of 108.3 ± 0.5 kJ mol−1 is certainly the more reliable although Holmes and Aubry have argued that a value of 110 kJ mol−1 is to be preferred 108 while Lo and Lau 109 have used CCSD(T)/CBS calculations including core–valence electronic corrections and scalar relativistic effect to derive 110.9 kJ mol−1 . Additionally they reported a value for cyclopentadiene, using the same level of theory, of 136.8 kJ mol−1 which is very close to the value employed here of 137.1 ± 1.7 kJ mol−1 . 28 ACS Paragon Plus Environment

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There is an extensive collection of values for methyl-substituted pyrroles available of varying quality, Table 10, taken from the NIST Chemistry WebBook Standard Reference Database Number 69. Table 10: Formation enthalpies of pyrroles kJ mol−1 species isodesmic atom. lit. pyrrole 109.2 ± 2.3 110.9 108.4 1-methyl 102.6 ± 1.6 104.1 103.1 2-methyl 73.8 ± 2.4 75.3 74.9 3-methyl 79.2 ± 1.5 80.6 80.2 1,2-dimethyl 66.6 ± 4.2 67.8 68.8 1,3-dimethyl 72.6 ± 4.2 73.8 75.1 3,4-dimethyl 47.1 ± 4.2 48.3 50.1 2,3-dimethyl 44.7 ± 4.2 45.9 68.3 2,4-dimethyl 43.5 ± 4.2 44.7 46.6 2,5-dimethyl 38.5 ± 4.1 39.7 39.8 1,2,3-trimethyl 37.7 ± 5.0 38.6 41.6 1,2,4-trimethyl 36.6 ± 5.0 37.5 41.0 1,2,5-trimethyl 32.5 ± 5.0 33.4 34.6 1,3,4-trimethyl 40.5 ± 5.0 41.4 45.2 2,3,4-trimethyl 12.1 ± 5.0 13.0 16.2 2,3,5-trimethyl 8.94 ± 5.0 9.9 13.9 1,2,3,4-tetra 5.23 ± 6.3 5.9 11.6 1,2,3,5-tetra 3.31 ± 6.3 4.0 9.3 2,3,4,5-tetra −22.8 ± 6.3 −22.1 −15.9

Pyrrolidine For pyrrolidine the picture is a lot less clear; Denis 110 has shown that determining the energy gap between the axial and equatorial conformers is a difficult problem even employing CCSD(T) and cc-pVXZ basis sets, where X = D → 6 and including scalar relativistic effects, anharmonicity, etc. His best estimates are ∆f H ◦ = −3.52 for the axial and −3.97 kJ mol−1 for the equatorial with vibrational contributions at the harmonic level. The equatorial conformer is more stable by 1.03 kJ mol−1 as shown by all four composite methods here. Isodesmic reactions involving propane, cyclopentane and dimethylamine together with one employing dimethyl ether, tetrahydrofuran 111 and dimethylamine results in a final value for 29 ACS Paragon Plus Environment


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the equatorial conformer of −5.13 ± 0.82 kJ mol−1 which in turn translates into −4.68 ± 1.5 kJ mol−1 for the equilibrium mixture.

Pyridine The experimental values for pyridine, C5 H5 N, are in closer agreement than one might have expected and are not ruled out by the atomization value, Table 9, nor by isodesmic reactions with propane, dimethylamine, ethene, benzene and methylenimine, CH2 −NH, all of which are present in the ATcT, as chaperons: C5 H5 N

+

138.29 ± 1.58 C5 H5 N 138.83 ± 1.75

C3 H8

=

−104.39 ± 0.29 +

C2 H4 52.56 ± 0.15

C6 H6

+

83.18 ± 0.26 =

C6 H6 83.18 ± 0.26

NH(CH3 )2

∆r H

−15.89 ± 0.69 33.39 ± 1.36 +

NH CH2

∆r H

88.70 ± 0.98 −19.51 ± 1.42

which yields a final 138.53±1.17 kJ mol−1 as against the experimental 140.2–140.6 kJ mol−1 . The mean of the latter two values, 140.4 ± 1.5 kJ mol−1 , is therefore adopted on which to anchor all subsequent formation enthalpies for derivatives. There is an extensive literature 112 for the methyl derivatives of pyridine primarily from calorimetric measurements of the heat of combustion; these have been re-analysed by Chirico et al. 113 who concluded that the work by Andon et al. 96 was most likely correct except for their value for 3-methylpyridine, Table 11. This work concurs with that assessment and also that the more recent determination for the 3-methyl by Gerasimov et al. 114 of 103.6 ± 1.3 kJ mol−1 is much nearer the mark. The agreement for the 3,5-dimethyl compound 115 is particularly pleasing, Table 11. Methoxy derivatives have been recently determined calorimetrically by Amaral and da Silva 116 who argue that the apparently low value for 2-methoxypyridine is due to extra stabilisation by N.... H intermolecular hydrogen bonding. Although the most stable conformer does have a N C O C dihedral angle of zero an NBO analysis 117 does not show any significant H-bonding which is also unlikely given the optimised geometry. In fact their 30 ACS Paragon Plus Environment

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Table 11: Formation enthalpies of pyridines kJ mol−1 species

isodesmic atom.

pyridine 2-methyl 3-methyl 4-methyl 2,3-dimethyl 2,4-dimethyl 2,5-dimethyl 2,6-dimethyl 3,4-dimethyl 3,5-dimethyl 2-methoxy 3-methoxy 4-methoxy 2,6-dimethoxy

140.4 ± 1.5 98.7 ± 1.6 105.9 ± 1.6 103.7 ± 1.6 64.3 ± 2.8 62.0 ± 2.7 64.8 ± 2.7 57.0 ± 2.7 67.9 ± 2.8 71.4 ± 2.7 −48.6 ± 2.3 −12.2 ± 2.5 −22.5 ± 2.3 −234.1 ± 3.6

literature

141.4 140.6 96 140.2 105 99.8 101.9 96 99.0 101 107.0 113.6 96 103.6 114 104.8 102.1 96 103.8 121 65.6 68.3 115 63.2 63.9 115 66.1 66.4 115 115 58.2 58.7 56.1 ± 1.5 96 69.2 70.0 115 72.6 72.8 115 −49.2 −42.7 116 −12.8 −10.8 116 −23.2 −18.2 116 −236.3 −233.5 116

measured values result in this reaction:

being regarded as endothermic by +7.7 kJ mol−1 , essentially negating their argument, whereas computed values show that it is slightly exothermic by −3.43 ± 0.55 kJ mol−1 . Their value of −10.8 ± 5.1 kJ mol−1 for 3-methoxy was estimated, not measured, based on an assumed increment for the meta position of pyridine. Direct calculation shows that this estimate is not unreasonable with an isodesmic of −12.2 ± 2.5 and an atomization of −12.8 ± 5.3 kJ mol−1 . Piperidine Piperidine exists in equatorial and axial forms 118 with the former being more stable by 3.2 kJ mol−1 . Working reactions which include propane, cyclohexane and dimethylamine, and, benzene, cyclohexane and pyridine (all ATcT species except for pyridine) yield −48.29±0.94 kJ mol−1 for the equatorial conformer. Hence, the computed value for piperidine, given a



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78.6:21.4 distribution of equatorial to axial amounts to −47.6 ± 1.5 kJ mol−1 which is in excellent agreement with the re-analysis by Cox and Pilcher 97 of the original Bedford data. 107 Much more recent experimental values are available from the Ribeiro da Silva group for some methyl-substituted piperidines. 119 Building on the piperidine base value that for Nmethylpiperidine, in which the methyl group now occupies an equatorial position, is −59.87± 1.31 which is in excellent agreement with the experimental value of −59.1 ± 1.7 kJ mol−1 if less so with an earlier value 120 of −61.39 ± 0.88 kJ mol−1 . The axial N-methylpiperidine is much less stable by 14.9 ± 0.3 kJ mol−1 , and hence does not contribute meaningfully to the overall heat of formation. Direct comparisons for the 2-, 3- and 4-methyl derivatives, all with equatorial methyl groups, yields relative enthalpies of 0 : 6.83 : 6.38 or in absolute terms −85.1, −78.3 and −77.8 kJ mol−1 which are to be compared to the experimental values of −84.5 ± 1.1, −79.5 ± 2.9 and −82.7 ± 3.2 kJ mol−1 respectively. 119,121 Apart from the 4-methylpiperidine result, which dates from 1972, the agreement is quite satisfactory, Table 12. As regards di-substituted methylpiperidines the 2,6-dimethylpiperidine can be obtained directly from a working reaction involving piperidine and 2-methylpiperidine; the computed reaction enthalpy change is 0.16±0.04 kJ mol−1 , that is, almost exactly thermoneutral for the equatorial conformers. Using the previous values for the parent and the 2-methyl derivative the formation enthalpy of eq/eq or ‘cis’ 2,6-dimethyl piperidine is calculated at −122.54±2.12 kJ mol−1 (atomization −123.5 ± 9.7). This is in very good agreement with their G3MP2B3 atomization calculations but not with their experimental result for nominally pure eq/eq of −111.2 ± 2.2 kJ mol−1 . As discussed by Ribeiro da Silva and colleagues their experimental result is probably at fault in this case. 119 An equilibrium mixture of all three conformers would have only a very slightly lower computed formation enthalpy of −122.4 kJ mol−1 as the ‘cis’ conformer is dominant > 98%. In a similar vein for 3,5-dimethylpiperidine the di-axial conformer lies 17.8 kJ mol−1 above the di-equatorial and hence makes very little contribution to the overall formation


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enthalpy which is −107.9 ± 2.5 kJ mol−1 derived from the di-equatorial −108.9 ± 2.2 and the trans at −103.5 ± 2.2 kJ mol−1 , as compared to the experimental value of −105.9 ± 1.8 kJ mol−1 . Finally, the 2,2,6,6-tetramethyl derivative is computed via a working reaction involving piperidine and two 2,6-dimethylpiperidines as −172.0 ± 3.2 kJ mol−1 (atomization −175.1 ± 12.7) which compare unfavourably with the experimental value 122 of −162.4 ± 2.1 kJ mol−1 . Further validation can be obtained by computing the formation enthalpy of 2-piperidinone which was recently determined calorimetrically 123 via the isodesmic reactions:

which rely on values obtained here for formamide, HCONH2 and acetamide, CH3 CONH2 . Reaction enthalpies of 1.61±1.28 and −23.33±1.11 kJ mol−1 lead to a final ∆f H ◦ (298.15 K) of −229.0±1.12 kJ mol−1 in excellent agreement with the experimental −228.0±1.9 kJ mol−1 . Note too that a working reaction which ties piperidine and piperidinone via acetone/propane chaperons results in ∆f H ◦ (298.15 K) of −228.2 ± 1.8 kJ mol−1 for piperidinone thus sealing the essential correctness of the calculations for these six-membered heterocycles. The N-methyl derivatives, 1-methyl-2-piperidinone and 1-methyl-4-piperidinone, have been determined calorimetrically at −232.9 ± 2.2 and 160.7 ± 1.7 kJ mol−1 and these are in moderate agreement with the computed values of −235.9 ± 1.7 and −164.8 ± 2.1 kJ mol−1 .

Isodesmic summary It is instructive to look at the results from the calculation of reaction enthalpies of isodesmic reactions and the scatter or deviation from the mean enthalpy for the four composite methods, Fig 2. For some 140+ reactions the scatter in the ∆r H ◦ values, defined as the deviation of each method from the mean, is less than 6 kJ mol−1 even though the reaction enthalpy varies by over 600 kJ mol−1 — in the Figure only the interval −60 → +60 is shown. Outliers 33 ACS Paragon Plus Environment


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Table 12: Formation enthalpies of piperidines kJ mol−1 species piperidine e piperidine a N-methylpiperidine e N-methylpiperidine a 2-methylpiperidine ee 2-methylpiperidine ea 2-methylpiperidine ae 2-methylpiperidine aa 3-methylpiperidine e 4-methylpiperidine e 2,2-dimethylpiperidine 2,6-dimethylpiperidine ee 2,6-dimethylpiperidine ea 2,6-dimethylpiperidine aa 3,5-dimethylpiperidine ee 3,5-dimethylpiperidine ea 3,5-dimethylpiperidine aa 2,2,6,6-tetramethylpiperidine 2-piperidinone 1-methyl-2-piperidinone 3-piperidinone 4-piperidinone 1-methyl-4-piperidinone

isodesmic −47.9 ± 1.0 −44.7 ± 1.0 −59.5 ± 1.3 −85.2 ± 1.3

−78.3 ± 1.4 −78.8 ± 1.4 −114.0 ± 2.2 −122.6 ± 2.1 −110.6 ± 2.2 −93.1 ± 2.2 −108.9 ± 2.2 −103.5 ± 2.2 −91.1 ± 2.2 −172.0 ± 3.2 −229.0 ± 1.2 −235.9 ± 2.0 −146.5 ± 1.7 −155.0 ± 1.7 −164.8 ± 1.7

atom. −46.7 ± 6.9 −43.5 ± 7.0 −59.3 ± 8.0 −44.4 ± 8.1 −85.0 ± 8.2 −72.8 ± 8.6 −71.2 ± 8.6 −80.9 ± 8.4 −78.2 ± 8.4 −78.6 ± 8.3 −114.9 ± 9.8 −123.5 ± 9.7 −111.5 ± 10.0 −94.0 ± 10.2 −109.8 ± 10.0 −104.4 ± 10.0 −92.0 ± 10.0 −175.1 ± 12.7 −227.0 ± 5.8 −235.0 ± 7.1 −144.6 ± 5.0 −153.1 ± 5.0 −163.9 ± 6.2


literature

−59.1 ± 1.7 119 −84.5 ± 1.1 121

−79.5 ± 2.9 119 −82.7 ± 3.2 121 −111.2 ± 2.2 119 −105.9 ± 1.8 119 −162.4 ± 2.1 119 −228.0 ± 1.9 123 −232.9 ± 2.2 123 −160.7 ± 1.7 123

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include highly exothermic reactions such as NH3 O + H2 −→ NH3 + H2 O with ∆r H ◦ = −344 kJ mol−1 but even here the standard deviation is only ±4.1 kJ mol−1 .

Figure 2: ∆r H ◦ (298.15 K) and scatter in same: CBS-QB3 , CBS-APNO •, G3 N, G4 H / kJ mol−1 The majority of the values with u > 3 kJ mol−1 involve species which suffer from spin ˙ 3 → [C6 H5 ]• + CH3 NH2 , which is also highly contamination, for example, C6 H5 NH2 + CH endothermic, and which should properly not be considered in the absence of suitable alternatives. Fortunately in this particular case there are suitable options:

C6 H5 NH2 + CH4 −→ C6 H5 CH3 + NH3 C6 H5 NH2 + CH3 OH −→ C6 H5 CH3 + NH2 OH with ∆r H ◦ of −5.59 ± 0.52 and 140.35 ± 0.81 kJ mol−1 respectively. Such an opportunity 35 ACS Paragon Plus Environment


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is not always available but even in worst case scenarios the uncertainty is small and can be reduced further by using more than one working reaction.

Figure 3: Method variation versus isodesmic formation enthalpy: CBS-QB3 , CBS-APNO •, G3 N, G4 H, average • / kJ mol−1 An alternative is to look at the comparison between each individual atomization value and their average and compute the difference between these and the isodesmic value, Figure 3. Note that the average of the atomization results (black circles) lie mainly between ±3.0 kJ mol−1 of the isodesmic value which covers the range −250 → +300 kJ mol−1 with only 8 out of 66 cases lying slightly outside and none ≤ −5.1 or ≥ +5.1 kJ mol−1 . The number of ‘heavy atoms’ spans the range from 3 → 10 and the mean unsigned error for all four chemistries is 1.64 kJ mol−1 . Individually of course the composite methods do not fare as well, for reasons discussed in earlier papers, 18,19 with CBS-QB3 in particular showing a large


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degree of scatter.

Conclusions Rapid screening with a number of composite model chemistries of the Active Thermochemical Tables for nitrogen-containing species shows that these archived values are generally of an excellent quality. One notable exception has surfaced, hydrazine, which is probably too low — certainly well outside the 95% confidence limits. In turn that impacts the formation enthalpies of the methyl derivatives which are used as rocket propellants and in optoelectronic production as sources of nitrogen. 124 Other slighter exceptions have surfaced such as the cyanic and fulminic acids. For these, high level calculations such as those initiated by Feller 125 at CCSD(T)-F12 with aug-cc-pV7Z basis sets, are probably required to produce a self-consistent set of results. The methodology is also useful for calculating the enthalpy of formation of newly discovered species such as the rather beautiful bicyclic CN2 O2 or 1,2-dioxa-4,5-diazaspiro[2.2]pent4-ene, 126 which bears very little resemblance to any of those in the ATcT; the atomization derived value of 387.8 ± 5.8 kJ mol−1 can be favourably compared to that recently computed by coupled cluster methods, CCSD(T), in the complete basis set limit at a B3LYP/aug-ccpVTZ geometry of ≈ 393 kJ mol−1 . Using multiple model chemistries is advantageous but is constrained by those cases for which one or more of them fail, for example, those methods involving two geometry optimizations. Thus HOON, formally H−O−O⊖ −N⊕ , does not survive the second energy minimisation routine, QCISD/6-311G(d,p), in-built into CBS-APNO and although it does succeed in the second step of G3, where MP2/6-31G(d) is used, the dramatic changes in geometry as well as a T1 of 0.096 are probably responsible for the wild variation, 120 ± 28 kJ mol−1 , encountered for this species. In quite elaborate high-level single, CCSD(T) & CCSDTQ, and multi-reference, CASPT2 & MR-AQCC, ab initio calculations Talipov et al 127



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reported a value of 95 kJ mol−1 for this ‘no longer a complex, not yet a molecule’ challenging system — although a single G4 computation returns 100 kJ mol−1 . A similar situation is found for CH3 OON where CBS-APNO also fails but the other three methods are now more consistent at 107.4 ± 3.2 kJ mol−1 although the G3 result has equally dramatic geometry changes and a large T1 . Despite these individual failings the overall benefit conferred by using multiple methods has been summarized by Cramer as “. . . the utility of exploring multiple methods [is] to ensure that one is not victimized by an otherwise unusual failure in accuracy”. 128 An expansion of the database by employing the now validated species of the ATcT as chaperons in isodesmic reactions using the same four composite methods is now possible and leads to generally good agreement with the rather sparse set of compounds whose formation enthalpy has been measured. In addition this protocol provides a useful check on any new experimental determinations which are to be carried out — given the many difficulties which have been encountered working with these compounds in the past this is a considerable additional benefit. It will not always be possible to postulate good isodesmic reactions for some species but the atomization procedure can be relied upon to provide a very reasonable estimate. For example, the six-membered ring compound 2,4(1H,3H )-pyrimidinedione, or uracil, and its methyl derivative, thymine, have recently been the subject of some controversy but calculations, of −299.5±3.4 and −338.2±4.2 kJ mol−1 are in good agreement with re-determined values from static bomb combustion calorimetry and transpiration experiments 129 of −298.1 ± 0.6 and −337.6 ± 0.9 kJ mol−1 respectively. Quite how extensible the current methodology is, is open to question. The most expensive computation, G4, will set a limit to the number of non-hydrogenic atoms in any species that can be treated within a reasonable timescale in purely atomization calculations. Employing well-framed isodesmic reactions means that much less-demanding theoretical methods can extend the molecular reach of the present database.


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Acknowledgement The author thanks the Irish Centre for High-End Computing, ICHEC, for generous grants of computer time.

Supporting Information Available A comprehensive listing of the Cartesian coordinates, scaled frequencies (symmetries and intensities of same), rotational constants, zero-point energies, method corrections, energies, enthalpies and free energy together with hindered rotor corrections are documented at each of the four levels of theory.

This material is available free of charge via the Internet at

http://pubs.acs.org/.

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D.

Statistical

Electronic

Structure

Calibration

Study

of

the

CCSD(T⋆ )-F12b Method for Atomization Energies. J. Phys. Chem. A 2015, DOI:10.1021/acs.jpca.5b00487 (126) He, F.; Zhang, X.; Ding, Y. Bicyclic CN2 O2 as a High-Energy Density Material: Promising or Not? RSC Adv. DOI: 10.1039/C5RA06797A



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A Database of Formation Enthalpies of Nitrogen Species by

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