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Enthalpy of Formation of NH (Hydrazine) Revisited David F. Feller, David Bross, and Branko Ruscic J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b06017 • Publication Date (Web): 20 Jul 2017 Downloaded from http://pubs.acs.org on July 21, 2017

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The Journal of Physical Chemistry

Enthalpy of Formation of N2H4 (Hydrazine) Revisited

David Feller,*,† David H. Bross,*‡ and Branko Ruscic*,‡↨ †

Department of Chemistry

Washington State University, Pullman, WA 99164-4630

‡

Chemical Sciences and Engineering Division

Argonne National Laboratory Argonne, IL 60439 ↨

Computation Institute,

The University of Chicago, Chicago, IL 60637

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ACS Paragon Plus Environment


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Abstract In order to address the accuracy of the long-standing experimental enthalpy of formation of gas-phase hydrazine, fully confirmed in earlier versions of Active Thermochemical Tables (ATcT), the provenance of that value is re-examined in light of new high-end calculations of the Feller-Peterson-Dixon (FPD) variety. An overly optimistic determination of the vaporization enthalpy of hydrazine, which created an unrealistically strong connection between the gas phase thermochemistry and the calorimetric results defining the thermochemistry of liquid hydrazine was identified as the probable culprit. The new enthalpy of formation of gas-phase hydrazine, based on balancing all available knowledge, was determined to be 111.57 ± 0.47 kJ/mol at 0 K (97.42 ± 0.47 kJ/mol at 298.15 K). Close agreement was found between the ATcT (even excluding the latest theoretical result) and the FPD enthalpy.

I. Introduction Compilations of thermochemical information, such as the NIST-JANAF Tables,1 the tables of Gurvich et al.,2 the organic compound tables of Pedley et al.,3 as well as the more recent Active Thermochemical Tables (ATcT),4-5 provide a convenient source of enthalpies of formation for use in multiple areas of chemical research. In particular, the information contained in these databases has often been used to benchmark electronic structure methods, ranging from density functional theory (DFT), which may contain empirical parameters to purely ab initio, highly correlated techniques.6 For the latter, advances in theoretical capabilities arising from improvements in hardware and software now enable theory to effectively compete with experiment across a wide range of smallto-medium size systems. This situation stands in sharp contrast to the earliest applications of theoretical methods in the 1950s which produced errors of nearly 200 kJ/mol (48 kcal/mol) even in diatomic dissociation energies.7 Developers of high-end theoretical techniques are in constant need of larger and ever-more-accurate reference sets in order to measure whether new approaches represent broad-based advancements across a wide range of systems, or a more narrowly-focused improvement with limited scope. Due to its unique construction, the ATcT provides the highest accuracy collection of thermochemical 2


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data presently compiled. Unlike traditional thermochemistry, which adopts a sequential approach to building thermodynamic quantities, the ATcT relies on a thermochemical network (TN) containing multiple experimental (or theoretical) properties (e.g. bond dissociation energies, reaction enthalpies, ionization potentials and electron affinities). The determinations included in the TN are effectively a set of conditional constraints that need to be simultaneously satisfied to the maximum extent possible by the resulting enthalpies of formation.8-9 The TN is statistically analyzed, iteratively corrected for inconsistencies, and then solved simultaneously for the enthalpies of formation of all included chemical species.4-5, 10-14 Articles by Karton et al.,15 Simmie16 and Dorofeeva et al.17 called into question the existing ATcT enthalpy of formation for N2H4 (hydrazine, 1A), an important chemical in the space industry and a foaming agent used in creating polymer foams. ATcT version 1.11218 lists a ∆fH°(0 K) of 109.66 ± 0.19 kJ/mol (∆fH°(298.15 K) = 95.51 ± 0.19 kJ/mol). The more recent ATcT ver. 1.118 value19 is only slightly different, ∆fΗ°(0 K) = 109.71 ± 0.19 kJ/mol (∆fΗ°(298.15 K) = 95.55 ± 0.19 kJ/mol). In both versions, the enthalpy is rather similar to the values listed either by the NIST-JANAF Tables1 (109.43 ± 0.8 kJ/mol at 0 K or 95.35 ± 0.8 kJ/mol at 298.15 K) or by the compilation of Gurvich et al.2 (109.34 ± 0.50 kJ/mol at 0 K or 95.18 ± 0.50 kJ/mol at 298.15 K). As will be discussed later in more detail, all of these values are based on experimental data. The experimental values can be compared to various ∆fH°(0 K) theoretical predictions, such as: 1) a 2008 Feller-Peterson-Dixon (FPD) value of 110.5 ± 2.5 kJ/mol;20 2) a 2009 value of 112.59 kJ/mol by Klopper et al.;21 3) a 2011 W4-based value of 111.77 kJ/mol by Karton et al.;15 or 4) the 2015 values of ∆fH°(0 K) = 115.4 ± 2.0 kJ/mol (∆fH°(298.15 K) = 99.4 ± 1.0 kJ/mol using isodesmic reactions) or 100.8 ± 2.0 kJ/mol (from atomization energy) obtained by Simmie.16 Karton et al.,15 who obtained an enthalpy of formation slightly (~2 kJ/mol) higher than the experimental value, suggested that the ATcT value (and thus by implication the underlying experimental measurement) “might be reconsidered”. The latest theoretical value was reported by Dorofeeva et al. and relies on Gaussian 4 and 75 isogyric reactions in which the number of electron pairs is conserved to yield a ∆fH°(298.15 K) of 97.0 ± 3.0 kJ/mol (∆fH°(0 K) approximately 111.2 3



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kJ/mol). Simmie’s value is significantly higher (~6 kJ/mol) than experiment and lies well outside the combined error bars. His analysis was based on the unweighted average of four mid-level “model chemistries” (CBS-QB3,22-23 CBS-APNO,24 G325 and G426) for the theoretical treatment. All four methods achieve their success by incorporating empirical parameters fitted to experimental data. In a subsequent paper, Simmie and Sheahan27 favored the smaller W3X-L ∆fH°(0 K) value of 112.1 kJ/mol of Chan and Radom.28 W3X-L is intended to be a lower cost alternative to W3.29 Vogiatzis et al. found a ∆fH°(0 K) value of 113.8 kJ/mol based on CCSD(T) calculations augmented with interferencecorrected second order perturbation theory.30 The “mid-level” label is meant to imply that the level of accuracy achievable in thermochemical calculations lies somewhere between density functional theory methods and much more time-consuming approaches based on coupled cluster theory or configuration interaction calculations. For the 299-member G2/97 test set of Curtiss et al.31-32 CBS-QB3 yielded a root mean square (RMS) deviation of 6.1 kJ/mol (1.45 kcal/mol) and G3 generated εRMS = 5.6 kJ/mol (1.33 kcal/mol). Maximum errors were on the order of 26 kJ/mol with both methods. For the larger 454-member G3/05 test set33 G4 has an εRMS = 5.0 kJ/mol (1.19 kcal/mol), with 18 molecules showing deviations in their enthalpies of formation > 8 kJ/mol, and a maximum error of 37.2 kJ/mol.26 More recently, Karton et al. found RMS deviations of 5.3 (G3), 2.7 (G4), 4.9 (CBS-APNO) and 6.6 kJ/mol (CBS-QB3) with respect to their 120-member W4-17 non-multireference dataset.34 For moderately multi-reference systems the εRMS values are roughly twice as large. Benchmark calculations of various DFT methods using the same dataset yielded RMS errors that were in the range of 9.7 – 15.5 kJ/mol. Simmie and Somers had previously shown that for a collection of 50 enthalpies of formation, a 5-method average (the above plus W1BD35) produced better error statistics than any method alone (εRMS = 2.40 kJ/mol) due to compensating errors.36 In light of the intrinsic limitations of the mid-level methods, it is difficult to know if the difference between their average and the experimental (or ATcT) value for hydrazine reflects an unexpectedly large error in the ATcT value, an associated uncertainty that is too small, or an example of poor performance for the mid-level average.

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The goal of the current study is to re-examine hydrazine’s enthalpy of formation both from the perspective of ATcT and in light of new high level calculations based on the FPD approach.37-41 FPD is a flexible, composite coupled cluster-based theoretical approach to the prediction of thermochemical and spectroscopic properties. To the best of our knowledge, the literature contains at least 187 named, fixed-recipe composite approaches. Although the details differ amongst approaches, many of them, including FPD, use some of the same basic components. Examples include Weizmann-n (Wn)42-45, High-accuracy Extrapolated Ab Initio Thermochemistry (HEAT),46-48 Correlation Consistent Composite Approach (ccCA), 49-51 and the Focal-Point Analysis (FPA) scheme.52-53 Like FPD, the last of these does not involve a fixed recipe. Due to the systematic nature of the FPD approach, it is possible to assign a crude estimate of the molecule-and-property specific uncertainty to the final results. Such assignment of uncertainties is not typical of most applications of electronic structure methods. Prior to attempting new calculations on hydrazine, it is prudent to consider whether the FPD approach is likely to be capable of sufficient accuracy to distinguish among hydrazine enthalpies of formation that differ by only a few kJ/mol. Using data stored in the Computational Results Database (CRDB)54 we find an RMS deviation of 1.46 kJ/mol (0.35 kcal/mol) across 206 enthalpies of formation comparisons with experiment, including experimental measurements with uncertainties exceeding 4.2 kJ/mol. Molecules in this comparison dataset span a range from those whose wave functions are strongly dominated by the Hartree-Fock configuration to those with moderate multi-configurational character (e.g. C2 and O3). The entire CRDB contains over 142,000 theoretical and experimental entries covering 541 chemical systems, with an emphasis on high-end methods. If the experimental reference values are restricted to only those with reported uncertainties ≤ 0.8 kJ/mol, εRMS falls to 0.48 kJ/mol (0.11 kcal/mol) over 122 comparisons. The maximum observed error (2.4 kJ/mol) corresponds to the enthalpy of formation of nbutane where a correction for conformational averaging has not been applied, but is in progress. Agreement is slightly better for Hartree-Fock dominant cases, such as hydrazine, whose leading configuration interaction coefficient in a natural orbital expansion is 0.94. Expanding the dataset to include electron affinities, ionization potentials and proton affinities leads to an εRMS of 1.25 kJ/mol (295 comparisons). Consequently, it appears 5



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probable that the FPD method will be capable of differentiating values that vary by as much as 6 kJ/mol. Table 1 contains the experimental values discussed earlier, together with a wider list of selected theoretical literature values for the enthalpy of formation of hydrazine.15-17, 19-21, 28, 38, 45, 49, 55-60

Ignoring the negative B3LYP enthalpy of formation, one can find a

low ∆fH°(0 K) of 99.85 kJ/mol and a high of 115.4 ± 2.0 kJ/mol. The ATcT ver. 1.112 value (109.66 ± 0.19 kJ/mol) and the ver. 1.118 value (109.71 ± 0.19 kJ/mol) fall within this range. Figure 1 presents a graphical version of some of the same data. II. Theoretical Approach The FPD approach has been described in detail elsewhere,40-41 but will nonetheless be summarized here for the sake of completeness. The method consists of a sequence of (up to) 13 steps, typically beginning with frozen core (FC) coupled cluster theory through single and double excitations, combined with a noniterative, quasiperturbative estimate of the effect of triple excitations, CCSD(T).61-64 Where appropriate, multi-reference singles and doubles configuration interaction (MRSD-CI) theory can be substituted for CCSD(T) for strongly multi-configurational systems or used as an adjunct to coupled cluster theory.65 One particle basis sets are chosen from the diffuse function augmented correlation consistent basis set family of Dunning, Peterson and co-workers.66-86 These basis sets are commonly denoted aug-cc-pVnZ, n = D, T, Q,…10, although for the sake of brevity we will shorten the names to aVnZ. CCSD(T) calculations with basis functions up through l = 6 (i-functions) were performed with MOLPRO.87 Calculations involving kfunctions, which are not currently supported in MOLPRO, were performed with Gaussian 09.88 While every attempt is made to use the largest possible basis sets, extrapolations of a contiguous sequence of basis set results are nevertheless performed in order to further minimize the error with respect to the complete basis set (CBS) limit. There are a number of different extrapolation formulas in the literature. Studies have shown that no single formula is superior for all ranges of basis sets and all classes of molecules.20, 81, 89 We

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have found an expression involving the inverse power of lmax, the highest angular momentum present in the basis set, to be a good compromise89-93, E(lmax) = ECBS + A/(lmax + ½)4

,

(1)

The spread among four (five for aVQ56Z) different formulas will be taken as a rough indicator of the uncertainty in the extrapolation. Experience has shown that this estimate of uncertainty is very conservative in most instances. Unless otherwise noted, all calculations are performed at the optimized geometries for each level of theory and basis set. This choice enables the procedure to produce accurate molecular structures. A statistical analysis of the agreement between FPD and experimental structures for molecules in the CRDB yielded RMS deviations in bond lengths of 0.0071 Å (212 comparisons, non-hydrogens) and 0.0088 Å (112 comparisons involving hydrogen). It should be noted that these statistics are skewed by a large number of re (theory) vs non-re (experiment) comparisons, i.e. equilibrium vs non-equilibrium. If the comparison is limited to molecules with experimental equilibrium re bond lengths, the RMS deviations drop to 0.0014 Å (98 comparisons, non-hydrogens) and 0.0029 Å (46 comparisons involving hydrogen). Bond angles exhibit an εRMS = 0.3°. The remaining components of the FPD approach are smaller and of varying sign. It is implicitly assumed that their contributions are additive, although in very high accuracy studies an approximate additivity correction can be made.40 Core/valence (CV) effects due to the inclusion of the outermost core orbitals (1s2 in the case of nitrogen) are recovered from CCSD(T)(CV) calculations with the weighted core/valence correlation consistent basis sets, cc-pwCVnZ, n = D, T, Q, 5.70 Scalar relativistic (SR) second order Douglas-Kroll-Hess (DKH) CCSD(T)(FC)94-95 calculations at DKH optimized geometries are obtained with the cc-pVQZ-DK recontracted correlation consistent basis sets.96 While CCSD(T) provides an excellent baseline method for chemical systems characterized by a Hartree-Fock dominant wave function, such as N2H4, more extensive correlation recovery is needed in order to converge thermochemical properties to within ± 4 kJ/mol. In the present study higher order (HO) correlation effects were recovered with CCSDT, CCSDT(Q) and CCSDTQ calculations performed with the MRCC program of 7



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Kállay and co-workers interfaced to MOLPRO.97 The same methods are used to describe the impact of higher order correlation on the core/valence contribution to the atomization energy. Ideally, one would prefer to use explicit full CI (FCI) to pick up the effects of higher order correlation, but FCI scales too rapidly to be practical for most systems. For the correlation contribution arising from higher than quadruple excitations we use a continued fraction (cf) approximant originally suggested by Goodson with Hartree-Fock (HF), CCSD and CCSD(T) energies.98 Unfortunately, benchmarking this approximation against FCI atomization energies revealed the original formulation lacked sufficient accuracy for our purposes.99 In many instances it failed to improve upon the raw CCSD(T) values. However, when the original 3-energy sequence was replaced by the CCSD, CCSDT and CCSDTQ sequence much better results were found. Strictly speaking, according to the analysis of Schröder et al., the cf CCSD/CCSDT/CCSDTQ approximant is limited to recovering the effect of 5-fold excitations, i.e. one order higher than the highest explicitly considered excitation level.100 For chemical systems of the size considered here, this distinction is of little significance, at least when it pertains to energy differences. Open shell calculations were based on the R/UCCSD(T) method, which begins with restricted open-shell Hartree-Fock (ROHF) orbitals, but allows a small amount of spin contamination in the solution of the CCSD equations.101-102 Orbital symmetry equivalence constraints were imposed on the isolated atoms. Gaussian 09 does not support the R/UCCSD(T) method. Consequently, it was necessary to estimate the R/U energies using the scheme described in an earlier work.81 The approach assumes that the difference between UCCSD(T) and R/UCCSD(T) energies for basis sets beyond 6ζ can be determined to an accuracy of ~10-6 Eh using results up through 6ζ. Anharmonic zero point vibrational energies (ZPEs) were based on a combination of the large harmonic component (via CCSD(T)(FC) frequencies) and the much smaller anharmonic corrections (via MP2(FC) calculations performed with Gaussian 09). Experience has shown that the anharmonic correction is relatively insensitive to the quality of the basis set. Consequently, we combined CCSD(T)/aVnZ with MP2/aV(n-1)Z. 8


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Studies indicate that this approach should provide ZPEs with sufficient accuracy for our purpose.103 While it would be possible to include a CV correction into the harmonic ZPE, it would likely lead to a less accurate value. CV and HO corrections to stretching frequencies are often of opposite signs and of comparable magnitudes. Computing a CCSDTQ correction to the harmonic frequencies even with the small VDZ basis set is a daunting computational challenge. For hydrazine, MOLPRO’s finite differencing algorithm would require 180 displacements in C1 symmetry each involving 4.3 x 108 determinants. As a results, CV and HO corrections were not attempted for the ZPE. Atomic spin-orbit (SO) coupling effects shift the energies of the isolated atoms relative to the spin multiplet average values obtained from standard CCSD(T). It is necessary to include the atomic SO contribution for accurate atomization energies. For this purpose, we have chosen to use the tabulated values of Moore.104 The commonly employed Born-Oppenheimer approximation assumes separation of electronic and nuclear motions. In systems with light atoms ignoring this effect can contribute a potentially significant error. In the present work a first-order, adiabatic correction, known as the diagonal Born-Oppenheimer correction (DBOC), will be obtained from CCSD(FC)/aVTZ calculations performed with the CFOUR program105 using CCSD(T)(FC)/aVTZ geometries. The open shell systems are based on unrestricted Hartree-Fock wave functions and UCCSD.

III. Theoretical Results and Discussion Table 2 contains the atomization energy results from the calculations performed as part of this study. As mentioned previously, the uncertainty estimate for the large CCSD(T)(FC)/CBS component was based on the span of CBS values obtained from four extrapolation formulas. The estimate for the CV component was obtained in the same way. Uncertainties for the other components were based on half the difference between the best and next-to-best values. Some components do not have an associated uncertainty either because multiple values were not available or because experience has shown very little sensitivity to the level of theory or the size of the basis set, such as for the DBOC

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correction. The overall uncertainty was taken as the simple sum of the individual uncertainties, i.e. the worst case scenario, which implicitly assumes that all error components are highly correlated. Experience covering hundreds of examples has shown that this approach to defining the overall theoretical uncertainty results in error bars that almost always encompasses subsequent, higher level calculations. As will be shown, the same was true for hydrazine, where the error bars from a 9 year old calculation encompass the current best estimate. The ∆fΗ°(0 K) value from the current study (111.63 ± 1.73 kJ/mol) is in good agreement with the W4 value (111.90 kJ/mol) reported by Karton et al.45 However, some of this is due to fortuitous cancellation of error, given the differences in the two approaches. Agreement is also good with the 2012 FPD value of 111.92 ± 1.67 kJ/mol).38 An alternative estimate of the uncertainty could be obtained by propagating the errors in quadrature [εTot = (ε12 + ε22 + ε32 +…)½], which implicitly assumes that the error components are entirely independent, and leads to error estimates that are approximately half as large as those produced by the worst case assumption. It should be emphasized that at best these are semi-quantitative values. Table 2 also contains the 0 Κ enthalpy of formation obtained from the computed atomization energy and enthalpies of formation for the atoms taken from ATcT, as well as the 298.15 K value obtained by using the current ATcT non-rigid rotor/anharmonic oscillator (NRRAO) partition function for hydrazine (vide infra). No attempt was made to ascribe an uncertainty to the temperature conversion. Consequently, the 0 K and 298.15 K theoretical uncertainties in Table 2 are identical. Table 3 presents the best composite theoretical equilibrium structure for hydrazine along with the available electron diffraction,106-107 microwave 108 and IR structures.106, 109 The theoretical and experimental structures are in fair agreement given the intrinsic difference between equilibrium (theory) and vibrationally-averaged ground-state (experiment) structures. IV. ATcT Results and Discussion The values for enthalpies of formation found in standard sequentially-built thermochemical tabulations, such as JANAF1 or Gurvich at al.,2 are traditionally derived

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entirely from experimental measurements. Since there are no relevant experimental gasphase measurements that can independently establish the enthalpy of formation of hydrazine, the sequence focuses first on deriving the enthalpy of formation of the liquid phase, and then uses the latter to derive the gas-phase value. For the condensed phase, JANAF1 considered the combustion calorimetry results of Hughes et al.110 on pure liquid hydrazine (including a subsequent slight adjustment by Cole and Gilbert111) and on hydrazine monohydrate, where the latter result was combined with the enthalpy of solution of hydrazine determined of Bushnell et al.112 to provide the necessary interconversion between the measurements on pure hydrazine and its monohydrate. The two possible paths, as analyzed by JANAF, produced ∆fH°(298.15 K) of liquid hydrazine of 50.4 and 50.9 kJ/mol, respectively, and JANAF selected as the final value an “intermediate result” of 50.626 ± 0.4 kJ/mol. Gurvich et al.2 considered the same measurements, as well as the later combustion calorimetry of Aston et al.113 (which produced 50.12 kJ/mol), and selected for ∆fH°(298.15 K) of liquid hydrazine a weighted mean value of 50.38 ± 0.30 kJ/mol. Clearly, the values found in JANAF and in Gurvich et al. are very similar, the slight difference of ~0.2 kJ/mol being well contained within the quoted uncertainties. The enthalpy of vaporization corresponds to the difference between the enthalpies of formation of liquid and gas-phase hydrazine. Both in JANAF1 and in Gurvich et al.,2 the relevant value comes from the measurements of Scott et al.,114 with the somewhat less accurate measurements of Hieber and Woerner115 cited as additional corroboration. From their vapor pressure measurements, Scott et al.114 derived ∆vapH°(298.15 K) = 10.700 ± 0.075 kcal/mol (44.77 ± 0.31 kJ/mol); Gurvich et al. slightly increased the originally quoted uncertainty, taking 44.8 ± 0.4 kJ/mol as the vaporization enthalpy used to derive the final enthalpy of formation of gas-phase hydrazine of 95.18 ± 0.50 kJ/mol at 298.15 K. JANAF, on the other hand, put an effort in reanalyzing the vapor-pressure measurement of Scott et al., and obtained from a 2nd law analysis a vaporization enthalpy of 10.683 ± 0.003 kcal/mol (44.698 ± 0.013 kJ/mol) and from a 3rd law analysis 10.696 kcal/mol (44.752 kJ/mol), crediting their choices of the partition functions for the unusually high consistency between the 2nd and 3rd law. From their reanalysis of the vaporization

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enthalpy of Scott et al. and their enthalpy of formation of liquid hydrazine, JANAF derives 95.35 ± 0.8 kJ/mol for the 298.15 K enthalpy of formation of gas phase hydrazine. The experimental determinations discussed above were included early on in the ATcT TN. As mentioned in the Introduction, both ATcT TN ver. 1.112 and ver. 1.118 produce an enthalpy of formation for hydrazine that is quite similar to the values derived in JANAF and Gurvich et al. purely from existing experimental data. Indeed, the variance decomposition approach, which reveals the detailed provenance of ATcT results,14, 116 confirms that in both ATcT TN versions the primary contributions to enthalpy of formation of gas-phase hydrazine are the experimental combustion calorimetric measurements leading to the enthalpy of formation of liquid hydrazine (Cole and Gilbert111 and Hughes et al.,110 as well as Aston et al.113), and hydrazine monohydrate (Cole and Gilbert111 and Hughes et al.110 together with Bushnell et al.112) while the link to gas-phase enthalpy of formation is provided by the highly accurate JANAF reevaluation of the vaporization enthalpy of Scott et al.114 Notably, the final error bar of the ATcT enthalpy of formation of liquid hydrazine, ± 0.19 kJ/mol, arises from the combined knowledge content of three mutually consistent calorimetries, where the top contributor alone is accurate to about ± 0.21 kJ/mol, and the other two calorimetries entirely agree within their uncertainties of ± 0.33 and ± 0.63 kJ/mol. ATcT TN ver. 1.112 and ver. 1.118 also included several theoretical results, such as the 2008 W4 calculations by Karton et al.45 (both the total atomization energy and the hydrogenation of N2H4 to produce two NH3 molecules), as well as the earlier CCSD(T)/CBS results of Feller et al.20 (which are similar to those of Matus et al.56) and CCSDT(Q)/CBS of Klopper et al.59 who used corrections based on explicitly correlated methods. In addition, these versions of the TN also contained the results of several standard mid-level computations (such as CBS-APNO, G3X, G4, CBS-QB3, all computed in-house), as well as the W1 result of Parthiban and Martin.117 Given the differences in the various approaches, it was not surprising that the theoretical data were not found to be entirely consistent with the experimental determinations. Furthermore, the underlying statistical analysis of ATcT found that the mutually consistent and apparently highly accurate (all sub-kJ/mol) experimental data on liquid hydrazine holds a cumulative

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statistical weight that is significantly larger than the nominally less accurate theoretical data on gas-phase hydrazine. One of the complications additionally disfavoring the theoretical data is that the latter set displays a spread of values that is somewhat higher than usual, suggesting that hydrazine is perhaps a moderately pathological species for one or more levels of theory. Consequently, the ATcT statistical analysis in ver. 1.112 and 1.118 of the TN ended up enlarging the prior (initially assigned) uncertainties of the theoretical entries by factors ranging between 1.1 and 2.1, further lowering their influence over the final result. Thus, in these versions of the ATcT TN, the relatively accurate and mutually consistent calorimetric measurements that determine the enthalpy of formation of liquid hydrazine hold a firm statistical grip over the resulting gas-phase enthalpy of formation via the nominally accurate JANAF redetermination of the vaporization enthalpy. However, in spite of the significant spread among the theoretical values for the gas-phase enthalpy of formation of hydrazine, they appear to be systematically higher than the corresponding ATcT enthalpy of formation (see Table 1, as well as the current theoretical result in Table 2), suggesting that the latter may have some hidden problem. While it is in principle possible that all three combustion calorimetric measurements of liquid hydrazine suffer from some unknown systematic problem, the resulting liquid-phase enthalpy of formation influences the gas-phase enthalpy of formation via a solitary link given by the JANAF redetermination of the vaporization enthalpy. Thus, in the absence of either a clear indication of a systematic problem in the calorimetry, or a credible indication that hydrazine is indeed a pathological case for theory, it seems appropriate to reexamine the vaporization enthalpy as a potential culprit for skewing the gas-phase result: By Occam's razor criterion, it is reasonable to suspect that a single determination is the most likely source of a problem. Admittedly, the ultra-tight uncertainty of ± 0.013 kJ/mol (0.003 kcal/mol), as assigned by JANAF to their 2nd law reinterpretation of the data of Scott et al.114 is very likely extremely optimistic, and, in fact, already at the time of generating the initial entry in the earlier versions of the TN, its prior uncertainty was increased by a factor of 3, and the determination was entered as 44.73 kJ/mol (10.69 ± 0.01 kcal/mol). Nevertheless, this led to the already discussed results in ATcT TN ver. 1.112 and 1.118. A second look at

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the JANAF vaporization enthalpy, taken while preparing revisions leading to ATcT TN ver. 1.122, suggested that even ± 0.04 kJ/mol (0.01 kcal/mol) is probably still too optimistic. In general, our experience gained over the years by preparing and analyzing ATcT TN data, is that vaporization enthalpies quite often (though by all means not always) tend to have uncertainties on the optimistic side. There are various reasons for this: possible systematic errors are often underestimated or ignored, resulting in a quoted uncertainty that reflects just the random scatter in the data, sometimes at the level of one standard deviation instead of the 95% confidence limit required in thermochemistry.8 Another frequent systematic error stems from the corrections from measured, real-gas behavior, to the ideal-gas behavior that is needed as input to derive thermochemical values, resulting often in inadequate or missing corrections. Thus, on a tentative basis, we have decided to entirely disregard the tight uncertainty assigned by JANAF to their reevaluation of the vaporization enthalpy, and assign a more generous prior uncertainty of ± 0.4 kJ/mol (0.1 kcal/mol) to the enthalpy of vaporization, guided both by the ± 0.31 kJ/mol (0.075 kcal/mol) uncertainty as originally assigned by Scott et al.114 (additionally rounded up to reflect the fact that their real-to-ideal correction, based on the Berthelot equation, was rather simplistic), as well as by the uncertainty of ± 0.4 kJ/mol assigned by Gurvich et al. to same measurement. It was felt that this reassignment as the estimated prior would be more in line with the expected general accuracy of such determinations. The relaxation of the prior uncertainty assigned to the vaporization enthalpy of hydrazine successfully loosened the statistical grip of experimental data over the gasphase enthalpy of formation of hydrazine, and made the theoretical entries related to hydrazine statistically relevant. Thus, in ATcT TN ver. 1.122,14, 118 which incorporates this change, the enthalpy of formation of gas-phase hydrazine is 111.84 ± 0.49 kJ/mol at 0 K or 97.68 ± 0.49 kJ/mol at 298.15 K, a change upwards by 2.13 kJ/mol compared to ATcT TN ver. 1.118. This value is in excellent agreement with the current theoretical value of 111.64 ± 1.73 kJ/mol at 0 K (or 97.49 ± 1.73 kJ/mol at 298.15 K), given in Table 2, as well as with a number of prior theoretical results given in Table 1. It should be noted that the current theoretical result is not included in ATcT TN ver. 1.122 and is hence not influencing the ATcT result, and thus the fact that they differ only by 0.20 kJ/mol - much less than the uncertainty of either of them - is extremely pleasing. On the other hand, the 14


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enthalpy of formation of liquid hydrazine stays largely unchanged in ver. 1.122: 50.68 ± 0.18 kJ/mol at 298.15 K (cf. to 50.82 ± 0.19 kJ/mol in ver. 1.118; the difference of 0.14 kJ/mol is entirely contained within the resulting uncertainty). The variance decomposition shows that the provenance of the enthalpy of formation of the liquid continues to rely on experimental calorimetry. However, the provenance of the enthalpy of formation of gasphase hydrazine is now largely decoupled from the liquid-phase and is rather distributed: it takes 45 contributors in order to justify the top 90% of the provenance. The top four contributors are the theoretical W4 hydrogenation enthalpy (21.3%), the atomization energy (14.8%), the decomposition energy into trans-HNNH and H2 of Karton et al.,15, 43, 45

and the hydrogenation enthalpy based on the explicitly correlated approach of Klopper

et al.119 The next contributor is the vaporization enthalpy of hydrazine based on the measurements of Scott et al.114 (discussed earlier), but with a posterior uncertainty further adjusted upward by an additional factor of 5.5 (leading to a posterior uncertainty of ± 0.55 kcal/mol or ± 2.3 kJ/mol). In fact, assuming that the calorimetric measurements on liquid hydrazine are correct, the ATcT value for the 298.15 K vaporization enthalpy of hydrazine from TN ver. 1.122 is 47.00 ± 0.52 kJ/mol (11.23 ± 0.13 kcal/mol), 0.53 kcal/mol higher that the value of 10.70 kcal/mol derived by Scott et al. It should be noted that the versions of ATcT discussed above use the partition function for gas-phase hydrazine imported from Gurvich et al.2 This is a rigid rotor harmonic oscillator (RRHO) partition function, based on then-available experimental fundamentals, with the ν7 (torsion) contribution replaced by an approximate hindered rotor contribution relying on an estimated barrier height. Though we were not expecting substantial differences at 298.15 K for the resulting enthalpy increment (which affects the 0 to 298.15 K conversion of the enthalpy of formation), for the sake of completeness we have computed an improved non-rigid rotor anharmonic oscillator (NRRAO) partition function. The latter is based on currently available experimental fundamentals (3398, 3329, 1642, 1312, 1077.24, 795.14, 376.40, 3390, 3297, 1625, 1265, and 937.16 cm−1 for ν1 through ν12)120-126 and experimental rotational constants (4.78556402, 0.80332241, 0.80288878 cm−1).127-128 The ν7 contribution is replaced by a state count over the solutions of a one-dimensional hindered rotor potential. The potential was computed at

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several levels of theory using relaxed scans (B3LYP/6-31G(2df,p), B3LYP/cc-pVTZ, B3LYP/aug-cc-pVTZ, B2PLYPD3/aug-cc-pVTZ, CCSD(T)/cc-pVTZ) and was solved using the DVR procedure of Colbert and Miller129 and a reduced moment of inertia adjusted such that the resulting fundamental corresponds to the experimental value of ν7 that is being replaced. All computed torsional potentials had two gauche (enantiomeric) minima separated by two maxima: the higher and the lower maximum corresponding to eclipsed and staggered NH2 moieties, respectively; the exception being the potential at the lowest, B3LYP/6-31G(2df,p), level of theory (which displayed an additional very shallow artifactual minimum at the top of the staggered maximum). After comparing the solutions of all computed potentials to the experimental band centers (and their splitting) of the first two overtones of the torsion126, 130 we have selected the B3LYP/cc-pVTZ potential as the apparent best match to experiment. The rotational contribution to the partition function includes nuclear spin statistics, the effect of centrifugal distortion, and a correction for low temperature, while the vibrational contribution includes corrections arising from anharmonic constants and vibration-rotation interaction,2, 130-134 with the necessary spectroscopic constants computed using second-order vibrational perturbation theory (VPT2) at the same level of theory as the selected hindered rotor potential. Though at higher temperatures (1000 K and up) the differences become more noticeable, at 298.15 K the new ATcT NRRAO partition function does not differ significantly from that used by Gurvich et al. (isobaric heat capacity, entropy, and enthalpy increment of 49.094 J/K/mol, 238.393 J/K/mol, and 11.457 kJ/mol, vs. 48.422 J/K/mol, 238.465 J/K/mol, and 11.449 kJ/mol in Gurvich et al.). In particular, the resulting difference between ∆fΗ°(298.15 K) and ∆fΗ°(0 K) of gas-phase hydrazine using the NRRAO partition function is 14.15 kJ/mol, essentially identical to 14.16 kJ/mol from Gurvich et al.; this can be compared to 14.16 kJ/mol that would be obtained if the new NRRAO partition function were to be simplified to an RRHO partition function with only a correction for internal rotor as described above. Parenthetically, an entirely RRHO partition function would produce 14.33 kJ/mol using the same experimental fundamentals as given above, or 14.39 kJ/mol using the computed fundamentals obtained at the CCSD(T)(FC)/aug-cc-pVQZ level of theory.

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The last part of the present ATcT analysis is to incorporate in the TN the current theoretical total atomization energy of 1693.65 ± 1.73 kJ/mol (see Table 2), as well as the improved partition function, and thus combine all available knowledge and obtain the best currently available thermochemistry of hydrazine. Since ver. 1.122, the TN has undergone several expansions related to other projects, producing subversions such as 1.122b,135 1.122d,136 122e,137 and 1.122h.138 The latest developmental version 1.122p, which incorporates the current theoretical result, produces the following enthalpies of formation at 298.15 K (0 K): gas-phase hydrazine: 97.42 ± 0.47 kJ/mol (111.57 kJ/mol) and liquid-phase hydrazine: 50.68 ± 0.18 kJ/mol (57.24 kJ/mol). The resulting enthalpy of vaporization at 298.15 K is 46.74 ± 0.50 kJ/mol, noticeably higher (~ 2 kJ/mol) than the value implied by the vapor pressure measurements of Scott et al., 10.70 kcal/mol (44.77 kJ/mol). The current ATcT enthalpy of formation for liquid hydrazine, 50.68 ± 0.18 kJ/mol at 298.15 K, continues to be in good accord with the previous values listed in JANAF (50.63 ± 0.4 kJ/mol), Gurvich et al. (50.38 ± 0.30 kJ/mol), and earlier version of ATcT (50.82 ± 0.19 kJ/mol, TN ver. 1.118). The current ATcT value for the gas-phase enthalpy 97.41 ± 0.47 kJ/mol at 298.15 K, is ~2 kJ/mol higher than the purely experimental values listed in JANAF (95.35 ± 0.80 kJ/mol), Gurvich et al. (95.18 ± 0.50 kJ/mol), as well as in earlier versions of ATcT (95.55 ± 0.19 kJ/mol), which also had a decisively experimental provenance, but is in excellent agreement with the current high-accuracy computational value based on the FPD approach (97.48 ± 1.73 kJ/mol). It is also in admirable agreement with a number of previous theoretical values listed in Table 1, such as those obtained from the approaches of Karton et al.15 Matus et al.,56-58 Feller et al.,20 or Klopper et al.59 As opposed to the very recent value of Dorofeeva et al.17 (97.0 ± 3.0 kJ/mol, arising from 75 working reactions handled with the G4 method), the value of Simmie,16 obtained by the 4-method average approach and quoted to have an uncertainty of ± 2 kJ/mol, is higher than the current ATcT value by nearly twice as much, and, in view of both the current results and earlier theoretical results listed in Table 1, appears to be an outlier. V. Conclusion

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In order to address the accuracy of the long-standing experimental enthalpy of formation of gas-phase hydrazine, presented in terms of 0 K values as 109.43 ± 0.8 kJ/mol (JANAF1), 109.34 ± 0.50 kJ/mol (Gurvich et al.2), or 109.71 ± 0.19 kJ/mol (ATcT TN ver. 1.118), its provenance was re-examined in light of new high-end calculations of the FellerPeterson-Dixon variety, which produce a value higher by ~2 kJ/mol, 111.64 ± 1.73 kJ/mol at the same temperature. A variance decomposition analysis of the provenance of the earlier ATcT result suggests that an apparently highly accurate determination of the vaporization enthalpy of hydrazine, based on the 2nd and 3rd law reinterpretation of the vapor pressure measurements of Scott et al.114 by the JANAF team, creates an unrealistically strong connection between the gas phase thermochemistry of hydrazine and the calorimetric results defining the thermochemistry of liquid hydrazine, and was identified as the probable culprit. Relaxing the corresponding uncertainty for the vaporization enthalpy allows the gas-phase theoretical results to become involved in determining the thermochemical pathways leading to the gas-phase enthalpy of formation. The new enthalpy of formation of gas-phase hydrazine, based on balancing all available experimental and theoretical knowledge included in the ATcT Thermochemical Network, was determined to be 111.57 ± 0.47 kJ/mol at 0 K (97.42 ± 0.47 kJ/mol at 298.15 K).

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Author Information *E-mail: [email protected]; [email protected]; [email protected].

Acknowledgments The work at Argonne National Laboratory (BR and DHB) was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences, under Contract No. DE-AC0206CH11357. Figure Cations 1. Variation in various hydrazine ∆fH°(0 K) theoretical and experimental values as a function of time.

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56. Matus, M. H.; Arduengo, A. J., III; Dixon, D. A., The Heats of Formation of Diazene, Hydrazine, N2H3+, N2H5+, N2H, and N2H3 and the Methyl Derivatives CH3NNH, CH3NNCH3, and CH3HNNHCH. J. Phys. Chem. A 2006, 110, 10116-10121. 57. Matus, M. H.; Nguyen, M. T.; Dixon, D. A., Heats of Formation of Diphosphene, Phosphinophosphinidene, Diphosphine, and Their Methyl Derivatives, and Mechanism of the Borane-Assisted Hydrogen Release. J. Phys. Chem. A 2007, 111, 1726-1736. 58. Matus, M. H.; Nguyen, M. T.; Dixon, D. A., Erratum: Heats of Formation of Diphosphene, Phosphinophosphinidene, Diphosphine, and Their Methyl Derivatives, and Mechanism of the Borane-Assisted Hydrogen Release. J. Phys. Chem. A 2009, 113, 944. 59. Klopper, W.; Ruscic, B.; Tew, D. P.; Bischoff, F. A.; Wolfsegger, S., Atomization Energies From Coupled-Cluster Calculations Augmented With Explicitly-Correlated Perturbation Theory. Chem. Phys. 2009, 356, 14-24. 60. Kiselev, V. G.; Gristan, N. P., Theoretical Study of the Primary Processes in the Thermal Decomposition of Hydrazinium Nitroformate. J. Phys. Chem. A 2009, 113, 11067-11074. 61. Purvis, G. D., III; Bartlett, R. J., A full coupled-cluster singles and doubles model: The inclusion of disconnected triples. J. Chem. Phys. 1982, 76, 1910-1918. 62. Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M., A fifth-order perturbation comparison of electron correlation theories. Chem. Phys. Lett. 1989, 157, 479-483. 63. Watts, J. D.; Gauss, J.; Bartlett, R. J., Coupled-cluster methods with non iterative triple excitations for restricted open-shell Hartree-Fock and other general single determinant reference functions. Energies and analytical gradients. J. Chem. Phys. 1993, 98, 8718-8733. 64. Bartlett, R. J.; Musiał, M., Coupled-cluster theory in quantum chemistry. Rev. Mod. Phys. 2007, 79, 291-352. 65. Feller, D.; Peterson, K. A.; Davidson, E. R., A Systematic Approach to Vertically Excited States of Ethylene using Configuration Interaction and Coupled Cluster Techniques. J. Chem. Phys. 2014, 141, 104302-1-104302-20. 66. Dunning, T. H., Jr., Gaussian basis sets for use in correlated calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007-1023. 67. Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J., Electron affinities of the first row atoms revisited. Systematic basis sets and wave functions. J. Chem. Phys. 1992, 96, 6796-6806. 68. Woon, D. E.; Dunning, T. H., Jr., Gaussian basis sets for use in correlated calculations. IV. Calculation of static electric response properties. J. Chem. Phys. 1994, 100, 2975-2988. 69. Woon, D. E.; Dunning, T. H., Jr., Gaussian basis sets for use in correlated calculations. V. Core-valence basis sets for boron through neon. J. Chem. Phys. 1995, 103, 4572-4585.

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96. de Jong, W. A.; Harrison, R. J.; Dixon, D. A., Parallel Douglas-Kroll energy and gradients in NWChem: Estimating scalar relativistic effects using Douglas-Kroll contracted basis sets. J. Chem. Phys. 2001, 114, 48-53. 97. Kállay, M.; Rolik, Z.; Ladjanszki, I.; Szegedy, L.; Ladoczki, B.; Csontos, J.; Kornis, B. MRCC, a quantum chemical program suite, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, www.mrcc.hu 2013. 98. Goodson, D. Z., Extrapolating the coupled-cluster sequence toward the full configuration interaction limit. J. Chem. Phys. 2002, 116, 6948-6956. 99. Feller, D.; Dixon, D. A., Coupled Cluster Theory and Multi-reference Configuration Interaction Study of FO, F2O, FO2 and FOOF. J. Phys. Chem. A 2003, 107, 9641-9651. 100. Schröder, B.; Sebald, P.; Stein, C.; Weser, O.; Botschwina, P., Challenging HighLevel ab initio Rovibrational Spectroscopy: The Nitrous Oxide Molecule. Z. Phys. Chem. 2015, 229, 1663-1691. 101. Knowles, P. J.; Hampel, C.; Werner, H.-J., Coupled cluster theory for high spin, open shell reference wave functions. J. Chem. Phys. 1993, 99, 5219-5227. 102. Deegan, M. J. O.; Knowles, P. J., Perturbative corrections to account for triple excitations in closed and open shell coupled cluster theories. Chem. Phys. Lett. 1994, 227, 321-326. 103. Pfeiffer, F.; Rauhut, G.; Feller, D.; Peterson, K. A., Anharmonic Zero Point Vibrational Energies: Tipping the Scales in Accurate Thermochemistry Calculations? J. Chem. Phys. 2013, 138, 044311-1-044311-10. 104. Moore, C. E., Atomic Energy Levels. Washington, D.C., 1971; Vol. Natl. Stand. Ref. Data Ser., National Bureau of Standards (U.S.) 35. 105. Stanton, J. F.; Gauss, J.; Harding, M. E.; Szalay, P. G.; from, w. c.; Auer, A. A.; Bartlett, R. J.; Benedikt, U.; Berger, C.; Bernholdt, D. E.; Bomble, Y. J.; Cheng, L.; Christiansen, O.; Heckert, M.; Heun, O.; et al.; and the integral packages MOLECULE (J. Almlöf and P.R. Taylor), P. P. R. T., ABACUS (T. Helgaker, H.J. Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A. V. Mitin and C. van Wüllen, http://www.cfour.de/ CFOUR, a quantum chemical program, 2010. 106. Kohata, K.; Fukuyama, T.; Kuchitsu, K., Molecular Structure of Hydrazine As Studied by Gas Electron Diffraction. J. Phys. Chem. 1982, 86, 602-606. 107. Morino, Y.; Iijima, T.; Murata, Y., An electron Diffraction Investigation of the Molecular Structure of Hydrazine. Bull. Chem. Soc. Jpn 1960, 33, 46-48. 108. Tsunekawa, S., Microwave Spectrum of Hydrazine-1,2-d2. J. Phys. Soc. Jpn. 1976, 41, 2077-2083. 109. Tsuboi, M.; Overend, J., Amino wagging and inversion in hydrazines: RR branch of the antisymmetric wagging band of NH2NH2. J. Mol. Spectrosc. 1974, 52, 256-268.

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110. Hughes, A. M.; Corruccini, R. J.; Gilbert, E. C., Studies on Hydrazine: The Heat of Formation of Hydrazine and of Hydrazine Hydrate. J. Am. Chem. Soc. 1939, 61, 26392642. 111. Cole, L. G.; Gilbert, E. C., The Heats of Combustion of Some Nitrogen Compounds and the Apparent Energy of the N-N Bond. J. Am. Chem. Soc. 1951, 73, 5423-5427. 112. Bushnell, V. C.; Highes, A. M.; Gilbert, E. C., Studies on Hydrazine: Heats of Solution of Hydrazine and Hydrazine Hydrate at 25°. J. Am. Chem. Soc. 1937, 59, 21422144. 113. Aston, J. G.; Rock, E. J.; Jsserow, S., The Heats of Combustion of the Methyl Substituted Hydrazines and Some Observations on the Burning of Volatile Liquids. J. Am. Chem. Soc. 1952, 74, 2484-2486. 114. Scott, D. W.; Oliver, G. D.; Gross, M. E.; Hubbard, W. N.; Huffman, H. M., Heat Capacity, Heats of Fusion and Vaporization, Vapor Pressure, Entropy and Thermodynamic Functions. . J. Am. Chem. Soc. 1949, 71, 2293-2297. 115. Hieber, W.; Woerner, A., Thermochemische Messungen an komplexbildenden Aminen und Alkoholen Z. Elektrochem 1934, 40, 252-256. 116. Ruscic, B.; Feller, D.; Peterson, K. A., Active Thermochemical Tables: Dissociation Energies of Several Homonuclear First‐Row Diatomics and Related Thermochemical Values. Theor. Chem. Acc. 2014, 133, 1415/1-12. 117. Parthiban, S.; Martin, J. M. L., Assessment of W1 and W2 theories for the computation of electron affinities, ionization potentials, heats of formation, and proton affinities. J. Chem. Phys. 2001, 114, 6014-6029. 118. Ruscic, B.; Bross, D. H., ATcT Enthalpies of Formation Based on Version 1.122 of the Thermochemical Network, available at ATcT.anl.gov. 2017. 119. Klopper, W.; Bachorz, R.; Tew, D. P.; Hättig, C., Sub-meV accuracy in firstprinciples computations of the ionization potentials and electron affinities of the atoms H to Ne. Phys. Rev. A 2010, 81, 022503-1-022503-6. 120. Catalano, E.; Sanborn, R. H.; Frazer, J. W., On the Infrared Spectrum of Hydrazine Matrix-Isolation Studies of the System NH2NH2:N2 (l). J. Chem. Phys. 1963, 38, 22652274. 121. Durig, J. R.; Griffin, M. G.; MacNamee, R. W., Raman Spectra of Gases. XV: Hydrazine and hydrazine-d4. J. Raman Spectrosc. 1975, 3, 133-141. 122. Ohashi, N., Fourier Transform Spectrum of the Torsional Band of Hydrazine. J. Mol. Spectrosc. 1986, 117, 119-133. 123. Gulaczyk, I.; Krezglewski, M.; Valentin, A., Antisymmetric Amino-Wagging Band of Hydrazine up to K' = 13 Levels. J. Mol. Spectrosc. 1997, 186, 246-248. 124. Durig, J. R.; Zheng, C., On the Vibrational Spectra and Structural Parameters of Hydrazine and some Methyl Substituted Hydrazines. Vib. Spectrosc. 2002, 30, 59-67.

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Table 1. Literature Values for the Enthalpy of Formation of Hydrazine (kJ/mol). Source

Method

Barreto et al. 2005a

B3LYP

∆fH°(0 K)

∆fH°(298.15 K)

-54.16

G2

99.85

G3

100.77

Matus et al. 2006b

coupled cluster

111.29

DeYonker et al. 2006c

ccCA-CBS-2

90.4

ccCA-CBS-2+SO+SR

92.9

Feller et al. 2008d

96.65

FPD

110.5 ± 2.5

W4

111.90

Klopper et al. 2009f

coupled cluster

111.29

Kiselev, Gristan 2009g

G3

Klopper et al. 2010h

coupled cluster

112.59

Karton et al. 2011i

W4

111.77

FPD

111.92 ± 1.67

Vogiatzis et al. 2014

coupled cluster

113.8

Chan, Radom 2015l

W3X-L

112.1

W1X-1

111.2

W2X

112.8

QB3

113.8

99.3

APNO

114.6

100.0

G3

118.2

103.7

G4

114.8

100.3

4-method avg.

115.4 ± 2.0

Karton et al. 2008

e

Feller et al. 2012j k

Simmie 2015m

96.2 ± 2.5

104.2

97.40 ± 1.67 97.5

Dorofeeva et al. 2017n

G4 + 75 reactions

NIST-JANAF 1998o

experimental

109.43 ± 0.8

95.35 ± 0.8

Gurvich et al.1989p

experimental

109.34 ± 0.50

95.18 ± 0.50

ATcT 1.112 2014q

experimental

109.66 ± 0.19

95.51 ± 0.19

31

97.0 ± 3.0



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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ATcT 1.118 2015r a

experimental

109.71 ± 0.19

Page 32 of 40

95.55 ± 0.19

Barreto, Vilela and Gargano.55 G3 approximates QCISD(T)/VTZ.

b

Matus, Arduengo and Dixon.56-58 Based on CCSD(T)(FC)/CBS(aVTQ5Z/mixed) +

∆ECV(CCSD(T)(CV)/wCVTZ + ∆ESR(CISD/aVTZ mass velocity + Darwin). The ZPE was based on the average of the CCSD(T)(FC)/aVTZ harmonic frequencies and the experimental fundamentals. Geometries were optimized at the CCSD(T)(FC)/aVTZ level of theory. c

DeYonker, Cundari and Wilson.49

d

Feller, Peterson and Dixon.20 Based on CCSD(T)(FC)/CBS(aVTQ5Z) +

CCSD(T)(CV)/wCV5Z + CCSD(T)(FC)-DK/VTZ-DK + CCSDT(FC)/VTZ + CCSDTQ(FC)/VDZ + cf est. FCI/VDZ. e

Karton, Tarnopolsky, Lamere, Schatz and Martin.45 Geometry taken from

CCSD(T)(FC)/cc-pVQZ. SCF: CBS(aV56Z), Karton/Martin CBS formula. CCSD(FC)/CBS(aV56Z), separate singlet, triplet pair extrapolations using 1/lmax3 and 1/lmax5, respectively. Frozen core triples: CBS(VDTZ), 1/lmax3. T3-(T3): CCSDTCCSD(T) CBS(VDTZ) formula not specified. T4: appears to be based on 1.10 x (CCSDT(Q)/VTZ - CCSDT/VTZ + CCSDTQ/VDZ - CCSDT(Q)/VDZ). T5: CCSDTQ(5)/DZ (Dunning/Hay, no d functions). CCSD(T)(CV): CBS(aCVTQZ) formula not specified. CCSD(T)-DK + DBOC: RHF-DBOC/aug-cc-pVTZ. ZPE: CCSD(T)(FC)/VQZ + a correction for CV effects based on CCSD(T)(CV)/MTsmall with anharmonic correction from a B97-1/pc-2 quartic force field. The value of ΣD0 was taken from Table 2 of this paper (404.73 kcal/mol or 1693.39 kJ/mol). It was converted to a 0 K enthalpy of formation using a sum of atomic enthalpies = 1805.28 kJ/mol. W4 approximates CCSDTQ5/CBS. f

Klopper, Ruscic, Tew, Bischoff and Wolfsegger.59 Explicitly correlated MP2. Geometry

taken from CCSD(T)(CV)/cc-pCVTZ. The value of ΣD0 was taken from Table 1 of this

32


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paper (1694.0 kJ/mol). It was converted to a 0 K enthalpy of formation using a sum of atomic enthalpies = 1805.28 kJ/mol. g

Kiselev and Gristan.60

h

Klopper, Bachorz, Hättig and Tew.21 Explicitly correlated CCSD-F12/def2-QZVPP

CCSD(T)(FC)/(cc-pCVQZ and cc-pCV5Z). Geometry taken from CCSD(T)(CV)/ccpCVTZ. The ZPE (141.2 kJ/mol) was based on CCSD(T)(CV)/cc-pCVTZ + anharmonic MP2/cc-pVDZ. ROHF-CCSD were used to determine the baseline CCSD atomic energies. UCCSD-F12 atomic calculations were used to determine the F12 correction. The value of ΣD0 was taken from Table 3 of this paper (1692.7 kJ/mol). It was converted to a 0 K enthalpy of formation using a sum of atomic enthalpies = 1805.28 kJ/mol. i

Karton, Daon and Martin.15 The value of ΣD0 was taken from a Supplementary Data

table of this paper (404.76 kcal/mol or 1693.52 kJ/mol). It was converted to a 0 K enthalpy of formation using a sum of atomic enthalpies = 1805.28 kJ/mol. j

Feller, Peterson and Dixon.38 Value based on a 5-formula CBS average using up through

the estimated aV7Z energy. Higher order correlation was recovered with CCSDT(FC)/VTZ and CCSDTQ(FC)/VDZ. k

Vogiatzis et al.30 Based on a CCSD(T)+F12+INT atomization energy of 1,691.5 kJ/mol

reported in their Table 5. l

Chan and Radom.28 ZPE based on scaled (0.9886) scaled B3LYP/cc-pVTZ harmonic

frequencies. Values taken from Table 7 and Supporting Information. W2X approximates CCSD(T)/CBS. m

Simmie.16 Average of CBS-QB3 (113.8), CBS-APNO (114.6), G3 (118.2) and G4

(114.8). n

Dorofeeva, Ryzhova and Suchkova.17

o

Chase.1

p

Gurvich et al.2

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q

Ruscic.18

r

Ruscic19

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Table 2. Atomization Energy/Enthalpy Components for N2H4 (1A) (kJ/mol). Component ΣDe R/UCCSD(T)(FC)/CBS(aV67Z)a ∆R/UCCSD(T)(CV)/CBS(wCVQ5Z)a ∆R/UCCSD(T)-DKH/cc-pVQZ-DK ∆CCSDT(FC)/cc-pVQZ ∆CCSDT(Q)(FC)/cc-pVTZ ∆Est. FCI(FC)/cc-pVDZ ∆CCSDT(CV) + CCSDT(Q)(CV)b ∆UCCSD(FC)-DBOC/aVTZ Best Composite ΣDe Estimate Anharm. ZPEb Best Composite ΣD0 Estimate ∆fΗ°(0 K) ∆fΗ°(298.15 K)c a

ΣDe/ΣD0/correction 1828.37 ± 0.92 4.77 ± 0.03 -2.13 ± 0.00 -1.72 ± 0.46 1.84 ± 0.04 0.21 0.13 0.46 1831.93 ± 1.45 -138.28 ± 0.28 1693.65 ± 1.73 111.63 ± 1.73 97.48 ± 1.73

CBS estimate based on 1/(lmax +0.5)4. Atoms are described with R/UCCSD(T) and

atomic symmetry is imposed. The uncertainty was based on the span of values obtained from four CBS extrapolation formulas: 1) E(n) = ECBS + Ae-bn,139 2) 2

E(n) = ECBS + Ae−(n −1) + Be−(n−1) ,140 3) 1/(lmax +0.5)4, 4) 1/lmax3.141 b

Anharmonic zero point vibrational energy is based on CCSD(T)(FC)/aug-cc-pVQZ

harmonic frequencies plus an MP2(FC)/aug-cc-pVTZ anharmonic correction. c

The 298.15 K temperature correction is based on the current ATcT NRRAO partition

function (see text). The RRHO approximation with the CCSD(T)(FC)/aug-cc-pVQZ + anharmonic frequencies results in a slightly lower ∆fΗ°(298.15 K) = 97.25 kJ/mol.

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Page 36 of 40

Table 3. Best Composite Equilibrium Structure and Available Experimental Parameters.a rNN

rNHA

rNHB

Bestb

1.4330

1.0119

1.0090

111.5

107.0

Expt.c rg

1.449

1.021

Expt.c avg.

1.447

1.015

1.015

112

106

Expt.d rm

1.449

1.022

1.022

112

Expt.d r0

NNHA

1.453

1.025

1.025

e

1.447

1.008

1.008

109.15

Expt.f

1.446

1.016

1.016

108.85

Expt.

a

NNHB

Dihe1

Dihe2

117.4

90.2 91

88.05

Units are Å and degrees. Z-matrix:

N NA 1 RNN HA 2 RNHA 1 NNHA HB 2 RNHB 1 NNHB 3 DIHE1 HA 1 RNHA 2 NNHA 4 DIHE2 HB 1 RNHB 2 NNHB 3 DIHE2 b

Best composite theoretical re structure is based on CCSD(T)(FC)/CBS(aVQ56Z) +

∆CCSD(T)(CV)/CBS(wCVTQ5Z) + ∆CCSD(T)(FC)-DK/cc-pVQZ-DK + ∆CCSDT(FC)/cc-pVTZ + ∆CCSDTQ(FC)/cc-pVDZ. c

Experimental gas phase electron diffraction structure from Kohata et al.106 The rg

uncertainties are: 1.449 ± 0.002, 1.021 ± 0.003 Å. The avg. uncertainties are: 1.447 ± 0.002, 1.015 ± 0.002 Å, 112 ± 2, 106 ± 2, 91 ± 2°. d

Experimental gas phase electron diffraction structure from Morino et al.107 The rm

uncertainties are: 1.449 ± 0.004, 1.022 ± 0.006 Å, 112 ± 1.5°. The r0 uncertainties are: 1.453 ± 0.005, 1.022 ± 1.020 Å. e

Experimental microwave structure for deuterated hydrazine from Tsunekawa.108 The

uncertainties are: 1.447 ± 0.005, 1.008 ± 0.008 Å, 109.15 ± 0.8°.

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f

Experimental IR structure from Tsuboi and Overend.109 Structural parameters estimated

from the rotational constants by Kohata et al.106

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Figure 1.

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TOC Graphic

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Variation in various hydrazine ∆fH°(0 K) theoretical and experimental values as a function of time. 108x76mm (300 x 300 DPI)


Page 40 of 40

Enthalpy of Formation of N2H4 (Hydrazine) Revisited - The Journal of

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