Validation of a Database of Formation Enthalpies and of Mid-Level

Article pubs.acs.org/JPCA

Validation of a Database of Formation Enthalpies and of Mid-Level Model Chemistries J. M. Simmie*,† and J. N. Sheahan‡ †

Combustion Chemistry Centre & School of Chemistry, National University of Ireland, Galway H91 TK33, Ireland School of Mathematics & Statistics, National University of Ireland, Galway H91 TK33, Ireland

‡

S Supporting Information *

ABSTRACT: In order to test new procedures for the calculation of basic molecular properties, a properly validated database and computational method appropriate to the range of species at hand is essential. Here formation enthalpies of chemical species CmHnNpOq from their constituent atoms are computed by midlevel composite model chemistries in order to check the contents of the best established and most accurate database, ATcT. Once discrepancies are identified alternative independent procedures and/or higher level model chemistries, which include CCSDT(Q) calculations, are employed to resolve the problems. Shortcomings of the midlevel methods used are signaled where these occur. In addition a more visual statistical analysis than is usual is presented which highlights the outliers and identifies the bias of each method together with associated error bars and the 95% limits of agreement and its error bars.

■

INTRODUCTION The establishment of a database of accurate thermochemical data such as enthalpies of formation1−19 is important for three reasons: 1 Testing of new high-level quantum methods capable of dealing with a wide range of chemical compounds 2 Using the well-validated data to expand the data set to species for which advanced quantum methods are currently too expensive from a computational viewpoint or for which experiment is much too difficult 3 The application of the data to simulation and modeling of combustion phenomena and atmospheric and other chemistries. At present there are a number of such databases in existence with perhaps the most well-known being the Active Thermochemical Tables20 (ATcT) followed by compendia such as the Third Millennium Database21 and the seminal text “Thermochemical Data of Organic Compounds” by Pedley, Naylor, and Kirby.22 The data sets have normally been assembled from experiment, with some input from theoretical quantum chemistry, but there has rarely been a comprehensive test of the data therein. Normally it has been assumed that those values are correct to within the stated uncertainty and methodologies have been tested against such data. So, for example, Karton et al.23 compared the total atomization energies (a precursor of the formation enthalpy) obtained from their W-n computations against a limited subset of the ATcT values. Although they highlighted one discrepancy, namely that of hydrazine, N2H4, they did not take the matter further. Similarly Vogiatzis et al. found differences greater than 4 kJ mol−1 for, inter alia, allene, © 2016 American Chemical Society

cyclopropane, ethane, and hydrazine in their computation of atomization energies via a CCSD(T) + F12 + INT composite scheme.24 An alternative approach is to argue that in order to validate computational approaches highly accurate theoretical reference values are essential; while purely theoretical values are useful, experimental results cannot be excluded. The mix of experiment and theory that goes into determining the tabulated values in the ATcT is nicely demonstrated by Ruscic.25 In general, there are two different approaches to compute the formation enthalpy of a chemical species from its isolated atoms. The first, which is exemplified by the work of Feller and others, is to evaluate in a step by step manner the various contributions that go into the final answer and to tailor these to the system under investigation in addition to estimating the uncertainties at each step.15 The second approach is more Procustrean, viz. a standardized, largely inflexible, method is uniformly applied irrespective of the actual nature of the species. Competing arguments can be framed as to the benefits of these approaches but for those of us dealing with thousands of chemical compounds, often of a fleeting and transient existence, the practical merits of the latter method are incontrovertible. Recent publications26−28 have shown that a combination of midlevel composite model chemistries can compute the enthalpy of formation of a number of CmHnNpOq closed and open shell molecules which are in good agreement with those in the best-known and validated compendium, the Active Received: July 26, 2016 Revised: September 1, 2016 Published: September 1, 2016 7370

DOI: 10.1021/acs.jpca.6b07503 J. Phys. Chem. A 2016, 120, 7370−7384

The Journal of Physical Chemistry A

■

Thermochemical Tables.20 In a very limited number of cases, such as 1,3-cyclopentadiene and hydrazine, disagreement was shown to be due to suspect tabulated values lying well outside the stated limits of accuracy. Here we revisit those works and present a more overarching view of the statistics with a more graphic nature than is usual. Initially we analyze the results of more than 120 CHNO species containing up to eight “heavy” atoms with midlevel model chemistries with the twin objectives of identifying cases where either the ATcT database values are incorrect or where the theoretical methods being used are insufficient for the task. For the first scenario, corrections to the tabulated values are suggested by independent procedures backed up by much higher level model chemistries and by a thorough review of the literature. For the second scenario, where it is judged that the tabulated values are correct, the shortcomings of the midlevel methods are identified and then more advanced but still affordable model chemistries are tested. Once a corrected data set has been obtained the results are analyzed by standard statistical measures which allows for the easier identification of outliers. Finally, the variable uncertainties in the ATcT are considered to see whether these can be taken into account in any meaningful analysis of the computational results.

RESULTS The contents of previous works are repeated here in Table 2 which together with Table 3 comprises the complete data set of 122 species under test; x¯ is the average computed formation enthalpy and u is defined in equn. 1. The bulk of the ATcT values were taken from version 1.112 but updated from recent publications25,41with the exception of ethylidyne 2CH3C the revisions are very small. Additional Species. Additional computations for 12 mainly open shell N-species have been made subsequently and the results are shown in Table 3. Preliminary Treatment. We amalgamate the results for all 122 species in order to get an overview of the performance of the composite methods. In the discussion which follows we largely adopt the terminology of Bland and Altman.42 The “mean” in Figure 1 below represents the average enthalpy of formation of all n species at 0 K computed from all four equally weighted model chemistries or x.̅ Thus, the x-axis is the average of the standard reference ATcT values and of x̅ or Xi = (ATcTi + xi̅ )/2 and the y-axis is the difference di = (ATcTi − xi̅ ). An estimated uncertainty, u, is defined as the sample standard deviation: 4

■

3

2

4

n

d̅ =

H ( S1/2)

N ( S3/2)

O ( P2)

0 298.15

711.38 716.87

216.034 217.998

470.573 472.435

246.844 249.229

(1)

n

∑ (ATcTi − xi̅ )/n = i

∑ (di)/n i

(2)

and the associated 95% limits of agreement are ≈1.96 sd where sd is the standard deviation in d¯ given by sd =

∑ (di − d ̅ )2 (n − 1)

(3)

assuming that the differences are normally distributed. Uncorrected Data Set. We begin by considering all the 122 compounds in our uncorrected data set without regard to whether they are closed or open shell. In this case the bias amounts to d¯ = +0.27 kJ mol−1 which in essence means that the compound method approach, that is averaging the four model chemistries, underestimates formation enthalpies by 0.27 kJ mol−1 relative to the ATcT values. The associated standard deviation is sd = 2.24 also in kJ mol−1; in what follows we omit the units since these are always in kJ mol−1. The estimated standard error in the bias is sd/√n which for n = 122 data-points amounts to 0.20; hence, the 95% limits of agreement, given by d̅ ± (1.96sd), are +4.67 and −4.13 for the upper and lower limits, d̅u and dS̅ , respectively. At the 95% confidence level the Student’s t-test for 121 degrees of freedom (n−1) is t = 1.980 and hence the 95% confidence intervals for the bias are d ̅ ± (tsd / n − 1 ) or 0.69 and −0.14 for the upper and lower intervals respectively or in a more compact notation +0.27 ± 0.40. The estimated standard error in the limits of agreement is approximately given by 1.709 sd/√n = 0.347, hence the 95% confidence intervals, uu, and uS , for the upper limit, u are du ± (tsd / n − 1 ) = 5.42 and 4.02 or more succinctly as 4.67 ± 0.69 and similarly for the lower limit, S , at SS = −4.82 and Su =

3

C ( P)

3

These resultant values are then compared against the ATcT with the mean difference or bias, expressed as

−1

T/K

∑1 (xi − xi)2

ui =

COMPUTATIONAL METHODOLOGY We follow the procedures detailed in our earlier work26−28 which can be summarized as follows: the composite model chemistries CBS-QB3,29 CBS-APNO,30 G3,31 and G432 are used to calculate, via the application Gaussian-09,33 the zeropoint corrected electronic energy at 0 K and the enthalpy at 298.15 K for each molecule and for the constituent atoms. The total atomization energies at 0 and 298.15 K are then computed and in conjunction with the experimental formation enthalpies of the atoms in their ground states, C (3P), H (2S1/2), N (4S3/2), and O (3P2), Table 1, the formation enthalpies of the molecules, Δf H°, are obtained. Table 1. Gaseous Atomic Formation Enthalpies/kJ mol

Article

Higher level calculations were used as an independent check; these were based on very recent methodologies developed by Chan and Radom34 stemming from the Weizmann-n family of Martin et al.35−37 Specifically the W2X protocol provides an approximation to the all-electron scalar-relativistic coupled cluster theory including single and double excitations with a perturbative treatment of triples CCSD(T) at the complete basis set limit via the application MOLPRO.38 While W3X-L builds on W2X by incorporating post-CCSD(T) correlation terms up to CCSDT(Q) which requires in addition the multireference coupled cluster code MRCC of Kállay et al.39 These two protocols optimize the structures and compute the frequencies with the B3LYP functional and the cc-pVTZ+d basis set using different scale factors for the zero-point energies, enthalpies, and entropies of 0.9886, 0.9926, and 0.9970 respectively. In tests against the G2/97 set of thermochemical properties40 Chan and Radom have shown that their W3X-L energies represent the highest level theoretical values currently available. 7371


Article

The Journal of Physical Chemistry A Table 2. Formation Enthalpies of Compounds at 0 K/kJ mol−1 QB3

APNO

1,3-butadiyne 1,3-Cyclopentadiene 1-butene 1-butyne 2,2,4-TMP gauche 2,3-butanedione 2-butyne acetic acid (cis) acetone allene benzene carbon monoxide cis-2-butene cyclobutene cyclohexane cyclopropane cyclopropene dimethyl ether dioxirane ethanal ethane ethene ethyne ethynol formaldehyde formic acid (syn) formic acid (anti) glyoxal (trans) glyoxal (cis) isobutane isobutene ketene methane methanediol methanol methyl formate (cis Z) methyl hydroperoxide n-butane o-benzyne oxirane propane propene propyne toluene trans-2-butene vinyl alcohol (anti) vinyl alcohol (syn)

species

468.4 161.4 28.7 188.4 −160.1 −315.2 165.9 −422.7 −200.5 202.3 107.2 −115.6 21.8 186.7 −74.0 76.7 298.9 −171.4 0.4 −156.9 −66.5 64.1 234.8 95.9 −110.2 −377.1 −360.1 −214.3 −194.9 −100.3 11.3 −45.5 −66.3 −385.2 −193.2 −354.1 −123.0 −92.4 477.3 −43.6 −79.0 40.3 198.6 80.5 16.6 −108.6 −112.7

462.1 148.2 15.7 178.0 −191.5 −319.8 155.8 −422.6 −207.5 196.5 91.8 −113.8 8.4 175.5 −97.3 65.6 292.3 −173.8 5.7 −159.0 −75.0 59.8 233.5 97.4 −107.1 −372.6 −356.1 −209.7 −190.7 −116.9 −1.8 −47.2 −70.9 −381.7 −193.5 −351.6 −117.6 −109.0 464.0 −44.3 −91.6 31.3 191.6 61.0 3.4 −110.9 −114.8

hydrogen azide HNNN nitrosyl hydride HNO peroxynitrous acid trans perp nitrous acid trans nitrous acid cis hydroxylamine trans hydroxylamine cis ammonia oxide ammonia nitric acid diazene trans-E diazene cis-Z isodiazene

297.2 105.6 −2.1 −78.4 −76.6 −36.4 −18.3 66.9 −37.1 −137.7 208.2 229.7 305.9

296.4 112.0 7.4 −72.2 −70.0 −31.1 −13.7 73.3 −38.4 −128.1 212.0 233.8 311.2

G3 462.0 155.7 22.4 181.7 −171.7 −313.4 160.3 −418.6 −200.8 196.6 103.8 −114.7 16.2 183.1 −82.6 73.8 295.8 −167.7 9.7 −155.7 −69.2 60.6 230.9 95.9 −107.2 −371.4 −354.8 −209.6 −190.3 −105.7 5.4 −47.1 −67.8 −378.4 −190.1 −348.6 −113.0 −97.9 471.0 −39.6 −83.0 35.5 193.7 75.0 10.7 −109.0 −112.7 Nitrogen Species28 303.0 113.3 12.5 −68.8 −66.1 −29.4 −11.2 76.9 −35.7 −122.7 212.8 235.0 312.8 7372

G4

x¯

u

ATcT

458.6 153.4 23.3 181.3 −169.3 −311.5 160.5 −416.9 −199.6 197.1 102.3 −117.6 16.9 180.3 −80.7 71.9 293.6 −166.8 6.9 −155.5 −67.4 60.8 229.2 95.8 −108.0 −371.4 −354.9 −210.6 −192.2 −103.8 5.6 −45.5 −66.6 −378.1 −189.9 −347.5 −114.1 −95.6 467.4 −41.4 −80.9 36.0 192.7 73.6 11.4 −108.1 −111.9

462.8 154.7 22.5 182.4 −173.1 −315.0 160.6 −420.2 −202.1 198.1 101.3 −115.4 15.8 181.4 −83.6 72.0 295.1 −169.9 5.7 −156.8 −69.5 61.3 232.1 96.2 −108.1 −373.1 −356.5 −211.0 −192.0 −106.7 5.1 −46.3 −67.9 −380.9 −191.6 −350.4 −116.9 −98.7 469.9 −42.2 −83.6 35.8 194.2 72.5 10.5 −109.2 −113.0

4.1 5.5 5.3 4.3 13.2 3.5 4.1 2.9 3.6 2.8 6.6 1.6 5.5 4.7 9.8 4.7 2.9 3.3 3.9 1.6 3.8 1.9 2.5 0.7 1.5 2.7 2.5 2.2 2.1 7.2 5.4 1.0 2.1 3.3 1.9 3.0 4.5 7.2 5.7 2.1 5.6 3.7 3.1 8.2 5.4 1.2 1.2

458.64 118.20 20.92 178.97 −171.20 −310.25 158.72 −419.59 −199.39 197.63 100.70 −113.803c 13.94 173.90 −82.52 70.76 292.64 −166.51 9.00 −154.98 −68.29c 60.96c 228.84c 94.80 −105.35c −371.62 −355.28 −206.85 −188.42 −106.76 3.46 −45.47 −66.550c −379.21 −189.83c −344.54 −114.99 −98.54 469.60 −40.17 −82.13 35.36 192.86 73.69 9.39 −107.93 −112.45

294.5 107.8 7.3 −73.5 −70.8 −31.1 −13.5 72.8 −35.7 −127.7 206.9 228.4 306.0

297.8 109.7 6.2 −73.2 −70.9 −32.0 −14.2 72.5 −36.7 −129.0 210.0 231.7 309.0

3.6 3.6 6.1 4.0 4.3 3.0 3.0 4.1 1.3 6.3 2.9 3.2 3.5

298.13 109.89 7.57 −73.044 −71.25 −33.12 −14.7 72.3 −38.565 −124.45 207.36 229.60 308.00


Article

The Journal of Physical Chemistry A Table 2. continued species

a

QB3

APNO

hydrazine hydrogen cyanide hydrogen isocyanide isofulminic acid HONC fulminic acid HCNOa isocyanic acid HNCO cyanic acid HOCN methylenimine methylamine dimethylamine cyanogen NCCN isocyanogen CNCN diisocyanogen CNNC nitrosobenzene trimethylamine

113.8 133.0 191.9 230.2 166.5 −118.7 −14.5 97.5 −4.9 6.4 310.6 409.0 608.5 216.9 3.4

114.6 134.2 194.2 234.3 170.4 −117.5 −9.9 97.9 −8.3 0.7 311.8 414.9 613.8 208.9 −4.8

1-cyclopropen-1-yl 1-hydroxyethyl anti 1-hydroxyethyl syn 1-propynyl 2-hydroxyethyl anti 2-hydroxyethyl syn 2-propynyl acetyl cyclopropenyl ethoxy ethyl ethylidene (singlet) ethylidene (triplet) ethylidyne ethynyl formyl formyloxy hydroperoxy hydroxyformyl trans hydroxyformyl cis hydroxyl hydroxymethyl hydroxymethylene trans hydroxymethylene cis hydroxymethylene g (triplet) isoformyl methoxy methyl methylene (singlet) methylene (triplet) methylidyne methylperoxy oxoethenyl phenyl vinyl vinylidene

534.2 −42.2 −40.4 540.2 −9.9 −11.8 358.8 −3.8 498.8 −1.1 135.5 377.8 367.3 512.3 568.5 40.2 −128.1 11.3 −185.9 −177.4 36.9 −10.1 111.1 129.6 219.5 216.7 25.6 151.8 428.5 395.7 592.7 16.8 177.6 368.1 304.5 415.5

529.1 −47.1 −45.6 532.7 −13.3 −15.6 351.8 −8.3 490.5 −4.4 127.5 373.1 359.9 510.1 571.7 39.8 −111.5 13.0 −184.7 −175.7 37.9 −11.5 113.2 132.0 217.7 219.1 26.0 147.1 429.4 391.9 593.3 17.5 173.1 354.0 302.3 412.2

G3 Nitrogen Species28 118.2 131.6 192.0 234.8 173.3 −117.6 −12.1 97.8 −3.8 7.3 306.3 409.1 610.7 219.5 4.0 Open Shell27 532.2 −41.7 −40.3 531.5 −10.4 −12.9 352.4 −4.0 493.2 0.5 130.7 373.8 360.3 509.2 566.9 40.5 −112.6 16.9 −181.2 −173.3 35.2 −9.4 111.4 131.1 217.3 217.6 28.4 145.0 425.9 386.2 587.2 22.4 176.6 360.4 299.6 409.9

G4

x¯

u

ATcT

114.8 128.6 190.5 230.6 167.0 −116.0 −13.8 95.3 −4.7 6.1 302.5 405.6 602.8 214.3 3.4

115.4 131.8 192.1 232.5 169.3 −117.6 −12.6 97.1 −5.4 5.1 307.8 409.6 609.0 214.9 1.5

2.0 2.4 1.5 2.4 3.1 0.8 2.0 1.2 2.0 3.0 4.2 3.9 4.6 4.5 4.2

109.66 129.66b 192.00b 234.68 170.8 −116.06 −12.25 96.61 −5.83 6.02 308.16 410.7 610.1 215.6 4.54

524.4 −43.9 −42.3 525.5 −13.1 −14.7 351.5 −6.7 489.5 −1.8 130.4 372.0 360.6 504.3 559.6 38.7 −122.8 15.5 −183.9 −177.0 36.1 −10.5 110.9 129.3 218.2 214.3 25.2 147.8 425.4 389.4 588.2 20.4 174.1 351.1 298.5 411.0

530.0 −43.7 −42.2 532.5 −11.7 −13.8 353.6 −5.7 493.0 −1.7 131.0 374.2 362.0 509.0 566.7 39.8 −118.7 14.4 −183.9 −175.8 36.5 −10.4 111.7 130.5 218.2 216.9 26.3 147.9 427.3 390.8 590.3 19.3 175.4 358.4 301.2 412.1

4.2 2.4 2.5 6.1 1.8 1.7 3.4 2.2 4.2 2.1 3.3 2.5 3.6 3.4 5.1 0.8 8.0 2.4 2.0 1.8 1.2 0.9 1.0 1.2 1.0 2.0 1.4 2.9 1.9 4.0 3.1 2.6 2.1 7.5 2.7 2.4

528.48 −41.88 −40.35 530.2 −9.73 −12.55 353.97 −2.9 491.35 1.94 130.92c 373.93c 361.45c 508.58c 563.87c 41.43c −123.31 12.27 −181.80 −173.26 37.250c −9.75 112.40c 130.86c 219.1 217.31c 28.90c 149.788c 428.62c 390.96c 592.78c 21.8 176.84 350.57 301.11c 411.29c

Original CBS-QB3 and G3 values were in error. bRevised ATcT values.41 cRevised ATcT values.25

−3.44, or −4.13 ± 0.69, see Table 4. These measures are shown in the graph, Figure 1, as error bars superimposed on the bias and the limits of agreement. Outliers. Remarkably there are only 4 outliers from the 122 species tested; “downliers” include hydrazine, cyclobutene, and

phenyl radical while the Z conformer of methyl formate is the only “uplier”, Figure 1. How reliable are the ATcT values for these compounds? In earlier work,26 we showed that 1,3cyclopentadiene was in disagreement by >20 kJ mol−1, and consequently, this has not been included in any subsequent 7373


Article

The Journal of Physical Chemistry A Table 3. Δf H(0 K) for Additional Nitrogen Species (kJ mol−1) species

QB3

APNO

G3

G4

x¯

u

ATcT

imidogen NH triplet amidogen Ṅ H2 diazenyl Ṅ NH cyano Ċ N cyanato Ṅ CO aminomethyl Ċ H2NH2 methylamidogen CH3Ṅ H hydrazyl NH2Ṅ H iminomethyl HĊ NH trans iminomethyl HĊ NH cis hydroxyamidogen HṄ OH trans hydroxyamidogen HṄ OH cis

360.7 191.1 251.5 442.5 122.9 163.7 191.5 236.5 277.7 295.7 99.2 121.3

360.4 190.7 254.2 441.4 126.3 159.8 188.9 236.9 276.9 296.4 101.3 122.9

352.4 189.0 259.0 443.2 122.0 163.4 190.7 240.4 278.2 296.9 102.2 124.6

355.4 188.7 252.2 439.0 122.9 161.0 187.4 236.4 273.3 290.7 101.3 123.0

357.2 189.9 254.3 441.5 123.5 162.0 189.6 237.5 276.5 294.9 101.0 123.0

4.0 1.2 3.4 1.8 1.9 1.9 1.8 1.9 2.2 2.8 1.3 1.4

358.74 188.94 252.40 436.68 126.89 159.63 187.81 235.51 276.2 294.6 101.54 123.5

C) present in the working reaction to calculate the formation enthalpy of the target molecule, T. The cancellation of error inherent in such a process is enhanced by using multiple working reactions and multiple calculations of each reaction enthalpy change. The former reduces the reliance on specific chaperons while the second provides an estimate, however crude, of the uncertainty in ΔrH. The latter is important in estimating an uncertainty in the target from a particular working reaction and hence in determining the contribution that that value makes to the final result. Other considerations include choosing approximately thermoneutral working reactions, which of itself is a sign of a good isodesmic reaction. Hydrazine. We have previously argued28 that hydrazine, H2NNH2, is incorrect and that Δf H(0 K) lies nearer to 115.4 kJ mol−1 than the ATcT 109.66 ± 0.19 kJ mol−1. That argument considered many recent high-level calculations all of which computed greater Δf H’s than that tabulated as well as isodesmic reactions involving diazenes as chaperons. Taken as a whole the best current estimate is probably that of Chan and Radom whose W3X-L calculations34 indicate Δf H(0 K) of 112.1 kJ mol−1. Such a shift of +2.4 kJ mol−1 in the value removes the outlier status from hydrazine since the difference (ATcT − mean) is now only 3.3 kJ mol−1. Cyclobutene. The value for cyclobutene appears to be heavily dependent on a 1968 calorimetric measurement by Wiberg and Fenoglio50 of Δf H(298.15 K) = 157 ± 2 kJ mol−1 which is to be found in several compendia including a book,22 “Thermochemical Data of Organic Compounds”, the Third Millennium Database,68 and review articles.51 Cyclobutene can be independently estimated preferably via a working reaction 1 such as the hyperhomodesmotic combination:49 or variants where (2) n-butane/cis-butene or where (3)

Figure 1. Mean difference graph for all methods at 0 K: bias (), limits of agreement (− − −), and error bars/kJ mol−1.

Table 4. Statistical Summary of Bland−Altman Plot variable mean difference or bias standard deviation of bias number of data points standard error in bias upper limit of agreement d¯u lower limit of agreement dS̅ degrees of freedom Student’s t at 95% confidence bias: error bars limits of agreement: error bars

original

revised

0.27 2.24 122 0.20 4.67 −4.13

0.30 2.07 122 0.19 4.36 −3.78

121 1.980 0.40 0.69

121 1.980 0.37 0.64

statistical treatments including this one. The second question is, how reliable is the four-method averaged methodology? Are there circumstances in which a failure of the composite methods is understandable or indeed not unexpected given that these are midlevel procedures, computationally affordable but somewhat short of the state-of-the-art? In order to answer the first question: how to double-check these outliers?; an approach is required which bears little or no relationship to the computational methods employed which highlighted the outliers. Therefore, we use the isodesmic approach48,49 which posits fictional working reactions: T + A → B + C computes their reaction enthalpy change, ΔrH, and uses the known formation enthalpies of chaperon species (A, B and

ethane/ethene replaces cyclopropane/cyclopropene in the example above. All of these depend upon the value for the chaperon cyclobutane which is not that well-established with only a 298.15 K enthalpy measurement22 of 28.4 ± 0.6 kJ mol−1; correction of this value to 0 K yields Δf H = 53.0 kJ mol−1. Adoption of this value leads to inconsistent results between reactions 1−3 and reactions 4 and 5 detailed below; hence, a value 49.6 kJ mol−1 is chosen, which is based on the most recent and highest level theoretical calculation by Chan and Radom.34 The computed reaction enthalpies at 0 K for reactions 1−3 are 94.1 ± 1.1, −14.5 ± 0.6, and 1.74 ± 1.12 kJ 7374


Article

The Journal of Physical Chemistry A mol−1 and therefore the target values are 177.5 ± 1.7, 177.1 ± 1.4, and 176.5 ± 1.5 kJ mol−1, respectively. An independent (of cyclobutane) estimate can be obtained from a working reaction 4 based on n-butane/cis-butenes: for

HCOOCH3 = CH3COOH

whose cis conformer is present in the ATcT at −419.59 ± 0.49 kJ mol−1 and second the working reaction HCOOCH3 + CH3OH  HCOOH + CH3OCH3. Reaction enthalpies of ΔrH = −69.78 ± 1.03 and −0.96 ± 0.43 kJ mol−1 respectively yield −349.81 ± 1.14 and −346.9 ± 0.7 giving rise to a final −347.7 ± 0.6 kJ mol−1 in moderate agreement with the atomization −350.4 ± 3.0 kJ mol−1 but in excellent agreement with the W3X-L value of −347.2 kJ mol−1 of Chan and Radom.34 It is likely therefore that the ATcT value underestimates the formation enthalpy by at least 2 kJ mol−1; the difference then of |−344.54 − (−350.4) | = +5.9 now amounts to | − 347.7 − (−350.4)| = +2.7 kJ mol−1 which removes the uplier status from methyl formate. Note that the change proposed here is opposite in sign to those for hydrazine and cyclobutene. Phenyl. The situation as regards phenyl is more difficult to resolve as it is the only aromatic open shell species in the database. A working reaction featuring:

which ΔrH(0 K) = −51.0 ± 1.4 kJ mol−1 leads to a formation enthalpy of 177.3 ± 1.6 kJ mol−1. An isomerization reaction 5 to trans-1,3-butadiene yields 178.3 ± 2.4 based on a reaction enthalpy change of −53.4 ± 2.3 kJ mol−1 and a formation enthalpy of 124.9 ± 0.6 kJ mol−1. The latter is not present in the ATcT database and so was estimated from Δf H°(298.15 K) values43,44 of 108.8 ± 0.79 and 111.9 ± 0.96 kJ mol−1 and a computed {H(298.15K) − H(0 K)} of +14.8 kJ mol−1. W2X and W3X-L calculations for trans 1,3-butadiene, the dominant conformer, return 0 K values of 125.1 and 125.3 kJ mol−1. The working reactions 1−5 are not ideal, but they do span a range of thermicities from strongly endothermal through thermoneutral to strongly exothermic. In each case the reaction enthalpy change is computed at all four levels of theory, the results averaged and the uncertainty is expressed as a sample standard deviation as shown in this example for reaction 3 where the zero-point corrected electronic energies are in Hartrees and enthalpies in kJ mol−1 (Table 5). From all five computed target enthalpies (177.5 ± 1.7, 177.1 ± 1.4, 176.5 ± 1.5, 177.3, ± 1.6 and 178.3 ± 2.4 kJ mol−1), a grand weighted average, x̅ and a weighted uncertainty, u̅ n

x̅ =

n

∑ (xi/ui2)/∑ (1/ui2) 1

̇ 3 Ċ 6H5 + CH4 = C6H6 + CH

yields 358.4 ± 4.6 kJ mol , fortuitously identical to the atomization average of 358.4 ± 7.5 kJ mol−1 but substantially greater than the ATcT 350.57 ± 0.59 kJ mol−1. The implications are that, when transposed to 298.15 K, the C−H dissociation energy would amount to 462 kJ mol −1 , considerably lower than that expected from ATcT data of 472 kJ mol−1 or indeed the identical value 472 kJ mol−1 from a comprehensive handbook of bond dissociation energies.47 However, the computed reaction enthalpy for reaction 4 shows a large scatter, ΔrH(0 K) = −41.3 ± 4.6, and more tellingly a marked difference between three of the methods and G4. Thus, the three average to −43.6 ± 0.7 while G4 reports −34.5 kJ mol−1. A similar disconnect is seen for working reactions involving:

n

u ̅ = {∑ (1/ui2)}−1/2

1

(4)

−1

1

−1

of 177.1 ± 0.7 kJ mol emerges which is 3.2 kJ mol−1 greater than the ATcT number of 173.9 ± 1.6 kJ mol−1. Note that the average derived from the purely atomization calculations is 181.4 ± 4.7 kJ mol−1; the difference (ATcT − mean) therefore reduces from (173.9 − 181.4) = −7.5 to (177.1 − 181.4) = −4.3 kJ mol−1, a shift of +3.2 kJ mol−1. Very recent W3X-L calculations34 report Δf H(0 K) of 176.7 kJ mol−1 identical to an earlier W3.2lite result by Karton et al. and somewhat lower than the 178.1 kJ mol−1 from a W3.2 computation by the same authors.45 The consensus thus appears to favor a somewhat higher formation enthalpy for cyclobutene of ∼177 kJ mol−1. Methyl Formate. Values for methyl formate (only the Z or cis OCOC conformer of HCOOCH3 is significant) at 298.15 K have been reported46 which range from −337 to − 362 kJ mol−1; correcting these to 0 K gives a range of −324 to − 349 kJ mol−1 with the ATcT recommendation toward the lower end at −344.54 ± 0.54 kJ mol−1. Two reasonable isodesmic reactions can be framed here: first, direct comparison with the isomeric acetic acid:

̇ 2 Ċ 6H5 + C3H8 = C6H5CH3 + CH3CH

(5)

propane/toluene/ethyl, reaction 5 of −73.0 ± 1.1 vs −66.3, and ammonia/benzene/amidogen: ̇ 2 Ċ 6H5 + NH3 = C6H6 + NH

(6) −1

−32.6 ± 0.6 vs −24.4 for reaction 6, all in kJ mol . These differences are significant and the G4 values are shown to be more valid when compared with W3X-L results ΔrH(0 K) of −32.4 for reaction 4 and −21.5 for reaction 6. These results are therefore a clear indication that the methods being used are unsuitable or unable to furnish correct estimates to the formation enthalpy for the phenyl radical even using the isodesmic method which maximizes cancellation of error. The probable reason for this behavior can be seen by considering a generalized working reaction:

Table 5. Reaction 3 Example cyclobutene QB3 APNO G3 G4 Δf H u

−155.646802 −155.878618 −155.824638 −155.854023 177.05 ±1.52

+

C2H6

=

−79.630569 −79.747982 −79.723390 −79.738106 −68.12 ±0.17

cyclobutane −156.859865 −157.093311 −157.040516 −157.069644 49.6 ±1.00

7375

+

C2H4

ΔrH

−78.416640 −78.532205 −78.507417 −78.521877 61.07 ±0.15

2.27 2.85 0.25 1.60 1.74 ±1.12


Article

The Journal of Physical Chemistry A R1• + M1 → R 2• + M 2

span of the limits of agreement. The standard error of the limits of agreement is also reduced and consequently their span also. The changes are slight but result in an overall improvement. It must be emphasized that the corrections are made based on calculations derived solely from very recent high-level theoretical calculations and/or isodesmic reactions which include chaperons present in the ATcT but which are not themselves of questionable accuracy except as noted. Apart from the cyano radical the agreement at first glance is encouraging. There has been considerable uncertainty in the enthalpy of formation of Ċ N with Chase quoting Δf H°(0 K) = 436.8 ± 10 kJ mol−1 in the NIST−JANAF Thermochemical Tables.52 This coupled with a T1 diagnostic of 0.1 which indicates that multireference methods are required to treat this system adequately  thus rendering the composite approaches used here as unsuitable since T1 > 0.02. This can be seen by comparing W2X and W3X-L values of 440.2 and 436.6 respectively versus the ATcT’s 436.7 kJ mol−1, Table 7. However, the recent literature is also confusing with some52,53 having Δf H°(0 K) > Δf H°(298.15 K) and others with the converse.20,54 However, the latter situation is correct55 and agrees with the conclusions of this study that Δf H°(0 K) < Δf H°(298.15 K). Note that it is the upward shift in both the bias and the limits of agreement from the original data set to the corrected data set that is largely responsible for Ċ N becoming an outlier. A regression analysis of the differences, di, versus the average, Xi, of the ATcT and the averaged formation enthalpies, x¯i, gives d = −(0.0043 ± 0.0007) X + (0.77 ± 0.17). For strongly unstable systems, that is, where X = +500 the predicted difference amounts to d = −1.4 and for strongly stable species where X = −500, d = +2.9; thus this combination of methods renders unstable species more unstable +500 → 501.4 and stable species more stable, −500 → −502.9 kJ mol−1. However, the data is skewed to some extent by a number of problematic species with Δf H(0 K) > 400 kJ mol−1 such as Ċ N, CNCN, CNNC, etc. In any case, what can be termed the “proportional bias” is quite small given the enormous range of 1 MJ mol−1 in formation enthalpies. G3 + G4 Combination. This combination has been shown in earlier work to perform quite well so both data sets are tested against the unweighted mean of G3 and G4, Figure 3. As before the standout outliers are cyclobutene and hydrazine with phenyl and methylidyne 2CH just outside the 95% limits of agreement. The final bias d̅ = 0.04 ± 0.36 and the 95% limits of agreement are d̅u = 4.0 ± 0.6 and dS̅ = −3.9 ± 0.6 are little changed from the values obtained for the uncorrected data set. The only outlier now is the methylidyne radical 2CH. A linear regression of the differences, (ATcT − [G3+ G4]/2) = d, versus the average formation enthalpies, (ATcT + [G3+ G4]/2) = X, yields d = (10.0 ± 8.3) × 10−4 X − (0.052 ± 0.20). Thus, at X = +500, d = +0.4 and at X = −500, d = −0.5; in other words, this particular methodology does not discriminate between very unstable species, X ≫ 1, and very stable species, X ≪ − 1. It appears that the changes wrought in G4 designed to overcome the problems thrown up by the architecture of the G3 composite method have worked to the extent that in combination behaves in a superior manner insofar as this data set is concerned. G4 Only. It has been shown that the best single method is G4 so the original uncorrected values are reanalyzed purely from this perspectivethe downliers included cyclobutene and hydrazine as before but not methyl formate or phenyl. The case

The reaction enthalpy change is Δr H ° = {Δf H °(M 2) − Δf H °(M1)} + {Δf H ° (R 2•) − Δf H °(R1•)}

Since there is a strong negative linear dependence, for radicals, of the difference between ATcT and an individual method X, {Δf H°(ATcT) − Δf H°(X)} for X = CBS-QB3 or G3, as a function of the number of valence electrons, but not for G4 which is approximately independent, this is not surprising. In contrast for closed shell species only CBS-APNO shows a strong positive dependence whereas the other three methods are essentially neutral. This behavior effectively means that the reaction enthalpy is similar for CBS-QB3, CBS-APNO and G3 but differs for G4. Note that G4 theory32 specifically includes a higher level correction (HLC) differential electron correlation term which differs for closed shell molecules and open shell systems and also for atoms; this type of correction is not present in the other methods. There have been extensive discussions of the comparative merits and pitfalls of such an HLC57−59 and on the performance of G4 with and without this correction term by Wilson et al.60 Hence, the only method of the four used here which performs in a satisfactory manner for a system like [C6H5]• is G4. An atomization value of 351.1 kJ mol−1 agrees with an isodesmic result of 352.4 kJ mol−1, all of these derived exclusively from G4 calculations from reactions 4−6, and in accord with the ATcT 350.57 ± 0.59 kJ mol−1. A W3X-L calculation yields 347.6 kJ mol−1 and a W3.2lite45 348.7 kJ mol−1 in only moderate agreement with the 352.7 ± 2.5 kJ mol−1 from experiment56 which was subsequently reanalyzed to 354.4 ± 2.3 by Ervin and DeTuri.61 In summary, given that the ATcT value for [C6H5]• lies in between the only experimental result and the most recent highlevel quantum calculations, it probably does represent the most credible value currently available from which one can conclude that its outlier status is therefore down to a failure of the CBSQB3, CBS-APNO, and G3 composite methods. Corrected. To summarize, in accordance with the previous discussion, modest corrections to the “exact” (ATcT) values are made and shown in Table 6. Table 6. Summary of Corrected Values species

ATcT

ATcT(u)

revised

change

cyclobutene hydrazine methyl formate

173.9 109.66 −344.54

1.6 0.19 0.59

177.1 112.1 −347.2

+3.2 +2.4 −2.7

The net result of these modest changes can be seen in the rightmost graph in Figure 2, where for convenience the results for the uncorrected data set shown earlier in Figure 1 have been replotted in the leftmost graph at the same scale. The corrections to the four species which have been implemented and for which new statistics have been computed are shown in Table 6 under the column headed “revised”. There is a slight increase in the mean difference or “constant bias”, d̅, of +0.03 kJ mol−1 which is understandable given that the corrections decreases the number of “downliers”. Concomitantly there is a decrease in the standard error of the bias and a reduction in the 7376


Article


Figure 2. All methods 0 K; lef t, uncorrected; right, corrected data sets.

0.5 ≥ u ≤ 1 while the final set have u > 1 kJ mol−1. There does not appear to be any significant correlation between the differences (ATcT − G4) and the uncertainty with which each ATcT value is associated. Some comfort might be taken from the fact that G4 performs equally badly. A more refined approach might estimate the weight, wi, to be attached to a particular value of di as given by ui−2. In consequence a weighted mean or bias, d̅w and a corresponding sample standard deviation, sw, results as given by

for slight changes to the ATcT for both cyclobutene and hydrazine has already been made so it is not reiterated hereit is sufficient to say that the modest proposed changes would remove their outlier status. The proposed change to methyl formate has no impact as regards its possible outlier status in either the uncorrected or the corrected data set. Thus, methyl formate shows up as a false negative in this particular case. Only diisocyanogen emerges as a strong outlierof which more will be said later. The G4 method shows a strong bias of d̅ = 0.91 ± 0.39 with 95% confidence limits of d̅u = 5.2 ± 0.7 and dS̅ = −3.3 ± 0.7 against the corrected data set, Figure 4, outlier CNNC. A linear regression of differences versus averages gives d = (3.7 ± 0.8) × 10−3 X + (0.57 ± 0.20); in other words, G4 tends to predict that unstable species are somewhat less unstable and that very stable species are somewhat more stable. In either case, the effects are small in comparison to the systematic bias, d¯, for this method. Uncertainty in Reference Values. Heretofore we have not taken into account the fact that the benchmark ATcT values are of variable uncertainty. Thus, for example, for a species like methane, Δf H°(0 K) = −66.550 ± 0.056 kJ mol−1; a figure which is the result of a network of over 1,200 determinations contributing 99% to the final number.25 By way of contrast the ethyl radical carries a 5-fold larger uncertainty, Δ f H° = 130.92 ± 0.28 kJ mol −1 , with some 1,800 determinations contributing 99% to the final value. More exotic or lesser known species such as cyclobutene, Δf H° = 173.9 ± 1.6 kJ mol−1, are even much less certain because of a distinct lack of inter-relationships which can be set up for a unique, in some respects, molecule. As far as we aware such a consideration has not previously been attempted for these comparisons. A crude “measure” results from classifying each species into three bands; the first set has uncertainties of less than 0.5 kJ mol−1, the second has

n

dw =

1

n

n

∑ (wdi i)/∑ wi 1

sw =

2 ∑1 (wd i i ) − n dw

2

(n − 1)

On the assumption that the weights are given by ̂ wi = 1/[Var{{ATcT( u)i /2}2 − xi̅ (ui)}] we find that because the uncertainties in the ATcT values are much smaller than the uncertainties in the averaged values they can therefore be neglected so that wi ≈ 1/Var(̂ xi̅ )however, the net result is that there is very little change in the regression equation. It should be noted that other weighting schemes could be employed and limits of agreement determined but this was deemed unneccesary here. Alternatively one could envisage a situation where the weighting is solely determined by ATcT(ui). However, while superficially attractive, this places an undue emphasis on the results for a very small number of species such as NH3, CO, Ȯ H and CH4 which is hardly a representative selection from the entire data set. The danger inherent in such an approach is obvioustuning a method to give good results for this subset at the expense of good results elsewhere. A more realistic set of uncertainties in the ATcT values is required to which quantum chemical computations can aspire too. This is not to say that ATcT(u)’s are unrealistic, simply that the reduction in uncertainty possible when taking into account many interrelated experimental and theoretical determinations will produce a f inal 7377


Article

The Journal of Physical Chemistry A Table 7. Formation Enthalpies of Compounds at 0 and 298.15 K/kJ mol−1 0K compound name 1,3-butadiyne 1,3-Cyclopentadiene 1-butene (gauche) 1-butyne 1-cyclopropen-1-yl 1-hydroxyethyl g-anti 1-hydroxyethyl g-syn 1-propynyl 2,3-butanedione 2-butyne 2-hydroxyethyl g-anti 2-hydroxyethyl g-syn 2-propynyl acetic acid cis acetone acetyl allene amidogen aminomethyl ammonia ammonia oxide benzene carbon monoxide cis-2-butene cyanato cyanic acid HOCN cyano radical cyanogen cyclobutene cyclohexane cyclopropane cyclopropene cyclopropenyl diazene cis Z diazene trans E diazenyl diisocyanogen CNNC dimethyl ether dimethylamine dioxirane dioxymethylene transc ethanal ethane ethene ethoxy ethyl ethylidene singlet ethylidene triplet ethylidyne ethyne ethynol ethynyl formaldehyde formic acid anti formic acid syn formyl formyloxy fulminic acid HCNO glyoxal cis

298.15 K

W2X

W3X-L

W2X

W3X-L

ATcT

u

459.3 147.4 19.6 179.2 526.6 −44.7 −43.4 528.5 −315.1 158.0 −13.1 −14.8 354.4 −419.2 −202.6 −4.5 197.0 189.6 160.2 −37.7 71.2 95.8 −113.2 12.4 129.3 −11.4 440.2 311.0 175.4 −87.5 69.1 291.4 488.5 230.9 209.7 254.6 615.9 −168.0 4.3 9.5 362.0 −156.0 −69.9 60.9 −2.3 130.2 372.7 359.8 506.7 230.3 94.9 564.8 −105.5 −355.7 −371.5 41.7 −119.2 173.4 −190.7

459.8 149.2 20.4 180.1 527.1 −44.9 −43.7 527.3 −314.6 159.0 −13.2 −15.0 354.4 −419.3 −202.2 −5.0 197.1 188.9 159.8 −38.2 70.4 99.1 −113.5 13.1 126.6 −12.0 436.6 310.0 176.8 −85.3 70.1 292.4 489.4 229.9 208.8 253.2 616.0 −167.6 4.5 8.8 350.6 −156.1 −69.7 60.8 −2.8 130.1 371.6 359.6 505.8 230.4 94.9 563.7 −105.9 −356.3 −372.1 41.0 −123.9 171.6 −191.3

460.5 130.2 −2.0 165.3 522.1 −58.2 −56.9 523.9 −331.8 146.0 −25.7 −28.1 351.8 −432.4 −218.7 −10.7 189.4 186.7 149.5 −44.7 60.0 78.2 −109.9 −8.6 129.3 −14.1 443.5 312.6 158.4 −126.9 51.9 282.6 484.0 223.7 202.6 251.7 618.6 −185.9 −17.6 1.8 359.6 −166.7 −85.7 52.3 −15.2 119.9 364.9 352.8 502.7 229.6 92.4 569.4 −109.4 −362.9 −378.9 42.1 −122.7 172.0 −196.1

461.0 132.0 −1.3 166.2 522.6 −58.4 −57.1 522.7 −331.5 147.0 −25.8 −28.3 351.7 −432.5 −218.3 −11.2 189.5 186.0 149.1 −45.2 59.2 81.5 −110.2 −7.9 126.5 −14.7 439.9 311.6 159.8 −124.7 52.9 283.6 484.8 222.7 201.6 250.3 618.7 −185.5 −17.4 1.0 348.2 −166.8 −85.5 52.2 −15.7 119.8 363.9 352.6 501.8 229.7 92.5 568.3 −109.8 −363.5 −379.5 41.4 −127.4 170.2 −196.8

460.37 101.3 −0.03 165.39 523.96 −55.29 −53.8 528.35 −326.54 145.76 −22.36 −25.83 351.51 −432.87 −216.07 −9.68 190.16 186.05 148.74 −45.558 61.1 83.18 −110.525 −7.33 127.36 −14.86 439.97 310.1 156.9 −122.08 53.61 283.91 486.81 222.47 200.22 249.48 613 −184.02 −15.89 1.6 356.6 −165.37 −83.91a 52.45a −11.95 119.86a 366.70a 354.45a 504.88a 228.27a 92.7 567.99a −109.19a −362.1 −378.51 41.80a −125.28 169.3 −193.86

0.87 2.5 0.48 0.85 0.87 0.62 0.87 1.01 0.82 0.79 0.86 0.61 0.48 0.49 0.37 0.40 0.37 0.15 1.01 0.030 1.7 0.26 0.026 0.53 0.39 1.01 0.15 0.43 1.6 0.68 0.53 0.59 0.88 0.83 0.56 0.56 1.7 0.44 0.69 1.2 5.9 0.32 0.14 0.13 0.50 0.28 0.86 0.82 0.87 0.13 1.4 0.15 0.10 0.41 0.25 0.10 0.61 1.2 0.73

7378


Article

The Journal of Physical Chemistry A Table 7. continued 0K

298.15 K

compound name

W2X

W3X-L

W2X

W3X-L

ATcT

u

glyoxal trans hydrazine hydrazyl hydrogen azide HNNN hydrogen cyanide hydrogen isocyanide hydroperoxy hydroxyamidogen cis hydroxyamidogen trans hydroxyformyl cis hydroxyformyl trans hydroxyl hydroxylamine cis hydroxylamine trans hydroxymethyl hydroxymethylene cis hydroxymethylene g triplet hydroxymethylene trans iminomethyl cis iminomethyl trans isobutane isobutene isocyanic acid HNCO isocyanogen isodiazene isoformyl isofulminic acid HONC ketene methane methanediol conrot g methanediol disrot g methanol methoxy methyl methyl formate cis Z methyl hydroperoxide methylamidogen methylamine methylene singlet methylene triplet methylenimine methylidyne methylperoxy n-butane nitric acid nitrosobenzene nitrosyl hydride nitrous acid cis nitrous acid trans o-benzyne oxirane oxoethenyl peroxynitrous acid cis/cis peroxynitrous acid cis/perp peroxynitrous acid trans/perp phenyl propane propene propyne

−208.1 112.7 236.0 301.5 132.0 193.0 16.3 123.8 102.4 −175.4 −182.0 37.1 −15.2 −32.1 −10.3 131.0 217.8 112.6 295.3 277.0 −108.6 2.3 −115.7 414.7 308.9 217.3 236.2 −45.2 −66.6 −381.3 −371.1 −191.5 26.9 149.4 −347.2 −114.7 188.8 −6.5 429.4 390.9 97.3 592.6 23.2 −101.3 −123.5 212.8 112.1 −68.2 −69.5 465.9 −41.3 177.5 −1.8 3.3 11.9 345.9 −85.2 33.9 192.3

−208.8 112.0 234.9 299.0 131.5 192.7 13.9 122.3 100.9 −176.7 −183.2 36.7 −16.0 −33.0 −10.7 129.9 217.1 111.6 294.2 276.0 −107.6 3.1 −117.0 414.5 307.7 216.4 235.6 −45.9 −66.7 −381.5 −371.3 −191.7 26.2 149.2 −347.2 −115.7 188.1 −6.6 428.2 390.7 96.9 591.9 21.0 −100.4 −126.1 n/a 110.6 −71.1 −72.7 468.7 −40.7 175.4 −6.7 −1.3 7.3 347.6 −84.6 34.2 192.8

−213.8 98.2 225.3 295.1 131.5 193.3 13.3 117.2 95.5 −178.5 −185.0 37.2 −25.7 −42.6 −17.1 127.2 214.7 108.8 291.8 273.3 −137.5 −19.2 −118.7 416.7 301.8 217.7 234.5 −48.4 −74.6 −395.4 −384.6 −202.6 19.3 146.2 −360.4 −127.6 178.0 −21.6 429.8 391.4 89.3 596.0 13.4 −130.0 −133.4 195.4 109.1 −74.7 −75.8 456.8 −53.9 178.5 −10.6 −3.8 4.7 332.5 −107.7 18.6 185.1

−214.5 97.5 224.3 292.6 131.0 193.1 11.0 115.6 94.0 −179.8 −186.2 36.8 −26.6 −43.4 −17.5 126.1 214.0 107.8 290.6 272.4 −136.5 −18.4 −120.0 416.5 300.6 216.7 233.9 −49.1 −74.7 −395.6 −384.9 −202.7 18.6 146.0 −360.4 −128.6 177.4 −21.7 428.6 391.2 89.0 595.3 11.2 −129.1 −136.0 n/a 107.6 −77.6 −79.0 459.7 −53.3 176.4 −15.5 −8.5 0.0 334.1 −107.1 18.9 185.6

−212.48 95.51 224.86 291.83 129.28b 192.39b 12.27 117.0 94.7 −177.06 −184.36 37.490a −25.2 −43.5 −16.06 127.11a 216.0 108.63a 291.1 272.6 −135.36 −17.6 −119.05 413.0 300.94 217.89a 233.15 −48.57 −74.520a −393.4 −381.82 −200.71a 21.53a 146.374a −357.8 −127.81 177.08 −20.91 429.03 391.52a 88.7 596.12a 12.06 −125.85 −134.16 198.6 106.92 −77.61 −79.188 460.8 −52.72 177.96 −14.57 −7.61 0.49 337.28 −104.41 20.35 185.8

0.59 0.19 0.93 0.58 0.10 0.57 0.17 1.4 1.00 0.62 0.55 0.016 1.5 0.49 0.44 0.34 1.1 0.33 1.4 1.4 0.4 0.53 0.37 1.6 0.81 0.67 1.02 0.15 0.056 0.96 1.00 0.16 0.34 0.080 0.59 0.91 0.89 0.53 0.13 0.12 0.98 0.10 0.9 0.38 0.18 1.5 0.11 0.39 0.079 1.4 0.44 0.6 0.38 0.54 0.42 0.59 0.29 0.33 0.38

7379


Article

The Journal of Physical Chemistry A Table 7. continued 0K compound name toluene trans-2-butene trimethylamine vinyl vinyl alcohol anti vinyl alcohol syn vinylidene a

298.15 K

W2X

W3X-L

W2X

W3X-L

ATcT

u

67.3 7.6 1.7 301.5 −110.3 −114.6 412.6

n/a 8.4 2.6 300.7 −110.5 −114.9 411.6

45.1 −13.5 −27.0 297.3 −121.1 −126.0 413.2

n/a −12.8 −26.1 296.5 −121.3 −126.2 412.2

50.41 −11.18 −24.02 296.91a −118.46 −123.71 412.20d

0.37 0.51 0.64 0.33 0.93 0.91 0.33

Values taken from ref 34. bRevised ATcT values.41 cConfirmed by W3.2 calculations.74 dRevised ATcT values.25

Figure 3. G3 + G4 0 K; lef t, uncorrected; right, corrected data set.

result with a drastically reduced uncertainty which is probably beyond the reach of even the highest-level theoretical computations available today. Naturally this statement is intended to apply to a data set of species containing more than a trivial number of “heavy” atoms. Higher Level Calculations. Variants of the Martin62 W-n family of methods developed by Chan and Radom34 are of a higher level than the CBS-x and G-n used earlier here and are, in addition, just about computationally affordable for the test data set. It is desirable therefore to see whether these protocols represent a considerable advance on the best-performing composite method G4 or not. Table 7 presents formation enthalpies at both 0 and 298.15 K, some of which are taken, or inferred, from their work,34 or else computed de novo. There are some very slight differences between the two approaches which arise from different choices in the keynote values for the formation enthalpies of the C, H, N, and O atoms in their ground electronic states. The Table contains values at the reference temperature of 298.15 K but these have been derived based on conventionally scaled harmonic B3LYP/cc-pVTZ+d

frequencies and do not include any hindered rotor corrections where appropriate. The differences between W2X and W3X-L reflect of course the post-CCSD(T) contribution which is a feature of the latter. In general for the 124 species under consideration here the differences are minor averaging less than 1 kJ mol−1 except for trans dioxymethylene HĊ OO where it exceeds 11 kJ mol−1, formyloxy HC(O)Ȯ by 4.6, and all the peroxynitrous acid conformers HO−ONO by ∼4.8 kJ mol−1. For these systems, the recommended T1 diagnostic of 0.02 is exceeded and this is particularly so for HĊ OO where it approaches 0.08; here too, the D1 diagnostic is some 3× greater than the 0.10 limit.63,64 In each of the above-mentioned cases problems were encountered earlier with the CBS-QB3, CBS-APNO, G3 and G4 calculations. Thus, for dioxymethylene the four composite methods gave wildly contrasting results of Δf H° = 366 ± 17 kJ mol−1 and for formyloxy −119 ± 8 kJ mol−1 while only the trans perp conformer of peroxynitrous acid yielded any result at all. 7380


Article


Initially the outliers were diisocyanogen CNNC and ethylidyne CH3C except that the latter has been very recently revised25 since this work was done by ca. − 4 kJ mol−1 from 512.7 ± 1.4 to 508.58 ± 0.87 kJ mol−1 and is now in line with the computations. Note that cyclobutene survives the test with a difference of −1.5 kJ mol−1 based on an uncorrected data set and even on correction the difference amounts to +1.6 kJ mol−1, well within the limits of agreement. Similarly the suggested changes to the reference value for methyl formate have no impact on its nonoutlier status. There are a number of neutral isomers of molecular formula C2N2 including cyclic structures but only the three lowest lying are present in the ATcT database, namely NCCN, CNCN, and CNNC. None of the composite methods employed here give a good account of the absolute formation enthalpies at 0 K save perhaps for CBS-QB3 which agrees within 2 kJ mol−1 for each of the three. This of itself is somewhat surprising since overall CBS-QB3 is the worst single method for atomization calculations. The disagreement is most pronounced for the outlier di-isocyanogen and for which there is remarkably little data in the literature. Chaudhuri et al. did carry out ab initio CASSCF calculations for the ground and excited states of seven isomers and they report relative ground state energies of 0:1.06:3.16 eV for the isomers in question; these are to be compared with the 0:1.05:3.12 eV reported by Ding et al. from QCISD calculations.65,66 The latter also reported CCSD(T)/6311G(d)//B3LYP/6-311G(d) relative zero-point corrected electronic energies for the four lowest isomers of 0:106:305:356 kJ mol−1 which, apart from the highest energy isomer diazadicarbon, CCNN, are in good agreement with the W3X-L values of 0:104.5:306.0:351.1 kJ mol−1. The poor performance of the G4 method is very surprising and hard to explain, as is the fact that the greatest disagreements between G4 and W2X values are to be found for the three C2N2 isomers. Irrespective it would appear that

Figure 4. G4 0 K. Corrected data set.

W2X Results. At first glance the W2X results (now for 124 species in total), shown in Table 7 and Figure 5, are disappointing; in terms of bias and limits of agreement the overall results of d̅ = 0.27 ± 0.39 and du = 4.57 ± 0.67 and dS = −4.02 ± 0.67 are little different from the results for the best single method G4, Table 4, except for a much weaker bias.

Figure 5. Mean-difference plot at 0 K/kJ mol−1: lef t, W2X; right, W3X-L. 7381


Article


refinement offered by W3X-L does just that in certain critical cases as shown for the peroxynitrous acids, HOONO, for example. Improvements: an accurate computation of the zero-point energy (ZPE) is essential for the determination of formation enthalpies and it might be thought that a harmonic frequency analysis at B3LYP/cc-pVTZ+d used by W2X and W3X-L which yields a ZPE of 255.2 kJ mol−1 for nitrosobenzene would be insufficient. However, for C6H5NO, one of the largest Abelian point group molecules present, an anharmonic frequency calculation at the same level of theory gives ZPE = 252.2 kJ mol−1, which is very close to the 252.3 kJ mol−1 obtained from scaling the harmonic ZPE by 0.9886 as recommended by Chan and Radom. Indeed in comparison to harmonic CCSD(T)/ aVTZ with MP2(VPT2) anharmonic corrections and a CCSD(T)-F12/VTZ-F12 + CCSD(T)-F12(VCI) approach71 for systems such as propane and furan the scaled B3LYP/ccpVTZ+d approach performs commendably, for example 267.97−267.85 vs 267.4 and 181.73−181.39 vs 181.3 kJ mol−1. Given the extra complexity and difficulty of calculating anharmonic frequencies at high levels of theory, it appears that this simple scaling procedure is sufficient; alternatively for larger systems, an estimation method as outlined by Császár and Furtenbacher or the quadratic correction procedure of Sibaev and Crittenden might be more suitable.72,73 For practical application the formation enthalpies at 298.15 K are required which involves computation of the enthalpy function, f(H) = HT − H0. Unfortunately, this is dominated by vibrational terms and, in particular, by low frequencies, which is where hindered rotors are usually to be found, if present at all. Now in addition to anharmonic vibrational modes a proper approach to rotors, hindered or free, is required. For cyclic systems, a consistent theoretical procedure for identifying and determining the potentials of ring puckering vibrations and their impact on thermochemical parameters is desirable. The model chemistries employed here are useful in screening tabulated values for those rare cases which are overly reliant on a very small number of determinations as in the case of 1,3cyclopentadiene, cyclobutene, and the ethylidyne radical. There are a surprisingly large number of composite methods available todayestimates put it at greater than 10075the set of values and the accompanying statistics for the procedures presented here should be useful in testing both existing and new variants under development.

the tabulated value is somewhat on the low side for CNNC. This behavior is also seen for the least stable linear isomer, diazodicarbon, for which only the G4 value lies outside the range Δf H(0 K) = 660 ± 2 kJ mol−1. W3X-L Results. In agreement with the previous data set diisocyanogen is a downlier as previously but now the trans conformer of dioxymethylene HĊ OO emerges as an uplier because of its substantial multireference character, Figure 5. The tabulated value carries a rather large uncertainty of ±5.9 kJ mol−1, a reflection of the scarcity of good experimental measurements or high-level theoretical calculations. On the basis of this work a substantial downward revision in the value for this less-stable conformer is indicated. The cis conformer (T1 = 0.052) was omitted in earlier work27 because of convergence problems with B3LYP/6-311G(2d,d,p) and B3LYP/cc-pVTZ+d chemistries which are integral to the CBS-QB3 and W1BD/W2X/W3X-L composite methods. However, minimization with the G4 optimizer B3LYP/631G(2df,p) does work and so these geometries were used as the basis for W2X and W3X-L runs. For the trans or anti conformer the difference between W2X results at the two different geometries viz. cc-pVTZ+d and 6-31G(2df,p) is less than 0.07 kJ mol−1 rising to 1.4 kJ mol−1 at W3X-L. On the assumption that similar differences arise for the cis conformer then a Δf H°(0 K) of 328 kJ mol−1 is indicated and 325 kJ mol−1 at 298.15 K. Both of these are consistent with the ATcT values of 332.1 ± 5.9 at 0 K and 329.9 ± 5.9 kJ mol−1. From this it can be concluded that the tabulated values for cis-HCOO are probably somewhat high but those for trans-HCOO are discrepant and require substantial revision. The not unrelated compound cyanoimidogen, or methanetetraylbis(amidogen), formally N−CN, in its triplet ground state (3Σ−g ) was present in ATcT v1.112 at Δf H°(0 K) = 445.3 ± 1.8 kJ mol−1 in reasonable agreement with averaged composite methods of 448.2 ± 3.2 although a marker perhaps that a somewhat higher value was indicated. Indeed a subsequent change by ∼+11 kJ mol−1 to 455.9 ± 1.3 has been made in ATcT v1.118.67 These latter are in accord with W2X and W3X-L values of 453.6 and 454.5 at 0 K. The impact that a fairly recondite number, such as Δf H°(298.15 K) for NCN, has in the real world is shown by recent extensive and conflicting discussions of the amounts of the pollutant NOx formed in flames and the particular influence of the NCN thermochemistry on the predicted values.68−70 The isomeric diazomethylene, CN⊕N⊖ (3Σ−), has suffered a similar increase from 572.8 ± 3.2 → 580.9 ± 2.4; the averaged composite methods lie midway at 576.4 ± 2.0 while W2X and W3X-L values of 578.8 and 577.5, respectively, are more closely aligned with the higher v1.118 numbers.

■

ASSOCIATED CONTENT

S Supporting Information *

■

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b07503.

CONCLUSIONS From a consideration of a wide range of both open and closedshell CHNO species, it emerges that G4 is the best single midlevel method to employ in computing the formation enthalpy via an atomization procedure out of the midlevel methods CBS-QB3, CBS-APNO and G3, G4. The computationally cheaper composite methods, CBS-QB3, CBS-APNO, and G3, are useful in determining the uncertainties associated with reaction enthalpies when isodesmic reactions are to be used, and the least expensive model chemistry, CBS-QB3, performs quite well in most of these situations. The higher-level composite method W2X does not represent a large improvement over G4 but the post-CCSD(T)

■

Summary of Gaussian output files including Cartesian coordinates, vibrational frequencies, symmetries, and rotational constants (PDF)

AUTHOR INFORMATION

Corresponding Author

*(J.M.S.) E-mail: [email protected]. Telephone: +35391-492451 +353-91-493103. Notes

The authors declare no competing financial interest. 7382


Article


■

Based Ab Initio CCSD(T) Limits Be Reconciled? J. Chem. Phys. 2016, 144 (21), 214101. (19) Goos, E.; Lendvay, G. Calculation of Molecular Thermochemical Data and Their Availability in Databases. In Cleaner Combustion: Developing Detailed Chemical Kinetic Models, Battin-Leclerc, F., Simmie, J. M., Blurock, E., Eds.; 2013; pp 515−547. (20) Ruscic, B. updated Active Thermochemical Tables (ATcT) values based on ver. 1.112 of the Thermochemical Network (2012); available at ATcT.anl.gov; Last update 30/11/2013. (21) Goos, E.; Burcat, A.; Ruscic, B. Ideal Gas Thermochemical Database with updates from Active Thermochemical Tables ftp://ftp. technion.ac.il/pub/supported/aetdd/thermodynamics; 13-Jan-2014. mirrored at http://garfield.chem.elte.hu/Burcat/burcat.html; 13-Jan2014. (22) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds. 2nd ed.; Chapman & Hall: London, 1986. (23) Karton, A.; Daon, S.; Martin, J. M. L. W4−11: A HighConfidence Benchmark Dataset for Computational Thermochemistry Derived from First-Principles W4 Data. Chem. Phys. Lett. 2011, 510, 165−178. (24) Vogiatzis, K. D.; Haunschild, R.; Klopper, W. Accurate Atomization Energies from Combining Coupled-Cluster Computations with Interference-Corrected Explicitly Correlated Second-Order Perturbation Theory. Theor. Chem. Acc. 2014, 133 (3), 1−12. (25) Ruscic, B. Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry. J. Phys. Chem. A 2015, 119 (28), 7810− 7837. (26) Simmie, J. M.; Somers, K. P. Benchmarking Compound Methods (CBS-QB3, CBS-APNO, G3, G4 and W1BD) against the Active Thermochemical Tables: A Litmus Test for Cost-Effective Molecular Formation Enthalpies. J. Phys. Chem. A 2015, 119, 7235− 7246. (27) Somers, K. P.; Simmie, J. M. Benchmarking Compound Methods (CBS-QB3, CBS-APNO, G3, G4 and W1BD) against the Active Thermochemical Tables: A Litmus Test for Cost-Effective Formation Enthalpies of Radicals. J. Phys. Chem. A 2015, 119, 8922− 8933. (28) Simmie, J. M. A Validated Database of Formation Enthalpies of Nitrogen Species by Compound Methods (CBS-QB3, CBS-APNO, G3 and G4). J. Phys. Chem. A 2015, 119, 10511−10526. (29) Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VII. Use of the Minimum Population Localization Method. J. Chem. Phys. 2000, 112, 6532− 6542. (30) Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A. A Complete Basis Set Model Chemistry.5. Extensions to Six or More Heavy Atoms. J. Chem. Phys. 1996, 104, 2598−2619. (31) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. Gaussian-3 (G3) Theory for Molecules Containing First and Second-Row Atoms. J. Chem. Phys. 1998, 109, 7764−7776. (32) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 Theory. J. Chem. Phys. 2007, 126, 084108. (33) Gaussian 09, Revision E.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian, Inc.: Wallingford CT, 2009. (34) Chan, B.; Radom, L. W2X and W3X-L: Cost-Effective Approximations to W2 and W4 with kJ mol−1 Accuracy. J. Chem. Theory Comput. 2015, 11, 2109−2119. (35) Martin, J. M. L.; de Oliveira, G. Towards Standard Methods for Benchmark Quality Ab Initio Thermochemistry  W1 and W2 Theory. J. Chem. Phys. 1999, 111 (5), 1843−1856. (36) Boese, A. D.; Oren, M.; Atasoylu, O.; Martin, J. M. L.; Kallay, M.; Gauss, J. W3 Theory: Robust Computational Thermochemistry in the kJ/mol Accuracy Range. J. Chem. Phys. 2004, 120 (9), 4129−4141. (37) Karton, A.; Martin, J. M. L. Explicitly Correlated Wn Theory: W1-F12 and W2-F12. J. Chem. Phys. 2012, 136 (12), 124114.

ACKNOWLEDGMENTS The Irish Centre for High-End Computing, ICHEC, is thanked for the provision of computational resources and their staff for their considerable assistance in carrying out some quite challenging computations. The guidance provided by Dr. Bun Chan (University of Sydney) was essential in navigating the complex series of calculations required to get WnX results.

■

REFERENCES

(1) Karton, A. A Computational Chemist’s Guide to Accurate Thermochemistry for Organic Molecules. WIREs Comput. Mol. Sci. 2016, 6, 292−310. (2) Dixon, D. A.; Feller, D.; Peterson, K. A. A Practical Guide to Reliable First Principles Computational Thermochemistry Predictions across the Periodic Table. Annu. Rep. Comput. Chem. 2012, 8, 1−28. (3) Peterson, K. A.; Feller, D.; Dixon, D. A. Chemical Accuracy in Ab Initio Thermochemistry and Spectroscopy: Current Strategies and Future Challenges. Theor. Chem. Acc. 2012, 131, 1079−1099. (4) Császár, A. G.; Allen, W. D.; Schaefer, H. F. In Pursuit of the Ab Initio Limit for Conformational Energy Prototypes. J. Chem. Phys. 1998, 108, 9751−9764. (5) Martin, J. M. L.; de Oliveira, G. Towards Standard Methods for Benchmark Quality Ab Initio ThermochemistryW1 and W2 Theory. J. Chem. Phys. 1999, 111, 1843−1856. (6) Boese, A. D.; Oren, M.; Atasoylu, O.; Martin, J. M. L.; Kallay, M.; Gauss, J. W3 Theory: Robust Computational Thermochemistry in the kJ/mol Accuracy Range. J. Chem. Phys. 2004, 120, 4129−4141. (7) Tajti, A.; Szalay, P. G.; Császár, A. G.; Kallay, M.; Gauss, J.; Valeev, E. F.; Flowers, B. A.; Vazquez, J.; Stanton, J. F. HEAT: High Accuracy Extrapolated Ab Initio Thermochemistry. J. Chem. Phys. 2004, 121, 11599−11613. (8) Bomble, Y. J.; Vazquez, J.; Kallay, M.; Michauk, C.; Szalay, P. G.; Császár, A. G.; Gauss, J.; Stanton, J. F. High-Accuracy Extrapolated Ab Initio Thermochemistry. II. Minor Improvements to the Protocol and a Vital Simplification. J. Chem. Phys. 2006, 125, 064108. (9) Karton, A.; Rabinovich, E.; Martin, J. M. L.; Ruscic, B. W4 Theory for Computational Thermochemistry: In Pursuit of Confident Sub-kJ/mol Predictions. J. Chem. Phys. 2006, 125, 144108. (10) Feller, D.; Peterson, K. A.; Dixon, D. A. A Survey of Factors Contributing to Accurate Theoretical Predictions of Atomization Energies and Molecular Structures. J. Chem. Phys. 2008, 129, 204105. (11) Harding, M. E.; Vazquez, J.; Ruscic, B.; Wilson, A. K.; Gauss, J.; Stanton, J. F. High-Accuracy Extrapolated Ab Initio Thermochemistry. III. Additional Improvements and Overview. J. Chem. Phys. 2008, 128, 114111. (12) Vázquez, J.; Harding, M. E.; Gauss, J.; Stanton, J. F. HighAccuracy Extrapolated Ab Initio Thermochemistry of the Propargyl Radical and the Singlet C3H2 Carbenes. J. Phys. Chem. A 2009, 113, 12447−12453. (13) 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 (4), 044311. (14) Feller, D.; Peterson, K. A.; Dixon, D. A. Further Benchmarks of a Composite, Convergent, Statistically Calibrated Coupled-ClusterBased Approach for Thermochemical and Spectroscopic Studies. Mol. Phys. 2012, 110, 2381−2399. (15) Feller, D.; Peterson, K. A.; Dixon, D. A. Refined Theoretical Estimates of the Atomization Energies and Molecular Structures of Selected Small Oxygen Fluorides. J. Phys. Chem. A 2010, 114 (1), 613−623. (16) Rogers, D. W.; Zavitsas, A. A.; Matsunaga, N. Determination of Enthalpies (‘Heats’) of Formation. WIREs Comput. Mol. Sci. 2013, 3 (1), 21−36. (17) Bakowies, D. Simplified Wave Function Models in Thermochemical Protocols Based on Bond Separation Reactions. J. Phys. Chem. A 2014, 118, 11811−11827. (18) Sylvetsky, N.; Peterson, K. A.; Karton, A.; Martin, J. M. L. Toward a W4-F12 Approach: Can Explicitly Correlated and Orbital7383


Article

The Journal of Physical Chemistry A (38) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. WIREs Comput. Mol. Sci. 2012, 2, 242−253. MOLPRO, version 2012.1, a package of ab initio programs, Werner, H.-J., Knowles, P. J., Knizia, G., Manby, F. R., Schütz, M., Celani, P., Korona, T., Lindh, R., Mitrushenkov, A., Rauhut, G., et al. http://www.molpro.net. 16/04/ 2012. (39) Rolik, Z.; Szegedy, L.; Ladjánszki, I.; Ladóczki, B.; Kállay, M. J. Chem. Phys. 2013, 139, 094105. MRCC, a quantum chemical program suite written by Kállay, M., Rolik, Z., Csontos, J., Ladjánszki, I., Szegedy, L., Ladóczki, B., Samu, G. http://www.mrcc.hu 16/09/2015. (40) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Stefanov, B. B. Assessment of Complete Basis Set Methods for Calculation of Enthalpies of Formation. J. Chem. Phys. 1998, 108 (2), 692−697. (41) Nguyen, T. L.; Baraban, J. H.; Ruscic, B.; Stanton, J. F. On the HCN−HNC Energy Difference. J. Phys. Chem. A 2015, 119 (44), 10929−34. (42) Bland, J. M.; Altman, D. G. Measuring Agreement in Method Comparison Studies. Stat. Methods Med. Res. 1999, 8, 135−160. (43) Prosen, E. J.; Maron, F. W.; Rossini, F. D. Heats of combustion, formation, and isomerization of ten C4 hydrocarbons. J. Res. NBS 1951, 46, 106−112. (44) Prosen, E. J.; Rossini, F. D. Heats of formation and combustion of 1,3-butadiene and styrene. J. Res. NBS 1945, 34, 59−63. (45) Karton, A.; Kaminker, I.; Martin, J. M. L. Economical PostCCSD(T) Computational Thermochemistry Protocol and Applications to Some Aromatic Compounds. J. Phys. Chem. A 2009, 113 (26), 7610−7620. (46) NIST Chemistry WebBook, NIST Standard Reference Database Number 69 http://http://webbook.nist.gov/chemistry/form-ser.html accessed 29-April 2015. (47) Luo, Y.-R. Comprehensive Handbook of Chemical Bond Energies; CRC Press: Boca Raton, FL, 2007. (48) Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. Molecular Orbital Theory of Electronic Structure of Organic Compounds.5. Molecular Theory of Bond Separation. J. Am. Chem. Soc. 1970, 92, 4796−4801. (49) Wheeler, S. E.; Houk, K. N.; Schleyer, P. V. R.; Allen, W. D. A Hierarchy of Homodesmotic Reactions for Thermochemistry. J. Am. Chem. Soc. 2009, 131, 2547−2560. (50) Wiberg, K. B.; Fenoglio, R. A. Heats of Formation of C4H6 Hydrocarbons. J. Am. Chem. Soc. 1968, 90, 3395−3397. (51) Dorofeeva, O. V.; Gurvich, L. V.; Jorish, V. S. Thermodynamic Properties of Twenty-One Monocyclic Hydrocarbons. J. Phys. Chem. Ref. Data 1986, 15, 437−464. (52) Chase, M. W., Jr., NIST-JANAF Thermochemical Tables (4th ed.), J. Phys. Chem. Ref. Data, 1998, Mono. 9, Suppl. 1. (53) Feller, D.; Ruscic, B.; Peterson, K. Improved Accuracy Benchmarks of Small Molecules using Correlation Consistent Basis Sets. Theor. Chem. Acc. 2014, 133, 1407. (54) Ruscic, B.; Feller, D.; Peterson, K. Active Thermochemical Tables: Dissociation Energies of Several Homonuclear First-Row Diatomics and Related Thermochemical Values. Theor. Chem. Acc. 2014, 133, 1415. (55) Personal communication from D. Feller, August 13th, 2015. The value for Ċ N should read Δf H°(298.15 K) = 439.65 ± 0.67 kJ mol−1. Feller, D.; et al. Erratum to: Improved accuracy benchmarks of small molecules using correlation consistent basis sets. Theor. Chem. Acc. 2015, 134, 130. (56) Davico, G. E.; Bierbaum, V. M.; Depuy, C. H.; Ellison, G. B.; Squires, R. R. The C−H Bond-Energy of Benzene. J. Am. Chem. Soc. 1995, 117 (9), 2590−2599. (57) Lin, C. Y.; Hodgson, J. L.; Namazian, M.; Coote, M. L. Comparison of G3 and G4 Theories for Radical Addition and Abstraction Reactions. J. Phys. Chem. A 2009, 113 (15), 3690−3697. (58) Chan, B.; Coote, M. L.; Radom, L. G4-SP, G4(MP2)-SP, G4SC, and G4(MP2)-SC: Modifications to G4 and G4(MP2) for the Treatment of Medium-Sized Radicals. J. Chem. Theory Comput. 2010, 6 (9), 2647−2653.

(59) Wang, L.; Tang, A. Bond Dissociation Enthalpies in Chlorinated Benzenes and Phenols and Enthalpies of Formation of Their Free Radicals: A Gaussian-4 Prediction. Int. J. Chem. Kinet. 2011, 43, 62−69. (60) Wilson, B. R.; DeYonker, N. J.; Wilson, A. K. Prediction of Hydrocarbon Enthalpies of Formation by Various Thermochemical Schemes. J. Comput. Chem. 2012, 33, 2032−2042. (61) Ervin, K. M.; DeTuri, V. F. Anchoring the Gas-Phase Acidity Scale. J. Phys. Chem. A 2002, 106 (42), 9947−9956. (62) 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 (14), 6014−6029. (63) Lee, T. J.; Taylor, P. R. A Diagnostic for Determining the Quality of Single-Reference Electron Correlation Methods. Int. J. Quantum Chem. 1989, 36, 199−207. (64) Lee, T. J. Comparison of the T1 and D1 Diagnostics for Electronic Structure Theory: A New Definition for the Open-Shell D1 Diagnostic. Chem. Phys. Lett. 2003, 372 (3−4), 362−367. (65) Chaudhuri, R. K.; Krishnamachari, S. L. N. G.; Freed, K. F. Ab Initio Description of the Ground and Excited States of Cyanogen Isomers. J. Mol. Struct.: THEOCHEM 2006, 768, 119−126. (66) Ding, Y.; Li, Z.; Huang, X.; Sun, C. CCNN: The last kinetically stable isomer of cyanogen. J. Chem. Phys. 2000, 113, 1745−1754. (67) Ruscic, B. updated Active Thermochemical Tables (ATcT) values based on ver. 1.118 of the Thermochemical Network (2012); available at http://atct.anl.gov/Thermochemical Data/version 1.118/; accessed 2016−07−12. (68) Goos, E.; Sickfeld, C.; Mauss, F.; Seidel, L.; Ruscic, B.; Burcat, A.; Zeuch, T. Prompt No Formation in Flames: The Influence of NCN Thermochemistry. Proc. Combust. Inst. 2013, 34, 657−666. (69) Lamoureux, N.; Merhubi, H. E.; Pillier, L.; de Persis, S.; Desgroux, P. Modeling of NO Formation in Low Pressure Premixed Flames. Combust. Flame 2016, 163, 557−575. (70) Bugler, J.; Somers, K. P.; Simmie, J. M.; Güthe, F.; Curran, H. J. On Modelling Nitrogen Species as Pollutants: Thermochemical Influences. J. Phys. Chem. A 2016. (71) 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. (72) Császár, A. G.; Furtenbacher, T. Zero-Cost Estimation of ZeroPoint Energies. J. Phys. Chem. A 2015, 119 (40), 10229−10240. (73) Sibaev, M.; Crittenden, D. L. Quadratic Corrections to Harmonic Vibrational Frequencies Outperform Linear Models. J. Phys. Chem. A 2015, 119 (52), 13107−12. (74) Chan, B. University of Sydney: Personal communication, November 2015. (75) Feller, D. Washington State University: Personal communication, May 2016.

7384


Validation of a Database of Formation Enthalpies and of Mid-Level

Recommend Documents