Size Effects on Cation Heats of Formation. II ... - ACS Publications

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Size Effects on Cation Heats of Formation. II. Methyl Substitutions in Oxygen Compounds Sydney Leach* LERMA-UMR 8112, Observatoire de Paris-Meudon, 5 place Jules Janssen, 92195 Meudon, France ABSTRACT: A relation between the heat of formation of molecular ions and cation size is used to study the effects of methyl substitution on a series of species containing oxygen. These include methanol, the hydroxymethyl radical, formaldehyde and related isomers, acetaldehyde and related isomers, ketene, formic acid, and acetic acid. This size-dependent relation is found to be valid in most cases, enabling a choice to be made among conflicting reported ion and neutral heat of formation values, but it holds much less well in methylsubstituted formaldehyde and its carbene isomers. The cations formed in methanol, hydroxymethyl, hydroxycarbene, and formic acid by methyl substitution at carbon sites were found to be more stable than those substituted at oxygen sites. Suggestions are made for investigating or reinvestigating the ionization energies and the heats of formation of several of the molecules studied in cases where multiple choices are available in the literature or where our analysis suggests that more reliable values are needed. PA(M) are often not known to better than 10 or 20 kJ/mol.3,4 Reported IEad(M) values are often based on subjective estimations of onset energies in a photoelectron spectrum first band. In very many cases of reported IEad(MH) values, they are determined by the subtraction of ΔfH(MH) from ΔfH(MH)+, where the latter is obtained via the proton affinity of the species M. Thus, independent methods of determining ΔfH(M+) or ΔfH(MH)+ can provide a check on values of IEad(M) or IEad(MH) if ΔfH(M) or ΔfH(MH) are accurately known. Furthermore, when IEad(M) is known to very high accuracy, an independent determination of the cation heat of formation can be used to deduce a value of the heat of formation of the neutral species. In our work, in cases where the heat of formation of a particular cation is derived from appearance energy measurements in dissociative ionization processes (eq 1), either by photon impact or by electron impact, we follow the usual approximation9 that two heat capacity terms in the full energy balance equation10 cancel each other so that the 298 K ΔfH values of fragment ions m1+ can be obtained from measured AEs using eq 2.

1. INTRODUCTION The present work on the heats of formation of the cations of methyl-substituted oxygen compounds is part II of a study that adopts the graphical approach of Holmes and Lossing1 in relating cation heats of formation to cation size. As in the case of nitrogenous molecules (Part I2), the results of the present work provide tests of the validity of this graphical method and also point to the necessity of investigating or reinvestigating the ionization energies and the heats of formation of several oxygen-containing molecules. In the literature,3,4 two principal methods have been used for determining the heats of formation of molecular cations: (i) For a molecular ion M+, the heat of formation ΔfH(M+) is given by ΔfH(M+) = IEad(M) + ΔfH(M), that is, the sum of IEad(M), the adiabatic ionization energy of the molecule M, and ΔfH(M), the heat of formation of M. (ii) For a so-called pseudomolecular ion (MH)+, the heat of formation ΔfH(MH)+ = ΔfH(M) + ΔfH(H+) − PA(M), where PA is the proton affinity (PA) of molecule M. The heat of formation of neutral species, ΔfH(M), listed in the NIST3 and Lias et al4 compilations as well as in several books,5,6 include experimentally determined values as well as estimated values derived by empirical or semiempirical methods based on the parametrization of structural similarities, notably involving group additivity schemes.7 More direct theoretical calculations, using modern computational ab initio molecular orbital, density functional theory, or Monte Carlo methods, are rarely able to achieve a so-called chemical accuracy of 5 kJ/mol, but they can be combined with group additive values to obtain useful values, often to ±10 kJ/mol, of the heats of formation of large molecules.8 In determining the heats of formation of molecular cations by the two methods described above, the values of IEad(M) and © 2013 American Chemical Society

M + hν /e− → M+ + e−/2e− → m1+ + mi AE + Δf Hgas(M) −

(1)

∑ [Δf Hgas(mi)] = Δf Hgas(m1+) (2)

Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: January 22, 2013 Revised: March 18, 2013 Published: March 18, 2013 10058

dx.doi.org/10.1021/jp400736y | J. Phys. Chem. A 2013, 117, 10058−10067

The Journal of Physical Chemistry A

Article

= −205 ± 10 kJ/mol (an average of nine values 3), ΔfH(CH3OH+•) becomes 841 ± 11 kJ/mol. There is apparently a fairly large uncertainty in ΔfH(CH3OH), which requires reinvestigation. We adopt ΔfH(CH3OH+•) = 845 kJ/ mol in Figure 1.

We note that parametric additivity methods for estimating the heats of formation of molecular cations are not generally successful, mainly because ionization energies are not simply proportional to the number of added subunits. However, Holmes and Lossing1,11,12 have shown that the effect on ΔfH(ion) due to substitution of a functional group (CH3, OCH3, OH, NH2) at the formal charge-bearing sites in both odd and even electron ions is, for each group, a simple function of ion size. They found that a plot of ΔfH(ion) as a function of ln(n), where n is the number of atoms, used as a simple referent for molecular size, often gives good straight lines. In the present work, we use this molecular size relation to study the effects of methyl substitution in a range of oxygencontaining compounds, three of which, CH2O+•, CH2OH+, and CH2CHOH+•, have previously been studied in part by Holmes and Lossing.1 In particular, we investigate differences between substitution at O and at C sites, giving information on relative stabilizing effects of methyl substitution. We have also used these correlations as a diagnostic tool in deciding between conflicting literature values of ΔfH(M+), leading on occasion to questioning published values of molecular ionization energies as well as values of heats of formation of neutral species. The results also bear on the limits of validity of the ln(n) relation.

Figure 1. Heat of formation of cations as a function of ln(n), where n is the number of atoms in the ion: methyl-substituted methanol. Line a: C-site and O-site substitution (see text); line b: C-site substitution; line c: O-site substitution.

2. METHYL SUBSTITUTION IN METHANOL Table 1 contains heat of formation data for the methanol cation and its derivatives methyl-substituted at carbon and oxygen Table 1. Heat of Formation of Cations As a Function of Size: Methyl-Substituted Methanol ion

no. of atoms (n)

ln(n)

C-Site Substitution H2O+• CH3OH+•

3 6

1.099 1.792

CH3CH3−2OH+• (CH3)2CHOH+• (CH3)3COH+• O-Site Substitution H2O+• CH3OH+•

9 12 15

2.197 2.485 2.708

3 6

1.099 1.792

CH3OCH3+• CH3OCH2CH3+• CH3OCH(CH3)2+• CH3OC(CH3)3+•

9 12 15 18

2.197 2.485 2.708 2.890

C-Site Substituted Species. Reported values for the ethanol cation are ΔfH(CH3CH2OH+•) = 775.6 ± 44 and 777 ± 4 kJ/mol,3 while for the isopropyl alcohol cation, the values are ΔfH((CH3)2CHOH+•) = 704 ± 8 kJ/mol (based on IE((CH3)2CHOH) = 10.12 ± 0.08 eV and ΔfH((CH3)2CHOH) = −272.5 ± 0.4 kJ/mol)4 and 709 ± 3 kJ/mol (based on IE((CH3)2CHOH) = 10.17 ± 0.02 eV, ΔfH((CH3)2CHOH) = −272 ± 1 kJ/mol.3 The next member of the series, the 2-methyl-2-propanol cation, has reported values of ΔfH((CH3)3COH+•) = 650 ± 54 and 643 ± 3 kJ/ mol.3 The latter value is derived from a PEPICO measurement of IE((CH3)3COH) = 9.90 ± 0.03 eV17 and ΔfH((CH3)3COH) = −312.6 ± 0.8 kJ/mol.18 A plot starting with H2O+• gives a good straight line up to and including CH3CH2OH+• (Figure 1, line a) and then deviates at higher values of ln(n) for the C-site-substituted species. However, a good straight line (Figure 1, line b) occurs starting at CH3CH2OH+• to higher n in the C-site-substituted species, supporting 650 rather than 643 kJ/mol (Table 1) for ΔfH((CH3)3COH+). This behavior is analogous to that in Csite substitution of methyl-substituted ammonium cations2 in a series beginning with NH4+, which is isoelectronic with H2O+•. O-Site Substitution. The heat of formation of the dimethyl ether cation, 783 kJ/mol,12 has been obtained by the sum of IE(CH3OCH3) = 10.25 ± 0.025 eV (PEPICO measurement) plus ΔfH(CH3OCH3) = −184.1 ± 0.5 kJ/mol.3 A comparison of the heats of formation of CH3CH2OH+• and CH3OCH3+• (Table 1) shows that methyl substitution on the O-site of CH3OH+• is only slightly less stabilizing than substitution on the C-site (783 compared to 776 kJ/mol), indicating that the charge density is only slightly greater at the carbon than that at the oxygen atom of the methanol cation. This is different than that in the neutral species, where the C-site-substituted species is much more stable, ΔfH(CH3CH2OH) = −234 kJ/mol compared to ΔfH(CH3OCH3) = −184 kJ/mol.3

ion heat of formation ΔfH kJ/mol 9754 846 ± 9, 857 ± 9 (see text), 845.3 ± 1.2,4 841 ± 113 775.6 ± 4,4 777 ± 43 709 ± 3,3 704 ± 84 643 ± 3,3 650 ± 54 9754 846 ± 9, 857 ± 9 (see text), 845.3 ± 1.2,4 841 ± 113 783 ± 2.5,3,12 783.34 721 ± 712 660 ± 53 6073

sites. It includes data on water because methanol is itself its methyl-substituted relative. We first discuss the origin of some of the data in this table, which are taken from various sources including the NIST3 and Lias et al.4 compilations and the book by Holmes et al.12 ΔfH(CH3OH+•). The two values, ΔfH(CH3OH+•) = (a) 846 ± 9 and (b) 857 ± 9 kJ/mol, are derived from IE(CH3OH) = 10.85 ± 0.03 eV,13 and ΔfH(CH3OH) = (a) −201 ± 6 and (b) −190 ± 6 kJ/mol quoted by Matus et al.14 Lias et al.4 give ΔfH(CH3OH+•) = 845.3 ± 1.2 kJ/mol, based on IE(CH3OH) = 10.85 ± 0.01 eV and ΔfH(CH3OH) = −201.6 ± 0.2 kJ/mol.6 Using the latest NIST-listed recommended values IE(CH3OH) = 10.84 ± 0.01 eV (probably based on photoion mass spectrometry (PIMS) measurements15,16) and ΔfH(CH3OH) 10059



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−201.5 ± 0.3 kJ/mol, which is only one of 10 different values in the NIST compilation for methanol.3 An analogous PIMS study by Ruscic and Berkowitz has led to ΔfH(CH2OH+) = 712 ± 1 kJ/mol.27 In our analysis, we use ΔfH(CH2OH+) = 711 kJ/mol, which is actually a good average of all proposed values of ΔfH(CH2OH+). Because the IE(M) appears to be known with good accuracy, there will be uncertainty in the value of Δ f H(CH 2 OH + ) in view of the spread of values in ΔfH(CH2OH), some of which are derived by reliance on values of IE(M), ΔfH(M), and so forth, which are not independent of each other. New measurements of the heat of formation of the hydroxymethyl radical are thus required. ΔfH(CH3CHOH+). The heat of formation of the 1hydroxyethyl radical cation ΔfH(CH3CHOH+) = 582 kJ/mol has been obtained from AE measurements.28 The value 593 kJ/ mol is derived by combining IE(CH3CHOH) = 6.7 eV given by Lias et al.4 and a calculated ΔfH(CH3CHOH) = −54.03 kJ/ mol.29 However, Lias et al.4 give ΔfH(M) = −66 ± 4 kJ/mol, and furthermore, the Lias et al. IE(CH3CHOH) = 6.7 eV is itself based on the difference Δ f H(CH 3 CHOH + ) − ΔfH(CH3CHOH), where ΔfH(CH3CHOH+) is derived from the PA of acetaldehyde, and ΔfH(CH3CHOH) is reported to be −66 ± 4 kJ/mol. The listed value ΔfH(CH3CHOH+) = 593 kJ/mol is therefore based on circular and ambiguous arguments. We note that Ruscic and Berkowitz,30 in a PIMS study on ethanol, deduce a value of ΔfH(CH3CHOH) = −57.3 kJ/ mol. Another value of the heat of formation of the 1hydroxyethyl radical cation is ΔfH(CH3CHOH+) = 576 kJ/ mol, derived by Dyke et al.31 from a PES measurement of IE(CH 3 CHOH) = 6.64 ± 0.03 eV and a value ΔfH(CH3CHOH) = −63.5 kJ/mol. Using PA(acetaldehyde), they obtain for the neutral radical ΔfH(CH3CHOH) = −56.8 kJ/mol, which would give ΔfH(CH3CHOH+) = 584 kJ/mol. In order to substantiate a satisfactory value of the heat of formation of the 1-hydroxyethyl radical cation, both IE(CH3CHOH) and ΔfH(CH3CHOH) require reinvestigation. ΔfH((CH3)2COH+). The values ΔfH((CH3)2COH+) = 499.512 and 490 kJ/mol4 are both based on the PAs of (CH3)2CO, which are given, respectively, as 81212 and 823 kJ/ mol,4 and on the heat of formation values ΔfH((CH3)2CO) = −218.5 ± 0.59 3 and −217.2 kJ/mol. 4 The value ΔfH((CH3)2COH+) = 502 kJ/mol has been obtained from electron impact AE measurements.28 A much lower value of the heat of formation of the ion, ΔfH((CH3)2COH+) = 453 ± 14 kJ/mol, is reported by Shao et al.32 from a PIMS and PEPICO study of tert-butyl alcohol ions. For the C-site values, Figure 2 indicates that a good straight line (line a) can be drawn connecting the n = 5, 8, and 11 ions at their respective heats of formation, 711, 593, and 490 kJ/ mol. This observation therefore tends to favor these values and to exclude ΔfHCH3CHOH+) = 582 kJ/mol (note the ambiguities in this 1-hydroxyethyl radical cation value discussed above) and ΔfH((CH3)2COH+) = 499.5 kJ/mol and quite definitely remove ΔfH((CH3)2COH+) = 453 kJ/mol as a valid heat of formation. We turn now to the data on the O-site-substituted hydroxymethyl radical ions. ΔfH(CH2OCH3+). The heat of formation of the methoxymethyl cation ΔfH(CH2OCH3+) = 657 kJ/mol has been obtained from AE measurements,28 whereas ΔfH(CH2OCH3+) = 671 kJ/mol has been derived from IE(CH2OCH3) = 6.94 eV3,28 and a calculated value of ΔfH(CH2OCH3) = 0.96 kJ/

Further substitution at the O-site in the ion gives a quite good straight line (see Figure 1, line a) from H2O+• down to CH3CH2OCH3+•, whose heat of formation, 721 ± 7 kJ/mol,12 is derived from IE(CH3CH2OCH3) + ΔfH(CH3CH2OCH3).4 The heats of formation deviate from this line at higher values of ln(n), becoming closer to the C-site line with each added methyl radical, and indeed, a good straight line (Figure 1, line c) can be drawn through the n = 12, 15, and 18 values for the O-site-substituted cations, whose heats of formation have been obtained by IE(M) + ΔfH(M) values listed in the NIST compilation.3 We remark that projecting the line c of Figure 1 to ln(n) = 2.197 would give a very different value, ΔfH(CH3OCH3+) ≈ 805 kJ/mol for this ion. It is thus relevant to question the value of the heat of formation of the dimethyl ether cation. However, the value ΔfH(CH3OCH3+) = 783 kJ/ mol is well substantiated by several studies, for example, refs 19−21.

3. METHYL SUBSTITUTION IN THE HYDROXYMETHYL RADICAL Reported heats of formation are given in Table 2 for cations created by methyl substitution at carbon and oxygen sites in the distonic hydroxymethyl radical ion CH2OH+. We now examine the origin of some of these data. Table 2. Heat of Formation of Cations As a Function of Size: Methyl-Substituted Hydroxymethyl no. of atoms (n)

ln(n)

ion heat of formation ΔfH kJ/mol

C-Site Substitution CH2OH+

5

1.609

CH3CHOH+

8

2.079

(CH3)2COH+ O-Site Substitution CH2OH+

11

2.398

711,12 718,3 712,24 703 ± 7, 718, 709,4 708.5 ± 0.08,22 721 (see text) 593(see text), 58230 576, 584 (see text and31) 490,4 453 ± 14,32 499.5,12 50228

5

1.609

CH2OCH3+ CH2OCH2CH3+

8 11

2.079 2.398

ion

711,12 718,3 712,27 703 ± 7, 718, 709,4 708.5 ± 0.1,22 721 (see text) 657,28 671 (see text) 602 ± 1328

ΔfH(CH2OH+). The ionization energy of CH2OH is 7.562 ± 0.004 eV.22 There are several reported values for the heat of formation of neutral CH2OH, (a) ΔfH(CH2OH) = −17.8 ± 1.322 and (b) −25.9 ± 6 kJ/mol,4 whereas NIST3 gives (c) −9 ± 4 kJ/mol from a review article by Tsang,23 and Dobé et al.24 give (d) −16.6 ± 1.3 kJ/mol. These lead to the following values for the cation: ΔfH(CH2OH+) = (a) 712 ± 2, (b) 704 ± 6, (c) 721 ± 4, and (d) 713 ± 2 kJ/mol. We note, however, that for the hydroxymethyl radical cation, the NIST compilation gives ΔfH(CH2OH+) = 718 ± 2 kJ/ mol.3 The Lias et al. compilation quotes three different values of ΔfH(CH2OH+), (i) 703 ± 7 kJ/mol from IE(CH2OH) = 7.56 ± 0.01 eV25 + ΔfH(CH2OH) = −25.9 ± 6 kJ/mol, (ii) 718 kJ/mol from the PA of formaldehyde, whose value is criticized,22 and (iii) 709 kJ/mol from AE measurements. The value of 711 kJ/mol is that recommended by Holmes et al.12 based on IE(CH 2 OH) = 7.562 ± 0.004 eV 22 and ΔfH(CH2OH) = −19 ± 1 kJ/mol.26 Traeger and Holmes26 propose 708.5 ± 0.8 kJ/mol from a TPES-MS measurement of the AE of CH2OH+ from methanol, based on ΔfH(CH3OH) = 10060



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and ΔfH(CH3CHO) = −166 ± 0.56 and −170.7 ± 1.5 kJ/ mol,36 to be added, respectively, to the IE(CH2O) = 10.874 ± 0.002 eV37 and IE(CH3CHO) = 10.229 ± 0.007 eV.3 The preferred value is ΔfH(CH3CHO+•) = 821 kJ/mol.12 However, extrapolating a straight line drawn between the formaldehyde and acetaldehyde cation heats of formation (Figure 3, line a)

Figure 2. Heat of formation of cations as a function of ln(n), where n is the number of atoms in the ion: methyl-substituted hydroxymethyl. Line a: C-site substitution; line b: O-site substitution.

mol.29 Another calculated value of ΔfH(CH2OCH3) is 3.8 kJ/ mol;33 other experimental values range from −5.4 ± 8 to −28.8 ± 5 kJ/mol,30 with resulting uncertainties in ΔfH(CH2OCH3+). ΔfH(CH2OCH2CH3+). The value of ΔfH(CH2OCH2CH3+) = 602 ± 13 kJ/mol results from electron impact AE measurements of Lossing.28 Taking into account the error bar of ±13 kJ/mol for this ion, Figure 2 indicates that a reasonable straight line (line b) can be drawn for the O-site-substituted ions, with ΔfH(CH2OCH3+) = 657 kJ/mol in preference to 671 kJ/mol. Comparison of C-site and O-site substitution data (Table 2 and Figure 2) shows that O-site methyl substitution creates cations that are less stable than C-site substitution of the same elemental composition. This shows that the charge density is greater at the C-site than that at O in these species.

Figure 3. Heat of formation of cations as a function of ln(n), where n is the number of atoms in the ion: methyl-substituted formaldehyde and its HCOH isomer. Lines a and b: C-site substitution in H2CO; line c: C-site substitution in HCOH; line d: O-site substitution in HCOH.

would predict ΔfH((CH3)2CO+•) ≈ 750 kJ/mol, whereas drawing it between the formaldehyde and acetone cation values (Figure 3, line b) would predict ΔfH(CH3CHO+•) ≈ 805 kJ/ mol. One might conclude, assuming the correctness of Δ f H(CH 2 O +• ), that the values Δ f H(CH 3 CHO +• ) and especially ΔfH((CH3)2CO+•) require reinvestigation by new measurements of the relevant ionization energies and neutral heats of formation. However, close examination of present determinations of these parameters indicates that these values are valid, so that it is more likely that the Holmes−Lossing graphical method breaks down in this case. In Table 3, there are given data on carbene isomeric relatives of the formaldehyde species. We consider first the HCOH+• ion and its C-site-substituted methyl derivatives. The heats of formation ΔfH(HCOH+•) = 974 kJ/mol and ΔfH(CH3COH+•) = 839 kJ/mol depend in part on various calculations,12 but uncertainties remain. Flammang et al.38 have calculated ΔfH(CH3CH2COH+•) = 805 kJ/mol. Bouma et al.39 determined ΔfH(CH3CH2COH+•) based on a calculation of the energy difference with respect to ΔfH(1-propen-2-ol), for which several values were given. Using IE(1-propen-2-ol) = 8.67 ± 0.05 eV40 and ΔfH(1-propen-2-ol) = −160 ± 8 kJ/ mol,41 one obtains ΔfH(1-propen-2-ol+•) = 677 ± 13 kJ/mol and ΔfH(CH3CH2COH+•) = 800 ± 13 kJ/mol. Another value for ΔfH(1-propen-2-ol) is −176 kJ/mol,42 leading to ΔfH(1propen-2-ol+•) = 661 kJ/mol and ΔfH(CH3CH2COH+•) = 784 kJ/mol. A straight line between the HCOH+• and the CH3COH+• values (Figure 3, line c) predicts ΔfH(CH3CH2COH+•) ≈ 750 kJ/mol, significantly below the values given in Table 3. O-site substitution provides a variety of reported values for the methoxycarbene and ethoxymethylene cations (those for HCOCH2CH3+• are based on a calculated difference between the heats of formation of this ion and the various reported

4. METHYL SUBSTITUTION IN FORMALDEHYDE AND RELATED SPECIES The heats of formation of the formaldehyde, acetaldehyde, and acetone cations are reasonably well-known (table 3), although there are small differences between two reported values for each of the formaldehyde and acetaldehyde ions due to differences in the reported heat of formation of the neutral species, ΔfH(CH2O) = −108.6 ± 0.0463 and −115.90 kJ.mol,3 Table 3. Heat of Formation of Cations As a Function of Size: Methyl-Substituted Formaldehyde and Related Isomeric Species ion

no. of atoms (n)

C-Site Substitution 4 CH2O+• CH3CHO+• 7 (CH3)2CO+• 10 Carbene Isomers: C-Site HCOH+• 4 CH3COH+• 7 CH3CH2COH+• 10 Carbene Isomers: O-Site HCOH+• 4 HCOCH3+• 7 HCOCH2CH3+• 10

ln(n)


1.386 1.946 2.303

941,3,4 934 (see text) 821, 816 (see text) 717,3 718.8 ± 0.7,34 719.24

1.386 1.946 2.303

97412 83912 805, 777, 793 ± 20, 788 ± 10, 800 ± 13, 784 (see text)

1.386 1.946 2.303

97412 930 ± 5,12 912, 909 calc,12 93635 828, 844 ± 20, 839 ± 1012 10061



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We now consider the enol isomers, whose heats of formation are given in Table 4. We note that in 1-propen-1-ol, the methyl group can be cis or trans to the hydroxyl group. Bouma et al39 calculate the cis to lie 2 kJ/mol below the trans form. The heats of formation of both isomers are given as 665 kJ/mol by Holmes et al.12 A good straight line can be drawn through the heats of formation of the three enol isomers (Figure 4, line c), supporting the value ΔfH(CH2CHOH+•) = 757 kJ/mol45 rather than 76846 or 771 kJ/mol.47 This confirms the earlier graphical study of these enol cations established by Holmes and Lossing.1 Table 4 and Figure 4 show that the eno isomers are more stable than their keto counterparts and increasingly so as the number of methyl groups increases. Table 5 gives heat of formation data on methyl substitution in ketone cations, starting with acetone. The value for the

experimental values for the enol form of acetone) and do not lead to satisfactory straight lines in the appropriate graphs (see, e.g., Figure 3, line d). There is manifestly a breakdown of the Holmes−Lossing graphical method. It is clear, however, that Csite-substituted methyl derivative cations are more stable than the corresponding O-site species.

5. METHYL SUBSTITUTION IN ACETALDEHYDE, ITS ENOL ISOMER, AND ACETONE The heats of formation of methyl-substituted acetaldehyde and its enol isomer are given in Table 4. The difference in the two Table 4. Heat of Formation of Cations As a Function of Size: Methyl-Substituted Acetaldehyde and Related Isomeric Species ion

no. of atoms (n)

ln(n)


CH3CHO+• CH3CH2CHO+• (CH3)2CHCHO+• (CH3)3CCHO+• CH2CHOH+• CH3CHCHOH+• (CH3)2CCHOH+•

7 10 13 16 7 10 13

1.946 2.303 2.565 2.773 1.946 2.303 2.565

816.4 ± 1.5,3 821.1 ± 0.44 772.93,4 7213,4 6743,4 757,45 768 ± 5,46 77147 66512 6074,48

Table 5. Heat of Formation of Cations As a Function of Size: Methyl-Substituted Acetone

values of ΔfH(CH3CHO+•) is essentially due to different values of ΔfH(CH3CHO). Lias et al.4 report ΔfH(CH3CHO) = −165.8 ± 0.4 kJ/mol from a compilation of Pedley and Rylance quoted in ref 4, whereas the NIST value ΔfH(CH3CHO) = −170.7 ± 1.5 kJ/mol3 is taken from Wiberg et al.36 Both sources3,4 use IE(CH3CHO) = 10.229 ± 0.0007 eV determined by the Rydberg series spectroscopic study of Walsh.43,44 A not very satisfactory straight line can be drawn through three points starting at the acetaldehyde cation (Figure 4, line a), but a good one exists starting with the propenal ion (Figure 4, line b), assuming error limits of ±≤5 kJ/mol in ΔfH of the ions (Figure 4). A reasonable straight line cannot be drawn through all four points. This is similar behavior to other cases of methyl substitution.

ion

no. of atoms (n)

ln(n)


CH3COCH3+• CH3CH2COCH3+• (CH3)2CHCOCH3+• (CH3) 3CCOCH3+•

10 13 16 19

2.303 2.565 2.773 2.944

717,3 718.8 ± 0.7,49 719.24 677,4 6803 636,3 634.94 591 (see text)

acetone cation is well-established.3,4,34 We remark that the heat of formation of ΔfH((CH3)3CCOCH3+•) = 591 kJ/mol has been derived from the NIST3 values IE((CH3)3CCOCH3) = 9.14 ± 0.03 eV and ΔfH((CH3)3CCOCH3) = −290.67 ± 0.88 kJ/mol. Methyl substitution in ketone ions gives a good straight line relation between the heats of formation and ln(n) (Table 5 and Figure 4, line d), thus confirming the validity of the Holmes− Lossing graphical method applied to these ketone ions, at least for the first three members of this series. The heat of formation of the fourth member, ΔfH((CH3)3CCOCH3+•) = 591 kJ/mol, is much lower than would be expected from line d, indicating an increased stabilizing effect of the third methyl group. Examination of the differences ΔΔfH of neutral heats of formation and ΔIE of ionization energies of successive members of the series indicates that the increased stability of the third methyl group affected by the cation reflects increased stability of the neutral rather than unusual ionization effects.

6. METHYL SUBSTITUTION IN KETENE Table 6 gives the heats of formation of a set of ketenes, compounds that are basic building blocks in organic chemistry. The spread of reported values for the ketene radical ion is limited to 874−883 kJ/mol, but there is a large variety of Table 6. Heat of Formation of Cations As a Function of Size: Methyl-Substituted Ketene

Figure 4. Heat of formation of cations as a function of ln(n), where n is the number of atoms in the ion: methyl-substituted acetaldehyde, its enol isomers, and acetone. Line a: methyl substitution in acetaldehyde; line b: methyl substitution in propenal; line c: methyl substitution in vinyl alcohol; line d: methyl substitution in acetone. 10062

ion

no. of atoms (n)

ln(n)

CH2CO+• CH3CHCO+•

5 8

1.609 2.079

(CH3)2CCO+•

11

2.398

ion heat of formation ΔfH kJ/mol 875, 883,49 874 ± 153 795,797,759,49 765 ± 5,52 783.5 ± 0.353 723,726,681,49 683 ± 5,51 719.3 ± 3.653



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methylketene and dimethylketene and of accessory relevant calculations, which could aid in making more precise the effects of methyl substitution in these species.

experimental and theoretical values for each of the two higher members of the series. For the methylketene ion CH3CHCO+•, the calculations of Ngyen and Ngyen49 lead them to propose 795 kJ/mol, but they argue also that the heats of formation of both neutral and cation methylketene are not well-established, questioning notably the reported ionization energy of methylketene. Lias et al.4 give ΔfH(CH3CHCO+•) = 759 kJ/ mol, based on the Bock et al.50 photoelectron spectroscopy (PES)-determined IE(CH 3 CHCO) = 8.95 eV and ΔfH(CH3CHCO) = −105 kJ/mol. The latter value has been argued to be around −95 kJ/mol.49 Aubry et al.51 propose ΔfH(CH3CHCO+•) = 765 ± 5 kJ/mol, close to the value listed by Lias et al.4 Indeed, Aubry et al.51 determined the ΔfH(M) values of each of the three ketenes in Table 6 by energyselected electron impact dissociation measurements of phenyl acetate, propionate, and isobutyrate. From IE(M) = 9.64, 8.95, and 8.45 eV, respectively,50 (9.58, 8.92, and 8.43 eV, respectively, from the calculations of Scott and Radom52) and ΔfH(M) = −54, −95, and −137 kJ/mol, respectively, they obtain for ionized methylketene ΔfH(CH3CHCO+•) = 765 ± 5 kJ/mol, and for dimethylketene, they find ΔfH((CH3)2CCO+•) = 683 ± 5 kJ/mol. J. C.Traeger53 carried out threshold photoionization mass spectrometry studies in which he measured the AEs of the ions from the same precursors of the three ketenes (of phenyl acetate, propionate, and isobutyrate). From his AE measurements, he reports ΔfH(CH2CO+•) = 874.4 ± 1.0 kJ/mol, ΔfH(CH3CHCO+•) = 783.3 ± 3.6 kJ/mol (which led him to suggest that the Bock et al.50 PES-estimated IEad is 150 meV too high), and ΔfH((CH3)2CCO+•) = 719.3 ± 3.6 kJ/mol. Lias et al.4 list ΔfH((CH3)2CCO+•) = 681 kJ/mol, based on a Bock et al.50 IE((CH3)2CCO) = 8.45 eV and ΔfH((CH3)2CCO) = −134 ± 4 kJ/mol. We note the large spread of reported values for the heat of formation of neutral methylketene, ΔfH(CH3CHCO) = −65,54 −105,4 and −95 kJ/mol.51 Figure 5 shows that it is possible to draw two different straight lines through the ketene series data. Line a, excluding the value of 797 kJ/mol, encompasses the higher values of the heats of formation of the methylketene and dimethylketene cations in Table 6, while line b satisfies the lower values of these cations. These results point to the necessity for further measurements on the heats of formation of neutral and cation

7. METHYL SUBSTITUTION IN FORMIC ACID AND ACETIC ACID In Table 7 are given heat of formation data for methylsubstituted formic acid and acetic acid. We first consider C-site Table 7. Heat of Formation of Cations As a Function of Size: Methyl-Substituted Formic Acid and Acetic Acid no. of atoms (n)

ion

C-Site Substitution in Formic Acid HCOOH+• 5 CH3COOH+• 8 CH3CH2COOH+• 11 (CH3)2CHCOOH+• 14 (CH3)3CCOOH+• 17 O-Site Substitution in Formic Acid HCOOH+• 5 HCOOCH3+• 8 HCOOCH2CH3+• HCOOCH(CH3)2+• HCOOC(CH3)3+• O-Site Substitution in Acetic CH3COOH+• CH3COOCH3+• CH3COOCH2CH3+• CH3COOCH(CH3)3+• CH3COOC(CH3)3+•

ln(n)


1.609 2.079 2.398 2.639 2.833

714.34 596.44 552,3 5674 517,4 49755 482 (see text), 4604

1.609 2.079

11

2.398

14 17 Acid 8 11 14 17 20

2.639 2.833

714.34 688,4 709, 697, 690, 684 (see text) 626,12 637,4 652, 662 (see text) 6024 see text

2.079 2.398 2.639 2.833 2.996

596.44 579,3 5814 5233,4 4824 see text

substitution in formic acid. The cation heats of formation are listed as 714.3 kJ/mol for formic acid in Lias et al.,4 and that for acetic acid is 596.4 kJ/mol. The relevant data are also given in NIST.3 Two different values are given in Table 7 for the propanoic acid cation, 5674 and 552 kJ/mol,3 derived from IE(CH3CH2COOH) and ΔfH(CH3CH2COOH) data given, respectively, in Lias et al.4 and NIST.3 The next member of the C-site substitution series is 2-methyl propanoic acid, whose cation heat of formation has two listed values, ΔfH((CH3)2CHCOOH+•) = 5174 and 497 kJ/mol.55 These values differ essentially in the use of different values for the ionization energy of 2-methyl propanoic acid, IE((CH3)2CHCOOH) = 10.33 ± 0.034 and 10.12 eV.55 A definitive value of the ionization energy is required. The last member of this particular series has a reported heat of formation of ΔfH((CH3)3CCOOH+•) = 460 kJ/mol,4 based on IE((CH3)3CCOOH) = 10.08 eV. This becomes 482 kJ/mol using IE((CH3)3CCOOH) = 10.3 eV reported by Green and Hayes.56 We note that the ΔfH((CH3)3CCOOH) = −512 kJ/ mol used in these determinations is an additivity-derived value and not an experimental value. These various values are plotted in Figure 6. A reasonable straight line (Figure 6, line a) can be drawn starting at the acetic acid cation. This tends to support the values 552, 517, and 482 kJ/mol and exclude 567, 497, and 460 kJ/mol for these respective n = 11, 14, and 17 C-site-substituted cations. The heats of formation of O-site methyl-substituted formic acid cations are also given in Table 7. For methyl formate, Lias et al.4 list 688 kJ/mol, based on IE(HCOOCH3) = 10.815 ±

Figure 5. Heat of formation of cations as a function of ln(n), where n is the number of atoms in the ion: methyl-substituted ketene. Lines a and b: methyl substitution in CH2CO. 10063



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This is similar for succeeding members of the C-site- and Osite-substituted species. The value of ΔfH(CH3COOCH3+•) = 579 kJ/mol is given by IE(CH3COOCH3) = 10.25 ± 0.02 eV and ΔfH(CH3COOCH3) = −410 kJ/mol.3 For the ethyl acetate cation, the NIST3 as well as the Lias et al.4 value of its heat of formation is ΔfH(CH3COOCH2CH3+•) = 523 kJ/mol. Values from 535 to 545 kJ/mol, dependent on various IE values, have also been proposed55 but are less reliable than the 523 kJ/mol value whose IE value is from a PEPICO measurement.62 The Lias et al. value of 482 kJ/mol for ΔfH(CH3COOCH(CH3)2+•)4 appears to be well-founded on a good value of IE(CH3COOCH(CH3)2) = 9.99 ± 0.03 eV. No heat of formation data are available for the n = 20 species CH3COOC(CH3)3+•. A reasonable straight line (Figure 6, line c) can be drawn starting at the n = 11 methyl enathoate and using the successive values 581 (n = 11), 523 (n = 14), and 482 (n = 17) kJ/mol. For the n = 20 cation, it predicts ΔfH(CH3COO(CH3)3+•) = 450 kJ/mol. This is of the same order of magnitude as the two different values of the heat of formation reported for the analogous species, ΔfH((CH3)3CCOOCH3+•) = 461 or 442 kJ/mol.3

Figure 6. Heat of formation of cations as a function of ln(n), where n is the number of atoms in the ion: methyl-substituted formic acid and acetic acid. Line a: C-site methyl substitution in HCOOH; line b: Osite methyl substitution in HCOOH; line c: O-site methyl substitution in CH3COOH.

0.005 eV (probably from an old photoionization measurement of Watanabe et al.15) and ΔfH(HCOOCH3) = −355.5 kJ/mol. A very accurate ZEKE measurement57 gave IE(HCOOCH3) = 10.835 eV. Several values have been given in NIST3 for the heat of formation of the neutral, ΔfH(HCOOCH3) = −336.9, −349, −355.5, and −362 kJ/mol, leading, respectively, to ΔfH(HCOOCH3+•) = 709, 697, 690, and 684 kJ/mol. For the next member of the series, ethyl formate, ΔfH(HCOOCH2CH3+•) is given as 637 kJ/mol by Lias et al.4 using ΔfH(HCOOCH2CH3) = −387 kJ/mol and IE(HCOOCH2CH3) = 10.61 eV,3,15 while other values of ΔfH(HCOOCH2CH3+•) are 662 or 626 kJ/mol according as ΔfH(HCOOCH2CH3) = −361.758 or −398 kJ/mol59 with IE(HCOOCH2CH3) = 10.61 ± 0.0115 and 10.61 ± 0.05 eV.60 Zha et al.60 give ΔfH(HCOOCH2CH3+•) = 652 kJ/mol, using ΔfH(HCOOCH2CH3) = −371 kJ/mol. The final member of the series, isopropyl formate, has a Lias et al. value of ΔfH(HCOOCH(CH3)2+•) = 602 kJ/mol.4 This is based on IE(HCOOCH(CH3)2) = 10.44 eV3 and the estimated value ΔfH(HCOOCH(CH3)2) = −405 kJ/mol. It is not wellestablished. The data for this series are plotted in Figure 6, alongside that for the formic acid/acetic acid derivatives. Provisionally accepting the value ΔfH(HCOOCH(CH3)2+•) = 602 kJ/mol makes it possible to draw several different lines through the points on the graph; line b is only one example. Indeed, it is certainly an invalid line, as can be ascertained by the following argument. We can estimate a maximum value for the heat of formation of the n = 17 species, tert-butyl formate, as Δ f H(HCOOC(CH 3 ) 3 +• ) < 537 kJ/mol, knowing that ΔfH(HCOOC(CH3)3) = −4573 or −468 kJ/mol and that the appearance energy of the fragment ion (CH3)3C+ from this species is 10.42 eV.61 Extrapolating line b to ln(n) = 2.83 predicts a value of ΔfH(HCOOC(CH3)3+•) ≈ 573 kJ/mol, well above the 537 kJ/mol upper limit. In Table 7 are also given data for the O-site-substituted compounds of acetic acid. The heat of formation of the methyl ethanoate cation, ΔfH(CH3COOCH3+•) = 581 kJ/mol,4 is greater than that of the corresponding C-site species, the propanoic acid cation, showing that the latter is more stable.

8. CONCLUDING REMARKS The Holmes−Lossing linear relation between cation heats of formation and ln(n) has previously proven to be a good guide to the validity of reported ΔfH(M+) values in methylsubstituted nitrogenous compounds2 and has been shown here to hold well for most of the oxygen compound species studied, at least starting with the first methyl-substituted species in each case. This has led to proposing best ΔfH(M+) values where multiple choices are possible among literature values. However, this linear relation is not universal, and the reasons for its applicability are not evident, although semiquantitative justifications have been made.1,2,12 In the present study, it appears to break down for methyl-substituted formaldehyde and its carbene isomers. Because ΔfH(M+) = IEad + ΔfH(M), when the Holmes−Lossing relation fails, it is legitimate to ask whether this is due to unusual or incorrect values of IEad or of ΔfH(M) in a particular function of size series of methylsubstituted species. Unexpected or aberrant values could be due to structural complications or to features such as the degree of proximity of the substituent to the charge site. In addition, direct measurement of IEad is quite often not possible, so that ΔfH(M+) values are then derived from proton affinity measurements, often susceptible to uncertainties than are modern ionization energy measurements. We note that additivity relations hold well for neutral methyl-substituted formaldehyde and its carbene isomers. Our results show that there are relative effects on thermodynamic stability by substitution at the carbon site or at the oxygen site in several of the oxygen compounds studied here. Greater stability on the C site was found for the cations of methanol, hydroxymethyl, hydroxycarbene, and formic acid, indicating that the C-site is a favored charge site for these ions. In addition, it was observed that methyl substitution on the vinyl alcohol enol ion leads to ions that are more stable than methyl substitution on the related keto ion acetaldehyde. The opposite is true for the neutral forms of these molecules.3,4 As a result of our study, we recommend further investigations of the heats of formation of oxygen compounds, presented in tabular form in Table 8. From our discussion of the heat of 10064



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Table 8. Recommended Further Studies of the Heats of Formation of Oxygen Compounds

species

maximum uncertainty ΔEmax in the reported cation heat of formation ΔfH(M+) kJ/mol

CH3OH CH2OH CH3CHOH (CH3)2COH CH2OCH3 CH2OCH2CH3 CH3CH2COH HCOCH3 HCOCH2CH3 CH3CHCO (CH3)2CCO CH3CH2COOH (CH3)2CHCOOH (CH3)3CCOOH HCOOCH3 HCOOCH2CH3 HCOOCH(CH3)2

36 25 17 63 14 26 40 27 36 38 48 15 20 22 25 36 uncertain

ionization energy IE(M) or appearance energy AE(M+) measure measure measure

neutral heat of formation ΔfH(M) measure measure measure measure

measure measure measure measure measure measure measure measure measure

measure

measure measure measure measure measure measure measure measure measure measure

REFERENCES

(1) (a) Holmes, J. L.; Lossing, F. P.; Fingas, M. Towards a General Scheme for Estimating the Heats of Formation of Organic Ions in the Gas Phase. Part I. Odd-Electron Cations. Can. J. Chem. 1981, 59, 80− 93. (b) Holmes, J. L.; Lossing, F. P. Towards a General Scheme for Estimating the Heats of Formation of Organic Ions in the Gas Phase. Part II. The Effect of Substitution at Charge-Bearing Sites. Can. J. Chem. 1982, 60, 2365−2371. (c) Holmes, J. L.; Aubry, C. Neutral and Ion Thermochemistry: Its Present Status and Significance. Mass Spectrom. Rev. 2009, 28, 694−700. (2) Leach, S. Size Effects on Cation Heats of Formation. I. Methyl Substitutions in Nitrogenous Compounds. Chem. Phys. 2012, 392, 170−179. (3) NIST Chemistry Webbook (June 2005) National Institute of Standards and Technology Reference Database; http://webbook.nist. gov (current 2010). (4) Lias, S. G.; Bartmess, J. E.; Libman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. Gas-Phase Ion and Neutral Thermochemistry. J. Phys. Chem. Ref. Data 1988, 17, Suppl. No. 1. (5) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic Press: New York, 1970. (6) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: London, 1986. (7) (a) Cohen, N.; Benson, S. W. Estimation of Heats of Formation of Organic Compounds by Additivity Methods. Chem. Rev. 1993, 93, 2419−2438. (b) Holmes, J. L.; Aubry, C. Group Additivity Values for Estimating the Enthalpy of Formation of Organic Compounds: An Update and Reappraisal. 1. C, H, and O. J. Phys. Chem. A 2011, 115, 10576−10586. (c) Holmes, J. L.; Aubry, C. Group Additivity Values for Estimating the Enthalpy of Formation of Organic Compounds: An Update and Reappraisal. 2. C, H, N, O, S, and Halogens. J. Phys. Chem. A 2012, 116, 7196−7209. (8) van Speybroeck, V.; Gani, R.; Meier, R. J. The Calculation of Thermodynamic Properties of Molecules. Chem. Soc. Rev. 2010, 39, 1764−1779. (9) Lias, S. G.; Bartmess, J. E. Gas-Phase Ion Thermochemistry. NIST Chemistry Webbook. http://webbook.nist.gov (2010). (10) Traeger, J. C.; McLoughlin, R. G. Absolute Heats of Formation for Gas Phase Cations. J. Am. Chem. Soc. 1981, 103, 3647−3652. (11) Aubry, C.; Holmes, J. L. Correlating Thermochemical Data for Gas-Phase Ion Chemistry. Int. J. Mass Spectrom. 2000, 200, 277−284. (12) Holmes, J. L.; Aubry, C.; Mayer, P. M. Assigning Structures to Ions in Mass Spectrometry; CRC Press: Boca Raton, FL, 2007. (13) Tao, W.; Klemm, R. B.; Nesbitt, F. L.; Stief, L. J. A Discharge Flow-Photoionization Mass Spectrometric Study of Hydroxymethyl Radicals (H2COH and H2COD): Photoionization Spectrum and Ionization Energy. J. Phys. Chem. 1992, 96, 104−107. (14) Matus, M. H.; Nguyen, M. T.; Dixon, D. A. Theoretical Prediction of the Heats of Formation of C2H5O• Radicals Derived from Ethanol and the Kinetics of β−C−C Scission in the Ethoxy Radical. J. Phys. Chem. A 2007, 111, 113−126. (15) Watanabe, K.; Nakayama, T.; Mottl, J. Ionization Potentials of Some Molecules. J. Quant. Spectrosc. Radiat. Transfer 1962, 2, 369− 382. (16) Berkowitz, J. Photoionization of CH3OH, CD3OH, and CH3OD: Dissociative Ionization Mechanisms and Ionic Structures. J. Chem. Phys. 1978, 69, 3044−3064. (17) Shao, J. D.; Baer, T.; Lewis, D. K. Dissociation Dynamics of Energy-Selected Ion-Dipole Complexes. 2. Butyl Alcohol Ions. J. Phys. Chem. 1988, 92, 5123−5128. (18) Wiberg, K. B.; Hao, S. Enthalpies of Hydration of Alkenes. 4. Formation of Acyclic tert-Alcohols. J. Org. Chem. 1991, 56, 5108− 5110. (19) Botter, R.; Pechine, J. M.; Rosenstock, H. M. Photoionization of Dimethyl Ether and Diethyl Ether. Int. J. Mass Spectrom. Ion Processes 1977, 25, 7−25. (20) Butler, J. J.; Holland, D. M. P.; Parr, A. C.; Stockbauer, R. A Threshold Photoelectron−Photoion Coincidence Spectrometric Study

section discussed 2 3 3 3 3 3 4 4 4 6 6 7 7 7 7 7 7

formation data, we have extracted the spread of reported values of the heat of formation for each species where the need for reinvestigation is most evident. This information, in the second column of Table 8 is presented as the maximum uncertainty ΔEmax in the reported cation heat of formation ΔfH(M+), independent of the conclusions from our graphical analyses. The nature of the chief uncertainties and the measurements or remeasurements required to obtain valid values are indicated in columns 3 (ionization energy or appearance energy) and 4 (heat of formation of the neutral species). Remeasurement of ΔfH(M+) can also include relevant proton affinity measurements. The remeasurement of ionization energies is particularly necessary when reported values have been derived from photoelectron spectroscopy, where estimation of adiabatic ionization energies is too often rather subjective. PIMS, ZEKE, or Rydberg spectroscopy measurements of adiabatic ionization energies, as well as even more sophisticated techniques also involving coincidence measurements, are much to be preferred. Finally, we stress that precise and reliable data on the heats of formation of radical cations and their neutral parents are required not only for studying chemical equilibria and reactions but also as necessary experimental landmarks for validating benchmark calculations of these thermochemical parameters, which is an increasingly active area of research.12,49,52,63−66

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 33-1-4507-7561. Fax: 33-1-4507-7100. E-mail: Sydney. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I warmly thank Martin Schwell for his help in preparing the figures. 10065



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