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

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Size Effects on Cation Heats of Formation. III. Methyl and Ethyl Substitutions in Group IV XH4, X = C, Si, Ge, Sn, Pb Sydney Leach* Laboratoire d’Etude du Rayonnement et de la Matière en Astrophysique (LERMA), CNRS-UMR 8112, Observatoire de Paris-Meudon, 5, place Jules Janssen, 92195 Meudon, France ABSTRACT: The heats of formation of alkyl-substituted XH4 (X = C, Si, Ge, Sn, Pb) molecular ions have often never been measured or are not known to better than 10 or 20 kJ/mol. The present study on these Main Group IV compounds adopts a graphical approach that relates cation heats of formation to cation size. A study of methyl substitution in XH4 is followed by a similar examination of heat of formation data on ethyl substitution in methane, silane, germane, stannane, and plumbane. The results provide tests of the validity of this graphical method as well as its use as a predictive tool for determining cation and neutral heats of formation. Suggestions are made of the need to investigate or reinvestigate the ionization energies and/or the heats of formation of several of the molecules studied. Results and conclusions are tabulated.

1. INTRODUCTION Reliable values of heats of formation of molecules and ions are required for quantitative interpretation of chemical equilibria and reactions. The dependence of an equilibrium or rate constant on heats of formation is crucial. A relatively small error in an activation energy or reaction enthalpy can lead to large errors in these constants of dynamic chemical processes. This study concerns the effects of methyl and ethyl substitutions on the heats of formation of cations of Group IV XH4 species, where X = C, Si, Ge, Sn, or Pb. It is part III of a general study of size effects on cation heats of formation. For neutral molecules heats of formation are listed in the NIST1 and Lias et al.2 compilations as well as in books.3,4 The reported values include not only experimentally determined values but also some that depend on estimations derived using empirical or semiempirical methods based on the parametrization of structural similarities, notably involving group additivity schemes.5 For molecular cations two principal methods of evaluation are used: (i) For a molecular ion M+, the heat of formation ΔfH(M+) is given by ΔfH(M+) = IEad(M) + ΔfH(M), i.e., 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 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. In many cases the values of IEad(M) and PA(M) are not known to better than 10 or 20 kJ/mol,1,2 especially since reported IEad values are often based on subjective estimations of onset energies in the first band of the photoelectron spectrum of M. In several cases the quoted IE values are obtained by the subtraction of ΔfH(MH) from ΔfH(MH)+, where the latter is obtained via the proton affinity of ΔfH(M). Independent methods of determining ΔfH(M+) or ΔfH(MH)+ can thus provide a check on values of IEad(M) or IEad(MH) if ΔfH(M) or ΔfH(MH) are accurately known. When IEad(M) is © XXXX American Chemical Society

known to very high accuracy, as is sometimes the case, an independent determination of the cation heat of formation can be used to give a value of the heat of formation of the neutral species. The present work on the heats of formation of the cations of methyl and ethyl-substituted Group IV XH4 species uses the graphical approach of Holmes and Lossing6 in correlating cation heats of formation with cation size. As in the case of molecules containing nitrogen (Part I7) and oxygen (Part II8) 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 of the molecules studied. The method has also been used, by graphical interpolation or extrapolation, to obtain useful new thermochemical information in many cases where there is a paucity of data. As in our earlier studies,7,8 if the heat of formation of a particular cation is derived from appearance energy (AE) 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: M + hν /e− → M+ + e−/2e− → m1+ + m i AE + Δf Hgas(M) −

(1)

∑ [Δf Hgas(m i)] = Δf Hgas(m1+) (2)

Additivity methods for semiempirically determining the heats of formation of molecular cations are not generally successful, in particular because ionization energies are not simply proportional to the number of added subunits. It has been Received: September 18, 2014 Revised: November 4, 2014

A

dx.doi.org/10.1021/jp509468z | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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shown, however, that the effect on ΔfH(ion) due to substitution of a functional group such as CH3 or NH2 at the formal charge-bearing sites in both odd and even electron ions is, for each group, a simple function of ion size.6,11,12 A plot of ΔfH(ion) as a function of ln(n), where n is the number of atoms, often gives good straight lines. In the present work we study methyl or ethyl substitution in related Group IV XH4 compounds, giving information on relative stabilizing effects of methyl and ethyl substitutions. 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 and on its use in estimating unmeasured heats of formation and/or ionization energies.

2.1. Methyl Substitution in Methane. Table 1 gives the heats of formation of the cations of methane and its substituted methyl derivatives. Table 1. Heats of Formation of the Cations of MethylSubstituted Methane as a Function of Size ion

no. of atoms (n)

ln(n)

ion heat of formation ΔfH(M+) kJ/mol

CH4+ CH3CH3+ CH2(CH3)2+ CH(CH3)3+ C(CH3)4+

5 8 11 14 17

1.609 2.079 2.398 2.639 2.833

1132, 1142 1028 909, 951 885, 896 818, 825, 827, 832, 834, 836

Methane. The value ΔfH(CH4+) = 1142 kJ/mol is based on ΔfH(CH4) = −74.87 kJ/mol and IEad(CH4) = 12.618 ± 0.004 eV,26 which was determined from pulsed-field-ionization (PFI) zero-kinetic-energy (ZEKE), rotationally resolved photoelectron spectra of CH4. This value of ΔfH(CH4+) is to be preferred over that of Lias et al.,2 who give ΔfH(CH4+) = 1132 kJ/mol based on ΔfH(CH4) = −74.5 ± 0.4 kJ/mol and IEad(CH4) = 12.51 eV. The value IEad(CH4) = 12.51 eV was given by Rabalais et al.27 in their interpretation of a high resolution HeI PES vibrational progression in which the adiabatic origin was determined by extrapolation, although the corresponding feature was not observed. Ethane. The heat of formation ΔfH(C2H6+) = 1028 ± 5 kJ/ mol seems reasonably firm. It is derived from the NIST IEad(C2H6) = 11.52 ± 0.04 eV and ΔfH(C2H6) = −84.2 ± 1 kJ/mol1 used by Holmes et al.12 These are essentially the same values as given by Lias et al.,2 IEad(C2H6) = 11.52 ± 0.01 eV and, from the compilation of Pedley and Rylance,28 ΔfH(C2H6) = −84.0 ± 0.2 kJ/mol. Confirming values of the ionization energy are IEad(C2H6) = 11.46 ± 0.04 eV,29 while a TPES study gave IEad(C2H6) = 11.5 ± 0.1 eV.30 Furthermore, a theoretical study by Zuilhoff et al.31 by the CBS-APNO(m) method gives IEad(C2H6) = 11.55 eV for the lowest lying form of ethane, the C2h symmetry isomer, but it overestimates the vertical ionization energy by over 500 meV. The value IEad(C2H6) = 11.52 ± 0.01 eV is to be preferred over that given by the PIMS study of Watanabe et al.,32 IEad(C2H6) = 11.65 ± 0.03 eV. Propane. For propane, the listed ΔfH(C3H8+) = 951 ± 5 kJ/ mol1 is derived from IEad(C3H8) = 10.94 ± 0.05 eV and ΔfH(C3H8) = −104.7 ± 0.5 kJ/mol and seems to be reasonably well established. However, the IEad(C3H8) = 10.94 ± 0.05 eV could refer to a C2v symmetry isomer of propane while a lowerlying Cs form has a reported ionization energy IEad(C3H8) = 10.51 ± 0.05 eV.33 The unpaired electron is localized in different moieties of the ion in the two isomers.31 We note that a CBS-APNO(m) modified procedure calculation of Zuilhoff et al.31 gives IEad(C3H8) = 11.03 eV, in good agreement with experiment for the C2v symmetry case, but here again this calculation method overestimates the vertical ionization energy by over 500 meV. An ab initio molecular orbital calculation of Olivella et al.34 gave IEad = 10.74 eV for the Cs lowest lying structure. A value of IEad(C3H8) = 10.51 ± 0.05 eV leads to ΔfH(C3H8+) = 909 ± 5 kJ/mol, which lies far off the straight lines a and b of Figure 1. This brings into question the IEad of the Cs isomer of propane from a threshold measurement assignment in the electron impact study of Denifl et al.,33 which thus requires confirmation.

2. METHYL SUBSTITUTION IN RELATED GROUP IV COMPOUNDS We begin by revisiting the data on methyl substitution in methane, previously studied by Holmes and Lossing,6 and extending this to a comparison with methyl substitution in the related Group IV species silane, stannane, germane, and plumbane. The bonding between the Group IV element and the carbon atom(s) in the alkyl-substituted species is predominantly covalent. Interest in these Group IV species is wide, from astrophysics (silane13 and germane14−16), through its use in semiconductor processing plasmas (silane17), to the suggestion that Group IV hydrides, including XH4, and in particular plumbane, might become metallic under pressures that are lower than is projected for pure H2 metalization.18,19 Silanes have also been found to be useful as scramjet and rocket fuels.20 Reliable thermodynamic data are thus required for understanding various physicochemical properties of these species. For the Group IV (group-14 in IUPAC recommended notation) compounds studied there is a general difficulty, apart from the case of carbon compounds, in measuring accurate heats of formation of the neutral species. Many are made by combustion methods (heats of explosive decomposition) in stationary or rotating bomb calorimeters.21 Determinations of heats of formation by these techniques require taking account of incomplete oxidation of the initial compounds as well as any additional reactions between combustion products.22 This can often be done adequately using the rotating bomb calorimeter method in which a solvent is used to dissolve the solid products and so enable one to obtain a well-defined final state for the combustion reaction.23,24 In general, although mentioning bomb calorimetry results, in determining heats of formation of the molecular ions we will disregard those obtained by static bomb techniques when there is other conflicting evidence. We note that a comparison of the results of static and rotating bomb calorimetry on organometallic compounds made by Pilcher25 concluded that the static bomb results on silanes, germanes, and plumbanes are doubtful because of difficulties of incomplete combustion and/or in identifying or accounting for solid residue combustion products, whereas more credit can be given to static bomb measurements in the case of stannanes. Use of the Holmes−Lossing cation size relation will be shown to provide means of verifying or proposing values of the heats of formation of neutral Group IV alkyl compounds. B



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and Worley, who studied the HeI PES, using a retarding-gridtype spectrometer, which gives good results for the first IE, obtained IEad(C(CH3)4) = 10.37 eV.42 This would give ΔfH(C(CH3)4+) = 834 kJ/mol. Hobrock and Kiser43 give ΔfH(C(CH3)4) = −157 kJ/mol, thus making ΔfH(C(CH3)4+) = 836 kJ/mol, using the value IEad(C(CH3)4+) = 10.29 eV, which is close to many reported values. We note, however, that the electron impact mass spectrometric AE(C5H12+) = 10.29 eV cited by Hobrock and Kiser,43 from Stevenson,44 is ambiguous in that it is noted as the appearance energy of the C5H9+ fragment ion in Stevenson’s report on neopentane.44 In this respect we remark that the parent ion in the mass spectrum of neopentane has an extremely small intensity, as is the case for all of the tetramethyl and tetraethyl Group IV compounds.1 This indicates that the parent ion has a short lifetime but it does not hinder the measurement of the ionization energy by photoelectron spectroscopy since electron ejection in photoionization occurs on a much faster time scale than ion dissociation. From IEad(C(CH3)4) = 10.21 eV and the NIST1 value ΔfH(C(CH3)4) = −167.9 ± 0.7 kJ/mol, we obtain ΔfH(C(CH3)4+) = 817.6 kJ/mol The graph for the alkanes (Figure 1) gives good straight lines starting from ΔfH(CH4+) = 1142 kJ/mol (line a) and from ΔfH(CH4+) = 1132 kJ/mol (line b), confirming the validity of the Holmes−Lossing cation size relation. Line a appears to be preferable and tends to favor ΔfH(CH4+) = 1142 kJ/mol rather than 1132 kJ/mol, the value ΔfH(C4H10+) = 885 kJ/mol for the isobutane cation rather than 896 kJ/mol, and the higher values ΔfH(C(CH3)4+) = 832 or 825 kJ/mol for the neopentane cation. The value ΔfH(C3H8+) = 909 ± 5 kJ/mol is clearly to be disregarded. The most outstanding new requirements that result from this study are good determinations of the adiabatic ionization energies and heats of formation of neopentane and further investigation concerning the ionization energies of isobutane and the various isomers of the propane cation. 2.2. Methyl Substitution in Silane. The published heats of formation of the cations of silane and its methyl derivatives depend to a considerable extent on the choice of the heat of formation of the neutral compounds. There are basically two different sets of values, those of the CATCH compendium45 and those given by Potzinger et al.,46 and there are a number of other values, including computed heats of formation of the neutral silanes. In the following we will discuss these various proposed values, which have been subject to earlier reviews47−49 that, however, leave unresolved the choice of best values. Table 2 lists the heats of formation of the cations of silane and its substituted methyl derivatives. Silane. The heat of formation of the silane radical ion, ΔfH(SiH4+) = 1096 kJ/mol, is derived from ΔfH(SiH4) = 34.31 kJ/mol and the evaluated IEad(SiH4) = 11.00 ± 0.02 eV.1 Berkowitz et al.50 observe a small PIMS signal for SiH4 at 1127

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 methane.

Isobutane. In the case of isobutane Lias et al.2 give a provisional value ΔfH(C4H10+) = 885 kJ/mol based on ΔfH(C4H10) = −134.5 ± 0.5 kJ/mol and IEad = 10.57 eV. Lias et al. do not give a source for this IE value although they do make an unclear reference to the book of Kimura et al.35 In this book the ionization energy is given as IE(C4H10) = 11.13 eV, which is that of the first PES band peak and is thus IEvert. From the published HeI PES of isobutane by Kimura et al.,35 we estimate that the onset of the PES first band is at 10.58 eV, and thus presume that this is the origin of the IEad value cited by Lias et al.2 The NIST compilation1 lists a conservative value IEad = 10.68 ± 0.11 eV, evaluated after consideration of 10 different ionization energy determinations that range from IEad = 10.5 to 11.4 eV. We note that the PIMS measurement of Watanabe et al.32 gave the onset value IE = 10.57 eV, but they were unable to estimate the error bars. Using the NIST value ΔfH(C4H10) = −134.20 ± 0.06 kJ/mol,1 we conclude that ΔfH(C4H10+) = 896 ± 11 kJ/mol. The straight lines a and b in Figure 1 are consistent with both ΔfH(C4H10+) = 896 and 885 kJ/mol. Neopentane. There are several proposed values for the heat of formation of the neopentane radical ion. Lias et al.2 give ΔfH(C(CH3)4+) ≤ 818 kJ/mol based on IE(C(CH3)4) ≤ 10.21 ± 0.04 eV and ΔfH(C(CH3)4 = −167.4 ± 0.7 kJ/mol. The ionization energy is that given by Traeger.36 NIST proposes an evaluated IE(C(CH3)4) ≤ 10.30 ± 0.08 eV,1 giving ΔfH(C(CH3)4+) ≤ 827 ± 8 kJ/mol. Kimura et al. give IEvert (C(CH3)4) = 10.90 eV.35 We estimate 10.28 eV for the signal onset in the HeI PES of neopentane published by Kimura et al.35 On assuming that the onset is at IEad, this would give ΔfH(C(CH3)4+) = 825 kJ/mol. We note, here too, that the PIMS measurement of Watanabe et al.32 gave an onset value IE(C(CH3)4+) = 10.35 eV, but again they were unable to estimate the error bars; this onset value would give ΔfH(C(CH3)4+) = 832 kJ/mol. Jonas et al.37 estimate 10.21 eV for the onset in their HeI PES, whereas our own estimate is 10.31 eV from their spectrum, while the HeI PES study of Evans et al.38 gave IEad(C(CH3)4) = 10.25 ± 0.10 eV. We consider IEad(C(CH3)4) = 10.21 eV to be the best available value, but for completeness we note the existence of some other neopentane ionization energy values: IEad(C(CH3)4) = 10.53 eV,39 IE(C(CH3)4) = 10.5 ± 0.3 eV,40 and IE(C(CH3)4) = 10.55 ± 0.10 eV.41 We note also that Dewar

Table 2. Heats of Formation of the Cations of MethylSubstituted Silane as a Function of Size

C

ion

no. of atoms (n)

ln(n)

ion heat of formation ΔfH(M+) kJ/mol

SiH4+ SiH3CH3+ SiH2(CH3)2+ SiH(CH3)3+ Si(CH3)4+

5 8 11 14 17

1.609 2.079 2.398 2.639 2.833

1096, 1159 1003, 1011 892, 899, 920 782, 792, 828 622, 659, 676, 711, 746, 754



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Tetramethylsilane. For tetramethylsilane Lias et al.2 give ΔfH(Si(CH3)4+) = 711 kJ/mol, based on IE(Si(CH3)4) = 9.80 ± 0.04 eV (source not reported, but this value is given as evaluated in NIST;1 we note that Jonas et al.37 give IEad = 9.79 eV from a HeI PES onset), and ΔfH(Si(CH3)4) = −233.0 ± 2.9 kJ/mol62 (−233.2 ± 3.2 kJ/mol from Long and Pulford63). NIST1 gives ΔfH(Si(CH3)4) = −286.60 kJ/mol from Chase.64 If we use this value then ΔfH(Si(CH3)4+) = 659 kJ/mol. We remark that IEad(Si(CH3)4) = 9.42 ± 0.10 eV was given in Evans et al.38 from a HeI PES study. Close examination of their Figure 2 confirmed their value. This IEad would lower the ΔfH(Si(CH3)4+) values by 40 kJ/mol, e.g., to 676 kJ/mol using the Steele62 value of ΔfH(Si(CH3)4) and to 622 kJ/mol from the NIST value.1 We note that Potzinger et al.46 give IEad(Si(CH3)4) = 9.6 eV, and report ΔfH(Si(CH3)4+) = 745.7 kJ/mol, based on ΔfH(Si(CH3)4) = −177.2 kJ/mol. The value ΔfH(Si(CH3)4+) = 681 kJ/mol given by Hobrock and Kiser43 is based on on IEad(Si(CH3)4) = 9.8 ± 0.15 eV and ΔfH(Si(CH3)4) = −263.3 kJ/mol. Their ionization energy is close to that of Lappert et al., IE(Si(CH3)4) = 9.85 ± 0.16 eV,65 who report also a rotating bomb calorimetry value ΔfH(Si(CH3)4) = −196.5 ± 25.1 kJ/mol, giving ΔfH(Si(CH3)4+) = 754 ± 25 kJ/ mol. Several other values of ΔfH(Si(CH3)4) have been reported: −245.4 kJ/mol cited by Frierson et al.,59 −229 ± 3 kJ/mol,66 and −226 kJ/mol.67 Static bomb calorimetric measurements gave −230 ± 4 kJ/mol21 and −288 kJ/mol.60 We note that ab initio calculations predict that the Jahn− Teller distorted ion has Cs symmetry and IE = 9.72 eV.57a Line a in Figure 2 is a good straight line starting from silane using the Lias et al.2 value for ΔfH(SiH4+). The ΔfH(SiH4+) =

Å (11.0 eV), and a TPES signal has been observed down to 1097 Å by Heinis et al.51 A PIMS observation of an ion current onset at 11.02 eV was attributed to a SiH2+ fragment ion by Börlin et al.,52 but Berkowitz et al.50 have given good counter arguments in favor of the parent ion SiH4+. Clarification is necessary since this is about 600 meV below the PES IEad = 11.65 eV given by Lias et al.2 The Berkowitz et al. results and interpretation are strongly supported by the PIMS measurements of Shin et al.,53 who observe IEad(SiH4) = 11.15 ± 0.10 eV. Lias et al. give ΔfH(SiH4+) = 1159 kJ/mol,2 but this is based on the value IEad(SiH4) = 11.65 eV; the origin of this IEad value is not given but it is most probably derived from a HeI PES measurement such as by Pullen et al.54 and Potts and Price,55 who report IEad(SiH4) ≈ 11.67 eV. We note that Potzinger et al.46 also give ΔfH(SiH4+) = 1159 kJ/mol, based on IEad(SiH4) = 11.7 eV, ΔfH(M) = 34.3 kJ/mol. There is general agreement on ΔfH(SiH4) = 34.3 kJ/mol.56 Ab initio and density functional calculations predict that Jahn−Teller distortion creates a SiH4+ ion of Cs symmetry and IE = 10.91 eV.57 The recent ab initio calculation of the Jahn− Teller potential energy surfaces of SiH4+ by Mondal and Varandas,58 which explores the complex vibrational motion underlying the first PES band of silane, does not provide a conclusive determination of the IEad of silane. Methylsilane. For methylsilane Lias et al. 2 give ΔfH(SiH3CH3+) = 1003 kJ/mol, based on IE(SiH3CH3) = 10.7 eV (source not given but probably from the study of Potzinger et al.,46 who give IEad = 10.7 eV), and ΔfH(SiH3CH3) = −29 ± 4 kJ/mol, which is the preferred value of Doncaster and Walsh.56 We note that Potzinger et al. 46 report ΔfH(SiH3CH3+) = 1011 kJ/mol, based on IEad(SiH3CH3) = 10.7 eV, and ΔfH(SiH3CH3) = −18.0 kJ/mol. A value ΔfH(SiH3CH3) = −33.4 kJ/mol is cited as experimental by Frierson et al.,59 although it is probably a CATCH tables value;56 this would lead to ΔfH(SiH3CH3+) = 999 kJ/mol. Dimethylsilane. For dimethylsilane Lias et al.2 give ΔfH(SiH2(CH3)2+) = 899 kJ/mol, based on IE(SiH2(CH3)2) = 10.3 eV (source not given but probably Potzinger et al.46), as reported in NIST,1 and ΔfH(SiH2(CH3)2) = −95 ± 4 kJ/mol. Potzinger et al.46 report ΔfH(SiH2(CH3)2+) = 920 kJ/mol, based on IEad(SiH2(CH3)2) = 10.3 eV from their appearance energy measurements, and ΔfH(SiH2(CH3)2) = −70.2 kJ/mol. We note other reported values of ΔfH(SiH2(CH3)2): −196 ± 12 kJ/mol,21 −175 kJ/mol,60 −101.6 kJ/mol cited as an experimental value by Frierson et al.,59 and −96.1 kJ/mol.48 We disregard the values −175 and −196 kJ/mol, which are from static bomb calorimetry measurements of Tannenbaum et al.21,60,61 The ΔfH(SiH2(CH3)2) = −101.6 kJ and −96.1 kJ/ mol values lead respectively to ΔfH(SiH2(CH3)2+) = 892 and 898 kJ/mol. Trimethylsilane. For trimethylsilane Lias et al.2 give ΔfH(SiH(CH3)3+) = 792 kJ/mol, based on IEad(SiH(CH3)3) = 9.9 eV46 and ΔfH(SiH(CH3)3) = −163 ± 4 kJ/mol.56 Potzinger et al.46 report ΔfH(SiH(CH3)3+) = 828 kJ/mol; this is based on their HeI PES IEad(SiH(CH3)3) = 9.9 eV and on ΔfH(SiH(CH3)3) = −123.7 kJ/mol. Other published values of ΔfH(SiH(CH3)3) are −173 kJ/ mol cited by Frierson et al.,59 −276 kJ/mol,21,61 and −251 kJ/ mol.60 Here too we disregard the static bomb calorimetry values of Tannenbaum et al.,60,61 and obtain ΔfH(SiH(CH3)3+) = 782 kJ/mol using ΔfH(SiH(CH3)3) = −173 kJ/mol.

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 silane.

1096 kJ/mol would give a much less satisfactory linear plot, illustrated by line b in Figure 2. It should be emphasized that it is particularly difficult to determine the IEad(M) from the onset of a PES first band or from a PIMS ion current curve in these cases of weakly stable species such as the silane cation. Rydberg series data can nominally help determine a more reliable value of IEad(SiH4). However, the broad, diffuse nature of silane Rydberg bands makes this an uncertain task68 and it is not facilitated by the Jahn−Teller nature of the ion ground state.69 Be this as it may, line a of Figure 2 is consonant with both ΔfH(SiH(CH3)3+) = 792 and 828 kJ/mol, predicting indeed D



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ΔfH(SiH(CH3)3+) = 812 kJ/mol, whereas line b is consonant with ΔfH(SiH(CH3)3+) = 828 kJ/mol but extrapolates to values of ΔfH(Si(CH3)4+) that are not observed, possibly indicating a breakdown of the linear relation in this case. Line a is also in favor of the higher values of ΔfH(Si(CH3)4+) = 746 and 754 kJ/mol rather than the 711 kJ/mol given by Lias et al.2 and the several lower values for this heat of formation given in Table 2. It is clear from the above discussion that renewed investigation of the ionization energies and the heats of formation of silane and its methyl-substituted derivatives is called for in order to improve the determination of the heats of formation of their radical cations. The finding that line a is better than line b does not prove that ΔfH(SiH4+) = 1096 kJ/mol is incorrect, calling into doubt IEad(SiH4) = 11.00 eV1,50 on which it is based, and for which good arguments exist (the neutral heat of formation appears incontrovertible). We have previously found cases in which the Holmes−Lossing linear relation holds only from the monosubstituted derivative toward polysubstituted derivatives, e.g., methyl substitution in acetaldehyde cations8 and methyl substitution at carbon sites in ammonium cations.7 Methyl substitutions in the methane cation could consitute a similar example. 2.3. Germanes. Table 3 lists the heats of formation of the cations of germane and its substituted methyl derivatives. This

We note that the potential energy calculations of Kudo and Nagase73 show that the ground state of the ion suffers from Jahn−Teller distortion and that the most probable lowest energy structure has Cs symmetry, with a calculated IEad = 10.2 eV. It is interesting to record that another calculation (OCE calculation), based essentially on a united atom model, gives IE = 7.87 eV74 without correlation energy correction. A similar calculation for SiH4 gives IE(SiH4) = 8.44 eV, which is 2.56 eV below the experimental value.75 Assuming a similar correlation energy correction, this would give 7.87 + 2.56 = 10.43 eV for IE(GeH4) which is similar to the lowest value of Rušcǐ ć et al.,72 although one might expect the correlation energy correction to be greater for the heavier species. Taking the experimental and the best calculated values of ΔfH(GeH4), respectively 90.3 ± 2.1 and 82.0 kJ/mol, the values of the heat of formation of the ion become ΔfH(GeH4+) ≤ 1106 and ≤1098 kJ/mol, with IEad Ge > Pb > Sn;111 this behavior and the alkyl-substituted compound anomalies perhaps reflect the introduction of f electrons in the electron configuration of lead, ...5p64f145d106s26p2. Finally, we consider the effects of methyl/ethyl substitution on isomeric cations. We can compare the cases for XC2H8, i.e., XH2(CH3)2 and XH3CH2CH3 and also those for XC4H12, i.e., X(CH3)4 and XH2(CH2CH3)2. For the XC2H8 Group IV series the difference is small between the heats of formation of the cation isomers, whereas for the XC4H12 cations the diethyl derivatives are about 110 ± 10 kJ/mol more stable than the tetramethyl-substituted ions. This may indicate that there is less steric strain in the XH2(CH2CH3)2 cations than in the X(CH3)4 cations. The Holmes−Lossing linear relation between cation size and heat of formation has been shown to be a fruitful diagnostic tool for testing published values of the heats of formation of neutral and cation molecular species and for revealing needed measurement or remeasurement of adiabatic ionization energies and heats of formation of neutral compounds, as listed in Table 11 for alkyl-substituted Group IV tetrahydrides. Reliable values of these data are required not only for the study of chemical equilibria but also as experimental landmarks for validating benchmark calculations of thermochemical quantities that are increasingly being carried out but as yet insufficiently so for Group IV XY4 compounds.

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(3) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic Press: New York, 1970. (4) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: London, 1986. (5) Cohen, N.; Benson, S. W. Estimation of Heats of Formation of Organic Compounds by Additivity Methods. Chem. Rev. 1993, 93, 2419−2438. (6) 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. (7) Leach, S. Size Effects on Cation Heats of Formation. I. Methyl Substitutions in Nitrogenous Compounds. Chem. Phys. 2012, 392, 170−179. (8) Leach, S. Size Effects on Cation Heats of Formation. II. Methyl Substitutions in Oxygen Compounds. J. Phys. Chem. A 2013, 117, 10058−10067. (9) Lias, S. G.; Bartmess, J. E. Gas-Phase Ion Thermochemistry; NIST Chemistry WebBook. (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, 2007. (13) Goldhaber, D. M.; Betz, A. I. Silane in IRC + 10216. Astrophys. J. 1984, 279, L55−L58. (14) Drossart, P.; Encrenaz, T.; Kunde, V.; Hanel, R.; Combes, M. An estimate of the PH3, CH3D and GeH4 abundances on Jupiter from the Voyager IRIS data at 4.5 μm. Icarus 1982, 49, 416−426. (15) Knoll, K. S.; Knacke, R. F.; Geballe, T. R.; Tokunaga, A. T. Evidence for germane in Saturn. Icarus 1988, 75, 409−422. (16) Carrier, W.; Osamura, Y.; Zheng, W.; Kaiser, R. I. Laboratory investigations on the infrared absorptions of germanium-bearing molecules Directing the identification of organo-germanium molecules in the atmospheres of Jupiter and Saturn. Astrophys. J. 2007, 654, 687−692. (17) Perrin, J. Plasma and surface reactions during a-Si:H film growth. J. Non-Cryst. Solids 1991, 137/138, 639−644. (18) Ashcroft, N. W. Hydrogen dominant metallic alloys: High temperature superconductors? Phys. Rev. Lett. 2004, 92, 187002. (19) Zaleski-Ejgierd, P.; Hoffmann, R.; Ashcroft, N. W. High pressure stabilization and emergent forms of PbH4. Phys. Rev. Lett. 2011, 107, 037002. (20) Hidding, B.; Pfitzner, M.; Simone, D.; Bruno, C. Review of the potential of silanes as rocket/scramjet fuels. Acta Astronaut. 2008, 63, 379−388. (21) Tel’noi, V. I.; Rabinovich, I. B. Thermochemistry of Organic Derivatives on Non-Transition Elements. Russ. Chem. Rev. 1980, 49, 603−622. (22) Long, L. H.; Norrish, R. W. G. The strengths of certain covalent metal bonds. Philos. Trans. R. Soc., A 1949, 241, 587−617. (23) Scott, D. W.; Good, W. D.; McCullough, J. P. Tetraethyllead: Heat of formation by rotating−bomb calorimetry. J. Phys. Chem. 1956, 60, 1090−1095. (24) Good, W. D.; Scott, D. W.; Lacina, J. L.; McCullough, J. P. Tetramethyllead: Heat of formation by rotating-bomb calorimetry. J. Phys. Chem. 1959, 63, 1139−1142. (25) Pilcher, G. Combustion calorimetry of organometallic compounds. In Energetics of Organometallic Species; Martinho Simoes, J. A., Ed.; NATO ASI Series C; Kluwer: Dordrecht, 1991; Vol. 367, pp 9−34. (26) Signorelli, R.; Merkt, F. The first rotationally resolved spectrum of CH4+. J. Chem. Phys. 1999, 110, 2309−2311. (27) Rabalais, J. W.; Bergmark, T.; Werme, L. O.; Karlsson, L.; Siegbahn, K. The Jahn-Teller effect in the electron spectrum of methane. Phys. Scr. 1971, 3, 13−18.

AUTHOR INFORMATION

Corresponding Author

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

The author declares no competing financial interest.

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ACKNOWLEDGMENTS John Holmes, a pioneer with the late Fred Lossing in the inception and development of these thermochemical studies, is warmly thanked for useful and pleasurable correspondence.

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REFERENCES

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