The Thermochemistry of Cubane 50 Years after Its Synthesis: A High

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The Thermochemistry of Cubane 50 Years after Its Synthesis: A High-Level Theoretical Study of Cubane and Its Derivatives. Filipe Agapito, Rui Centeno Santos, Rui M. Borges dos Santos, and José Artur Martinho Simões J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 03 Mar 2015 Downloaded from http://pubs.acs.org on March 5, 2015

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The Journal of Physical Chemistry

The thermochemistry of cubane 50 years after its synthesis: a high-level theoretical study of cubane and its derivatives. Filipe Agapito,*,† Rui C. Santos, † Rui M. Borges dos Santos,*,†,‡ and José A. Martinho Simões†

†

Centro de Química e Bioquímica, Faculdade de Ciências, Universidade de Lisboa,

1749-016 Lisboa, Portugal ‡

Institute for Biotechnology and Bioengineering Center for Molecular and Structural

Biomedicine, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal

Corresponding Authors * [email protected] (Filipe Agapito); [email protected] (Rui M. Borges dos Santos)

ACS Paragon Plus Environment

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Abstract The gas-phase enthalpy of formation of cubane (603.4 ± 4 kJ mol-1) was calculated using an explicitly correlated composite method (W1-F12). The result obtained for cubane together with the experimental value for the enthalpy of sublimation, 54.8 ± 2.0 kJ mol-1, led to 548.6 ± 4.5 kJ mol-1 for the solid-phase enthalpy of formation. This value is only 6.8 kJ mol-1 higher than the 50-year-old original calorimetric result. The carbon-hydrogen bond dissociation enthalpy (C−H BDE) of cubane (438.4 ± 4 kJ mol-1), together with properties relevant for its experimental determination using gas-phase ion thermochemistry, namely the cubane gas-phase acidity (1704.6 ± 4 kJ mol-1), cubyl radical electron affinity (45.8 ± 4 kJ mol-1), cubane ionization energy (1435.1± 4 kJ mol-1), cubyl radical cation proton affinity (918.8 ± 4 kJ mol-1), cubane cation appearance energy (1099.6 ± 4 kJ mol-1), and cubyl ionization energy (661.2 ± 4 kJ mol-1), were also determined. These values were compared with those calculated for unstrained hydrocarbons (viz., methane, ethane, and isobutane). The strain energy of cubane (667.2 kJ mol-1) and cubyl radical (689.4 kJ mol-1) were independently estimated via quasihomodesmotic reactions. These values were related via a simple model to the C−H BDE in cubane. Taking into account the accuracy of the computational method, the comparison with high-precision experimental results, and the data consistency afforded by the relevant thermodynamic cycles, we claim an uncertainty better than ±4 kJ mol-1 for the new enthalpies of formation values presented.


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Table of Contents (TOC)/Abstract Graphic

Keywords: Cubane; cubyl radical; cubyl anion; cubyl cation, cubyl radical cation; thermochemistry; enthalpy of formation; bond dissociation enthalpy; strain energy; explicitly correlated methods


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Introduction Cubane (pentacyclo[4.2.0.02,5.03,8.04,7]octane, C8H8; Figure 1) has captured the interest of many chemists due to its unusual structure: although the eight carbon atoms are sp3 hybridized, they define a perfect cubic arrangement, the hydrogen atoms lying along the cube diagonals.1-4 As the 90° carbon-carbon bond angles are far from the usual 109.5° value, a significant amount of strain could be predicted for the molecule, indicating that it should be thermodynamically unstable.

Figure 1

The structure of cubane.

The conclusion about the thermodynamic instability could have been questioned when cubane was synthetized for the first time by Eaton and Cole, 50 years ago.5 However, a few years later it was shown that cubane stability had a kinetic origin (decomposition temperature above 220 ºC).6 As it happens with many other molecules, cubane decomposition pathways involve high activation energies.7 The first thermodynamic studies, involving static-bomb combustion calorimetry and the Knudsen effusion method, were reported in 1966 by Kybett et al.,8 yielding 541.8 ± 3.3 kJ mol-1 for the standard enthalpy of formation of the crystalline compound, 80.3 ± 1.7 kJ mol-1 for the standard enthalpy of sublimation, and 622.1 ± 3.7 kJ mol-1 for the standard enthalpy of formation of cubane in the gas phase (the


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enthalpy of formation data include a correction due to incomplete combustion of the sample). All these results have been considered inaccurate by several authors. For instance, estimates by Kirklin et al.,9 viz. ∆ f H o (cr) = 585.0 ± 4.5 kJ mol-1, relying on combustion calorimetry experiments of 1,4-dimethylcubane dicarboxylate, indicated that the early value is over 40 kJ mol-1 too low. The enthalpy of sublimation value determined by Kybett et al. 8 was also questioned. Bashir-Hashemi et al. obtained 55.2 ± 2.0 kJ mol-1, by using a method that combined the vaporization enthalpy at 298.15 K with the fusion enthalpy and the enthalpy of a solid-solid phase transition.10 This lower value is in keeping with estimates made by the same and also by other authors.10,11 More recently, Chickos 12 made new measurements with cubane and found a similar value for the sublimation enthalpy: 54.8 ± 2.0 kJ mol-1. To the best of our knowledge, no other experimental values for the enthalpies of formation of solid and gaseous cubane are available. There are, however, many literature results calculated using additivity, semiempirical, molecular mechanics, and ab initio methods.7,9,13-40 The list is indeed large (see Supplementary Material) but unfortunately, as shown in Figure 2, the values for the gas-phase enthalpy of formation vary over a broad range, viz. 415–716 kJ mol–1. This dispersion is considerably reduced by considering only the values computed with the most accurate methods, viz. the Gn family and CBS-QB3 (Figure 3), but these data still vary between 596 and 628 kJ mol–1.


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Figure 2

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Calculated gas-phase enthalpies of formation of cubane obtained from additivity (diamonds), semiempirical (squares), molecular mechanics (triangles), and quantum chemistry methods (circles). The solid line shows the value obtained in the present work.


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Figure 3

Selected values of gas-phase enthalpies of formation of cubane obtained from Gn (circles) and CBS-QB3 methods (squares). The solid line shows the value obtained in the present work (603.4 ± 4 kJ mol-1), and the dashed line represents the average of CQB-QB3 and Gn values (609.3 ± 9 kJ mol-1).

High-level quantum chemistry calculations of gas-phase enthalpies of formation are now as reliable as the best experimental procedures.41-48 This does not apply to molecules in the solid phase, since the theoretical methodologies which address the energetics of intermolecular interactions are not yet able to predict chemically accurate enthalpy of sublimation data for organic molecules. However, experimental determinations of enthalpies of sublimation can be carefully made (by using properly characterized solid samples) and yield data that are much less prone to errors than combustion calorimetry experiments. Therefore, gas-phase enthalpies of formation derived from high-level quantum chemistry calculations, coupled with experimental values of enthalpies of sublimation, can lead to accurate results of solid-phase enthalpies of formation, as we recently demonstrated.41 Using this idea, in the present paper we propose new values for the gas- and solid-phase enthalpies of formation of cubane. The C–H bond dissociation enthalpy of cubane (BDE) has been determined much more recently,49 and the proposed value still has a large uncertainty (± 17 kJ mol-1). The C–H BDE in an organic molecule RH, DH o (C − H) , corresponds to the enthalpy of reaction 1, where all the molecules are in the ideal gas phase (isolated). It is related


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to the thermodynamic stability of the corresponding carbon-centered radical R•, as measured by its standard enthalpy of formation ∆f H o (R • ,g) , through eq 2.

RH (g) → R• (g) + H• (g)

(1)

DH o (C − H) = ∆f H o (R • ,g) + ∆f H o (H• ,g) − ∆f H o (RH, g)

(2)

Although the importance of BDEs is all too evident, it can be illustrated in the present context by noting that the enthalpies of formation of radicals are essential for modeling complex reactions such as combustion (cubane is a candidate for novel fuels, propellants and explosives) or to assess synthetic pathways (the rigid frame of cubane renders it as a unique platform for pharmaceuticals development).50 In general, this kinetic modeling requires “chemical accuracy” of about ±4 kJ mol-1. But while enthalpies of formation are well established for many stable compounds, the state of the art is considerably less advanced for radicals, simply because traditional calorimetric techniques are not suited to the study of such short-lived species. The cubane BDE determination above was accomplished using ion thermochemistry techniques, which relate the desired BDE to measurements on ions through thermodynamic cycles and, in this particular case, through a negative ion cycle.49 Many properties can be measured in this regard, and several interrelated cycles can be established using complementary techniques, increasing the accuracy of the BDE determination.51 Using the same computational method we have calculated the gas-phase enthalpies of formation of the cubyl radical, cubyl anion, cubyl radical cation, and cubyl cation. This allowed us to construct the traditional thermodynamic cycles for the experimental determination of the cubane BDE using ion


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thermochemistry techniques. Besides the cubane BDE, we obtained new values for its gas-phase acidity, the electron affinity of the cubyl radical, the ionization energy of cubane, the proton affinity of the cubyl radical, the appearance energy of the cubane cation, and the ionization energy of the cubyl radical. The same procedure was applied for simpler molecules (viz. methane, ethane, and isobutane) for which highprecision experimental data are available. Finally, no work on cubane is complete without addressing its strain, a subject which has also captured the interest of many scientists over the last few decades (see Supplementary Material).7-9,16-18,20,22-24,29,32-34,36,37,52-60 Since strain can affect parent molecules and radicals differently, we must discriminate between these two before trying to relate strain with BDEs. While quantifying strain in the parent molecules is straightforward,61 the situation for radicals is more complex. We have used a previously tested methodology62 based on selected homodesmotic reactions63 to determine cubane and cubyl radical strain independently. Our previously proposed model was then used to relate the resulting strain energies to the cubane BDE. This provided a simple picture explaining the high BDE of cubane, which further reinforces the consistency and accuracy of the thermochemical results presented herein.

Theoretical calculations Ab initio calculations were performed for cubane, cubyl radical, cubyl anion, cubyl cation, and cubyl radical cation. In addition, theoretical calculations were also performed for methane, ethane, isobutane, as well as for their respective radicals, anions, cations, and radical cations (see Table 1). The structures of all molecules


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were optimized with the B3LYP-D3 dispersion corrected64 hybrid density functional65,66 using with the cc-pVTZ basis set.67 Zero-point and thermal enthalpy corrections at T = 298.15 K were obtained from frequencies calculated with the same method (scaled by 0.985, see ref. 68) under the rigid rotor and harmonic oscillator approximations. The enthalpies of all species were subsequently determined with the W1-F12 procedure.68 By relying on explicitly correlated calculations69 and a judicious choice of basis set and extrapolation techniques, this composite procedure is capable of yielding data close to the all-electron relativistic CCSD(T) complete basis set limit.68,70 Apart from geometry optimizations, which were performed as described above, no other changes were made to the W1-F12 protocol. The optimized geometries and frequencies were determined with NWChem 6.2.71 CFOUR72 was used to obtain the diagonal Born–Oppenheimer corrections73-75 required by the W1F12 procedure. All other calculations were performed with Molpro 2012.1.76

Results and discussion The enthalpies of formation obtained with the W1-F12 procedure for the molecules under study are collected in Table 1, together with the available experimental data.63,77-80

TABLE 1 Enthalpies of formation determined using the W1-F12 method, together with the available experimental data. All values in kJ⋅mol-1. ∆fH0K (calcd)

∆fH298.15K (calcd)

∆fH298.15K (exptl)

cubane

628.3

603.4

[596.1 to 665.3] a

cubyl radical

844.4

823.8

[806.5 to 875.7] a

cubyl anion

798.6

778.0

[756.1 to 825.3] a


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cubyl cation

1504.2

1485.0

cubyl radical cation

1464.3

1442.5

methane

–66.6

–74.2

–74.532 ± 0.057 b

methyl radical

149.6

146.7

146.487 ± 0.081 b

methyl anion

144.2

140.5

144.4 ± 1.2 b

methyl cation

1099.4

1096.1

1095.492 ± 0.077 b

methyl radical cation

1151.2

1144.6

1143.81 ± 0.27 b

ethane

–69.4

–84.6

–83.79 ± 0.17 b

ethyl radical

130.6

121.0

119.93 ± 0.36 b

ethyl anion

150.9

139.6

144.6 ± 2.5 b

ethyl cation

914.7

903.1

902.53 ± 0.41 b

ethyl radical cation

1040.3

1026.9

1029.93 ± 0.63 b

isobutane

–107.0

–134.8

–135.36 ± 0.40 b

tert-butyl radical

74.3

52.5

51.5 ± 1.7 c

tert-butyl anion

77.3

52.9

64 ± 8 d

tert-butyl cation

733.2

711.7

711 ± 4 e

tert-butyl radical cation

903.8

879.1

895 ± 15 f

isobutyl radical

96.4

73.8

70 ± 2 g

isobutyl anion

83.5

59.7

64 ± 8 d

a

Ranges calculated from the data in Refs. 8, 9, 10, 12 and 49. b Ref. 63. c Ref. 79. d Refs. 77,78. e Ref. 77. f Determined from the ionization energy of isobutane in ref. 77. g Ref. 80.

Analysis of Table 1 reveals an excellent agreement between the high-precision experimental results and the theoretical gas-phase enthalpies of formation. Based on this observation and on the overall performance of W1-F12 41,68,70 an uncertainty of ± 4 kJ⋅mol-1 is ascribed to the theoretical values in Table 1. The large deviations observed for the tert-butyl and isobutyl anions coincide with the also large uncertainties in the experimental data for these species, which were determined from the gas-phase acidity of their parent hydrocarbons.77,78 These acidity data were derived from silane cleavage branching ratios 78 and are anchored on the gas-phase acidity of methane and benzene. While this method is invaluable in the study of weakly acidic compounds, some studies advise caution in the use of silane cleavage for measuring acidities.81,82 An excellent agreement is also observed between the


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experimental and theoretical data for cations and radical cations. An exception is observed for the tert-butyl radical cation, yet the best experimental data for the enthalpy of formation of this compound has an uncertainty of ca. 15 kJ mol-1. This stems from the high uncertainty in the ionization energy of isobutane 77 (see Table 2), from which the enthalpy of formation of the radical cation was derived. The W1-F12 calculations led to 603.4 ± 4 kJ mol-1 for the gas-phase enthalpy of formation of cubane. Considering only the most accurate theoretical results, determined with the Gn and CBS methods (Figure 3), one obtains a mean value of 609.3 ± 9 kJ mol-1 for the enthalpy of formation of cubane, where the uncertainty represents the standard deviation of the mean for this data subset. This mean value is thus in keeping with that proposed in the present work. The result obtained for cubane, together with the most recent experimental value for the enthalpy of sublimation,12 54.8 ± 2.0 kJ mol-1, yields 548.6 ± 4.5 kJ mol-1 for the solid-phase enthalpy of formation. Incidentally, this value is only 6.8 kJ mol-1 higher that the 50-year-old original calorimetric result by Kybett et al., 541.8 ± 3.3 kJ mol-1.8 The data in Table 1, together with the enthalpies of formation of the hydrogen atom, 217.998 ± 0.000 kJ⋅mol-1,63 and the hydrogen atom cation, 1530.047 ± 0.000 kJ⋅mol-1,63 can be used to derive the ion thermochemical quantities, namely the proton affinities (PA), electron affinities (EA), gas-phase acidities (∆Hacid), and appearance energies (AEs), for the species therein (Table 2).


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TABLE 2 Thermochemical properties calculated using the data in Table 1. Experimental data listed in square brackets. All data in kJ⋅mol-1 at T = 298.15 K unless otherwise stated. R DH(R−H) a

cubyl 438.4 [428.4 ± 16.7 h]

methyl 438.9 [439 ± 0.1]

ethyl 423.6 [421.7 ± 0.4]

tert-butyl 405.3 [404.9 ± 1.7]

isobutyl 426.6 [423.4 ± 2]

∆Hacid (RH)b

1704.6 [1690 ± 13 h]

1744.7 [1748.9 ± 1.2]

1754.2 [1758.4 ± 1.2]

1717.7 [1729.2 ± 8.4]

1724.5 [1729.2 ± 8.4]

EA(R•) c

45.8 i; 45.8 [48.1 ± 8.4 h]

5.4 i; 6.2 [2.4 ± 1.2 i, j; 2.1 ± 1.2]

–20.3 i; –18.6 [–24 ± 2.5 i, j; –24.7 ± 1.3]

–3 i; –0.4 [–15.6 ± 8.9 i, k; –12.3 ± 8.6]

12.9 i; 14.1 [5 ± 12 i, k; 6.2 ± 8.6]

PA(R•) d

911.3

532.1 [532.7 ± 0.3]

624.1 [620 ± 0.7]

703.4 [686.4 ± 10.7]

724.7 [704.9 ± 10.8]

AE(R+, RH) e

1099.6

1388.3 [1388 ± 0.1]

1205.7 [1204.3 ± 0.4]

1064.5 [1064.4 ± 4]

IE(R•)

f

IE(RH) g

a

659.8 i; 661.2

949.8 i; 784.1 i; 658.9 i; 949.4 782.1 659.2 i, j i, j [949.4 ± 0.1 ; [783.8 ± 0.5 ; [646.5 ± 2.9 i, k; 949.0 ± 0.1] 782.6 ± 0.6] 659.5 ± 4.3]

836 i; 839.1

1217.8 i; 1109.7 i; 1010.8 i; 1010.8 i; 1218.8 1111.5 1013.9 1013.9 [1216.7 ± 1.0 i, k; [1111.5 ± 3.9 i, k; [1030.5 ±10.6 i, k; [1030.5 ±10.6 i, k; 1218.3 ± 0.3] 1113.7 ± 0.6] 1030.5 ± 10.6] 1030.5 ± 10.6]

C−H bond dissociation enthalpy (RH → R• + H).

b

Gas-phase acidity of RH (RH →

R− + H+). c Electron affinity of R• (R− → R• + e−). Property defined at T = 0 K.

d

Proton affinity of R• (RH+• → R• + H+). e Appearance energy of R+ from RH (RH → R+ + H + e−). f Ionization energy of R• (R+ → R• + e−). Property defined at T = 0 K. g i

Ionization energy of RH (RH → RH+• + e−). Property defined at T = 0 K. j

63

Value at T = 0 K. Ref. .

k

h

Ref. 49.

Ref. 77.


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These properties, which are experimentally accessible, are related to the bond dissociation enthalpies (BDEs) through equations (3), (4), and (5). They define three experimental approaches for BDE determination, namely, the proton affinity or positive-ion cycle (eq. 3), the acidity or negative-ion cycle (eq. 4), and the appearance energy cycle (eq. 5).51

DH(R−H) = PA(R •) + IE(RH) - IE(H•)

(3)

DH(R−H) = ∆ acidH(RH) + EA(R•) - IE(H•)

(4)

DH(R−H) = AE(R+,RH) - IE(R•)

(5)

Figure 4 illustrates how these properties are related for the case of cubane, together with the corresponding values computed in this work. The underlying need for internal consistency of these properties reinforces the accuracy of the data. Note that all data reported in the present work adheres to the “ion convention”.83


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Figure 4

Energy level diagram depicting the gas-phase ion thermochemistry of cubane, relating its carbon—hydrogen BDE [DH(C—H)] through a proton affinity cycle (where IE(RH) is the ionization energy of cubane and PA(R•) the proton affinity of the cubyl radical cation), a negativeion cycle (where ∆Hacid(RH) is the gas-phase acidity of cubane and EA(R•) the cubyl radical electron affinity), and an appearance energy cycle (where AE(R+,RH) is the appearance energy of the cubane cation and IE(R•) the ionization energy of cubyl radical). IE (H•) is the accurately known ionization energy of the hydrogen atom. Gas-phase enthalpies of formation determined in this work are shown in parenthesis below each species. All data in kJ⋅mol-1 at T = 298.15 K.

A very good agreement between experimental and theoretical values is observed for the majority of the data in Table 2. In particular, all thermochemical properties


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calculated for cubane are in keeping with the available experimental data.49 Although larger deviations are present for most properties of isobutyl or tert-butyl species, these are linked to the large uncertainties in corresponding experimental data (Table 1). The adiabatic electron affinity of the tert-butyl radical was recently determined by Sokolov et al. 84 at the CCSDT(Q)/CBS level as –2 kJ⋅mol-1 using the focal-point analysis technique. As noted by these authors, the value of this EA has been the subject of controversy. The value herein proposed, –3.1 kJ⋅mol-1, is in excellent agreement with that of Sokolov et al., and thus corroborates their conclusion that the electron attachment is energetically unfavourable. The fact that this value can be so accurately reproduced using W1-F12 provides further proof of the accuracy of this method. Consequently, the gas-phase enthalpies of formation for isobutyl and tertbutyl anions at 298.15 K should indeed be 59.7 ± 4 kJ mol-1 and 52.9 ± 4 kJ mol-1, respectively. The tert-butyl anion is thus ca. 7 kJ mol-1 more stable that the isobutyl anion, which contradicts the experimental data indicating that both have the same enthalpy of formation,63 namely 64 ± 8 kJ mol-1. Furthermore, given the confirmed accuracy of the W1-F12 procedure, together with its good performance for the remaining radical cations in Table 1, a value of 879.1 ± 4 kJ mol-1 can be posited for the enthalpy of formation of the tert-butyl radical cation. A brief discussion of the thermodynamic properties for the simpler alkyl radicals, anions, cations, and radical cations listed in Table 2 provides a deeper understanding of the energetics of cubane and its derivatives. A rationalization for the stability trend for alkyl anions, evidenced by the acidities and electron affinities in Table 2, has been given by DePuy et al. 78 and Gronert.85 Methyl groups in an α position relative to the carbanion have two opposing effects. On the one hand they are polarizable and thus disperse the charge and stabilize the carbanion. On the other hand they destabilize it


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because they are electron donors. This destabilizing effect explains why ethane is less acid (i.e., has a higher ∆Hacid) than methane. Further proof of the instability of the ethyl anion is provided by the large and negative EA of the ethyl radical (–20.3 kJ mol-1), whereas the methyl radical has a positive albeit small EA (5.4 kJ mol-1). As more α methyl groups are added the stabilizing effect becomes dominant, causing the H atom attached to the tertiary carbon of isobutane to be more acidic than those of methane or ethane. The same authors78,85 also noted that for β methyl groups the stabilizing polarization effect is largely predominant, and the introduction of each methyl group enhances the stability of the carbanion. This can be seen in Table 2 by comparing ∆Hacid(isobutyl–H) with ∆Hacid(ethyl–H). While both cleavages lead to primary carbanions, the former is significantly smaller (more acidic) than the latter. In addition, electron attachment to the isobutyl radical is a favorable process (EA = 12.9 kJ mol-1). These facts explain the higher electron affinity of the cubyl radical and the lower gas-phase acidity of cubane, when these properties are compared with those for tert-butyl. Analysis of the proton affinity, ionization energy, and appearance energy data in Table 2 provides an insight into the stability of alkyl cations and radical cations. For these species a simpler trend is found, with stability directly related with the higher degree of substitution near the charge center, which can be rationalized in terms of hyperconjugation and electron transfer from neighboring methyl groups.86 The isobutyl cation is highly unstable, and readily converts into the tert-butyl cation through a proton shift.86 This was also observed in our theoretical calculations. Indeed, our efforts to obtain the optimized structure of the isobutyl cation were unsuccessful without the use of geometry constraints, which precludes a discussion of the effect of β methyl groups in carbocation stability. Nevertheless, given the


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similarity of the ionization energies of the cubyl and tert-butyl radicals, one can infer that their effect should be small. The trend for C–H bond dissociation enthalpies of the small molecules in Table 2 can also be rationalized in terms of hyperconjugation of the resulting radical.87 Each α methyl group leads to a further stabilization of the radical, and consequently to a lower BDE. This explains the trend observed for methyl, ethyl, and tert-butyl in Table 2. Contrary to what was noted above for anions, β methyl groups have little impact on the stabilization of radicals. This leads to very similar C–H BDEs for ethane (423.6 kJ mol-1) and isobutane (resulting in the isobutyl radical, BDE = 426.6 kJ mol-1). Cubane C–H BDE, however, despite corresponding to the formation of a tertiary carbon-centered radical, is akin to that of methane (438.4 kJ mol–1 vs. 438.9 kJ mol–1 respectively). This is reasonable if we bear in mind that C–H bond cleavage leads to the formation of an sp2 hybridized carbon center, whose planarity requirements are very far from being met by the cubic framework of cubane (Figure 5).

Figure 5

Side view of (from left to right) cubane, cubyl radical, cubyl anion, cubyl radical cation, and cubyl cation carbon framework. Bond lengths are indicated in pm, and bond angles in degree.


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Figure 6

Pipek-Mezey localized molecular orbitals (cutoff = 0.10), obtained at the HF/aug-cc-pVTZ level using B3LYP-D3/cc-pVTZ optimized structures, of: (a) the cubane HOMO, (b) the cubyl radical cation SOMO, (c) the cubyl radical HOMO, (d) the cubyl radical SOMO, (e) the cubyl anion HOMO, and (f) the cubyl cation LUMO.

Figure 7

ROHF/aug-cc-pVTZ spin densities (cutoff = 0.02) for: (a) the cubyl radical, (b) the cubyl radical cation. Calculations performed using B3LYP-D3/cc-pVTZ optimized structures.


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Further insight into the structural features of these species can be gained from the analysis of their highest occupied molecular orbitals (HOMO), singly occupied molecular orbitals (SOMO), or lowest unoccupied molecular orbitals (LUMO), as well as from the spin densities for the radicals (Figures 6 and 7). These were obtained from a (RO)HF/aug-cc-pVTZ single point calculations, using the B3LYP-D3/ccpVTZ optimized structures, followed by Pipek-Mezey localization.88 The cubane HOMO is comprised by a set of six degenerate orbitals, each of which is an ungerade combination of two opposing σ(C—C) bonding orbitals (Figure 6a). Removal of one electron from cubane, yielding the cubane radical cation, leads to the lengthening of a C—C bond (Figure 6b), leaving the unpaired electron in a σ(C—C) bonding orbital (Figure 7b). Subsequent abstraction of an H atom results in a contraction of this C—C bond in the cubyl cation, leaving the HOMO located in the opposing C—C bond (Figure 6c), which is now no longer degenerate due to the loss of symmetry. The (now empty) 2p orbital which was involved in the σ(C—H) bond with the abstracted H atom is the cubyl cation LUMO (Figure 2f). This is similar to the cubyl radical SOMO ensuing from a C—H bond cleavage in cubane (Figures 6d and 7a). Electron attachment to the cubyl radical deposits an electron in its SOMO, which takes on a morphology typical of a hybrid sp3 orbital in the cubyl anion HOMO (Figure 6e). Following the above reasoning about the geometry of the cubyl radical, it could be tempting to attribute the high C–H BDE in cubane solely to the geometrical constraints of this radical, that is to say, to its strain. Cubane is, however, also highly strained (cf. Figure 5), so one could argue conversely that this should in fact lower its C–H BDE, as e.g. in cyclopentane vs. cyclohexane (403.0 kJ mol–1 vs. 414.6 kJ mol–1 respectively, vd. infra).62 Both explanations are obviously incomplete. BDEs


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represent a difference between two states, so a complete explanation requires considering the thermodynamic stabilities of both the radical cubyl and the parent compound cubane. Consequently, the effect of strain on both species has to be taken into account. In previous works we used this simple notion to rationalize, through thermodynamic cycles, BDEs with various possible effects at play (viz. hyperconjugation in the radical, conjugation in the parent compound,87 and strain in both62). Figure 8a presents such a simple model, relating cyclohexane and cyclopentane C–H BDEs to strain. It is clear from the picture that the lower C–H BDE in cyclopentane should result from a higher strain destabilization of cyclopentane (relative to cyclohexane) when compared with the strain destabilization of cyclopentyl (relative to cyclohexyl).62 A more accurate depiction of the effect of strain on BDEs, representing the quantitative model of eq 6, is presented in Figure 8b for cubane.

a

b


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Figure 8

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a. Relation between the C–H BDEs in cyclohexane and cyclopentane (solid arrows) and the strain destabilization in both pentane and pentyl radicals relative to cyclohexane and cyclohexyl radical, respectively (dotted double-arrows). b. Model relating the strain energies ( Estr ) of the parent molecule and its radical, to DH o (C − H) and the BDE of a o suitable strain free reference molecule, DH ref (C − H) . For the case of

cubane the reference molecule is isobutane (yielding the tertiary radical tert-butyl, see text).

o ∆DH o (C − H) = DH o (C − H) − DH ref (C − H) = Estr (R • ) − Estr (RH)

(6)

In eq 6, as in Figure 8b, it is assumed that the BDE difference between cubane and the reference molecule is only due to strain, in cubane and cubyl radical. The C3–H BDE in isobutane is therefore the correct anchor to assess that difference, since both cubane and isobutane yield tertiary radicals. This reflects the conventional definition of strain of Cox and Pilcher,61 i.e. including all the stabilizing and destabilizing effects in relation to a strain-free reference molecule, regardless of its cause. Equation 7 is a typical way of calculating the strain energy ( Estr ) according to this definition, as the difference between the enthalpies of formation of the compound of interest RH and the strain-free reference compound RH*, usually obtained through a bond additivity scheme.62

Estr (RH) = ∆ f H o (RH,g) − ∆ f H o (RH*,g)


(7)

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While the application of eq 7 is straightforward for stable molecules, it is not generally applicable for radicals, due to the scarcity of thermochemical data for the latter.89 An alternative route to group additivity schemes is provided by the use of computational chemistry to evaluate appropriately constructed balanced reactions, generally called homodesmotic.63 These reactions are intertwined with such additivity schemes, and can be successful applied to derive the enthalpy difference of eq 7.62,63,90 Reactions 8 and 9 are the result of this exercise, applied to the estimation of the strain energy ( Estr ) of cubane and cubyl radical, respectively, using the theoretical enthalpy of formation data in Table 1.

(8)

(9)

Doing so leads to a strain of 667 kJ mol–1 and 691 kJ mol–1 respectively for cubane and cubyl radical. The strain of cubane has been subject of several studies (see Supplementary Material).7-9,16-18,20,22-24,29,32-34,36,37,52-60 Also in this case the value obtained with the current work is in keeping with previous determinations, particularly if only data obtained with high-level composite methods (e.g., Gn and CBS-QB3) is considered. According to the equation 6 model, represented in Figure 8b, strain leads to an increase of 24 kJ mol-1 on the C–H BDE in cubane (i.e. its BDE is 24 kJ mol-1 higher than the BDE in a strain-free reference hydrocarbon leading to a tertiary radical like


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tert-butyl), due to the fact of cubyl radical being that much strained than cubane. The actual difference between the computed BDEs is higher, 33 kJ mol-1, but this 9 kJ mol-1 discrepancy is actually included in the respective uncertainties. The reason for this disagreement can be traced to the difference between the C–H BDE in ethane and isobutane (leading to isobutyl radical). As noted above, while it was expected that they should be identical, the computed values still differ by 3 kJ mol-1, a difference that is amplified by the calculations involved in the application of the model in Figure 8b and eq 6 (that difference is multiplied by a factor of 3, resulting in the 9 kJ mol-1 discrepancy between the difference in strain energies and the relative BDEs, see Supporting Information). Throughout this work, we strived to provide new thermochemical data for cubane and related molecules with chemical accuracy, and the 3 kJ mol-1 difference indicated above is certainly within this goal. However, this example also shows that to properly deal with such fine details, “subchemical” accuracy would be required.

Conclusions A comprehensive survey of the available experimental and theoretical enthalpy of formation data for cubane was performed. Using the composite W1-F1268 method, which relies on explicitly correlated CCSD(T)-F12 calculations to obtain a high accuracy at a reasonable computational cost,68,69 the gas-phase enthalpies of formation of cubane, cubyl radical, cubyl anion, cubyl cation, and cubyl radical cation were determined as 603.4 ± 4 kJ mol-1, 823.8 ± 4 kJ mol-1, 778.0 ± 4 kJ mol-1, 1485.0 ± 4 kJ mol-1, and 1435.1 ± 4 kJ mol-1, respectively. Combining the calculated gas-phase enthalpy of formation of cubane with the most recent data for its sublimation


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enthalpy,12 54.8 ± 2.0 kJ mol-1, led us to propose a value of 548.6 ± 4.5 kJ mol-1 for the solid-phase enthalpy of formation cubane. This value is very close to the original calorimetric result reported 50 years ago by Kybett et al. (541.8 ± 3.3 kJ mol-1),8 despite the ca. 20 kJ mol-1 difference observed between the present gas-phase enthalpy of formation and that proposed by Kybett et al. 8 The results of this analysis will serve as a warning against indiscriminate use of the available thermodynamic data for cubane as key reference data for molecular mechanical and ab initio calculations. Still today, the 1966 gas-phase enthalpy of formation value for cubane is used as a reference for the assessment of capabilities of modern quantum chemistry methods. For instance, a value of 644.3 kJ mol-1 (some 40 kJ mol-1 higher than the value determined in the present work) was very recently proposed.91 The bond dissociation enthalpies (BDEs), proton affinities (PAs), electron affinities (EAs), gas-phase acidities (∆Hacid), and appearance energies (AEs) determined from theoretical data computed with W1-F12 were found to be in good agreement with the available experimental data. Following DePuy et al. 78 and Gronert 85, the trend for electron affinities and gas-phase acidities were rationalized in terms of the stabilization/destabilization of the resulting anion due to α methyl substituents, as well as the stabilizing effect of β methyl groups. The trends observed for proton affinities, ionization energies, appearance energies, and BDEs were rationalized in terms the stabilizing effect of α methyl groups86,87 on the resulting species. The EA calculated for the tert-butyl radical was found to be in excellent agreement with the most recent high-level theoretical data 84. In addition, new gasphase enthalpies of formation were proposed for the tert-butyl (52.9 ± 4 kJ mol-1) and


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the isobutyl (59.7 ± 4 kJ mol-1) anions, as well as for the tert-butyl radical cation (879.1 ± 4 kJ mol-1). Finally, the strain energies of cubane and cubyl radical were determined using quasihomodesmotic reactions,63 justifying the high C–H BDE of cubane in terms of its strain and of its radical through a simple model, based on the often overlooked notion that BDEs represent the difference between two states.

Acknowledgments This work was supported by Fundação para a Ciência e a Tecnologia (FCT), Portugal (PTDC/QUI-QUI/110542/2009, PEst-OE/QUI/UI0612/2013, and PEstOE/EQB/LA0023/2013). F. A. thanks FCT for post-doctoral grant (SFRH/BPD/74195/2010).

Supplementary data Tables containing computed optimized geometries and total energies for cubane, cubyl radical, cubyl anion, cubyl cation, and cubyl radical cation. Comprehensive survey of the gas-phase enthalpy of formation of cubane and its strain energy. This material is available free of charge via the Internet at http://pubs.acs.org.


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The Thermochemistry of Cubane 50 Years after Its Synthesis: A High

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