1
Theoretical study on the coplanar double-cage dodecahedrane C35H30

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

2
Using geometry optimization and DFT method at the B3LYP/6-31G* level of theory for C35H30, an equilibrium geometry is identified that has the form of a coplanar double-cage dodecahedrane.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res1

3
Vibrational frequencies and the IR spectrum are computed at the same level of theory.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj2

4
The heat of formation for C35H30 has been estimated in this paper.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj3

5
The heat of formation of C35H30 as well as the vibrational analysis indicates that this system enjoys sufficient stability to allow for its experimental preparation.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

Introduction

6
Since the discovery of C60 in 1985, numerous papers have been published on the investigation of polyhedral molecules, such as fullerenes and polyhedral hydrocarbons.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

7
Each of these molecules has only one cage, for example C60 and dodecahedrane.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

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As is known, every carbon atom can form four bonds with other atoms.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

9
Since each of the carbon atoms at the cage surface of the polyhedral molecule only forms three bonds with other carbon atoms at the cage surface, it may form another bond with other atom.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

10
When two cages share a same polygon, a coplanar double-cage molecule can form.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

11
This is similar to two benzene rings sharing one CC bond to form a naphthalene molecule.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

12
However, until now, only a few coplanar poly-cage molecules have been reported.1

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

13
It has been stated that “the dodecahedrane geometry is exquisite in its perfection”.2

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

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The two landmark syntheses of dodecahedrane, by Paquette3a and by Prinzbach and Weber,3b were of great interest.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

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Owing to its unusual structure, dodecahedrane has also provided theorists with a severe test case for the calculation of geometry and properties.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

16
These include assessments of its vibrational frequencies,4 ordering of orbital energies,5,6 formation of inclusion compounds,6,7 NMR spin–spin coupling constants,8 and heat of formation.9

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met1

17
When two dodecahedrane cages share a same pentagon, a coplanar double-cage dodecahedrane molecule C35H30 can form.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

18
In this case, every carbon atom at the shared polygon forms four bonds with other carbon atoms.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

19
To the best of our knowledge, the coplanar double-cage dodecahedrane C35H30 molecule has not been reported before.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot1

20
This paper is a theoretical attempt to study C35H30 by using the DFT method at the B3LYP/6-31G* level of theory.10

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

21
For the sake of understanding the thermodynamic stability of C35H30, the heat of formation ΔH0f of C35H30 was estimated according to the calculated energy change for the process:and the experimental heat of formation for dodecahedrane C20H20.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa1

22
ΔH0f of C35H30 is 51.3 kcal mol−1, it is larger than that of dodecahedrane, but smaller than that of the cubane C8H8.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res2

23
Thus we believe that C35H30 has sufficient stability to allow its experimental preparation.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

Computational details

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The predicted structure of molecule C35H30 is shown in Fig. 1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

25
The full geometry optimization was performed by the energy gradient method at the B3LYP/6-31G* level of theory with the GAUSSIAN 94 program11 system.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met2

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In the starting geometry of optimization for C35H30 it was assumed that each C20 cage in the C35H30 molecule is similar to that of dodecahedrane.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

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To summarize, the length of the carbon–carbon bonds is 1.54 Å and that of carbon–hydrogen bonds is 1.09 Å, the CCC angle is 108° and the CCH angle is 110.9°.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

28
In the optimization, the symmetry was restricted to D5h.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

29
Vibrational frequencies were determined first to verify the nature of the stationary point structure, second to examine zero-point energy corrections on calculating the heat of formation of the molecule, and third to predict vibrational frequencies for unknown stable species for the sake of their future experimental identification by IR spectroscopy and the assignment of the observed frequencies.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj4

Results and discussion

Geometry and some properties

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For the sake of comparison, the geometry of dodecahedrane C20H20 was first optimized at the B3LYP/6-31G* level of theory.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met3

31
The bond length of C–C is 1.556 Å and that of C–H is 1.096 Å, respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

32
The bond length of C–C is slightly larger than the experimental range of C–C bond lengths, 1.535–1.541 Å, reported for the X-ray structure.12

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs1

33
The bond angle of CCC is 108° and the HCC angle is 110.9°.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

34
The geometry of C35H30 optimized at the B3LYP/6-31G* level is shown in Table 1 with the numbered system of carbon and hydrogen atoms given in Fig. 1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs2

35
Net atomic charges of C35H30 obtained at the B3LYP/6-31G* level of theory are listed in Table 2 and those of dodecahedrane are also given in Table 2 for the sake of comparison.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

36
All hydrogen atoms of C35H30 have positive net charges and values very close to that of dodecahedrane.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

37
As for carbon atoms, only at shared pentagon do they have positive charges, while the others have negative charges.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

38
Some other properties of C35H30 obtained at the B3LYP/6-31G* level of theory are listed in Table 3 and those of dodecahedrane also listed here.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

39
The energies of the HOMO and LUMO of C35H30 at the B3LYP/6-31G* level of theory are −6.91 and 0.86 eV, respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

40
The HOMO is doubly degenerate and the LUMO is non-degenerate.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

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The energies of the HOMO and LUMO for dodecahedrane at the same level of theory are −7.09 and 0.89 eV, respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

42
A large HOMO–LUMO gap has long been recognized as being correlated with kinetic and structural stability while a small gap is associated with reactivity.13–19

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac7

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The HOMO–LUMO gaps of C35H30 and dodecahedrane are 7.77 and 7.99 eV, respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

44
This illustrates that C35H30 is more likely to react by electron donation than dodecahedrane, and is more likely to react by accepting electrons than dodecahedrane.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

45
Thus the stability of C35H30 is lower than that of dodecahedrane.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

Vibrational frequencies

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In order to verify whether C35H30 is a minimum at the potential energy hypersurface or not, vibrational frequencies have been calculated at the B3LYP/6-31G* level of theory.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa2

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The predicted vibrational frequencies for C35H30 are listed in Table 4.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs5

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Vibrational frequencies in Table 4 are not scaled.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs5

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From Table 4, it can be seen that the molecule C35H30 has no imaginary vibrational frequency and is a true minimum at the potential energy hypersurface.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

50
The symmetry of C35H30 is helpful in making the assignments.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac8

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Decomposition of the reducible representation of vibrational degrees of freedom assuming the D5h point group, gives Γvib = 13a1′(R) + 6a1″ + 19e1′(IR) + 18e1″ + 6a2′ + 12a2″(IR) + 20e2′(R) + 19e2″of which the a1′, a1″, e1″, a2′, e2′ and e2″ normal modes are IR forbidden by symmetry and their IR intensities are identically zero.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

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The other modes e1′ and a2″ are IR active, but many theoretical IR intensities of these modes are smaller than 1.0 km mol−1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

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The modes a1′ and a2″ are Raman active.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

54
As is well known quantum-chemical methods tend to overestimate the values of vibrational frequencies.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

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For dodecahedrane, the experimental values of IR allowed frequencies20 (symmetry t1u) are 728, 1298 and 2945 cm−1, but those obtained here at the B3LYP/6-31G* level of theory are 732.4, 1350.6 and 3091.8 cm−1; the experimental values of Raman allowed frequencies20 (symmetry ag and hg) are 480, 676, 840, 1092, 1164, 1324, 2938 and 2954 cm−1, and those obtained here at the B3LYP/6-31G* level of theory are 481.7, 674.0, 854.5, 1114.7, 1203.6, 1376.5, 3077.0 and 3105.2 cm−1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

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Comparing the experimental values exp and the B3LYP/6-31G* theoretical values calc of vibrational frequencies for dodecahedrane, the differences between exp and calc at different frequency ranges are different.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

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Scaling factors for the B3LYP/6-31G* level of theory have been estimated by using the experimental and theoretical vibrational frequencies for dodecahedrane given above.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

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When vibrational frequencies are <1000 cm−1, the average scaling factor is 0.9941; when vibrational frequencies are in the range of 1000–2000 cm−1, the average scaling factor is 0.9674; when vibrational frequencies are in the range of 2000–4000 cm−1, the average scaling factor is 0.9529.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

59
According to vibrational frequencies in Table 4 and the average scaling factors given above, the IR spectrum of C35H30 has been simulated and reported in Fig. 2 and Fig. 3.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met4

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In Fig. 2, the IR allowed vibrational frequencies are in the range of 600–1400 cm−1; in Fig. 3, the IR allowed vibrational frequencies are in the range of 2880–2980 cm−1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs6

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In the other ranges, vibrational frequencies are not IR active or the IR intensities are zero.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs7

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The simulated IR spectrum can be used as evidence to identify the molecule C35H30.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

Calculation for heat of formation

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What is the stability of the molecule C35H30?

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac10

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In order to answer this, the approach to a theoretical estimate for the heat of formation ΔHof of the molecule C35H30 is presented here.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa3

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First, the energy change ΔHr for reaction (1):was estimated by using the total energy E and the ZPE for C35H30, dodecahedrane and H2 at the B3LYP/6-31G* level of theory.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

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The values of E and ZPE for C35H30 and dodecahedrane are given in Table 3, and those for H2 are −1.17548 au and 6.4 kcal mol−1, respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res16

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The energy change ΔHr of the reaction (1) was calculated as follows:

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

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When the energy change ΔHr of the reaction (1) and the heat of formation ΔHof for C20H20 and H2 are known, the heat of formation ΔHof for C35H30 can be estimated according to reaction (1).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

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The result is as follows: The experimental heat of formation ΔHof for C20H20 and H2 are 18.2 kcal mol−1,21 and zero, respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res17

70
The energy change ΔHr of the reaction (1) has been calculated above.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met5

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Thus ΔHof for the molecule C35H30 can be estimated as follows: The estimated heat of formation for the molecule C35H30 is 51.2 kcal mol−1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res18

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This is larger than that of dodecahedrane, but smaller than that of cubane, 148.7 kcal mol−1.22

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

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So, purely from the thermodynamic point of view the coplanar double-cage dodecahedrane molecule C35H30 is more stable than cubane C8H8.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

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Since cubane has been synthesized, C35H30 has sufficient stability to allow its experimental preparation.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

Discussion

75
The thermodynamically stable geometry of the coplanar double-cage dodecahedrane molecule C35H30 was optimized at the B3LYP/6-31G* level of theory; its structure is of D5h symmetry.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met6

76
According to heat of formation of the molecule estimated here, C35H30 is more stable than cubane.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res19

77
Since cubane has been synthesized, C35H30 should have sufficient stability to allow its experimental preparation.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

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The coplanar double-cage dodecahedrane molecule C35H30 is a molecule with only one type of cage, a C20 cage.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac11

79
We believe that coplanar poly-cage molecules could form with the same or different kind of cages.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp1

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A coplanar double-cage molecule C25H20 with different cages is shown in Fig. 4.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac12

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The variety of coplanar poly-cage molecules of hydrocarbons is large.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac13

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If coplanar poly-cage hydrocarbons could be prepared, the number of polyhedral hydrocarbons might be increased substantially.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6