X-ray spectroscopic identification of strain and structure-based resonances in a series of saturated carbon-cage molecules: Adamantane, twistane, octahedrane, and cubane

Nanocarbon materials are widely studied for their unique properties, including novel electronic structures. For example, carbon nanotubes and graphene have unique semiconducting and semimetal electronic properties for carbon-based nanoelectronics, while nanodiamond materials have a relatively large electronic bandgap¹ and can exhibit negative electron affinity.² For broadening the possibilities, a fundamental understanding of how molecular strain and/or bond orientation perturbs the electronic structure and properties is an essential step in designing atomic-scale nanocarbon based circuitry.^3,4

As one of his graduate students in the early 2000s, Chuck Fadley allowed the first and corresponding author of this work to deviate somewhat from x-ray photoelectron spectroscopy into the electronic and physical structure of organic self-assembled monolayers and novel molecular electronic structures.^5–7 These studies, in addition to x-ray photoemission, heavily used near-edge x-ray absorption fine structure (NEXAFS) spectroscopy. The work, particularly after graduate school, evolved into examining diamondoids and other carbon cage structures.^2,8–13 This direction of research continues herein.

In this paper, we investigate a benchmark series of saturated carbon cage structures to study how molecular strain and cage configuration affect electronic structure. Figure 1 presents this series of molecules. Adamantane, C₁₀H₁₆, the smallest diamondoid, consists of ten carbon atoms that lie at diamond lattice positions. All carbons have four single bonds (i.e., are sp³ hybridized), and the surfaces are completely hydrogen terminated. Twistane has the same chemical formula, but the fixed cyclohexane twist conformation of the central ring introduces higher strain and bond angles that deviate from tetrahedral, ∼109.5° bond angles. Octahedrane¹⁴ [(CH)₁₂] and cubane^15–17 [(CH)₈] are considerably more strained, culminating in cubane where atoms sit at cube vertices, and carbon–carbon bonds lie either parallel or orthogonal to one another. An alternative view of the difference between these two is that if the carbon atoms forming equilateral triangles at each end of the molecule and associated hydrogens in octahedrane are replaced with a single carbon and hydrogen, the resulting structure is cubane. An evolution in the electronic structure is observed with increasing molecular strain in this series of T_d-adamantane (6.5 kcal/mol),¹⁸ D₂-twistane (26.1 kcal/mol),¹⁹ D_3d-octahedrane (83.7 kcal/mol),¹⁴ and O_h-cubane (159 kcal/mol).²⁰ 

The hydrocarbons under consideration are either commercially available (adamantane) or were prepared in our laboratories using established protocols for cubane,^21,22 twistane,²³ and octahedrane.²⁴ 

Gas-phase x-ray absorption spectra were acquired at beamline 10.1 (and 8.2) at the Stanford Synchrotron Radiation Lightsource at the SLAC National Accelerator Laboratory.^25,26 The gas cell was isolated from the UHV beamline using an ultrathin aluminum window supported by a nickel mesh. The beam was passed through a simple capacitive cell, with ∼20 mTorr of a given molecule at room temperature. A potential of 100 V was maintained between the electrodes, and the current between these plates was monitored and used as the total ion yield absorption current. This current was normalized for a constant offset, as well as the incident beam flux using the total electron yield current from a clean gold grid, simultaneously acquired in the upstream UHV portion of the beamline directly before the aluminum window. The spectra were energy-calibrated with the absorption of gaseous CO₂ acquired periodically throughout the acquisition of molecules using the carbon π* at 290.77.^27–30 The data were acquired with variable energy steps as small as 25 meV near the absorption onset. The beamline, with the parameters used, had a measured resolution better than 80 meV based on the FWHM of the sharpest features in the CO₂ calibration scans. Furthermore, repeated successive scans using the same gas volume, refreshed gas volumes, and varying x-ray flux and using different beamlines yielded identical spectra, when normalized, within the signal-to-noise ratio of the measurement.

X-ray absorption spectra were computed using the stobe code.³¹ Each spectrum was generated by calculating the absorption at each atomic center, using iii_iglo^31,32 orbitals around the atom of interest, pseudopotential cores around remaining carbons, and computing the overlap between the C 1s and the unoccupied states with a fictitious ½ electronic charge remaining in one of the C 1s states. Energies were calibrated by aligning the lowest-energy excitation in this calculation with the difference in energy between the ground state and the energy of a molecule with only one electron in the C 1s and one electron occupying the LUMO of the ground state. Identical orbitals and methods were used for all of the molecules, and an identical arbitrary smoothing of the excitations was used across the series. The peaks were convoluted with a Gaussian of width 0.5 eV below 299.75, and a Gaussian of linearly increasing width to 11 at 320 eV. This smoothing led to the best match between the experimental and computed spectra of cubane and octahedrane.

Figure 2 presents the x-ray absorption spectrum of gas-phase adamantane, twistane, octahedrane, and cubane; striking progressions in the C–C σ* resonances occur in the series. Adamantane possesses C–C σ* resonances similar to those observed in various saturated hydrocarbons;³³ the most intense manifold is from about 290 to 295 eV and a second σ* as a shoulder from about 295 to 303 eV. In twistane, the main σ* manifold is apparent as two resonances within the peak. In octahedrane, these are more intense and sharper in energy than in twistane. The progression culminates in cubane, where two very distinct and intense resonances occupy the energy range where only a single manifold appeared in adamantane. These are surprisingly narrow and distinct in this spectrum.

Figure 3 presents a close-up view of the near-edge region for the four molecules. Adamantane generally has two manifolds of resonances, due to C–H bonding, in the region 286.5 to about 288.5 eV. The lower-energy manifold is primarily (but not uniquely) associated with tertiary carbons, while the second is mainly associated with the methylene groups.⁸ Oscillations appear in the spectrum from this highly symmetric molecule and are closely associated with vibrational modes in C–H bonds.⁸ Twistane and adamantane are both C₁₀H₁₆ isomers. The same two CH and CH₂ manifolds are present in the twistane spectrum, but the different symmetry dampens the vibrational structure in this region. This is similar to the differences in spectra acquired from adamantane and adamantanethiol.¹² Octahedrane and cubane both consist of only tertiary carbons, i.e., each carbon bonds with three other carbons and one hydrogen atom; the lack of CH₂ groups in these molecules is evident in the pre-edge features.

The most striking difference between octahedrane and cubane spectra is that the lowest-energy peak in the cubane spectrum is much more intense than in the octahedrane spectrum, even though local chemical carbon environments are three carbon bonds and a single hydrogen. The cubane peak intensity is about two times the intensity of octahedrane, while the integrated intensity is 2.8 times larger. The peak width is about 50% broader in cubane than octahedrane.

Figure 4 presents the computed x-ray absorption spectra. The computed spectra reproduce the main features of the experimental data. The computed lowest-energy peak for cubane is much more intense than the octahedrane peak. Also, in general, the simulation underestimates the intensity of the lowest-energy manifold, except in the case of cubane. The overall shapes and progressions in the C–C σ* resonances from about 290 to 303 eV are also reproduced.

This series of carbon cage molecules under consideration here represents a means to isolate the effects of molecular shape and strain from chemical variation. NEXAFS probes unoccupied states by exciting a core-level electron into nearby unoccupied orbitals and is thus a very localized spectroscopy. Often, unique NEXAFS signatures identify chemical moieties; the carbon spectra of polymers can successfully be approximated as a linear combination of the contributions from each carbon atom.³³ This framework is known as the “building-block” approximation. The framework has known shortcomings for the gas versus condensed phase,³⁴ and when unoccupied states are not localized on a particular moiety, they have a strong molecular orbital character.³⁵ Adamantane, twistane, octahedrane, and cubane are prime examples of molecules where drastic apparent differences in the electronic structure, revealed using NEXAFS, arise from the molecular shape rather than from local carbon chemical environments.

The most distinct manifold associated with C–C σ* orbitals in adamantane evolves into two distinct, strong, and narrow peaks through the molecular series. These changes are correlated with, and we postulate are a signature of, increasing strain in these molecules (Fig. 1).^{14,18–20,22,24,36} The two sharp and intense C–C σ* resonances in cubane, to our knowledge, are unique in an alkane consisting of one carbon atom type or environment. The C–C σ* sharpening with strain has been observed in gas-phase EELS of the series of cyclohexane, cyclopentane, cyclobutane, and cyclopropane;³⁷ however, only a single sharp σ* resonance is observed in cyclopropane.

The series can be divided into two groups: adamantane and twistane with the same chemical formula, and same number of secondary (CH₂) and tertiary (CH) carbon environments, as well as octahedrane and cubane, consisting only of tertiary (CH) carbons. The distinct x-ray absorption spectra, especially for octahedrane and cubane, demonstrate that molecular shape or geometry is solely responsible for the differences in electronic structure.

A striking contrast between octahedrane and cubane is the higher intensity in the lowest-energy cubane resonance. Resonances in this energy regime are generally attributed to peripheral carbon–hydrogen bonding.⁸ The shape and shift to lower energy are also reminiscent of π* features in, for example, graphite,³³ but here they occur in cubane with no carbon double bonds.

Analyzing the output of the stobe calculations, particularly for cubane, this lowest-energy manifold consists of multiple resonances. In the ½ core-hole approximation, observing the absorption at only one carbon atomic center, the LUMO, LUMO + 1, LUMO + 2, and LUMO + 3 states align energetically with this resonance. The LUMO [Fig. 5(a)] has a strong s-character and thus does not contribute significantly to the K-edge spectrum. LUMO + 1, LUMO + 2, and LUMO + 3 degenerate in the ground state calculation, to appear as relatively delocalized, p-like molecular orbitals [Fig. 5(b)]. The increased p-content in the hybridization is in line with prior theoretical analysis.¹³ We also note that as a simulation artifact, all of these orbitals [LUMO + 1, Fig. 5(c), but particularly LUMO + 2 and LUMO + 3] can be perturbed somewhat in the actual stobe x-ray absorption simulation by the unphysical ½ core-hole. Even with these limitations, the strong p-p interactions among the parallel and perpendicular C–C bonds, with arguable resemblance to a π orbital or symmetry, lead to this starkly intense, low energy resonance in cubane.

The next cubane peak, also appearing in octahedrane, experimentally appears at about 288.2 eV (about 289.4–289.9 eV in the stobe calculations). This resonance is not clearly resolved in a shoulder within either adamantane or twistane spectra. In the stobe calculation, this peak is directly associated with localized orbitals with strong C–H σ* character [Fig. 5(d)]. A postulated reason for their large intensity is that in cubane and octahedrane, tertiary carbon bonds experience largest deviation from a relaxed 109.5° bond angle, with octahedrane as small as 60° and all carbon bonds 90° from one another in cubane. Electrostatic repulsion due to carbon-bond proximity may be causing the increased intensity in this resonance in cubane and octahedrane. Finally, in the stobe calculations for cubane, the resonance at 291.4 eV has clear C–C σ* character, as do many of the states at ∼294 eV, as expected.

The gas-phase x-ray absorption spectra of adamantane, twistane, octahedrane, and cubane reveal how cage geometry, beyond local carbon atom chemical environments, affects the electronic structure. Two major progressions across this series occur. First, a broad C–C σ* resonance in the absorption splits into two more narrow and intense resonances with increasing molecular strain. Second, the first manifold of states previously associated with tertiary C–H σ* in the diamondoid series appears to broaden and shift to lower energy with increasing molecular strain. This feature is more than twice as intense in cubane as in octahedrane, even though these two molecules have only tertiary carbons, with the chemical formula (CH)_x. The spectral differences are entirely due to the shape of the molecules, and we attribute the additional intensity to a high degree of p-p interaction between parallel and perpendicular C–C bonds, reminiscent of π-like states, in cubane.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344, and funded by Laboratory Directed Research and Development as well as a UCOP management fee grant. Portions of this research were carried out at the Stanford Synchrotron Radiation Lightsource, a Directorate of SLAC National Accelerator Laboratory and an Office of Science User Facility operated by the U.S. Department of Energy Office of Science by Stanford University. The authors acknowledge useful discussions with Heather Whitley and Mao Xi Zhang, LLNL; Chris Mundy, PNNL; David Prendergast, LBNL; and Dimosthenis Sokaras, SLAC.

The data that support the findings of this study are available from the corresponding author upon reasonable request.