The absolute photoabsorption cross sections for thiophene in the 5.0–10.7 eV range were measured using synchrotron radiation. New theoretical calculations performed at the time-dependent density functional theory level were used to qualitatively interpret the recorded photoabsorption spectrum. The calculations facilitated a re-analysis of the observed vibronic and Rydberg structures in the photoabsorption spectrum. Here a number of features have been re-assigned, while a number of other features have been assigned for the first time. This represents the most comprehensive and self-consistent assignment of the thiophene high-resolution photoabsorption spectrum to date.
I. INTRODUCTION
Thiophene (C4H4S) is a heterocyclic aromatic compound of significant importance in materials science, as it is a building block in the synthesis of conjugated π-systems. In particular, the electronic properties of thiophene polymers can be adjusted through additional side-chains and by controlling the polymer lengths, giving them high potential as components of organic electronic devices.1 Thiophene derivatives are also biologically active compounds and form the basis of many pharmaceutical drugs.2 However, the metabolism of some thiophene compounds can induce toxicity.3 The use of thiophene-derived materials in medicine and technology makes the understanding of the structure and electronic and vibrational spectroscopic character of the base thiophene unit important. The desire to control and understand thiophene-based material optoelectronic properties such as photo-stability and conductivity has led to significant investigations of thiophene photochemistry. In particular, the photochemical behaviour of thiophene and α-oligothiophenes has attracted significant experimental and theoretical attention. These investigations address complex issues regarding the vertical and adiabatic ordering of its lowest-lying singlet and triplet states and the competition between possible decay routes, i.e., inter-system crossing, internal conversion, and fluorescence.4–10
The relatively simple structure of thiophene, along with its strong structural similarities to furan and pyrrole, has made it an important target for experimental and theoretical investigations. This has led to numerous investigations on the structure of thiophene in its neutral and cationic states to determine the ionization energies and the ion vibrational structure,11–13 ionized orbital characters,14 and interaction potentials.11 These ionization investigations have been supported by numerous theoretical calculations.9,15–17 Rennie et al.15 also reported absolute cross sections for photoabsorption (8.9–35.0 eV) through synchrotron photoionization experiments. The synchrotron photoabsorption spectrum for thiophene was observed using a transmission method reported by Palmer et al.18 and was recently remeasured for thiophene using a Fourier transform spectrometer at the Soleil DESIRS beamline.19 In the more recent work by Holland et al., a relative photoabsorption spectrum was obtained (5.0–12.5 eV) and normalized to the absolute photo-ion spectrum.15
The technological importance of thiophene, and thiophene-based materials, has also stimulated interest in its interactions with electrons. This interest has attracted recent attention, as electron scattering phenomena play important roles in efficiently breaking chemical bonds (through dissociative electron attachment) and driving reactions in plasma-like environments.20,21 This is of particular relevance to materials science where non-thermal plasmas are gaining increasing use for functionalizing surfaces and synthesizing novel nanomaterials.22,23 To this end, total electron scattering cross sections for thiophene have recently been reported.24 Differential cross sections for elastic scattering have been reported as a function of incident electron energy for fixed scattering angles to investigate resonance behaviour in thiophene,25 building on early electron transmission spectroscopic investigations.26 These investigations have been supported by theoretical calculations at the R-matrix25,27 and Schwinger Multichannel (SMC)28 level, with cross sections having also been calculated using an additivity rule.29 The electronic structure of thiophene has also been investigated by electron energy loss spectroscopy.18,30,31
Recent investigations have demonstrated the important role that the ground and excited electronic states play in electron scattering calculations.32–39 In this respect, adequately describing electronic excited states is essential in Schwinger Multichannel (SMC) calculations, where multichannel coupling allows flux to flow out of the elastic scattering channel and into discrete electronic state excitation processes. In ring-compounds, in particular, it has been observed that the channel space must be built from states that well-describe all energetically available electronic states to enable sufficient flux to couple into inelastic scattering channels to produce a reliable elastic scattering cross section.34 The ability to combine experimental and theoretical photon- and electron-impact collisional investigations has been important in building complete datasets that are suitable for modelling collisional environments, such as radiation damage, plasma processing, and charged-particle transport,40–44 and in part has formed the motivation for this work.
In this manuscript, we therefore report a new absolute photoabsorption cross section measurement and supplement this work with new time dependent density functional theory (TDDFT) calculations. In Sec. II, we describe our experimental and theoretical methods. Our results are presented and discussed in Sec. III. Finally, our conclusions from this work are summarized in Sec. IV.
II. METHODS
The high resolution vacuum ultraviolet (VUV) photoabsorption spectrum of thiophene was measured using the AU-UV beam line at the ASTRID2 storage ring, Aarhus University, Denmark. The experimental configuration has been described in detail elsewhere.45,46 Briefly, the monochromatized light with a resolution of 0.08 nm passes through a gas cell that is filled with thiophene vapour. Light transmitted through the cell passes through a MgF2 window and is detected using a photomultiplier tube. The MgF2 window sets the lower limit of detection at 115 nm. The pressure of the thiophene vapour in the gas cell is monitored using a 1 Torr full scale capacitance manometer (Chell model CDG100D). Absolute photoabsorption cross sections (σ in units of Mb ≡ 10−18 cm2) are obtained using the Beer-Lambert attenuation law
Here I0 is the intensity of the incident light (measured as that transported through an evacuated gas cell), It is the measured intensity of the light transmitted through a gas cell of l absorption path length, l = 15.5 cm, that is filled with thiophene vapour at a molecular number density, N. The light intensity at each wavelength is kept quasi-constant through ASTRID2 operating in a “top-up” mode that compensates for the constant beam decay. To compensate for the slight intensity variations (∼3%), the incident flux is normalized to the accurately determined beam current in the storage ring. Using this procedure, the absolute photoabsorption cross sections are determined to within ±5%.
Our photoabsorption cross section measurements were supported by theoretical calculations performed at the time-dependent density functional theory (TDDFT) level of approximation.47 The thiophene geometry was optimized, with a frequency calculation performed using a B3LYP functional48 and an augmented correlation consistent polarized valence triple-zeta basis (aug-cc-pVTZ).49,50 The TDDFT calculation was then performed at the optimized geometry, using the same model chemistry. We have implemented this methodology for assisting in the interpretation of the thiophene photoabsorption spectrum, as similar model chemistries have enabled us to assign the photoabsorption spectra of other large ring-based compounds.32,37,51 All of these calculations were performed in the Gaussian 09 package.52 For discussion of our theoretical assignments, we orient the molecule in the yz-plane (see Fig. 1 inset).
The VUV photoabsorption cross section for thiophene in the 5.0–10.7 eV range. The inset shows the structure of thiophene and its reference Cartesian coordinate system used in discussing its electronic transitions.
The VUV photoabsorption cross section for thiophene in the 5.0–10.7 eV range. The inset shows the structure of thiophene and its reference Cartesian coordinate system used in discussing its electronic transitions.
III. RESULTS AND DISCUSSION
The VUV photoabsorption spectrum of thiophene measured at room temperature is shown in Fig. 1. The absolute cross sections are similar to those observed by Rennie et al.15 in the overlapping regions (8.8–10.7 eV). Here Rennie et al. determined the absolute photoabsorption cross section using synchrotron radiation and a double ion chamber to collect all photo-ions produced. This absolute scale was used to normalise relative photoabsorption data from Holland et al.19 over the 5.0–12.5 eV range. We see good agreement between our photoabsorption cross section and that produced by Holland et al. over the entire overlapping regions. This demonstrates the reliability in the reported high-resolution photoabsorption cross sections for thiophene. To assist in the interpretation of this spectrum, our TDDFT calculations are summarized in Table I. We now discuss the photoabsorption behaviour and the excited state electronic structure in energetic bands identified in Table I and indicated in Fig. 1. The spectroscopic assignments for the various bands are detailed in Tables II–V. To assist in understanding the vibrational assignments, our calculated vibrational frequencies, along with the experimental and theoretical vibrational frequencies available for thiophene in both the neutral and cationic states, are summarized in Table VI.
The dominant excited electronic states of thiophene obtained with the time-dependent density functional theory calculations assigned to the dominant photoabsorption spectrum (PAS) band features. See the text for further details.
. | . | TDDFT calculation . | |||
---|---|---|---|---|---|
Expt. feature . | PAS energy (eV) . | State . | Dominant configuration . | Energy (eV) . | f0 . |
I | 5.0-6.55 | 1B2 (ππ*) | 1a2 → 4b1 | 5.67 | 0.078 |
1A1 (ππ*) | 3b1 → 4b1 | 5.75 | 0.079 | ||
1B1 | 1a2 → 8b2 (3p) | 5.80 | 0.012 | ||
1B1 | 1a2 → 9b2 (3p/d) | 6.34 | 0.014 | ||
II | 6.55-7.7 | 1B1 | 3b1 → 13a1 (3p) | 6.65 | 0.028 |
1B2 | 1a2 → 5b1 (px) | 6.98 | 0.069 | ||
1A1 (ππ*) | 1a2 → 2a2/3b1 → 5b1(px) | 7.22 | 0.256 | ||
1B2 (ππ*) | 3b1 → 2a2 | 7.41 | 0.088 | ||
1A1 | 3b1 → 5b1 | 7.49 | 0.053 | ||
1A1 | 1a2 → 3a2 | 7.82 | 0.010 | ||
III | 7.7-8.9 | 1A1 | 11a1 → 12a1 | 8.54 | 0.077 |
IV | 8.9-9.5 | ||||
V | 9.5 |
. | . | TDDFT calculation . | |||
---|---|---|---|---|---|
Expt. feature . | PAS energy (eV) . | State . | Dominant configuration . | Energy (eV) . | f0 . |
I | 5.0-6.55 | 1B2 (ππ*) | 1a2 → 4b1 | 5.67 | 0.078 |
1A1 (ππ*) | 3b1 → 4b1 | 5.75 | 0.079 | ||
1B1 | 1a2 → 8b2 (3p) | 5.80 | 0.012 | ||
1B1 | 1a2 → 9b2 (3p/d) | 6.34 | 0.014 | ||
II | 6.55-7.7 | 1B1 | 3b1 → 13a1 (3p) | 6.65 | 0.028 |
1B2 | 1a2 → 5b1 (px) | 6.98 | 0.069 | ||
1A1 (ππ*) | 1a2 → 2a2/3b1 → 5b1(px) | 7.22 | 0.256 | ||
1B2 (ππ*) | 3b1 → 2a2 | 7.41 | 0.088 | ||
1A1 | 3b1 → 5b1 | 7.49 | 0.053 | ||
1A1 | 1a2 → 3a2 | 7.82 | 0.010 | ||
III | 7.7-8.9 | 1A1 | 11a1 → 12a1 | 8.54 | 0.077 |
IV | 8.9-9.5 | ||||
V | 9.5 |
Energies and spectral assignments of the observed features in Band I. (s)-shoulder; (w)-weak feature. Also shown are energy separations (ΔE) of vibrational progressions, taken from the progression onsets. Values in parentheses show progression shifts from primary progression onset, denoted in bold.
Energy (eV) . | ΔE (meV) . | Assignment . | Energy (eV) . | ΔE (meV) . | Assignment . |
---|---|---|---|---|---|
5.051 | (−106) | 5.838(w) | |||
5.079 | (−78) | 5.882(w) | |||
5.107 | 0.0 (−50) | 5.958(w) | |||
5.134 | 0.0 (−23) | 5.992 | 0.0 | 1a2 → 3p | |
5.157 | 0.0 | 6.064 | 72 | 1a2 → 3p | |
5.176 | 0.0 (19) | 6.107 | −50 | 1a2 → 3p/3d | |
5.186 | 0.0 (29) | 6.118 | 0.0 (−39) | 1a2 → 3p/3d | |
5.210 | 0.0 (53) | 6.135(w) | 143 | 1a2 → 3p | |
5.227 | 120 | 6.157 | 0.0 | 1a2 → 3p/3d | |
5.236 | 0.0 (79) | 6.160 | 0.0 (3) | 1a2 → 3p/3d | |
5.255 | 121 | 6.169 | 51 | 1a2 → 3p/3d | |
5.276 | 119 | 6.191 | 0.0 (34) | 1a2 → 3p/3d | |
5.297 | 121 | 6.205 | 48 | 1a2 → 3p/3d | |
5.306 | 120 | 6.210 | 50 | 1a2 → 3p/3d | |
5.329 | 119 | 6.221 | 103 | 1a2 → 3p/3d | |
5.357 | 121 | 6.227(w) | 0.0 (70) | 1a2 → 3p/3d | |
5.374 | 240 | 6.239(w) | 48 | 1a2 → 3p/3d | |
5.395 | 238 | 6.254 | 97 | 1a2 → 3p/3d | |
5.419 | 243 | 6.257 | 97 | 1a2 → 3p/3d | |
5.424 | 238 | 6.272 | 154 | 1a2 → 3p/3d | |
5.447 | 237 | 6.280(w) | 53 | 1a2 → 3p/3d | |
5.476 | 240 | 6.287(w) | 96 | 1a2 → 3p/3d | |
5.485(ws) | 6.297 | ||||
5.496(w) | 362 | 6.304 | 147 | 1a2 → 3p/3d | |
5.515 | 358 | 6.306 | 146 | 1a2 → 3p/3d | |
5.539 | 363 | 6.311(s) | |||
5.546 | 360 | 6.321 | 203 | 1a2 → 3p/3d | |
5.566 | 356 | 6.331(w) | 104 | 1a2 → 3p/3d | |
5.595 | 359 | 6.339(w) | 148 | 1a2 → 3p/3d | |
5.616(w) | 6.350 | 193 | 1a2 → 3p/3d | ||
5.624(w) | 0.0 | 6.357 | 197 | 1a2 → 3p/3d | |
5.633 | 476 | 6.396 | 239 | 1a2 → 3p/3d | |
5.658 | 482 | 6.406 | 246 | 1a2 → 3p/3d | |
5.685 | 475 | 6.422(ws) | |||
5.713 | 477 | 6.446 | 289 | 1a2 → 3p/3d | |
5.745 | 121 | 6.461 | 301 | 1a2 → 3p/3d | |
5.779(w) | 6.488(ws) | ||||
5.807(w) | 6.500(ws) |
Energy (eV) . | ΔE (meV) . | Assignment . | Energy (eV) . | ΔE (meV) . | Assignment . |
---|---|---|---|---|---|
5.051 | (−106) | 5.838(w) | |||
5.079 | (−78) | 5.882(w) | |||
5.107 | 0.0 (−50) | 5.958(w) | |||
5.134 | 0.0 (−23) | 5.992 | 0.0 | 1a2 → 3p | |
5.157 | 0.0 | 6.064 | 72 | 1a2 → 3p | |
5.176 | 0.0 (19) | 6.107 | −50 | 1a2 → 3p/3d | |
5.186 | 0.0 (29) | 6.118 | 0.0 (−39) | 1a2 → 3p/3d | |
5.210 | 0.0 (53) | 6.135(w) | 143 | 1a2 → 3p | |
5.227 | 120 | 6.157 | 0.0 | 1a2 → 3p/3d | |
5.236 | 0.0 (79) | 6.160 | 0.0 (3) | 1a2 → 3p/3d | |
5.255 | 121 | 6.169 | 51 | 1a2 → 3p/3d | |
5.276 | 119 | 6.191 | 0.0 (34) | 1a2 → 3p/3d | |
5.297 | 121 | 6.205 | 48 | 1a2 → 3p/3d | |
5.306 | 120 | 6.210 | 50 | 1a2 → 3p/3d | |
5.329 | 119 | 6.221 | 103 | 1a2 → 3p/3d | |
5.357 | 121 | 6.227(w) | 0.0 (70) | 1a2 → 3p/3d | |
5.374 | 240 | 6.239(w) | 48 | 1a2 → 3p/3d | |
5.395 | 238 | 6.254 | 97 | 1a2 → 3p/3d | |
5.419 | 243 | 6.257 | 97 | 1a2 → 3p/3d | |
5.424 | 238 | 6.272 | 154 | 1a2 → 3p/3d | |
5.447 | 237 | 6.280(w) | 53 | 1a2 → 3p/3d | |
5.476 | 240 | 6.287(w) | 96 | 1a2 → 3p/3d | |
5.485(ws) | 6.297 | ||||
5.496(w) | 362 | 6.304 | 147 | 1a2 → 3p/3d | |
5.515 | 358 | 6.306 | 146 | 1a2 → 3p/3d | |
5.539 | 363 | 6.311(s) | |||
5.546 | 360 | 6.321 | 203 | 1a2 → 3p/3d | |
5.566 | 356 | 6.331(w) | 104 | 1a2 → 3p/3d | |
5.595 | 359 | 6.339(w) | 148 | 1a2 → 3p/3d | |
5.616(w) | 6.350 | 193 | 1a2 → 3p/3d | ||
5.624(w) | 0.0 | 6.357 | 197 | 1a2 → 3p/3d | |
5.633 | 476 | 6.396 | 239 | 1a2 → 3p/3d | |
5.658 | 482 | 6.406 | 246 | 1a2 → 3p/3d | |
5.685 | 475 | 6.422(ws) | |||
5.713 | 477 | 6.446 | 289 | 1a2 → 3p/3d | |
5.745 | 121 | 6.461 | 301 | 1a2 → 3p/3d | |
5.779(w) | 6.488(ws) | ||||
5.807(w) | 6.500(ws) |
Observed features and tentative spectral assignments in Band II. Also shown are energy separations (ΔE) of vibrational progressions, taken from the progression onsets, denoted in bold. Values in parentheses show progression shifts from an alternate reference energy. Refer to the text for further details. (b)-broad; (s)-shoulder; (w)-weak; (r)-resonance position.
Energy (eV) . | ΔE (meV) . | Assignment . | Energy (eV) . | ΔE (meV) . | Assignment . |
---|---|---|---|---|---|
6.604 | 0.0 (−82) | 3b1 → 3p | 7.171 | 262 | 1a2 → 3px |
6.639(w) | 35 (−47) | 3b1 → 3p + | 7.200(b) | 291 | 1a2 → 3px |
6.686 | 82 (0.0) | 3b1 → 3p | 7.419(r) | 0.0 | 3b1 → 3p′ |
6.713 | 109 (27) | 3b1 → 3p | 7.495(r) | 76 | 3b1 → 3p′ |
6.737 | 133 (51) | 3b1 → 3p | 7.539(s) | 120 | 3b1 → 3p′ |
6.758 | 154 (72) | 3b1 → 3p | 7.570 | 151 | 3b1 → 3p′ |
6.784 | 180 (98) | 3b1 → 3p | 7.583 | 164 | 3b1 → 3p′ + |
6.827 | 223 (141) | 3b1 → 3p | 7.599 | 180 | 3b1 → 3p′ + |
6.855(s) | 251 (169) | 3b1 → 3p + | 7.609 (wbs) | −10 | 1a2 → 4p |
6.869 | 265 (183) | 3b1 → 3p + | 7.619 | 0.0 | 1a2 → 4p |
6.897(bs) | −12 | 1a2 → 3px | 7.643 | 224 | 3b1 → 3p′ + |
6.909 | 0.0 | 1a2 → 3px | 7.678(w) | 59 | 1a2 → 4p |
6.963 | 54 | 1a2 → 3px | 7.695(w) | 76 | 1a2 → 4p |
6.985 | 76 | 1a2 → 3px | 7.718(w) | 99 | 1a2 → 4p |
7.049 (b) | 140 | 1a2 → 3px | 7.762 (vw) | 143 | 1a2 → 4p |
7.123 | 214 | 1a2 → 3px |
Energy (eV) . | ΔE (meV) . | Assignment . | Energy (eV) . | ΔE (meV) . | Assignment . |
---|---|---|---|---|---|
6.604 | 0.0 (−82) | 3b1 → 3p | 7.171 | 262 | 1a2 → 3px |
6.639(w) | 35 (−47) | 3b1 → 3p + | 7.200(b) | 291 | 1a2 → 3px |
6.686 | 82 (0.0) | 3b1 → 3p | 7.419(r) | 0.0 | 3b1 → 3p′ |
6.713 | 109 (27) | 3b1 → 3p | 7.495(r) | 76 | 3b1 → 3p′ |
6.737 | 133 (51) | 3b1 → 3p | 7.539(s) | 120 | 3b1 → 3p′ |
6.758 | 154 (72) | 3b1 → 3p | 7.570 | 151 | 3b1 → 3p′ |
6.784 | 180 (98) | 3b1 → 3p | 7.583 | 164 | 3b1 → 3p′ + |
6.827 | 223 (141) | 3b1 → 3p | 7.599 | 180 | 3b1 → 3p′ + |
6.855(s) | 251 (169) | 3b1 → 3p + | 7.609 (wbs) | −10 | 1a2 → 4p |
6.869 | 265 (183) | 3b1 → 3p + | 7.619 | 0.0 | 1a2 → 4p |
6.897(bs) | −12 | 1a2 → 3px | 7.643 | 224 | 3b1 → 3p′ + |
6.909 | 0.0 | 1a2 → 3px | 7.678(w) | 59 | 1a2 → 4p |
6.963 | 54 | 1a2 → 3px | 7.695(w) | 76 | 1a2 → 4p |
6.985 | 76 | 1a2 → 3px | 7.718(w) | 99 | 1a2 → 4p |
7.049 (b) | 140 | 1a2 → 3px | 7.762 (vw) | 143 | 1a2 → 4p |
7.123 | 214 | 1a2 → 3px |
Observed spectral features tentatively assigned in Band III. Also shown are energy separations (ΔE) of vibrational progressions, taken from the progression onsets, denoted in bold. See the text for further details.
Energy (eV) . | ΔE (meV) . | Assignment . | Energy (eV) . | ΔE (meV) . | Assignment . |
---|---|---|---|---|---|
7.775 | −18 | 1a2 → 4px | 8.297 | 76 | 1a2 → 5px |
7.783 | −10 | 1a2 → 4px | 8.319 | 0 | 3b1 → 4p |
7.793 | 0 | 1a2 → 4px | 8.349 | 128 | 1a2 → 5px |
7.847 | 54 | 1a2 → 4px | 8.360 | 139/170 | 1a2 → 5px /1a2 → 5p |
7.855 | 62 | 1a2 → 4px | 8.375(s) | 154 | 1a2 → 5px |
7.868 | 75 | 1a2 → 4px | 8.388 | 167 | 1a2 → 5px |
7.888 | 95 | 1a2 → 4px | 8.394(s) | 75 | 3b1 → 4p |
7.900 | 107 | 1a2 → 4px | 8.424 | −10 | 1a2 → 6px |
7.914(s) | 121 | 1a2 → 4px + | 8.434 | 0 | 1a2 → 6px |
7.924 | 131 | 1a2 → 4px | 8.450 | 131 | 3b1 → 4p |
7.932 | 139 | 1a2 → 4px | 8.457 | 138/236 | 3b1 → 4p /1a2 → 5px |
7.944 | 151 | 1a2 → 4px | 8.489 | 0 | 3b1 → 4p′ |
7.957 | 164 | 1a2 → 4px | 8.509 | 75 | 1a2 → 6px |
7.993(s) | −11 | 11a1 → 3s | 8.519 | 200 | 3b1 → 4p |
8.004 | 0 | 11a1 → 3s | 8.525 | 206 | 3b1 → 4p |
8.024 | 20/231 | 11a1 → 3s /1a2 → 4px | 8.547 | −13 | 1a2 → 7px |
8.052 | 48 | 11a1 → 3s | 8.560 (b) | 0/71 | 1a2 → 7px/3b1 → 4p′ |
8.068 | 64 | 11a1 → 3s | 8.584 (s) | 150 | 1a2 → 6px |
8.078 | 74 | 11a1 → 3s | 8.592 | 158 | 1a2 → 6px |
8.099 | 95 | 11a1 → 3s | 8.613 | 179 | 1a2 → 6px |
8.108 | 104 | 11a1 → 3s | 8.636 | 0 | 1a2 → 8px |
8.141(b) | 137 | 11a1 → 3s | 8.657 | 168 | 3b1 → 4p′ |
8.154 | 150 | 11a1 → 3s | 8.668 | 234 | 1a2 → 6px |
8.168 | 164 | 11a1 → 3s | 8.675 | 186 | 3b1 → 4p′ |
8.190 | 0 | 1a2 → 5p | 8.688 | 0 | 1a2 → 9px |
8.214(s) | −7 | 1a2 → 5px | 8.714 | 78 | 1a2 → 8px |
8.221 | 0 | 1a2 → 5px | 8.725 | 0 | 1a2 → 10px |
8.243 | 239 | 11a1 → 3s | 8.762 | 74 | 1a2 → 9px |
8.265 | 75 | 1a2 → 5p | 8.779 | 0 | 3b1 → 5p |
8.274 | 53 | 1a2 → 5px + | 8.801 | 76 | 1a2 → 10px |
Energy (eV) . | ΔE (meV) . | Assignment . | Energy (eV) . | ΔE (meV) . | Assignment . |
---|---|---|---|---|---|
7.775 | −18 | 1a2 → 4px | 8.297 | 76 | 1a2 → 5px |
7.783 | −10 | 1a2 → 4px | 8.319 | 0 | 3b1 → 4p |
7.793 | 0 | 1a2 → 4px | 8.349 | 128 | 1a2 → 5px |
7.847 | 54 | 1a2 → 4px | 8.360 | 139/170 | 1a2 → 5px /1a2 → 5p |
7.855 | 62 | 1a2 → 4px | 8.375(s) | 154 | 1a2 → 5px |
7.868 | 75 | 1a2 → 4px | 8.388 | 167 | 1a2 → 5px |
7.888 | 95 | 1a2 → 4px | 8.394(s) | 75 | 3b1 → 4p |
7.900 | 107 | 1a2 → 4px | 8.424 | −10 | 1a2 → 6px |
7.914(s) | 121 | 1a2 → 4px + | 8.434 | 0 | 1a2 → 6px |
7.924 | 131 | 1a2 → 4px | 8.450 | 131 | 3b1 → 4p |
7.932 | 139 | 1a2 → 4px | 8.457 | 138/236 | 3b1 → 4p /1a2 → 5px |
7.944 | 151 | 1a2 → 4px | 8.489 | 0 | 3b1 → 4p′ |
7.957 | 164 | 1a2 → 4px | 8.509 | 75 | 1a2 → 6px |
7.993(s) | −11 | 11a1 → 3s | 8.519 | 200 | 3b1 → 4p |
8.004 | 0 | 11a1 → 3s | 8.525 | 206 | 3b1 → 4p |
8.024 | 20/231 | 11a1 → 3s /1a2 → 4px | 8.547 | −13 | 1a2 → 7px |
8.052 | 48 | 11a1 → 3s | 8.560 (b) | 0/71 | 1a2 → 7px/3b1 → 4p′ |
8.068 | 64 | 11a1 → 3s | 8.584 (s) | 150 | 1a2 → 6px |
8.078 | 74 | 11a1 → 3s | 8.592 | 158 | 1a2 → 6px |
8.099 | 95 | 11a1 → 3s | 8.613 | 179 | 1a2 → 6px |
8.108 | 104 | 11a1 → 3s | 8.636 | 0 | 1a2 → 8px |
8.141(b) | 137 | 11a1 → 3s | 8.657 | 168 | 3b1 → 4p′ |
8.154 | 150 | 11a1 → 3s | 8.668 | 234 | 1a2 → 6px |
8.168 | 164 | 11a1 → 3s | 8.675 | 186 | 3b1 → 4p′ |
8.190 | 0 | 1a2 → 5p | 8.688 | 0 | 1a2 → 9px |
8.214(s) | −7 | 1a2 → 5px | 8.714 | 78 | 1a2 → 8px |
8.221 | 0 | 1a2 → 5px | 8.725 | 0 | 1a2 → 10px |
8.243 | 239 | 11a1 → 3s | 8.762 | 74 | 1a2 → 9px |
8.265 | 75 | 1a2 → 5p | 8.779 | 0 | 3b1 → 5p |
8.274 | 53 | 1a2 → 5px + | 8.801 | 76 | 1a2 → 10px |
Rydberg state assignments, energies, and quantum defects (δ). Where the assignment of the band origin is ambiguous, the alternative assignment and the quantum defect are shown in parentheses. See the text for further details.
Assignment . | Energy (eV) . | δ . |
---|---|---|
IE (1a2) = 8.874 eV12 | ||
3p | 5.992 | 0.83 |
3p/3d | 6.157 | 0.76 |
3px | 6.909 | 0.37 |
4p | 7.619 | 0.71 |
4px | 7.793 | 0.45 |
5p | 8.190 | 0.54 |
5px | 8.221 | 0.44 |
6px | 8.434 | 0.44 |
7px | 8.560 | 0.42 |
8px | 8.636 | 0.44 |
9px | 8.688 | 0.45 |
10px | 8.725 | 0.44 |
IE (3b1) = 9.58 eV11 | ||
3p | 6.604 (6.686) | 0.86 (0.83) |
3p′ | 7.419 | 0.49 |
4p | 8.319 | 0.71 |
4p′ | 8.489 | 0.47 |
5p | 8.779 | 0.88 |
IE (11a1) = 12.04 eV11 | ||
3s | 8.004 | 1.16 |
Assignment . | Energy (eV) . | δ . |
---|---|---|
IE (1a2) = 8.874 eV12 | ||
3p | 5.992 | 0.83 |
3p/3d | 6.157 | 0.76 |
3px | 6.909 | 0.37 |
4p | 7.619 | 0.71 |
4px | 7.793 | 0.45 |
5p | 8.190 | 0.54 |
5px | 8.221 | 0.44 |
6px | 8.434 | 0.44 |
7px | 8.560 | 0.42 |
8px | 8.636 | 0.44 |
9px | 8.688 | 0.45 |
10px | 8.725 | 0.44 |
IE (3b1) = 9.58 eV11 | ||
3p | 6.604 (6.686) | 0.86 (0.83) |
3p′ | 7.419 | 0.49 |
4p | 8.319 | 0.71 |
4p′ | 8.489 | 0.47 |
5p | 8.779 | 0.88 |
IE (11a1) = 12.04 eV11 | ||
3s | 8.004 | 1.16 |
Vibrational modes of thiophene. Also shown are vibrational energy shifts (ΔE) observed between the neutral and ionized state configurations.
. | . | C4H4S calculated . | . | C4H4S+ (X 2A2)12 . | |||
---|---|---|---|---|---|---|---|
. | . | Frequency . | Energy . | . | Frequency . | Energy . | ΔE . |
Mode . | Symmetry . | (cm−1) . | (meV) . | Expt. (meV)53,54 . | (cm−1) . | (meV) . | (meV) . |
ν1 | A1 | 3144 | 390 | 388 | |||
ν2 | A1 | 3107 | 385 | 384 | |||
ν3 | A1 | 1394 | 173 | 175 | 1505 | 187 | 12 |
ν4 | A1 | 1350 | 167 | 169 | 1307 | 162 | −7 |
ν5 | A1 | 1068 | 132 | 134 | 1117 | 138 | 4 |
ν6 | A1 | 1020 | 126 | 128 | 1050 | 130 | 2 |
ν7 | A1 | 813 | 101 | 104 | |||
ν8 | A1 | 595 | 74 | 75 | 602 | 75 | 0 |
ν9 | A2 | 904 | 112 | 111 | |||
ν10 | A2 | 682 | 85 | 85 | |||
ν11 | A2 | 564 | 70 | 70 | 463 | 57 | −13 |
ν12 | B1 | 871 | 108 | 107 | |||
ν13 | B1 | 709 | 88 | 88 | |||
ν14 | B1 | 448 | 56 | 56 | 372 | 46 | −10 |
ν15 | B2 | 3141 | 389 | 387 | |||
ν16 | B2 | 3094 | 384 | 384 | |||
ν17 | B2 | 1500 | 186 | 187 | 1342 | 166 | −21 |
ν18 | B2 | 1240 | 154 | 156 | 1260 | 156 | 0 |
ν19 | B2 | 1070 | 133 | 135 | 965 | 120 | −15 |
ν20 | B2 | 852 | 106 | 108 | 841 | 104 | −4 |
ν21 | B2 | 728 | 90 | 93 | 483 | 60 | −33 |
. | . | C4H4S calculated . | . | C4H4S+ (X 2A2)12 . | |||
---|---|---|---|---|---|---|---|
. | . | Frequency . | Energy . | . | Frequency . | Energy . | ΔE . |
Mode . | Symmetry . | (cm−1) . | (meV) . | Expt. (meV)53,54 . | (cm−1) . | (meV) . | (meV) . |
ν1 | A1 | 3144 | 390 | 388 | |||
ν2 | A1 | 3107 | 385 | 384 | |||
ν3 | A1 | 1394 | 173 | 175 | 1505 | 187 | 12 |
ν4 | A1 | 1350 | 167 | 169 | 1307 | 162 | −7 |
ν5 | A1 | 1068 | 132 | 134 | 1117 | 138 | 4 |
ν6 | A1 | 1020 | 126 | 128 | 1050 | 130 | 2 |
ν7 | A1 | 813 | 101 | 104 | |||
ν8 | A1 | 595 | 74 | 75 | 602 | 75 | 0 |
ν9 | A2 | 904 | 112 | 111 | |||
ν10 | A2 | 682 | 85 | 85 | |||
ν11 | A2 | 564 | 70 | 70 | 463 | 57 | −13 |
ν12 | B1 | 871 | 108 | 107 | |||
ν13 | B1 | 709 | 88 | 88 | |||
ν14 | B1 | 448 | 56 | 56 | 372 | 46 | −10 |
ν15 | B2 | 3141 | 389 | 387 | |||
ν16 | B2 | 3094 | 384 | 384 | |||
ν17 | B2 | 1500 | 186 | 187 | 1342 | 166 | −21 |
ν18 | B2 | 1240 | 154 | 156 | 1260 | 156 | 0 |
ν19 | B2 | 1070 | 133 | 135 | 965 | 120 | −15 |
ν20 | B2 | 852 | 106 | 108 | 841 | 104 | −4 |
ν21 | B2 | 728 | 90 | 93 | 483 | 60 | −33 |
A. Band I (5.0–6.55 eV)
In Band I, we see a broad spectral feature (see Fig. 2), overlayed with a large number of vibrational progressions that are detailed in Table II. The photoabsorption cross section in this region has significant intensity, peaking at 19.8 Mb. Analysis of this region indicates that 8 progressions of the ν6 vibrational mode are prominent in this band, with the average ν6 vibrational spacing being 120 meV. Our calculations suggest that there are two prominent ππ* electronic transitions, lying close in energy and with comparable oscillator strengths (f), that may contribute to this feature. These transitions are dominated by HOMO-LUMO and (HOMO-1)-LUMO promotions in the 1B2 [1a2 → 4b1] (5.67 eV) and 1A1 [3b1 → 4b1] (5.75 eV) states, respectively. The existence of two-closely lying and comparable intensity electronic features may explain the high density of ν6-progressions observed in this region. This observation is consistent with previous high level calculations, also placing these two electronic transitions within 0.3 eV of each other and with comparable optical oscillator strengths.19 The vertical S0-S1 band origin has been previously identified at 5.157 eV, see Palmer et al.18, while the lower energy bands are associated with hot bands, sequence bands, and S0-S2 transitions (possible origin at 5.051 eV) accessible through a Franck-Condon overlap.5 The complexity in the vibronic structure makes further refinement of the spectroscopic features in this region difficult such that we label each ν6-progression identified.
The VUV photoabsorption cross section for thiophene in the 5.0–5.9 eV range.
On the higher energy side of this band (Fig. 3), we observe a single progression of the ν8 mode (72 meV spacing) in a 1B1 [1a2 → 3p] Rydberg state excitation (5.992 eV). A second 1B1 [1a2 → 3p/3d] Rydberg state (6.157 eV) is also located in this energy region. This state appears with 5 progressions of the ν14 mode, with an average spacing of 50 meV. At around 6.3 eV, we see a change in the peak profile and a shift in vibrational spacing towards 46 meV, suggesting a broadening of the potential energy surface. The Rydberg states are discussed in more detail below.
The VUV photoabsorption cross section for thiophene in the 5.90–6.55 eV range.
B. Band II (6.55–7.70 eV)
This broad spectral feature is shown in detail in Fig. 4, with the observed spectral features being summarized in Table III. The absorption in this region is very strong, with the maximum cross section intensity being 66.9 Mb. The structural features observed above this feature are also broad and originate as a part of the Rydberg (1a2)−1 and (3b1)−1 series. The Rydberg states display a significant vibrational structure and are discussed in more detail below. The broad underlying feature originates from ππ* excitations. These excitations are reflected in the TDDFT calculation through two states, 1A1 [1a2 → 2a2] at 7.22 eV (f = 0.256) and 1B2 [3b1 → 2a2] at 7.41 eV (f = 0.088). Our calculations are again consistent with the higher level calculation of Holland et al.19 with regard to the energy ordering, separation, and intensity of these two electronic features. In our calculation, the 1A1 state displays mixing between the 1ππ* (1a2 → 2a2) and Rydberg (1b1 → 3p) configurations. We believe that this mixing leads to the resonance-like structure observed at the high energy side of this feature, with the TDDFT calculation providing an additional 1A1 [1b1 → 5b1(3px)] Rydberg state, 7.49 eV (f = 0.053). As both of these systems have contributions from the [1b1 → 5b1(3px)] configuration, there may be avoided crossings in this energy region to produce the rapid rises and falls in the photoabsorption intensities.
The VUV photoabsorption cross section for thiophene in the 6.5–7.7 eV range. See the text for further details.
The VUV photoabsorption cross section for thiophene in the 6.5–7.7 eV range. See the text for further details.
C. Bands III—V (7.70–8.9 eV; 8.9–9.5 eV; 9.5–10.7 eV)
Band III (7.70–8.9 eV) of the photoabsorption spectrum is dominated by a large number of sharp, well-resolved spectral lines that correspond to Rydberg transitions (discussed in detail below), which are shown in detail in Fig. 5. The spectral assignments in this energy region are contained in Table IV. These Rydberg transitions lie above a weak constant background intensity relating to absorption, although the present calculation does not reveal any underlying valence excitations within the region that this can be attributed to. In band IV (8.9–9.5 eV), we observe a broad, relatively structure-less feature. In this region, we expect that photoionization to the (1a2)−1 state begins to dominate the spectrum and so reduces the observable structures within the region. Here the maximum photoabsorption cross section peaks at 66.8 Mb. Significant cross section intensity is also maintained in region V (9.5–10.7 eV). Here the cross section tends to increase with increasing photon energy, although it does reveal some broad structures above the underlying strong absorption cross section. We expect region V to be dominated by photoionization processes, including the opening of the (3b1)−1 ionization channel. The observed structures may also have origins as higher members of the (11a1)−1 Rydberg series.
The VUV photoabsorption cross section for thiophene in the (a) 5.80–10.20 eV and (b) 7.75–8.85 eV ranges. See the text for further details.
The VUV photoabsorption cross section for thiophene in the (a) 5.80–10.20 eV and (b) 7.75–8.85 eV ranges. See the text for further details.
D. Rydberg series
The photoabsorption spectrum of thiophene displays strong and well–resolved features across bands I-V relating to the Rydberg states converging to the (1a2)−1, (3b1)−1, and (11a1)−1 cation states. Each of these Rydberg progressions also displays a significant vibrational structure in addition to the main spectral features (see Tables II–IV). The primary Rydberg features have been analyzed in terms of their quantum defects, with the results summarized in Table V. The ionization energies used to perform the Rydberg quantum defect analysis are experimental values obtained from photoelectron spectroscopy experiments.11,12 Palmer et al.18 and Holland et al.19 have previously provided tentative assignments to many of the observed Rydberg transitions. We therefore pay particular attention to cases where our present assignments may differ from the previously reported values.
Holland et al.19 had previously assigned the first Rydberg state at 5.992 eV to a vibronically induced [1a2 → 3s] 1A2 transition, with a forbidden adiabatic threshold at 5.88 eV (δ = 0.87). Palmer et al. also tentatively assigned this feature in this way, noting that the transition was likely Rydberg in nature as it was not observed in condensed phase spectra. They further noted that the assignment to the [1a2 → 3s] 1A2 transition was complex as it did not exhibit the vibrational structure reminiscent of the photoelectron spectrum for the (1a2)−1 state.18 Following our TDDFT calculation, we therefore propose that this 5.992 eV feature should be assigned to a 1B1 [1a2 → 8b2(3p)] state [5.80 eV, f = 0.012] which is dipole-allowed, but not particularly strong. In this case, a larger quantum defect of 0.83 is observed, reflecting the mixing between the σ*/3p characters. Also, as thiophene contains a larger group 3 element (sulphur), we may expect that the observed quantum defects increase compared to species that contain elements from only groups 1 and 2. We also provide an assignment for the [1a2 → 9b2(3p/d)] 1B1 state at 6.157 (δ = 0.76) which has previously been unassigned. Here we expect a mixing between the 3p/d Rydberg characters. The higher members of this Rydberg progression are less mixed, and the quantum defect reduces to 0.71 and 0.54 for 4p and 5p states, respectively. The intense vibronic structure at 6.909 eV is also assigned as a member of the (1a2)−1 Rydberg series, with the quantum defect δ = 0.37. This intense feature is assigned to a 1B2 [1a2 → 5b1(px)] state, supported by our TDDFT calculation that indicates the existence of a 1B2 state at 6.98 eV (f = 0.069). Here the planar nature of thiophene leads to a significant energy splitting between in-plane (py, pz) and out-of-plane (px) Rydberg states, owing to the ability of the in-plane states to mix atomic orbital contributions. As such, the out-of-plane (npx) states display a lower quantum defect (minimum penetration of the orbital into the nuclei) compared to the in-plane npy,z/d states. The 1B2 [1a2 → 5b1(px)] state is the most intense feature of the (1a2)−1 Rydberg series, and the higher npx series members up to n = 10 are assigned in the 7.7–8.8 eV range. These npx features all yield quantum defects in the 0.37–0.45 range. We believe that the consistent quantum defects observed for all of the npx members provide confidence in the present assignments, as earlier quantum defects exhibited a broader range between 0.048 and 0.55 and were also assigned in conjunction with nd states which appeared with a larger range of quantum defects. In addition, the present vibrational progressions originating from these transition origins are consistent with the prominent vibrational features observed in the (1a2)−1 zero-kinetic energy photoelectron spectra.12 Finally, we note that no Rydberg [1a2 → ns] series is observed.
Holland et al.19 assigned a ν8 vibrational progression of the 1B2 [1a2 → 3p] state, with a band origin at 6.603 eV (δ = 0.552). Our TDDFT calculation yields a 1B1 [3b1 → 3p] state at 6.65 eV (f = 0.028). We therefore assign this feature to a 1B1 [3b1 → 3p] state (δ = 0.86). Our theoretical calculations, and the more sophisticated calculations in Holland et al., are consistent in that the 1B1 [3b1 → 3p] and 1B2 [1a2 → 3p] states lay close in energy. They also agree in that the intensity of the 1B2 state should be larger than that of the 1B1 state. Higher members of this Rydberg series are observed with comparable quantum defects and spectral intensities. We believe that the consistent quantum defects observed over the range of np spectral features in both the (1a2)−1 and (3b1)−1 Rydberg series support the present assignment, over the earlier assignment. We also note that the assignment of the band origin is also complicated, and we tentatively assign it at 6.603 eV, noting that the true origin may be 6.686 eV. Here the most intense feature lies at 6.686 eV, being 82 meV above the feature at 6.603 eV. Holland et al. assigned both features as a part of the ν8 progression, but the 82 meV energy difference found exceeds the 72–75 meV energy spacing observed for the ν8-vibration in the ground and cationic states. Furthermore, and as noted by Holland et al.,19 the spacing between the higher ν8-vibrational series members of this band is 73 meV. As such, we tentatively assign this feature at 6.686 eV to either a ν10/ν13 excitation from the 6.603 eV origin. Here we also assign other states in the vibrational progressions (originating from either the ground or ν10/ν13 modes) that are consistent with the vibrational features observed in the photoelectron spectra and the prominent features in the threshold photoelectron spectrum. This provides additional support for the refined vibrational assignments proposed in this region.
Our TDDFT calculation reveals a 1A1 [11a1 → 12a1 (3s)] state with excitation energy 8.54 eV and a considerable optical oscillator strength, f = 0.077. We therefore assign the feature at 8.004 eV (δ = 1.16) to the 1A1 [11a1 → 3s] transition. While this quantum defect is larger than may be expected for a 3s Rydberg state, we believe it is reasonable as greater penetration of the nuclei is expected with the presence of elemental sulphur. Holland et al. had previously assigned this intense feature to a 1A1 [1a2 → a2 (4d)] state (δ = 0.048), although no [1a2 → 3d] series member is observed. We therefore believe that our assignment of this feature offers a more correct physical picture of the Rydberg state excitations.
Finally, many of the features associated with the [1a2 → np], [1a2 → npx], and [11a1 → 12a1 (3s)] Rydberg transitions also display bands associated with sequence transitions (see Tables III and IV). Some states are assigned to sequence transitions associated with either the ν14/ν21 modes. The intensity observed for these spectroscopic features (see Fig. 5) is commensurate with the expected populations of both of these vibrational modes at room temperature. Here the assignment to the ν21 mode occurs as its frequency is known to change significantly between the ground and first cationic electronic states and is in agreement with the changes observed in the excited state sequence structure.
IV. CONCLUSIONS
We have reported a new absolute photoabsorption cross section measurement of thiophene over the 5.0 to 10.7 eV range. The absolute values of the present measured cross sections were found to be in good accord with earlier studies where their energies overlapped. Our experiments were supplemented by theoretical calculations performed at the time-dependent density functional theory level. These calculations facilitated new spectral assignments of the thiophene spectrum and a Rydberg state analysis. These assignments supersede earlier interpretations of the absorption spectrum and enable a more self-consistent assignment of the complete spectrum.
ACKNOWLEDGMENTS
This work was partly supported by the Australian Research Council Grant Nos. DP160102787 and DP180101655. M.M. and F.F.d.S. acknowledge the Portuguese National Funding Agency FCT through Grant No. PD/BD/106038/2015 and the Researcher Contract No. IF-FCT IF/00380/2014, together with P.L.-V. the Research Grant Nos. UID/FIS/00068/2013, PTDC/FIS-AQM/31215/2017, and PTDC/FIS-AQM/31281/2017. This work was also supported by Radiation Biology and Biophysics Doctoral Training Programme (RaBBiT, No. PD/00193/2010); No. UID/Multi/04378/2013 (UCIBIO). The beam time awarded at the ASTRID2 synchrotron facility for this work was supported by the project CALIPSOplus under Grant Agreement No. 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020.