An experimental and theoretical investigation into the excited electronic states of phenol.

An experimental and theoretical investigation into the excited electronic states of phenol D. B. Jones, G. B. da Silva, R. F. C. Neves, H. V. Duque, L. Chiari, E. M. de Oliveira, M. C. A. Lopes, R. F. da Costa, M. T. do N. Varella, M. H. F. Bettega, M. A. P. Lima, and M. J. Brunger Citation: The Journal of Chemical Physics 141, 074314 (2014); doi: 10.1063/1.4893116 View online: http://dx.doi.org/10.1063/1.4893116 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A study of electron scattering from benzene: Excitation of the 1B1u , 3E2g , and 1E1u electronic states J. Chem. Phys. 134, 134308 (2011); 10.1063/1.3575497 Benchmarks for electronically excited states: Time-dependent density functional theory and density functional theory based multireference configuration interaction J. Chem. Phys. 129, 104103 (2008); 10.1063/1.2973541 Interaction of low-energy electrons with linear diphenylethynyl derivatives in the gas phase J. Chem. Phys. 127, 084316 (2007); 10.1063/1.2772617 The triplet state of cytosine and its derivatives: Electron impact and quantum chemical study J. Chem. Phys. 121, 11668 (2004); 10.1063/1.1812533 Electronic excitation spectrum of thiophene studied by symmetry-adapted cluster configuration interaction method J. Chem. Phys. 114, 842 (2001); 10.1063/1.1332118

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THE JOURNAL OF CHEMICAL PHYSICS 141, 074314 (2014)

An experimental and theoretical investigation into the excited electronic states of phenol D. B. Jones,1 G. B. da Silva,1,2 R. F. C. Neves,1,3,4 H. V. Duque,1,3 L. Chiari,1,a) E. M. de Oliveira,5 M. C. A. Lopes,3 R. F. da Costa,6 M. T. do N. Varella,7 M. H. F. Bettega,8 M. A. P. Lima,5 and M. J. Brunger1,9,b) 1

School of Chemical and Physical Sciences, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia Universidade Federal de Mato Grosso, Barra do Garças, Mato Grosso, Brazil 3 Departamento de Física, UFJF, Juiz de Fora, MG, Brazil 4 Instituto Federal do Sul de Minas Gerais, Campus Poços de Caldas, Minas Gerais, Brazil 5 Instituto de Física “Gleb Wataghin,” Universidade Estadual de Campinas, 13083-859 Campinas, São Paulo, Brazil 6 Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-580 Santo André, São Paulo, Brazil 7 Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970 São Paulo, Brazil 8 Departamento de Física, Universidade Federal do Paraná, CP 19044, 81531-990 Curitiba, Paraná, Brazil 9 Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia 2

(Received 18 July 2014; accepted 4 August 2014; published online 20 August 2014) We present experimental electron-energy loss spectra (EELS) that were measured at impact energies of 20 and 30 eV and at angles of 90◦ and 10◦ , respectively, with energy resolution ∼70 meV. EELS for 250 eV incident electron energy over a range of angles between 3◦ and 50◦ have also been measured at a moderate energy resolution (∼0.9 eV). The latter spectra were used to derive differential cross sections and generalised oscillator strengths (GOS) for the dipole-allowed electronic transitions, through normalization to data for elastic electron scattering from benzene. Theoretical calculations were performed using time-dependent density functional theory and single-excitation configuration interaction methods. These calculations were used to assign the experimentally measured spectra. Calculated optical oscillator strengths were also compared to those derived from the GOS data. This provides the first investigation of all singlet and triplet excited electronic states of phenol up to the first ionization potential. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4893116] I. INTRODUCTION

The conversion of renewable biomass into biofuels offers a path to address global energy demand in a sustainable manner.1 However, biomass recalcitrance represents a significant challenge in making the de-polymerization of biomass into fermentable sugars cost-effective.1, 2 It has been demonstrated that free-electrons or radical species formed within plasmas have the potential to overcome biomass recalcitrance to yield high value chemicals.3–6 This has renewed interest in the electronic structure of biomass subunits, in view of identifying efficient mechanisms to induce chemical break down. In particular, low-energy electrons produced in plasma-like environments have significant potential to induce chemical breakdown through dissociative electron attachment and electronimpact excitation- or ionization-fragmentation processes.7 Phenol (C6 H5 OH) represents a key structural subunit of lignin, and is therefore an ideal target for potential electroninduced damage to complex biomolecules. Specifically, phenol is known to exhibit conical intersections that enable it to efficiently fragment following photo-excitation.8–12 This phenomenon, combined with phenol being a chromophore a) Present address: Department of Physics, Tokyo University of Science, 1-3

Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan.

b) Author to whom correspondence should be addressed. Electronic mail:

[email protected] 0021-9606/2014/141(7)/074314/8/$30.00

of amino acids,13 has made the electronic structure of phenol the subject of several studies.10, 11 However, to the best of our knowledge, a complete investigation of the singlet- and triplet-excited states of phenol, up to its first ionization potential, is missing. This is a prerequisite to improving and understanding plasma- or electron-driven processes targeting phenol-derivatives in biomass14 or hazardous organic material degradation.15–17 In the present study, we perform electron-impact experiments on phenol to obtain electron energy loss spectra. Here, we perform low-energy, E0 = 20 or 30 eV, highresolution electron-impact excitation experiments where the electron scatters at either θ = 90◦ or 10◦ , respectively, to provide a detailed assignment of the singlet and triplet states of phenol. Additional lower-resolution electron energy loss spectra are measured for an incident electron energy of E0 = 250 eV over the θ = 3◦ –50◦ angular range. These electron energy loss spectra are converted into differential cross sections (DCS) for electron-impact excitation to facilitate the determination of the generalised and optical oscillator strengths for the dipole-allowed transitions. These latter experiments are supplemented with theoretical calculations to provide a quantitative assessment of the singlet and triplet states of phenol. The structure of this paper is as follows. In Sec. II, we describe our experimental method, while in Sec. III details

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of our theoretical electronic structure calculations are given. The present results pertaining to the spectroscopy of phenol are provided in Sec. IV, while a discussion of our differential cross sections and optical oscillator strengths is presented in Sec. V. Finally, some conclusions from this investigation are given.

GOSi0 =

II. EXPERIMENTAL METHOD

Electron energy loss spectra have been measured using two different electron scattering spectrometers at low or intermediate incident electron energy. Both of these spectrometers have been described previously,18, 19 although we do note that the energy resolution of the low-energy apparatus is typically ∼70 meV, full width at half maximum (FWHM), while that for the intermediate-energy apparatus is typically ∼0.9 eV (FWHM). The underlying features of those spectrometers are common to both experiments, and are now briefly described. Here, a well-collimated electron beam, with a well-defined energy spread, is incident on an orthogonal beam of phenol molecules. In this case the phenol beam is prepared by heating a phenol sample (T∼35 ◦ C–45 ◦ C) and allowing the vapour from that sample to enter the collision region through a needle. Here, the vapour flow was regulated using a variable leakvalve. Note that the phenol sample (Ajax Unilab/GPR-BDH; >99% assay) had been degassed through repeated freezepump-thaw cycles. Electrons with a well-defined energy and momentum (E0 , k0 ) that scatter from the phenol molecules through an angle, θ , referenced to the incident beam direction, enter a hemispherical analyser where they are energy analysed. Electrons with the correct scattered energy (Ea ) are then detected using a channel-electron multiplier. This defines the energy loss of the scattered electron, EL = E0 − Ea .

(1)

Energy loss spectra at each incident electron energy and scattering angle are accumulated by recording the number of electrons detected while repeatedly scanning over a range of energy-loss values. The incident electrons that scatter through an angle, θ , with a particular energy loss (EL ) have momentum (ki ) that defines the momentum transferred to the target in the excitation process K = k0 − ki .

(2)

Each energy loss spectrum is de-convolved into individual components by fitting Gaussian functions to the observed spectral features. The ratio of the areas contained within the inelastic (Ai ) and elastic features (A0 ) is directly proportional to the ratio of the differential cross sections for the inelastic process, σ i (E0 , θ ), and the elastic scattering process, σ 0 (E0 , θ ), at that incident energy and scattering angle. The inelastic cross section can then be obtained if the elastic scattering cross section is known, and the relative analyser response calibrated, through σi (E0 , θ ) =

Ai σ (E , θ ). A0 0 0

Note that the energy loss spectra measurements are repeated between 2 and 5 times to ensure reproducibility in the derived differential cross sections. The measured differential cross sections can then be converted into generalised oscillator strengths (in atomic units) through the standard formula20

(3)

k 1 EL i K 2 σi (E0 , θ ). 2 k0

(4)

The properties of the generalised oscillator strengths (GOS)20, 21 have led to the following analytic formula being proposed22 for the structure of a dipole-allowed transition: GOS(x) =

∞ fm x m 1 . (1 + x)6 m=0 (1 + x)m

(5)

In Eq. (5), x = K2 /α 2 , and α and fm are fitting coefficients determined using a least-squares procedure. This functional form is particularly useful in that the f0 coefficient approximates the optical oscillator strengths (OOS). This procedure has proved useful in determining OOS for a number of other molecular targets.23–25 III. THEORETICAL METHODS

Quantum chemical calculations have been performed within a minimal orbital basis–single configuration interaction (MOB-SCI) framework.26 Here, the MOB-SCI calculations form the basis of electron scattering cross section calculations that require a minimal basis set to become tractable. In order to assess the limitation of the quantum chemical model for the electron scattering calculations, full singleconfiguration interaction (Full SCI) calculations were also performed using the same basis set. Five singlet and seven triplet states lying below 7 eV are represented in the MOBSCI framework with similar quality to that obtained in the Full SCI calculation. These electronic structure calculations were conducted in the GAMESS suite of programs27 using the same geometry and Cartesian Gaussian basis that was adopted to obtain elastic cross sections for the phenol molecule in a previous study.14 Owing to the high computational cost of CI methods used to describe target states in scattering calculations, only a small set of states is recovered from these calculations. In fact, only 16 singlet excited states, 5 very close to the Full SCI states lying below 7 eV and 11 pseudo states above this energy, and 16 triplet states, 7 very close to the Full SCI states lying below 7 eV and 9 pseudo states above this energy, were obtained by a judicious choice of 16 pairs of one hole-one particle single excitations within the MOB-SCI approach. In order to provide a complete interpretation of the excited electronic states, additional calculations were performed using time-dependent density functional theory (TD-DFT)28, 29 with the Becke 3-parameter Lee, Yang and Parr functional and Dunning’s augmented correlation consistent valence double zeta basis set (B3LYP/aug-ccpVDZ).30–32 These calculations were performed within Gaussian 09.33 To check the quality of this method for describing the electronic structure of phenol, additional calculations were performed for benzene, which can be considered as


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the parent molecule of phenol, using the same model chemistry. These calculations for benzene were found to yield excitation energies and oscillator strengths that were consistent with previous experimental measurements25, 34 and theoretical calculations.35, 36 This provides us with confidence that the TD-DFT calculation can provide a reasonable description of the excited electronic state behaviour of phenol.

1.0

(a) E0=20 eV, θ=90o

IV

0.5

V III

II

I

Phenol has Cs symmetry, and resides in a, X1 A [(1a ) (2a ) (3a ) (4a ) (5a ) (6a ) (7a ) (8a ) (9a ) 2

2

2

2

2

2

2

2

(10a ) (11a ) (12a ) (13a ) (14a ) (15a ) (16a ) (17a ) 2

2

2

2

2

2

2

2

2

(18a ) (1a ) (19a ) (20a ) (21a ) (2a ) (3a ) (4a ) ], 2

2

2

2

2

2

2

2

ground electronic state.37 In Figure 1, we present our measured electron energy loss spectra. Here, spectra are presented for the following different kinematical condition; (a) low energy (E0 = 20 eV) and a large scattering angle (θ = 90◦ ); (b) low-energy (E0 = 30 eV) and a small scattering angle (θ = 10◦ ); and (c) intermediate-energy (E0 = 250 eV), and a small scattering angle (θ = 10◦ ). In Fig. 1(a), the low incident electron energy and large scattering angle allows dipole-forbidden excitations to have comparable intensities to dipole-allowed excitations. This is in contrast to Figs. 1(b) and 1(c) where the small scattering angle mimics a dipole-induced transition, and the spectrum is dominated by dipole-allowed excitations. In particular, we note the exceptional qualitative agreement obtained between the present spectra obtained in Figs. 1(b) and 1(c), to an earlier electron-energy loss spectrum measurement at E0 = 70 eV, θ = 0◦38 and a photo absorption spectrum.39 In order to assign the excited state spectra of phenol, calculations have been performed at the MOB-SCI, Full-SCI, and TD-DFT levels. The detailed summary of our experimentally observed and theoretically assigned bands is contained in Table I. The spectroscopic assignments of each experimentally observed band are now discussed in more detail. First, in Fig. 1(a), we see a band at EL ∼ 3.4–4.3 eV (Band I) that is prominent under the E0 = 20 eV, θ = 90◦ scattering condition, but is extremely weak under the other kinematical conditions studied. This is characteristic of dipole-forbidden singlet-triplet excitations. Here, both the TD-DFT and CI calculations are in good agreement that there are two low-lying triplet states located within this experimental band. Note that the existence of triplet state(s) in this region is independently supported by a phosphorescence measurement of phenol.40 The second experimental feature (Band II) is located in the EL ∼ 4.3–5.4 eV range. Both the TD-DFT calculation and CI calculations support the assignment of this Band II to a weak dipole-allowed π π * transition, and a number of other dipole-forbidden or extremely weak dipole-allowed transitions. Note that the line profile for this band changes with the experimental kinematical conditions. This suggests that in addition to the singlet states, there is an underlying triplet state(s) in this band. All of our theoretical calculations support this notion, with 3 triplet states being predicted in this energy

Intensity (Arb. Units)

0.0

IV. SPECTROSCOPY OF PHENOL

1.0

(b) E0=30 eV, θ=10o

IV

0.5

III

II

V

0.0 1.0

(c) E0=250 eV, θ=10o

IV

III

0.5

II 0.0 3

4

5

6

7

8

9

Energy Loss (eV) FIG. 1. Typical electron energy loss spectra measured at (a) E0 = 20 eV, θ = 90◦ ; (b) E0 = 30 eV, θ = 10◦ ; and (c) E0 = 250 eV, θ = 10◦ . The overall spectral deconvolution is shown by the solid line (—). Fits for the individual spectral features (i.e., Bands I–V) are denoted by dashed lines (– –). See text for further detail.

loss region. We note that both the MOB-SCI and Full-SCI calculations overestimate the majority of the excitation energies, except for the first triplet state for which that energy is underestimated. The MOB-SCI and Full-SCI state assignments are therefore based on the dominant one-hole one-particle configurations. The states in Band II have attracted significant interest as the observed dipole-allowed 1 A (π π *) transition couples to the weakly-allowed 1 A (π σ *) state through a conical intersection. The 1 A state proceeds to photo-dissociate along an OH reaction coordinate owing to the anti-bonding character of the OH bond.8–12, 41, 42 The dominant ground state occupied and virtual orbitals obtained at the B3LYP/aug-ccpVDZ level for these states are shown in Fig. 2. Interestingly, the symmetry-breaking addition of the OH group to benzene energetically splits the aromatic π * virtual orbitals, which are further separated by a σ * virtual orbital. It is therefore not surprising that the potential energy surface of phenol displays conical intersections that enable efficient radiationless transitions between excited states. The characterisation of electronimpact excitation of this experimental band is therefore particularly important in assessing the potential of electron-driven degradation of phenolic species, such as lignin. Band III in the EL ∼ 5.4–6.3 eV range is also dominated by dipole-allowed excitations. Here both the TD-DFT


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TABLE I. Experimental and calculated excitation energies, assignments, dominant configurations, and optical oscillator strengths (f0 ). TD-DFT Band I

Expt. energy (eV)

State

3.4–4.3

3 A 3 A

II

4.3–5.4

3 A 1 A 3 A 1 A 3 A

III

5.4–6.3

3 A 1 A 1 A 3 A 1 A 3 A 1 A 3 A

IV

6.3–7.3

1 A 3 A 1 A 3 A 1 A 3 A 1 A 1 A 1 A 3 A 3 A 3 A 1 A 1 A 3 A 1 A 3 A 3 A 1 A 3 A 3 A

V

7.3–8.6

1 A 1 A 3 A 3 A

Energy (eV)

MOB-SCI

Dominant excitation(s)

f0

Full-SCI

Energy (eV)

f0

Energy (eV)

f0

3.71 4.10

3a →5a ; 4a →6a 4a →5a

0 0

3.57 4.73

0 0

3.29 4.49

0 0

4.53 4.99 5.06 5.13 5.30

3a →5a ; 4a →6a 3a →6a ; 4a →5a 4a →22a 4a →22a 3a →6a

0 0.0312 0 0.0001 0

4.90 6.09 6.16 6.21 6.03

0 0.0248 0 0.0001 0

4.78 5.82 5.94 6.06 5.73

0 0.0381 0 0.0001 0

5.53 5.57 5.76 5.90 5.92 5.95 5.98 6.27

4a →23a 4a →23a 3a →5a ; 4a →6a 3a →22a ; 4a →24a 4a →24a 3a →22a ; 4a →24a 3a →22a 4a →25a

0 0.0034 0.0328 0 0 0 0.0021 0

6.78 6.86 6.80 6.92

0 0.0274 0.0031 0

6.53 6.68 6.12 6.73

0 0.0177 0.0025 0

6.99

0

6.86

0.0020

6.31 6.32 6.35 6.52 6.54 6.63 6.66 6.66 6.71 6.84 6.85 6.93 6.93 7.01 7.07 7.08 7.11 7.19 7.22 7.27 7.29

4a →25a 3a →23a 3a →23a 4a →26a 4a →26a 3a →24a 3a →6a 3a →24a 3a →5a ; 4a →6a 4a →27a ; 4a →28a 2a →5a 4a →7a 4a →27a ; 4a →28a 4a →7a 3a →25a 3a →25a 2a →6a 4a →27a ; 4a →28a 4a →27a ; 4a →28a 21a →5a 3a →26a

0.0115 0 0.0010 0 0 0 0.3744 0.0202 0.5827 0 0 0 0.0009 0.0148 0 0 0 0 0.0005 0 0

7.32 7.57 7.58 7.59

3a →26a 21a →5a 4a →29a 3a →27a ; 3a →28a

0.0002 0.0043 0 0

and CI calculations give weak spectral intensities to the 1 A and 1 A states. Indeed the calculated oscillator strength from states recovered in this energy-loss region is significantly below that expected, in relation to that observed experimentally for Bands II and IV. Here, we note that similar behaviour is observed for benzene in that the vertical excitation process is weak. In benzene, however, it has been revealed that the geometric perturbations which accompany the vibrational motion significantly enhance the π π * transition. This point will be discussed further in relation to the experimentally derived oscillator strengths. In the EL ∼ 6.3–7.3 eV energy loss range, corresponding to Band IV, we observe a strong band relating to the π π * transition associated with the aromatic ring. Here, the addition

of the OH group only gives rise to a small energetic splitting of the two 1 A states. The calculated excitation energy values obtained with the TD-DFT calculation are consistent with the experimental observations in that no noticeable energy splitting is observed. Finally, significant experimental intensity is observed in the EL ∼ 7.3–8.6 eV range (Band V). This region is mostlikely dominated by a large number of Rydberg-like excitation processes leading up to the first ionization potential (IP = 8.64 eV37 ). Here, a number of Rydberg like excitations have been predicted using a 2nd order perturbation correction to a complete active space self-consistent field (CASSCF) calculation.36 The present energy resolution at the lower energies (E∼70 meV) does not allow for a more quantitative


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E0=250eV Phenol Benzene (elastic) EL=4.3-5.4eV IA M-SE P (x0.653) IA M-SE P EL=5.4-6.3eV Expt EL=6.3-7.3eV

Cross Section (10-16cm2/sr)

1000

-1)

100

10

1

0.1

0.01

1E-3 0

10

20

30

40

50

60

Angle (degrees) FIG. 3. Electron-impact differential cross sections at E0 = 250 eV. (♦) Experimental, (- - -) theoretical, and (—) re-scaled theoretical elastic scattering cross sections from benzene; adapted from Ref. 49: () excitation to Band II (EL = 4.3–5.4 eV) of phenol, (●) excitation of Band III (EL = 5.4–6.3 eV) of phenol, and () excitation of Band IV (EL = 6.3–7.3 eV) of phenol. See text for further details.

FIG. 2. Diagrammatic representation of the dominant molecular orbitals participating in the ground to excited state transitions in the region of the conical intersection.

assignment of the Rydberg-like transitions. In this respect, a high-resolution photoabsorption study would be particularly useful to fully assess any Rydberg-state progressions in phenol. The present spectroscopic interpretation of singletsinglet transitions is consistent with that from an earlier CASSCF calculation,36 although there are significant differences observed between the CASSCF excitation energies and those obtained experimentally. Finally, we also note that the spectroscopy of phenol displays strong similarities to the triplet and singlet excited states observed for the parent benzene structure25 or benzene analogues, such as pyrimidine.43–45 Those similarities, combined with the extensive studies available for these benzene-related targets, support the present interpretation of the excited states of phenol. V. DIFFERENTIAL CROSS SECTIONS AND OSCILLATOR STRENGTHS FOR EXCITATION PROCESSES

In order to convert energy loss spectra into differential cross sections for excitation processes using Eq. (3), we require absolute elastic scattering differential cross sections. To the best of our knowledge, no experimental or theoretical elastic scattering differential cross data have been reported for phenol with an incident electron energy of E0 = 250 eV. However, phenol is a mono-substituted derivative of the extensively studied benzene. Further, experimental studies from benzene and the substituted benzenes toluene (C6 H5 CH3 ) and

benzotrifluoride (C6 H5 CF3 ) have revealed that their elastic scattering DCS are very similar in shape and magnitude.46 Additionally, low-energy elastic DCS calculations obtained with the Schwinger multichannel method, performed at the static exchange level, also found the phenol47 and benzene48 cross sections to be similar. In the current absence of elastic differential cross sections from phenol, we therefore use elastic cross section data from benzene. Further justification for the choice of employing the benzene elastic scattering differential cross sections to represent elastic scattering from phenol will appear elsewhere.47 In order to obtain elastic scattering data over the complete angular range of our 250 eV measurements (θ = 3◦ –50◦ ), we use elastic DCS data obtained within an independent atom model static exchangepolarization (IAM-SEP) framework.49 Note that the IAMSEP values have been renormalised to match the available elastic scattering data from benzene in the 10◦ –60◦ range of the experiments. Here, all the 250 eV experimental and theoretical elastic data have been obtained through an averaging of data measured or calculated at 200 and 300 eV. In Fig. 3, we show the excellent agreement between the rescaled IAM-SEP cross sections and the available experimental data.49 The experimental energy loss spectra measured at 250 eV and over the θ = 3◦ –50◦ range are converted, using our spectral deconvolution and Eq. (3), into differential cross sections for electron-impact excitation of dipole-allowed Bands II, III, and IV. These cross sections are plotted and tabulated, together with the elastic scattering cross section, in Fig. 3 and Table II, respectively. Note that the elastic scattering data are also included in Table II to enable a possible rescaling of the experimental excitation data, if reliable experimental or theoretical phenol elastic scattering data were to become available. The cross sections for these excitation bands are all strongly forwarded peaked at the small electron scattering angles. This


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TABLE II. Differential cross sections (10−16 cm2 /sr) for electron-impact elastic and electronic excitation processes in phenol at E0 = 250 eV. See text for details.

Scattered angle (deg) 3 4 5 6 7.5 10 12 15 20 30 40 50 a

Elastic49,a

Band II (EL = 4.3–5.4 eV)

Band III (EL = 5.4–6.3 eV)

Band IV (EL = 6.3–7.3 eV)

σ

σ

σ

σ

σ

σ

σ

σ

419 313 220 148 78 26.4 12.7 6.1 3.27 1.09 0.75 0.38

84 62 44 30 16 5.3 2.5 1.2 0.65 0.22 0.15 0.08

1.8 0.58 0.245 0.174 0.093 0.029 0.018 0.006

1.1 0.27 0.077 0.046 0.070 0.014 0.011 0.005

6.4 3.08 1.39 0.91 0.43 0.172 0.094 0.026 0.016

2.5 0.78 0.38 0.21 0.13 0.040 0.023 0.008 0.007

46 23.3 9.5 4.9 1.98 0.79 0.420 0.201 0.064 0.029 0.012 0.012

13 5.4 2.4 1.1 0.46 0.18 0.094 0.045 0.016 0.007 0.003 0.004

Elastic scattering cross sections have been derived by averaging the IAM-SEP calculations at 200 and 300 eV, then rescaled by a factor of 0.653 to match the experimental data.49

reflects the strong-nature of the dipole-allowed π π * excitation processes characteristic of these excitation bands. These DCS for electron-impact excitation are converted to GOS using Eq. (4). The derived GOS for Bands II, III, and IV are shown in Fig. 4. These GOS have then been fitted using the analytic functional form of the GOS [Eq. (5)],22 with the fits also being shown in Fig. 4. Here, we observe that the qual0.06

(a) EL= 4.3-5.4 eV 0.04

Generalized Oscillator Strength (a.u.)

0.02

0.00

(b) EL= 5.4-6.3 eV

0.16

0.08

0.00

(c) EL= 6.3-7.3 eV

1.2 0.8 0.4 0.0 0.01

0.1

1

10

100

2

K (a.u.) FIG. 4. Experimentally derived generalised oscillator strengths for excitation to (a) Band II (EL = 4.3–5.4 eV), (b) Band III (EL = 5.4–6.3 eV), (c) and Band IV (EL = 6.3–7.3 eV) of phenol. See text for further details.

ity of the fit to each set of the experimental data is excellent. These fits, in the limit of K2 →0, converge to the OOS. The derived OOS are shown in Table III, together with previously measured OOS from photo-absorption spectra.39 Also contained in Table III are calculated OOS obtained by summing up the OOS for states assigned to each experimental band. In the case of the MOB-SCI and Full SCI calculations, we note that in some cases the sum of states is only over those states recovered in the calculation. Here, we note the very good agreement between the present OOS derived within the GOS formalism and those obtained from photo-absorption spectra. This observation independently cross checks the validity of employing the benzene elastic scattering cross sections for the normalisation of the inelastic DCS in this work. The results in Table III do, however, suggest that the present OOS are slightly below those observed from the photo-absorption work, but this might be expected as the incident electron energy of E0 = 250 eV may not be sufficiently large to adequately approach the optical limit.50 Notwithstanding that latter point, in this case, the derived OOS are consistent with those from the previous photoabsorption measurements to within 25%, which is comparable to the uncertainty in the derived DCS/GOS values. Thus, we believe, in this case, that the present OOS are reliable. Now comparing our OOS and the photoabsorption OOS to the calculated values, we see that for Band II the TD-DFT, MOB-SCI, and Full-SCI calculations predict values that are in good agreement with the experimentally determined values. The TD-DFT calculation also provides an optical oscillator strength that is consistent with the experimental value for Band IV. However, in Band III, all of the calculations significantly underestimate the experimentally observed values of the OOS. This behaviour is consistent with experimental and theoretical calculations on the similar excitation band in benzene (1 B1u ).25, 35 In the equilibrium geometry, where the calculations are performed, the π π * transition has a weak optical intensity. The vibrational motion of the target can, however, couple to the excitation process to produce the much larger


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TABLE III. Experimentally-derived and calculated optical oscillator strengths (f0 ). Experimental

Present calculations

Band

EL (eV)

Present

Photo-absorption39

II III IV

4.3–5.4 5.4–6.3 6.3–7.3

0.016 ± 0.003 0.103 ± 0.010 1.068 ± 0.076

0.020 0.132 1.103

a

TD-DFT

MOB-SCI

Full-SCI

0.031 0.038 1.006

0.025 0.031a

0.038 0.020a

Indicates the partial sum over states recovered in the calculation.

OOS observed experimentally.51 Here, we note that for Bands III and IV, the observed oscillator strengths are comparable to those obtained for benzene. For Band II, the symmetry breaking makes the excitation process much more favourable in phenol to that found in benzene. The excellent agreement observed between the photoabsorption OOS and those derived using the GOS approach suggests that in the absence of additional experimental or theoretical electron scattering data, the GOS fit may be utilised to derive differential cross sections for inelastic electron scattering for the dipole-allowed transitions of phenol over an extended energy range.

VI. CONCLUSIONS

In this study, we have obtained experimental electron energy loss spectra measured under different incident electron energies and scattering angle conditions. These spectra enabled a detailed classification of the excited triplet and singlet states. Detailed quantum chemical calculations performed at the TD-DFT level also enabled the first spectral assignments of the excited triplet states of phenol. Experimentally derived differential cross sections for 250 eV impact energy are also presented. These cross sections were utilised to obtain the generalised oscillator strengths for the dipole-allowed transitions. In the optical limit, those derived oscillator strengths were found to be in very good agreement with previous optical oscillator strength measurements from a photoabsorption study and values calculated at the TD-DFT level. The spectroscopic assignments derived from this work will form the basis for interpreting a comprehensive set of electron scattering cross section measurements and calculations that our team is currently undertaking. ACKNOWLEDGMENTS

This research was supported by the Australian and Brazilian Governmental Funding Agencies (ARC, CNPq, and CAPES). D.B.J. thanks the ARC for a Discovery Early Career Researcher Award. G.B.S. and H.V.D. acknowledge financial support from CAPES and Flinders University during their stay in Australia. R.F.C.N. acknowledges CNPq and Flinders for assistance, while M.J.B. thanks CNPq for his “Special Visiting Professor” award. R.F.C.N. and H.V.D. thank the Science without Borders scheme for their opportunity to study in Australia. E.M.O., R.F.C., M.T.N.V., and M.A.P.L. acknowledge financial support from FAPESP. R.F.C., M.T.N.V., M.H.F.B., M.C.A.L., and M.A.P.L. acknowledge financial support from CNPq. We thank Professor Lee and Pro-

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