Correlation effects in the valence ionization spectra of large conjugated molecules: p-Benzoquinone, anthracenequinone and pentacenequinone

Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

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Correlation effects in the valence ionization spectra of large conjugated molecules: p-Benzoquinone, anthracenequinone and pentacenequinone S. Knippenberg a,b , M.S. Deleuze b,∗ a b

Institut für Physikalische und Theoretische Chemie, Johann Wolfgang Goethe Universität Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt am Main, Germany Research Group Theoretical Chemistry, Department SBG, Hasselt University, Agoralaan, Gebouw D, B-3590 Diepenbeek, Belgium

a r t i c l e

i n f o

Article history: Available online 6 May 2009 Keywords: Electronic correlation and relaxation Shake-ups Excited states Conjugated molecules Chemical accuracy Low band gap systems Polycyclic aromatic hydrocarbons

a b s t r a c t A review of an extensive series of theoretical studies of the valence one-electron and shake-up ionization spectra of polycyclic aromatic hydrocarbons is presented, along with new results for three planar quinone derivatives, obtained using one-particle Green’s function (1p-GF) theory along with the so-called third-order algebraic diagrammatic construction [ADC(3)] scheme and the outer-valence Green’s function (OVGF) approximation. These results confirm both for the ␲- and ␴-band systems the rapid spreading, upon increasing system size, of many shake-up lines with significant intensities at outer-valence energies. Linear regressions demonstrate that with large conjugated molecules the location of the shake-up onset in the ␲-band system is merely determined by the energy of the frontier (HOMO, LUMO) orbitals. Electron pair removal effects are found to almost compensate the electron relaxation effects induced by ionization of ␲-levels, whereas the latter effects strongly dominate the ionization of more localized lone-pair (n) levels, and may lead to inversions of the energy order of Hartree–Fock (HF) orbitals. Therefore, although it increases upon a lowering of the HF band gap, and thus upon an increase of system size, the dependence of the one-electron ionization energies onto the quality of the basis set is lesser for ␲-levels than for ␴-levels relating to electron lone pairs (n). Basis sets of triple- and quadruple-zeta quality are therefore required for treatments of the outermost ␲- and n-ionization energies approaching chemical accuracy [1 kcal/mol, i.e. 0.04 eV]. When 1p-GF theory invalidates Koopmans’ theorem and the energy order of HF orbitals, a comparison with Kohn–Sham orbital energies confirms the validity of the meta-Koopmans’ theorem for density functional theory. © 2009 Elsevier B.V. All rights reserved.

1. Introduction The interaction of radiation with neutral molecules leading up to the production of positive ions, and the experimental analysis of the kinetic energy of the released electrons brought forth the field of photoelectron spectroscopy. Despite the advent of intense and energy-tunable photon sources, called synchrotron [1], electron correlation remains for most experimentalists in this field one of the less easily amenable aspects of electronic structure theory, in particular when dealing with large organic molecules, or extended systems such as polymers, surfaces, or solids. It is most commonly understood that the Hartree–Fock (HF) wave function is a single (Slater) determinant approximation to the solution of the many-body Schrödinger equation [2]. In the frozen-orbital and single-determinant approximations, single electronic transitions carry all the ionization intensity (one-electron picture of ionization), and ionization energies become equal, after a change in sign,

∗ Corresponding author. E-mail address: [email protected] (M.S. Deleuze). 0368-2048/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2009.04.013

to HF orbital energies (Koopmans’ theorem). For decades, this simple model was assumed to enable qualitatively correct enough insights into core and valence ionization experiments. However, experimental evidence from measurements employing X-ray and synchrotron photoelectron spectroscopy (PES) [3] has been mounting, showing most clearly that the energy released by electronic relaxation during a vertical ionization process leads to the appearance of extra-structures, referred to as satellites and correlation bands, which can borrow a highly significant fraction of the ionization intensity of “parent states”, in both core and valence regions. Several computational studies employing one-particle Green’s function (1p-GF) theory [4,5], configuration interaction [6] theory, or symmetry-adapted-cluster configuration interaction (SAC-CI) theory [7] brought forth a proper interpretation of these satellite structures as manifestations of electronic correlation. These take the form of strong interactions between one-hole (1h) and electronically excited [e.g. two-hole-one-particle (2h-1p), threehole-two-particle (3h-2p), . . .] configurations of the cation, yielding a redistribution of the ionization intensity of “parent states” associated to 1h configurations over many “shake-ups” or “correlation states” of the same symmetry, which are described by wave

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functions involving mixing of many excited configurations (Slater determinants) of the cation. Even for weakly correlated systems such as n-alkanes, 1p-GF calculations of valence ionization spectra resorting to a highly efficient band-Lanczos diagonalization algorithm have shown that correlation bands [8] may extend up to electron binding energies of 60 eV and beyond. With large molecular systems, shake-up lines are most usually not resolvable and their experimental identification may not always be straightforward, because of the pronounced congestion of valence bands. Most often, a reliable fingerprint of a breakdown of the orbital picture of ionization is typically a strong broadening of spectral bands (see e.g. ref. [9]), which may easily be mistaken with a vibrational progression. Advanced “orbital imaging” techniques such as Electron Momentum Spectroscopy [10] or Penning Ionization Electron Spectroscopy [11] have proven particularly useful in detailed investigations of the origin of valence shake-up lines and their relationships with the main spectral bands. By studying the azimuthal angular dependence [10e,f] or the collision-energy dependence [11] of partial cross sections in (e, 2e) electron-impact ionization processes (M + e− → M+ + 2e− ) or chemi-ionization experiments upon collision with a noble-gas atom in a metastable excited state (M + Ar* → M+ + Ar + e− ), respectively, it has been in particular possible to experimentally confirm in a non-ambiguous way the presence of low-lying ␲−2 ␲*+1 shake-up lines at outer-valence ionization energies, in excellent agreement with early 1p-GF calculations [3h,5c]. More recently, an extensive series of 1p-GF calculations on large polycyclic aromatic hydrocarbons [PAHs] [12] has shown that for planar and strongly correlated systems characterized by a low energy gap between the valence (occupied) and conduction (unoccupied) one-electron bands, the shake-up onset in the ␲-band system can lie at electron binding energies as low as 8 eV, whereas the one-electron picture of ionization holds up to 13 eV in the ␴-band system. This class of compounds is particularly promising for the making of biosensors [13] or semi-conducting organic thin films [14], and certainly worth further studies therefore. In continuation to this latest series of 1p-GF studies on polycyclic aromatic hydrocarbons, and in view of the available experimental and theoretical evidences so far, we wish therefore to emphasize in this special issue of the Journal of Electronic Spectroscopy and Related Phenomena on X-ray Photoelectron Spectroscopy and its Applications in the Solid Phase that great care remains needed in investigations, by means of conventional photoelectron spectroscopies, of the electronic structure of large conjugated molecules. Our target systems for the present work are the three quinones displayed in Fig. 1. Quinones in general are known to play an important role in many biochemical processes pertaining to respiration and photosynthesis [15,16]. The archetype of the family, p-benzoquinone (BQN), is present in anthracyclines, a family of compounds which have shown high efficiency in antitumor treatments [17]. BQNderivatives, such as tetramethyltetrathiafulvalene – tetradecane – tetracyano-p-quinodimethane (TMTTF – C14 TCNQ), are also commonly used as acceptor components in charge transfer complexes of large conjugated chains [18] in low dimensional conducting films produced by selective electrochemical oxidation of an insulating precursor Langmuir–Blodgett film. Larger members of the quinone family are the anthracenequinone and pentacenequinone compounds (Fig. 1b and c), which can be synthesized through selective oxidation of anthracene [19] and pentacene [20], respectively. Anthracenequinone derivatives are known to initiate DNA cleavage [21] and to be key-compounds in liquid crystal technology [22]. Because of the relatively limited size and high symmetry (D2h ) of this compound, the valence ionization spectrum of p-benzoquinone has attracted early interest. Review of the relevant literature starts with a series of high-resolution photoelectron measurements and semi-empirical calculations focusing specifically on the first outer-

Fig. 1. (a) p-Benzoquinone (C6 H4 O2 , D2h ); (b) anthracenequinone (C14 H8 O2 , D2h ) and (c) pentacenequinone (C22 H12 O2 , D2h ).

valence bands [23–26] at electron binding energies ranging from 9.5 to 11.5 eV. Very few studies have analysed completely the outervalence ionization spectrum of this compound. In 1970, Turner et al. published the He(I) photoelectron spectrum (PES) of pbenzoquinone [27]. Lacking reliable theoretical data, bands could not be assigned at electron binding energies larger than 14 eV [25]. Of relevance also is an experimental PES study [28] by Lauer et al., which only discussed the four lowest ionization states of pbenzoquinone and anthracenequinone. The most reliable study [29] so far of the valence ionization spectrum of p-benzoquinone is the one-particle Green’s function (1p-GF) study by von Niessen et al. employing the outer-valence Green’s function (OVGF) [4b] method and the extended two-particle-hole Tamm–Dancoff approximation (extended 2ph-TDA) [4f,30], a level which is now most commonly referred to as the third-order algebraic diagrammatic construction scheme [ADC(3)], together with Huzinaga’s basis sets of doublezeta quality [31]. This treatment did not enable accuracies better than 0.4 eV, presumably because of the too limited size of the basis set. Accuracies of 0.2–0.3 eV on the one-electron ionization energies of large conjugated molecules are commonly reached nowadays with third-order treatments, provided large enough basis sets are used and calculations are performed on geometries optimized with an approach that accounts for electronic correlation. In the present study, our understanding of the ADC(3) ionization spectrum of pbenzoquinone is improved from a quantitative view point through a stringent comparison with ADC(3) or OVGF results obtained using the Pople’s standard 6-31G basis set, and Dunning‘s correlationconsistent polarized valence basis sets (cc-pVXZ) of double (D), triple (T), and quadruple (Q) zeta quality. Also for the sake of quan-

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63

titative insights, ADC(3)/6-31G calculations of the one-electron and shake-up ionization spectra of anthracenequinone and pentacenequinone are supplemented by OVGF/cc-pVDZ calculations of one-electron ionization energies and of the corresponding pole strengths. We conclude this review through a comparison with all available ADC(3) results in the PAH series so far, in order to draw general trends regarding the location of the shake-up onset and the dependence of the ionization threshold upon the quality of the employed basis set. 2. Outline of theory At the so-called ADC(3) level, the search of the poles of the oneparticle Green’s function (1p-GF) amounts to solving an eigenvalue problem of the form [30]: HX = XE

(1)

with X a unitary matrix and

⎡

H=⎣

␧ + (∞) (U+ )

†

− †

U+ K+ + C+

(U )

0

U− 0

⎤ ⎦

(2)

K− + C−

The above matrix is cast over all one-hole (1h) and two holeone particle (2h-1p) cationic states, as well as over all 1p and 2p-1h anionic states of the molecule of interest; the block-matrices K+ + C+ and K− + C− are therefore defined as coupling amplitudes between shake-on (2p-1h) and shake-up (2h-1p) configurations, respectively. K± are diagonal matrices which correspond to the zeroth-order (i.e. Hartree–Fock, HF) estimates of the corresponding 2p-1h and 2h-1p transition energies. C± are non-diagonal matrices which contain first order energy shifts. U± contain second-order amplitudes coupling the 1h- and 1p- configurations to the (2h1p)-shake-up and (2p-1h)-shake-on states of the cation and anion, respectively. These block-matrices relate to the dynamic (energydependent) components of the electron self-energy for a 1p- (+) or 1h- (−) state, as follows: +

M± (ω) = (U± ) (ω − K± − C± ) M+ (ω)

−1

U±

(3)

M− (ω)

and account on a finite timescale for the polarization of a correlated electron system in the presence of a moving extra-electron or hole, respectively. Returning to Eq. (2), ε denotes a diagonal matrix containing the HF orbital energies, and (∞) represents the static (energy-independent, ω → ∞) component of the self-energy, which describes the (instantaneous, t → 0) electrostatic potential felt by an incoming or outgoing particle due to correlation corrections to the HF ground-state density. At the ADC(3) level, (∞) and M± (ω) are recovered through fourth and third order in the electron correlation potential, respectively, i.e. these self-energies amount to infinite but partial series of Feynman diagrams that are complete up to fourth and third orders (see Fig. 1 of Ref. [30d] in particular for a concise review of all recovered self-energy terms, and note from this figure that the vectors of coupling amplitudes, U± , can be regarded as screened bielectron interactions in a correlated medium). In the present work, the size intensivity of (∞) is ensured by a slight rescaling enforcing the charge-consistency of the related one-electron densities [32]. The intensity ratio between satellite and one-electron ionization lines originating from the same orbital is equal to the ratio of their pole strengths, which are given as the norm of the related 1h and 1p components of the ADC(3) eigenvectors. Like bielectron integrals, the coupling amplitudes U± decrease inversely to system size, by virtue of the delocalization properties of canonical molecular orbitals [see Ref. [32] and references therein]. Therefore, regardless of energy considerations, the individual intensity of shake-up lines tends, on average, to decrease inversely to the square of system size.

Fig. 2. Comparison between the experimental He(I) data in (a) Brundle et al. [25] and (b) Turner et al. [27], with theoretical (c) ADC(3)/6-31G and (d) ADC(3)/cc-pVDZ ionization spectra of p-benzoquinone (C6 H4 O2 , D2h ), using a FWHM of 0.5 eV.

64

Table 1 ADC(3) and OVGF calculation results for the ionization spectrum of p-benzoquinone (C6 H4 O2 ). The binding energies are given in eV, along with the ADC(3) and OVGF spectroscopic factors (in parentheses)a . E(HF/cc-pVDZ)

1

4b3g (n)

11.918

9.890

(0.864)

10.110

(0.859)

2

5b2u (n)

12.516

10.290 13.239

(0.835) (0.009)

10.428 13.459

3 4

2b3u (␲) 1b1g (␲)

11.187 11.169

10.453 10.794 18.794

(0.861) (0.900) (0.005)

5

3b3g (n)

15.839

13.524 13.826 16.109

6

1b2g (␲)

14.996

ADC(3)/6-31G

ADC(3)/cc-pVDZ

OVGF/6-31G

OVGF/cc-pVDZ

OVGF/aug-cc-pVDZ

OVGF/cc-pVTZ

OVGF/cc-pVQZ

Exp.II

Exp.III

9.792

(0.895)

9.966

(0.889)

10.324

(0.886)

10.282

(0.885)

10.388

(0.884)

10.11

10.11

(0.837) (0.008)a

10.319

(0.873)

10.409

(0.874)

10.802

(0.871)

10.724

(0.869)

10.840

(0.868)

10.41

10.41

10.649 10.903

(0.864) (0.895)

10.472 10.499

(0.893) (0.913)

10.598 10.736

(0.892) (0.909)

10.942 10.916

(0.888) (0.903)

10.869 10.972

(0.888) (0.904)

11.123 11.055

(0.886) (0.903)

11.06 11.25

11.06 11.23

(0.220) (0.581) (0.119)

13.684 13.923 16.130

(0.277)b (0.533) (0.100)

13.739

(0.874)

13.807

(0.875)

14.117

(0.873)

14.071

(0.871)

14.164

(0.870)

13.43

13.43

12.769 14.456 15.979 17.475

(0.317) (0.402) (0.051) (0.090)

12.980 14.402 15.875 17.451

(0.341)c (0.393) (0.053) (0.076)

13.897

(0.829)*

13.846

(0.840)*

14.239

(0.838)*

14.061

(0.838)*

14.157

(0.837)*

14.38

14.18

14.922

(0.853)

14.826

(0.856)

15.035

(0.857)

15.027

(0.852)

15.112

(0.851)

14.254

(0.899)

14.378

(0.895)

14.753

(0.891)

14.651

(0.889)

14.746

(0.888)

7

1b3u (␲)

16.154

14.525 17.615

(0.638) (0.249)

14.588 17.559

(0.662) (0.226)d

8

8ag (␴)

16.408

14.295 14.426

(0.273) (0.596)

14.366 14.603

(0.043)e (0.826)

⎫ ⎪ ⎬

14.46 ⎪ 14.34

⎫ ⎬

⎪ ⎭

⎪ ⎭

9 10

7b1u (␴) 4b2u (␴)

17.070 17.423

14.953 15.645 15.978

(0.833) (0.809) (0.049)

15.160 15.661 15.966

(0.844) (0.788) (0.072)

14.928 15.506

(0.894) (0.895)

15.028 15.480

(0.888) (0.883)

15.286 15.652

(0.884) (0.879)

15.253 15.687

(0.882) (0.878)

15.341 15.699

(0.881) (0.879)

15.05 15.55

14.74 15.37

11

6b1u (␴)

18.701

16.376 19.872

(0.817) (0.053)

16.567

(0.809)

16.360

(0.870)

16.492

(0.867)

16.774

(0.862)

16.685

(0.862)

16.770

(0.861)

16.46

16.10

12

7ag (␴)

19.376

16.935 18.171

(0.730) (0.058)

17.069 17.285 18.324

(0.645) (0.126) (0.040)

17.017

(0.866)

17.076

(0.862)

17.353

(0.857)

17.270

(0.856)

17.357

(0.855)

16.92

16.61

13

3b2u (n)

19.468

15.710 17.273 17.604 18.556

(0.118) (0.431) (0.272) (0.042)

15.784 17.234 17.583

(0.093) (0.547) (0.169)f

17.018

(0.855)

16.858

(0.855)

17.112

(0.853)

17.070

(0.850)

17.166

(0.849)*

19.290 19.543 20.423 20.811

(0.144) (0.248) (0.177) (0.284)

19.140 19.421 20.252 20.305 20.822 20.969

(0.060) (0.231) (0.298) (0.080) (0.097) (0.082)

19.795

(0.805)*

19.696

(0.803)*

20.889

(0.825)*

20.704

(0.825)*

14

6ag (␴)

22.581

15

2b3g (␴)

23.755

20.616 20.841 20.960 21.478 21.635

(0.059) (0.457) (0.046) (0.050) (0.118)

20.659 21.486 22.055

(0.526) (0.112) (0.048)

16

5b1u (␴)

26.249

22.650 22.788 23.255 23.422

(0.051) (0.118) (0.382) (0.043)

22.659 22.813 23.105

(0.197) (0.064) (0.347)

–

20.899

–

(0.819)*

–

20.889

–

(0.818)*

–

20.967

–

(0.816)*

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

M.O. I

Label

Dominant electronic configurations and their weights: (a) [s2 ]: [0.548] 4b3g −1 2b3u −1 2b2g +1 [(HOMO-2)−1 (HOMO-1)−1 LUMO+1 ]; (b) [s3 ]: [0.448] 5b2u −1 2b3u −1 2b2g +1 [(HOMO-3)−1 (HOMO-1)−1 LUMO+1 ]; (c) [s1 ]: [0.388] 2b3u −2 2b2g +1 [(HOMO-1)−2 LUMO+1 ]; (d) [0.292] 2b3u −2 3b3u +1 [(HOMO-1)−2 (LUMO + 3)+1 ]; (e) [s4 ]: [0.579] 1b1g −1 4b3g −1 2b2g +1 [HOMO−1 (HOMO-2)−1 LUMO+1 ]; (f) [0.248] 1b1g −1 4b3g −1 1au +1 [HOMO−1 (HOMO-2)−1 (LUMO + 1)+1 ]. I Between brackets, the nature of the bond is indicated: oxygen lone pair (n), ␲ -bond and ␴-bond. II Turner et al. [27]. III Brundle et al. [25]. a At binding energies larger than 14.0 eV, only the ADC(3)/6–31 G and ADC(3)/cc-pVDZ ionization lines with pole strengths larger than 0.04 are given here; see Table 2 for further data. * Breakdown of the MO picture of ionization; see J. Chem. Phys., 116 (2002) 7012.

(0.047) (0.042) 34.140 34.290 (0.045) (0.042) 38.511 4ag (␴) 20

35.685 35.853

(0.040) 33.569 (0.050) (0.050) 38.447 4b1u (␴) 19

35.471 35.859

(0.155) (0.086) (0.042) (0.075) (0.046) 26.484 26.767 26.890 27.720 28.805 (0.042) (0.066) (0.071) (0.048) (0.055) 31.599 5ag (␴) 18

26.762 27.133 27.201 27.954 29.287

29.325 2b2u (␴) 17

24.683 25.490 25.716 25.938 26.193 27.014

(0.043) (0.048) (0.064) (0.252) (0.048) (0.059)

24.469 25.163 25.404 25.544

(0.041) (0.151) (0.172) (0.136)

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65

A size-consistent description of correlation bands is correspondingly ensured at the ADC(3) level by a quadratic increase in the number of shake-up states to compute per parent orbital [8,32] The diagonalization of the secular matrix H is performed in two steps. In a first step, one takes advantage of the large energy interval between shake-up and shake-on states to project the (N + 1)-block K+ + C+ pertaining to the 2p-1h shake-on states onto a pseudo electron attachment spectrum of much lower dimension, through the interplay of a proper rescaling of the U+ coupling amplitudes using the band-Lanczos diagonalization procedure [33–35]. In a second step, the so reduced H-matrix is then fully diagonalized by means of the block–Davidson method [36,37]. 3. Computations The ADC(3) calculations on p-benzoquinone (C6 O2 H4 ), anthracenequinone (C14 O2 H8 ) and pentacenequinone (C22 O2 H12 ) were performed using Pople’s 6-31G basis set, thus incorporating on total 80, 160 and 240 basis functions in the calculations, respectively. In the case of p-benzoquinone, an ADC(3) calculation was also performed using Dunning’s correlation-consistent polarized valence basis set of double-zeta quality [cc-pVDZ [38]], implying thus a molecular orbital basis of dimension 140. The original code, interfaced to the GAMESS package of programs [39], has been employed to carry out these 1p-GF calculations. At the self-consistent field (SCF) level, the requested convergence on each of the elements of the density matrix was fixed to 10−10 . The spectra have been calculated up to binding energies of 37 eV for p-benzoquinone, and of 22 eV for anthracenequinone and pentacenequinone, retaining all eigenvalues of the ADC(3) secular matrix with a pole strength equal or larger than 0.005. The assumption of frozen core electrons has been used throughout and symmetry has been exploited to the extent of the D2h point group for all three compounds. Convoluted densities of states have been obtained from the ADC(3) ionization spike spectra, using as spread function a combination of a Gaussian and a Lorenzian with equal weight and with a full width at half maximum (FWHM) of 0.5 eV. Line intensities have been simply scaled according to the computed ADC(3) pole strengths, neglecting thereby the varying influence of molecular orbital photoionization cross sections. To evaluate the sensitivity of the computed ionization energies onto the quality of the basis set, we also present results obtained from outer-valence Green’s function (OVGF [4b]) calculations. For these benchmark computations of one-electron ionization energies, three basis sets have been used for all compounds: Pople’s standard 6-31G basis set, and Dunning’s correlation-consistent polarized valence basis sets of double and triple-zeta quality [ccpVDZ, cc-pVTZ, (Ref. [38])]. The issue of basis set completeness has been assessed in more details with p-benzoquinone, through OVGF calculations in conjunction with Dunning’s correlation-consistent polarized valence basis set of quadruple zeta quality (cc-pVQZ [38]), as well as with the cc-pVDZ basis augmented by a set of diffuse {s, p} functions on the hydrogen atoms together with a set of diffuse {s, p, d} functions on the carbon atoms [aug-cc-pVDZ (Refs. [38,40])]. The ADC(3) and OVGF calculations presented here are based on molecular geometries that were optimized using the nonlocal hybrid and gradient corrected Becke three-parameter Lee–Yang–Parr functional (B3LYP) [41,42] in conjunction with Dunning’s cc-pVTZ basis set. It has previously been shown that this approach delivers excellent equilibrium geometries [43,44], of quality comparable to that reached with benchmark coupled cluster calculations. The vertical double ionization energy thresholds (VDIPs) of the target compounds have been determined through a series of single-

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Table 2 Further ionization lines identified at the ADC(3)/6-31G and ADC(3)/cc-pVDZ level for p-benzoquinone. Label

M.O.I

ADC(3)/6–31 GII

ADC(3)/cc-pVDZII

5

3b3g (n)

18.530 (0.007), 18.809 (0.008), 22.755 (0.006)

18.339 (0.006), 18.928 (0.005), 22.471 (0.006)

6

1b2g (␲)

16.191 (0.011), 18.867 (0.016), 21.047 (0.013) 24.200 (0.006)

16.212 (0.006), 18.835 (0.012), 20.781 (0.011) 24.025 (0.009)

7

1b3u (␲)

18.456 (0.013), 20.414 (0.008), 21.219 (0.010) 24.157 (0.010), 24.533 (0.008)

20.210 (0.009), 20.962 (0.007), 23.899 (0.007)

9

7b1u (␴)

14.431 (0.008)

10

4b2u (␴)

20.978 (0.020)

20.606 (0.021), 23.913 (0.009)

11

6b1u (␴)

17.727 (0.031), 21.114 (0.009), 23.966 (0.010)

17.973 (0.024), 19.744 (0.019), 19.939 (0.015) 21.102 (0.023), 21.311 (0.013)

12

7ag (␴)

17.270 (0.035), 19.048 (0.005), 20.030 (0.008) 20.260 (0.015), 24.747 (0.008)

24.348 (0.009)

13

3b2u (n)

16.650 (0.024), 17.997 (0.031), 19.002 (0.008) 19.472 (0.017), 19.791 (0.010), 24.999 (0.018)

16.770 (0.030), 18.159 (0.008), 18.481 (0.039) 19.076 (0.015), 19.378 (0.011), 19.712 (0.008)

14

6ag (␴)

20.849 (0.016), 21.769 (0.018), 22.935 (0.012) 23.318 (0.009), 23.773 (0.006), 25.475 (0.013)

19.011 (0.016), 19.978 (0.015), 21.716 (0.015) 22.855 (0.006), 23.036 (0.011), 23.364 (0.008) 24.685 (0.007), 28.150 (0.006)

15

2b3g (␴)

22.030 (0.020), 22.370 (0.039), 23.658 (0.016) 24.425 (0.005), 25.261 (0.008), 25.774 (0.012)

17.472 (0.005), 20.879 (0.034), 21.237 (0.025) 21.298 (0.009), 21.605 (0.022), 23.310 (0.016) 24.013 (0.008), 25.158 (0.007), 27.862 (0.006) 28.162 (0.006), 28.307 (0.006)

16

5b1u (␴)

20.843 (0.023), 20.951 (0.034), 21.187 (0.020) 21.849 (0.009), 22.425 (0.008), 23.062 (0.011) 23.641 (0.027), 23.670 (0.017), 24.160 (0.019) 24.800 (0.031), 25.104 (0.006), 25.169 (0.015) 25.872 (0.007), 26.080 (0.008), 26.232 (0.006) 26.472 (0.010), 28.640 (0.009), 30.616 (0.006)

20.697 (0.018), 20.751 (0.031), 21.615 (0.009) 22.235 (0.008), 22.344 (0.009), 23.271 (0.030) 23.386 (0.008), 23.807 (0.009), 23.981 (0.013) 24.382 (0.007), 24.495 (0.012), 24.768 (0.011) 24.844 (0.014), 25.505 (0.011), 25.884 (0.005) 28.241 (0.008), 30.249 (0.007), 31.320 (0.006)

17

2b2u (␴)

21.098 (0.008), 22.694 (0.009), 23.569 (0.006) 23.852 (0.013), 24.467 (0.021), 24.771 (0.015) 25.639 (0.038), 25.822 (0.027), 26.063 (0.008) 26.447 (0.020), 26.832 (0.017), 27.246 (0.008) 27.399 (0.015), 28.111 (0.008), 28.385 (0.008)

20.942 (0.006), 22.288 (0.007), 23.290 (0.006) 23.766 (0.027), 24.123 (0.012), 24.308 (0.009) 24.367 (0.007), 24.555 (0.028), 25.227 (0.023) 25.362 (0.006), 25.469 (0.012), 25.620 (0.007) 25.910 (0.005), 25.977 (0.010), 26.134 (0.007) 26.803 (0.027), 26.928 (0.010), 27.111 (0.009) 27.265 (0.006), 29.709 (0.006)

18

5ag (␴)

25.293 (0.006), 25.552 (0.009), 25.933 (0.006) 26.183 (0.015), 26.673 (0.009), 27.003 (0.005) 27.018 (0.023), 27.080 (0.027), 27.279 (0.025) 27.493 (0.024), 27.634 (0.012), 27.684 (0.006) 27.767 (0.027), 27.846 (0.013), 28.180 (0.023) 28.234 (0.037), 28.482 (0.016), 28.761 (0.006) 28.961 (0.023), 29.053 (0.014), 29.398 (0.006) 29.505 (0.007), 29.627 (0.020), 29.652 (0.005) 29.694 (0.019), 29.982 (0.025), 30.088 (0.018) 30.199 (0.011), 30.307 (0.021), 30.628 (0.015) 30.724 (0.011), 31.373 (0.013), 31.428 (0.005) 32.353 (0.010), 32.972 (0.006), 33.406 (0.009)

24.983 (0.009), 25.467 (0.008), 25.707 (0.012) 25.865 (0.006), 26.393 (0.005), 26.634 (0.031) 27.069 (0.007), 27.087 (0.010), 27.364 (0.023) 27.552 (0.018), 28.056 (0.008), 28.273 (0.008) 28.331 (0.033), 28.529 (0.036), 28.651 (0.016) 28.965 (0.018), 29.334 (0.009), 29.490 (0.015) 29.978 (0.018), 29.988 (0.009), 30.521 (0.006) 30.936 (0.012), 31.187 (0.005), 32.055 (0.014) 32.096 (0.005)

19

4b1u (␴)

30.852 (0.006), 30.998 (0.032), 33.067 (0.008) 33.241 (0.006), 33.401 (0.009), 33.654 (0.011) 33.880 (0.012), 33.892 (0.008), 34.324 (0.007) 34.591 (0.012), 34.654 (0.005), 34.777 (0.008) 34.829 (0.011), 34.899 (0.014), 34.984 (0.006) 35.016 (0.007), 35.048 (0.021), 35.100 (0.007) 35.149 (0.014), 35.574 (0.014), 35.600 (0.010) 35.650 (0.015), 35.659 (0.015), 35.732 (0.011) 35.830 (0.009), 36.040 (0.021), 36.165 (0.010) 36.193 (0.006), 36.268 (0.033), 36.332 (0.012) 36.382 (0.015), 36.391 (0.005), 36.414 (0.024) 36.650 (0.016), 36.759 (0.006), 37.066 (0.009) 37.115 (0.006), 37.363 (0.008)

30.516 (0.006), 30.647 (0.011), 30.820 (0.026) 30.832 (0.007), 31.370 (0.010), 32.228 (0.008) 32.361 (0.008), 32.452 (0.006), 32.632 (0.007) 32.806 (0.010), 32.917 (0.007), 33.412 (0.008) 33.436 (0.006), 33.572 (0.009), 33.665 (0.008) 33.793 (0.017), 33.937 (0.017), 33.988 (0.016) 34.026 (0.008), 34.071 (0.011), 34.196 (0.009) 34.284 (0.007), 34.406 (0.038), 34.479 (0.031) 34.502 (0.012), 34.567 (0.008), 34.587 (0.024) 34.626 (0.008), 34.659 (0.019), 34.695 (0.020) 34.711 (0.021), 34.740 (0.007), 34.950 (0.010) 35.005 (0.015), 35.026 (0.008), 35.122 (0.005) 35.171 (0.011), 35.261 (0.019), 35.639 (0.022) 35.716 (0.008), 35.844 (0.006), 35.914 (0.011) 36.117 (0.023)

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

67

Table 2 (Continued ) Label

M.O.I

ADC(3)/6–31 GII

ADC(3)/cc-pVDZII

20

4ag (␴)

29.121 (0.013), 31.015 (0.008), 31.289 (0.008) 32.344 (0.022), 32.626 (0.011), 33.276 (0.008) 33.759 (0.009), 34.085 (0.007), 34.305 (0.039) 34.487 (0.016), 34.814 (0.021), 34.977 (0.005) 34.987 (0.023), 35.075 (0.017), 35.130 (0.030) 35.208 (0.006), 35.280 (0.026), 35.439 (0.018) 35.619 (0.007), 35.653 (0.034), 35.741 (0.019) 35.894 (0.011), 35.997 (0.013), 36.316 (0.010) 36.344 (0.007), 36.506 (0.016), 36.521 (0.012) 36.622 (0.006), 36.659 (0.012), 36.708 (0.010) 36.833 (0.008), 36.885 (0.006)

28.835 (0.009), 31.054 (0.005), 31.082 (0.005) 31.209 (0.014), 31.758 (0.008), 31.843 (0.013) 31.954 (0.013), 32.114 (0.008), 32.217 (0.007) 32.268 (0.007), 32.593 (0.013), 32.815 (0.008) 33.153 (0.013), 33.226 (0.014), 33.297 (0.007) 33.449 (0.017), 33.534 (0.014), 33.623 (0.008) 33.714 (0.034), 34.083 (0.013), 34.192 (0.036) 34.265 (0.008), 34.310 (0.011), 34.405 (0.007) 34.666 (0.022), 34.720 (0.011), 34.782 (0.023) 34.804 (0.013), 34.998 (0.017), 35.033 (0.025) 35.246 (0.009), 35.262 (0.006), 35.342 (0.016) 35.376 (0.010), 35.589 (0.011), 35.661 (0.018) 35.699 (0.011), 36.008 (0.019), 36.104 (0.009) 36.146 (0.006), 36.312 (0.020)

I

Between brackets, the nature of the bond is indicated: oxygen lone pair (n), ␲-bond and ␴-bond. Binding energies are given in eV, along with the associated pole strengths in brackets.

II

point calculations on the neutral and dicationic species upon the B3LYP/cc-pVTZ geometries for the neutrals. These calculations have been conducted at the level of HF theory, second-, third- and partial fourth-order Møller–Plesset (MP2, MP3, MP4SDQ) theories [45,46], and by means of coupled cluster theories, including single and double excitations (CCSD) as well as a perturbative estimate of connected triple excitations (CCSD(T)) [47]. The vertical ionization potential p-benzoquinone has been in addition determined by means of a focal point analysis (FPA): a series of single-point calculations at the Hartree–Fock (HF), MP2, MP3, CCSD and CCSD(T) levels with the cc-pVDZ, cc-pVTZ and cc-pVQZ basis sets were performed upon the ground-state B3LYP/cc-pVTZ geometry. An extrapolation of the HF energies to the limit of an asymptotically complete (cc-pV∞Z) basis set has been done with an exponential fit, as suggested by Feller [48], while a three-point version of Schwarz’s extrapolation [49] was applied for extrapolating the successive correlation corrections (MP2, MP3, CCSD, CCSD[T]) to the HF energy. All single-point, density functional theory (DFT) and OVGF computations performed in this work have been carried out at Hasselt University using the GAUSSIAN98 [50] quantum chemistry package. 4. Results and discussion 4.1. para-Benzoquinone The ADC(3)/6-31G and ADC(3)/cc-pVDZ spike and convolved ionization spectra displayed in Fig. 2 reveal straightforwardly the extent of the shake-up contamination in the inner-valence region of p-benzoquinone, where most orbitals undergo a significant breakdown of the orbital picture of ionization. The reader is referred to Tables 1 and 2 for a detailed assignment of lines and comparison with available experimental ionization energies. In these tables, although they formally contribute by symmetry to the ␴Table 3 Focal point analysis of the vertical ionization potential of BNQa .

HF MP2 MP3 MP4SDQ CCSD CCSD(T) a

cc-pVDZ

cc-pVTZ

cc-pVQZ

cc-pV∞Z

10.843 9.334 10.180 10.234 10.157 9.719

10.873 9.680 10.514 10.615 10.498 10.051

10.892 9.823 10.646 10.765 10.627 10.185

10.923 9.859 10.680 10.802 10.659 10.219

Results are given in eV; the calculations are based on a B3LYP/cc-pVTZ geometry. An exponential fit according to Feller’s suggestion [48a,b] has been applied for HF; a three-point version of Schwarz’s extrapolation [49] was used for the Møller–Plesset and coupled cluster results.

band system, we differentiate those four orbitals that, in view of their LCAO composition, dominantly relate to the oxygen lone-pairs (n) of the target compound. The one-electron picture of ionization is partly preserved for the 2b3g (15) and 5b1u (16) ␴-orbitals, which dominantly emerge from the shake-up background in the form of 1h lines at electron binding energies of ∼20.6 and ∼23.1 eV, with spectroscopic strengths ( ) of 0.53 and 0.34, respectively. The shake-up onset [s1 ] in the outer-valence region belongs to the ␲band system and is located at ∼13.0 eV, where it takes the form of a particularly intense satellite ( = 0.34) of the 1b2g orbital (6), which relates to the 2b3u −2 2b2g +1 (HOMO-1−2 , LUMO+1 ) excited configuration of the cation. In view of its intensity, this low-lying ␲−2 ␲*+1 satellite can be unambiguously ascribed to the rather sharp and well-resolved peak at 13.43 eV in the HeI records. The n- and ␲-orbitals [3b3g (5), 1b3u (7), 3b2u (13)] above this energy threshold are also very naturally prone to a significant dispersion of the ionization intensity over shake-up lines. In the ␴-band system, the orbital picture of ionization holds up to electron binding energies of 17.1 eV, in the form of a 1h line ( = 0.65) associated with the 7ag (12) orbital. The ADC(3)/6-31G and ADC(3)/cc-pVDZ spectra are merely very similar, the improvement of the basis set resulting essentially into a redistribution of the shake-up intensity over many more states, but without any significant alterations of the computed spectral envelopes. Significant enough shifts in the relative positions of oneelectron lines are nonetheless observed at binding energies ranging from 16 to 18 eV, upon replacing a basis set of double-zeta quality only, such as 6–31 G, by the polarized cc-pVDZ basis. This methodological improvement results in this energy region into noticeable changes in the convolved spectrum, in much better agreement with the available HeI measurements. The vertical double ionization energy threshold of para-benzoquinone is located at ∼24.6 eV, according to CCSD(T)/cc-pVDZ calculations. Sets of shake-up ionization lines above this energy threshold ought to be rather dependent upon the inclusion of diffuse and/or continuum functions in the basis set, and should more correctly be regarded therefore as discrete approximations to continuous shake-off bands. Correlation and electron relaxation effects take also the form of a reversal of the four outermost one-electron ionization lines, compared with the energy order that is expected at the level of Koopmans’ theorem (KT). Due to their more strongly localized nature and enhanced orbital and electron pair relaxation (ORX, PRX) effects in the final state [2,51], the two outermost oxygen lone-pairs [4b3g (1), 5b2u (2)] are subject to very substantial shifts towards lower-binding energies, of the order of ∼2.0 eV. In contrast, since the two lowest unoccupied molecular orbitals of para-benzoquinone belong to the ␲-band system, the two outermost ␲-orbitals [2b3u (3), 1b1g (4)] are by symmetry subject

68

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

Table 4 ADC(3) and OVGF calculation results for the ionization spectrum of anthracenequinone (C14 H8 O2 ). The binding energies are given in eV, along with the ADC(3) and OVGF spectroscopic factors (in parentheses)a . Label 1

M.O.I 2b2g (␲)

E(HF/cc-pVDZ) 9.597

ADC(3)/6-31G 9.107

(0.868)

OVGF/6-31G 8.933

OVGF/cc-pVDZ (0.894)

9.090

(0.889)

OVGF/cc-pVTZ 9.451

(0.882)

2 3

2b1g (␲) 1au (␲)

9.604 9.699

9.131 9.257

(0.881) (0.876)

8.826 9.006

(0.899) (0.898)

9.175 9.354

(0.891) (0.889)

9.400 9.570

(0.886) (0.884)

4 5 6

3b3u (␲) 9b3g (n) 11b2u (n)

10.045 11.562 12.123

(0.889) (0.883) (0.869)

9.351 9.397 9.929

(0.887) (0.878) (0.868)

9.579 9.664 10.180

(0.882) (0.873) (0.863)

2b3u (␲)

13.360

(0.852) (0.855) (0.834) (0.009) (0.674) (0.095)a (0.895) (0.892)

9.191 9.235 9.838

7

9.274 9.365 9.833 13.541 11.732 12.434 12.112 12.507

11.897

(0.839)*

11.995

(0.836)*

12.164

(0.830)*

8 9

14ag (␴) 10b2u (␴)

13.924 14.263

10

8b3g (n)

14.550

12.512 12.950 13.780

(0.840) (0.008)b (0.019)c

11

1b1g (␲)

14.240

12.351 12.610 13.197 16.908 17.100 13.150 13.233 13.748 12.316 12.593 13.312 13.946 16.027 16.710 13.438 13.876 14.298 14.419 15.995 17.213 17.482 17.957 14.394 14.445 14.937 14.733 15.315 15.399 14.778 19.234 14.871 15.886 15.839 15.937 16.122 16.372 16.522 17.822 17.868 18.109 18.292 18.429 18.130 18.215 18.384 18.784 19.058 19.671 19.913 20.002 20.443 20.461 20.699 20.937 21.745

(0.008)d (0.749) (0.007) (0.050) (0.049) (0.142)e (0.741) (0.008) (0.137)f (0.039)g (0.391) (0.066) (0.062) (0.057) (0.056) (0.054) (0.321) (0.167) (0.077) (0.042) (0.047) (0.047) (0.839) (0.765) (0.174)h (0.526) (0.328) (0.094) (0.809) (0.052) (0.841) (0.848) (0.223) (0.577) (0.743) (0.633) (0.140) (0.095) (0.156) (0.136) (0.066) (0.128) (0.375) (0.256) (0.062) (0.432) (0.059) (0.393) (0.094) (0.075) (0.082) (0.051) (0.160) (0.040) (0.055)

12

13

14

12b1u (␴)

1b2g (␲)

1b3u (␲)

15.036

14.920

16.253

15 16

13ag (␴) 9b2u (␴)

16.563 16.570

17

7b3g (␴)†

16.947

18

10b1u (␴)

17.506

19 20 21

11b1u (␴) 12ag (␴) 8b2u (␴)

16.733 17.980 17.934

22 23

6b3g (␴)† 11ag (␴)

18.338 18.922

24

7b2u (␴)†

20.436

25

9b1u (␴)

20.792

26

10ag (␴)

21.573

27

6b2u (␴)

22.734

28

5b3g (␴)

23.602

11.831 12.424

(0.905) (0.834)*

12.054 12.458

(0.894) (0.891)

12.279 12.662

(0.889) (0.887)

12.404

(0.886)

12.543

(0.880)

12.744

(0.875)

12.252

(0.903)

12.531

(0.824)*

12.701

(0.816)*

13.579

(0.828)*

13.160

(0.888)

13.360

(0.883)

12.973

(0.900)

13.515

(0.837)*

13.675

(0.833)*

14.469

(0.820)*

14.387

(0.819)*

14.554

(0.812)*

14.261 14.114

(0.877) (0.883)

14.374 14.121

(0.872) (0.875)

14.551 14.317

(0.867) (0.870)

14.784

(0.876)

14.866

(0.868)

15.037

(0.863)

15.056

(0.855)

15.080

(0.851)

15.184

(0.845)*

14.622 15.651

(0.888) (0.872)

14.722 15.652

(0.877) (0.859)

14.894 15.801

(0.872) (0.853)

15.598 15.915 16.386

(0.867) (0.864) (0.854)

15.558 15.930 16.494

(0.857) (0.856) (0.848)*

15.711 16.084 16.597

(0.850) (0.849)* (0.842)*

17.833

(0.837)*

17.718

(0.832)*

17.862

(0.824)*

18.082

(0.854)

18.077

(0.842)*

18.198

(0.835)*

18.718

(0.825)*

18.652

(0.813)*

18.771

(0.800)*

19.751

(0.815)*

19.646

(0.804)*

19.764

(0.790)*



Exp.II 9.28

 9.50

9.63 9.77 11.62



11.84 12.28

12.41

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

69

Table 4 (Continued ) Label

M.O.I

E(HF/cc-pVDZ)

ADC(3)/6-31G

29

9ag (␴)

24.486

30 31 32 33 34 35 36 37 38

8b1u (␴) 5b2u (␴) 4b3g (␴) 7b1u (␴) 8ag (␴) 4b2u (␴) 7ag (␴) 6b1u (␴) 6ag (␴)

25.348 28.269 28.470 28.582 29.641 32.064 32.471 38.107 38.169

20.849 21.030 21.227 21.350 21.478 21.488 21.837 21.577

OVGF/6-31G

OVGF/cc-pVDZ

OVGF/cc-pVTZ

Exp.II

(0.044) (0.061) (0.096) (0.097) (0.054) (0.040) (0.084) (0.093)

Dominant electronic configurations together with their weights in brackets: (a) [s3 ]: [0.189] 2b2g −1 3b3u −1 3b2g +1 + [0.164] 2b2g −2 4b3u +1 + [0.196] 2b1g −1 1au −1 3b2g +1 [HOMO−1 (HOMO-3)−1 LUMO+1 + HOMO−2 (LUMO+1)+1 + (HOMO-1)−1 (HOMO-2)−1 LUMO+1 ]; (b) [s5 ]: [0.516] 2b2g −1 9b3g −1 3b2g +1 [HOMO−1 (HOMO-4)−1 LUMO+1 ]; (c) [0.394] 11b2u −1 3b3u −1 3b2g +1 [(HOMO-5)−1 (HOMO-3)−1 LUMO+1 ]; (d) [s2 ]: [0.331] 1au −1 3b3u −1 3b2g +1 + [0.318] 2b1g −1 2b2g −1 3b2g +1 [(HOMO-2)−1 (HOMO-3)−1 LUMO+1 + (HOMO-1)−1 HOMO−1 LUMO+1 ]; (e) [0.202] 2b1g −1 11b2u −1 3b2g +1 + [0.291] 9b3g −1 1au −1 3b2g +1 [(HOMO-1)−1 (HOMO-5)−1 LUMO+1 + (HOMO-4)−1 (HOMO-2)−1 LUMO+1 ]; (f) [s1 ]: [0.333] 3b3u −2 3b2g +1 + [0.210] 2b1g −2 3b2g +1 [(HOMO-3)−2 LUMO+1 + (HOMO-1)−2 LUMO+1 ]; (g) [s4 ]: [0.493] 2b2g −2 3b2g +1 [HOMO−2 LUMO+1 ]; (h) [0.212] 9b3g −1 3b3u −1 3b2g +1 [(HOMO-4)−1 (HOMO-3)−1 LUMO+1 ]. I Between brackets, the most important contribution to the nature of the bond is indicated: oxygen lone pair (n), ␲-bond and ␴-bond. II Lauer et al. [28]. a At binding energies larger than 14.0 eV, only the ADC(3)/6-31G ionization lines with pole strenghts larger than 0.04 are given here; see Table 5 for further data. * Breakdown of the MO picture of ionization; see [12b]. † Important minor contribution of an oxygen lone pair.

to enhanced electron pair removal (PRM) effects [2,51], resulting in a destabilization of the cation, and a positive contribution to the ionization energy therefore, by virtue of the removal of the electron correlation that is associated in the initial state with the ionized electron. For these two orbitals, which define the HOMO and HOMO-1 levels of the target molecule at the HF level, the orbital and electron pair relaxation contributions still dominate the corrections to the KT estimates of the corresponding ionization energies, but the energy shifts towards lower electron binding energies do not exceed ∼0.6 eV. For similar reasons (see also the early school case studies by Cederbaum of the n- and ␲-ionization thresholds of N2 [4b,52]), a reversal of the energy order between the 3b3g (n, 5) and 1b2g (␲, 6) orbitals is observed when comparing the 1p-GF (ADC(3), OVGF) results with the KT estimates. It is worth mentioning that, although they strongly underestimate the experimental ionization energies as a result of the self-interaction error that is inherent to standard exchange-correlation functionals [53], and the too fast decay therefore of the electronic potential at large distances [54], the corresponding B3LYP/aug-cc-pVDZ Kohn–Sham (KS) orbital energies [55] are found to correctly reproduce the reversal of ␲- and n-levels among the six outermost lines: this can be seen as a manifestation of the meta-Koopmans theorem [56] for density functional theory, which after a change in sign assimilates KS orbital energies to relaxed ionization energies. The interested reader is referred in particular to Ref. [56b] for a formal derivation of this approximate relationship employing Dyson orbitals and their spectroscopic (pole) strenghs. This approximation becomes an exact equality for the highest occupied molecular orbital (Janak’s theorem [57]), provided the exact exchange-correlation functional is used. The first four outermost bands in the HeI photoelectron spectra are sharp, which is in line with their n- or ␲-nature. As usual, due to the enhancement of vibrational couplings, one-electron lines relating to ␴-levels associated with C–C and/or C–O chemical bonds are found to be more strongly broadened. ADC(3) calculations along with the cc-pVDZ basis set provide in general insights within ∼0.2 eV accuracy into one-electron ionization energies, with the noticeable exception of the outermost ␲-orbital [2b3u (3)] for which a particularly strong discrepancy, of ∼0.4 eV, is noted. This

is a reminiscence of our above remark regarding the dominance of PRM effects upon the ionization of ␲-levels: since these effects are described through the interplay of double electronic excitations across the gap between occupied and virtual levels, they are known to enhance the dependence of the ␲-ionization energies of large conjugated systems onto the quality of the basis set [12d,58]. Comparison with the OVGF results displayed for one-electron ionization lines in Table 1 shows indeed that this discrepancy is partly ascribable to limitations of the basis set. The ionization energies characterizing the four outermost orbitals are found to increase by ∼0.3 to ∼0.5 eV when replacing the cc-pVDZ basis set by the cc-pVTZ and cc-pVQZ basis set. Taking into account the differences between the OVGF/cc-pVDZ and ADC(3)/cc-pVDZ results, one gets through extrapolations ADC(3)/cc-pVQZ estimates of 10.24 and 11.07 eV for the n- and ␲-ionization thresholds, to compare with experimental [He I, i.e. adiabatic] values of 10.11 and 11.06 eV, respectively. The ADC(3)/cc-pVQZ estimate for the first ionization energy compares also highly quantitatively, within 0.06 eV, with the results of calculations, at the confines of non-relativistic quantum mechanics [CCSD(T)/cc-pVQZ level], of the vertical energy difference between para-benzoquinone in its neutral ground state and its lowest ionized state (Table 3). Extrapolation to the limit of an asymptotically complete (cc-pV∞Z) basis set using Feller’s [48] and 3-point Schwarz’s [49] regressions for HF and correlation energies, respectively, indicates in turn convergence of this vertical ionization energy threshold within chemical accuracy (1 kcal/mol = 0.04 eV), with regards to further improvements of the basis set. An estimate of 10.06 eV is thereby correspondingly obtained for the adiabatic ionization threshold, in almost perfect match with the He(I) value (10.11 eV), upon adding B3LYP/cc-pVTZ corrections for geometrical relaxation effects (−0.063 eV) and change in zero-point vibrational energies (−0.095 eV) to the CCSD(T)/cc-pV∞Z vertical ionization energy of para-benzoquinone. 4.2. Anthracenequinone Compared with the results of the preceding section for parabenzoquinone, the ADC(3)/6-31G spike spectrum that is displayed in Fig. 3, along with the numerical data of Tables 4 and 5, indi-

70

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

Fig. 3. Comparison between the (a) experimental PE spectrum (Lauer and Schäfer [28]) and (b) theoretical ADC(3)/6-31 G ionization spectrum of anthracenequinone (C14 H8 O2 , D2h ) using an FWHM value of 0.5 eV.

cates overall a strengthening of many-body effects upon an increase of system size, and a closure of the fundamental (HOMO–LUMO) gap therefore. In line with this closure, we note in particular that (1) the outermost oxygen lone-pair levels are subject to particularly strong relaxation effects (−2.2 eV); (2) the shake-up fragmentation indeed intensifies, yielding more strongly broadened spectral bands and less resolved signals therefore; and (3)

the shake-up onset [s1 ] in the ␲-band system decreases to 12.3 eV, whereas the related pole strength drops to  = 0.137. This line is a satellite of the 1b2g orbital (13) that relates dominantly to the 3b3u −2 3b2g +1 [(HOMO-3)−2 LUMO+1 ] and 2b1g −2 3b2g +1 [(HOMO1)−2 LUMO+1 ] electronic configurations of the cation (Table 4). The 2b2g −2 3b2g +1 [(HOMO)−2 LUMO+1 ] configuration borrows its intensity to the same parent state, to yield a second satellite with

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

71

Table 5 Further ionization lines identified at the ADC(3)/6-31G level for anthracenequinone. Label

M.O.I

ADC(3)/6-31GII

1

2b2g (␲)

19.102 (0.007), 19.402 (0.011)

2

2b1g (␲)

19.301 (0.006)

3

1au (␲)

19.202 (0.010)

7

2b3u (␲)

15.890 (0.026), 16.085 (0.019), 16.286 (0.034), 19.277 (0.009)

11

1b1g (␲)

17.225 (0.008), 17.378 (0.010), 18.786 (0.006)

13

1b2g (␲)

14.665 (0.032), 15.081 (0.013), 15.461 (0.022), 15.830 (0.021), 17.367 (0.011), 17.485 (0.009), 17.969 (0.007), 19.137 (0.005)

14

1b3u (␲)

15.097 (0.025), 15.402 (0.015), 16.645 (0.009), 16.903 (0.032), 17.657 (0.010), 18.536 (0.006), 18.705 (0.009), 18.761 (0.008), 19.585 (0.023)

15

13ag (␴)

20.918 (0.006)

18

10b1u (␴)

20.787 (0.007)

20

12ag (␴)

16.633 (0.007), 21.644 (0.005)

21

8b2u (␴)

15.237 (0.024), 20.809 (0.010)

22

6b3g (␴)†

16.368 (0.020), 16.722 (0.025), 17.104 (0.012), 17.522 (0.009), 17.666 (0.006)

23

11ag (␴)

17.326 (0.006), 17.745 (0.011), 18.469 (0.017), 19.480 (0.019), 19.626 (0.024)

24

7b2u (␴)†

17.341 (0.038), 17.539 (0.013), 18.025 (0.035), 18.167 (0.031), 18.267 (0.032), 18.472 (0.030), 18.631 (0.036), 19.363 (0.009), 21.206 (0.006)

25

9b1u (␴)

17.632 (0.017), 17.686 (0.011), 17.896 (0.036), 18.059 (0.010), 18.303 (0.008), 18.415 (0.019), 18.480 (0.024), 18.550 (0.037), 18.592 (0.010), 20.132 (0.005), 20.394 (0.005)

26

10ag (␴)

18.153 (0.006), 18.298 (0.010), 18.635 (0.009), 18.756 (0.037), 18.863 (0.010), 19.104 (0.025), 19.206 (0.008), 19.395 (0.025), 19.445 (0.038), 19.720 (0.023), 19.767 (0.036), 19.931 (0.005), 20.352 (0.007), 20.748 (0.015), 21.789 (0.029)

27

6b2u (␴)

19.098 (0.006), 19.166 (0.012), 19.342 (0.008), 19.427 (0.013), 19.514 (0.007), 19.788 (0.015), 19.827 (0.016), 20.108 (0.016), 20.131 (0.008), 20.195 (0.009), 20.209 (0.012), 20.285 (0.018), 20.361 (0.017), 20.572 (0.009), 20.781 (0.007), 20.877 (0.009), 21.227 (0.009), 21.315 (0.007), 21.662 (0.010), 21.689 (0.016), 21.725 (0.011), 21.821 (0.014), 21.865 (0.007)

28

5b3g (␴)

18.936 (0.006), 19.518 (0.008), 19.542 (0.009), 19.619 (0.012), 19.671 (0.005), 19.895 (0.027), 20.012 (0.037), 20.048 (0.009), 20.083 (0.023), 20.121 (0.007), 20.160 (0.009), 20.404 (0.013), 20.533 (0.011), 20.561 (0.013), 20.724 (0.023), 20.757 (0.015), 20.806 (0.011), 20.835 (0.032), 20.927 (0.024), 21.162 (0.010), 21.185 (0.014), 21.220 (0.012), 21.248 (0.006), 21.581 (0.009), 21.636 (0.007), 21.742 (0.022)

29

9ag (␴)

19.648 (0.013), 20.237 (0.011), 20.287 (0.013), 20.406 (0.007), 20.536 (0.022), 20.711 (0.006), 20.781 (0.011), 21.063 (0.008), 21.290 (0.012), 21.314 (0.006), 21.582 (0.022), 21.683 (0.006), 21.927 (0.009)

30

8b1u (␴)

19.940 (0.007), 20.278 (0.006), 20.423 (0.007), 20.808 (0.007), 21.024 (0.008), 21.221 (0.011), 21.288 (0.021), 21.425 (0.006), 21.510 (0.005), 21.710 (0.012), 21.743 (0.013), 21.816 (0.014), 21.839 (0.006), 21.846 (0.020)

I

Between brackets, the nature of the bond is indicated: oxygen lone pair (n), ␲ -bond and ␴-bond. Binding energies are given in eV, along with the associated pole strengths in brackets. † Important minor contribution of an oxygen lone pair.

II

the same symmetry [s4 ] at 12.6 eV [ = 0.04]. It appears therefore that, compared with para-benzoquinone, the very limited intensity of the shake-up onset of anthracenequinone is not only the result of the enhanced delocalization of ␲-orbitals, but also the outcome of the near-energy degeneracies, within ∼0.2 eV, of the four outermost orbitals, which all belong to the ␲-band system. In the ␴-band system, the one-electron picture of ionization holds up to 16.4 eV. He(I) measurements will remain free of shake-off bands, since CCSD(T)/cc-pVDZ calculations locate the vertical double ionization threshold at ∼22.2 eV. In spite of the strength of relaxation effects for the levels that dominantly relate to the oxygen lone pairs (n), OVGF and ADC(3) results for anthracenequinone demonstrate this time that the KT energy order remains valid up to the shake-up onset at 12.4 eV. In qualitative agreement with the available He(I) measurements, the ADC(3) simulation of Fig. 3b points out to two bands extending

from 9.2 to 10 eV, and from 11.7 to ∼12.6 eV. The outermost ionization line relates to a ␲-orbital, namely 2b2g . An ADC(3)/cc-pVTZ estimate of 9.63 eV is correspondingly obtained for the vertical ionization threshold, upon combining the available ADC(3)/6-31G, OVGF/6-31G and OVGF/cc-pVTZ results. More quantitative insights into the He(I) ionization threshold are amenable by also taking into account (at the B3LYP/cc-pVTZ level) the geometrical relaxation energy (−0.016 eV) and changes in zero-point vibrational energy (−0.152 eV) that are associated with an adiabatic process: added to the above ADC(3)/cc-pVTZ estimate, these corrections yield a theoretical adiabatic ionization threshold of 9.46 eV, in rather good match with the experimental value of 9.28 eV. Some care is needed however in view of the near-energy degeneracies of the five lowest electronic configurations of the cation in a vertical depiction of ionization, from which multistate nuclear dynamical complications may be anticipated.

72

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

Fig. 4. ADC(3)/6-31G ionization spectrum of pentacenequinone (C22 H12 O2 , D2h ) (FWHM = 0.5).

4.3. Pentacenequinone

4.4. General trends and comparisons with large PAH compounds

Many-electron effects in the ionization spectrum strengthen further with pentacenequinone (Fig. 4, Tables 6 and 7 ). We note in particular that: (1) the outermost oxygen lone-pair levels are subject to a shift of 2.3 eV towards lower electron binding energies; (2) the shake-up fragmentation again intensifies, yielding more strongly broadened spectral bands and less resolved signals therefore in the outer-valence ␴-bands as well as in the innervalence region; and (3) the shake-up onset [s1 ] in the ␲-band system decreases further to 10.4 eV, where it emerges from the ADC(3) spike spectrum in the form of a rather well-separated and intense satellite of the 3b3u (9) orbital, characterized by a very significant spectroscopic (pole) strength of  = 0.21. In line with the near degeneracy of the two outermost orbitals, this satellite is merely a mixture of the 2au −2 5b3u +1 [HOMO−2 (LUMO + 1)+1 ] and 3b2g −2 5b3u +1 [(HOMO-1)−2 (LUMO + 1)+1 ] configurations of the cation. The [(HOMO-1)−2 (LUMO + 1)+1 ] configuration (3b2g −2 5b3u +1 ) borrows its intensity to another parent state, namely the 2b2g (7) orbital, to yield a minor satellite [ = 0.02] at slightly higher electron binding energies, around 10.8 eV. Clearly, due to interchange of the symmetry characteristics of the outermost ␲orbitals of the three investigated quinones, as well the totally different energy distribution of the related 1h parent states, it seems impossible to grasp on intuitive (chemical) grounds the evolution with system size of the ionization intensity which is individually borrowed by the lowest-lying shake-up states, without an actual calculation employing the ADC(3) or an equivalent scheme. Here again, the KT energy order appears to be valid up to the shake-up onset at 10.4 eV. In view of the dependence of the obtained OVGF results upon the basis set, the ADC(3)/cc-pVTZ vertical ionization threshold is predicted to lie at 8.38 eV. The adiabatic ionization threshold is correspondingly anticipated at 8.29 eV, upon incorporating in the model B3LYP/cc-pVTZ corrections for geometry relaxation (−0.05 eV) and changes in zero-point vibrational energies (−0.036 eV). The vertical double ionization threshold is equal to ∼19.3 eV, according to CCSD(T)/cc-pVDZ calculations.

Results from the preceding sections confirm the view [12] that the ␲- and ␴-band systems display two different shake-up ionization onsets, and indicate that the evolution of the actual intensities of individual shake-up lines is hardly predictable from the evolution of the underlying HF band structure. One may therefore wonder whether there exists a simple mean to foretell those situations were a breakdown of the orbital picture of ionization is to be expected, without having to perform prohibitively expensive ADC(3) or comparable calculations of all vertical excited states of the cation. Scrutinizing in details the results provided in Tables 1, 4 and 6 yields a positive answer to this most basic but legitimate question. In line with many other works from our group at Hasselt University (see e.g. Refs. [5o,9b,11,12]), significant breakdowns of the orbital picture of ionization level at the ADC(3) level can be anticipated from a drop of OVGF pole strengths below 0.85 (the threshold of 0.90 that was retained in the first implementations of this approach [4b,f,g] was obviously too restrictive). We would like thereby to advocate again [12b] some care in using the OVGF approach that has been implemented in the Gaussian98 or Gaussian03 packages of programs for computations of one-electron ionization energies, or results obtained with these softwares, since warning statements about the validity of the approach are not issued unless the OVGF pole strengths become smaller than 0.80. In spite of our concerns [12b], basic misunderstandings of the meaning of OVGF results (both for ionization energies and pole strengths) have already led to the most astonishing conclusions (see ref. [10e] and comments therein), and an urgent revision of the corresponding algorithms in the Gaussian package of programs appears therefore also to be highly desirable. If individual shake-up intensities are hard to apprehend, the extent of the shake-up contamination can on other hand be quite easily anticipated from changes in the underlying HF band structure, for instance upon increasing system size or upon substituting an atom by another atom or chemical group. This suggestion is supported by Fig. 5, in which we display the evolution of the shake-up onset [E(s1 ), in eV] as a function of the HF band gap [Eg (HF), in eV] of the three investigated quinones, as well as of benzene and a rather

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

73

Table 6 ADC(3) and OVGF calculation results for the ionization spectrum of pentacenequinone (C22 H12 O2 ). The binding energies are given in eV, along with the ADC(3) and OVGF spectroscopic factors (in parentheses)a . Label

M.O.I

E(HF/cc-pVDZ)

ADC(3)/6-31G

OVGF/6-31G

OVGF/cc-pVDZ

OVGF/cc-pVTZ

1

3b2g (␲)

8.267

7.827

(0.855)

7.694

(0.887)

8.026

(0.880)

8.250

(0.876)

2

2au (␲)

8.224

7.832 13.992

(0.860) (0.007)

7.637

(0.890)

8.026

(0.882)

8.238

(0.877)

3 4 5 6

3b1g (␲) 4b3u (␲) 14b3g (n) 17b2u (n)

9.028 9.387 11.422 11.876

8.495 8.647 9.054 9.463

(0.864) (0.839) (0.834) (0.814)

8.265 8.566 8.941 9.478

(0.890) (0.884) (0.871) (0.860)

8.434 8.762 9.174 9.649

(0.884) (0.880) (0.865) (0.857)

8.840 9.155 9.421 9.882

(0.876) (0.872) (0.860) (0.851)

7

2b2g (␲)

10.826

9.933 10.851

(0.823) (0.023)a

9.802

(0.873)

9.972

(0.867)

10.124

(0.862)

8

1au (␲)

10.917

10.055 12.363 13.069

(0.837) (0.011)b (0.009)

9.871

(0.876)

10.046

(0.868)

10.198

(0.864)

9

3b3u (␲)

12.167

10.362 10.698 13.899

(0.206)c (0.536) (0.052)

10.712

(0.839)*

10.855

(0.836)*

11.031

(0.830)*

10.722 11.010 11.192 13.759

(0.016)d (0.152)e (0.603) (0.014)

11.010

(0.843)*

11.167

(0.833)*

11.330

(0.826)*

10

2b1g (␲)

12.585

11 12

20ag (␴) 16b2u (␴)

13.379 13.483

11.514 11.644

(0.889) (0.890)

11.246 11.399

(0.898) (0.898)

11.499 11.650

(0.888) (0.887)

11.698 11.838

(0.883) (0.882)

13

13b3g (␴)†

14.025

11.884 12.062 12.574 13.281

(0.599) (0.254) (0.021) (0.024)

11.771

(0.885)

11.961

(0.876)

12.147

(0.871)

14

17b1u (␴)

14.239

12.301 12.363

(0.790) (0.092)

12.052

(0.893)

12.270

(0.882)

12.455

(0.877)

15

2b3u (␲)

14.409

12.008 12.403 12.493 12.870 13.330 13.559 15.428 15.967

(0.104) (0.263) (0.162) (0.128) (0.089) (0.012) (0.040) (0.046)

12.666

(0.821)*

12.780

(0.815)*

12.913

(0.809)*

12.398

(0.887)

12.591

(0.877)

12.789

(0.872)

13.271

(0.817)*

13.242

(0.825)*

13.393

(0.821)*

12.958

(0.814)*

13.062

(0.804)*

13.202

(0.797)*

12.919 13.824

(0.885) (0.880)

13.102 13.955

(0.874) (0.870)

13.283 13.686

(0.870) (0.866)

13.466

(0.880)

13.507

(0.871)

14.120

(0.865)

14.178

(0.800)*

14.121

(0.796)*

14.279

(0.786)*

16

19ag (␴)

14.624

12.625 12.654

(0.294) (0.572)

17

1b2g (␲)

14.776

11.522 12.159 12.442 12.720 12.815 13.066 13.207 13.384 13.685 13.837 15.484

(0.021) (0.040) (0.165) (0.133) (0.063) (0.019) (0.010) (0.120) (0.018) (0.007) (0.048)

12.049 12.550 12.623 12.943 13.122 13.280 13.497 13.571

(0.007) (0.079) (0.212) (0.052) (0.061) (0.018) (0.218) (0.049)

13.077 13.184 13.795 13.939 13.846 14.091

(0.286) (0.575) (0.522) (0.380) (0.408) (0.541)

13.231 13.631 13.702 13.938

(0.010) (0.056) (0.061) (0.232)

18

1b1g (␲)

14.955

19

15b2u (␴)

15.119

20

14b2u (␴)

16.042

21

12b3g (␴)

16.011

22

1b3u (␲)

16.139

74

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

Table 6 (Continued ) Label

M.O.I

E(HF/cc-pVDZ)

23 24

16b1u (␴) 15b1u (␴)

16.261 16.847

25

18ag (␴)

16.621

26

11b3g (␴)†

16.700

ADC(3)/6-31G

OVGF/6-31G

14.543 14.669 16.389

(0.048) (0.138) (0.050)

14.232 14.389 14.454 14.418

(0.828) (0.657) (0.137) (0.812)

14.291 14.491 14.695 14.990

(0.041) (0.332) (0.347) (0.050)

14.673 14.914 14.988 15.163 15.397 15.530 15.536 15.752 15.779

(0.839) (0.710) (0.090) (0.712) (0.046) (0.290) (0.502) (0.667) (0.087)

27 28

17ag (␴) 14b1u (␴)

16.906 17.251

29

10b3g (␴)

17.334

30

13b2u (␴)

17.766

31

13b1u (␴)

18.187

32

16ag (␴)

18.548

15.908 16.219 16.224 16.224

(0.539) (0.088) (0.056) (0.056)

33

12b2u (␴)

18.565

16.152 16.197 16.338 16.770

(0.183) (0.298) (0.260) (0.043)

17.064 17.078 17.125 17.194

(0.068) (0.386) (0.137) (0.131)

34

15ag (␴)

19.466

OVGF/cc-pVDZ

OVGF/cc-pVTZ

14.105 14.407

(0.881) (0.863)

14.253 14.528

(0.870) (0.863)

14.404 14.686

(0.865) (0.857)

14.273

(0.870)

14.358

(0.863)

14.512

(0.858)

14.309

(0.865)

14.398

(0.859)

14.567

(0.854)

14.410 14.885

(0.872) (0.861)

14.517 15.086

(0.861) (0.851)

14.665 15.036

(0.856) (0.840)*

15.074

(0.863)

15.175

(0.851)

15.303

(0.846)*

15.248 15.647

(0.856) (0.856)

15.241 15.757

(0.845)* (0.845)*

15.372 15.873

(0.838)* (0.839)*

16.065

(0.858)

16.043

(0.846)*

16.147

(0.832)*

15.934

(0.845)*

16.056

(0.838)*

16.175

(0.839)*

16.961

(0.845)*

16.953

(0.833)*

17.079

(0.825)*

35

9b3g (␴)

20.008

17.310 17.433 17.469 17.534 17.587

(0.141) (0.099) (0.041) (0.089) (0.111)

17.245

(0.838)*

17.221

(0.825)*

17.343

(0.815)*

36

11b2u (␴)†

20.115

17.641 17.972 18.118

(0.103) (0.051) (0.043)

17.424

(0.822)*

17.356

(0.815)*

17.485

(0.806)*

37

14ag (␴)

21.293

17.918 18.444 18.454 18.714 18.807

(0.073) (0.076) (0.085) (0.079) (0.122)

38

12b1u (␴)

21.761

18.703 18.863 18.970

(0.112) (0.092) (0.099)

39

10b2u (␴)

22.520

19.485 19.610 19.921 20.000

(0.049) (0.056) (0.153) (0.078)

40

13ag (␴)

22.632

19.293 19.492 19.535 19.764 20.031 20.037 20.343

(0.054) (0.061) (0.070) (0.059) (0.052) (0.044) (0.044)

41

9b2u (␴)

23.519

20.190 20.234 20.452 20.510 20.627

(0.054) (0.091) (0.059) (0.056) (0.042)

42 43 44

8b3g (␴) 11b1u (␴) 12ag (␴)

23.607 24.967 25.117

20.683

(0.060)

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

75

Table 6 (Continued ) Label

M.O.I

E(HF/cc-pVDZ)

45 46 47 48 49 50 51 52 53 54 55 56

7b3g (␴) 10b1u (␴) 8b2u (␴) 11ag (␴) 6b3g (␴) 9b1u (␴) 7b2u (␴) 10ag (␴) 6b2u (␴) 9ag (␴) 8b1u (␴) 8ag (␴)

27.393 27.602 27.945 28.874 29.206 29.223 30.755 31.281 32.600 32.729 37.848 37.910

ADC(3)/6-31G

OVGF/6-31G

OVGF/cc-pVDZ

OVGF/cc-pVTZ

Dominant electronic configurations: (a) [s3 ]: [0.265] 2au −2 4b2g +1 & [0.465] 3b2g −2 4b2g +1 [HOMO−2 LUMO+1 & (HOMO-1)−2 LUMO+1 ]; (b) [0.215] 2au −1 4b3u −1 5b3u +1 [HOMO−1 (HOMO-3)−1 (LUMO+1)+1 ]; (c) [s1 ]: [0.212] 2au −2 5b3u +1 & [0.202] 3b2g −2 5b3u +1 [HOMO−2 (LUMO+1)+1 & (HOMO-1)−2 (LUMO+1)+1 ]; (d) [s2 ]: [0.243] 2au −2 4b1g +1 & [0.214] 3b2g −1 2au −1 5b3u +1 [HOMO−2 (LUMO+2)+1 & (HOMO-1)−1 HOMO−1 (LUMO+1)+1 ]; (e) [s4 ]: [0.282] 3b2g −1 2au −1 5b3u +1 & [0.249] 3b2g −2 4b1g +1 [(HOMO-1)−1 HOMO−1 (LUMO+1)+1 & (HOMO-1)−2 (LUMO+2)+1 ]. I Between brackets, the most important contribution to the nature of the bond is indicated: oxygen lone pair (n), ␲-bond and ␴-bond. a At binding energies larger than 14.0 eV, only the ADC(3)/6-31G ionization lines with pole strenghts larger than 0.04 are given here; see Table 7 for further data. * Breakdown of the MO picture of ionization; see [12b]. † Important minor contribution of an oxygen lone pair.

large set of PAH compounds [12] – see Table 8 for details. Obviously, the relationship is merely linear [E(s1 ) = 1.271Eg (HF) − 1.261, r2 = 0.87]. The quality of the regression improves slightly (Fig. 6) if we compare the ADC(3) shake-up onset with a zeroth-order estimate obtained by subtracting to the HF band gap the HF energy of the HOMO [E(s1 ) = 0.544 [Eg (HF) + VIP(KT)] + 1.030, r2 = 0.89], provided benzene is excluded from the fit. Due to the interruption of ␲-conjugation in the central ring (Table 8), we note for instance that, compared with anthracene (pentacene), the vertical ionization energy of anthracenequinone (pentacenequinone) increases by ∼1.9 (1.9) eV (OVGF/cc-pVDZ results), which reflects an opening of the HF band gap by ∼1.8 (2.7) eV, yielding in turn an increase of the shake-up onset by ∼1.9 (2.4) eV. The OVGF/cc-pVDZ values for the vertical ionization energies that are provided in Table 8 are almost equal to results obtained using third-order Møller–Plesset Perturbation (MP3) theory and the same basis set: at the MP3/cc-pVDZ level, the VIE’s of benzene, naphthalene, anthracene, naphthacene, pentacene and hexacene amount to 9.13, 8.01, 7.24, 6.74, 6.40 and 6.16 eV, to compare with benchmark [CCSD(T)/cc-pV∞Z] estimates [58] of 9.22, 8.14, 7.41, 6.91, 6.56, and 6.42 eV, respectively. It appears therefore that one-electron ionization energies related to extensively delocalized ␲-levels are in general not extremely sensitive to methodological

Fig. 5. Linear regression of the shake-up onset as a function of the HF band gap (y = 1.271x − 1.261, r2 = 0.870).

improvements beyond third-order in correlation and upgrades of the cc-pVDZ basis set. In contrast, if the OVGF/cc-pVDZ values for the vertical electron affinities of the above listed oligoacene compounds are comparable with MP3/cc-pVDZ results [in the same order: −2.52, −1.25, −0.38, +0.19, +0.59 and +0.87 eV], they are still very far from convergence to the Full-CI limit, due to the limitations in the basis set and its inability to describe couplings with the continuum: at the CCSD(T)/cc-pV∞Z level, the VEA’s of benzene, naphthalene, anthracene, naphthacene, pentacene and hexacene are located at −1.53, −0.48, +0.28, +0.82, +1.21, and +1.47 eV, respectively [59]. Within the quinone series (Tables 1, 4 and 6), it appears overall that, due to the presence of more localized (lone-pair) levels that result into stronger relaxation effects, basis sets of triple-zeta quality are required for ensuring accuracies around ∼0.25 eV on one-electron ionization energies. Note again that, as the recapitulating Fig. 7 illustrates, the quality of OVGF/cc-pVDZ results for the first ionization energy deteriorates significantly as a result of the limitation of the basis set with a lowering HF band gap, and, thus, increasing system size, due to the increased importance of the pair removal contribution [58].

Fig. 6. Linear regression of the shake-up onset as a function of a zeroth-order estimate of the energy required for a HOMO−2 LUMO+1 shake-up ionization (y = 0.702x − 1.389, with r2 = 0.811; upon excluding benzene from the fit: y = 0.544x + 1.030, with r2 = 0.887).

76

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79 Table 7 Further ionization lines identified at the ADC(3)/6-31G level for pentacenequinone. Label

M.O.I

ADC(3)/6-31GII

3

3b1g (␲)

15.863 (0.006)

9

3b3u (␲)

14.352 (0.008), 14.964 (0.023), 15.372 (0.006), 16.102 (0.009)

10

2b1g (␲)

14.483 (0.012), 15.171 (0.012), 15.243 (0.023), 15.664 (0.019), 15.961 (0.005)

15

2b3u (␲)

14.229 (0.033), 15.203 (0.022), 16.040 (0.011), 16.885 (0.007), 16.967 (0.005), 18.840 (0.019), 18.931 (0.006)

17

1b2g (␲)

14.069 (0.006), 14.275 (0.013), 14.323 (0.019), 14.440 (0.038), 14.619 (0.016), 14.723 (0.012), 14.911 (0.023), 15.311 (0.005), 15.341 (0.019), 15.790 (0.011), 15.984 (0.011), 16.100 (0.014), 17.501 (0.006), 17.622 (0.013), 17.759 (0.009)

18

1b1g (␲)

14.142 (0.031), 14.315 (0.036), 15.288 (0.006), 15.511 (0.023), 15.520 (0.013), 16.162 (0.037), 16.456 (0.006), 16.869 (0.015), 17.139 (0.009), 18.614 (0.006), 18.858 (0.016)

22

1b3u (␲)

14.855 (0.016), 15.189 (0.023), 15.284 (0.008), 15.741 (0.027), 15.741 (0.027), 15.801 (0.036), 16.202 (0.022), 16.666 (0.026), 16.666 (0.026), 17.208 (0.016), 17.366 (0.006), 17.616 (0.011), 18.234 (0.009), 18.412 (0.010), 18.513 (0.011), 18.751 (0.005), 19.127 (0.006)

29

10b3g (␴)

15.501 (0.026), 15.518 (0.030), 17.598 (0.027)

31

13b1u (␴)

15.372 (0.030), 15.610 (0.022), 16.228 (0.023)

32

16ag (␴)

15.511 (0.031), 16.156 (0.022)

33

12b2u (␴)

16.224 (0.030), 16.816 (0.033)

34

15ag (␴)

16.867 (0.025), 17.625 (0.021)

35

9b3g (␴)

17.384 (0.031), 17.681 (0.014), 17.742 (0.015), 18.013 (0.017), 18.094 (0.015), 18.166 (0.012)

36

11b2u (␴)†

17.703 (0.024), 17.884 (0.028), 18.060 (0.021)

37

14ag (␴)

17.986 (0.026), 18.053 (0.030), 18.203 (0.035), 18.243 (0.025), 18.267 (0.024), 19.303 (0.022)

38

12b1u (␴)

18.627 (0.025), 18.727 (0.026), 18.751 (0.033), 18.800 (0.028), 18.900 (0.022), 18.919 (0.024), 18.994 (0.023)

39

10b2u (␴)

19.236 (0.023), 19.261 (0.037), 19.402 (0.036), 19.562 (0.022), 19.695 (0.022), 19.889 (0.029), 19.930 (0.028)

40

13ag (␴)

19.468 (0.029), 19.572 (0.034), 19.677 (0.025), 19.924 (0.033), 20.116 (0.022), 20.429 (0.032)

41

9b2u (␴)

20.089 (0.033), 20.193 (0.023), 20.354 (0.021), 20.391 (0.033), 20.470 (0.024), 20.600 (0.031)

42

8b3g (␴)

19.496 (0.014), 19.551 (0.015), 19.587 (0.012), 19.993 (0.014), 20.066 (0.012), 20.114 (0.022), 20.266 (0.013), 20.385 (0.030), 20.388 (0.015), 20.458 (0.028), 20.488 (0.011), 20.499 (0.010), 20.522 (0.032), 20.542 (0.027), 20.620 (0.016), 20.629 (0.011), 20.633 (0.011), 20.668 (0.019), 20.685 (0.025), 20.954 (0.022), 21.043 (0.011), 21.051 (0.018), 21.073 (0.014)

I

Between brackets, the nature of the bond is indicated: oxygen lone pair (n), ␲ -bond and ␴-bond. Binding energies are given in eV, along with the associated pole strengths in brackets. † Important minor contribution of an oxygen lone pair.

II

5. Conclusions and outlook for the future Owing to their high symmetry point group, and a natural division of their electronic structure into merely independent ␲- and ␴-band systems, polycyclic aromatic hydrocarbons and many of their planar derivatives represent highly ideal systems for studying the consequences of electron correlation onto valence ionization spectra. In the present work, we have confronted an extensive series [12] of OVGF and ADC(3) calculations on benzene, azulene, oligacenes and related angular benzolog compounds with new results obtained for quinone derivatives, namely p-benzoquinone, anthracenequinone, pentacenequinone. From the present review, we may conclude that the shake-up onset in the ␲-band system of large conjugated molecules increases linearly as a function of the HF band gap. Therefore, any disruption of long-range ␲conjugation by a chemical substituent or departure from planarity will obviously restrict the extent of the shake-up contamination in the outer-valence region, and in the ␲-band system in par-

ticular. The present review also shows that the dependence of the outermost one-electron ionization energies onto the quality of the basis set increases in an approximately linear way as the HF band gap decreases, due to the enhancement of electron pair removal effects. Although they yield a disruption of ␲-conjugation, substituents bearing more localized lone-pairs may also enhance the basis set dependence of OVGF or ADC(3) results, this time because of the exacerbation of orbital and electron pair relaxation effects. These latter effects may in some extreme cases, as for instance p-benzoquinone, result into an inversion of the energy order of ␲- and lone-pair levels, compared with a firstorder depiction of ionization (Koopmans’ theorem). In this case, a comparison with the order of Kohn–Sham orbital energies confirms the validity of the meta-Koopmans’ theorem for density functional theory. Basis sets of triple-zeta quality are therefore usually required for ensuring accuracies of ∼0.2 to ∼0.3 eV in OVGF calculations of the one-electron ionization energies of large conjugated systems con-

S. Knippenberg, M.S. Deleuze / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 61–79

77

Table 8 Correlation between the vertical ionization potential (VIP) and vertical electron affinity (VEA) of PAH compounds with the extent of the largest sequence of conjugated benzenoid units in a row (N) for these compounds, and the HOMO–LUMO HF or OVGF quasi-particle band gap (Eg = VIP − VEA). IP describes the discrepancy between the theoretical OVGF/cc-pVDZ predictions and the best experimental values available so far. Eg measures the contribution of electronic correlation and relaxation to Eg and Es1 denotes the energy of the first shake-up line, obtained using ADC(3)/6-31G. All results are expressed in eV* . N p-Benzoquinone Benzene Anthracene–quinone Naphthalene Pentacene–quinone Triphenylene Phenanthrene Chrysene Pyrene Azulene Coronene Anthracene Perylene 1.2, 3.4 Dibenz-anthracene 1.2, 5.6 Dibenz-anthracene 1.2, 7.8 Dibenz-anthracene 1.12 Benzo-perylene Anthanthrene Naphthacene 1.2, 6.7 Diben-zopyrene Pentacene Hexacenee

0 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 5 6

VIP (OVGF) 9.966 9.044 9.090 7.847 8.026 7.630 7.634 7.302 7.090 7.057 7.031 7.202 6.601 7.119 7.073 7.105 6.824 6.313 6.533 7.130 6.150 5.865

IP (Exp)a 10.0 ± 0.1 9.243 ± 0.000 9.25 ± 0.12 8.144 ± 0.001 – 7.87 ± 0.02 7.891 ± 0.001 7.60 ± 0.01 7.426 ± 0.001 7.42 ± 0.02 7.29 ± 0.03 7.439 ± 0.006 6.96 ± 0.01 7.39 ± 0.02c 7.38 ± 0.02c 7.40 ± 0.02c 7.17 ± 0.02 6.92 ± 0.04 6.97 ± 0.05 7.40 ± 0.04d 6.63 ± 0.05 6.40 ± 0.04

IP 0.0 ± 0.1 0.200 0.16 ± 0.12 0.297 ± 0.001 – 0.24 ± 0.02 0.26 ± 0.03 0.30 ± 0.01 0.336 ± 0.001 0.37 ± 0.02 0.26 ± 0.03 0.24 ± 0.04 0.36 ± 0.01 0.27 ± 0.02 0.31 ± 0.02 0.29 ± 0.02 0.35 ± 0.02 0.61 ± 0.04 0.44 ± 0.04 0.37 ± 0.04 0.48 ± 0.05 0.54 ± 0.04

VEA (OVGF) +0.553 −2.605 +0.307 −1.304 +0.214 −1.094 −1.141 −0.763 −0.536 −0.303 – −0.438 −0.005 −0.429 −0.431 −0.435 – – +0.158 – +0.585 +0.909

Eg (HF) 11.417 12.798 10.244 10.215 9.095 10.061 9.996 9.280 8.654 8.385 8.58 8.483 7.597 8.807 8.786 8.832 8.11 6.81 7.278 9.01 6.403 5.737

Eg (OVGF) 9.413 11.649 8.783 9.151 7.812 8.724 8.775 8.065 7.626 7.360 – 7.640 6.606 7.548 7.504 7.540 – – 6.375 – 5.565 4.956

Eg −2.004 −1.149 −1.461 −1.064 −1.283 −1.337 −1.221 −1.215 −1.028 −1.025 – −0.843 −0.991 −1.259 −1.282 −1.292 – – −0.903 – −0.838 −0.781

Es1 12.769 16.858 12.316 10.623 10.362 11.37 10.91 9.75 9.48b 9.566 9.332 10.371 8.01 9.39 10.11 9.41 8.982 7.422 8.991 9.522 8.014 –

*

This table partly summarizes results published in Deleuze et al. [12a]; Deleuze [12b]; Deleuze et al. [58]; Deleuze [12c,d]. The data given in italics result from this work. Ref. [63].× b ADC(3)/6-31G* data. c Schmidt [64]. d Boschi et al. [65]. e OVGF computations performed using 359 correlated molecular orbitals only. From a test on pentacene, this truncation of the “active space” is expected to yield an overestimation of the IP and EA by 5 and 8 meV, respectively. a

taining heteroatoms. Extrapolations indicate that, for a compound like p-benzoquinone, accuracies of ∼0.06 eV onto the outermost oxygen lone-pair electron binding energies will be amenable through ADC(3) calculations in conjunction with basis sets of quadruple zeta quality. When no heteroatom is present, theoretical insights into one-electron ␲-ionization energies approaching chemical accuracy (1 kcal/mol, i.e. ∼0.04 eV) are already achievable at the ADC(3) level with basis sets of triple-zeta quality, as was for instance the case in recent 1p-GF studies of the ionization spectra of large PAH compounds [12d], or C60 [60].

The scaling properties of shake-up bands with increasing system size make their computations far more challenging, because 2h-1p shake-up intensities tend on average to decrease inversely to the square of system size, whereas the number of 2h-1p shake-up states per 1h parent state increases quadratically [8,32]. A most tempting solution is to consider that most shake-up lines are not worth any mention or study, since their individual intensity is not really significant. However, shake-up lines with very limited pole strengths, say  < 0.02, may altogether borrow a very significant fraction of the ionization intensity (30% or more), and yield correlations bands that extend over several eV (see Tables 2, 5 and 7). To conclude the present review, we would like therefore to advocate the incorporation of band-Lanczos diagonalization techniques [32] into the highly powerful, semi-direct, and integral-driven algorithms that are already available in the Gaussian package of programs, for complete enough ADC(3) studies of the shake-up and correlation bands of large conjugated systems. In view of the most impressive accuracies that can be achieved nowadays for the outermost ionization energies of such systems, it would also make sense to reconsider the outcome of possible logarithmic divergences with increasing system size of the ADC(3) static self-energy, due to the long-range character of the Coulomb force [61] and slight violations of electroneutrality [32,62]. Acknowledgments

Fig. 7. Linear regression of the underestimation (IP) of the experimental ionization threshold at the OVGF/cc-pVDZ level (y = −0.067x + 0.912, r2 = 0.702).

This work has been supported by the FWO-Vlaanderen, the Flemish branch of the Belgian National Science Foundation, and by the Special Research Fund (Bijzonder OnderzoeksFonds) of Hasselt University. S.K. acknowledges also financial support from the German Alexander von Humboldt Foundation. He is most grateful to Prof. A. Dreuw for his hospitality and support at Frankfurt University.

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