Near-edge core photoabsorption in polyacenes: model molecules for graphite

Chemical Physics ELSEVIER

Chemical Physics 196 (1995) 47-58

Near-edge core photoabsorption in polyacenes: model molecules for graphite Hans/~gren a, Olav Vahtras a, Vincenzo Carravetta b a Institute of Physics and Measurement Technology, University of Link6ping, S-581 83 Link@ing, Sweden b lstituto di Chimica Quantistica ed Energetica Molecolare del C.N.R., Via Risorgimento 35, 56100 Pisa, Italy Received 12 January 1995

Abstract We present calculations on near-edge X-ray absorption fine structures (NEXAFS) for pyrene and for molecules in the polyacene series; benzene, naphthalene, anthracene, and tetracene. Results from these model molecules are used to characterize the NEXAFS spectrum of graphite. Calculations are carried out with an ab initio static exchange method recently made applicable to large species. The trends of different NEXAFS features with respect to the site of ionization and with respect to the number of hydrocarbon rings are studied. In contrast to the linear polyene series, which shows a decay in intensity and delocalization of the first rr* level with the size of the system, the polyacene series shows a rapid build-up of 7r* excitons, with constant energy and intensity, conforming with a recent experimental observation of a zr* excitonic state for graphite. The excitonic character is though different for the symmetry non-related carbon atoms in the polyacene series. The salient double peak feature in these spectra is firmly established as due to chemical shifts. Except for the end atoms, there is only one zr* exciton per site. Possible excitonic character of the ~* resonances in graphite is discussed in terms of trends found for the polyacene series of the NEXAFS spectra.

1. Introduction Currently there is much debate over the appearance o f excitons, the effect o f the localized core hole, and the use o f initial and final state rules for interpreting near-edge core absorption spectra (NEXAFS) in various types of compounds. For small molecules the consensus is that the energy levels shift and relocalize according to the creation of each particular core hole, i.e. they would follow a 'final state' rule, while for large or infinite systems with a reduced electronhole interaction, the notion of an 'initial state rule' has been put forward, meaning that the interpretation of NEXAFS spectra can be conducted in terms of the energy bands and density o f states (DOS) of

the ground state. Connected to the latter notion is the building block picture. For a homologous series of compounds, such as polyenes or the polyacenes here studied, this means that the energy and intensity features of NEXAFS spectra should be understood from the properties of their subunits (units cells) and, e.g., the excited ~- and or levels should evolve similar to what is found in Hiickel type energy diagrams [ 2]. For heterogeneous compounds the building block picture predicts additivity of the spectra referring to the different diatomic subunits. The initial state rule has in some cases been verified on purely experimental grounds, through comparison with inverse photoemission spectra or with electron transmission spectra, however, this notion and the building block picture have also been

0301-0104/95/$09.50 (~) 1995 Elsevier Science B.V. All rights reserved SSD10301-0104(95)00091-7

48

H. ftgren et al./Chemical Physics 196 (1995) 47-58

contested in several recent studies. Computations are of great value for resolving the issues referred to above, since each core site, each molecule, in a homologous series can be studied separately, and all trends in the NEXAFS spectra going from small to large, and eventually to the infinite system, can be followed. The direct atomic orbital static exchange method, developed by the present authors [ 1 ], has the potential for such studies as recently demonstrated in Refs. [ 1,3,4] for a few different types of oligomer chains. Likewise, defect band type calculations, using e.g. the Koster-Slater formalism, are useful for deciding the role of the core hole in the corresponding infinite system [ 5-7]. Polyenes represent perhaps the most natural onedimensional system for a systematic study of the size extensivity and convergence of NEXAFS spectra, graphite and diamond represent the corresponding two- and three-dimensional systems. The recent studies of polyenes in Ref. [ 3 ] predicted a strong decrease of 7r* intensity with the length of the oligomer chain, calling in question any excitonic feature of polyacetylene. A calculation on polyacetylene using a Greens function technique adapted for NEXAFS was consistent with this; a very low ¢r to o- intensity ratio was predicted [5]. In the one-dimensional system, the polyenes, the reduced ~r* excitation intensities refer to the delocalization induced by ~" conjugation. For diamond, excitonic states have been indicated experimentally in resonance X-ray emission [8] while for the two-dimensional system, graphite, the excitonic character of the NEXAFS spectrum has been disputed. Thus calculations based on ground state DOS only [9,10] as well as those obtaining the final state core hole perturbed DOS [ 6] have claimed agreement with measured NEXAFS data. Very recently, Br0hwiler et al. gave experimental evidence of both 7r* and o-* type excitons in graphite by identifying non-radiative participator decay at the relevant excitation energies [ 11]. From the above discussion it seems motivated to explore the graphite NEXAFS spectrum by simulating model molecules. In the present work we accomplish this by calculations of molecules in the polyacene series; benzene, naphthalene, anthracene, tetracene, and by calculations of pyrene.

2. Method and calculations

The static exchange Hamiltonian corresponding to a two open-shell singlet final state: N/2 ~-[J = h + Z ( 2 J i - g i ) i~j = F -

--~ Jj -~- g j

(1)

Jj + 2Kj

is computed. Here spin-restricted orbitals are assumed, j is the ionized shell, F is the standard Fock operator for double occupancy of the orbitals and Jj and Kj are the usual Coulomb and exchange operators. The molecular orbitals building up the static exchange Hamiltonian are obtained by an SCF optimization for the jth hole. As described in our previous work [ 1 ]. the direct approach uses an atomic orbital (AO) representation in which the STEX Hamiltonian matrix is constructed as 7-[Jab = hab + y ~ [ 2 ( a b l c d ) D C a - cd

(aclbd)DXd]

(2)

by modifying the density corresponding to double occupancy according to 1 Dcc = Dcd -- ~CcjCdj ,

(3)

Dcx = Dcd -- 2C~jCdj.

(4)

Here ccj is component c in MO vector j, and D the density matrix in atomic basis. The elements of the latter are used to screen small integral elements. We summarize the computational procedure as: (1) optimization of the ground and core hole orbitals by direct SCF and ASCF calculations; (2) computation of the modified core hole densities and the STEX Hamiltonian matrix in an augmented atomic orbital basis set; (3) transformation of the STEX matrix; (1 P ) ~ J ( 1 - P), where P projects out the occupied orbitals; (4) diagonalization of the projected STEX matrix to yield eigenvalues and eigenvectors; (5) computations of transition moments over the non-orthogonal sets of ground state and STEX molecular orbitals, which, together with the eigenvalues, provide the primitive (discrete and discretized continuum) NEXAFS spectrum;

H. figren et aL /Chemical Physics 196 (1995) 47-58

(6) Stieltjes imaging of the primitive spectrum to obtain the continuum profile of the NEXAFS spectrum. The bound molecular orbitals are obtained from the SCF and ASCF optimizations in step 1 by projection on a standard molecular basis set. This basis set is augmented in the STEX calculation in step 2 with a large diffuse basis set on the ionization site. This leads to an efficient calculation of the STEX matrix and therefore NEXAFS spectra close to the basis set limit. This means that we can obtain a close-to-correct independent particle interpretation of the NEXAFS spectrum. The remaining error stems from residual relaxation of the bound electrons due to screening induced by the excited electron. This error was noticeable for the lowest 7r* excited states for 'one-dimensional' polymers (and could be checked for by ASCF calculations), but negligible for Rydberg series of transitions [ 3]. Broken-symmetry core hole localized solutions are employed, since these are required to obtain the correct relaxation contributions. These solutions can be superposed and the matrix diagonalized in this basis to regain solutions which adapt to the point group symmetry of the molecule. Localization of ground state core orbitals is obtained by the method given in Ref. [12].

49

cal shifts of the ionization potentials and 7r* transition energies, the build up of ~r and tr transitions and the excitonic features, and the overall size and site dependency of the NEXAFS spectra (Section 3.4). Since NEXAFS spectra are positional dependent and chemically shifted, the convergence trends depend on which ionization sites are chosen; inner positions presumably converge to graphite while end or nearend positions do not. The different carbon atoms are labelled 1, 2, 3 .... counting from the 'mid' position to the end, with prefixes B (benzene), N (naphthalene), A (anthracene), T (tetracene), P (pyrene) for the different studied molecules, as depicted in Fig. 1. Fig. 8 plots the core ionization potentials for all series; end-, mid-, all-atom series. All results are obtained with the common large diffuse basis set described in the computational section, using the dipole length gauge for the transition operator. 3.1. Benzene Although studied both experimentally [ 13-15 ] and theoretically [ 14,16] on many occasions the NEXAFS spectrum of benzene has not been unequivocally as1

[ ~

benzene

3. Results and discussion

In previous applications of this method we have taken interest in the overall convergence of the NEXAFS spectra with respect to the length of the oligomer chain. For NEXAFS spectra of heterogeneous side groups, like the nitrogen spectra in n-alkylnitriles, the convergence is very rapid [ 1], while in conjugated systems, like the polyenes, it turns out to be quite slow [3]. Systems, with strong polar constituents show more irregular trends due to strong ground state contributions to the spectra and energy shifts, see e.g. Ref. [4]. Aromatic rings provide another set of systems with a presumably different convergence behaviour. In the following we investigate this behaviour by first analyzing the benzene spectrum in detail, Section 3.1, then the polyacene series naphthalene, anthracene and tetracene in Section 3.2. The NEXAFS spectrum of pyrene and its association to the graphite spectrum is given in Section 3.3. Finally we discuss in general terms some of the salient features of the chemi-

~ ~ ~

2 3 1

naphthalene

3 4 2

anthracene

4 5 tetracene

pyrene

Fig. 1. Diagram of investigated molecules indicating excitation sites for the computed NEXAFS spectra.

H. ~gren et aL /Chemical Physics 196 (1995) 47-58

50

j

......

~

11

I

L__

Benzene dz

a

Benzene tzp

b

2 0

--"

i

'

/

280

290

J

r

3~0

300 photon energy (eV)

L

t

,L

0.03

c

17r*e~u

0.02

Benzene dz

0.01 0 0.03

I e2u

d

Benzene tzp

0.02 0.01

e T 286

288

a

o

~° b2~ 290

photon energy (eV)

Fig. 2. Cls NEXAFS spectra from benzene. (a) Convoluted spectra with ligand DZ basis set. (b) Convoluted spectra with ligand TZP basis set. (c) Bar diagram of discrete part of (a). (d) Bar diagram of discrete part of (b). The convoluted spectra use a gaussian with FWHM = 0.5 eV.

signed. On a coarse scale the benzene NEXAFS spectrum shows four features, two discrete and two continuous type resonances. The symmetries of these resonances were assigned as ~-* for the discrete and tr* for the continuous resonances by Horsley et al. [ 14] who studied NEXAFS of free benzene and of benzene absorbed on a Pt( 111 ) surface. As discussed in Ref. [2] this contradicts the building block picture which predicts only one 7r* and only one o'* resonance in the NEXAFS spectrum because of the equivalence of all carbon-carbon bonds. In the MsXa picture this was explained as a form of resonance interaction between localized molecular states [ 14]. However, a subsequent polarization selective NEXAFS study of benzene on an Ag( 111 ) surface indicated o- character of the second discrete resonance at 289 eV, and was suggested by Yokoyama et al. [ 16] as due to a C l s ---,

tr* (CH) transition, basing on their CNDO/S calculations. At higher resolution the K-shell electron energy loss spectrum of Hitchcock et al. [ 13] uncovered two weaker transitions, at roughly 287 and 288 eV, thus preceding the 289 eV resonance. From energy considerations Schwarz et al. [ 17] assigned these as due to 3s(o-*CH) (287 eV), 3p (s, d) (288 eV), and 7r* b2g (289 eV) transitions. These authors also predicted a configuration splitting of the second ~r* b2g transition into two main components, the second component residing below the strong continuum resonance at 294 eV, and called in question the existence of a single C 1s---,b2g excitation. The simulated NEXAFS spectra of the polyacenes, presented in Figs. 2-7 for the different series, cover 30 eV and include a large part of the continuum. They are given in the 'a' figures using a convolution function of width 0.5 eV. The discrete parts are also given as bars in an enlarged scale, in the 'b' figures. In the STEX method all the discrete features from the EELS experiment come out well, and may therefore be used as a ground for an assignment (for instance, comparing two different off-center basis sets, 'DZ' and 'TZP', see computational section, there is only a common shift of 0.4 eV and very little change of intensity). This is true for the bound states and also for the second lowest 7r state residing right at the IP. The intensity distribution of the four-peak feature is well recapitulated, excitation energies are somewhat compressed and shifted upwards on an absolute scale. The shift of the lowest valence like 7r* and o-* levels is typical for STEX and refers to a residual screening effect (some of the enhancement of the first continuous o- resonance can be referred to multi-electron contributions as discussed below). The STEX calculations, which thus are close to the basis set limit, add three discrete peaks in addition to the first strong 7r* resonance, a fifth weak transition resides very close to the IE We obtain the five discrete peaks as being of ~r, o-, o-, tr and ~" character, respectively. Thus not only the number of resonances but also their order in terms of ~r and o- symmetries contrast the building block picture. A similar conclusion was recently reached for the short polyenes [ 3 ]. Concerning the 289 eV resonance, out results corroborate those of Yokoyama et al. [ 16 ] giving a o- assignment (O'CH). The too low intensity of the 294 eV resonance might confirm Schwarz' pre-

H. Agren et al./Chemical Physics 196 (1995) 47-58

51

a •

J_

J

1

i

I

F--

I

I

i

Naphtalene 1

Naphtalene 1

Naphtalene 2

Naphtalene 2

2 0 6

4 0 Q

2

"K

.

0 6

/

Naphtalene 3

,

I

T

[

,

Naphtalene 3

4

0.0

2 0 280

290

300 photon energy (eV)

~

310

2 6

o

2 8 photon energy (eV)

290

Fig. 3. Cls NEXAFS spectra from the three symmetry independent core sites of naphthalene. (a) Convoluted spectra (FWHM = 0.5 eV). (b) Bar diagram of discrete parts.

a

b 0.03

6

Anthracene 1

Anthracene 1

4

0.02

2

0.01

0 6

0 0.03

J

v

~

Anthracene 2

Anthracene 2

4

0.02

2

0.01

0 6

0 0.03

lr

L

Anthracene 3

Anthracene 3

4

0.02

2

0.01 0 0.03

0

Anthracene 4

Anthracene 4

I "K

0.02

4

0.01

280

~

290

1 300 photon energy (eV)

T

T 310

0 - - T 286

T-288 photon energy (eV)

290

Fig. 4. Cls NEXAFS spectra from the four symmetry independent core sites of anthracene. (a) Convoluted spectra (FWHM = 0.5 eV). (b) Bar diagram of discrete parts.

H. Agren et al./Chemical Physics 196 (1995) 47-58

52

b

a h

I

I

i

i

I

- - -

_.L

0"03 I Tetracene 1

7t-

I

Tetracene

1

i

~.-f-

0.03~ Tetracene 2

Tetracene 2 0.02 0.011-

ol

I

,

t IT

,,

,

,

0.03[ Tetraeene 3

Tetracene 3 0.021

7r

0.01

ol

11"

0.03t Tetraeene 4

Tetracene 4 0.02t lr

Tetracene 5

0.01 ~

o"

01 0.031

,

0

,

I

~

r

290

photon energy (eV)

,

d

Tetracene 5

0[

280

,

0.021 0.01 I

2~

I . I

oI

286

,

I

I

~

,

t

288 photon energy (eV)

Fig. 5. C l s NEXAFS spectra from the five symmetry independent core sites of tetracene. (a) Convoluted spectra (FWHM = 0.5 eV). (b) Bar diagram of discrete parts.

diction for a second CI b2g component, however, the existence in this region of so-called shake transitions associated to the very strong 7r*e2u resonance, provides an alternative explanation for the strength of this band. Apart from role of the building block picture in determining the number and character of visible states, the NEXAFS spectrum of benzene has been discussed concerning core hole induced symmetry breaking [18,19]. The first strong ~-* resonance shows some particular vibronic structure, which has been interpreted in terms of antisymmetric excitations that follow from pseudo Jahn-Teller type symmetry breaking o f the core excited state [ 18]. On the other hand recent X-ray emission spectra of benzene obtained by resonant excitation to the first e2u state strongly indicates interpretation in terms of full D6h symmetry of this state.

Many features of the benzene spectrum can be traced also in the larger polyacenes, in particular the sparse character in the discrete part, with only one dominating 7r* transition (for benzene the e2u transition). These strong 7r* transitions can also be traced in the smallest carbon containing molecules, e.g. carbon monoxide, where it is sometimes coined a discrete shape resonance [20], due to the collapse of the zr* orbital into the carbon site upon opening of a core hole. These 7r* transitions collect much of the total oscillator strength, which implies a considerably weakened Rydberg series in comparison with those of the constituent atoms. One can conclude that the NEXAFS spectrum of the smallest polyacene (benzene) is trivially excitonic; an initial state rule using the localization of the empty ground state e2u orbital, and the local 'p density of states' cannot explain the strongly enhanced ~r* transition. The STEX

H. Agren et al./Chemical Physics 196 (1995) 47-58

53

a

~ 6 4 2 0 6

_L

A_

•

J

Benzene

b a

Naphthalene 1

1

L

t

t_

A

4

L

Benzene

2 0 6 Anthracene 2 4

2

Anthracene 1

Tetracene 1

4 2 0 6

4 2 0 280

~ ^

Pyre ne 1

Tetracene 2 r

--r~'--------T

290

300 photon energy (eV)

310

280

T - - T

290

I

300 photon energy (eV)

I

310

Fig. 6. Cls N E X A F S spectra from mid-bottom (a) and mid-top positions (b) of polyacenes and of pyrene.

method obtains NEXAFS intensities from mutually non-orthogonal sets of ground and final state orbitals, and these intensities are therefore the properties of two, the initial- and the final-, states, being of quite different in character. For smaller molecules, the initial and final state rules should probably be replaced by a 'transition state' rule in which p-populations and natural orbitals referring to the transition density matrix are used.

3.2. Polyacenes The NEXAFS spectra of larger polyacenes (naphthalene in Ref. [21 ], tetracene and pentacene in Ref. [ 16] ) are quite similar to that of benzene, with a dominating LUMO 7r* transition in the discrete part of the spectra, and two features in the continuum. The main difference is that the strong discrete resonance appears in doublets, with a progressive increase of intensity for

the second component, and that the overall continuum cross section increases with the size of the chain. The different features of the benzene NEXAFS spectrum develop somewhat differently as more rings are added to the system. The continuum regions are enhanced and form a double to a triple resonance structure. As for benzene we find, except for some end-atom spectra (see below), only one intense zr* transition per core hole. Another salient feature is that the center of gravity for the chemically shifted 7r* transition energies varies only little along the series. Both features accord with experimental observations [ 16] but contrast an initial state rule which interprets the NEXAFS spectrum through the formation of the energy bands in the ground state. In electron transmission spectroscopy [ 22 ], which probes the negative ion states, there is a decrease in energy of the first ~r* signal in accordance with the lowering of the band edge. The constancy of the ~'* level in NEXAFS has been

54

1-1..~gren et al./Chemical Physics 196 (1995) 47-58

experimentally verified for several other ring containing compounds [ 16]. It is also in line with the observation for graphite that the concentration of oscillator strengths at the bottom of the unoccupied bands is not predicted by the density of states (core hole perturbed DOS calculations by Mele and Ritsko [6] ). As discussed below, the 7r* resonance develops somewhat differently depending on the site of excitation.

3.2.1. Site spectra

There are some salient features in the polyacene series of spectra, see Figs. 2-6. The series across the sites develops in a systematic way from benzene to tetracene, and spectra of a given site show consistent trends from one molecule to the other. We first note that in the polyacenes two chemically different carbon atoms can be distinguished, here called midbottom and mid-top carbon atoms; likewise there are end-bottom and end-top carbon atoms terminating the chain of rings. Taking anthracene as an example, these atoms are represented by sites 2, 1, 4, 3 given in Fig. 1, respectively. We discuss here the series of NEXAFS spectra pertaining to these four types of atoms. Starting with the discrete part of the site dependent spectra, we see for naphthalene split end-bottom (N3) and end-top (N2) spectra while the mid-bottom (N1) atom shows a very clean 'benzene-like' spectrum with only one strong 7r* peak. The anthracene end-spectra A4 and A3 are strikingly similar to those of the corresponding naphthalene positions (N3 and N2), while the mid-bottom (A2) position has become split with two closely spaced peaks. The mid (or mid-top, A1 ) spectrum is again very benzene-like on a coarse scale. Tetracene repeats this trend, but with even larger splitting in the T3 spectrum compared to the corresponding anthracene and naphthalene positions. Only one position, the mid-bottom position (T1), retains a complete benzene-like spectrum. Also for the continuum parts we observe trends, namely that the double-resonance feature is more pronounced for the inner than for the outer positions, i.e. opposite to the discrete part where the doubling of the (Tr*) resonances is more pronounced for the end positions. For the site dependent series we note that the difference in excitation energy and intensity of the first LUMO-zr* level is larger between the two midpositions than between the two end-positions. Also

the mid-atom difference grows larger with the chain size, i.e. it is larger for tetracene than for anthracene. Presumably, this difference converges to a bulk value beyond the chain lengths investigated here, and leads to a double-peak feature of the NEXAFS spectrum of polyacene. Comparing the trend for the mid-bottom positions (B, N1, A2, T1, P1), see Fig. 6a, we observe a remarkably constancy of intensity (6 Mb at 0.3 eV resolution), and only a slight, upward, shift of the excitation energy for the LUMO level. Both these facts are signatures of excitons; a non-excitonic character would imply a decrease in both intensity and energy (A2 deviates somewhat from the trend, but this position is the only in the series which is not centrosymmetric). Comparing the mid-top spectra (B, N2, A1, T2), Fig. 6b, we observe actually a smooth decrease of both intensity and energy, going from 5 Mb (N2) to 3.5 Mb (T2). With the signature used above, we thus anticipate the mid-top spectra to be less excitonic. End-bottom (B, N3, A4, T5) shows a very regular intensity shift; a decrease of the first ~r* and an increase of the second 7r* level. Only a marginal lowering of intensity is observed, and the full pattern seems to have converged with tetracene. Finally, the end-top series (B, N2, A3, T4) shows a trend quite similar to the end-bottom series (B, N3, A4, T5), thus a regular decay of LUMO intensity, from 6 Mb (B) to 3.5 Mb (T4), the increase of the second 7r* intensity is not as marked as for the endbottom atoms. Again the LUMO energy is very stable throughout the series, marking excitonic character.

3.2.2. Total spectra

The total spectra given in Fig. 7 can be compared with experimental spectra for benzene [ 13,14], naphthalene [21], tetracene [16] and pentacene [16], while the NEXAFS spectrum of anthracene, to our knowledge, is missing. A salient feature in the discrete part of these spectra is the double peak; this feature seems to split up and shift intensity to the second peak for increased chain lengths. The origin of the double peak behaviour has been the subject for some discussion, basically arguing if it is due to a chemical shift or due to the presence of a second strong ~'* excitation. The present simulations give an unequivocal answer; it is the chemical shift of the two symmetry independent polyacene carbon atoms

H. ,~gren et al./Chemical Physics 196 (1995) 47-58

b

a i

6

,

55

i

_

i

i

_

Benzene

4 2 0

20

Naphthalene

I ~ / ~

285

290

295

10 0 25

20

....

I ....

I ....

I ....

I ....

I''''

2O

1(3

15 10

:I

~

5

Tetracene

0

.... 280

270

280

290

300 photon energy (eV)

290

I 310

300

I 320

,/ 0 330

310

_J ,I,

280

Fig. 7. (a) Total Cls NEXAFS spectra of polyacenes and pyrene. (b) Experimental spectra. FLrst (top); electron energy loss spectrum of benzene by Hitchcock et al. [ 13] ; second: NEXAFS spectrum of benzene by Horsley et al. [ 14] ; third: NEXAFS spectrum of naphthalene by Hitchcock et al. [ 13 ]; fourth (bottom): NEXAFS spectra of evaporated thin films of tetracene and pentacene by Yokoyama et al. [ 16] (recorded at magic angle).

270

12345 L ,l

290

6

7

8

,,,I,,,

300

260 290360

,I , , ~ I

310

3i0'

P H O T O N ENERGY l eV

32C

320

56

H. ~tgren et aL /Chemical Physics 196 (1995) 47-58

which give rise to the double-peak structure, (here the mid-bottom and mid-top atoms), and there is only one 7r* level represented. We can also see that the apparent splitting and shift to the second peak actually is due to that the first, mid-top, peak lowers its energy and intensity for increasing chain length, while the second, mid-bottom, peak, being strongly excitonic, is stable both with respect to energy and intensity, compare Figs. 6a and 6b. Because the end-atoms do show strong second 7r* levels, the spectra for the shorter members in the polyacene series will be slightly complicated with respect to the longer ones, for which the end-atoms soon loose any importance. The continuum parts of the total spectra are unchanged for the longer chains of the series. In the experimental spectra of the shorter members (benzene and naphthalene) one discerns two features, at 295 and 300 eV, while the longer ones (tetracene and pentacene) have one additional resonance at 305 eV. Our simulation seems to reproduce the appearance of the 300 and 305 eV resonances in the series, while like for benzene, it gives much too low intensity at the 295 eV resonance. We associate this to a multi-electron nature of this low-energy resonance.

3.3. Pyrene and graphite The singly occupied p-orbitals of graphite form an intra-planar ~- system that is responsible for special optical properties and for the semi-metal character. The band gap is closing, but with a very low density of states at the closing positions. Polyacene, on the other hand has a finite, and quite large, band gap, and may for this reason not be considered an ideal representation of graphite. Pyrene contains the same number of rings as tetracene, but is evidently a better model for graphite, due to the more symmetrical positions of the rings. Still, the mid-atom (mid-bottom) spectra of the two molecules show very similar characteristics. This, together with the similarity between anthracene and tetracene concerning the mid-bottom spectrum, which is the only relevant one for pyrene, indicates that convergence to graphite features can be obtained with few building blocks, at least in the discrete part. This fast convergence can as such be taken as an indication of an excitonic character of the graphite NEXAFS spectrum.

The main difference between the graphite spectrum [ 11 ] on one hand and the pyrene and the polyacene spectra (experimental and theoretical) on the other is the positioning of the two o-* resonances. These reside very near the ionization edge and are close in energy for graphite. Brtihwiler et al. [ 11 ] derived excitonic character by observing signals in the corresponding non-radiative participator decay spectra, which were taken as indications that the core excited state is well-localized during the core-hole lifetime. They concluded that only the first of the two o-* states was sufficiently longlived to be seen as a participator in the following non-radiative deexcitation. Comparisons with benzene (see above), and also with small carbon containing compounds, in particular CO [23], indicate that the first 'o-*' exciton is associated with one or several multi-electron transitions, while the second (and possibly the third) might be an 'ordinary' closed channel shape resonance. Both of them are Feshbach resonant (they transcend the first ionization potential) and decay primarily non-radiatively. From calculations on small species we can suspect that the multi-electron transitions can be seen as satellites to the very strong Cls-~'* transition, and then as a discrete analogue of a shake-up transition. One can anticipate such 'analogous shake transitions' [ 23] to be particularly strong for aromatic compounds, because of the large relaxation and the ultra-strong oscillator strength for the 7r* level. One can speculate that the different character, discrete multi-electron-, versus shape resonant-, of the two lowest continuous resonances is of relevance for the fact that only the first resonance gives a participator decay signal and not the second [ 11 ].

3.4. Trends in the NEXAFS spectra In our previous work on polyenes [3] we studied the convergence behaviour of the NEXAFS spectra in three series: the end-atom, mid-atom and all-atom series. The end-atom series showed a monotonic and smooth convergence to the polymer value, the midatom a monotonic but non-smooth behaviour, while the all-atom, site dependent, series showed strong alternations. This alternant feature was most conspicuous for ionization potentials and 7r* excitation energies, but was present also for other spectral features. In spite of the limited number of sites and units investigated in the present work for the polyacenes, we

H. ~tgren et al./Chemical Physics 196 (1995) 47-58 Mid-bottom atoms

End-bottom atoms ~B ~-290.5 I

>•-290.5 ~IA4

e~

~1

>,

:~N3 ~-5

290

:~A2 ~7

290

.~

._N C _o

g

289.5

289.5

Mid-top atoms

End-top atoms ~B ~-290.5

>•290.5

>,

>,

:~N2

c ~_

c

~3

290

~4

.£

290

.N_ C 0

.g

289.5

289.5

~2

Tetracene all atoms

~-290.5 :~3

g

290

~5

~1

:~4

c _o 289.5 ~-2

Fig. 8. Core ionization potentials for mid-bottom, mid-top, end-bottom and end-top series, and for all tetracene sites. The x-axis denotesthe numberof rings in the system, except in the last figure, where it denotes the position of the excited carbon atom. can conclude that alternating features are present for the aromatic series of molecules studied here as well. The trends for the size dependency are for all cases monotonous both with respect to energies and intensities. However, the direction of the trends are quite different for polyacenes and polyenes, the former showing the largest differences in mid positions, the latter in the end positions. This is also reflected in the computed ionization potentials, as shown in Fig. 8 for the different series. The variation between two adjacent carbon atoms, A = IPn - IP,-I is largest for the midatoms, while for polyenes za increases towards the endatoms, d increases with chain size, it has the largest value for tetracene in the studied series. As shown recently [ 24] the trends of ionization po-

57

tentials of conjugated linear and cyclic hydrocrabons can be understood as truly final state effects due to the polarization induced by the core hole (initial state contributions to the IPs covary with the relaxation contributions but are of the order of 5 times weaker [24] ). The alternant behaviour could be very well rationalized in terms of a chemical shift model based on perturbation and 7r electron theories. Although the underlying 7r electron theory is more complicated for polycyclic compounds, it explains the quite different characteristics of polyacenes as well. It can be noted that alternant behaviour of this kind has been observed for substituted benzenes with respect to chemical shifts, proton affinities, and substituent constants [ 25 ], and is a basic property of these hydrocarbon systems. The size dependency of NEXAFS spectra of homologous compounds is stronger than for heterogeneous compounds, such as those with a side group attached to the hydrocarbon chain [ 1 ]. However, different homologous systems converge differently, and, as seen in the present work, different sites may have different size dependences. In the NEXAFS spectra of the polyacenes a noticeable decrease of 7r to tr intensity ratios with the number of ring subunits is predicted for the mid-top atom, while the spectra of mid-bottom sites are remarkably constant. This indicates quite different 'correlation lengths' for the two chemically shifted core sites. However, the decrease of zr* intensity is not as dramatic as for the linear polyene series even for the mid-top atoms. This indicates a qualitative difference in aliphatic and aromatic conjugation of the ~r* levels with respect to delocalization of the core-excited states.

4. Conclusions From the simulations presented in this work we arrive at the following conclusions. (i) The benzene NEXAFS spectrum is reinterpreted. After the first strong 7r* (e2u) excitation the discrete spectrum consists of three or states preceding the next 7r* state. (ii) We find that the double peak feature in the polyacene spectra is given by the chemical shifts of the 'bottom' and 'top' atoms, and not by multiple ~* states. Only terminal atoms show multiple structure in the discrete part.

58

H. /tgren et aL /Chemical Physics 196 (1995) 47-58

(iii) The NEXAFS spectra of the polyacenes show excitons. The excitonic character is site dependent; bottom-atom spectra show a strongly excitonic, benzene-like, feature, with constant energy and intensity, while top-atom spectra show a smooth decay in intensity and excitation energy with respect to the size of the polyacene chain. (iv) From comparisons of the discrete parts of the polyacene and pyrene spectra with that of graphite [ 11 ], we conclude that the latter is strongly excitonic, and refers to the benzene-like bottom-atom spectra of the polyacenes. (v) Several size and site dependent trends for the NEXAFS spectra of polyacenes have been unravelled. Most conspicuous is the alternant site dependent trends in the ionization potentials and the first core Cls-zr* excitation energies. (vi) Comparison between polyacenes and polyenes [ 3 ] reveals interesting differences. The latter show a strong decay of 7r* intensity, indicating little or no excitonic feature for the polymer (polyacetylene), thus contrasting the polyacene (graphite) case. The polyacenes show the strongest alternation effect for the mid (bulk) atoms rather than for the terminal atoms as the polyenes do. This indicates different delocalization of the screening 7r electrons for aliphatic and aromatic conjugations. Common for the polyacenes and the polyenes [ 5,3 ] is that the spectral features are more complex than predicted by the building block principle; apart from the first zr* excitation, the weak reminder of the discrete energy region is quite complex with many types of transitions. Concerning the continuous parts of the NEXAFS spectrum of graphite our conclusions are not as clearcut. Our close to basis set limit results account only for a minor fraction of the intensity for the first resonance, which is argued as due to strong multi-electron contributions. Secondly, the experimental graphite and polyacene spectra are different in the continuum, which might be due to the multi-layer structure of the former. Except for the first resonance we still find energy and intensity trends to be correctly interpreted by the STEX calculations also in the continuum parts of the polyacene spectra; for instance the development of a third resonance for the longer molecules is predicted. Tentatively we suggested that the multi-electron versus the shape type character of the two first o'* resonances could explain differences in the corresponding

participator decay spectra of graphite [ 11 ].

Acknowledgement We thank Paul Brtihwiler for communicating his graphite results prior to publication. This work was supported by a grant from CRAY Research Inc.

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