Reevaluation of electronic polarization energies in organic molecular crystals

Chemical Physics 115 (1987) 269-277 North-Holland, Amsterdam

269

REEVALUATION OF ELECTRONIC POLARIZATION ENERGIES IN ORGANIC MOLECULAR CRYSTALS

Naoki SAT0 ’

Department of Chemistry, Faculty of Science, Kumamoto Universiiy, Kurokami, Kumamofo 860, Japan

Hiroo INOKUCHI and Edger A. SILINSH 2

Institute for Molecular Science, Myodaiji, Okazaki 444, Japan

Received 1 December 1986

Effective electronic polarization energies for positive P& and negative P,; charge carriers in polyacene crystals have been reevaluated. By comparing the P& and P,; values obtained from the analyses of reported energy parameters with calculated data, it is shown that the widely accepted assumption that P,, + = P,;, in polyacene crystals is not valid. By applying recently reported data on optical Ez’ and adiabatic E:” energy gap values, the contribution of molecular (vibronic) polarization in the total effective polarization energies W$r and I+& has been estimated, and modified energy diagrams for polyacene crystals have been presented. Further, due to practically constant values of observed and calculated P& and P,;t in polyacenes, the gap energies between positive and negative charge carrier conduction levels have been estimated for several related aromatic hydrocarbons.

1. Introduction

Organic molecules in the solid state, due to weak van der Waals interaction, maintain their molecular identities to a large extent. This leads to a strong localization of excess charge carriers on individual molecules. As a result, a typical localization time rh of an excess carrier on a lattice site is, in anthracene crystals, two orders larger than the characteristic relaxation time 7, of electronic polarization of surrounding molecules in the lattice (ref. [l], p. 45). Therefore, electronic polarization is one of the most fundamental electronic processes in organic molecular crystals (OMC). It practically determines the self-energy of the charge carrier, and, consequently, the position of conductivity levels in the energy diagram of ionized states of the crystal [1,2].

t Present address: Department of Chemistry, College of Arts and Sciences. The University of Tokyo, Komaba, Meguro, Tokyo 153, Japan.

* Permanent address: Institute of Physics and Energetics, Academy of Sciences of Latvian SSR, 226006 Riga, USSR.

The many-electron interaction for the carrier forms, in fact, the conceptual base for the polarization model of ionized states in OMC, known as the Lyons model, and its modified variations (cf. ref. [l], p. 57).

According to the initial Lyons model [3,4], the electronic polarization energy P+ for a positive

charge carrier in OMC can be determined by the difference between the ionization energies of a free molecule Io and the crystal I,:

P’=I,-zc. (1)

Thus the polarization energy P+ can directly be evaluated from experimental ionization potentials obtained by ultraviolet photoelectron spectroscopy in the gaseous and solid states.

The polarization energy P- for a negative charge carrier is given by the second main pos- tulate of the Lyons model, i.e.

P-=A,-A,, (2)

where A, and A, are the electron affinities of a molecule and the crystal, respectively.

In this case experimental determination of the

0301-0104/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

210 N. Sato et al. / Polarization energies in poiyacene crystals

P- value is more complicated. Firstly, there are gap EG values in polyacene crystals, we have rather few reliable experimental data of A, mea- reevaluated the effective polarization energies, in- surements. Secondly, the A, value cannot be ob- dependently for negative WeTf and positive W&

tained from direct measurements. It can be esti- charge carriers. By comparing the W& and W$

mated only indirectly, by knowing the energy gap values with recently refined and extended polari- EG for a given crystal [l]. However, reliable data zation energy calculations, we shall demonstrate of EG values, as we shall see later, have only that the inequality W,T, # WTf is due to the contri- recently been obtained, even for anthracene-like bution of other kinds of charge carrier interaction, crystals. and thus the equality (4) is practically inualid.

Historically, the situation has been simplified by an ad hoc assumption that the polarization energy P according to eqs. (1) and (2) for non-polar aromatic OMC is practically determined only by charge-induced dipole interactions, and that the possible contribution of charge interaction with higher permanent and/or induced multipoles, or nuclear subsystem might be negligible [l-3].

Further, we shall demonstrate that, owing to the observed constancy of W,T, values for poly- scene crystals, it is possible to estimate the energy gap EG values for several other polycyclic aromatic hydrocarbons.

The charge-induced dipole interaction term Pid

can be obtained in isotropic approximation as the sum of the interaction for a charge e located on the molecule at the origin of coordinate (O,.O, 0) with all the other N - 1 neutral molecules of the crystal [3,1]:

2. Conceptual basis for reevaluation of polarization energies in polyacene crystals

New theoretical data for reevaluation have been provided by electronic polarization energy calculations in a series of recent studies by Munn and co-workers [5--71. The authors of ref. [5] extended the self-consistent polarization field approach of ref. [8] and developed a novel method for polarization energy calculations in terms of Fourier trans- formed lattice multipole sums. They also sub- stituted a point-charge approximation by a submolecular approach as a charge distributed over the rings of polyacene molecules. This made it possible to obtain reliable calculated Pid values not only for naphthalene and anthracene but also for naphthacene and pentacene crystals [7] (see table 3 below). In addition, as a matter of more importance, in the calculations of Munn and co- workers [5,7] plausible evaluation data of charge- permanent quadrupole interaction terms were obtained for the first time for polyacene crystals.

N-l

Pid = C ( e2ii/2r,4), k=l

(3)

where Cr is the mean isotropic polarizability of the molecule, and rk is the distance between the localized charge carrier and the k th molecular site.

It follows from the assumption that the polarization terms P+ and P- in eqs. (1) and (2) are caused on/y by charge-induced dipole interactions, i.e. P+ = Pid and P- = Pid, so that, further- more, since the term Pid is independent of the sign of a charge carrier according to eq. (3), the following equality could be valid:

P+=P-=Pi,. (4)

This equality which postulates the symmetry of electronic polarization for charge carriers of both signs has been generally believed to be valid and widely used as conceptual basis for drawing ionized-state energy diagrams in polyacene crystals L4.

In this work we have reexamined the present situation of polarization energy determination in OMC, and using recent reported data on energy

Non-polar organic molecules like polyacenes have no permanent dipole moment. However, due to the planar structure of the molecules, they have a permanent quadrupole moment f? which increases rapidly with increasing number of aromatic rings in the molecule.

Using reliable quadrupole moment 0 values estimated recently [9], the authors of refs. [5,7] calculated the charge-quadrupole interaction terms We, for polyacene crystals. These theoreti-

IV. Sat0 et al. / Polarization energies in polyacene crystals 271

cal evaluations show that the interaction term We, for polyacene crystals is of the order of 0.2 eV (see table 3 below) and, therefore, cannot be neglected.

Another important aspect is that in the case of charge-permanent quadrupole interaction the corresponding polarization energy component WA:’ is proportional to etl/rk, viz.

WA,“’ a eO/rk . (5)

As can be seen from eq. (5), the interaction energy in this case depends both on the sign of charge e and the quadrupole moment 19.

Therefore, as shown by Munn and co-workers [5,7], the total charge-quadrupole interaction terms have, in polyacenes, different signs, viz.

we’,= -we,. (6)

Thus, the assumed symmetry of electronic polarization for opposite charge carriers is broken, and the equality (4) widely used so far, is obviously not valid. This means that the effective electronic polarization energy P,,, determined experimentally should be different for positive and negative charge carriers, viz.

P& = P; + we” (7)

and

(8)

On the other hand, the calculation of Pia values, using the submolecular approach of a distributed charge [5,7], confirms, similarly with the case of the point-charge approximation, the following equality:

P~=P,=Pid, (9)

which should be used instead of the equality (4). This means that P& > P,T, viz.

PA - Gf = 2 I we, I. 00)

We have so far discussed only electronic polarization effects. However, at the present time there exists direct experimental evidence that the total effective polarization energy of a charge carrier includes, in addition to the electronic polarization energy terms Pid and We,, also a nuclear (vibronic) polarization term E,.

Firstly, the observation of the temperature-de- pendent component in the photoemission spectra of isopropylbenzene [lo] and violanthrene A [ll] films shows that the positive charge remaining in the bulk of molecular solids after photogeneration, in addition to the electronic polarization of surrounding molecules, polarizes also the intramolec- ular vibration modes of the molecule on which it is located, as well as dipole active modes of the nearest neighbouring molecules [lo], thus forming an extended ionic state in the crystal. As described previously [12,13], the new quasi-particle many- body interaction may be phenomenologically described in the framework of a nearly small molecular polaron approach.

Secondly, it has been shown that the relaxation energy E,, gained in the process of formation of a molecular polaron, can be determined experimentally from the difference between the optical EgP' and adiabatic E$ energy gaps of the crystal as follows [12,13]:

E, = $( E;P’ - E;d). (11)

Reliable values of EgP’ and E&_” have been recently obtained for anthracene, naphthacene and pentacene crystals (cf. ref. [13]): EgP’ from elec- tromodulation spectra [14,15] and EGd determined [14,13] from the activation energy spectra E.fh(hv)

of intrinsic photogeneration [16,17]. Consequently, in order to obtain the total effec-

tive polarization energy Weff, gained by the charge carrier in the crystal, the E, value of molecular (vibronic) polarization should be added to the terms of effective electronic polarization in eqs. (7) and (8).

As a result, we obtain the final equations for the evaluation of total effective polarization energies

(a) for the positive charge carrier:

W,:,=P,:,+E,=P,+ WQ+o+EE,, 02)

(b) for the negative charge carrier:

W& = P,; + E, = P, + We, + E,. (13)

(It has been assumed in eqs. (12) and (13) that Eb’=E, =E,, where E, is the mean value obtained according to eq. (11): see table 2 below.)

212 h? Sat0 et al. / Polarization energies in pobacene cfystah

Eqs. (12) and (13) will be applied in section 4 for semi-empirical evaluation of total polarization energies W,:f and F&r using the values of Pid and We, calculated in refs. [5,7] (see table 3 below) and the values of E, estimated experimentally [13] (see table 2 below). These values will be compared with independent estimates based on experimentally determined energy parameters, viz.

(a) for the positive charge carrier:

(b) for the negative charge carrier:

05)

3. Experimental and calculated energy parameters used for reevaluation of polarization energies in polyacene crystals

Most extensive studies have so far been per- formed on the effective polarization energy Wsr of the positive charge carrier according to eq. (14), based on measurements of the corresponding ionization potentials IG and I, using UV photoelectron spectroscopy. Thus, the W,:f (noted as P, so

far) values have been estimated for a number of organic solids including polyacene crystals [18-241.

Table 1 presents the most reliable data reported on I, and I, values for anthracene, naphthacene and pentacene.

The ionization energy IG can be determined by a number of independent methods, the most pre- ferable being ultraviolet photoelectron spectroscopy (UPS) and photoionization (PI), as well as some special spectroscopy techniques, such as Rydberg spectra (cf. ref. [l], p. 128). It must be borne in mind that UPS methods yield, as a rule, the vertical ionization potential I:, whereas photoionization and spectroscopic methods presuma- bly yield the adiabatic potential I&*. However, in polyacenes the difference AI = I: - I&* is sup- posed to be small, of the order of AI < 0.05 eV, i.e. it is smaller than the distribution range of reported values of 1, obtained by the UPS method (cf. ref. [l]). Therefore, one may suggest that the reported values of Io presented in table 1 have, most probably, almost equal reliability, and for this reason we prefer to use the aueruge value (Io) of these reported Io values for W,t evaluation.

The situation is similar, or even more com-

Table 1 Experimental values of the ionization energies of a molecule lo and the crystal I,-, and molecular electron affinities A, reported for

polyacenes (all values in eV)

Compound IG czG) k (*cd AG a)

(-4~)

anthracene 1.41 b, 1.42 5.95 h’ 5.71 0.55 I’ 0.58 1.42 =) 5.85 h, 0.51 I) 7.41=) 5.15 i, 0.60* s, 1.40 *I 5.61 j) OH* Q 1.38 ‘1 5.65 h,

naphthacene 1.04 b, 6.98 5.40 k, 5.26 0.88 ‘) 1.03 1.01 *) 5.30 ‘) 0.95* u)

6.91’) 5.25 m, 1.03 “’ 6.88 o 5.10 @ 1.10 * s,

1.18 ”

pentacene 6.74 b, 6.64 5.10 0) 5.01 1.19 U, 1.31 6.64 *) 5.01 P) 1.31”) 6.61 =I 5.00 9) 1458 s, 6.55 @ 4.85 n, 1:51* S)

a) * indicates calculated A, values. b, Ref. 1251. ‘) Ref. [l, p. 1211. *) Ref. 1261. ‘) Ref. 121). o Ref. 1281. @ Ref. 1291. h, Ref. 11, p, 129). i, Ref. 123,301. j) Ref. [30]. ‘) Ref. [31]. r) Ref. [32]. m, Ref. [33]. n, Ref. [18]. @ Ref. [24]. P) Ref. (341. * Ref. [l, p. 1251. ‘) Ref. [l, p. 1281. ‘) Ref. [35]. ‘) Ref. [36]. “) Ref. (311. “) Ref. [38].

i?. Sat0 et al. / Polarization energies in polyacene crystals 213

Table 2 Reported experimental values of optical ET’ and adiabatic E$ energy gaps and corresponding relaxation energies of molecular (vibronic) polarization in polyacene crystals (all values in eV)

Compound EZ’ E” G

anthracene 4.40 a) 4.10 a) naphthacene 3.43 b, 3.13 @ pentacene 2.83 b, 2.41’)

a) Ref. [15]. b, Ref. [14]. ‘) Ref. [13].

‘%

0.15 0.15 0.18

plicated [18] in the case of reported 1, values. The ionization energy of the crystal, I,, can be determined by two main methods - from the threshold of spectral dependence of photoemission quantum yield (SDQY) and/or from the energy distribution curves (EDC) of photoemitted elec- trons, according to Einstein’s law (cf. ref. [l], p. 124). Both methods yield slightly different results (see ref. [24]). Besides, the measured I, values may be influenced by the crystalline state of the sample [30,39], surface effects and so on. In order to decrease the role of possible methodological deviations, also in this case, we have preferred to use the average value (I,) of reported I, data (see table 1).

Since there are only few reliable experimental data of A, values for polyacenes, we have used the average (Ao) values from both experimental and reliable calculated A, data reported (see table

1). Table 2 presents the optical EgP’ and adiabatic

,!?A,” energy gaps recently estimated for anthracene,

naphthacene and pentacene [12-151 and the corresponding molecular (vibronic) polarization energies E,, used in eqs. (ll)-(13). Finally, table 3 lists the calculated values of the electronic polarization components, viz. pid, II’& II’& and the corresponding effective electronic polarization energies P& and P,;, of polyacenes according to MUM and co-workers [5,7], obtained by the Four- ier transformation method in submolecular approximation.

4. Results of polarization energy reevaluation for polyacene crystals

The effective polarization energies W$ and W,;, of positive and negative charge carriers, respectively, in anthracene, naphthacene and pentacene crystals, obtained according to eqs. (14) and (15), are presented in table 4. In the evaluation proce- dure average experimental values of the energy parameters, viz. (Io), (I,) and (Ao), were used (see table l), as well as reported experimental adiabatic gap energies Eg’ (table 2).

In table 4 theoretically evaluated W,:f and W,T, values obtained from eqs. (12) and (13) are also given. In this case values of parameters Pid, we’, and We,, as calculated by MUM and co-workers [5,7], were used (see table 3), the only experimentally determined parameter being E, (see table 2).

As can be seen from table 4, both experimental and theoretical evaluation data unambiguously demonstrate the asymmetry of polarization terms: Wzf is considerably, by a value of 0.4-0.5 eV,

Table 3 Reported calculated values of charge-induced dipole Pid and charge-permanent quadrupole Wo’, and WC0 interaction energies, as well as corresponding effective electronic polarization energies of positive P& and negative Pe;t charge carriers in polyacene crystals according to Mmm and coworkers [5,7] (all values in eV)

Compound Coordinates of local- ‘id %% Cf T70 PeTf

iced charge carrier

anthracene (0, 090) 1.19 0.18 1.38 -0.18 1.01 naphthacene a) (0, 070) 1.14 0.22 1.36 -0.22 0.93

(l/2,1/2,0) 1.14 0.23 1.38 -0.23 0.91 pentacene ‘) (0, 0,O) 1.08 0.22 1.29 -0.22 0.86

(l/2,1/2,0) 1.07 0.24 1.31 - 0.24 0.83

a) Naphthacene and pentacene crystals, belonging to the triclinic modification, yield slightly different values of We, for charge carriers localized on the non-equivalent molecules.

214 N. Sato et al. / Polarization energies in polyacene crystals

Table 4 Experimental and calculated values of effective polarization energies for positive We& and negative W,;, charge carriers in polyacene crystals (all values in eV)

Compound Experimental

G according to eq. (14)

anthracene 1.65 naphthacene 1.72 pentacene 1.63

mean value 1.67

a) AW,, = W,:, - W,;,.

w,;,

according to eq. (15)

1.09 1.10 1.17

1.12

AKfr ‘)

0.56 0.62 0.46

0.55

Calculated

Cf


1.52 1.52 1.48

1.51

Kf


1.16 1.07 1.02

1.08

Wfr =)

0.36 0.45 0.46

0.42

larger than W&. The calculated data also show the main physical source of this asymmetry in the case of polyacene crystals. This is obviously caused by different signs of the total charge-quadrupole interaction terms We, for opposite charge carriers (cf. eq. (6) and table 3). This means that the so-far presumed equality of the polarization terms P,& = P,T may be valid only for such OMC as benzene, the molecules of which have a negligible permanent quadrupole moment (cf. refs. [5,7]).

Results presented in table 4 also demonstrate sufficiently good agreement between experimental and theoretically calculated evaluation data. Ex- perimental estimates of the parameter W$ yield values = 10% higher than the theoretically evaluated ones (this might be caused by a sys- tematic error in the determination of I, values by the threshold approximation); both evaluated values appear to be almost constant for the three compounds. On the other hand, experimental estimates of W,;r appear to slightly increase, whereas calculated estimates appear to slightly decrease, with increasing number of condensed rings in a molecule. However, the mean values of I+& are pretty close in both cases, viz. (We~f)~~~ = 1.12 and (WeTf)ca, = 1.08 eV (see table 4).

Due to the observed asymmetry of polarization energy, it is necessary to change the conceptual base for drawing energy level diagrams of ionized states in OMC, and to introduce modified energy diagrams in which this asymmetry is taken into account [13]. Such a modified energy level diagram for an anthracene crystal is shown in fig. 1.

In order to draw this diagram, experimental gap energies Eid and Egpp’ (see table 2) and calculated electronic polarization terms Pid, I+& I+& (see table 3), as well as calculated vertical molecular electron affinity& (ref. [35]) have been used.

As can be seen from fig. 1, the asymmetry, due to the quadrupole term I+$,, does not influence the energy gap values but shifts the conductivity levels M< and Mp’ upwards.

There are some other notable consequences of the reevaluated data. As shown in fig. 1, additive

7

6

5

L > al

23

2

1

a I -

c

I,= 7.39

s1 B x I,=5.86

1 E,op’=4.L0

E,M=I.lO

TI - ! 4 ---+------- - lEJ,,=O.15 f

M’p 1 E’p

P$=P;+w;fi.3a so -_I_________-_____L__--_

a b

,oyL .l

,2

-3

-L

-5

-6

-7

-a

Fig. 1. A modified energy level diagram for an anthracene crystal; (a) neutral, (b) ionized state levels; Ez’ and E6d - optical and adiabatic energy gaps; E:, EP - electronic polaron states; M$, MP - conductivity states for molecular polarons.

(For other notations see the text).

N. Sato et al. / Polarization energies in polyacene crystals 215

6

2

-A A _&Jca, 1 _v

_.__---- _ a_------ o_P”

ei 01 ’ I I I

3 L 5

N Fig. 2. Dependences oi the main energy parameters for poly- scene crystals. (O), (+) - values of ionization energies of a molecule I, and the crystal I,-, respectively, calculated by semi-empirical approach. The error bars show the distribution of experimental values of these parameters according to table 1. AZ - calculated values of vertical electron affinities of

molecule (ref. [35]). (For other notations see the text)

summation of the energy parameters of A& P& E“p’ and P& yields the corresponding values of I,“, and in a similar manner I,, which can be regarded as semi-empirical calculated parameters, since Egp’ is the only empirical parameter used in the summation.

In fig. 2 calculated terms (Zo)_, and (Zc)cal, obtained in such a semi-empirical approach, are compared with the experimental Zo and Zc values. In practice, when one takes account of experimental errors, all calculated values of Zo and I, for anthracene, naphthacene and pentacene lie within the distribution bars of the experimental values according to table 1. These results may be regarded as additional proof of the consistency and plausibility of the submolecular approach in the electronic polarization energy calculations by MUM and co-workers [5,7].

Fig. 2 shows another important characteristic of the effective electronic polarization, Peff, terms. While the terms Zo, I,, ZQ” and Egd decrease and the term AL increases with increasing num-

ber N of condensed rings in polyacene molecules, the values of P& and P,T remain practically constant (see also table 4). The constant nature of P& according to eq. (14) has been observed also for a number of other polycyclic aromatic hydrocarbons [18]. By examining the data in table 3, it may be seen that the constancy of the effective polarization energy Peff is most probably due to the fact that the decrease in the component Pid of the charge-induced dipole interaction with increasing size of the molecule is compensated by the increasing charge-quadrupole interaction term We,, in addition to the balance between the mean molecular polarizability and the molecular pack- ing density in the solid as pointed out previously

P81.

5. Estimation of the adiabatic energy gap E$ values for several polycyclic aromatic hydrocarbon Cl@llS

The constant nature of the effective polarization energy terms P,, and W,, allows estimation of the adiabatic energy gap EGd for other hydrocarbon crystals, when the values of related energy parameters Z, and A, are known. For this purpose the following equation can be used (see eq. (15)):

E;d=IC-A,- (W,;,). (16)

The E&d values estimated according to eq. (16) for several polycyclic hydrocarbons, which mainly consist of four or five aromatic rings, are listed in table 5. The mean value of (I&r) = 1.12 eV, estimated for polyacenes (see table 4), has been used in eq. (16), as well as experimental Zc values determined in ref. [18] (see table 5). The choice of A, values is the most critical, since there are only few reported data, and the same with unchecked reliability. We have predominantly used the experimental values of A, obtained by the electron- capture method (cf. refs. [40,41]). However, for some compounds we were compelled to use less reliable calculated values (cf. ref. [42]).

From among the ten compounds listed in table 5, only for perylene and naphthalene are reported data available on direct experimental determina-

276 N. Sate et al. / Polarization energies in polyacene crystals

Table 5 Estimated adiabatic energy gap E$ values according to eq. (16) for several polycyclic aromatic hydrocarbon crystals

Compound

naphthalene 2 6.4 0.15 =) 5.13

benz[a]anthracene 4 5.64 (0.66) ‘) 3.86

chrysene 4 5.8 0.41=) 4.27

triphenylene 4 6.2 0.28 =) 4.80

dibe&a,h]anthracene 5 5.55 (0.64) d, 3.79

picene 5 5.7 4.06

pyrene 4 5.8 4.09

perylene 5 5.2

(0:88)=@ $05) ,“’ 3.20

1.06 o 3.02

benzo&hi]perylene 6 5.4 (0.73) e, 3.55

coronene 7 5.52 (0.54) =) 3.86

‘) Zc values according to ref. [18]. b, The A, values in parentheses are less reliable. The mean

value of W,;, for polyacenes has been used in eq. (16), viz. W& = 1.12 eV (see table 4).

‘) Ref. [40]. d, Ref. [41]. @ Ref. [42]. f~ Ref. [43].

tion of the E$ values from spectral threshold measurements of intrinsic photoconductivity. This method yields EAd = 3.10 eV for perylene [44] and E&’ = 5 eV for naphthalene [45]. These reported data are in good agreement with estimated EAd values listed in table 5 and, therefore, it may be concluded that the estimation of gap energies based on eq. (16) seems to be reasonable.

Lyons [46] has tried to estimate the EG values for some aromatic hydrocarbons by adding the magnitudes of their oxidation and reduction potentials in solution taking into account correc- tions for ion solvation energies. The obtained values of E, are as follows: 4.25 eV for benz[a]anthracene, 4.70 eV for chrysene, 4.37 eV for pyrene and 3.50 eV for perylene. Comparison of these values with the EAd values listed in table 5 shows that the Lyons approach gives values of EG overestimated by about 0.3-0.4 eV. Similarly, for polyacenes, Lyons has obtained EAd values larger than those listed in table 2. It should be noticed that in his approach Lyons uses a relation which is equivalent to the assumption that P& = P,T,. There are also some uncertainties in the work [46] concerning dielectric constants used as one of the parameters.

At present there are only a few organic crystals

of polar heterocyclic molecules for which the ionized state energies are experimentally determined. In particular, only for tetracyanoquinodimethane (TCNQ), widely used as a strong electron acceptor in ion-radical salts, reported energy parameters are sufficiently available for the evaluation of the We;r and W& values. According to ref. [47] the most reliable A, value for TCNQ equals 2.84 eV and the E6d value has been found equal to 1.7 eV from intrinsic photoconductivity threshold measurements [48]. On the other hand, ultraviolet photoelectron spectroscopy yields 1, = 7.4 eV and W$ = Io - I, = 9.5 - 7.4 = 2.1 eV [18]. Using these values in the ionized state energy diagram of a TCNQ crystal (see fig. 3) it is possible to estimate also the magnitude of W& = 2.9 eV.

As described above, for TNCQ crystals, unlike aromatic hydrocarbons, we obtain W& > I+$. It may be suggested that this relationship is caused by the strong electron acceptor nature of TCNQ, and may be characteristic also of other heterocyclic electron acceptors. Thus one may conclude that the asymmetry of electronic polarization energies for opposite charge carriers is more general than the so-far presumed equality of P& and P,T,, which may be regarded as a particular exception to the general rule.

NC -CN

NC-CN

I ,I’ We:,= 2.1 eV

_c___-J____-____-___--_

Molecule Crystal

Fig. 3. Schematic energy level diagram of ionized states for crystalline tetracyanoquinodimethane (TCNQ). VL - vacuum

level; other notations are the same as in figs. 1 and 2.

N. Sate et al. / Polarization energies in polyacene crystals 277

Acknowledgement [22] N. Sato, G. Saito and H. Inokuchi, Chem. Phys. 76 (1983) 79.

One of the authors (EAS) is deeply indebted for cordial hospitality, friendly cooperation and excellent working conditions during his three months stay at the Institute for Molecular Science, resulting in the present common work.

[23] N. Karl, N. Sato, K. Seki and H. Inokuchi, J. Chem. Phys. 77 (1982) 4870.

[24] E.A. Sihnsh, A.I. BeIkind, D.R. BaIode, A.J. Biseniece, V.V. Grechov, L.F. Taure, M.V. Kurik, J.I. Vertzymacha and I. Bok, Phys. Stat. Sol. A 25 (1974) 339.

(251 R. Boschi, J.W. MurreII and W. Schmidt, Faraday Discus- sion Chem. Sot. 54 (1972) 116.

[26] P.A. Clark, F. Brogh and E. Heilbronner, Helv. Chim. Acta 55 (1972) 1415.

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Reevaluation of electronic polarization energies in organic molecular crystals