Piezoreflection spectra of single crystals of an organic charge transfer complex

SURFACE

SCIENCE 37 (1973) 937-946 0 North-Holland

Publishing Co.

PIEZOREFLECTION SPECTRA OF SINGLE CRYSTALS OF AN ORGANIC CHARGE TRANSFER COMPLEX C. J. ECKHARDT

and J. MERSKI

Department of Chemistry, University of Nebraska, Lincal~, Nebraska 68.508, U.S.A. Piezoreflectance has been measured for single crystals of an electron donor-acceptor complex, pyromellitic dianhydride-anthracene, over the wavelength region of the charge transfer transition. Stress modulation of the optical reflectance was achieved by cementing single crystals at the center of a PZT disk which was set into resonant radial oscillation. Spectra were obtained with a microspectroreflectometer with light polarized paraiief and perpendicular to the c axis of the crystal for the (010) face. An enhancement of structure over that of the single crystal spectrum is observed .The observed piezoreflection is found to resemble the numerically calculated first derivative of the unmodulated reflection spectrum but this structure is somewhat blue-shifted from the calculated curve. These results are discussed in terms of Mulliken’s theory of electron donor-acceptor complexes.

1. Iutroduction The use of modulation techniques in molecular spectroscopy has paralled, and in some cases preceded, similar studies on the solid state. A modulated Stark effect has been employed in the investigation of molecular spectra of condensed phasesr). Quite common is the determination of circular dichroism by modulation of light by means of a Pockels ceils). The clearest examples of modulation spectroscopy in chemistry are found in the magnetic resonance spectroscopy of molecules. However, save for the modulated Stark effect, optical molecular spectroscopy has few examples of moludation techniques if one takes the term to imply modulation of the sample by a periodic external perturbation. In the study of molecular crystals there are even fewer such studies. The work of Hochstrasser and co-workers3) using the modulated Stark effect on organic crystals is the only recent example of such work in the optical spectroscopy of molecular crystals. This situation is rather surprising. Modulation spectroscopy can be useful in the assignment of transition moment polarizations. For example, external perturbations may be employed along specific directions of the molecular crystal to ascertain information concerning the symmetries of the states involved in the transition. Along this line, the perturbation can also be used to break symmetry in the crystal and thus induce the lifting of degeneracies. 937

938

The intensities

C.J.ECKHARDT

of the transitions

AND

J.MERSKI

can also be influenced

by external

modul-

ation, and the coupling of states to allow intensity borrowing can also be studied. Intensity stealing can be deliberately induced, and if the perturbation is vectorial in nature, the symmetries of the interacting states may be obtained. Understanding of the exciton spectra of molecular crystals may also be enhanced by modulation spectroscopy. The study of exciton-phonon interactions appears to be especially suited to such investigations, Further information may also be obtained on the forces that are responsible for the binding of molecular crystals. Another obvious use of modulation spectroscopy lies in its ability to obtain structure from otherwise featureless bands, Indeed, this appears to be a great deal of the motivation behind the initial modulation spectroscopy experiments on solids. In itself, this affords justification to the molecular spectroscopist who is often plagued with band spectra comprised of a great number of overlapping components. Any method that permits their resolution is useful for that reason alone, and it is the purpose of this investigation to use modulation spectroscopy for the study of the electronic spectra of a molecular crystal with particular attention focused on the enhancement of structure. A survey of the current techniques of modulation spectroscopy, which may be used in the study of the optical spectra of molecular crystals, suggests that piezomodulation may be quite advantageous. It does not suffer from problems of interpretation, and the experimental difficulties regarding field dependance and penetration encountered in electromodulation are avoided. While thermomodulation may be useful, it suffers from being an isotropic perturbation and thus is not as versatile a probe as piezomodulation. Because a linear response to the applied perturbation is usually desired, piezomodulation is a reasonable choice”). The relationship of the lattice deformation potentials to the electronic structure is conceptually straightforward because stress modulation allows the chemist to visualize the perturbation as affecting the overlap between the molecules. As mentioned, the application of uniaxial stress in selected directions is also an advantage of the technique, and when this is coupled to polarization studies, the molecular spectroscopist has a powerful analytical tool for prying information from his usually complex and often badly overlapped band spectra. The technique does suffer from the paucity of information on the elastic properties of organic molecular crystals. Indeed, there is no strong theoretical development available for molecular crystals either. The few systems for which such information is known permit only a reasonable estimate of the upper bounds on the elastic moduli of these crystals5). Nevertheless, this information, while it would be quite useful in understanding the interactions

PIEZOREFLECTION

SPECTRA

939

of molecules in crystals under stress, is not necessary to the use of piezomodulation in the elucidation of the spectra of molecular crystals. Several systems suggest themselves for such an investigation. The study of excitons in scene and mixed crystals is an obvious choices). Also of particular interest would be the piezomodulation spectra of metallically reflecting dyes 7). However, these systems have very small values for their elastic constants5) and thus may be expected to be difficult to study using piezomodulation. A more likely class of crystals to study would be those crystals that may be Ionic crystals (alkali halides), covalent crystals referred to as “bonded”. (Si, Ge), and metallic crystals (Au, Cu) have already been investigateds). However, there has been no published work to date on hydrogen bonded crystals or on crystals of charge transfer complexes. In this paper the piezoreflection spectra of the pyromellitic dianhydrideanthracene (PMDA-A) charge transfer complex crystal will be investigated. Because the effect of pressure or stress on the charge transfer (CT) interaction may be unfamiliar, it is discussed in the next section. The third section describes the apparatus used in the experiment. The fourth section presents the data for the specular reflection spectra and the piezoreflection of the complex which are subsequently discussed. 2. Pressure effects on the charge transfer transition The nature of the charge transfer interaction has been of great interest to chemists since the formulation of a theory of charge transfer complexes by Mulliken in 19529). The nature of the interaction is particularly suggestive of pressure studies. The key concept in the Mulliken theory is that the stabilization of the complex is associated with a resonance interaction of a no-bond state (D, A) with a polar state ID+, A-). It is th’is resonance stabilization that permits the formation of the complex. The ground state may be described by the wavefunction IN) = ID, A) + CIID+, A-)

+ y ID-, A+) + ...

= IO) + lx/l) + y/2) +..*, where higher excited states may be considered in the interaction. For most complexes y < c1G 1. Unique identification of a CT complex is made by the appearance of an absorption band that is not associated with the absorption spectra of the constituent molecules comprising the complex. This band is a result of an electronic transition to a highly polar excited state. This excited state arises from the transfer of an electron from a donor molecule orbital to an acceptor mole-

940

C. J. ECKHARDT

cule’s vacant

orbital.

AND J. MERSKI

This state may be described

IE) = ID+, A-)

+ p10, A) + 6(0_,

by A+) +..,

= 11) + PlO) + 612) +..., where 6 Q/I 4 1. In both of the above wavefunctions terms beyond the second are usually neglected. The intensity, polarization, and energy of the electronic transition afford the connection to quantum theory. The transition moment for the CT transition may be written kT

=

e
r

IN),

where r is a translational operator and e is the electronic charge. Using the above wavefunctions and the orthogonality conditions on 1E) and IN) one may write kT

= e((Ol

r 11)- Sol (01r IO>)+ e(),

where it can be shown that SO, = (0 1 1) = (JW

1A-))/(1

+ I(0 1A-x2)“.

Evidently, the intensity of the CT transition depends upon the overlap of the donor and anionic acceptor molecules’ orbitals. The energy of the CT transition is obtained from the solution of the Schrodinger equation for the complex. This yields hrc, = WE - w, = 2[+(H11

- H,,)2

+ POP,]+/(1 - s&>,

where Hij = (il A? lj)

and

pi = H,,

- HiiS,,

.

Thus the energy of the CT transition is also dependent upon the overlap between the donor and acceptor orbitals. The pressure shift of the CT transition frequency can be represented aslo)

Avc, = A(ff,, -

Ho,)

+

A t-(P:+ P;MHII

-

Ho,)1

2

where the first term represents changes in the energy differences between the no-bond and dative structures as pressure is applied. With increasing pressure a red shift is to be expected because Ho0 increases and HI, decreases with decreasing distance between the donor and acceptor molecules. The second term, which is descriptive of the resonance or charge transfer interactions, gives rise to a blue shift upon increase of pressure because the overlap integral, SOI, should increase with pressure but the denominator will decrease. Now the Ho0 term includes classical electrostatic interactions as well as

PIEZOREFLECTION

SPECTRA

941

London force interactions and steric and repulsive interactions. H,, reflects those interactions, which arise from the exchange forces arising from the formation of a very weak chemical bond, but it is largely dominated by the coulomb attraction for the cationic donor and anionic acceptor molecules. Thus the frequency shift depends upon whether the resonance interaction dominates the other dielectric effects lo). From the above discussion it is evident then that CT transitions should be quite sensitive to any perturbation that will affect the overlap between the donor and acceptor molecular orbitals. Offenrl) and Drickameris) have studied the effect of hydrostatic pressure on the CT transition of some randomly oriented samples of crystalline complexes. Only gross changes in intensity and frequency could be observed in these interesting studies. It was observed that generally complexes whose donor and acceptor orbitals are pi orbitals show an increase of the intensity of the CT transition and its wavelength of peak absorption with increasing pressure. CT bands are characterized as being rather broad and structureless, and thus it is difficult to obtain detailed information from the study of isotropic systems at room temperature. However, it may be expected that the application of a uniaxial stress along the direction of overlap of the donor and acceptor pi orbitals may provide more detailed information. In any case, it is clear the CT transition should be subject to stress modulation. A survey of crystalline charge transfer complexes showed the PMDA-A complex could be a good system for a stress modulation study. The 15.7% reflectivity is among the highest known for a CT transition. The crystal grows as small thin plates with (010) as the prominent face. The triclinic space group of the crystalls) is also helpful in this survey case because any coupling effects through strain are most likely to occur in this crystal system. However, the main goal of the experiment is to ascertain if piezomodulation can resolve the structure of the CT band. 3. Experimental Organic molecular crystals are small being typically less than 1 mm wide and only 2 to 3 mm long. Microscopes are typically used in obtaining the spectra of such small specimens. The normal incidence specular reflection spectra as well as the piezoreflection spectra were obtained with a microspectroreflectometer described elsewhere7). A block diagram of the entire instrument is given in fig. 1. The system is similar to other apparatus used in piezoreflection studiess) save for the use of the microscope. However, care was taken to have an ultra-

942

C. .I. ECKHARDT

AND

J. MERSKI

P IP28 PMT

I

Fig. 1.

Power SUPP fY

Iris

Block diagram of the piezoreflectometer.

stable power suppiy for the 150 W Xe arc and to have an extremely sharp active filter (60 dB/octave roll OR). The PZT-4 piezoceramic disk is 5 cm in diameter and 2 mm thick and is driven in its radial resonant mode of approximately 42 kHz. Care was taken to monitor the stability of the disk by monitoring the waveform detected at the disk electrodes with an oscilloscope. The frequency of the signal was also monitored and not allowed to vary more than L-5 Hz. The disk itself was clamped between rubber O-rings so vibrational coupling to the rest of the apparatus was eliminated. No signals were detected due to mechanical vibrations transferred by the disk to the photomultiplier tube, the arc, or the microscope assembly. The disk was also electrically shielded to prevent any possible electrical interference. Samples of PMDA-A were mounted over the center node of the disk with epoxy. Curing was carried out under a stream of dry nitrogen to prevent etching of the crystal surface by any vapors due to the epoxy. The apparatus was tested by obtaining the piezoreflection from the (111) face of silicon in the region of Ed. The resulting piezoreflection spectra are in excellent agreement with those published by othersI% 4. Results Crystals of the PMDA-A complex have the alternating stacks of donor and acceptor molecules typical of an-bn type complexes. All stacks are identical and there is some interleaving. The molecular planes of the component

PIEZOREFLECTION

SPECTRA

943

molecules in a given stack are parallel with an interplanar spacing of 3.23 A. This distance is less than the sum of the Van der Waals radii and indicates significant overlap between the donor and acceptor moieties. Projection of the single complex in the unit cell onto the (010) face is given in fig. 2. The plate face investigated was assigned from its X-ray precession photograph. The polarized specular reflection spectra obtained at 298 K for both principal directions of (010) are shown in fig. 3. For the electric vector of the light polarized along the c axis, the peak rellectivity occurs at 18200 cm-‘. A prominent shoulder is observed at 19200 cm-‘, and some asymmetry is for the direction perpenindicated around 21000 cm- i. For the polarization dicular to the c axis (designated ct) no structure is observed. Thus the CTtransition is polarized along the c crystallographic axis, which is also the axis of elongation of the crystal. The piezoreflection spectra obtained for light polarized along both principal directions is shown by the solid line in fig. 4. The frequencies of the experimentally determined peaks, troughs, and inflection points of the bands, which are referred to as I, II, and III going toward increasing frequency are given in table 1. For comparison, the reflection spectrum polarized in the c-axis direction was numerically differentiated. The resulting curve is plotted as a dashed line in fig. 4. The frequencies of the peaks, troughs, and inflection points of this curve are also given in table 1. Within the experimental error of both deter-

Fig. 2.

Projection of the PMDA-A complex onto (010).

944

C. J.ECKHARDT

16

18 WAVENUMBER

AND J. MERSKI

20

22

2L

X lO‘3

Fig. 3. Specular reflection spectra of PMDA-A for (010) at 298 K. The c-axis polarization is designated by the solid line and the ct-axis polarization is designated by the dashed line.

16

22 It3 20 WAVENUMBER X lO-3

24

Fig. 4. Piezorefection spectra of PMDA-A at 298 K. The c-axis spectrum is shown by a solid line and the ct-axis spectrum is given by the dot-dash line. The derivative calculated for the c-axis direction in fig. 3 is given by the dashed line.

945

PIEZOREFLECTION SPECTRA TABLE 1 a Troughs

Peaks Exper.

Band I Band II Band III

17900 19550 20850

Calc.

17700 19400 21350

Inflections

Exper.

Calc.

Exper.

Calc.

188.50 20250 21300

18650 20350 21750

18350 19700 21100

18150 19800 -b

a All energies are cm-l. b Indeterminate.

minations the curves may be accepted to be in agreement. However, the piezoreflection spectrum and the calculated curve show poor agreement beyond 20000 cm-‘. The band III peak in the piezoreflection spectrum does correspond to the observed region of asymmetry in the reflection band. The piezoreflection spectrum in the ct direction shows no structure. This spectrum is given by the mixed dash-dot line. The lack of structure is to be expected because there is no projection of the CT transition moment in the ct direction. However, the curve may possibly serve as an indication of the magnitude of the background signal in the experiment. The average frequency spacing of the observed piezoreflection bands is 1400 cm-‘, which is the order of vibrational energies of molecules. In fact, the vibrational sequence for the first anthracene transition is 1400 cm-‘. Thus, the piezoreflection spectrum has resolved the first two vibrational levels of the CT band and quite likely has revealed the third such level. Of course, it is also possible that the observed shifts are significant. This would indicate the crystal may be stressed beyond its elastic limit or that the CT state is quite sensitive to deformation of the crystal. It should also be noted that organic molecular crystals are reasonably compressible but that they are not capable of withstanding any but small extensions5). Thus, the reflectivities for elongation and compression may not be symmetric about the unstressed state. Frequency shifts may then be expected. These shifts can be rationalized in terms of the CT theory. If the observed blue shift is significant, it would indicate the dominance of the resonance interaction. Unfortunately, the CT forces are responsible not only for the formation of the complex but also are involved in the formation and binding of the crystal. Therefore, the spectra observed here are deceivingly simple in appearance but probably are not open to such simple interpretation. If the most naive interpretation is taken wherein the CT transition is resolved by the modulation, then the energies of the bands under the CT band envelope should be obtainable from suitable lineshape analysiss). To a

946

C. J. ECKHARDTANDJ. MERSKI

first approximation these energies should be given by the inflection points of the observed curves. The experiment demonstrates that optical modulation spectroscopy can be of great use in molecular spectroscopy. It is likely that the greatest use will be in the probing of energy states of molecules and the determination of their symmetry. Acknowledgements Support of the University acknowledged.

of Nebraska

Research

Council

is gratefully

References 1) C. J. Eckhardt, J. Chem. Phys. 56 (1972) 3947. 2) L. Velluz, M. Legrand and M. Grosjean, Optical Circular Dichroism, Principles, Measuremenfs and Applications (Verlag Chemie, Weinheim, 1965). 3) R. M. Hochstrasser and L. J. Noe, Chem. Phys. Letters 5 (1970) 489. 4) D. D. Sell, Surface Sci. 37 (1973) 896. 5) A. Bondi, Physical Properties of Molecular Crystals, Liquids and Glasses (Wiley and Sons, New York, 1968) ch. 4. 6) D. P. Craig and S. H. Walmsley, Excitons in Molecalar Crystals (Benjamin, New York, 1968). 7) C. J. Eckhardt and R. R. Pennelly, Chem. Phys. Letters 9 (1971) 572. 8) M. Cardona, in: Solid State Physics, Suppl. II (Academic Press, New York, 1969). 9) R. S. Mulliken. J. Am. Chem. Sot. 64 (1952) 811. 10) H. W. Offen and T. T. Nakashima, J. Chem. Phys. 47 (1967) 4446. 11) A. H. Kadhim and H. W. Offen, J. Chem. Phys. 48 (1968) 749. 12) G. A. Samara and H. G. Drickamer, J. Chem. Phys. 39 (1962) 474. 13) J. C. A. Boeyens and F. H. Herbstein, J. Phys. Chem. 69 (1965) 2160. 14) G. W. Gobeli and E. 0. Kane, Phys. Rev. Letters 15 (1965) 142. 15) In the wavelength region studied the dispersion of principal directions was found to vary 8”. This was not found to significantly affect the spectra and the c axis and ct axis were taken as the average principal directions.

Discussion Question (by H. MORAWITZ): Have you tried to use the Hubbard model extended to take account of the effect of strain on the model parameters? Speaker’s reply (by C. J. ECKHARDT): No.