A calculation of the ground state vibrational phenomena (site shifts and splittings, orientation effects and exciton structure) and of the crystal lattice states has been performed for these systems. In Part II, the location and identification of the first and second triplet states of benzene (3B1u and 3E1u) are given.
INTRODUCTION
It should further be noted that the relative signs of the coupling constants only matter if the convention used to define the crystal wavefunctions is given explicitly. While the magnitudes and relative signs of exciton coupling constants (see Section II-F) can be obtained from studies.
THEORY
The factor group Q2h for the benzene crystal is created as the direct product of the site group a. and the exchange group, 1.2_2 x g.i for the special case of the proper exchange group. We now proceed to determine the elements of the Hamiltonian matrix for the specific case of the benzene crystal.
EXPERIMENTAL METHODS AND RESULTS
First, the assumed ideal mixed crystal value of the transition energy (€+ 6.) is obtained by correcting the observed 0-0 transition of the isotope. Using the exchange group Q2 and accepting: subject to the exchange group assignments of the observed.
SUMMARY
Here we are interested in the effect of the crystal site on a given molecule in the absence of resonance terms. The subscript nq of cf>~q and cf>~q now refers to the crystal position of the impurity molecule.
EXPERIMENTAL
We will document that the effect of isotope substitution by host or guest on these interactions is negligible (that is, the potentials governing these interactions are independent of isotope substitution), while the most important factor for their determination is the amplitude of the atomic displacements caused by the isotope substitution. given vibration mode. Intersite Fermi resonance is discussed for host-guest systems in which a strong guest transition is in resonance with another. Such a technique typically produces a cell that is vacuum-tight (i.e., the container can be evacuated from the outside without loss of liquid benzene within the cell).
All linewidths are believed to be instrument limited in some cases, but generally depend on the quality of the crystal and the concentration of the isotope being studied.
DISCUSSION
We can resort to the spectra of the benzene crystal to understand both the physical state of the molecule in the crystal and the nature of the distorting environment. The significance of the site shifts for the interpretation of exciton theory has already been discussed. In the case of degenerate vibrations, the displacement can be measured from the gas phase value to each of the crystal components and can.
In group theory, this means that a degenerate irreducible representation of a molecular group maps to at least one nondegenerate irreducible representation in a site group. This mixing of states is due to the distortion of the molecule by the crystal site field. This coupling, as in standard Fermi resonance treatments, is affected by the anharmonic terms present in the new force field due to the distortion of the crystal site of the molecule.
4 and 5) gives us information about the shape of the molecule in place (or the distortion of the molecule from the place). However, approximately 10% of C6D6 (there are 12 neighboring molecules in the benzene crystal) will not have inversion site symmetry.
CONCLUSION
The 2u of C6D5H at 527 cm - i is very intense (of the order of the other bands of the C6D6 spectrum) and we propose that this is due to intermolecular intensity borrowing through the Fermi resonance mechanism. Note that the effect should be very pronounced here as the a bands of both molecules. It is very difficult to say anything quantitative about the intermolecular crystal Fermi resonance due to the lack of an accurate crystal zone wave function~ Clearly this is only a crystal effect, and a subtle one at that.
Although we cannot use the Davyd formalism as described here to... discuss this phenomenon, because the single-site exciton function is used and the assumption is that there is no overlap between the two sites, we can clearly consider this phenomenon at a higher order than the usual Fermi resonance. Only out-of-plane vibrations show three orientation lines, which is consistent with and strongly supports the above conclusion. Out-of-plane vibrations are expected to be sensitive to the intermolecular potential, since the atomic displacements of these foundations are larger (on average by almost a factor of five) than for in-plane vibrations.
These larger-amplitude atomic displacements are thus the reason that the large crystal effects are always found associated with the out-of-plane states (b2g, e1g, ~u'e2u in Q6h symmetry). On the other hand, the ground state contributions to the orientation effect do not cancel out as they do for the location partitioning.
ACKNOWLEDGMENT
INTRODUCTION Since the ciassic work of Halford, 1
These early works are partly concerned with the crystal site effect on degenerate molecular states. For experimental and historical reasons, most of these investigations concern ground state vibrations observable by infrared spectroscopy. Since it is of theoretical importance to know whether such effects are present or not for all classes and types of vibrations, in this paper we search for the above effects in the vibronic transitions of C6~ and some of its deuterated isotopes: the spectra of the phosphorescence, fluorescence, and absorption of various mixed isotopic benzene crystals.
Thus, in the infrared absorption spectra from the g-ground state, only £-vibrations are observable, while. Similarly, for an orientation effect, the C6IfsD data should overlap with both techniques, while there would be no direct data overlap for p-C6fLiD2. With such a study, we hope to provide a complete picture of the crystalline effects on the vibrations of the benzene molecule for all classes and types, thereby providing a good test for theoretical calculations of intramolecular and intermolecular force fields and potentials in solid benzene.
A vibrational analysis of the benzene phosphorescence spectrum in EPA at 77°K was first published by Shull. The benzene emission spectra in amorphous solids generally do not show solvable crystal effects on the ground state vibrations.
THEORETICAL CONSIDERATIONS OF CRYSTAL EFFECTS ON VIBRATIONS
Therefore, a non-degenerate molecular vibration could produce three lines in the spectrum, each due to differently oriented molecules at three physically equivalent but different sites. Thus, the number of lines observed in the spectrum for a particular vibration is an indication of the effective symmetry of the site.
EXPERIMENT AL
The thick crystals were grown by lowering the optical cells through a temperature gradient of about 100 °C/cm directly in a liquid N2 cooled chamber at the rate of approximately 1 cm/day. Thin crystals are grown in the same type of tube by suspending the carrier in a dewar approximately 20 cm above the liquid N2 surface and then cooling to helium temperatures. After the crystal holder is completely submerged under liquid helium, the cell is opened over the graded seal to ensure good thermal contact with the coolant.
The emission spectra of the guest triplet and singlet states were excited by absorption in the singlet exciton band of the C6D6 host from which the excitation energy is rapidly transferred to the lowest excited singlet and triplet guest states. These extend approximately 30 cm1 for the lowest energy for each substituted hydrogen in C6D6 • The guests thus serve as effective energy traps from which emission is observed at low temperatures. When higher orders were used, a small Bausch and Lomb monometer was used as a predispersing element or order separator.
Only the most intense vibronic lines of C6fls were imaged, requiring exposure times of 40 μ. entrance crack of four hours. 4 meter instrument using the fourth order of the lowest resolution grating giving a dispersion of approximately 1.
EMISSION SPECTRA
In general, the same ground state vibrations are observed in the fluorescence spectrum as in the phosphorescence. The intensity of the totally symmetric fundamental v1 relative to the most intense vibronic origin is much greater in the fluorescence than in the phosphorescence. For the mixing to be strong, the vibrations must have similar frequencies and the same symmetry in the.
Nine out of ten degenerate vibrations were assigned from phosphorescence and fluorescence spectra. Because of the larger fluorescence linewidth, the cleavage site in 1120 can be as large as 3 cm-1 and cannot be resolved. The impermeability of the remaining vibrations again suggests that the molecular symmetry classifications are still approximately valid in C.
A partial analysis of the spectrum is given in the figure, where the average bandwidth of the triplets is about 13 cm - ie. This structure represents the differences in the orientational effects of the ground and lowest excited singlet states, including the vibrational contribution to them.
DISCUSSION AND CONCLUSIONS
For lower-symmetry isotopes exhibiting orientational effects, mixing between vibrations, particularly at the £i site, tends to equalize the vibrational amplitudes. The assignment of the "Ila component" in the Fermi doublet is made by comparing the intensity of the members of the Fermi pair with the fundamental value of va in fluorescence and phosphorescence emissions (cf. the decrease in the measured Va splitting for C6Ha in the Fermi pair is clearly due to resonance. does not appear in the second half of the v8 pair • In sym-C6H3D3, this same j is closer to the harmonic value.
A further possible indication of the magnitude of the crystal location-induced effects can be obtained from anharmonicities. The only other vibrations whose overtones are observed are v16 and v10, but in these cases Fermi resonance at the crystal site between the three components of the overtone complicates the analysis of the anharmonicities. The general conclusion from the coarse vibrational structure is that neither the energies nor the symmetry classifications of the vibrations are strongly disturbed by the crystal.
This is particularly shown by the magnitude of site shifts, splittings and orientational effects and by the dominance of e2g vibrations in the singlet and triplet spectra. Bernstein, "Calculation of Ground State Vibrational Structure and Phonons of Isotopic Benzene Crystals," J.
