Isotopic Mixed Crystals Research Articles

EPR and optical studies of the lowest nπ* triplet state of p-benzoquinone in an isotopic mixed crystal

EPR and optical studies of the lowest <i>n</i>π* triplet state of <i>p</i>-benzoquinone in an isotopic mixed crystal

Etude par spectroscopie de vibration des hexahydroxodialuminate et digallate de potassium

Infrared and Raman spectra of K AlO 2, 1,5 H 2O and K GaO 2, 1,5 H 2O are interpreted on the basis of [Al 2O(OH) 6] 2− and [Ga 2O(OH) 6] 2− ions. They support a previous X-ray study on the potassium hexahydroxodialuminate. These ions are constituted by two MO 4 tetrahedra sharing one oxygen atom. Spectra show very little difference between the three external MO bonds and the internal one, around each metal atom. On the other hand, due to the presence of a cristallographic symmetry axis on the oxygen atom of the MOM bridge, the spectra of isotopic mixed crystals allow us to characterize only three OH (or OD) bonds of different lengths. The hydrogen bonds lengths obtained from the v(OH) frequencies agree very well with the observed external oxygen-hydrogen distances. The MO 4 tetrahedra of a M 2O 7 unit are slightly coupled and the study of MO 3 group frequencies shows that the MO bond strength increases when aluminium is replaced by gallium. This fact explains increase and decrease of bending and stretching OH vibrations.

Resolved emission from compound states in heavily doped isotopic mixed benzene crystals

The 4·2 K fluorescence spectra of C6H6/C6H5D mixed crystals were studied as a function of concentration. The results were compared to theoretical predictions based upon coherent potential approximation (CPA) calculations of partial density-of-states functions. The separation of the emission from each ‘partial density-of-states’ into resolved spectral features has established the physical significance of these functions. The excellent quantitative agreement between the experimental and theoretical results indicated the validity of both the ideal mixed crystal hamiltonian (H) and the CPA for the calculation of benzene mixed crystal density-of-states functions, even at concentrations as low as 5 per cent C6H6. These new experiments have also confirmed the validity of the previously determined pure crystal density-of-states and band mean for the S1 (0, 0) band of crystalline benzene.

Temperature dependence of a vibrational exciton: Some methyl motions of durene

An intramolecular vibrational frequency in a molecular crystal has been found to show a significant temperature dependence. The low lying intramolecular mode at 272 cm−1 (room temperature value) of durene-h14 (and the corresponding durene-d14 frequency at 242 cm−1) shows an increase of [inverted lazy s] 9 cm−1 in frequency in going from room temperature to 100°K. A theoretical discussion is presented on the role of various interactions that may give rise to the temperature dependence of the intramolecular mode. The theoretical considerations suggest that, although the thermal expansion of the lattice may be contributing to this temperature dependence, the dominant contribution is due to the cubic anharmonic interactions involving methyl torsions. It is suggested that in complex molecular crystals, where there are some very low lying intramolecular modes, the distinction between lattice modes and intramolecular modes based on the criterion that only lattice modes show frequency shift with temperature may be misleading. In such cases our mixed crystal criterion that the phonons obey the amalgamation limit in isotopic (H–D) mixed crystals, whereas intramolecular vibrations are in the separated band limit, should be more reliable. This is clearly demonstrated in the case of durene.

Molecular motions and λ phase transition: Raman and far-ir studies of neat and isotopic mixed hexamethylbenzene crystal

Raman and far-IR studies of hexamethylbenzene (HMB) low temperature crystalline phases (neat and isotopic mixed) are presented. The Raman phonon spectrum changes drastically during the λ-phase transition. Site splittings on two intramolecular modes of HMB- h 18 (but on only one corresponding HMB- d 18 mode) are observed in the room temperature phase (phase II) spectrum. These splittings disappear in the lower temperature phase (phase III). The methyl torsional bands are identified and a significant shift is observed for them during the phase transition. Also, while the λ-phase transition takes place at 113°K (± 2°K) for HMB- h 18 crystal, the transition temperature is 133°K (± 2°K) for HMB- d 18. Our results suggest that (for phonon interactions) the symmetry in phase Ill is close to D 3d and reduces to C i in phase II. Furthermore, the results support the mechanism of phase transition which involves a tilting of the methyl groups out of the benzene ring.

Electronic states of 1,3,5-(sym)-triazine. I. Absorption spectra of pure and mixed crystals

Spectra of pure and isotopic mixed crystals of sym-triazine are presented which indicate that the 3455 Å triplet state is E″3(nπ*). These same results confirm previous assignment of the state at 3330 Å as E″3(nπ*). Absorption spectra of sym-triazine in sym-trioxane chemical mixed single crystals are presented and further corroborate these conclusions. Out-of-plane (parallel) vibrations of sym-triazine are considerably affected by crystal fields in both crystal systems. It is demonstrated that assigned state symmetries are not inconsistent with previously obtained experimental results on these states. The nature and type of intermolecular interactions and exciton effects present in the triazine system are briefly discussed. A synthetic route is described which yields substantial quantities of high purity sym-triazine, an absolutely essential part of present and forthcoming work on this system.

Phonons in disordered molecular solids: Raman spectra of heavily doped mixed crystals of benzene and perdeuterobenzene

Raman spectra of mixed crystals of benezene-h6 and benzene-d6 have been studied throughout the whole concentration range (0%–100%). They are discussed in the virtual crystal limit, suitable for small trap depths. It is shown that within this limit: (1) All the phonons are delocalized in mixed crystals; (2) k-designation is still valid, and (3) no appreciable broadening is expected in mixed crystals. In particular, because the trap depths are the same for all three rotations in benzene mixed crystals, it is further inferred that: (1) There is a one-to-one correspondence between the mixed crystal absorption and the pure crystal absortion; (2) spectral line positions depend on the concentration linearly; and (3) the normal coordinates in the mass (or moment of inertia)-weighted coordinates remain unchanged from benzene-h6 to mixed crystals to benzene-d6. All these conclusions are supported by the experimental data. More general cases, where trap depths are different for different degrees of freedom, are also discussed. Implications of the phonon delocalization in isotopic mixed crystals to the interpretation of phonon sidebands of electronic spectra of isotopic mixed crystals are also pointed out.

Vibrational, torsional, and librational excitons in molecular crystals: Raman spectra of neat and isotopic mixed durene

A theoretical comparison of the conventional phonon and exciton approaches is made and the validity of the concept of a librational exciton is discussed. An experimental investigation of the Raman active librations, torsions, and other vibrations, in the neat and isotopic mixed crystals of durene at 100 and 25°K, is presented. The results obtained are explained in a uniform and consistent way by using the exciton concept (librational exciton, torsional exciton, and vibrational exciton). The librational excitons obey the amalgamation limit while the torsional and vibrational excitons fit the separated band limit of the mixed crystal. Davydov splitting has been observed on one torsional, one vibrational but not on any librational excitons (phonons). Intermolecular contributions to the methyl torsions are discussed.

Entire Phonon Spectrum of Molecular Crystals by the Localized Exciton Sideband Method: Naphthalene

The complete one-phonon density-of-states of a molecular crystal can be mapped out by a carefully chosen exciton sideband involving a localized molecular internal excitation in a dilute isotopic mixed crystal. A theoretical derivation shows that the necessary criteria are: absence of localized in-band phonons; applicability of a phonon amalgamation limit for the mixed crystal; weak exciton-phonon, guest-lattice coupling and weak guest-host exciton interaction. Experimentally, at least two exciton-phonon sidebands should be investigated, so as to exclude trap and defect transitions, and at least one of the guest transitions should belong to the deep-trap limit and have sidebands weak enough to minimize multiphonon transitions. The above is demonstrated for the naphthalene crystal by high-resolution fluorescence and phosphorescence spectra of 0.25% C10H8 in C10D8 and by phosphorescence of 0.14% 2-DC10H7 in C10D8 at 2°K. The phosphorescence phonon sidebands correlate surprisingly well with Pawley's ``atom-atom'' calculated phonon density-of-states, and seems to give a much better phonon density map than the very recent high-resolution inelastic, incoherent neutron scattering data. New Raman data are also presented, showing defect (isotopic impurity) induced bands, which are interpreted in terms of the above phonon density-of-states peaks. Applications to reversible and irreversible thermodynamics are mentioned.

Isotope effects on intermolecular interactions in crystalline benzene

Spectroscopic studies of pure and isotopic mixed benzene crystals have shown that for the S 1 ← S 0 transition (i) the resonance interactions in pure C 6H 6 and C 6D 6 are identical; (ii) the effects of the static (binding) forces are the same in pure C 6H 6 and C 6D 6 crystals; and (iii) the gas-to-crystal shift of a dilute guest in an isotopic mixed crystal is different from that of the host. These results provide a consistent explanation of the differences between calculated and experimental spectra of heavily doped isotopic mixed benzene crystals.

Variable Trap Problem in Isotopic Mixed Crystals of s-Triazine

Theoretical treatments of isotopic mixed crystals, in general, have assumed that the intermolecular interactions are equal and that the problem can be reduced to a consideration of the free molecule excitation energies. It is shown that for the isotopic s-triazines the intermolecular interactions are different and that now it is necessary to consider a trap depth which is both concentration and distribution dependent. This has necessitated a modification of the existing theories. Experimental results have been obtained over the entire concentration range for the s-triazined-0/s-triazined-3 mixed crystal system, and the results have been qualitatively explained in terms of a concentration dependent trap depth.

External spin—orbit coupling. The T 1 state of naphthalene in a dibromobenzene host cyrstal

The origin of the T 1 state of naphthalene in a p-dibromobenzene host crystal is shown to be the strongest line in the spectrum at 20720.9 cm −1. The vibronic activity of the naphthalene phosphorescence indicates that a spin—orbit coupling mechanism different from the one vibronically induced in an isotopic mixed naphthalene crystal is active in a chemically mixed crystal with a halogen-containing host.

Raman Phonon Spectra of Isotopic Mixed Naphthalene Crystals: Librational Exciton Model and the Amalgamation Limit

We present an experimental Raman study of lattice modes in neat and mixed (10%–90%) crystals of naphthalene-h8 and naphthalene-d8 at 100°K with 1 cm−1 resolution. The spectral features of the neat crystals are preserved in the heavily doped mixed crystals, with small shifts and broadenings characteristic of an amalgamation limit that assumes weakly coupled excitation bands in the restricted Frenkel-Davydov limit. Rotation-translation interaction does not affect the mixed crystal spectra, thus making the Raman technique uniquely suited for the investigation of the librational (rotational) phonon band structure. The evidence is against localized or pseudolocalized phonons in these isotopic mixed crystals.

Random Lattice Calculations on Frenkel Excitons in Disordered Molecular Crystals—1B2u Naphthalene

Using the recently acquired exciton dispersion relations for crystalline naphthalene, we have calculated the density-of-states functions for heavily doped isotopic binary mixed crystals of naphthalenes with arbitrary compositions and various energy separations (trap depths). This constitutes the first attempt to extend the negative factor counting (NFC) method, developed originally for lattice phonons, to a real physical system of three-dimensional molecular excitons. In most calculations, a total of 1280 molecules were included. The exciton interactions, which included both the translationally equivalent and the interchange equivalent ones, involved all 16 neighbors. Calculations based on the coherent potential approximation (CPA) were also performed for comparison. It was concluded that these two sets of calculations compared very well except in the split-band limit and at low concentrations. Under these conditions the cluster or conglomerate states become important and the computer-simulated density-of-states functions revealed some fine structure, which was completely indiscernible in the density-of-states function based on CPA. This fine structure is experimentally significant. The relationship between the Green's function method and the moment trace method was investigated in the light of these new results. Particularly, some of the lower moments were calculated for the density-of-states functions and compared with those calculated from the exact expressions in our previous paper. It was shown numerically that the CPA results indeed agree with the exact moments up to the seventh order.

Energy States and Intermolecular Interactions in Molecular Aggregates: Resonance Pair Spectra of Crystalline Naphthalene

Very high-resolution optical spectra reveal fine structure in the B2u1 → 1Ag and B1u3 → 1Ag electronic transitions of naphthalene isotopic mixed crystals, C10H8 as a guest in a C10D8 host. Extensive experimental data allow the spectral lines to be characterized and assigned. Some of the structure corresponds to the resonance splitting arising from neighboring pairs of guest molecules in the host lattice. In the Frenkel tight-binding approximation, this structure gives directly the intermolecular excitation transfer matrix elements responsible for the exciton mobilities and the energy band structures of both pure and mixed molecular crystals. For the B2u1 state the largest interchange equivalent interactions are approximately + 15.3 cm−1 and + 3 cm−1 while the largest translation equivalent interactions are approximately + 3.7, − 5.1, − 7.9, and − 3.3 cm−1. For the B1u3 state the largest interchange equivalent interaction is 1.25 cm−1.

Phosphorescence Spectrum, Vibronic Analysis, and Lattice Frequencies of the Naphthalene Molecule in a Deuteronaphthalene Crystal

The phosphorescence spectrum of naphthalene showing 94 transitions between 21 224 and 16 880 cm−1 has been obtained. These data help resolve uncertainties in the vibrational assignments, suggest the presence of localized lattice vibrations in isotopic mixed crystals, and may indicate the relative importance of singlet–triplet coupling mechanisms in naphthalene and some halogenated naphthalene derivatives. The data have been used to identify the corresponding absorption and phosphorescence of the pure crystal and might be used in explaining temperature, environmental, and isotope effects on the radiative or radiationless transition probabilities of the naphthalene molecule.

Information on the Exciton Band Structure of the 1B2u State of Crystalline Naphthalene from the Variation of Energy Denominators Method

Perturbation shifts of guest levels in isotopic mixed crystals of naphthalene have been determined. These data verify that the density function for exciton states is almost symmetric over the entire exciton band of the first singlet state. This result agrees with the entire band structure as observed in band-to-band transitions and disagrees with the band structure calculated from the octopole model for the inter-molecular interaction. The transition energies of guest levels also disagree with a model for the exciton splitting involving configuration interaction with charge transfer states. A possible source of the exciton splitting is suggested, and the available data for evaluating theoretical descriptions are outlined.

Site Effects in Isotopic Mixed Crystals—Site Shift, Site Splitting, Orientational Effect, and Intermolecular Fermi Resonance in the Vibrational Spectrum of Benzene

A modification of the Davydov theory of energy levels in molecular crystals is applied to experimental observations on ground-state vibrations of various isotopic substituted benzene crystals. Three distinct and characteristic crystal-induced phenomena have been observed experimentally: (1) site group splitting—involving degenerate vibrations of the molecule that map into nondegenerate site modes; (2) orientational effects—concerning isotopic benzenes of symmetry D2h or lower, and their relative positioning in two or more distinct orientations at crystal sites; and (3) intermolecular Fermi resonance—near-resonance interaction between two adjacent-site molecules of different isotopic compositions. The first two phenomena give rise to 10 cm−1 ≲ splittings. A general mechanism is proposed to account for this, and the differences and similarities between these two effects are discussed. The importance of observed gas-to-crystal energy shifts is also discussed in the light of these experimental findings. In addition to intersite Fermi resonance, solid-enhanced intrasite Fermi resonance is reported and discussed qualitatively. Applying the Davydov theory for the case of no resonance interactions, one can obtain information concerning the shape of the molecule in the site field, the symmetry of the site field, and the general nature of the intermolecular interactions.

Electronic and Vibrational Exciton Structure in Crystalline Benzene

The purpose of this paper is to lay a consistent theoretical framework for the discussion of a series of forthcoming experimental papers on the absorption and emission of light by benzene crystals. Emphasis will be placed not only on the usual Davydov splittings but also on k≠O states and band-to-band transitions in neat (pure) crystals, and on orientational effects, site splittings, shifts, and resonance pair spectra in isotopic mixed crystals. The role of translationally equivalent interactions will be discussed. The interchange-group concept is used in order to simplify the theoretical analysis. From the four possible interchange groups D2, C2υa, C2υb, C2υc, the D2 group is found to be the most convenient for the classification of benzene exciton functions. A differentiation between static and dynamic interactions is made in the limit of Frenkel excitons, and the concepts of site distortion energy and the ideal mixed crystal are introduced to aid in this distinction. Data pertaining to site shifts and splittings and resonance and quasiresonance interaction terms for the B2u1 electronic exciton band and the vibrational ν12(b1u), ν15(b2u), and ν18(e1u) exciton bands are discussed in order to illustrate briefly the theoretical concepts.

Static Crystal Effects on the Vibronic Structure of the Phosphorescence, Fluorescence, and Absorption Spectra of Benzene Isotopic Mixed Crystals

The phosphorescence, fluorescence, and absorption spectra of the isotopic benzenes C6H6, C6H5D, p-C6H4D2, and sym-C6H3D3, present as dilute guests in a C6D6 host crystal at 4.2°K, are obtained with sufficient spectral resolution to ascertain the magnitude of the crystalline site effects. The relative vibronic intensities in fluorescence and phosphorescence are compared. Two site effects are emphasized: site splitting of degenerate fundamentals and orientational effects. The former can occur for the isotopes C6H6 and sym-C6H3D3, while the latter is possible only for isotopes with less than a molecular threefold rotation axis. The observations show that both site-splitting and orientational effects do occur as a general rule on vibronic and vibrational states in benzene isotopic mixed crystals. An empirical correlation between the magnitudes of the site splitting, orientation effect and site (gas-to-crystal) shifts for in-plane and out-of-plane modes is noted. The phosphorescence of C6H6 and sym-C6H3D3 has been completely analyzed out to 0, 0 − (ν8 + ν1), while for that of C6D5H the analysis of only the more intense bands near the electronic origin has been carried out. Some ground-state vibrations of p-C6H4D2 are also presented but the phosphorescence spectrum, complicated greatly by both ground- and excited-state orientational effects, is not fully analyzed in the present work. Absorption spectra of these mixed crystals have yielded information concerning the orientational effect on the first excited singlet state of C6H5D and p-C6H4D2 as well as site splitting of the ν6′ vibrational levels of C6H6. On heavily exposed photographic plates it has been possible to assign a number of transitions in the 13CC5H6 emission spectra. The 13CC5H6−nDn0,0 absorption spectra have also been identified. New absorptions, in the region of the 0, 0 transition of C6H6 and C6H5D have been tentatively assigned on the basis of their intensity behavior as a function of guest concentration to resonance-pair lines and to lines from 13CC5H6-nDn and 13C2C4H6-nDn.