William T. Simpson

Influence of Exciton Phonon Interaction on Metallic Reflection from Molecular Crystals

Abstract Reflection spectra of a number of polymethine dyes are presented and analysed. Characteristic features of these spectra appear to be outside the framework of the Lorentz-Lorenz theory. An alternate approach based on an appropriate linear response function for surface excitation is developed. The linear response at a particular frequency involves a sum over all k-dependent Greens functions. Damping is brought in through the exciton-phonon interaction. A model Hamiltonian is introduced which can be diagonalized exactly for the single molecule. For the crystal, this permits the treatment of single phonon effects in the strong coupling limit almost as if they were multiple phonon effects. Structure, mainly associated with damping, in the reflection spectrum is expected and found in those regions of the exciton dispersion curve where the density of momentum states is large. Reasonably good agreement is found between the theoretical and experimental reflection curves.

Polarizations of Electronic Transitions from Azimuthal Variation in Fluorescence Intensity—with Application to Biphenyl

It is shown that the angle between absorbing and emitting transition moment vectors may be obtained from a ratio of intensities measured in fluorescence; the intensities to be taken from an azimuthal circle with the propagation vector of the incident beam as polar axis. The incident light must be polarized and the intensities are measured at azimuthal stations selected according to the direction of polarization. Results are compared with those obtained using conventional polarized fluorescence—for aniline and for indole. The azimuthal ratio method is then used to obtain polarizations for biphenyl and substituted biphenyls. Use of the method may facilitate penetration into the region below 200 nm; in fact a determination using excitation at 197 nm has already been made. Finally, the results for biphenyl are interpreted so as to constitute several new assignments of electronic transitions.

Assignment of the Second Singlet in Carbonyl

Marked increases in extinction going from crystalline to melted samples are observed for the electronic absorption at ∼1850 A (second singlet) in various appropriately selected aliphatic ketones. These changes probably indicate that the transition moment in the crystal is perpendicular to the plane of incidence. Taken together with the crystal geometry this leads to assignment of the second singlet as n→σCO*. The polarized spectrum of 9‐heptadecanone is extended from 56 to 65 kK and extinction coefficients are included. A dichroic ratio anomaly observed in the polarized spectrum is interpreted as involving different amounts of hypo‐ (hyper‐) chromism for parallel and perpendicular polarization directions.

Franck‐Condon principle as involving torsional oscillations: Height of the potential barrier to internal rotation in an electronically excited state of ethane

The effect of restricted internal rotation on electronic spectra can be considered in the light of the Franck‐Condon principle. For usual values of the temperature and the molecular constants, internal rotation can have a heavy influence on the width and shape of a vibronic line, conceivably even to the extent of masking the shape due to external rotation. These ideas are pursued in the case of the zero‐zero and one other vibronic line of ethane. Spectra at ∼ 1400 A for ethane and perdeuteroethane from −78−260°C are presented, as are spectra theoretically calculated for various temperatures, and barriers ranging from zero to 27 kcal/mole. A detailed comparison of calculated and actual spectra leads to an educated guess for the excited‐state barrier height as 1.7 kcal/mole, close to the calculated value of Salahub and Sandorfy of 1.3 kcal/mole. In a discussion of the assignment of the electronic transition, the Innes and Pearson finding that the transition is perpendicular is accepted, but it is suggested ...

Metallic reflection in a crystalline polymethinium dye and in crystalline TCNQ: Theory of the damping

Metallic reflection occurs in molecular crystals when a stopping band associated with a strong molecular electronic transition emerges. Variations in reflectivity over the band are studied here theoretically for two cases—1,5‐bis (dimethylamino)pentamethinium perchlorate (BDP) and tetracyanoquinodimethane (TCNQ). The variations are described by a frequency dependent damping term Γ (ω) in the expression for the polarizability. For the case of one molecule per unit cell (BDP), the observed reflection band shape can be matched using a theoretical expression iΓ (ω) = (γ2/N) Σk 1/(ω−ωk−Δ), where γ is a molecular vibrational relaxation constant and Δ is the frequency of a single active vibration. The variation of ωk with k is approximated by the long‐wave method. For the case of two molecules per unit cell (TCNQ) a more complicated expression is obtained which predicts a reflection spectrum richer in structure than in the case of one molecule per unit cell. The number and location of features in the theoretical...

Structural Features from Reflection Spectra: Orientation of 1, 3,-bis-(Dimethylamino) trimethinium Perchlorate Molecules in the Crystal

Abstract If the orientation of a molecular electronic transition moment with respect to the molecular framework is known, reflection spectra of crystalline samples on various faces may be used to locate the molecules in question. This can be done through projection of the transition moment on the faces, or through use of the optical indicatrix. The two methods are briefly compared, and the preferred indicatrix method is applied to crystals of the dye 1,3-bis-(dim-ethylamino)trimethinium perchlorate. Along each principal axis of the indicatrix, best fit values for reasonant frequency, plasma frequency, and damping constant are obtained in the frequency range of the first singlet. Parameters of the crystal structure having to do with the orientation of the dye molecules are then deduced from this information.

Consolidated Configuration‐Interaction Perturbation Method: The Ground State of Beryllium

A method is developed for consolidating the configuration‐interaction method and Rayleigh–Schrodinger perturbation theory. The technique requires the existence of a more or less conventional unperturbed Hamiltonian but not its eigenfunctions. The method depends crucially upon a particular partitioning of terms among perturbed and unperturbed parts of the full Hamiltonian expressed in spectral representation, and leads to having some perturbation denominators significantly different from the Rayleigh–Schrodinger ones. The beryllium ground‐state energy was calculated as a test. An hydrogeniclike basis was obtained by interacting the Shull–Lowdin discrete Laguerres over an appropriate one‐electron Hamiltonian. A single screening constant was employed and a rather unique method was used to treat the (zero‐order) degeneracy of the | 1s22s2〉 and | 1s22p2〉 functions. Some two‐electron integrals were calculated by the method of Jones and Brooks and others by modifying the formula of Brown. The value − 14.659 a.u....

Absorptive trapping in thin dye layers

Films of organic dyes having thicknesses of ∼200 A when illuminated in a manner which would give rise to attenuated total reflection spectra show unexpectedly high absorptions. Generally speaking, the phenomenon is interpreted via Maxwell’s macroscopic equations. A surprising feature of the interpretation is that an angle, film thickness, and frequency can be found such that no fraction whatsoever of the incident light is either reflected or transmitted. A special formalism is introduced, which is judged to facilitate a particularly direct interpretation, wherein emphasis is given to the role played by dissipation. The phenomenon as viewed in the framework of this formalism, and with the help of qualitative ideas taken from the microscopic theory, can be further explained: The s− and p−polarized incident beams excite, respectively, lightly damped transverse and longitudinal polariton modes, so that the maximum effect in the two cases comes essentially at the corresponding resonances, ω− and ω+.