Willem Siebrand

Radiationless Transitions in Polyatomic Molecules. I. Calculation of Franck—Condon Factors

Radiationless transitions between two electronic states are studied for a system consisting of a polyatomic molecule in a medium where vibrational relaxation is rapid. The transition rate is then governed by a vibronic matrix element and a vibrational overlap factor. Only the latter, known as the Franck—Condon factor and denoted by F, is investigated in detail. For harmonic oscillators F derives from shifts in equilibrium distance (displacements) and shifts in frequency (distortions). It is shown that for radiationless transitions involving large energy gaps (E), F is dominated by distortions, whereas for optical transitions it is dominated by displacements of the oscillators. These distortions lead to an approximately exponential decrease of F with increasing E. An isotope rule for F is derived which is valid for both displaced and distorted oscillators provided E is not too small. Since all formulas are of the form F (E), where E is the principal variable, comparison with experiment is only possible for...

Radiationless Transitions in Polyatomic Molecules. II. Triplet‐Ground‐State Transitions in Aromatic Hydrocarbons

The theory of Part I is applied to nonradiative transitions from the lowest triplet state to the ground state of aromatic hydrocarbons. A previously communicated empirical relation between triplet energy, triplet lifetime, and the relative number of hydrogen atoms per molecule is substantiated and its physical implications are discussed. It is transformed into a relation between the Franck‐Condon factor of the transitions and the triplet energy. In this form it can be compared with the theoretical expressions derived in Part I. No satisfactory theoretical representation of the empirical formula could be obtained on the basis of a harmonic‐oscillator description of the normal modes of the molecules. However, introduction of anharmonicity leads to excellent agreement between theory and experiment. A one‐parameter formula is derived which accounts with good accuracy for the dependence of the triplet lifetime on the triplet energy and the number of carbon and hydrogen atoms in the molecule. This formula shows...

Laser Generation of Excitons and Fluorescence in Anthracene Crystals

Experimental and theoretical studies are reported of the short‐lived and delayed fluorescence of anthracene single crystals, excited by single‐ and double‐photon absorption. A giant‐pulse ruby laser provides the primary source of radiation of 14 400 cm−1 (up to 1027 photons/cm2·sec) and is also used to generate second‐harmonic radiation from ADP, as well as stimulated Raman radiation of 12 800 and 17 500 cm−1 from liquid oxygen. The time dependence of the fluorescence intensity is studied as a function of laser intensity, crystal temperature and excitation wavelength. The very intense fast fluorescence with a half‐life of 30 nsec at 300°K, characteristic of singlet exciton decay, and the relatively weak delayed fluorescence which involves intermediate triplet states, are separated using sectored disks. It is concluded that the triplet state at 14 750 cm−1 can be populated (i) by direct absorption of laser photons involving an activation energy of 350 cm−1; (ii) via two‐photon absorption, presumably leadin...

Model for the direct photo-isomerization of stilbene

Abstract The photo-chemical cis-trans isomerization of stilbene is re-interpreted after the introduction of a low-energy doubly excited state.

Spin–Orbit Coupling in Aromatic Hydrocarbons. Analysis of Nonradiative Transitions between Singlet and Triplet States in Benzene and Naphthalene

Rate expressions for intersystem crossings in aromatic hydrocarbons are formulated by treating both the spin–orbit coupling and the nuclear kinetic‐energy operators as perturbations causing the nonradiative transition. General expressions are derived for the corresponding matrix elements, which are shown to fall into three groups, corresponding to three different mechanisms. In the first, which is subject to an electronic orbital selection rule, the transition is caused by spin–orbit coupling only. In the second and third, spin–orbit coupling and vibronic coupling act together, namely, Herzberg–Teller vibronic coupling in the second, and diabatic (non‐Born–Oppenheimer) coupling, caused by the nuclear momenta, in the third mechanism. It is shown that in aromatic hydrocarbons spin–orbit coupling between π states governs the second mechanism and spin–orbit coupling between π and σ states the third mechanism. The three mechanisms are distinguished by the effect of partial deuteration on the rate constant, whi...

Radiationless Transitions in Polyatomic Molecules. III. Anharmonicity, Isotope Effects, and Singlet‐to‐Ground‐State Transitions in Aromatic Hydrocarbons

The work on Franck–Condon factors for radiationless transitions in polyatomic molecules, as reported in Parts I and II of this series, is extended and generalized, starting from the theoretical expression for Franck–Condon factors in aromatic hydrocarbons, which was derived and applied to triplet‐to‐ground‐state transitions in Part II. The role played in this expression by the anharmonicity and symmetry of CH‐stretching modes is clarified. As a preliminary step towards application of this expression to singlet‐to‐ground‐state transitions in aromatic hydrocarbons, the appropriate Franck–Condon factors are studied spectroscopically by measuring the long‐wavelength part of the fluorescence spectra of anthracene‐h10 and ‐d10. These experimental Franck–Condon factors are used to determine the anharmonicity parameter in the theoretical expression for the singlet‐to‐ground‐state radiationless‐transitions rate constant. Theoretical rate constants for the transition calculated on this basis compare favorably with ...

Anharmonicity in Polyatomic Molecules. The CH‐Stretching Overtone Spectrum of Benzene

A long series of CH‐stretching overtones in the infrared and visible spectrum of benzene can be analyzed using a single anharmonicity constant (− 57.5 cm−1). This anharmonicity is associated with an independently vibrating local CH oscillator and the spectrum is interpreted in terms of such a local‐mode representation. A transformation is made to normal modes which leads to five different normal‐mode anharmonicity constants, which are representative of the 13 different CH‐stretching anharmonicity constants that characterize benzene. The CH‐overtone spectrum of benzene is described in terms of its normal‐mode components. A method of assigning relative intensities to these components is developed, and, along with the calculated normal‐mode anharmonicity constants, is used to construct the overtone spectrum as a superposition of Lorentzian bands calculated for each individual component. The maxima of these bands compare favorably with the observed band maxima. By adjusting the local‐mode anharmonicity consta...

Theory of vibronic intensity borrowing. Comparison of Herzberg‐Teller and Born‐Oppenheimer coupling

The Herzberg‐Teller theory of vibronic intensity borrowing is reinvestigated. A potentially serious deficiency is found in the conventional approximation scheme based on neglecting vibronic perturbation of the ground state relative to that of the excited state. Simple theoretical models are studied and show systematic cancellation of the lowest‐order induced transition dipole moment if both vibronic perturbations are included. As a result the vibronic coupling between Born‐Oppenheimer states via nuclear momenta, for which such a cancellation does not occur, tends to contribute measurably to the induced transition moment, contrary to what usually is assumed. Two methods to distinguish between Herzberg‐Teller‐type (HT) and Born‐Oppenheimer‐type (BO) contributions are discussed, namely the absorption‐emission asymmetry and the isotope effect. The former results from interference between HT and BO terms, which is usually constructive in absorption and destructive in emission; the latter is due to the fact tha...

Franck–Condon effects in resonance Raman spectra and excitation profiles

Resonance Raman spectra and excitation profiles are calculated for totally symmetric vibrations not involved in vibronic coupling and thus deriving all their intensity from Franck–Condon effects. Theoretical results are derived for harmonic oscillators undergoing displacements and frequency shifts upon electronic excitation of the molecule. The model does not only consider the effect of interference between several totally symmetric modes but also includes a number of basic refinements absent from most previous treatments such as inhomogeneous line broadening, perturbation of a weak resonance transition by the preresonance spectrum of a strong neighboring transition, and normal coordinate rotation (Dushinsky effect). The model calculations are used to interpret observed Raman spectra and excitation profiles of totally symmetric modes in the chromate ion and the β‐carotene molecule.

Charge-transfer excitons in anthracene crystals and their role in optical charge carrier generation

Abstract The energy of an electron-hole pair in anthracene is calculated for a complete range of separations and the resulting change-transfer exciton potentials are used to analyze optical charge carrier generation as a function of wavelength and temperature.