Mise au point. Theorie des effets de couplage vibronique multimodes. Probleme a 2 etats. Couplage vibronique mettant en jeu des modes et des etats degeneres. Effets du couplage vibronique multimodes en spectroscopie. Comportement statistique des niveaux d'energie vibroniques. Intersections coniques et evolution temporelle de la fluorescence

Multimode molecular dynamics beyond the Born-Oppenheimer approximation

Multimode Molecular Dynamics Beyond the Born‐Oppenheimer Approximation

A general scheme for calculating relative nonradiative decay rates of initially selected vibronic levels in polyatomic molecules is developed. Here we are concerned only with relative rates corresponding to initial vibronic states in some particular electronic manifold decaying into some other particular electronic manifold. Therefore we need only consider the exact density‐of‐states‐weighted‐Franck—Condon factor accounting for the vibrational contribution to the over‐all nonradiative decay rate. This contribution is calculated approximately in the large molecule (statistical) limit by deriving the appropriate (modified) energy gap law. The contributions of ``special'' modes (e.g., optically excited modes, and modes with large geometry and/or frequency shifts) are partitioned from those of the other modes by techniques similar to ones developed earlier to treat cis—trans isomerism and are calculated explicitly. Excellent agreement with the recent low pressure experimental results of Spears, Abramson, and Rice for the S1→ T1 intersystem crossing rates from individual vibronic states in benzene and perdeuterobenzene is obtained, but only by taking proper account of the effects of geometry and frequency changes of the various vibrational modes involved in the transition. The sharp dependence of the relative nonradiative rates for a progression in an optical mode upon the frequency shift in that mode leads to the possibility of evaluating the vibrational frequencies in an electronic state by measuring the radiationless decay rate into that electronic state (e.g., in the benzene case determining T1 vibrational frequencies from S1→ T1 decay rates). Finally, we comment upon recent low pressure experimental results for β‐naphthylamine, monofluorobenzene, and upon some observed temperature dependences of radiationless transition rates in matrices.

Dependence of Radiationless Decay Rates in Polyatomic Molecules upon the Initially Selected Vibronic State: General Theory and Application

We review response theory and calculations of molecular properties involving spin-orbit interactions. The spin-orbit coupling is evaluated for reference states described by single- or multi-configuration self-consistent field wave functions. The calculations of spin-orbit related properties rest on the formalism of linear and quadratic response functions for singlet and triplet perturbations when no permutational symmetry in the two-electron operators is assumed and from which various triplet as well as singlet response properties are derived. The spin-orbit coupling matrix elements between singlet and triplet states are evaluated as residues of (multi-configuration) linear response functions, and are therefore automatically determined between orthogonal and non-interacting states. Spin-forbidden radiative transition intensities and lifetimes are determined from the spin-orbit coupling induced dipole transitions between two electronic states of different multiplicity and are obtained as residues of quadratic response functions. The potential of the theory and its range of applications is illustrated by a selection of recent investigations covering different molecular phenomena. The applications include second-order energy contributions, intensity rearrangement in electron spectra, calculation of predissociative lifetimes of dicationic states, assignment of triplet bands in absorption spectra, intersystem crossings and reactivity, external heavy atom effects on S-T transitions, phosphorescence spectra and radiative lifetimes of triplet states. We give an outlook on spin-orbit interaction induced phenomena in extended systems and on applications to general spin catalysis phenomena.

Response Theory and Calculations of Spin-Orbit Coupling Phenomena in Molecules

The direct absorption spectrum of benzene in a free jet has been measured in the 130–260 nm region (S1, S2, and S3 states, Rydberg series, and the first ionization limit) using synchrotron radiation as a light source. The absolute molar extinction coefficients (e) of benzene in jets have been determined by scaling measured free‐jet values to the known value in the vapor phase for a broadband at 200.1 nm in the S2 state. The vibrational temperature for ν16 mode was estimated to be 185 K. The maximum value of e of the S1 absorption system was found to be 1400 l mol−1 cm−1 (spectral bandwidth=0.065 nm). A shoulder observed at 205.45 nm in the S2 absorption system is assigned to the S2 origin, induced by pseudo‐Jahn–Teller distortion.

Direct absorption spectra of jet-cooled benzene in 130-260 nm

The 3B1u → 1A1g intrinsic absorption spectra of C6H6 and C6D6 at 4.2°K have been obtained for the first time at high resolution using the phosphorescence–photoexcitation method. The spectrum exhibits very clear evidence of a pseudo‐Jahn–Teller distortion of the normally hexagonal benzene molecule upon excitation to the triplet state. Factor‐group splitting of the 0–0 and 0–0 + ν1 exciton bands have also been observed. The position of the mean of the 0–0 exciton band of C6H6 when compared to the phosphorescence origin of a C6H6 guest in a C6D6 crystal, indicates that the “static” intermolecular interactions between guest and host are different for C6H6 and C6D6 hosts. This result has important implications for the applicability of mixed crystal theories to benzene.

D. M. Burland

Papers

Experimental Observation of Singlet–Triplet Absorption in Pure Crystalline Benzene

Experimenteller nachweis der singulett-triplett-absorption in reinem kristallinen benzol