Hans Kupka

Multidimensional Franck–Condon integrals and Duschinsky mixing effects

A general method for calculating multidimensional Franck–Condon integrals for polyatomic molecules is given. These integrals are derived by means of a multivariable generating function which incorporates both the transformation of the normal mode coordinates between initial and final electronic states and their frequency changes. The normal mode transformation or mode mixing (Duschinsky effect) scrambles the occupations of the normal modes, leading to unusual distributions, which at certain values of the angles of rotation are confined to some of the modes only or even to a single mode. Mathematically, this selectivity can be described in terms of normal mode displacements generated by the rotation matrix from the potential minima of the ground and excited states. These normal mode displacements, as well as the set of mixed frequency change parameters due to mode mixing, have no counterparts in the parallel mode approximation and are the reason that multidimensional Franck–Condon integrals are of formidab...

Low temperature luminescence spectra of the d10s2 complexes Cs2MX6 (M = Se, Te and X = Cl, Br). The Jahn—Teller effect in the Γ−4(3T1u) excited state

Abstract The emission spectra of the title compounds in microcrystalline form have been measured at 10 K. The extensive vibrational progression in the e g mode is indicative of a tetragonal Jahn—Teller distortion in the Γ − 4 ( 3 T 1u ) excited state. The vibronic coupling of a threefold electronic state with a doubly degenerate e g mode (T—e coupling), linear in the nuclear coordinates, has been reinvestigated considering spin—orbit coupling up to second order perturbation on energy levels which result from an a 1 1g t 1 1u electron configuration. For an estimation of Jahn—Teller coupling constants, the intensity distributions in the progressions were compared with the theoretical line shape functions which were obtained from a model which also permits the determination of potential energy minima and vibrational fundamentals of the excited state. The unusually large increase in the e g vibrational frequency compared to the ground state is due to Jahn-Teller forces which distort the potential surface, yielding steeper excited state energy curves.

Pseudolocal phonons in p-terphenyl : pentacene single crystals

The structural nature of the phonon sidebands in the fluorescence and excitation spectra of pentacene guests in p‐terphenyl crystals at 4.2 K are investigated using site‐selective spectroscopy. The distinct features in the phonon sideband structure were observed to depend significantly on the guest site configuration of pentacene occupying four inequivalent sites in the triclinic p‐terphenyl lattice. The sharp peaks dominating the phonon sideband structure are assumed to arise from the pseudolocal phonons. The eigenvalues and eigenvectors of the pseudolocal phonons are calculated carrying out a modified normal mode analysis on the distinct pentacene site configurations including the contribution of all intermolecular atom‐pair interactions.

Clusters as crystal fragments of silicon bulk

Abstract Silicon clusters of 13 to 43 atoms were studied with the semi-empirical method SINDO1. Crystalline structures of face-centered cubic (fcc), hexagonal close packed (hcp) and diamond type and noncrystalline structures of icosahedral type were compared. Noncrystalline structures are most stable for clusters up to 13 atoms. Clusters with 19 and more atoms of the fcc structure are preferable to the less dense diamond structure. With more than 35 Si atoms, the diamond structure is favored over the hcp structure. The binding energy of fcc and hcp structures decreases and that of the diamond structure increases with increasing cluster size. A similar trend is observed for the HOMO-LUMO energy gap which is taken as a measure of the band gap.

Intramolecular distributions. III. N coupled modes

A previous theory of intramolecular distributions (ID) is extended to N (Duschinsky) mixed vibrational modes. For this case a multidimensional ID is derived which provides a comprehensive, complete, and unified description of vibronically assisted electronic transitions in polyatomic molecules. The multidimensional ID is introduced with the aid of a multivariable generating function. The latter quantity incorporates both the transformation of normal mode coordinates between the initial and final electronic states and its frequency changes. This normal coordinate transformation leads to the generation of additional sets of geometrical displacements which cannot be uniquely assigned to normal mode displacements as in the parallel mode approximation. It is shown that normal coordinate rotation causes the final state vibrational distribution or the spectral line shape to deviate considerably from that observed at parallel modes. A further derivable property of the multidimensional ID is its selectivity which ...

Intramolecular distributions. II. Recurrence solutions

The general theory developed in the first paper (hereafter referred to as I) of this series is applied directly to the problem of finding the values of the intramolecular distributions (ID). This is achieved by deriving four term recurrence equations. On the basis of these solutions, the dependence of the ID on the normal mode rotation is investigated; this gives qualitative information concerning the complexity of the mode mixing (rotation). We have also demonstrated the influence of mode mixing on the spectral line shape showing that for special values of the rotation angle the scrambling effect disappears and the spectrum exhibits single mode progressions. In this connection it is pointed out that the widely used parallel mode approximation is inadequate to explain the complex phenomena which occur in spectroscopy and related fields.

Intramolecular distributions. I. Theory

In this paper, a theory of intramolecular distributions for polyatomic molecules is presented. This approach has been found to be of great value in calculating radiative and nonradiative transitions. The intramolecular distributions (ID) are introduced by the aid of generating functions which incorporate typical molecular effects such as electronic origin and force constant shifts, and mode mixing. For some special cases, the main properties of multidimensional intramolecular distributions, which involve the effect of the density of final and initial states, are formulated in terms of an addition theorem; further use of these distributions in problems of molecular spectroscopy is discussed. Finally, the symmetry behavior of the ID’s is derived and its significance in establishing general relations and correlations between transitions in absorption and emission is discussed.

The vibrational fine structure of the 1A2g ← 1A1g polarized absorption band of trans-[Co(NH3)4(CN)2]+. The excited state geometry

Abstract The low temperature polarized absorption, far-infrared, and Raman spectra of trans-[Co(NH 3 ) 4 (CN) 2 ]Cl (H) and of the deuterated (D) compound

Calculation of the bandshape of vibronically-allowed d-d transitions

Abstract Absorption and emission line shapes are calculated in transition-metal ions. It is shown that for the case of “strong vibronic coupled” electronic states the emission or absorption bands are of gaussian shape.

Triplet-triplet absorption spectra of phenanthrene and azaanalogues

Abstract Triplet-triplet (T-T) absorption spectra of phenanthrene and several azaanalogues were measured in the spectral range from 25000 to 17000 cm −1 at 83 K. For the first time a vibrational structure of the main band systems in the T-T spectra could be detected. The vibrational modes producing these progressions are associated with the lower T 1 state. The assignment of the vibrational structure to the T 1 state has been confirmed by computation of the T-T spectra with the help of a lineshape function. Furthermore, in the spectra of the azaanalogues an additional absorption band appears which is assigned to a T-T transition from the T 2 state.