The aim of this work is twofold. In the first part, a detailed description is given of a specific vibrational model, designed for calculations on the vibrational energy levels in benzene and benzene isotopic species of D 6h symmetry. For the description of the C-H stretch system in benzene, a local mode (LM) formalism was applied, while, for the remaining non-C-H stretch vibrations, a symmetrized mode (SM) treatment was applied: this was called the combined LM/SM model. The model is based on a set of complex symmetrized curvilinear vibrational coordinates, which can be expressed as simple linear combinations of Whiffen's coordinates. The description in terms of complex symmetrized coordinates and wave functions allows for the construction of a separable symmetrized infinite-dimensional vibrational basis set, which is of crucial importance for large-scale calculations. In the second part of this work, using the described complex symmetrized LM/ SM vibrational model, calculations have been carried out on a large number of vibrational energy levels of four benzene D 6h isotopomers. The aim of the calculations was to redetermine a reliable set of harmonic force constants for benzene. Some of the force constant values obtained in the present work are substantially different from previous determinations by other authors. Using the presently determined set of harmonic force constant values in the calculations, a very good fit has been obtained to a large number of experimentally measured vibrational (both fundamental and overtone) energy levels of various symmetries, belonging to all four D 6h benzene isotopomers: C

In this work a fully symmetrized quantum mechanical description of vibrational motion in terms of complex vibrational coordinates and complex basis wavefunctions is outlined, designed for studying vibrational level mixing and intramolecular vibrational energy redistribution (IVR) around CH stretch overtone states in benzene. Symmetrized local mode (LM) formalism has been applied to the CH stretch system, while the remaining benzene vibrations (including out-of-plane modes) were treated as normal modes (NM). Using the outlined approach a model calculation of the absorption spectrum of the first overtone state CH (n=2) at ∼6000 cm−1 has been carried out.

ABSTRACT:The aim of this work is to introduce specific complex coordinates and wave functions (Hamiltonian eigenfunctions) for the description of vibrational motion in benzene. When suitably chosen, these complex functions are shown to possess interesting transformation behavior under the symmetry operations of the molecular symmetrical top point group D 6 . This behavior is analyzed and classified as "complex symmetry types" (CSTs). CSTs can be defined for all symmetrical top point groups. The description in terms of complex symmeterized coordinates and wave functions allows for the construction of a separable symmeterized vibrational basis set for benzene. New results from calculations on vibrational energies and redeterminations of harmonic force constants in benzene, obtained using the CST description, are presented.

In this work, the problem for the quality of empirically determined harmonic force constants in ground electronic state benzene has been carefully reexamined, for the case when strongly anharmonic vibrations are involved and in particular for the A 1g (ν 1 and ν 2 ) vibrational system. A numerical procedure, based on a local bond Hamiltonian representation for the C-H stretch system and a symmetrized coordinate treatment for the ν 1 (C-C) mode, has been described and applied to the determination of the harmonic F 1,1 , F 2,2 , and F 1,2 , and some important (diagonal) anharmonic force constants, instead of the traditional FG analysis. As a reference data for the determination of the required force constants, the set of experimentally observed ν 1 and ν 2 fundamentals for four D 6h benzene species C 6 H 6 , C 6 D 6 , 13 C 6 H 6 , and 13 C 6 D 6 have been employed. The harmonic force constants as well as harmonic frequencies obtained in this work have substantial deviations from previous determinations. Using the presently determined force constant values, a very good fit of the calculated to the experimentally observed frequencies has been achieved.

The vibrational level mixing at the second CH stretch overtone state CH(v=3) in benzene has been studied quantum mechanically using a completely symmetrized vibrational basis set in terms of a combined local mode/normal mode description. The employed symmetrized approach has helped to reduce the dimensionality of coupling Hamiltonian matrices and thus allowed for the inclusion of all 30 vibrational modes in the calculations. The absorption spectrum and dynamical intramolecular vibrational redistribution characteristics for initial excitation of a symmetrized local mode “bright” state in the CH(v=3) overtone manifold have been calculated and analyzed in connection with the degree of localization of the CH stretch overtone vibrational system in benzene.

The aim of this work is to present a full set of 34 empirically determined harmonic force constants F i,k for benzene (in symmetrized Whiffen's coordinates), as well as the corresponding set of 20 harmonic normal mode (NM) frequencies for all four D 6 h isotopomers:  C6H6, C6D6, 13C6H6, 13C6D6. The reliability of the obtained harmonic force constant values is reinforced by their ability to reproduce satisfactorily the experimentally measured fundamental vibrational frequencies of the four D 6 h benzene isotopomers. A specific combined LM (local mode)/SM (symmetrized modes) complex symmetrized nonperturbative vibrational model, developed in our previous work, has been employed for calculations on the vibrational energy levels in benzene, using the harmonic force constants F i,k and a few diagonal anharmonic parameters, as input data. A set of local (valence) harmonic force constants has also been derived from the empirically determined symmetrized force constants F i,k , and their physical meaning was discussed. The set of 20 harmonic NM frequencies ω k for all four D 6 h benzene isotopomers, calculated in the present work using the empirically determined set of F i,k values, have been analyzed and compared to previous empirical and ab initio determinations by other authors.

In this work we have carried out a theoretical investigation on the role of out-of-plane vibrational modes in vibrational level mixing and intramolecular vibrational energy redistribution (IVR) in benzene. A fully symmetrized vibrational basis set, based on a combined local mode (LM)+normal modes (NM) formalism was employed in the study. The Hamiltonian formalism for description of out-of-plane vibrations has been developed in due detail. Model calculations on the absorption spectrum and IVR dynamics at the second overtone state CH(v=3) at ∼8800 cm−1 have been carried out, supplementing previous studies and demonstrating the importance of out-of-plane modes in benzene.

We propose and develop theoretically a general mechanism for the involvement of rotational motion into the nonradiative transitions that occur in an isolated polyatomic molecule. The treatment is based on the different rotational constants and different (asymmetric top-symmetric top) molecular structures in the two combining electronic states. We focus our attention on the T(1)-->S(0) intersystem crossing (ISC) transition in thiophosgene and show how the rotational mechanism could lead to a considerable enhancement in the effective level density for the process. Inserting the rotational mechanism into our recently developed technique and algorithm for combined spin-orbit coupling+intramolecular vibrational redistribution analysis, we have carried out large-scale calculations that have led to a better understanding of the ISC (T(1)-->S(0)) in thiophosgene.