CALCULATION AND ASSIGNMENT OF RYDBERG LEVELS IN BENZENE
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Date
1974
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University
Abstract
High resolution optical spectra taken by Wilkinson showed four Rydberg Series converging to the first ionization potential at 9.247 eV. He designated these series $R$, $R^{\prime}$, $R^{\prime\prime}$, $R^{\prime\prime}$. The $R$ and $R^{\prime}$ series are the most intense and presumably are due to the allowed $e_{1u} \leftarrow$ $e_{1g}$ and $a_{2u}$ $\leftarrow$ $e_{1g}$ transitions where $e_{1g}$ is the highest occupied molecular orbital and has $\pi$ symmetry, and $e_{1u}$ and $a_{2u}$ are Rydberg orbitals with Per and $P\pi$ symmetry, respectively, in the united-atom limit. The relative size of the quantum defects suggests that the R^{\prime} series is $e_{1u}$ $\leftarrow$ and $e_{1g}$ and that the R^{\prime} series is $a_{2u}$ $\leftarrow$ $e_{1g}$ while pseudopotential calculations have not been conclusive. We have carried out self-consistent-field calculations on these states with a fairly large Gaussian basis set, (10$_{s} 6p/4_{s}$), $[5_{s}$ $3p/2_{s}$] where one set of Gaussians represents C $3_{s}$ orbital and one set represents C 3$_{p}$ orbita1s. The calculated $e_{1u}$ $\leftarrow$ $e_{1g}$ excitation energy (average of $A_{1u}$, $A_{2u}$, and $E_{2u}$) is 6.71 eV., and the calculated $a_{2u}$ $\leftarrow$ $e_{1g}$ excitation energy ($E_{1u}$) is 6.94 eV. The splitting between the two is expected to be more reliable than the absolute excitation energy. The lowest energy Rydberg state computed is a $E_{1g}$ state at 6.31 eV., which comes from a forbidden excitation to an $a_{1g}$ orbital (3s in the united-atom limit).
Description
Author Institution: Department of Chemistry, The Ohio State University; Department of Physics, University of Chicago; Department of Chemistry, The Ohio State University