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I am looking for a textbook and/or internet resource where I can find the reference for assignment of symmetry of electronic states systematically.

For example, $$ \ce{^1\Delta^{}_{g}}, \ce{^3\Sigma^{}_{g}}, \ce{^1\Sigma^{}_{g}} \hspace{1em} \text{for ground state} \hspace{1em} \ce{O_{2}}$$

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    $\begingroup$ Pretty much any containing an introduction on electronic structure theory. I prefer $Carl J. Ballhausen:$ "Introduction to Ligand Field Theory". $\endgroup$ – Rudi_Birnbaum Jun 10 '17 at 18:57
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    $\begingroup$ Ballhausen is a pretty tough book to start learning with; try Carter 'Molecular Symmetry and Group Theory' and an older book Bishop 'Group Theory and Chemistry'. Easier books are Molloy 'Group Theory for Chemist ' and for beginners very good tutorial type book Vincent ' Group Theory for Chemists'. Most phys chem textbook also cover these topics but usually briefly. You could also look at specialist spectroscopy books of which there are many. $\endgroup$ – porphyrin Jun 11 '17 at 8:57

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