Somogyi, Wilfrid S,; (2025) Method Development for Higher Order Transitions in Homonuclear Diatomic Molecules. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The central aim of this thesis is to develop a new computational methodology for calculating linestrengths, Einstein coefficients and absorption intensities of electric quadrupole and magnetic dipole transition moments in diatomic molecules. The system chosen to demonstrate this methodology is the \oxygen\ molecule, and specifically the atmospheric and infrared transitions. A unified treatment of the electric quadrupole and magnetic dipole moments has been developed \textit{a priori} from the molecular Hamiltonian in the Born-Oppenheimer approximation. Using this treatment, expressions for the line strengths, Einstein coefficients and absorption intensities for transitions generated by these multipole interactions have been derived and implemented in computer code as an extension to the \Duo\ program. This implementation has been tested and demonstrated for a range of homonuclear and heteronuclear diatomic molecules. Using symmetry properties of these transition moments, and a reduction to the irreducible tensor representation, straightforward expressions have been given for the transformation from the basis of Abelian symmetry groups to the of Hund's case (a) basis. A set of potential energy, quadrupole moment, electronic angular momentum and spin-orbit coupling curves have been produced using high-level electronic structure calculations for seven electronic states of \oxygen. A property-based procedure for diabatising electronic structure properties has been presented and successfully used to transform electronic structure properties of some highly excited $\Pi$ states of molecular oxygen to the adiabatic representation. This is a key step in accurately reproducing the complicated rotational structure of the electric quadrupole absorption bands. This diabatic model has subsequently been used to produce the first complete rovibronic line list for transitions between the three lowest lying electronic states (\Xstate, \astate, and \bstate) using the extended ExoMol methodology for higher order transition moments. This line list has been produced through empirical refinement of the spectroscopic model and is widely applicable for a range of temperatures and in the wavenumber range \SIrange{0}{20000}{\per\cm}.

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