Vibronic spectroscopy is a branch of molecular spectroscopy concerned with vibronic transitions: the simultaneous changes in electronic and vibrational energy levels of a molecule due to the absorption or emission of a photon of the appropriate energy. In the gas phase, vibronic transitions are also accompanied by changes in rotational energy. Vibronic spectra of diatomic molecules have been analysed in detail; emission spectra are more complicated than absorption spectra. The intensity of allowed vibronic transitions is governed by the Franck–Condon principle. Vibronic spectroscopy may provide information, such as bond length, on electronic excited states of stable molecules. It has also been applied to the study of unstable molecules such as dicarbon (C2) in discharges, flames and astronomical objects.
Principles
Electronic transitions are typically observed in the visible and ultraviolet regions, in the wavelength range approximately 200–700 nm (50,000–14,000 cm−1), whereas fundamental vibrations are observed below about 4000 cm−1. When the electronic and vibrational energy changes are so different, vibronic coupling (mixing of electronic and vibrational wave functions) can be neglected and the energy of a vibronic level can be taken as the sum of the electronic and vibrational (and rotational) energies; that is, the Born–Oppenheimer approximation applies. The overall molecular energy depends not only on the electronic state but also on vibrational and rotational quantum numbers, denoted v and J respectively for diatomic molecules. It is conventional to add a double prime (v″, J″) for levels of the electronic ground state and a single prime (v′, J′) for electronically excited states. Each electronic transition may show vibrational coarse structure, and for molecules in the gas phase, rotational fine structure. This is true even when the molecule has a zero dipole moment and therefore has no vibration-rotation infrared spectrum or pure rotational microwave spectrum. It is necessary to distinguish between absorption and emission spectra. With absorption the molecule starts in the ground electronic state, and usually also in the vibrational ground state v″ = 0 because at ordinary temperatures the energy necessary for vibrational excitation is large compared to the average thermal energy. The molecule is excited to another electronic state and to many possible vibrational states v' = 0, 1, 2, 3, .... With emission, the molecule can start in various populated vibrational states, and finishes in the electronic ground state in one of many populated vibrational levels. The emission spectrum is more complicated than the absorption spectrum of the same molecule because there are more changes in vibrational energy level.
For absorption spectra, the vibrational coarse structure for a given electronic transition forms a single progression, or series of transitions with a common level, here the lower level v″ = 0. There are no selection rules for vibrational quantum numbers, which are zero in the ground vibrational level of the initial electronic ground state, but can take any integer values in the final electronic excited state. The term values G(v) for a harmonic oscillator are given by
G ( v ) = ν ¯ electronic + ω e ( v + 1 2 ) {\displaystyle G(v)={\bar {\nu }}_{\text{electronic}}+\omega _{e}\left(v+{\tfrac {1}{2}}\right)\,}
where v is a vibrational quantum number, and ωe is the harmonic wavenumber. In the next approximation the term values are given by
G ( v ) = ν ¯ electronic + ω e ( v + 1 2 ) − ω e χ e ( v + 1 2 ) 2 {\displaystyle G(v)={\bar {\nu }}_{\text{electronic}}+\omega _{e}\left(v+{\tfrac {1}{2}}\right)-\omega _{e}\chi _{e}\left(v+{\tfrac {1}{2}}\right)^{2}\,}
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