Vibronic spectroscopy

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 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.

[4] 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.

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.

[6] 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.

For higher values further anharmonicity terms are needed as the molecule approaches the dissociation limit, at the energy corresponding to the upper (final state) potential curve at infinite internuclear distance.

In accordance with the Born-Oppenheimer approximation, where electronic motion is near instantaneous compared to nuclear motion, transitions between vibrational levels happen with essentially no change in nuclear coordinates between the ground and excited electronic states.

These nuclear coordinates are referred to as classical "turning points", where the equilibrium bond lengths of the initial and final electronic states are equal.

The width of this progression itself is dependent on the range of transition energies available for internuclear distances close to the turning points of the initial vibration state.

As the "well" of the potential energy curve of the final electronic state grows steeper, there are more final vibrational states available for transitions, and thus more energy levels to yield a wider spectrum.

Emission spectra are complicated due to the variety of processes through which electronically excited molecules can spontaneously return to lower energy states.

[9] There is a tendency for molecules to undergo vibrational energy relaxation, where energy is lost non-radiatively from the Franck–Condon state (the vibrational state achieved after a vertical transition) to surroundings or to internal processes.

Resonance fluorescence, however, is not very common and is mainly observed in small molecules (such as diatomics) in the gas phase.

This lack of prevalence is due to short radiative lifetimes of the excited state, during which energy can be lost.

Vibronic spectra of diatomic molecules in the gas phase have been analyzed in detail.

The vibronic spectra of diatomic molecules in the gas phase also show rotational fine structure.

The values of the rotational constants may differ appreciably because the bond length in the electronic excited state may be quite different from the bond length in the ground state, because of the operation of the Franck-Condon principle.

[note 2] In the rigid rotor approximation the line wavenumbers lie on a parabola which has a maximum at

For example, the bond length in the excited state may be derived from the value of the rotational constant B′.

[17] The Swan bands in hydrocarbon flame spectra are a progression in the C–C stretching vibration of the dicarbon radical, C2 for the

[18] Vibronic bands for 9 other electronic transitions of C2 have been observed in the infrared and ultraviolet regions.

In both gas and liquid phase the band around 250 nm shows a progression in the symmetric ring-breathing vibration.

[21] As an example from inorganic chemistry the permanganate ion, MnO−4, in aqueous solution has an intense purple colour due to an O → Mn ligand-to-metal charge transfer band (LMCT) in much of the visible region.

[23] The individual lines overlap each other extensively, giving rise to a broad overall profile with some coarse structure.

[24] d–d electronic transitions in atoms in a centrosymmetric environment are electric-dipole forbidden by the Laporte rule.

In the case of the octahedral actinide chloro-complex of uranium(IV), UCl62− the observed electronic spectrum is entirely vibronic.

At the temperature of liquid helium, 4 K, the vibronic structure was completely resolved, with zero intensity for the purely electronic transition, and three side-lines corresponding to the asymmetric U–Cl stretching vibration and two asymmetric Cl–U–Cl bending modes.

[26] Later studies on the same anion were also able to account for vibronic transitions involving low-frequency lattice vibrations.