Electronic Spectra of Molecules

Molecules exhibit electronic spectra from transitions between electron energy levels. These spectra are more complex than those of atomic spectra which involve transitions between electron energy levels which typically produce sharp line spectra. The energies associated with molecular electronic spectra (typically in the optical or uv region) are typically much larger than those associated with vibrational spectra (typically in the infrared) and rotational spectra (typically in the microwave region). This contributes to the complexity of the electronic spectra since the transitions from a multitude of vibrational and rotational levels produce many spectral lines, a "band" of frequencies.

Electronic transitions are essentially instantaneous, so there is no time for appreciable motion of the nuclei. So the transitions appear as vertical lines with no change in internuclear distance. This is referred to as the Franck-Condon principle. The spectra are strongly affected by the probability that an electron is at a location to contribute to such a "vertical" transition. That probability is the wavefunction squared, and at least the lowest vibrational states are approximated by the quantum harmonic oscillator.

The energy level diagrams contain much information about the molecule. The v=0 ground ground vibrational state has the highest probability at the center of the potential well, but the higher vibrational states have the highest probabilty at maximum displacement from that center. The transition above demonstrates one result of those facts: the center of the ground state is at the same internuclear distance as the v=1 state of the first electronic excited state. So that transition is highly probably and produces a strong spectral line. Transitions involving other vibrational states are observed, but significantly weaker.

The illustration of the v=0 to v=1 transition above shows it as being broader, which is partly due to its greater intensity, but also because there can be many molecular rotational states associated with the vibrational states, giving a band of many transitions close to the same frequency. The higher inherent intensity makes more of those transitions visible and broadens the line.

This is a depiction of multiple electronic transitions from a common vibrational state in the ground electronic state to successive vibrational levels in an excited electronic state. There are no limiting selection rules, so transitions between many pairs of levels can occur. The lines are broadened because of the multiple rotation states associated with the vibrational levels.

The representation above was patterned after Taylor, Zafiritos and Dubson's treatment. The section of an actual photographic record of such a spectrum at right is from Blatt and attributed to J. A. Marquisce. It is a portion of the emission spectrum of N2.

The Franck-Condon principle is an important part of the understanding of molecular electronic spectra. The relevant internuclear separations in an electronic excited state may be essentially the same as in the ground state, but if they are different, it has major effects on the nature of the electronic spectrum. Such differences may lead to the phenomenon of fluorescence in some molecules, and phosphorescence in others.

Molecular Fluorescence

A qualitative understanding of many molecular electronic spectral phenomena can be obtained from the molecular potential diagrams with the application of the Franck-Condon principle and the nature of the quantum harmonic oscillator energy levels. The diagram above follows the suggestion of Beiser to explain how molecular fluorescence can occur. The electronic absorption shown follows the Franck-Condon principle in making the vertical transition from the highest probability location of the ground vibrational state to a high probability location of the v=4 vibrational state of the excited electronic state. Vibrational transitions can bring the electron down to the ground vibrational state where it has a high probability of transition to the v=2 vibrational level of the ground electronic state. This process can occur rapidly, so the molecule can absorb a high energy photon and quickly emit a photon of lower quantum energy, a process which is called fluorescence.

Molecular Phosphorescence

A qualitative understanding of many molecular electronic spectral phenomena can be obtained from the molecular potential diagrams with the application of the Franck-Condon principle and the nature of the quantum harmonic oscillator energy levels. The diagram above follows the suggestion of Beiser to explain how molecular phosphorescence can occur. The electronic absorption shown follows the Franck-Condon principle in making the vertical transition from the highest probability location of the ground vibrational state to a high probability location of the v=4 vibrational state of the excited electronic state. Vibrational transitions can bring the electron down to lower vibrational states, but in this case there is also a triplet excited electronic state. From the v=2 state, the electron can make a transition to this triplet state, and further vibrational deexitations leaves it trapped since transition to the singlet ground state is forbidden. Vibrational transitions can take the electron to the ground vibration state, and this diagram shows a high probability path down to the v=3 vibrational level of the ground state by the Franck-Condon principle. The fact that it is "forbidden" by the selection rules doesn't mean it can't happen, just that it is low in probability. Such transitions have a very long halflife and the lower quantum energy phosphorescent radiation may be emitted minutes or even hours after the initial absorption.

Singlet and Triplet Molecular States

If a pair of electrons occupy the ground electronic state of a molecule, the electron spin states of these two electrons must be opposite according to the Pauli exclusion principle. This state with net zero spin angular momentum will not be split by the application of a magnetic field (Zeeman effect) and is called a "singlet state".

If one electron is elevated to an excited state, the two electrons may be either paired (singlet) or unpaired with both electrons oriented in the same direction. The unpaired spin state has a spin s=1 and has three possible orientations with respect to an applied magnetic field. It is called a "triplet state".