Transitions between Stationary State Energy Levels

Transitions between Stationary State Energy Levels 

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Transitions between Stationary State Energy Levels... 

Atomic and Molecular Energy Levels. Absorption and emission of electromagnetic radiation can occur by any of several mechanisms. Those important in spectroscopy are resonant interactions in which the photon energy matches the energy difference between discrete stationary energy states (eigenstates) of an atomic or molecular system = hv. This is known as the Bohr frequency condition. Transitions between... 

A comparison between the minimum energy structure and the transition state of the tridimensional surface with the corresponding stationary points located at the full potential energy surface at the MP2 level (with full optimisation but the forced planarity of the cyclopentadienyl group) shows just very slight differences in geometries, this validates the reduced surface used (the true MP2 energy barrier turns out to be 14.1 kcal/mol). 

If we take the energy values of the stationary states of the molecule as being given by equation (21-15), then according to equation (2-2) there follows for the frequency vj j of the rotational transition between the levels v, J and J +1... 

The vibrational motion of the nuclei thus results in stationary states with quantized vibrational energy levels via the time-independent SE and its boundary conditions. Transitions between the energy levels give rise to a spectrum in the infrared (IR) region. 

Quantum mechanics gives us a way to deal with the behaviour of matter at the molecular level. In this approach, molecular vibrations are stable only in specific stationary states which define energy levels for the system. While in a stationary state the vibration still takes place, but no radiation is emitted. Radiation is only emitted or absorbed on transition between energy levels (see Figure 6.2). The state of a system, such as a vibrating molecule, is described in quantum mechanics by a wavefunction, and we will see below how the use of a wave-like description naturally gives discrete energy levels. 

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