13.S: Molecular Spectroscopy (Summary)
- Page ID
- 550568
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In this chapter, we talk about what happens when light (expressed as an oscillating electric field) interacts with a quantum system, especially focusing on molecules. This requires use of time-dependent Schrödinger equation. What we will see is that a transition between two quantum states can take place when two conditions are met: first, the frequency of the electric field oscillation must be nearly equal to the energy difference between the two states, and second, the “transition dipole moment” between the states must be nonzero. Then, we will talk about the complete molecular Hamiltonian (instead of just the electronic Hamiltonian we’ve been discussing previously), and show how in many cases, we can separate it into an electronic part, a vibrational part, and a rotational part. We’ll conclude by looking at a variety of types of spectroscopic processes in a general sense, as indicated by a Jablonski diagram.
By the end of this chapter, you should know the following:
- Solutions to the time-dependent Schrödinger equation
- Why light can cause a transition to occur between stationary states
- The significance of the transition dipole moment integral
- The resonance condition for absorption and emission
- How the nuclear Hamiltonian depends on the electronic Hamiltonian
- Nuclear degrees of freedom
- Which regions of the electromagnetic spectrum correspond to which types of molecular transitions
- How Jablonski diagrams illustrate types and energies of spectroscopic transitions
- Zero-point vibrational energy
Skill goals (what you should be able to do/calculate):
- Determine the time-dependent behavior of a stationary state
- Identify the degrees of freedom of a molecule (both the number and their types)
- Draw and label Jablonski diagrams, use them to calculate transition energies
- Compute frequencies and wavelengths of spectroscopic transitions in a variety of units
- Use simple approximations for electronic and vibrational structure to estimate transition energies
- Define zero-point vibrational energy, know where it comes from, and indicate it on a Jablonski diagram