Transition dipole moment of diatomic molecules

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SUMMARY

The transition dipole moment (TDM) between two electronic states of a diatomic molecule is not the same in both directions. Specifically, the TDM from state A to state B is represented as ##\langle B|d|A \rangle##, while the TDM from state B to state A is the complex conjugate, expressed as ##\langle A|d|B \rangle = (\langle B|d|A \rangle)^*##. This relationship is due to the hermitian nature of the dipole moment operator. Understanding this distinction is crucial for accurate calculations in molecular spectroscopy.

PREREQUISITES
  • Understanding of transition dipole moments (TDMs)
  • Familiarity with quantum mechanics and hermitian operators
  • Knowledge of diatomic molecular electronic states
  • Basic grasp of complex conjugates in mathematical expressions
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  • Study the properties of hermitian operators in quantum mechanics
  • Explore the role of transition dipole moments in molecular spectroscopy
  • Learn about the implications of complex conjugates in quantum state transitions
  • Investigate computational methods for calculating TDMs in diatomic molecules
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Researchers in molecular physics, quantum chemists, and students studying electronic transitions in diatomic molecules will benefit from this discussion.

sams
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Hello Everyone,

A little question regarding the TDMs between two different electronic states of a diatomic molecule. If I am calculating the TDM from state A to state B, is it the same if we are calculating the TDM from state B to state A? Are these two transitions the same?

Thank you so much in advance?
 
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Almost. The dipole moment operator is hermitian. So the TDM from A to B is ##\langle B|d|A \rangle## while the TDM for B to a is ##\langle A |d| B \rangle=(\langle B|d|A \rangle)^*##, i.e. the complex conjugate.
 
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Thank you very much DrDu for your help.
 

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