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Transition between vibronic states and the meaning of transition dipole moment

Physics Asked on February 28, 2021

Let’s say we have a molecule which belongs to $D_{3h}$ point group. The IRREPs of inital and final states are as follows $A’_{1}$, $E’$. Hence, the IRREP for the dipole moment has to be $E’$ so that the transition is allowed. Does this mean the external electric field has to have $x$ and $y$ components to interact with the molecule’s dipole moment? Can we also say that the molecule’s dipole moment vector has $x$ and $y$ components?

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