# How to calculate state population from MCTDH?

In this reference, the author investigates electronic population dynamics from a MCTDH calculation. My question is how to generate state populations over time from an MCTDH calculation? Is there a formula for that?

"The timedependent (TD) vibronic wavefunction of the system is computed solving the TD Schroedinger Equation. It is written as $$|\Psi_i(\mathbf{q},t)\rangle = \sum_i |d_i\rangle |\Psi(\mathbf{q},t)\rangle$$ so that electronic populations are simply $$P_i(t) = \langle \Psi_i (\mathbf{q},t) | \Psi_i (\mathbf{q},t) \rangle$$."
Basically you propagate the wavefunctions for each state labeled by $$i$$ using MCTDH, and then do the inner products $$\langle \psi_i | \psi_i \rangle$$ for each $$i$$.
• I closed the paper, but if I recall correctly, the $d_i$ were diabatic states. – Nike Dattani May 3 at 1:38