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?


1 Answer 1


The part of the paper where they give the formula for the populations is here:

"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 $i$.

  • $\begingroup$ Thanks for the answer. May I ask the state population here is adiabatic state or diabatic state? $\endgroup$
    – Paulie Bao
    May 3, 2021 at 1:36
  • $\begingroup$ I closed the paper, but if I recall correctly, the $d_i$ were diabatic states. $\endgroup$ May 3, 2021 at 1:38

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