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To construct time operators for chemical systems, one might begin with the full Hamiltonian operator of non-relativistic electrons and nuclei, interacting with the quantized electromagnetic field:  \begin{equation}  \hat{H} = \hat{H}_{el} + \hat{H}_{n} + \hat{H}_{em} + \hat{H}_{el-n} + \hat{H}_{el-em} + \hat{H}_{n-em},  \label{full_H}  \end{equation}  where the first three terms represent free electrons, nuclei and photons while the last three are there respective interactions. A time operator $\hat{t}$ operator, $\hat{t}$,  is then constructed the imposing the canonical commutation relation relation:  \begin{equation}  \hat{t} \hat{H} - \hat{H} \hat{t} = i \hbar \hbar,   \label{full_H}  \end{equation}  over a certain domain of the Hilbert space. Having constructed $t$ we can investigate its spectrum look at its spectrum and answer questions about chemical events such as: When does a molecule absorb or emit a phonton? When does the absorbed energy fully dissipate into nuclear vibrational energy? How long does it take for a chemical reaction between two molecules to occur?  The task of constructing a time operator for the full Hamiltonian in eq.~\ref{full_H} will need to be performed numerically and will be computationally demanding. My group has vast computational resources available to accomplish this task. However, for chemistry it is often possible to make approximations to simplify eq.~\ref{full_H}. By invoking the Born-Oppenheimer approximation (BO), one can treat the nuclei classically as well as the electromagnetic field and arrive at the electronic Hamiltonian:  satisfying canonical commutation relations with the chemical Hamiltonian and not a parameter. I propose to e will construct time operators