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Time-dependent processes in chemistry are ubiquitous. Chemical reactions occur as molecules collide with one another, exchanging kinetic and potential energy as chemical bonds are formed and broken. Similarly, in photochemical processes photons are absorbed and emitted as energy is channeled into different degrees of freedom (electronic, rotational vibrational). For instance, the formation of a chemical bond or photodissociation of a molecule can be regarded as a "chemical event" and it is natural to ask not only where this event occurs, but also \textit{when}. In order to address this question, time must be regarded as an observable quantity, i.e. a dynamical variable represented by an operator and not a parameter.  Given a Hamiltonian $\hat{H}$, its associated time operator, $\hat{t}$, is then constructed the imposing the canonical commutation relation:  \begin{equation}  \left[\hat{t}, \hat{H} \right] |\psi_n \rangle= i \hbar |\psi_n \rangle,   \end{equation}~\label{full_t}   over a certain domain of the Hilbert space spanned by the states $\{ |\psi_n \rangle \}$. Note that eq.~\ref{full_t} is a non-linear eigenvalue problem, as one must find both the operator $\hat{t}$ and the eigenvectors $\{ |\psi_n \rangle \}$.  Constructing time operators for single particle quantum systems is a fairly straight forward task.  For example, consider the Ha  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}, 
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The task of constructing a time operator for the full Hamiltonian in eq.~\ref{full_H} will be computationally demanding. Approximate and model Hamiltonians are often used to simply quantum many-body calculations. Each model Hamiltonian gives rise to a corresponding model time operator through the solution to eq.~\ref{full_t}. Another area of research will be to construct and classify time operators for different model Hamiltonians of varying degrees of complexity. For example, in 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:  \begin{equation}  \hat{H} = \int d^3 r \Psi^+(\mathbf{r})\left[ -\frac{\hbar^2}{2 m} \nabla^2 + v_{ext}(\mathbf{r},t) \right] \Psi(\mathbf{r}) + \int d^3 r \Psi^+(\mathbf{r})\left[ -\frac{\hbar^2}{2 m} \nabla^2 + v_{ext}(\mathbf{r},t) \right] \Psi(\mathbf{r}) \Psi(\mathbf{r}).  \end{equation}  Further simplification gives rise to the Hubbard model, or spin Hamiltonians such as the Heisenberg model. Table 1 lists different model Hamiltonians for which we intend to construct time operators and the types of chemical events to be studied.  %satisfying canonical commutation relations with the chemical Hamiltonian and not a parameter. I propose to e will construct time operators