## 2 Model, Concept, Theory and Methods
### Model and Basic Theory  
Our model assumes that all nuclei are fixed at the global minimum structures of the molecules in the electronic ground state, as in the previous approaches (cf. Section 1). We consider the scenario of an oriented molecule with its center of mass at the origin of the laboratory frame. This frame has a right-handed Cartesian set of unit vectors \(\vec{e}_{x},\vec{e}_{y},\vec{e}_{z}\) which are determined by the laser pulses. For example, in the present application to benzene, the laser pulses propagate along \(\vec{e}_{z}\) with perpendicular circular polarizations that yield maximum field strength of the first laser pulse along \(\vec{e}_{x}\) at time \(t_{b}\). The benzene molecule is oriented in the \(xy\)-plane of the laboratory frame, with two carbon nuclei on the \(y\)-axis, as in Refs. [17; 24; 25; 26]. The laser carrier frequencies \(\omega_{b}=2\pi\
u_{b}\) and \(\omega_{r}=2\pi\
u_{r}\) correspond to wavelengths \(\lambda_{b}=c_{0}/\
u_{b}\) and \(\lambda_{r}=c_{0}/\
u_{r}\), respectively, that are much longer than the molecular sizes. In the molecular domain that is of interest here, the electric fields of the laser pulses be considered as homogeneous. The model Hamiltonian of the molecule interacting with the laser pulses is  
\[H(t)=H_{e}-\vec{d}\cdot\vec{\epsilon}(t), \tag{2}\]  
where  
\[H_{e}=T_{e}+V_{c} \tag{3}\]  
is the electronic Hamiltonian that accounts for the kinetic energies \(T_{e}\) of the electrons and for their intramolecular Coulomb interactions \(V_{c}\) with all particles (electrons and fixed nuclei). The scalar product \(\vec{d}\cdot\vec{\epsilon}(t)\) represents the semiclassical interaction of the electric dipole operator \(\vec{d}\) and the electric field \(\epsilon(t)\) of the two laser pulses that break and restore electronic structure symmetry. The electronic eigenfunctions \(|\Psi_{k}\rangle\) and their energies \(E_{k}\) are calculated as solutions of the time-independent Schrodinger equation (TISE)  
\[H_{e}|\Psi_{k}\rangle=E_{k}|\Psi_{k}\rangle. \tag{4}\]  
The labels \(k\) denote sets of quantum numbers, which include the IRREPs. Specifically, \(k=g\) and \(k=e\) denote the electronic ground state (\(IRREP_{g}\)) and the specific excited state (\(IRREP_{e}\)) that constitute the superposition state which is prepared by the first laser pulse,  
\[|\Psi(t_{c})\rangle=c_{g}(t_{c})|\Psi_{g}\rangle+c_{e}(t_{c})|\Psi_{e}\rangle \tag{5}\]with coefficients \(c_{g}(t_{c})\) and \(c_{e}(t_{c})\) at the central time \(t_{c}=0\) between the two laser pulses. The new strategy uses the second laser pulse to excite this superposition (Equation (5)) to the final state  
\[|\Psi(t_{f})\rangle=e^{i\eta_{ef}}|\Psi_{e}\rangle \tag{6}\]  
with irrelevant phase factor \(e^{i\eta_{ef}}\) for the phase \(\eta_{ef}\equiv\eta_{e}(t_{f})\) of the excited state at \(t=t_{f}\). Preparation of the final state (Equation (6)) restores the original point group of the initial (\(t=t_{i}\)) ground electronic state  
\[|\Psi(t_{i})\rangle=|\Psi_{g}\rangle. \tag{7}\]  
The inherent two-state scenario that leads from the initial ground state (Equation (7)) via the superposition state (Equation (5)) to the excited target state (Equation (6)) is justified in the beginning of Section 2.3. The laser driven electronic wave function \(|\Psi(t)\rangle\) is calculated as solution of the time dependent Schrodinger equation (TDSE)  
\[i\hbar\frac{\partial}{\partial t}|\Psi(t)\rangle=H(t)|\Psi(t)\rangle \tag{8}\]  
subject to the initial condition in Equation (7). Expanding the wave function \(|\Psi(t)\rangle\) in terms of a finite set of the eigenfunctions  
\[|\Psi(t)\rangle=\sum_{k}c_{k}(t)|\Psi_{k}\rangle \tag{9}\]  
yields the algebraic version of the TDSE  
\[i\hbar\frac{d}{dt}\mathbf{c}(t)=\mathbf{H}(t)\mathbf{c}(t), \tag{10}\]  
with vector \(\mathbf{c}(t)\) of the coefficients \(c_{k}(t)\) and corresponding initial condition  
\[c_{k}(t_{i})=\delta_{gk}, \tag{11}\]  
where \(\delta_{gk}\) denotes the Kronecker delta.