## 2 Model, Concept, Theory and Methods
### Extended Theory for the New Strategy  
For the \"proof-of-principle\", we apply the general theory of Section 2 to the new strategy, using a specific form of the electric fields of the circularly right (+) laser pulses that break the symmetry \(D_{6h}\) of the electronic ground state (\(IRREP_{g}=A_{1g}\)) of benzene, and restore it in the excited state (\(IRREP_{e}=E_{1u}\)). Adapting the derivations in Ref. [42] and using the conditions in Equations (32) and (33), we obtain  
\[ \begin{array}{ccl}\vec{e}_{b}(t)=\left(\epsilon_{bx}(t),\epsilon_{by}(t),0 \right)&=&\epsilon_{b}s_{b}(t)\cdot\left(\cos\left[\omega(t-t_{b})\right], \sin\left[\omega(t-t_{b})\right],0\right),\\ \vec{e}_{r}(t)=\left(\epsilon_{rx}(t),\epsilon_{ry}(t),0\right)&=&\epsilon_{r }s_{r}(t)\cdot\left(\cos\left[\omega(t-t_{r})\right],\sin\left[\omega(t-t_{r })\right],0\right)\\ &=&\epsilon_{r}s_{r}(t)\cdot\left(\cos\left[\omega(t-t_{b})\right],\sin\left[ \omega(t-t_{b})\right],0\right).\end{array}  \tag{42}\]  
The temporal and the spectral profiles of the intensities of the laser pulses are Gaussian,  
\[ \begin{array}{c}I_{b}(t)=0.5\epsilon\epsilon_{0}|\epsilon_{b}(t)|^{2}=0.5 \epsilon c_{0}\epsilon_{b}^{2}e^{-(t-t_{b})^{2}/\tau^{2}},\\ I_{r}(t)=0.5\epsilon c_{0}|\epsilon_{r}(t)|^{2}=0.5\epsilon c_{0}\epsilon_{r}^{2}e ^{-(t-t_{r})^{2}/\tau^{2}},\end{array}  \tag{43}\]\[ \begin{array}{l}I_{b}(E)=0.5c\epsilon_{0}|\epsilon_{b}(E)|^{2}=0.5c\epsilon_{0} \epsilon_{b}^{2}e^{-(E-(E_{e}-E_{g}))^{2}\tau^{2}/\hbar^{2}},\\ I_{r}(E)=0.5c\epsilon_{0}|\epsilon_{r}(E)|^{2}=0.5c\epsilon_{0}\epsilon_{b}^{2} e^{-(E-(E_{e}-E_{g}))^{2}\tau^{2}/\hbar^{2}}.\end{array}  \tag{44}\]  
The spectral profiles (Equation (44)) are shown in Figure 2, together with the levels of the lowest electronic states of benzene, and their IIREPs. These energies have been calculated by means of the CASSCF(6,6) level of quantum chemistry, with aug-cc-PVTZ basis. Apparently, the broad bandwidths of the laser pulses cover several energy levels, but the present target state is the only state with \(IRREP_{e}=E_{1u+}\). All other states within the laser bandwidths have different IIREPs. The chosen circular polarizations of the present laser pulses then imply selective population transfer from the ground state (\(IRREP_{g}=A_{1g}\)) exclusively to the target state (\(IRREP_{e}=E_{1u+}\))--this is indicated by the vertical arrow in Figure 2. All other transitions are dipole-forbidden--these are symbolized by vertical arrows that are crossed out in Figure 2.  
The condition in Equation (29) for the sum of the two laser pulses then yields the electric field of the designated resonant \(\pi\)-pulse,  
\[\vec{\epsilon_{\pi}}(t)=\left(e_{\pi x}(t),\epsilon_{\pi y}(t),0\right)= \left[e_{b}s_{b}(t)+\epsilon_{r}s_{r}(t)\right]\cdot\left(\cos\left[\omega(t- t_{b})\right],\sin\left[\omega(t-t_{b})\right],0\right). \tag{45}\]  
Next, we invoke the two-state \((g,e+)\) approximation, i.e., we assume that the laser pulses induce exclusively transitions between the ground state \(\left|\Psi_{g}\right\rangle\) and the selective excited target  
Figure 2: (**Left**) Electronic energy levels of the lowest states of benzene, with assignment of the IIREPs. The present circularly polarized laser pulses yield exclusive population transfer from the electronic ground state \(A_{1g}\) to the excited target state \(E_{1u+}\), illustrated by the vertical arrow. All other transitions to excited states that are within the spectral width of the laser pulses with different IIREPs are dipole forbidden, symbolized by vertical arrows that are crossed out. The two-photon process at 16.42 eV is also found to be off-resonance. (**Right**) Spectral profile of the laser pulses of duration 0.47 fs (red line), including a potential two-photon contribution at \(\Delta E=2\hbar\omega=16.42\) eV (grey line). state \(|\Psi_{e+}\rangle=|\Psi_{E_{1u+}}\rangle\).