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Recent theoretical investigations claim that tailored laser pulses may selectively steer benzene's aromatic ground state to localized non-aromatic excited states. For instance, it has been shown that electronic wavepackets, involving the two lowest electronic eigenstates, exhibit subfemtosecond charge oscillation between equivalent Kekule resonance structures. In this contribution, we show that such dynamical electron-localization in the molecule-fixed frame contravenes the principle of the indistinguishability of identical particles. This breach stems from a total omission of the nuclear degrees of freedom, giving rise to nonsymmetric electronic wavepackets under nuclear permutations. Enforcement of the latter leads to entanglement between the electronic and nuclear states. To obey quantum statistics, the entangled molecular states should involve compensating nuclear-permutation symmetries. This in turn engenders complete quenching of dynamical electron-localization in the molecule-fixed frame. Indeed, for the (six-fold) equilibrium geometry of benzene, group-theoretic analysis reveals that any electronic wavepacket exhibits a (D-6h) totally symmetric electronic density, at all times. Thus, our results clearly show that the six carbon atoms, and the six C-C bonds, always have equal Mulliken charges, and equal bond orders, respectively. However, electronic wavepackets may display dynamical localization of the electronic density in the space-fixed frame, whenever they involve both even and odd space-inversion (parity) or permutation-inversion symmetry. Dynamical spatial-localization can be probed experimentally in the laboratory frame, but it should not be deemed equivalent to charge oscillation between benzene's identical electronic substructures, such as Kekule resonance structures.
We discuss an efficient Hierarchical Effective Mode (HEM) representation of a high-dimensional harmonic oscillator bath, which describes phonon-driven vibrational relaxation of an adsorbate-surface system, namely, deuterium adsorbed on Si(100). Starting from the original Hamiltonian of the adsorbate-surface system, the HEM representation is constructed via iterative orthogonal transformations, which are efficiently implemented with Householder matrices. The detailed description of the HEM representation and its construction are given in the second quantization representation. The hierarchical nature of this representation allows access to the exact quantum dynamics of the adsorbate-surface system over finite time intervals, controllable via the truncation order of the hierarchy. To study the convergence properties of the effective mode representation, we solve the time-dependent Schrodinger equation of the truncated system-bath HEM Hamiltonian, with the help of the multilayer extension of the Multiconfigurational Time-Dependent Hartree (ML-MCTDH) method. The results of the HEM representation are compared with those obtained with a quantum-mechanical tier-model. The convergence of the HEM representation with respect to the truncation order of the hierarchy is discussed for different initial conditions of the adsorbate-surface system. The combination of the HEM representation with the ML-MCTDH method provides information on the time evolution of the system (adsorbate) and multiple effective modes of the bath (surface). This permits insight into mechanisms of vibration-phonon coupling of the adsorbate-surface system, as well as inter-mode couplings of the effective bath.