Abstract
Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D6h and D4h of the nuclear scaffolds are conserved. At the same time, the symmetries of the one-electron densities are broken, however, to specific subgroups of G for the excited superposition states. These subgroups depend on the polarization and on the electric fields of the laser pulses. They can be determined either by inspection of the symmetry elements of the one-electron density which represents charge migration after the laser pulse, or by a new and more efficient group-theoretical approach. The results agree perfectly with each other. They suggest laser control of symmetry breaking. The choice of the target subgroup is restricted, however, by a new theorem, i.e., it must contain the symmetry group of the time-dependent electronic Hamiltonian of the oriented molecule interacting with the laser pulse(s). This theorem can also be applied to confirm or to falsify complementary suggestions of electron symmetry breaking by laser pulses.
Highlights
= D4h ), respectively, to various subgroups S(ρp (r,t)) of G. These results are based on the evidence of the symmetry elements of the one-electron density ρp (r,t) which represents charge migration right after the laser pulses labeled p
This case holds for well-designed sequences of laser pulses with polarization vectors e which break and restore electron symmetry [2,3,4], or which induce attosecond charge migration represented by superpositions of electronic eigenstates with the same irreducible representations (IRREPs) as the ground state, see, e.g., Refs. [36,37,38]
Specific designs of laser pulses with selective polarization vectors and electric fields yield a large variety of electron symmetry breakings, from the original symmetry point group G of the electron density for the electronic ground state to various subgroups of G for excited superposition states
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Electron symmetry breaking by laser pulses, with an explicit comparison of the symmetries before and after the laser pulses, was documented first by Ulusoy and Nest in their fundamental work on quantum control of aromaticity, with application to the benzene molecule with a specific orientation of its nuclear scaffold [1] For this example, the nuclear point group symmetry is D6h ; the corresponding IRREPs of the electronic ground state S0 and the first and second excited electronic singlet states S1 and S2 are 1 A1g , 1B. The pioneering papers [1,2,3,4,5] call for the following extensions: (a) Rigorous assignments of electron symmetry breaking in supplementary examples for oriented benzene and for oriented Mg-porphyrin For this purpose, we design linearly polarized laser pulses that initiate selective types of attosecond charge migration with corresponding electron symmetry breaking while conserving nuclear symmetry. There is no unique “logic” or “ideal” order of the presentations which could avoid this problem
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