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Non-Born–Oppenheimer quantum dynamics of H+ 2 excited by shaped one-cycle laser pulses linearly polarised along the molecular axis have been studied by the numerical solution of the time-dependent Schrödinger equation within a three-dimensional model, including the internuclear separation, R, and the electron coordinates z and ρ. Laser carrier frequencies corresponding to the wavelengths λ l = 25 nm through λ l = 400 nm were used and the amplitudes of the pulses were chosen such that the energy of H+ 2 was close to its dissociation threshold at the end of any laser pulse applied. It is shown that there exists a characteristic oscillation frequency ωosc ≃ 0.2265 au (corresponding to the period of τosc ≃ 0.671 fs and the wavelength of λosc ≃ 201 nm) that manifests itself as a ‘carrier’ frequency of temporally shaped oscillations of the time-dependent expectation values ⟨z ⟩ and ⟨∂V/∂z ⟩ that emerge at the ends of the laser pulses and exist on a timescale of at least 50 fs. Time-dependent expectation values ⟨ρ⟩ and ⟨∂V /∂ρ⟩ of the optically passive degree of freedom, ρ, demonstrate post-laser-field oscillations at two basic frequencies ωρ 1 ≈ ωosc and ωρ 2 ≈ 2ωosc. Power spectra associated with the electronic motion show higher- and lower-order harmonics with respect to the driving field.
Spectral density functions are central to the simulation of complex many body systems. Their determination requires making approximations not only to the dynamics but also to the underlying electronic structure theory. Here, blending different methods bears the danger of an inconsistent description. To solve this issue we propose an all-DFTB approach to determine spectral densities for the description of Frenkel excitons in molecular assemblies. The protocol is illustrated for a model of a PTCDI crystal, which involves the calculation of monomeric excitation energies and Coulomb couplings between monomer transitions, as well as their spectral distributions due to thermal fluctuations of the nuclei. Using dynamically defined normal modes, a mapping onto the standard harmonic oscillator spectral densities is achieved.
Effects of thermal fluctuations on the electronic excitation energies and intermonomeric Coulomb couplings are investigated for a perylene-tetracarboxylic-diimidecrystal. To this end, time dependent density functional theory based tight binding (TD-DFTB) in the linear response formulation is used in combination with electronic ground state classical molecular dynamics. As a result, a parametrized Frenkel exciton Hamiltonian is obtained, with the effect of exciton-vibrational coupling being described by spectral densities. Employing dynamically defined normal modes, these spectral densities are analyzed in great detail, thus providing insight into the effect of specific intramolecular motions on excitation energies and Coulomb couplings. This distinguishes the present method from approaches using fixed transition densities. The efficiency by which intramolecular contributions to the spectral density can be calculated is a clear advantage of this method as compared with standard TD-DFT. Published by AIP Publishing.