Abstract
In this work, a theoretical and computational set of tools to study and analyze time-resolved electron dynamics in molecules, under the influence of one or more external pulses, is presented. By coupling electronic-structure methods with the resolution of the time-dependent Schrödinger equation, we developed and implemented the time-resolved induced density of the electronic wavepacket, the time-resolved formulation of the differential projection density of states (ΔPDOS), and of transition contribution map (TCM) to look at the single-electron orbital occupation and localization change in time. Moreover, to further quantify the possible charge transfer, we also defined the energy-integrated ΔPDOS and the fragment-projected TCM. We have used time-dependent density-functional theory (TDDFT), as implemented in ADF software, and the Bethe–Salpeter equation, as provided by MolGW package, for the description of the electronic excited states. This suite of postprocessing tools also provides the time evolution of the electronic states of the system of interest. To illustrate the usefulness of these postprocessing tools, excited-state populations have been computed for HBDI (the chromophore of GFP) and DNQDI molecules interacting with a sequence of two pulses. Time-resolved descriptors have been applied to study the time-resolved electron dynamics of HBDI, DNQDI, LiCN (being a model system for dipole switching upon highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) electronic excitation), and Ag22. The computational analysis tools presented in this article can be employed to help the interpretation of fast and ultrafast spectroscopies on molecular, supramolecular, and composite systems.
Highlights
Recent impressive developments in both tunable ultrafast sources and in efficient algorithms for the propagation of the time-dependent Schrödinger equation, opened the way to the control of chemical reactions and electron processes triggered by ultrashort light pulses.[1,2] On the one hand, molecular vibrations, which are the underlying elementary dynamical steps of any chemical reaction, are best controlled using femtosecond (1 fs = 10−15 s) light pulses.[1]
We report the results of the application of time-dependent density-functional theory (TDDFT) and GW/BSE postprocessing, i.e., populations, induced density, ΔPDOS, and transition contribution map (TCM), on the HBDI molecule, which is the chromophore of the GFP protein,[79−91] the DNQDI fluorophore, which has been used to study the interplay between electronic and vibrational quantum coherence,[92,93] the LiCN molecule, which has been chosen as a computational model for dipole switching, as reported in the literature,[21,43,45,94,95] and a small metal cluster Ag22, which is the prototype of systems with collective optical responses.[96]
LiCN is the well-known prototype of dipole-switch systems: this property is analyzed by our time-dependent formulation, as shown below
Summary
Article characterize and describe the electron dynamics under different conditions, in particular here we present how to compute, in a time-resolved manner and in a molecular framework the following: (1) the populations of electronically excited states, by exploiting transition dipole moments between excited states; (2) the induced density; (3) the differential PDOS of molecular orbitals (ΔPDOS); and (4) the TCM, starting from the definition in ref 42 These tools are of general purpose since they can be applied to gain insights into a wide range of physical processes and systems, as multiple-pulse time-resolved spectroscopies on single molecules,[60] pump-probe experiments,[1,61−67] molecular nanoplasmonics,[15,68−75] plasmon-assisted catalysis,[76−78] etc. The article is organized as follows: in Section II, we focus on the definition of the descriptors introduced above, computational details are collected in Section III, results are presented and discussed in Section IV, while in Section V, main outcomes are summarized and perspectives for future work are indicated
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