Time-dependent electron localisation function: A tool to visualise and analyse ultrafast processes
Authors: A. Castro, T. Burnus, M.A.L. Marques, and E.K.U. Gross
Ref.: in "Analysis and Control of Ultrafast Photoinduced Reactions", ed. by O. Kühn, L. Wöste, Springer Series in Chemical Physics Vol. 87, Springer, Heidelberg, 555-576 (2007)
Abstract: The time-dependent electron localisation function (TDELF) is a generalisation of the electron localisation function (ELF) proposed by A. D. Becke and K. E. Edgecombe [J. Chem. Phys. 92, 5397 (1990)], which allows for time-resolved observation of the formation, the modulation, and the breaking of chemical bonds, and can thus provide a visual understanding of complex reactions involving the dynamics of excited states. We discuss the rationale behind the definition of the ELF, and sketch the general derivation that permits its use for the analysis of time-dependent processes. We present some examples: First, ground-state results showing the characteristic topology of the ELF for various prototypical chemical cases. Secondly, the time-dependent ELF of a few processes is monitored, which demonstrates how it permits to enhance our visual intuition of the electronic behaviour during fast phenomena: the chemical reaction leading to the formation of the water molecule following the collision of a proton and a hydroxide ion, the capture of a proton by the lone pair of the electron rich, smallest imine or unprotonated Schiff base (formaldimine), and the bond breaking of the ethyne triple bond due to the interaction with a strong and ultrashort laser pulse. Finally, the chapter is closed with a discussion about electron localisation in a model that includes the quantum-mechanical motion of the nuclei. For this purpose, the concept of a (time-dependent) anti-parallel spin ELF is also introduced.