Real Space-Real Time Evolution of Excitonic States Based on the Bethe-Salpeter Equation Method

Excited-State Forces with GW-BSE Through the Hellmann-Feynman Theorem

We introduce a method for calculating the atomic forces of a molecular or extended system in an excited state described through the GW-BSE approach within the Tamm-Dancoff approximation. The derivative of the so-called excitonic Hamiltonian is obtained by finite differences and its application to the excited state is made possible through the use of suitable projectors. The scheme is implemented with the batch representation of the electron-hole amplitudes, allowing for avoiding sums over empty one-particle orbitals. The geometries of small excited molecules, namely, CO and CH2O, were in excellent agreement with the results from quantum chemistry methods.

A quantitative model of charge injection by ruthenium chromophores connecting femtosecond to continuous irradiance conditions

A kinetic framework for the ultrafast photophysics of tris(2,2-bipyridine)ruthenium(II) phosphonated and methyl-phosphonated derivatives is used as a basis for modeling charge injection by ruthenium dyes into a semiconductor substrate. By including the effects of light scattering, dye diffusion, and adsorption kinetics during sample preparation and the optical response of oxidized dyes, quantitative agreement with multiple transient absorption datasets is achieved on timescales spanning femtoseconds to nanoseconds. In particular, quantitative agreement with important spectroscopic handles-the decay of an excited state absorption signal component associated with charge injection in the UV region of the spectrum and the dynamical redshift of a ∼500 nm isosbestic point-validates our kinetic model. Pseudo-first-order rate coefficients for charge injection are estimated in this work, with an order of magnitude ranging from 10¹¹ to 10¹² s^-1. The model makes the minimalist assumption that all excited states of a particular dye have the same charge injection coefficient, an assumption that would benefit from additional theoretical and experimental exploration. We have adapted this kinetic model to predict charge injection under continuous solar irradiation and find that as many as 68 electron transfer events per dye per second take place, significantly more than prior estimates in the literature.