Calculating time-resolved differential absorbance spectra for ultrafast pump-probe experiments with surface hopping trajectories

Abstract

We report a surface hopping approach for modeling the full time- and frequency-resolved differential absorbance spectra (beyond the inhomogenous limit) obtained in ultrafast pump-probe experiments. In our approach, we combine dynamical information obtained from ensembles of classical trajectories propagated on the ground and on the excited potential energy surfaces to directly calculate optical response functions and hence spectral lineshapes. We demonstrate that our method is exact for the model problem of two shifted harmonic potentials with identical harmonic frequencies in the absence of electronic relaxation. We then consider a model three state system with electronic relaxation and show that our method is able to capture the effects of nonadiabatic excited state dynamics on the time-dependent differential absorbance spectra. Furthermore, by comparing our spectra against those spectra calculated with either an (1) inhomogenous expression, (2) ground-state Kubo theory, or (3) excited-state Kubo theory, we show that including dynamical information from both the ground and excited potential energy surfaces significantly improves the reliability of the semiclassical approximations. As such, our surface hopping method should find immediate use in modeling the time-dependent differential abosrbance spectra of ultrafast pump-probe experiments.

Appraisal of Surface Hopping as a Tool for Modeling Condensed Phase Linear Absorption Spectra

“…31,59 Note that this approach effectively combines the dynamical information present in eqs 7 and 8. We previously demonstrated that eq 10 is exact for the case of uncoupled shifted harmonic potentials with identical harmonic frequencies and agrees with the formalism of Kapral and Martens in the short-time limit.…”

“…31,59 Note that this definition combines information from both the electronic wave functions carried by the FSSH trajectories and the active adiabatic surfaces that they are propagated on at time t. Similarly, the electronic coherence between diabats a and b can be obtained by combining eq 16 with U(x⃗ ) …”

“…31,59 Previously, we ensured the continuity of C μμ (FSSH) (t) by choosing the signs of the square roots in eq 18 such that each lies closest in the complex plane to its value from the previous time step.…”

A surface-hopping method for semiclassical calculations of cross sections for radiative association with electronic transitions

“…Field-induced couplings were the subject of more studies where the absorption spectra [35][36][37]54 or laser-induced transitions 33,[38][39][40][41] were calculated with the surfacehopping methodology. Spin-orbit and dipole couplings have been recently treated simultaneously with surfacehopping method 31,33,43,44 .…”

“…The surface-hopping methodology allows the study of radiative association with electronic transitions to be extended to arbitrary polyatomic system. The surface-hopping method is widely used in the modeling of nonadiabatic molecular processes [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] . The idea of this method originally put forward by Bjerre and Nikitin 48 and later advanced by others [49][50][51][52][53] .…”