Single vibronic level fluorescence spectra from Hagedorn wavepacket dynamics.

In single vibronic level (SVL) fluorescence experiments, the electronically excited initial state is also excited in one or several vibrational modes. Because computing such spectra by evaluating all contributing Franck-Condon factors becomes impractical (and unnecessary) in large systems, here we propose a time-dependent approach based on Hagedorn wavepacket dynamics. We use Hagedorn functions-products of a Gaussian and carefully generated polynomials-to represent SVL initial states because in systems whose potential is at most quadratic, Hagedorn functions are exact solutions to the time-dependent Schrödinger equation and can be propagated with the same equations of motion as a simple Gaussian wavepacket.

Finite-temperature vibronic spectra from the split-operator coherence thermofield dynamics.

We present a numerically exact approach for evaluating vibrationally resolved electronic spectra at finite temperatures using the coherence thermofield dynamics. In this method, which avoids implementing an algorithm for solving the von Neumann equation for coherence, the thermal vibrational ensemble is first mapped to a pure-state wavepacket in an augmented space, and this wavepacket is then propagated by solving the standard, zero-temperature Schrödinger equation with the split-operator Fourier method. We show that the finite-temperature spectra obtained with the coherence thermofield dynamics in a Morse potential agree exactly with those computed by Boltzmann-averaging the spectra of individual vibrational levels.

Semiclassical Approach to Photophysics Beyond Kasha's Rule and Vibronic Spectroscopy Beyond the Condon Approximation. The Case of Azulene.

Azulene is a prototypical molecule with an anomalous fluorescence from the second excited electronic state, thus violating Kasha's rule, and with an emission spectrum that cannot be understood within the Condon approximation. To better understand the photophysics and spectroscopy of azulene and other nonconventional molecules, we developed a systematic, general, and efficient computational approach combining the semiclassical dynamics of nuclei with electronic structure. First, to analyze the nonadiabatic effects, we complement the standard population dynamics by a rigorous measure of adiabaticity, estimated with the multiple-surface dephasing representation.