Short-Time Dynamics Through Conical Intersections in Macrosystems

The short-time dynamics through a conical intersection of a macrosystem with a vast number of nuclear degrees of freedom (modes) is investigated. For convenience, the macrosystem is decomposed into a system carrying a few modes and a “bath.” By transforming the bath modes to new ones, it is shown that only three effective bath modes contribute to the conical intersection. They govern—together with the system’s modes—the short-time dynamics of the macrosystem. The remaining bath modes do not directly couple the electronic states and become relevant at longer times. An extensive numerical example is presented.

Figure 1

(a) Autocorrelation function of butatriene coupled to a bath of 20 modes. The exact result and those of the effective modes are nearly indistinguishable up to 12 fs. (b) The corresponding band shape of the spectrum. The band shape is obtained by a Fourier transform of the autocorrelation function up to 200 fs, convoluted with a Gaussian of FWHM 0.13 eV. The exact result and those of the effective modes are nearly indistinguishable. Solid line (red online): exact result for the full system plus bath (22 modes). Dotted line (pink online): result for the system alone (2 modes). Dashed line (blue online): result for the system $+3$ effective modes for the bath. Long-dashed line (green online): result for the 3 effective modes defined to include the system plus bath.