Model of Ultrafast Intersystem Crossing in Photoexcited Transition-Metal Organic Compounds

The mechanism behind fast intersystem crossing in transition-metal complexes is shown to be a result of the dephasing of the photoexcited state to the phonon continuum of a different state with a significantly different transition metal-ligand distance. The coupling is a result of the spin-orbit interaction causing a change in the local moment. A recurrence to the initial state is prevented by the damping of the phonon oscillation. The decay time is faster than the oscillation frequency of the transition metal-ligand stretch mode, in agreement with experiment. For energies above the region where the strongest coupling occurs, a slower “leakage-type” decay is observed. If the photoexcited state is lower in energy than the state it couples to, then there is no decay.

Figure 1

Schematic of fast intersystem crossing. The initial photoexcitation from state $|{\psi }_0⟩$ into state $|{\psi }_{1n}⟩$ occurs with minimal lattice distortion; i.e., the number of excited phonons $n$ is small. State $|{\psi }_{1n}⟩$ couples to state $|{\psi }_{2n}⟩$ under the excitation of phonons. The coupling strength (red curve) creates an effective phonon density of states.

Figure 2

The probability $P_1$ (solid red curve) of finding state 1 and the relative change in transition metal-ligand distance (dotted blue curve) with $x/x_1=1,0$ for the equilibrium positions of 1 and 2, respectively, as a function of the time $t$ after the photoexcitation. (a) No phonon damping; ${\epsilon }_{ij}$ indicates the change in coupling to the lattice between states $i$ and $j$. Here the change in lattice occurs between states 1 and 2; (b) same as (a), but with phonon damping; (c) with phonon damping, but now the strongest change in lattice parameters occurs in the photoexcitation from 0 to 1 (only $P_1$ is shown). The total change is ${\epsilon }_{02}=0.2\mathrm{eV}$ and ${\epsilon }_{01}=0.2$ (solid curve) and 0.15 eV (dotted curve).

Figure 3

The probability $P_1$ [alternating solid dark gray (dark blue) lines and dotted dark gray (red) lines] of finding state 1 and the relative change in transition metal-ligand distance [alternating dotted light gray (light blue) lines and dark gray (red) lines] $x/x_1$ with the 1 and 0 values indicated on the left and right axes, respectively, in corresponding colors. The dependence as a function of time $t$ is given for different positions of $|{\psi }_{10}⟩$ with respect to the effective phonon density of states $\rho (E)$ of state 2; see bottom part of the figure.