Spin-Vibronic Mechanism for Intersystem Crossing

Abstract

Intersystem crossing (ISC), formally forbidden within nonrelativistic 9 quantum theory, is the mechanism by which a molecule changes its spin state. It plays an 10 important role in the excited state decay dynamics of many molecular systems and not 11 just those containing heavy elements. In the simplest case, ISC is driven by direct spin− 12 orbit coupling between two states of different multiplicities. This coupling is usually 13 assumed to remain unchanged by vibrational motion. It is also often presumed that spin-14 allowed radiationless transitions, i.e. internal conversion, and the nonadiabatic coupling 15 that drives them, can be considered separately from ISC and spin−orbit coupling owing 16 to the vastly different time scales upon which these processes are assumed to occur. 17 However, these assumptions are too restrictive. Indeed, the strong mixing brought about 18 by the simultaneous presence of nonadiabatic and spin−orbit coupling means that often 19 the spin, electronic, and vibrational dynamics cannot be described independently. Instead of considering a simple ladder of states, 20 as depicted in a Jablonski diagram, one must consider the more complicated spin-vibronic levels. Despite the basic ideas being 21 outlined in the 1960s, it is only with the advent of high-level theory and femtosecond spectroscopy that the importance of the 22 45 3.1.2. Time-Dependent Methods I 46 3.1.3. Including Temperature J 47 3.2. Quantum Dynamics Methods J 48 3.2.1. Multi-Configurational Time-Dependent 49 Hartree Approach J 50 3.2.2. Including Temperature K 51 3.2.3. Spin-Vibronic Model Hamiltonian L 52 3.3. On-the-f ly Dynamics Methods M 53 3.3.1. Trajectory Surface Hopping M 54 3.3.2. Methods Based upon Gaussian Wave-55

Insights into the Photoinduced Isomerization Mechanisms of a N,C–Chelate Organoboron Compound: A Theoretical Study

“…The (S 1 /T 2 /T 1 ) X intersection is 0.53 eV higher than R‐S 1 , and the S 1 →T 1 ISC with the T 2 state as a bridge via the (S 1 /T 2 /T 1 ) X intersection cannot be fully ruled out. The SOC value between S 1 state and T 2 state at (S 1 /T 2 /T 1 ) X is 1.17 cm −1 , which must be underestimated because only the one‐electron term was considered in our calculation on SOC while the spin‐vibronic couplings are not included . Similar to our results, the around 1.5 cm −1 SOC values between S 1 state and T 1 state were obtained as evidence for the low but non‐negligible ISC probability, allowing triplet state population and weak phosphorescence in pyridine(Py)‐substituted boron cluster B 16 H 18 Py 2 .…”

The DFT/MRCI method

“…Spin‐dependent properties are available within the spin‐orbit coupling kit Spock and its extension to spin–spin coupling treatment Spock.Sistr . Spock provides electronic SOC matrix elements of DFT/MRCI wavefunctions required for the computation of ISC and reverse ISC rate constants . Spin–orbit mixed DFT/MRCI wavefunctions either from a quasi‐degenerate perturbation theory (QDPT) or a variational multireference spin–orbit configuration interaction treatment are further used to determine second‐order spin‐dependent properties such as phosphorescence lifetimes and g ‐matrices .…”

Spin‐inversion mechanisms in O2 binding to a model heme complex revisited by density function theory calculations

“…This is probably due to the importance of nonlocal nonadiabatic transitions missing in one‐dimensional description. Thus, nonadiabatic quantum dynamics calculations, which can take into account the spin‐vibronic effects, should be performed to fully understand the spin‐inversion mechanisms in O 2 binding to the heme complex. In fact, the energy differences between different spin multiplicities in the long Fe–O distance region can be small and are comparable to the magnitude of spin–orbit couplings.…”