An explanation of the highly efficient magnetic quenching of fluorescence in intermediate case molecules based on two manifold models
Authors: Kono Hirohiko , Ohta Nobuhiro 
Published: July 2002

The magnetic quenching of fluorescence in intermediate case molecules is modeled by including two triplet manifolds {‖bj〉} and {‖cj〉} mutually shifted by the zero-field splitting Egap (though a triplet has three spin sublevels); the {‖bj〉} are coupled to a bright singlet state ‖s〉 by intramolecular interaction V and the two manifolds are coupled by a magnetic field. For the two manifold Bixon–Jortner model where the level spacings and the couplings to ‖s〉 are constant and no spin–vibration interactions exist (the Zeeman interaction connects only the spin sublevels of the same rovibronic level j), there are two sets of field dressed eigenstates, {‖b̂j〉} and {‖ĉj〉}, of the background Hamiltonian H−V. ‖b̂j〉 and ‖ĉj〉 are liner combinations of ‖bj〉 and ‖cj〉. We call the energy structure ‘‘eclipsed (E)’’ when the two sets of dressed states overlap in energy and call it ‘‘staggered (S)’’ when every ‖b̂〉 state is just between two adjacent ‖ĉ〉 states.
The E and S structures alternatively appear with increasing Zeeman energy hZ. As hZ increases, the number of effectively coupled background levels, Neff, increases for the S structure but remains unchanged for the E structure. The S structure is in accord with the experimental result that the quantum yield is reduced to 1/3 at anomalously low fields (hz/Egap≪1): in the far wing regions of the absorption band the mixing between the manifolds is determined by the ratio hZ/Egap, but near the band center the intermanifold mixing is enhanced by the presence of ‖s〉. Using a random matrix approach where H is constructed of the rotation–vibration Hamiltonians HB and HC arising from the manifolds {‖bj〉} and {‖cj〉}, we show that an S structure can be formed in real molecules by nonzero ΔHBC≡HB−HC−Egap (Egap is the zero-field splitting at the equilibrium nuclear configuration). Indirect spin–vibration interactions lead to ΔHBC≠0; the vibrational ΔHBC caused by spin–spin and vibronic interactions and the rotational ΔHBC caused by spin–rotation and rotation–vibration interactions. The matrix elements of H are written down in terms of the eigenfunctions {‖j〉} of the average Hamiltonian (HB+HC)/2. If the vibrational modes are strongly coupled (the energies of levels are given by a Wigner distribution and the coupling strengths are given by a Gaussian distribution), the vibrational 〈j‖ΔHBC‖j′〉 for wave functions of roughly the same energy are Gaussian random.
As the rms of 〈j‖ΔHBC‖j′〉 approaches the average level spacing (on excitation into higher vibrational levels), the efficiency of magnetic quenching becomes as high as in the S case. Nonzero 〈j‖ΔHBC‖j′〉 let isoenergetic levels belonging to different manifolds vibrationally overlap: the ΔHBC, together with the magnetic field, causes level repulsion leading to the S structure and opens up isoenergetic paths between the manifolds. The efficient magnetic quenching in pyrazine can be explained by the vibrational ΔHBC, since the S1–T1 separation is as large as 4500 cm−1. If Coriolis couplings cause K scrambling considerably, the rotational ΔHBC mixes {‖j〉}. This mechanism explains the rotational dependence of magnetic quenching in s-triazine of which S1–T1 separation is only ∼1000 cm−1.