### Abstract

The magnetic quenching of fluorescence in intermediate case molecules is modeled by including two triplet manifolds {|b_{j}>} and {|c _{j}>} mutually shifted by the zero-field splitting E_{gap} (though a triplet has three spin sublevels); the {|b_{j}>} 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, {|b_{j}>} and {|ĉ _{j}>}, of the background Hamiltonian H-V. |b̂_{j}> and |ĉ_{j}> are liner combinations of |b_{j}> and |c_{j}>. 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 h_{Z}. As h_{Z} increases, the number of effectively coupled background levels, N_{eff}, 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 (h_{z}/E_{gap}≪1): in the far wing regions of the absorption band the mixing between the manifolds is determined by the ratio h_{Z}/E_{gap}, 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 H_{B} and H _{C} arising from the manifolds {|b_{j}>} and {|c _{j}>}, we show that an S structure can be formed in real molecules by nonzero Δ_{BC}≡H_{B}-H_{C}-E _{gap} (E_{gap} is the zero-field splitting at the equilibrium nuclear configuration). Indirect spin-vibration interactions lead to ΔH_{BC}≠0; the vibrational ΔH_{BC} caused by spin-spin and vibronic interactions and the rotational ΔH_{BC} 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 (H_{B} + H_{C})/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|ΔH_{BC}|j′> for wave functions of roughly the same energy are Gaussian random. As the rms of <j|ΔH _{BC}|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|ΔH_{BC}|j′> let isoenergetic levels belonging to different manifolds vibrationally overlap: the ΔH_{BC}, 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 ΔH_{BC}, since the S_{1}-T_{1} separation is as large as 4500 cm^{-1}. If Coriolis couplings cause K scrambling considerably, the rotational ΔH_{BC} mixes {|j>}. This mechanism explains the rotational dependence of magnetic quenching in s-triazine of which S^{1}-T_{1} separation is only ∼1000 cm^{-1}.

Original language | English |
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Pages (from-to) | 162-181 |

Number of pages | 20 |

Journal | The Journal of Chemical Physics |

Volume | 103 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1995 Jan 1 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

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## Cite this

*The Journal of Chemical Physics*,

*103*(1), 162-181. https://doi.org/10.1063/1.469655