An explanation of the highly efficient magnetic quenching of fluorescence in intermediate case molecules based on two manifold models

Hirohiko Kono, Nobuhiro Ohta

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The magnetic quenching of fluorescence in intermediate case molecules is modeled by including two triplet manifolds {|bj>} and {|c j>} 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, {|bj>} and {|ĉ j>}, 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 H C arising from the manifolds {|bj>} and {|c j>}, we show that an S structure can be formed in real molecules by nonzero ΔBC≡HB-HC-E gap (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|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|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.

Original languageEnglish
Pages (from-to)162-181
Number of pages20
JournalThe Journal of Chemical Physics
Issue number1
Publication statusPublished - 1995 Jan 1

ASJC Scopus subject areas

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


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