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

Abstract

Articles you may be interested inHigh efficiency fluorescent excimer lamps: An alternative to mercury based UVC lamps Rev. Sci. Instrum. 84, 123108 (2013); 10.1063/1.4842296 Divergence in Møller-Plesset theory: A simple explanation based on a two-state modelThe 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 sublevels͒; the ͕͉b j ͖͘ are coupled to a bright singlet state ͉s͘ 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 ͉s͘ are constant and no spin-vibration interactions exist ͑the Zeeman interaction connects only the spin sublevels of the same rovibronic level j͒, there are two sets of field dressed eigenstates, ͕͉b j ͖͘ and ͕͉ĉ j ͖͘, of the background Hamiltonian HϪV. ͉b 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 ͉b ͘ 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 Ӷ1͒: 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 ͉s͘. 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 ⌬H BC ϵH B ϪH C ϪE gap ͑E gap is the zero-field splitting at the equilibrium nuclear configuration͒. Indirect spin-vibration interactions lead to ⌬H BC 0; the vibrational ⌬H BC caused by spin-spin and vibronic interactions and the rotational ⌬H BC caused by spin-rotation and rotation-vibration interactions. The matrix elements of H are written down in terms of the eigenfunctions ͕͉ j͖͘ of the average Hamiltonian (H B ϩH 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 distribution͒, the vibrational ͗ j͉⌬H BC ͉ jЈ͘ for wave functions of roughly the same energy are Gaussian random. As the rms of ͗ j͉⌬H BC ͉ jЈ͘ approaches the average level spacing ͑on excitation into higher vibrational levels͒, the efficiency of magnetic quenching becomes as high as in the S case. Nonzero ͗ j͉⌬H BC ͉ jЈ͘ let isoenergetic levels belonging to different manifolds vibrationally overlap: the ⌬H BC , together with the magne...

Rotational State Dependence of the External Magnetic Field Effect on the Fluorescence of Pyrimidine-d4 at the S1 Origin

“…Here, the following assumptions are employed: the line widths of the mixed states can be substituted by the average value of γ; the line widths of the zero-order triplet states are the same (γ T ). The quantity N eff is given by the inverse of the time-averaged probability of finding the system in |S〉; N eff + 1 ≡ 1/∑ n | a n | 4 . , The quantum yield of the slow component, denoted by Φ F , is where Γ S represents the radiative width of |S〉.…”

“…However, the above equations indicate that a magnetic field mixes not only the spin sublevels of the single rovibronic level but also the sublevels belonging to different rovibronic levels of the triplet states through the interaction of these triplet states to the same singlet state; i.e., H plays a role to increase N eff , as mentioned above. This type of mixing among different rovibrational levels becomes stronger as the energy of the sublevels which are uncoupled with the singlet state at zero field is closer to ε S , which is called isoenergetic intermanifold mixing (IIS) …”

“…It should be added that the efficiency of magnetic quenching, however, reaches the ceiling. When N eff at zero field is extremely large, the average energy separation among spin sublevels becomes small accordingly, but the average coupling strength of IIS decreases because of the large density of rovibrational levels sharing the |S〉 component 3 Fluorescence decays observed at zero field (solid line) and at 158 G (dotted line) on excitation at the P(2) line (lower) and P(4) line (upper).

4 Plots of the fluorescence lifetime (τ F ) as a function of the field strength ( H ) at various rotational line excitations.

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“…This type of mixing among different rovibrational levels becomes stronger as the energy of the sublevels which are uncoupled with the singlet state at zero field is closer to S , which is called isoenergetic intermanifold mixing (IIS). 11 N eff can be shown to be increased by a factor of 3 by high fields, if the assumptions which are employed to derive eqs 2 and 3 are used. Further, the efficiency of mixing among spin sublevels, which is directly related to the efficiency of magnetic quenching of fluorescence, is considered to become larger with increasing N eff since an increase of N eff plays a role to decrease the average energy separation among spin sublevels, as demonstrated in our model calculation.…”

“…When N eff at zero field is extremely large, the average energy separation among spin sublevels becomes small accordingly, but the average coupling strength of IIS decreases because of the large density of rovibrational levels sharing the |S〉 component. 11 As mentioned previously, the relation between γ S /N eff and γ T for the 0 0 pyrimidine-d 4 is considered to be an intermediate between case ii and case iii. The fact that both magnetic quenching of fluorescence and lifetime lengthening occur for most excitations is well understood by assuming that N eff is increased by H (see eqs 2 and 3).…”