A main purpose of this paper is to present a density matrix treatment of the magnetic quenching of molecular luminescence. Unlike the previous theories, which only consider the magnetic effect on the nonradiative rate constant, the present theory describes the time-evolution of the system under the action of a magnetic field. Our theory can treat both the steady state and transient molecular luminescence affected by a magnetic field.
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INTRODUCfIONMagnetic quenching of molecule fluorescence in the gas phase was lust observed for CS 2 by Matsuzaki and Nagakura.' Since this work, similar magnetic effects have been observed for a number of molecules such as S02, 2 formaldehyde.I" glyoxal'" pyrazine,"!' pyrimidine,12.13 and striazine. 14) To interpret the magnetic effect on radlationless transitions of molecules, some theoretical investigations have been reported.":" The magnetic field effect on fluorescence in isolated molecules has recently been reviewed by Ohla.'s Magnetic quenching of fluorescence implies that the nonradiative decay in the singlet excited state is accelerated by a magnetic field. This magnetic field acceleration of nonradiativc decay arises from a field-induced change in level mixing between the initially prepared level and the dark manifold of the neighboring levels by the Zeeman interaction. Two mechanisms have been proposed. According to the direct mechanism, which originates from non-diagonal matrix elements of the Zeeman term between singlet states, the internal conversion is accelerated by the field-induceddirect coupling between the two different electronic states. According to the indirect mechansim, which arises from non-diagonal matrix elements of the Zeeman term among the spin sublevels in a triplet state, the intersystem crossing rate from the prepared singlet level to the triplet manifold is increased by such a coupling.In this paper, we apply the density matrix method to study the dynamics of the system in the presence of a magnetic field. We shall carefully examine the nature of the short-time decay and the long-time decay. Our theoretical treatment takes into account both direct and indirect mechanisms of magnetic quenching; it can also treat both the steady state and transient molecular luminescence affected by a magnetic field. We shall also study the effect of a magnetic field on single-rovibronic-level rate constants of radiationless transitions.
THEORYThe time-resolved properties of a molecular system are best described in a zeroth-order representation essentially determined by experimental excitation and detection conditions." One thus introduces a model where a clear distinction is made between the optically bright states which can be initially prepared by impulsive excitation and tl\e reo maining dark states. These states are not cigenstates of the true molecular Hamiltonian Ii and are mixed by the intramolecular interaction tr and the Zeeman interaction fr z (if an external magnetic field exists). The resulting excitation energy exchanges between the bright and dark man...