The microwave-induced delayed phosphorescence (MIDP) resignal. Kinetic information is obtained by analyzing the MIDP sponses of several molecules in their excited triplet state are anaresponses as t is varied in a series of measurements. lyzed globally by least-squares minimization of the residuals, x 2 .
It has been customary to consider only the height of the
The analysis considers not only the initial amplitudes of the MIDP phosphorescence transient that is initially induced by the responses which has been customary in the past, but also all data microwave pulse or fast passage. The height of the transient points (up to about 20,000) contained in a data set consisting of produced by the transition between the T i and T j sublevels all three zero-field transitions and a range of delay times. It is at t ร
t is given by shown that global fitting of the data cannot be carried out successfully without including both sublevel decay to the ground singlet
state and spin-lattice relaxation (SLR). Thus a complete data set containing at least two of the zero-field transitions when analyzed globally yields both sublevel decay constants and the SLR rate where Dn ij (t) ร
n j (t) 0 n i (t) is the population difference constants. Results are reported for tryptophan (Trp), 5-hydroxyat t ร
t, k r i , j are radiative rate constants, and C depends tryptophan (5-Htrp), the anion of 5-Htrp obtained by ionization on the experimental arrangement and the fractional populaof the hydroxyl proton, and 7-azatryptophan (7-Atrp). It is found tion transfer induced by the pulse or fast passage. Usually, that the T z sublevel (z is the out-of-plane axis) decays principally MIDP measurements are made at the lowest possible temperby SLR even at about 1.2 K; k z ร
0 within experimental error ature where it may happen that spin-lattice relaxation (ร{0.01 s 01 ) except for 5-Htrp anion, where it is measurable and (SLR) is negligible. In this case, is the smallest of the k values. For each triplet state, except for 5-Htrp anion, SLR is least efficient between the T x and T y sublevels. This relaxation process requires an angular momentum compo-Dn ij (t) ร
n j (0)exp(0k j t) 0 n i (0)exp(0k i t). [2] nent along z. Since the z component of spin-orbit coupling is the weakest one in 3 (p, p*) states, the van Vleck relaxation process In Eq. [2], k i , j are the individual decay constants of sublevels is suggested for Trp, 5-Htrp, and 7-Atrp. For the 5-Htrp anion, T i ,j . Analysis of MIDP data has been restricted thus far to the most efficient SLR occurs between T x and T y , suggesting a the special case where k i ำท k j and to t sufficiently large different mechanism, possibly direct phonon modulation of the that the second term on the rhs of Eq. [2] may be neglected.
zero-field splittings.