where Mp and Sn-S0 are the transition dipole moments of the T1-S0 and Sn-S0 transitions in the T1-geometry, respectively; mp n contributed to Mp by borrowing intensity from the Sn state; <Sn|HSO|T1> is the spin-orbit coupling (SOC) matrix element between the Sn and T1 states. Equations (1-3) provide two insights: (i) mp n , and hence kp, increase when Sn states of a large (spin-allowed) Sn-S0 couple with the T1 state; and (ii) the coupling increases when SOC with energetically close Sn states is effective. It should be emphasized that a large SOC matrix element is insufficient because matching of the three factors in Eq (3) via the same Sn states is the requisite for a significant kp. Time-dependent density-functional theory (TDDFT) calculations for the T1-optimized TP geometry of 1a yielded kp = 5200 s -1 (for n = 1-10), which excellently reproduced the experimental value of 5300 s -1 . Remarkably, the T1 state strongly coupled with the S3 state, with a large SOC matrix element <S3|HSO|T1> = 167 cm -1 and a reasonable ES3-T1 = 1.74 eV (Figure ). The efficient coupling allowed 1a to borrow the strong intensity of the spin-allowed S3-S0 transition (|S3-S0| = 4.68 D), realizing a large |mp 3 | = 56 × 10 -3 D.