Correlation Function Formalism for Triplet Excited State Decay: Combined Spin–Orbit and Nonadiabatic Couplings

Abstract

Based on the second-order perturbation combining spin-orbit and nonadiabatic couplings, we derived an analytical formula for nonradiative decay rate between the triplet and singlet states by using the thermal vibration correlation function (TVCF) approach. Origin displacement, distortion, and Duschinsky rotation of the potential energy surfaces are taken into accounts within the multiple harmonic oscillator model. When coupled with first-principles calculation for the anthracene, the theoretical phosphorescence spectrum is in good agreement with the experiment. Furthermore, we found that the intersystem crossing from the first excited singlet state (S1) to the triplet states S1(Bu)→T2(Ag) is forbidden by direct spin-orbit coupling at the first-order perturbation but becomes allowed through combined spin-orbit and the nonadiabatic couplings at the second-order perturbation, and the rate is calculated to be 0.26 × 10(8) s(-1), in good agreement with the experiment. Such formalism is also applied to describe the phosphorescence quantum efficiency and the temperature dependent optical emission spectrum for fac-tris(2-phenylpyridine) iridium. We predict that the radiative decay rate is 6.36 × 10(5) s(-1), the nonradiative decay rate is 5.04 × 10(4) s(-1), and the phosphorescence quantum efficiency is found to be 92.7% from T1 to S0, which reproduce well the corresponding experimental measurements.

Understanding the efficiency drooping of the deep blue organometallic phosphors: a computational study of radiative and non-radiative decay rates for triplets

“…Based on the fundamental first-order perturbation rate theory, 22 the radiative rate constant is directly proportional to the spin-orbit coupling (SOC) between the emitting states and the perturbing intermediate states with different multiplicities, and the electric transition dipole moment between the involved electronic states with the same multiplicity, but it is inversely proportional to the energy gap between the interacting triplet and singlet excited states. The non-radiative decay rate constant between the triplet and singlet states depends on the SOC, energy gap and vibronic coupling.…”

Vibration Correlation Function Investigation on the Phosphorescence Quantum Efficiency and Spectrum for Blue Phosphorescent Ir(III) Complex

“…最近, 彭谦等 [12] 发展了将自旋-轨道耦合与非绝热 耦合相结合的微扰理论, 为计算系间窜越速率和磷光速 率和光谱提供了普适性的公式. 该理论形式由于采用了 振动关联函数, 借助高维积分的解析推导和快速傅里叶 变换, 使得计算量随分子尺度从指数增长极大地降到仅 仅是矩阵运算的 N 3 [13] , 并首次实现了复杂的有机过渡 金属配合物的磷光效率的定量预测 [12] .…”

“…该理论形式由于采用了 振动关联函数, 借助高维积分的解析推导和快速傅里叶 变换, 使得计算量随分子尺度从指数增长极大地降到仅 仅是矩阵运算的 N 3 [13] , 并首次实现了复杂的有机过渡 金属配合物的磷光效率的定量预测 [12] . 磷光材料中, fac-tris (2-(4,6-difluorophenyl)pyridyl iridium (facIr(F 2 ppy) 3 )是一个常见的蓝光磷光材料, 已经得到详尽 的实验研究和简单的理论计算 [7,14～16] .…”

TDDFT study on recognition mechanism for the oxygen sensing of the cyclometalated platinum (II) complex

“…In addition, the frontier molecular orbitals and electronic configurations were calculated with the ADF 2012 program, by employing the GGA: PBE functional and the slater-type TZP basis sets [42,43]. The MOMAP package [44][45][46][47][48] was employed to calculate the rate constants of the photophysical processes of the Lxp1 and the Lxp1-O 2 complex. The binding energies of hydrogen bonds were calculated using the counterpoise method.…”