| IL |
Intraligand |
| LLCT |
Ligand-to-ligand charge transfer |
| LMCT |
Ligand-to-metal charge transfer |
| MLCT |
Metal-to-ligand charge transfer |
| SOC |
Spin–orbit coupling |
| LR |
Linear response |
| SS |
State-specific |
| EQ |
Equilibrium |
| NEQ |
Non-equilibrium |
| PCM |
Polarizable continuum model |
| FCF |
Franck–Condon factor |
| PES |
Potential energy surface |
| Expt |
Experimental |
| Calc |
Calculated |
| eddm |
Electron difference density map |
|
μ
GS
|
Dipole moment of the ground state |
|
μ
T1
|
Dipole moment of the T1 excited state |
|
c
d
|
Coefficient of Au(d-orbital) |
|
Q GS 0 |
Optimized ground state (GS) geometry |
|
Q ES 0 |
Optimized excited state (ES) geometry |
| ΔESSem |
Emission energy evaluated within the state-specific (SS) approach; eqn (1), Fig. 1
|
|
E ES EQ (QES0) |
Energy of the excited state (ES) with equilibrium (EQ) solvation at the optimized excited state geometry, Fig. 1
|
|
E GS NEQ (QES0) |
Energy of the ground state (GS) with non-equilibrium (NEQ) solvation at the optimized excited state geometry, Fig. 1
|
|
E GS EQ (QES0) |
Energy of the ground state (GS) with equilibrium (EQ) solvation at the optimized excited state geometry, Fig. 1
|
|
E GS EQ (QGS0) |
Energy of the ground state (GS) with equilibrium (EQ) solvation at the optimized ground state geometry, Fig. 1
|
|
λ
s
|
Solvent reorganization energy; eqn (2) |
|
λ SS V |
Intramolecular reorganization energy evaluated within the state-specific (SS) approach; eqn (3) |
|
λ FC V |
Intramolecular reorganization energy obtained from Franck–Condon (FC) calculation; eqn (13) |
|
υ′ |
Vibrational quantum number of the first triplet (T1) excited state |
|
υ′′ |
Vibrational quantum number of the ground state (S0) |
|
χ
υ′
|
Vibrational wavefunction of the T1 excited state |
|
χ
υ′′
|
Vibrational wavefunction of the ground state |
|
η
|
Solvent refractive index |
|
M
T
α
(Q) |
Transition dipole moment of the T1α → S0 transition at geometry, Q |
|
M
T
α
(QT10) |
Transition dipole moment of the T1α → S0 transition evaluated at the optimized T1 geometry, QT10; eqn (9) |
|
M
Sm, j(QT10) |
j-axis projection of the transition dipole moment of the Sm → S0 transition evaluated at the optimized T1 geometry, QT10; j = x, y, or z
|
|
I(ν̃) |
Emission intensity at (ν̃) |
|
ν̃
fcf
|
Franck–Condon factor weighted emission energy; eqn (7) |
|
H
SOC
|
Spin–orbit coupling operator |
| ΔE00
|
Zero-point energy difference between the emitting state and the ground state |
|
ħω
j
|
Vibrational frequency of the jth normal mode (in cm–1) |
| ΔQj
|
Equilibrium displacement of the jth normal mode |
|
S
j
|
Huang-Rhys factor of the jth normal mode; eqn (12c) |
|
ħω
lf
|
Vibrational frequency of the low-frequency (lf) normal modes: ħωlf ≤ 1000 cm–1
|
|
λ
lf
|
Intramolecular reorganization energy contributed by the low-frequency (lf) normal modes; eqn (12b) |
|
ħω
m
|
Vibrational frequency of the high-frequency (hf) normal modes in the range: 1000 < ħωm ≤ 1800 cm–1
|
|
ħω
M
|
Mean frequency of the high-frequency normal modes, ωm; eqn (14c) |
|
λ
M
|
Intramolecular reorganization energy contributed by the high-frequency normal modes ωm; eqn (14b) |
|
S
M
|
Effective electron-phonon coupling strength or Huang-Rhys factor of the effective normal mode, ωM; eqn (12d) and (14a) |
|
n
M
|
Number of vibrational quanta of ħωM; eqn (12e) |
