I did a batch of test calculations of phosphorescence, and found that the phosphorescence lifetimes calculated by Dalton are different from the ones I calculated. Here is the output of one teiplet state:
The formula of Einstein A-coefficient can be found in Eq. (3) in Langhoff and Bauschlicher, Astrophys. J. 340, 620 (1989)
Code: Select all
Transition energy: 12.225 eV or 101.415 nm Length gauge / mean field spin-orbit integrals: Partial rates (AMFI): X-polarization 89048. Transition moment : 6.771E-03 Length gauge / mean field spin-orbit integrals: Partial rates (AMFI): Y-polarization 89048. Transition moment : 6.771E-03 Length gauge / mean field spin-orbit integrals: Partial rates (AMFI): Z-polarization 0.0000 Transition moment : 0.00 Phosphorescence - length gauge / mean field spin-orbit integrals: Oscillator strength (/2PI) (AMFI) 4.370526E-06 Dipole strength [a.u.] (AMFI) 9.168345E-05 Dipole strength E-40 [esu**2 cm**2] 5.923186E+00 Total transition rate (AMFI) 5.936506E+04 s-1 Total phosphorescence lifetime (AMFI) 1.684493E-05 s
A = 2.026E-6 * E**3 * D**2
where A in s**-1, E in cm**-1, and D in a.u.
(The same formula was also obtained by me independently and some other authors, so I believe it is correct.)
According to the results above,
E = 12.225 eV = 9.86012265E4 cm**-1,
D**2 = 6.771E-03 * 6.771E-03 + 6.771E-03 * 6.771E-03 = 9.1692882E-5,
T = 1 / A = 5.615E-6 s
which is only one third of the result of Dalton:
3*T = 1.684E-5 s
Another formula of lifetime is
T = 3 / (2 * f * E**2)
where E in cm**-1. Since
f = 4.370526E-06 * 2 * PI = 2.7460825E-5
E = 9.86012265E4 cm**-1
one gets T = 5.618E-6 s.
Is this a bug? Or, is the phosphorescence lifetime defined by a different formula than the fluorescence one in experiments?