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### Why the phosphorescence lifetime is scaled by 3?

Posted: 28 Dec 2015, 03:40
Dear Developers,

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:

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
``````
The formula of Einstein A-coefficient can be found in Eq. (3) in Langhoff and Bauschlicher, Astrophys. J. 340, 620 (1989)
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,
One obtains
T = 1 / A = 5.615E-6 s
which is only one third of the result of Dalton:
3*T = 1.684E-5 s