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

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**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:

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

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?

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
```

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

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?