Hello,
I'm calculating TD-DFT by Gaussian16 program and want to define the energy levels (singlet & triplet). This is because the material shows dual-emission properties so I want to know the energy levels not only the first excited level but the higher one with oscillator strength.
After optimization of the ground state, I used this lines in the input file:
# opt td=(singlets (or triplets), nstates=10, root=1) b3lyp/6-311+g(d,p)
scrf=(cpcm,solvent=dichloromethane)
And then I got these results:
Excited State 1: Singlet-A 2.0948 eV 591.86 nm f=1.2147 =0.000
93 -> 94 0.70498
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-DFT) = -1077.48878673
Copying the excited state density for this state as the 1-particle RhoCI density.
Excited State 2: Singlet-A 2.8711 eV 431.84 nm f=0.1327 =0.000
92 -> 94 -0.69279
Excited State 3: Singlet-A 3.5652 eV 347.76 nm f=0.0041 =0.000
91 -> 94 0.69723
Excited State 4: Singlet-A 3.6874 eV 336.24 nm f=0.0206 =0.000
90 -> 94 -0.62082
93 -> 95 0.31857
Excited State 5: Singlet-A 3.9388 eV 314.78 nm f=0.2617 =0.000
90 -> 94 0.30403
93 -> 95 0.60292
93 -> 96 -0.13762
.
.
.
From the calculation, I could define the first singlet state as 2.09 eV from 93 to 94 states. So, as far as I understood, the second excited state should be between 93 and 95 states. It could be found in 'Excited State 4' and 'Excited State 5', but there are also other contributions such as '90 --> 94'.
The question is from here: How to calculate the second excited singlet state? I also want to know how to explain the transition when the oscillator strength is over 1. Some contributions show negative values, but it doesn't matter because the percentage of the contribution is calculated by **2*100, right? Any reference or explanation is welcome!
I also tried with 'root=2' which means stabilizing the second excited state.. and the results are as follows:
Excited State 1: Singlet-A 2.0735 eV 597.94 nm f=1.1144 =0.000
93 -> 94 0.70313
Excited State 2: Singlet-A 2.7104 eV 457.44 nm f=0.1487 =0.000
90 -> 94 0.10217
92 -> 94 -0.69214
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-DFT) = -1077.46288164
Copying the excited state density for this state as the 1-particle RhoCI density.
Excited State 3: Singlet-A 3.4496 eV 359.41 nm f=0.0111 =0.000
91 -> 94 -0.69945
Excited State 4: Singlet-A 3.5721 eV 347.09 nm f=0.0467 =0.000
90 -> 94 -0.66797
93 -> 95 0.18771
Excited State 5: Singlet-A 3.9781 eV 311.67 nm f=0.2186 =0.000
90 -> 94 0.17473
93 -> 95 0.64953
93 -> 96 -0.18243
Again, there is also no single excited state of '93 -> 95'.
Anyone can help me?
Last, please recommend other ways if there are efficient or accurate ways to calculate the excited energy levels..
Thank you.
Before entering in details, a comment on your output. The root=1 + opt leads to the geometry optimization of the first excited state (ES1), but you should also add td=read and density=current, as in the following example:
%chk=mol_opt
#p pbe1pbe 6-31g(d,p) opt integral=ultrafine
pop=full gfinput gfprint
Neutral single molecule GS optimization
0,1
--link1--
%oldchk=mol_opt
%chk=mol_td
#p pbe1pbe chkbasis geom=allcheck guess=read
td=nstates=10
pop=full gfinput gfprint
! TD calc
--link1--
%oldchk=mol_td
%chk=mol_es1_opt
#p pbe1pbe chkbasis geom=allcheck
opt td=(read,root=1) density=current
pop=(full) gfinput gfprint
! Optimization of ES1
You could go on by calculating the electronic structure of the GS at the geometry of ES1 followed by the TD calc to evaluate the lowest emission energy.
By the way, this is only the implementation of the calculation reported by Carlo Adamo in Chemical Physics Letters 421 (2006) 272–276 for the QM-evaluation of the fluorescent emission of formaldehyde and benzene. I suggest you to verify you results on those reported in this paper (Table 2, p. 274).
I recently happened to extend this approach to much more complex bifluorene derivatives. You might want to give a glance at Article On the role of torsional dynamics in the solid-state fluores...
I hope this may help.
Dear Yunho Ahn
You already calculated the 2nd excited state:
"I also tried with 'root=2' which means stabilizing the second excited state.."
Which can be confirmed at the end of opt iterations:
Look in the output for "Optimized Parameters"
and check out the final order of excited states to see which 2nd exicited state was optimized. Then you can repeat the process with root=n to obtain the excited state you want.
root=n works for the geometry optimization of the n excited state.
Best, Pablo
Dear Pablo Mtz
Yes I was a bit stupid, but another question is from here,
As the geometry of excited states is optimized, how the transition occurs?
Because this is not absorption anymore, and is it better to say emission transition? In this case, I wonder the optimized ground state that I wrote in the input file is fixed during the transition or it finds the another structure (like vibrational states).
Best,
Yunho
In order to get the emission energy, you may want to get the SCF electronic structore of the GS at the ES geometry, and the perform a TD calc. Since the energy GS—>ES is the same as ES—>GS, you will get the emission energy. This is exactly the method reported in the paper mentioned above (Chem. Phys. Lett. 421 (2006) 272–276).
Dear Yunho Ahn I reply as follows.
'As the geometry of excited states is optimized, how the transition occurs?
Gaussian does a single-point TD calculation at each iteration of the geometry optimization. You can describe the transition only at the end of the calculation, when the geometry is optimized. Otherwise it is meaningless since optimization iterations are not actual physical-chemical states.
'Because this is not absorption anymore, and is it better to say emission transition?'
Again, you shouldn't describe physical-chemical processes with geometry optimization iterations.
'In this case, I wonder the optimized ground state that I wrote in the input file is fixed during the transition or it finds the another structure'
The ground state, or any starting structure, is not fixed, unless you run a single-point TD calculation, which is not the case.
Please see the 'examples' tab here:
https://gaussian.com/%20scrf/
Here the absorption / emission processes are explained in detail (fluorescence of acetaldehyde).
Best, Pablo
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