Greetings to all.
I have some questions about setting up DFT calculations in Gaussian software (I am a beginner in these matters), and trying to calculate the energy of the first excited triplet state T1; also I want to calculate the energy of the first excited singlet state S1.
- the above, with the purpose of obtain the quantity called Singlet-Triplet Splitting Energy ΔE_ST. I ask you please, that someone could clear up some doubts I have, about whether my procedure is correct:
You see, I try to follow these "steps":
1. First, I optimize the molecule (I use DFT and some hybrid functional) in ground state and do the frequency analysis with
%chk=optgroundstate.chk
#p opt freq=noraman functional/base
0 1
Calculation from which I get the electronic energy as:
SCF Done: E(RB3LYP) = -[some quantity in a.u.]
2. Then I calculate the vertical excitation energies based on the ground state geometry for “N” states of interest with TD-SCF
%oldchk=optgroundstate.chk (from step 1)
%chk=step2.chk
#p td=(nstates=N) functional/base geom=check guess=read
0 1
from which I get information about the first N excited states
Excited State 1: Singlet-A [some quantity] eV [some quantity] nm f=[some quantity] =[some quantity] .
.
3. Next, I optimize the geometry of the excited state (singlet) using TD-DFT and making a slight perturbation of the geometry by changing one or a couple of dihedral angles (for example, of atoms A, B, C, D ) with:
%oldchk=step2.chk
%chk=step3.chk
#p opt td=(nstates=N,root=1,read) functional/base geom=modify guess=read
0 1
A B C D [some slight angle modification]
. . . . ……
And then, if I subtract Total Energy, E(TD-HF/TD-DFT) obtained in the “stept 3”, from the energy SCF Done: E(RB3LYP) from the ground state optimization, in principle:
- Would I obtain the energy of the first state excited? Since in step 3, I specified to focus on root = 1 ??
- And well, if the above is correct, Can I calculate the energy of the first triplet state by performing an optimization calculation on the excited state of the triplets as follows?
4. Optimize the geometry of the excited state (triplet) using TD-DFT
%oldchk=step3.chk
Dear Erick,
When you say in TD-DFT "root=n", it will be the root whose geometry will be optimized (if you ask for opt, as in your case). With the "TD" keyword, root=1 is the first excited state. So yes, you are optimizing the excited state. Although be careful, if you modify the geometry, you should check that you are optimizing the state of your interest. A change in the geometry could induce a crossing between excited states.
To optimize the first singlet (T1 state if the ground state is a singlet), you don't need to use TD, because you are interested in the lower singlet -> you can't get a triplet below the lower triplet! So TD is not necessary, just 0 3 in charge-multiplicity (as you did) is ok!
An important remark: if you optimize your states you will get the "adiabatic" energy difference. You can also fix the geometry and you will get the "vertical" excitation energy.
Hope it helps!
Best,
Fernando
Dear Dr. Fernando Aguilar-Galindo, thank you for your kind reply.
I was wondering if in the second paragraph of your answer, when you say: "To optimize the first singlet (T1 state if the ground state is a singlet)"
you mean that first triplet excited state?
What happens is that, I try to design TADF emitters. And in that sense I am very interested in the energy that the first triplet state (T1) has, and also the energy of the first singlet state (S1); from where I hope by subtracting said energies to obtain the value of ∆EST (energies that in the best case for my thesis they should be less than 0.2-0.3 eV).
Can I trust the margin of error a calculation of the triplet energy by vertical excitation would imply? I have done some tests on this and find variations from 0.3 eV to almost one eV (with respect to the energy obtained, optimizing the corresponding excited state).
Thanks again for answering my question.
Best regards
Hallo, Erick!
There are 2 types of electron transitions:
1) vertical el. transitions - the geometry is preserved, the energy differences can be obtained directly by TD-DFT method . This type calculations are used for UV/vis spectra analyses (assumption of much slower nuclear relaxation than the electron excitation).
2) adiabatic el. transitions - correspond to the energy differences between adiabatic potential minima of individual el. states. In this case you must optimize the geometries of both el. states (if the above assumption is not fulfilled).
Except ground singlet and triplet states (= optimized geometries of ground states), you must optimize the excited state geometries (usually at TD-DFT, TD-HF or CIS level, using keyword Root=n for the n-th excited state). It must be mentioned that such a geometry optimization might be problematic due to possible crossing of potential surfaces of some excitedel. states.
I suppose that for your purposes it might be sufficient to optimize the ground singlet state geometry and then evaluate the singlet-triplet energy difference using TD-DFT method (vertical el. transitions). If it might be insufficient, you should optimize your system in both singlet and triplet ground states independently and then evaluate the singlet-triplet energy difference as the energy difference of their optimized structures.
Best wishes
mb
p.s.; The above procedure for vertical el. transitions is valid if the singlet state is energeticall lower than the triplet one. If the triplet el. state has lower energy, you must optimize its geometry and then use TD-DFT method for its opt. geometry.
Erick Alfonso Sánchez
Dear Erick Alfonso Sánchez
When I said "T1" I wanted to clarify something: if the ground state is a singlet, we call it "S0". The first singlet excited state is "S1", the second "S2" and so on. In that case there is no "T0". The zero is only used for the absolute ground state, regardless of its spin. So, if the most stable spin is a singlet, that state is the S0 and the lowest triplet you can get is T1. And in this case you don't need to use TD-DFT. Sorry if I didn't explain correctly.
Now, regarding you question... If you want to study TADF emitters, you need to get the geometry of the triplet, since it is a long-lived state and the energy exchange will be observed from this geometry. In order to have a probability to go from T1 to S1 you need both states to be close in energy at the same geometry. Then, you will move to S1 and from S1 you will have the fluorescence.
I made a very basic scheme. I would recommend you:
1- optimize T1 (TD option is not required, just regular DFT but asking for triplets)
2- from this geometry, TD-DFT (but setting 1 as multiplicity) to get the vertical excitation T1->S1 (to see if S1 is close in energy)
3- If S1 is close to T1, optimize the geometry of S1 (TD option, root=1, although it is not necessary, since it is the default). If the energy difference you got in step 2 is small, geometries will be similar (probably).
4- From the optimized S1, run a single point TD-DFT. You will get emission energy.
Best,
Fernando
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