# Difference in energy between first excited singlet and first excited triplet with DFT in Gaussian

I want to ask a further question related to this one.

I have performed the calculations as explained and obtained a difference in energy of 0.71eV with the TDA-DFT level of theory.

Then, I tried to do the same calculation but with DFT level of theory. I first optimized the first excited singlet S1:

    # opt M062X/6-311g* scrf=(solvent=dichloromethane) Geom=AllCheck int=ultrafine Nosymm

molecule1

0 2


and the first excited triplet state T1

 # opt M062X/6-311g* scrf=(solvent=dichloromethane) Geom=AllCheck int=ultrafine Nosymm

molecule1

0 3


However, the result of the first calculation is

 SCF Done:  E(RM062X) =  -1315.49716286     A.U. after    6 cycles


and for the second is

SCF Done:  E(RM062X) =  -1315.49716286     A.U. after    6 cycles


Leading to a difference in energy of exactly zero. Where does this big difference come from? Is there something wrong with the inputs?

• Shouldnt the singlet be multiplicity of 1? Dec 10, 2023 at 18:49
• Your first calculation is indicating a doublet with "0 2". I don't know how a molecule could be both neutral doublet and a neutral triplet. Also, the "R" in the output suggests it was run as RHF calculation, which doesn't fit with either doublet or triplet spin states. Dec 10, 2023 at 19:55
• Indeed, I noticed the error on the singlet state and I think it should be corrected to '1 1'. However, for the triplet T1, it should be '0 3' and just changed to unrestricted? Dec 11, 2023 at 8:52
• Hi, I think you should do td-dft in order to optimize the singlet, so it should be like that tda(singlets,nstates=you can select number of states,root=1). Regarding the triplet, it can be as you already did. Dec 11, 2023 at 12:16
• I have actually read that triplet states can be quite unstable. For this reason, TD/TD+TDA can be better. Dec 11, 2023 at 16:29

(1) When you write Geom=AllCheck, the Title Card, charge and spin multiplicity would not be read by Gaussian, i.e.

molecule1

0 2


would not be read. So is the case in your triplet calculation. They would be read from the .chk file specified by %chk=xxx.chk. It means that you are performing the same calculations repeatedly, so the obtained SCF energies are, of course, identical.

(2) If you want to read geometry meanwhile use a new spin multiplicity, you should write geom=check, and write the Title Card, charge and spin multiplicity below the Route section.

(3) Assuming the ground state of your molecule is singlet and you want to optimize the S1 state, you should use TDDFT, e.g.

#p opt TD M062X/6-311g* scrf(solvent=dichloromethane) guess=read Geom=AllCheck int=ultrafine Nosymm



For the lowest triplet T1, it is recommended to use UDFT to get what you want

#p opt UM062X/6-311g* scrf(solvent=dichloromethane) Geom=Check int=ultrafine Nosymm

molecule1

0 3


You can also use TDDFT to calculate the T1 state, but it takes more computational cost and its energy would not be identical to UDFT's result (but very similar geometries could be expected)

#p opt TD(triplet) M062X/6-311g* scrf(solvent=dichloromethane) guess=read Geom=AllCheck int=ultrafine Nosymm



By the way, if you are using Gaussian 16, int=ultrafine is not needed since this is the default.

• would the T1 state be more accurate when calculating it with TD? and this would be equivalent in a single calculation using 'opt td=(nstates=...,50-50)...' right? Dec 22, 2023 at 21:34
• (1) There is no convincing evidence about that the TD(triplet) calculation based on the singlet ground state would be more accurate than triplet UDFT calculation. (2) I don't what and what is equivalent. But opt td=(nstates=...,50-50) DOES NOT mean that you can perform the geometry optimizations for S1 and T1 states simultaneously. It only means that you can compute the energies of several excited states in a calculation, but the geometry optimization will still be conducted upon the lowest excited state (which could either be S1 or T1, system dependent). Dec 25, 2023 at 2:33
• If I want to perform the geometry optimization upon the S1 state, I'll not use TD(50-50) because I know that triplet states are useless for me. In fact, the TD(50-50) keyword is often used when the ground state geometry optimization is done and one wants to calculate the vertical absorption. Dec 25, 2023 at 2:33
• (1) in this publication chemrxiv.org/engage/chemrxiv/article-details/… they state that the triplet would be better computed with TDA. Should this be enough evidence? Why do you say that is recommended UDFT? (2) I am not sure I understand. If I would like to calculate the difference in energies between the singlet S1 and triplet T1 states, by optimising both states, shouldn’t one compute the ‘opt tda(50-50,root=1)’? Dec 26, 2023 at 14:15
• In fact, here mattermodeling.stackexchange.com/questions/12060/…, the usage of TDA was recommended to me. Dec 26, 2023 at 14:34