How can I calculate the energy gap between the singlet and triplet state using ORCA?

Question

I came across this publication that calculates the $S_1$ - $T_1$ energy gap using TDDFT as implemented in Gaussian. I would like to do the same using ORCA. Im extremely new to ORCA and local orbital codes in general and would like to know how to do the same with an example of an input file.

Answer 1

First of all, if you are only interested in molecules with about the same size as the ones in the article you cited, then TDDFT is probably not the best method for this purpose. ORCA supports many methods that are much more reliable than TDDFT for singlet-triplet gaps, yet are still affordable for molecules of this size, for example DLPNO-STEOM-CCSD, NEVPT2, ICE etc. (For details please refer to the ORCA manual.) They give singlet-triplet gaps that are usually accurate to 0.1~0.2 eV, while for TDDFT, errors around ~0.5 eV are quite common. But that being said, it's still a good idea to start with TDDFT calculations, to get familiar with ORCA and the problem at hand.

If you want to reproduce the Gaussian result in this paper as closely as possible, you can write the input file as follows:

(1) Optimize the structure

! B3LYP/G 6-311++G(d,p) Opt Freq
%pal nprocs 8 end # this parallelizes the calculation over 8 processes
* xyz 0 1 # change 0 and 1 to the actual charge and multiplicity
# atomic coordinates here, in Angstrom
*

After the job finishes, check if the geometry optimization converges and there is no imaginary frequency. If yes, prepare and run a second input file:

(2) TDDFT calculation

! B3LYP/G 6-311++G(d,p)
%pal nprocs 8 end
%tddft
tda false
nroots 5 # calculate 5 singlet excited states
triplets true # calculate an equal number of triplet excited states
end
* xyzfile 0 1 xxx.xyz # xxx.xyz is the xyz file generated by the optimization job

Note that the calculation will not exactly reproduce the Gaussian result, because Gaussian uses Cartesian d functions in the 6-311++G(d,p) basis set, while ORCA uses spherical d functions. The difference is expected to be within about 0.05 eV.

If reproducing the literature result isn't a primary concern, it is probably better to optimize the structure at the wB97X-D3/def2-SVP level of theory, and do the TDDFT calculation at the wB97X-D3/def2-TZVP level of theory. This is because (1) B3LYP sometimes predict wrong bond length alternation patterns in large conjugated molecules; (2) B3LYP tends to underestimate the energies of triplet excited states; (3) ORCA is more optimized for the def2 basis sets, and less optimized for the Pople basis sets (6-31G(d), 6-311G(d,p) and the like). For serious research, it is advised to survey benchmark papers to decide on which DFT functional to use.

Finally, there is a great resource for new ORCA users: the ORCA input library. You can easily find example input files for the most common types of ORCA jobs.