Calculating vertical excitation energies at the DLPNO-STEOM-CCSD Theory level

Question

I want to calculate the vertical excitation energy using the DLPNO-STEOM-CCSD method, on molecules previously optimized using TD-DFT. the parameters being used are as follows:

STEOM-DLPNO-CCSD,
Basis set: def2-TZVP,
Nroots 5,
TIGHTPNO settings, and RIJCOSX approximation. 

I am unsure as to whether I can use the ESD(Abs) to calculate this absorbance data (as with a TD-DFT calculation) or whether I need to use another method.

Answer 1

You probably can, but even if you can, such a calculation is not the recommended practice, since:

1. The DLPNO-STEOM-CCSD analytic gradient is not available, and probably will not be available anytime soon. Therefore, the gradient of the DLPNO-STEOM-CCSD energy (which is required in an ESD calculation) has to be evaluated numerically, which is very costly (takes $6N_{atom}\times$ the time of a DLPNO-STEOM-CCSD single point calculation).
2. Even worse, the analytic gradient of DLPNO-CCSD is not available either (although it may become available in a couple of years), so the ground state Hessian (which is also required by ESD) has to be evaluated by a twice numerical differentiation of the DLPNO-CCSD energy, rather than a seminumerical differentiation (differentiate once analytically, then once numerically). This is not only extremely costly, but also introduces considerable numerical noise.
3. If you could really afford all of these calculations, then you could achieve better accuracy using the same computational time, by going beyond the harmonic approximation employed by ESD, e.g. with path integral molecular dynamics on a machine learned potential energy surface fitted against DLPNO-STEOM-CCSD data.

Therefore, the usually recommended practice is to calculate the gradients and Hessians under the DFT/TDDFT level, and use DLPNO-STEOM-CCSD only to provide a better estimate of the adiabatic excitation energy. Therefore, the input file should be written as if it is a TDDFT ESD calculation; meanwhile you can calculate the adiabatic excitation energy using DLPNO-STEOM-CCSD and enter the result using the keyword DELE (for details, see ORCA manual). Similarly, the DLPNO-STEOM-CCSD transition dipole moment can be entered using the TDIP keyword. This gives you an absorption spectrum where, roughly speaking, the 0-0 peak as essentially DLPNO-STEOM-CCSD accuracy, and the splitting between the vibrational fine structures has TDDFT accuracy, which is sufficient for most purposes (and as I said, in case the TDDFT vibronic structure is not accurate enough for your purpose, the intrinsic limitation of the ESD module's harmonic approximation to the PES is likely non-negligible either).

Even more, as you can afford the DLPNO-STEOM-CCSD single point calculations anyway, you can use your DLPNO-STEOM-CCSD results to guide the selection of a density functional that best suits your system. By this way, the TDDFT part of the calculation can become more reliable than if you selected your functional without relying on the DLPNO-STEOM-CCSD benchmark results.