isosurfaces of the difference densities (DD) and molecular orbitals (MOs) of the lowest electronic states of nitrobenzene |

this simple-looking but nasty system had me thinking a lot for the past months.

the problem with its theoretical investigation in a single sentence goes as follows: even high-level and usually very reliable methods (e.g. perturbative coupled-cluster of second order, CC2) systematically deliver largely inaccurate results for very simply properties such as the ground state geometry and vertical excitation energies.

Therefore, expensive third order methods such as the Algebraic Diagrammatic Construction scheme of third order ADC(3) and (Equation of Motion) Coupled-Cluster Singles and Doubles (EOM)-CCSD are required for the vertical excitation energies and the ground- and excited state geometries, respectively.

It took me almost a year (I wasn't constantly working on the topic) to realize that there's something wrong with CC2 due to something that is quite typical for the field I'm working in:

If you calculate the molecular ground state geometry of NB with CC2 and subsequently use this geometry to calculate vertical excitation energies with linear-response (LR-)CC2, the outcome is just fine. Fits experimental values without any large unexpected errors and everything seems fine and consistent.

However, if you compare the CC2 geometry to experimental measurements or results from CCSD calculations, you will find that one essential parameter it is systematically wrong (N-O bonds are 125 instead of 122 pm) and it turns out: The vertical excitation energies are only in agreement with the experiment for exactly this wrong geometry.

If experimental parameters or a CCSD optimized geometry is used, the excitation energies with CC2 are all 0.3-0.5 eV too high. Now that I know this, I started to systematically investigate the influence of geometry, which threw up more questions than it answered.

*an elaborate and fortuitous cancellation of errors*. In case of NB and CC2 it goes like that:If you calculate the molecular ground state geometry of NB with CC2 and subsequently use this geometry to calculate vertical excitation energies with linear-response (LR-)CC2, the outcome is just fine. Fits experimental values without any large unexpected errors and everything seems fine and consistent.

However, if you compare the CC2 geometry to experimental measurements or results from CCSD calculations, you will find that one essential parameter it is systematically wrong (N-O bonds are 125 instead of 122 pm) and it turns out: The vertical excitation energies are only in agreement with the experiment for exactly this wrong geometry.

If experimental parameters or a CCSD optimized geometry is used, the excitation energies with CC2 are all 0.3-0.5 eV too high. Now that I know this, I started to systematically investigate the influence of geometry, which threw up more questions than it answered.

In the next posts I will probably discuss the influence of geometry on the vertical excitation energies and explain all the shiny pictures above.

So long!

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