continuing the story of dratted nitrobenzene

ω(r[NO])

I finished investigating the influence of the NO bond length (symmetric stretch) onto excitation energies at ADC(3)/SVP level of theory! The result is as expected: due to the population of the π* orbital at the nitro group (see first post concerning nitrobenzene) in all lower excited-states, the influence of this bond length is quite large in the following way: along the symmetric NO stretching mode, the energy of the ground state largely increases, while the absolute energies of the excited states decrease (see Figure 1).

Figure 1) Run of the absolute ground- and excited state energies along symmetric NO-stretching coordinate starting from the CCSD/def2-TZVP optimized structure. The scan was a rigid one, i.e. without reoptimizing the structural paramaters for each r(NO) but keeping them at the value of the original geometry.

For the vertical excitation energies (ω) these effects add up and the ω of all states drop rapidly by about 0.1 eV/pm (Figure 2), which explains for the large difference between CC2 geometry with 125 pm NO-bonds and the CCSD geometry with 120 pm NO-bonds.

Figure 2) Run of the vertical excitation energies along the symmetric NO-stretching coordinate. The gradient is about 0.1 eV/pm. The equilibrium value for the NO distance is 120 pm at the CCSD/def2-TZVP level of theory (compare Figure 1). One can clearly distinguish between the local excited state of the nitro group and the valence excited states, since the latter have a slightly smaller gradient.

 Now I know why and how strong excitation energies depend on the NO bond length, but one very important question remains: Why is the ADC(3)  result for the excitation energy  of the lowest excited singlet state (almost 4.1 eV) so far off from the experiment (3.65 eV)? From a third order method like ADC(3) one would expect 0.1-0.3 eV deviation at max, in particular for singly excited states. Maybe the reason is lying in the dynamics of the molecule, cause in the experiment, this bond vibrates like any other bond. I will have a look into this using born-oppenheimer ab-initio molecular dynamic in the next post.

 so long!

Accidential Accuracy

 Why chocolate makes you fat but TNT doesn't

TNB: an explosive that is
closely related to TNT

Yesterday we carried out some (as we thought) very approximate calculations for a little 2 hrs quantum chemistry workshop that we will give during the annual meeting of my graduate school next week.

I thought it would be fun to calculate and compare detonation energy of an explosive to the energy content of "chocolate", which basically is sugar and fat 50:50. In doing so, one will find that you could never get fat from TNT because it actually contains only a small fraction of the chemical energy that is stored in chocolate.

a mono sugar: Glucose
(sucrose is too big)

Since we only have two hours for the whole workshop we've chosen to employ an approximate level of theory from the density functional theory (DFT) corner called B3LYP with a small SVP basis on model compounds. Furthermore, we decided to ignore all entropic, thermal and environmental influences to keep it simple. For the detonation of TNB we used a simplified reaction equation yielding only CO, N2 and H2 which circumvents the calculation of electronically complex (radical) nitroxides and such. At this level of theory, all calculations take about 1 hour on a modern laptop computer.

a fat model: Octanoic acid
(real triglycerides are to big)

The trickiest part to get right is the energy of liquid water, which is needed since we have physiological conditions. Here, we extrapolated from a few calculations (one water, one water using a solvent model (PCM), two water + PCM, four water+PCM, eight water+PCM) to to energy of liquid water.

Despite the crude model and level of theory we hoped to achieve at least qualitative agreement with the experiment, but then something not completely unexpected happened.

For comparison (taken from wikipedia)
- The experimental detonation energy of TNB is 3.8-3.9 kJ/g
- The physiological energy content of sugar is 17 kJ/g
- that of fat is 39 kJ/g.

Now look at the B3LYP/SVP results:

results of the B3LYP/SVP thermochemistry calculations

I think the explanation for this astounding accuracy is again a fortuitous cancellation of errors: The intermolecular interactions we neglect on the left side of the equation are obviously of the same or very similar size as the entropic and thermal corrections we neglect on the right side of the equation.

After all, its just spooky how well error cancellation can work out, in particular for DFT/B3LYP. This is not always a good thing! In my last post on nitrobenzene for example, you can read how error-cancellation can be quite problematic.

dratted nitrobenzene!

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: 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!

EΨ ~ HΨ

 I decided to blog about my workaday thoughts about my Ph.D. in the field of computational quantum chemistry. Might it help those concerned with similar thoughts!