Montag, 10. Juli 2017

ADC/SS-PCM at glance? Part one.

Dear colleagues,
 
in the framework of a recent project published in this article, I for the first time had the chance to systematically study the performance of ADC/SS-PCM for a group of click-chemistry generated molecules with varying charge-transfer character in their emitting excited state.
The common motif of these molecule is that they consist of an electron-pushing triphenylamin group (right side of the molecule in the figure below) and an electron-pulling group (left side), whose strength can be modulated by oxidizing the contained sulphur atom. In the lowest excited singlet state of all of these systems, an electron is excited from the electron-pushing triphenylamine to the electron pulling part of the molecule. While the excitation-hole turned out to be essentially identical in all of these systems and all solvents, the location and structure of the excited electron differed significantly depending on the molecule and environment.
The figure below shows the structures of the molecules as well as the location of the excited electron computed at the ADC2/SS-PCM/SV level of theory for the non-polar solvent cyclohexane on the left and for the polar solvent acetonitrile in the right.


Since the discussion of the performance of the methodology was (as usual) quite brief in the article, I will share some more methodological insights here and in the following posts.
The central observation, which also made it into the paper, was that the solvent effects are systematically overestimated for this group of molecules, leading to too low emission energies in polar solvents (here acetonitrile, ACN). In the non-polar solvent cyclohexane (CHX) the error seems to cancel out with the systematic overestimation of the emission energies by the quantum-chemical method (ADC2 with a small, non-polarized split-valence basis), leading to a very reasonable agreement. 

Something that we only mentioned but did not show in the article was that the spin-opposite scaled variant of ADC(2), SOS-ADC(2) [short: SOS(2)] improves on this systematic error. After the article was published I took a closer look at this and recomputed all of the numbers also with SOS(2). Turns out this method pretty much nails the emission energies in ACN, with those in CHX getting a little worse:
Fluorescence energies of a series of molecules calculated with ADC(2) and SOS-ADC(2)/SS-PCM/SV using TD-uPBE/6-31+G(d) geometries. Geometry optimizations were conducted in the gas phase, i.e., without any solvent model.
While these trends are most certainly interesting to know for future investigations (use SOS-ADC/SV for polar solvents and ADC/SV for non-polar ones), the question that remains is if this systematic overestimation of the solvent-stabilization is due to A) the quantum-chemical methodology, B) the solvent-model, C) the nature of these molecules or D) a combination of all three. 
Speaking for A) is that I have observed before how ADC(2) yields too low energies for charge-transfer states compared to locally excited states. Since in this case the picture was very consistent, including the fact that the problem is corrected by ADC(3), I'm pretty confident that A) contributes at least to some extent. The question that really bothers me, however, is if B) is also the case, because so far, I am pretty sure that the self-consistent treatment of solvent polarization is the one and only physically correct way to do it. You can find my arguments for that in the respective article (same as above).
To further look into the issue, let us eliminate the inherent error of the quantum-chemical methodology as far as possible by looking at the CHX to ACN shifts in the emission energy. Let us furthermore include the emission energies from the first solvent-field iteration in the comparison, i.e. the ones calculated with the solvent field obtained for the excited-state computed in the relaxed ground-state solvent field (ptSS-calculation).


Seeing this plot for the first time literally shocked me. The agreement of the one-shot approach with the experimental data is so apparent and convincing that I immediately starting looking for the fundamental flaw in the self-consistent approach. The latter apparently overestimated the shifts by about a factor of two. Did I say about? For ADC(2), its pretty much exactly a factor of two:


Can this be a coincidence? Exactly a factor of two? The lines are pretty much on top of each other. Yet, I'm pretty sure (as sure as it gets for a scientist) that this is indeed a coincidence, for a number of convincing reasons, which I will elaborate in the next post. And the best thing will be, that we can still learn from this coincidence!

So long,
Jan






Mittwoch, 5. Juli 2017

Boron-substituted aromatics - part two: thermochemical calculations

In my last post I described how I calculated vibrationally resolved UV/vis absorption spectra for a couple of boronaromatics and their acetonitrile (ACN) adducts and how this helped to resolve the mystery of their odd solvatochromism (solvent dependent absorption spectra). The one question that remained open was: Do DBI and DBA exclusively form 1:1 monoadducts with ACN or also the 1:2 diadducts? Since the latter are predicted to have essentially no absorption in the relevant spectral range, i.e., between 300 and 700 nm, I could neither confirm nor exclude their formation.

To answer this question, I started to conduct what was planned as a "brief" thermochemical analysis of formation of the respective mono- and diadducts. However, since the first results were inconclusive the I ended up employing a hierarchy of methods of increasing sophistication (and computational demand), which only eventually (at the very highest level of theory) cumulated in a good enough agreement with the experimental observations. I think the convergence of the results with respect to level of theory and employed basis-sets is quite instructive (without having much experience in quantum-thermochemistry), but at the same time too long and theoretical to be included in the article, and hence provides a nice topic for this blog. Lets get to it!

The initial plan was to just collect and investigate the results from the calculations I had already conducted to model the vibrationally resolved spectra. These include all optimizations and normal-mode analyses for naked DBI, DBA and DBP as well as their monoadducts and trans-diadducts, such that solely the respective calculations for ACN were missing. Having completed the latter and putting together all the numbers (computed at the same level of theory as the vibronic spectra, i.e., B3LYP-D3BJ/SVP) afforded the following picture:
Thermochemical data for the formation of the ACN mono- and diadduct of DBI, DBA and DBP (only trans-diadduct of DBI is shown) calculated at the B3LYP-D3BJ/SVP level of theory (using the COSMO solvation model to mimic the influence of the solvent ACN here and in all of the following results). The leftmost value termed "electronic" is computed from the electronic energies only. "ZPE" additionally includes the energy changes due to zero-point vibrations, which make the formation of additional B-N lewis-bonds more expensive compared to electronic energies only (since some energy goes into the zero-point vibrations of these new bonds). "RT" adds thermal corrections for room-temperature on top of that, which is the energy is is stored in the low-frequency (torsional and collective) modes that are thermally excited already at room temperature. ZPE and RT corrections are computed from the result of the normal-mode analyses of the molecules.
The good news is that at least the ordering suits the experimental obervsations with the DBI monoadduct attaining the lowest energy, followed by DBA and eventually DBP. The bad news is that all values are about 20 kJ/mol too low to explain the experiment. The negative values of the free energies of formation ("+RT" values) for all mono-adducts suggest a quantitative formation for all of them, even if only traces of ACN are present. Remembering the experimental observations (no changes in the spectrum of DBP even in pure ACN, weak influence for DBA at high ACN concentrations, major changes only for DBI), the values are apparently systematically too low.
Considering that thermochemical calculations are (in contrast to the excited-state calculations) quite sensitive to basis-set size and that I have employed the small SVP basis, this should not really be a surprise. The magnitude of the effect, however, did surprise me. The underlying problem is that small incomplete basis sets are susceptible to the so-called basis-set superposition error (BSSE). In a nutshell, BSSE is the result of an artificially constrained electronic wavefunction. Consequently, any calculation for a larger system (e.g. adducts, dimers) attain energies that are systematically lowered compared to respective calculation for the respective subs systems (their isolated constituents, mononers), since in the supermolecular calculation the wavefunction of a fragment A can also use the basis-functions on fragment B and vice versa.
Although there are corrections for the BSSE, the straightforward approach is typically to use a larger (augmented) basis set, which is what I did. To save time in the calculations with the larger (def2-TZVP) basis set, I skipped the optimization of the the geometries and used the ones from before, which is a quite common thing to do since geometries are not as sensitive as energies to basis-set size. To save even more time I used another common trick: I did not redo the normal-mode analyses for the ZPE and RT corrections but used the ones obtained with SVP, since they are also much less basis-set dependent. Such a combined approach is abbreviated B3LYP-D3BJ/def2-TZVP//SVP (behind  the double-slash follows the level used for the geometries/corrections).
Electronic energies obtained at the B3LYP-D3BJ/def2-TZVP//SVP level of theory.
With the larger basis set, the results are already in much better agreement with the experimental observations. With the main difference being a systematic shift to lower energies of formation by about 25 kJ/mol, also the energy of the DBP adduct has moved up slightly relative to the DBI and DBA adducts. Although the values do not yet fully agree with the experiment, we can at this point most certainly answer the initial question about the formation of diadduct: Judging from these results, their formation can most certainly be excluded. The values for the DBA and DBP diaddcuts (not shown) are very similar to those of DBI with all free energies of formation well above +30 kJ/mole.

However, I wasn't quite satisfied with the agreement and more importantly just curious how ab-initio methods would compare to the DFT results. So I eventually conducted additional SCS-MP2 and CEPA/1 (a coupled-cluster variant) calculations. To also improve on the structures, I re-optimized them at the SCS-MP2/SVP level of theory and later refined them at the SCS-MP2/def2-TZVP level of theory (this was JUST possible for the DBI diadduct). For the final energies at the SCS-MP2 and CEPA/1 levels of theory, I even conducted complete basis-set (CBS) extrapolations using the def2-SVP and def2-TZVP sets. This technique estimates the energy that would be obtained with a hypothetical, complete set of basis functions from the differences between the energies of two limited sets.  The free energies of formation for the monoadducts of DBI DBA and DBP are summarized in this final figure:
Summary of the free energies of formation of the monoadducts at (from left to right) increasing levels of theory.
SCS-MP2 with the small SVP basis yields an even stronger overbinding than B3LYP, most certainly for the very same reasons (mainly BSSE). This is not too surprising since correlated methods are said to be in general more prone to basis-set incompleteness errors than DFT.
The systematic overbinding is improved but not eliminated at the mixed approach with the larger basis (def2-TZVP//SVP), and becomes slightly worse at the fully consistent SCS-MP2/def2-TZVP level of theory. Note that the difference between the mixed SVP//def2-TZVP and fully consistent def2-TZVP approaches is quite small, whereas the mixed approach is MUCH cheaper.
The CBS extrapolation, which I would have expected to correct the systematic errors, actually worsens the agreement with the experiment. All energies of formation are again systematically reduced, such that even the DBP monoadduct is suggested to be stable at this level. I had heard that MP2 tends to overbind organic molecules, but this is a larger error than I expected. In particular since I have used the spin-component scaled variant, which should be less prone to these problems.
Only at the CEPA/1/CBS level of theory do the calculated free energies of formation ultimately agree with the observed behaviour: DBI showing quantitative monoadduct formation is weakly bound, DBA showing weak but significant monoadduct formation at high MeCN concentrations is energy-neutral, and DBP, which does not show any signs of adduct formation, is strongly endothermic. To make the coupled-cluster calculations possible for these already quite large systems, I employed the very handy domain-localized pair natural orbital (DLPNO) approximation implemented in Orca, and still burned a lot of computer time.

At the time, I found it quite instructive (and ultimately satisfying) to see how these numbers eventually converge to agree with the experimentally observed behaviour at the highest level of theory, and how all of the methods show the issues I had heard about, but never observed before. I hope you has a similar experience and can take something home. If you have any questions please leave a comment.

The next post will be about the investigation of the mechanism underlying the different fluorescence quantum yields of DBI, DBA and DBP.

So long!
Jan