Montag, 24. Juli 2017

ADC/SS-PCM at glance! - part two

This post is a follow up on my last post, in which I discussed the accuracy of the ADC/SS-PCM approach for a number of push-pull systems. So if you haven't read part one yet, please do so before you continue.
Part one ended with the finding that solvent effects were significantly over-estimated for the type of molecule under investigation. More specifically, the shift of the fluorescence energy between non-polar cyclohexane (chx) and polar acetonitrile (acn) solution calculated with ADC(2)/SS-PCM was exactly twice as large as the experimental numbers - for almost all of the systems. Even more surprisingly, the theoretically ill-defined one-shot approach (quick reminder: one-shot means that I use the result from the first step of the solvent-field iterations) seemingly provides a much better agreement with the experiment than the converged solvent-field:

I ended that first part with the promise to explain why I'm sure that this is a coincidence, what/how we can learn from it, and what underlying cause is responsible for the problem. So let's go:

Why is the fact that the calculation is of by almost exactly a factor of two in 5 out of 6 molecules for which there is experimental data a (more or less) lucky coincidence and not a simple bug (factor of two missing somewhere in the code)? I think there is a number of reasons, the most important of which is the crude level of theory that has been applied. First of all, we've used the same gas-phase optimized omega-PBE/6-31+g* geometries for all of the ADC/SS-PCM calculations. Hence, we are neglecting all structural effects of the the solvent stabilization. While this is probably okay for the weaker solvents (chx), it will most certainly affect the results in acn and thus modulate the chx to acn shifts. Secondly, the ADC calculations are carried out with a really small, non-polarized split-valence basis set (def2-SV), which is simply to limit the computational demands for these already quite large molecules. In calculations exploring this issue for ZMSO2-14 with the partially polarized def2-SV(P) and def2-SVP, the calculated shifts decreased by about 0.1 eV and the suspicious factor of two (actually 1.97) becomes a less suspicious factor of 1.87. (Mind that def2-SVP is still a rather small basis). Thirdly, the molecules are all very similar, such that it is not really surprising to find the same systematic error for 5 out of 6 of them. So far, I have never observed something even remotely similar for any of the other (push-pull) systems I have computed with this method. After all, I'm convinced that the factor of two is a coincidence.

But if it is a coincidence, what can we learn from it?
The fact that the error is so suspiciously constant just means that it is very systematic. Systematic errors are much nicer than statistic ones, because its very straightforward to correct them. In this particular case, the correction is simply dividing the shifts by two. Inspecting the plot of the results above, you will find that the results from the converged solvent field divided by two (green line) reproduce the experiment even better than the one-shot results. Or in other words: Although the one-shot approach is much closer to the experiment in absolute numbers, the converged results follow the experimental trend more closely, i.e., their statistical error is smaller. The good news is that after all, this shows that the solvent-field iterations indeed improve the results compared to the one-shot approach. This was just difficult to see because of a large systematic error. Eventually, we are left with the remaining question:

What is the reason for this large systematic error?
As I already mentioned on a number of occasions, ADC(2) seems to over-stabilize states with large density shifts, such as CT states. I think this due to too large orbital-relaxation effects. Orbital relaxation is the response of the molecular density to the primary electron transfer during an excitation. While this is quite difficult to explain in words, it is quite apparent from a comparison of the the electron and hole densities of an excitation (initial electron transfer) to the total attachment and detachment densities (including orbital relaxation). Here I have calculated and visualized all of these for  ZMSO2-14:

While the electron (top left) and hole (top right) densities appear to be rather independent (positions and sizes of the visible blobs are uncorrelated), they show that in this excited state an electron from the nitrogen lone-pair is excited into a pi* orbital. The attachment (bottom left) and detachment (bottom right) densities are, in contrast to that, clearly not independent, but correlated. Wherever there is a positive contribution in the hole/attachment density (e.g. the extra electron in the pi-system in the left part of the molecule), one can find negative blue (orbital-relaxation) contributions at the same place in the sigma system in the detachment density. Vice versa, wherever density vanishes, e.g. from the nitrogen lone-pair, there are positive relaxation contributions in the attachment density, which are clearly not there in the primary electron density. This response of the density to the initially excited electron/excitation-hole is exactly what I understand to be orbital relaxation. To have an even more intuitive picture, I should probably go ahead and plot just the difference between the electron/hole and  attachment/detachment densities, but for now the pictures above must suffice.

However, while these pictures are nice to illustrate the effect, one needs a more quantitative measure to see how strong orbital relaxation is in these molecules, and to compare it to other molecules. For this purpose, its advisable to look at the so-called promotion numbers, which can be seen as integrals over the attachment/detachment densities, or in other words the number of electrons that is involved in/shifted around during the excitation. A typical locally excited state would have a promotion number of around 1.5, meaning that in addition to the initially excited electron, a total of 0.5 electrons make up the orbital relaxation. For charge-transfer states which do in general have stronger orbital relaxation (because more charge is shifted around), these numbers are closer to or maybe even larger than two. Let us now take a look how the promotion numbers of ZMS-14 and ZMSO2-14 evolve during the solvent-field iterations in chx, diethylether (eth), dichloromethane (dcm) and acn (please focus only on the reddish and blueish lines for now):
Plot of the promition numbers of the weak and strong push-pull systems ZMS-14 and ZMSO2-14 as well as the TADF chromophore termed F1 calculated during the solvent-field iterations in chx, eth, dcm and acn at the ADC(2)/SS-PCM/SV level of theory. While the iterations in chx converge in 4-5 steps (here including the vertical excitation as step 1), it takes 6-11 steps to converge in the polar solvent acn. Beginning at roughly the same value of 2 in all solvents for ZMS and ZMSO2-14, the promotion numbers hardly change for ZMS in chx, while there is a large increase to about 2.6 for in ZMSO2 in the polar solvents. For F1, the changes are much smaller and the promotion numbers are virtually unaffected by the solvent-field.

Apparently, there is a significant increase of the promotion numbers and thus the amount of orbital relaxation during the solvent-field iterations in polar solvents, even for the weaker push-pull systems. The promotion numbers increase to unphysically large values of 2.5 and larger for ZMSO2-14 in polar solvents and reach 2.2 even in chx. In general, I was surprised that the promotion number change at all during the iterations, which is something I have never observed before. I have investigated a number of large push-pull systems designed for TADF with the very same methodology and small systems such as DMABN with ADC2 and ADC3/SS-PCM, for which I obtained much better agreement for the calculated chx to acn shifts. Also, in all of these examples, the promotion numbers hardly ever change during the iterations, as evident from the the representative example termed F1 shown in the figure above as greenish lines (the molecule is taken form this article).

A similar problem with unphysically large promotion numbers accommodated by faulty excitation energies at the ADC(2) level of theory was reported by my friend and colleague Felix in an investigation of iridium complexes. In his case, the problem appeared in the gas-phase calculation and was corrected at the ADC(3) level of theory.

After all, I tend to think this is an ADC(2) problem that is amplified/unveiled during the solvent-field iterations.  Consequently, one should carefully check the evolution of the promotion numbers during the solvent field iterations (they can be obtained by activating "state_analysis = true" and "nto_pairs = 2" in the $rem block of the input file). If there are large changes, one should be extra careful with the results of the method.

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,

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!

Montag, 19. Juni 2017

Q-Chem 5.0 with ADC/SS-PCM has been released!

While I'm still in the process of writing the second post about boron-subtituted aromatics, let me quickly mention that Q-Chem 5.0 has recently been released. 

Why is this special, you may ask? It is, because it contains the ADC/SS-PCM approach that I have developed during my PhD and that has been discussed numerous times in this blog. With this approach, you can accurately model your favourite excited states and transitions from (emission) and to (absorption) them in solution at the ADC level of theory at up to third order in perturbation theory, i.e., ADC(3), a very accurate benchmark method.
You can also employ e.g. the very efficient riSOS-ADC(2) approach and investigate quite large molecules (say: materials) with up to 500 basis functions. Since ADC is, in contrast to TD-DFT, an ab-initio method, it does provide complete and physically sound description of the electrostatics of the systems as well as its interaction with the solvent/dielectric environment. We compared the ADC2/SS-PCM and ADC3/SS-PCM approaches already in the publication presenting the method.

I'm currently in the final steps of publishing another article about a project with my friend and colleague Felix (find his blog in the menu), which turned out to be a nice showcase for the model. Turns out I just made this table-of-contents graphic, which I want to share with you:

It shows the excitation-hole (in blue) and excited electron (in red) of the lowest excited singlet state (S1) of an already quite large push-push system that we studied in the article. In the top left corner, it shows the excited electron computed with the SS-PCM simulating the non-polar solvent cyclohexane, and in the bottom right corner with parameters for the polar solvent acetonitrile. From this quite intuitive visualization it becomes clear how the electron-hole or in other word charge separation (the distance between the blue and red blops) increases as it is stabilized by the polar solvent and, more importantly, how this affects the properties of the system. I'll post a link to the article as soon as it appears online. (*Link)

A brief description of the theory behind the ADC/SS-PCM model and its capabilities can be found in the Q-Chem 5.0 online manual, which you can find here.

Please note that very unfortunately, due to a last minute change of some defaults of the PCM solvent model that was not communicated very well, the description of ADC/SS-PCM in the in the manual is incomplete concerning one detail: For all calculations with the model the line "ChargeSeparation Marcus" has to be included in the $pcm block of the input file. This bug will be fixed with the next release (5.0.1) in July.

So long,

Dienstag, 6. Juni 2017

A story about boron-substituted aromatics - part one

Another project I have been working on last year was concerned with the quantum-chemical investigation of a bunch of boron-containing aromatics that have been synthesized and studied in the group of Prof. Wagner in Frankfurt. This project is interesting for a number of reasons, the most story-worthy of which is that Prof. Wagners lecture "Allgemeine und Anorganische Chemie" marked the very beginning of my academic career in October 2005. This cooperation was a nice opportunity to "turn the spit" and explain aspects of photochemistry to the Professor who introduced me to chemistry as a scientific discipline some 10 years ago. But also from a scientific point of view this project is exciting. These boron compounds do in general have a number of quite unique photophysical properties (some e.g. exhibit temperature-dependent delayed fluorescence with a curios solvent-dependency), and the project turned out to provide the opportunities to try out a couple of methods I had wanted to try out for a while. The paper itself can be found here. In the following I want to shed some light onto aspects that didn't get too much attention in the brevity of a scientific article.

Two of the four investigated molecules can be derived from anthracene and pentacene by replacing the middle carbons with boron atoms and are named accordingly: Dibora-anthracene (DBA) and dibora-pentacene (DBP). Diborinine (DBI) consists of two antiaromatic biphenylene subunits bridged via the dibora-benzylic motif, while iso-DBP is an asymetric variant of DBP, in which the boron-containing ring is shifted to one side.

The initial motivation for the project was to find an explanation for the surprisingly different fluorescence quantum yields of these closely related molecules. While isoDBP and DBP exhibit high quantum yields of 90% and 50%, respectively, DBA is hardly fluorescent (2%) and DBI completely dark. But let us postpone this question to one of the upcoming posts about this project and start  off with another question that popped up while I was inspecting the absorption spectra of these compounds in various solvents: DBI and to some extent also DBA exhibit a huge influence of some solvents onto the shape of the absorption spectra. Specifically, the main peaks of the absorption spectrum of DBI in non-polar cyclohexane (CHX) are blue-shifted and almost vanish in acetonitrile (ACN), while this is not the case in other polar solvents. We concluded that there has to exist an specific interaction between the lewis-basic solvent ACN and the lewis-acidic boron-atoms in DBI, or in other words that ACN behaves as a non-innocent solvent.

As a first step to confirm this hypothesis, I computed the structures and electronic energies of one mono- and two di-adducts (cis and trans) with a cheap and fast (exploratory) methodology (B3LYP-D3BJ/SVP, today I would use PBEh-3c). The resulting structures are shown together with the structure of bare DBI in the following picture:

Calculated ground-state minimum structures of bare DBI (a), the ACN-monoadduct (b), the trans-diadduct (c) and the cis-diadduct (d). Already from these cheap, approximate calculations it was evident that only the mono- and trans-diadduct are energetically feasible.
For the energetically feasible adducts of DBI and DBA, I subsequently calculated vibrationally resolved absorption spectra, which can be directly compared to the experimental spectra. For this purpose, I used the same methodology, namely TD-B3LYP with a small SVP basis, since it is fast and due to a surprisingly stable inherent error compensation typically also quite accurate (but also not reliable).

The calculation of vibrationally resolved spectra is one of the things I wanted to try out for a while now and hence, I'll briefly explain the hows and whys in the following. To make this type of calculation possible for such a large molecule, one has to employ a drastic-sounding approximation with a very long name: Independent-mode-shifted-harmonic-oscillator (IMDHO)-approximation. This is necessary to reduce the untraceable problem of knowing the shape of all potential-energy surfaces of all excited-states of interest around the initial (ground-state) geometry to something actually doable. Using IMDHO, the problem at hand is reduced to knowing the vibrational frequencies (normal modes) of the ground-state and the gradients along them in each of the excited states of interest. The assumptions required to get there are:
  1. All modes can be approximated as a harmonic oscillator. (Common and not too bad for the ground state, crude for excited states)
  2. The vibrational frequencies in the excited states are so similar to those of the ground state than we can treat them as being identical (Very crude)
From these assumptions, it follows that the only difference between the ground- and excited-state PES is the position of the respective minima, which is why its called "shifted"HO. Since we are in the harmonic approximation, all we need to know this shift w.r.t. to ground-state minimum are the gradients along these normal modes in the excited states of interest. Hence, to obtain the vibrationally resolved absorption spectrum within the IMDHO approximation, one first computes the ground state vibrational frequencies (normal-modes), and subsequently the gradient along these normal-modes for each of the excited-states. Having these quantities, we (actually the handy tool ORCA_ASA does that for us) can build the approximate PES and compute the coupling between the electronic and vibrational excitations, yielding the spectra, which are shown together with the absorption spectra recorded in various mixtures of CHX and ACN in the following picture:

Comparison of measured (top) and calculated (bottom) absorption spectra of DBI and DBA and their respective ACN mono- and diadducts. Calculations of the vibrationally resolved spectra were carried out at the (TD)B3LYP/SVP level of theory employing the so-called independent-mode-shifted-harmonic-oscillator (IMDHO)-approximation. Considering the crude IMDHO approximation and the poor level of electronic structure theory, the agreement between experiment and calculation is surprisingly good.

Due to the very reasonable agreement between experiment and calculation, in particular for DBI, we can doubtlessly identify the ACN-monoadduct in the spetra recorded in ACN. However, it is difficult to say this with certainty since the trans-diadduct is essentially dark (no absorption) and would not show up in the spectra. Thus, to further investigate the issue I conducted a thorough thermochemical analysis of the formation of the ACN adducts for DBA, DBI and DBP, which I will present and discuss in the upcoming post.

So long!

Freitag, 26. Mai 2017

Reporting Back

Fellow scientists,

it has been quiet here for way over a year now, and I feel I'm owing an explanation: After I was awarded a Feodor-Lynen fellowship early in 2016 (thank you very much for this opportunity, Alexander-von-Humboldt Foundation!), I spent much of the year preparing to move to the other side of the planet to become a Postdoc in Peter Schwerdtfegers research group. On top of that my daughter was born in February, which did the rest to keep me from posting here. But now that we are settled in and out of the worst baby-issues I want to keep this blog alive. For this purpose, I'll first write a couple of posts about articles I've published since my last contribution and eventually about my current projects in the Schwerdtfeger group, namely the development of a polarizable forcefield for Methyl-ammonium lead iodide and the generation of pseudopotentials for super-heavy elements.

Let me begin this series with a project that I have already mentioned in my last three posts: The work on self-consistent, state-specific PCM equilibrium solvation. This self-consistent variant of the SS-PCM approach constitutes a theoretical framework to treat "long-lived" excited states in solution and completes the developments started during my PhD. It allows to equilibrate the excited-state wavefunction with its self-induced polarization, which is the way to go whenerver an excited-states lives for a couple of picoseconds ("long-lived"). Since this is the case for most of the experimentally accessible properties and/or processes originating from excited states, this is a quite important capability. Combined with the perturbation-theoretical variant of the state-specific approach that I've implemented during my PhD, these models enable a calculation and investigation of virtually all photochemical processes in solution, like e.g. ground- and excited state absorption, emission as well as photochemical reactivity. The interface works with all orders and variants of the Algebraic-Diagrammatic Construction (ADC) method developed in Andreas Dreuws group. The article on the topic eventually appeared in PCCP in early 2017. It is available in Q-Chem from version 4.4.2, but documented in the manual starting only from version 5 (release date 1st of June), where you can also find a brief introduction into the theory. It follows a brief summary of the article:

We demonstrated that a general, state-specific PCM in  combination with an ADC(2) or ADC(3) description of the solute’s electronic structure provides excellent energies of solvent-relaxed states and vertical transitions in solution. Since we limited our approach to the state-specific picture, where the solvent effect enters the quantum-chemical calculation only via one-electron charge-density Coulomb integrals, the underlying ADC  equations are unmodified and the model can be used in combination with any flavor of ADC. Moreover, due to this clear separation between quantum-chemical part of the calculation and the solvent model, the results are presumably of general validity for both, the SS-PCM approach as well as the excited-state method.
To validate ADC/SS-PCM, a set of symmetric, ionized dimers was employed, whose lowest energy CT states are formally identical to the broken-symmetry ground state. Computing the latter using the well-established MP/PTE approach and comparing the results to the CT state computed using ADC/SS-PCM, the  deviation between the two methods was found to be 0.02 eV over a wide range of dielectric constants. This holds even for the challenging nitromethane case where electron correlation effects are large.
Ultimately, ADC/SS-PCM was employed to investigate solvent-relaxed potential energy surfaces of 4-(N,N)-dimethylamino-benzonitrile. The agreement with experimental fluorescence data is excellent for the LE state under all circumstances, in particular with ADC(2). For the CT state, however, it was demonstrated that an intra-molecular twisting coordinate has to be considered in detail to achieve a similar agreement. In general, the agreement of ADC(2)/SS-PCM is consistently better than for ADC(3) for fluorescence energies. For the relative energies of the LE and CT states, however, only ADC(3) yields results that are consistent with the experimental observation of dual fluorescence in polar solvents but not in non-polar ones. This was traced back to an underestimation of the energy of the CT state compared to the LE state at second order of perturbation theory.

In my next post, I'll write about an article that originated from a cooperation with the experimental group of Prof. Wagner in Frankfurt, who basically introduced me to chemistry at university level.

So long!

Freitag, 8. Januar 2016

A summary of recent publications and their connection to equilibrium solvation - happy 2016!

Let me begin 2016 with a summary of a couple of papers that have been accepted for publication in recent weeks before I use one of them to lead over to the ongoing work I reported in the last two posts.

A few weeks ago, my wife Steffi and I celebrated our first "Mewes & Mewes et al" paper making it into PCCP. It offers a fresh perspective onto the electronic structure of excitons in poly(para-phenylene vinylene) or short PPV, which is something like the guinea pig of the organic electronics community. We studied PPV using highly accurate ab-initio quantum-chemical methods (ADC of up to third order) in combination with the very handy wavefunction analysis routines developed by Felix and Steffi.

Furthermore, two other papers to which I contributed were published recently:
  • Firstly, there is this work in PNAS on signatures and control of strong-field dynamics in a complex (i.e. molecular) system. My contribution to this work were quantum-chemical insights, which eventually helped Kristina and her co-workers to set up a theoretical model to simulate the exposure and response of molecules to strong laser pulses.
  • Secondly, we finally managed to publish the second paper on our  non-equilibrium PCM in Q-Chem. This second article is concerned with unexpected discrepancies between two alternative schemes of separating the fast and slow components of the polarization (I explained this in one of my recent posts). Zhi-Qiang found that the so-called Pekar and Marcus partitioning of the polarization, which should formally lead to identical results, yield significantly different results. In the article, he traces this back to the discretization of the PCM equations for the actual, numerical implementation. Eventually, he demonstrates that SSVPE (one of the three common flavours of PCMs besides the conductor-like approximation (C-PCM) and the integral-equation formalism (IEF-PCM)) exhibit the largest deviations (they are still rather small and in the ballpark of 0.01~eV)
Interestingly, this last finding directly relates to my current work on equilibrium solvation models. I fortuitously found very similar results for C-PCM, IEF-PCM and SSVPE while doing a little sanity test of my solvent-field equilibration code. For this purpose, I combined the perturbative non-equilibrium formalism with the new, self-consistent equilibrium solvation functionality. My expectation was that the non-equilibrium corrections for any state should become zero during the solvent-field equilibration for the respective state. Why? Because the non-equilibrium correction constitutes a perturbative estimate of how the relaxation of the fast component of the polarization with respect to a certain excited state would reduce its energy. But obviously, the energy should not be changed if the solvent field is already fully equilibrated for the respective state.
Surprisingly, the non-equilibrium terms do become zero only with C-PCM and IEF-PCM, but not with SSVPE. The deviations I find are in the same ballpark as the differences between the Pekar and Marcus schemes. Currently, I'm in the process of writing up these results and hence, expect more updates the in near future.

So long!