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.

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!

Mittwoch, 2. Dezember 2015

excited-state solvent-field equilibration in pratice

Sketch of a solvent-field equilibration for
the cationic ethene dimer.
In my last post, I introduced the cationic ethene dimer shown on the right to illustrate and evaluate a solvent model for excited states. Despite its neat size and simplicity,  quantum-chemical calculations on this system were a bit tricky to converge onto the desired states. This is due to its open-shell (doublet) electronic structure exhibiting multiple, energetically almost degenerate SCF solutions. While these problems can be circumvented for the gas-phase calculation with one little trick, the actual solvent-field equilibration requires for more drastic measures, some of which I want to present in this post. Here are the three main problems and how I approached them:
  1. The SCF converges on an undesired solution: Without a PCM as well as for low dielectric constants and large basis set, the initial SCF converges onto the symmetrically charged (both ethenes + ½) solution, instead of the asymmetrically charged one I want to investigate.

    To convince the SCF algorithm to converge onto the asymmetrically charged solution, I use sequential jobs. In my favorite quantum-chemistry program, this can be triggered by adding a line “@@@” after the first input and appending the second one. The advantage of this is that results stored on disk, like e.g. MOs, state-densities and PCM surface-charges are available in the following step. I want to use the first job to create a set of asymmetric orbitals, which I employ as initial guess in the second one. For this purpose, I shorten the C-H bonds of one of the molecules by 0.1 A to introduce an asymmetry that triggers the SCF to converge onto the asymmetrical solution. Using the resulting orbitals as starting point for the SCF, I can give the second job the undistorted geometry (otherwise it would by default use the one from the first job). Starting from the asymmetrical guess orbitals, the second SCF also converges onto the desired solution, even for the now symmetric geometry. This trick was necessary for all gas-phase calculations, as well as for the calculations with large (cc-pVQZ) or augmented (aug-cc-pVDZ) basis sets, even if a PCM with high epsilon is used.

  2. The energetic ordering of the excited states switches: While the charge-inverse excited state is one of the higher lying states in the ground-state equilibrated solvent field (2.-4., depending on epsilon and the basis), it becomes the lowest one as soon as its solvent field is relaxed.

    Changes in the energetic ordering of the excited-states during excited state geometry optimizations are very common, if not inherent to the problem and I guess every theoretical photochemist knows the case. Using symmetry in the calculation can help, but does not necessarily solve the problem. Surprisingly few quantum-chemistry codes feature a decent root homing algorithm to identify excited-states via their overlap with the results from the previous step to guide the optimization. For the solvent-field optimizations of this predictable toy system the solution is rather trivial: Since I have not yet implemented a proper iteration loop, but use a script to generate sequential input files with a fixed number of iteration steps, I can just adapt the state_to_opt variable separately in each of the iteration steps. Nevertheless, I wanted to point out how practical root homing would be as a common feature in quantum-chemistry codes.

  3. The SCF "follows" the solvent field: The first SCF calculation in the solvent-field of the excited state converges onto a solution resembling the former excited-state wavefunction, since the latter is much lower in energy in the new, excited-state relaxed solvent field.

    This one was the trickiest one to tackle. Although I do per default use the orbitals of the previous step as a guess for the solvent-field iterations all of the available SCF algorithms slowly crawl to the solution of the energetically much lower state. Obviously, the excited-state solvent field is just too attractive for the positive charge. In my favorite quantum-chemistry program, however, there is a very nice feature which I want to introduce in a little more detail in the following. The maximum overlap method (MOM) is basically a kind of inter-step root-homing for the SCF, which was developed by Andrew Gilbert and Peter Gill for the calculation of excited-states wavefunctions. For this purpose, converged HF orbitals from a previous calculation are rotated in such a way that they resemble the excited state, e.g. via  "excitation" of an electron from the HOMO to the LUMO. One drawback of the method is that for this to succeed, the overlap between the ground- and respective excited state wavefunction has to be rather small. Hence, the approach does in general only work for dark excited states. If you are interested any further: I discussed the advantages and drawbacks of this method for the description of excited states in combination with coupled-cluster theory somewhat more extensively in a work on nitrobenzene. For the problem at hand, i.e. forcing the SCF to converge onto the local minimum provided in the guess orbitals, MOM works like a charm and I consider making its use the default for my equilibrium solvation approach.
After all, the results I obtained with these tricks are promising: If the solvent-fields are fully relaxed for the respective, correlated MP2 or ADC2 density, the energy difference between the ground- and charge-inverse excited state stay within 0.01 eV of the gas-phase value for the whole range of epsilon:
Energy difference between the solvent equilibrated ground (MP2/cc-pVTZ) and charge-inverse excited (ADC2/cc-pVTZ) states (left y-axis) as a function of the dielectric constant (x-axis). For clarity, I have subtracted the gas-phase value of 0.34 eV from the results. For relation, the total solute-solvent interaction energy for one of the states is given with respect to the right y-axis.

Since this post has already become quite long and the day quite old I will continue with a more detailed survey of the results as well as a description of the differences between the PTE, PTD and PTED schemes in my next post.

So long!

Dienstag, 24. November 2015

excited-state solvent models and a toy system

My latest projects are focused around a solvent model I extended and interfaced to the excited state methods developed in our group during my PhD. But before I write about the toy system I came up with to test my latest work, let me briefly introduce you to polarizable-continuum solvation models. PCMs basically compute a set of point charges on the molecular surface which depend on the molecular electrostatic potential (ESP) to mimic the interaction with solvent molecules. These (point) charges are added to the one-electron Hamiltonian (just like the nuclei) during the self-consistent field (SCF) calculation and updated in every iteration. Eventually, one obtains a wavefunction of a molecule in solution and the interaction between the point charges and the molecular ESP corresponds to the solute-solvent interaction. The single parameter used to describe the solvent (more parameters are used, e.g. for the cavity construction) is its macroscopic dielectric constant epsilon.
Visualization of the PCM surface-charges (blue -, red +) obtained for my beloved example nitrobenzene in its electronic ground state. As one would expect, the surface-charge close to the negatively charged nitro group (front right) is positive - just like the potential nitrobenzene would exhibit in a polar solvent.
 After finishing and extensively evaluating a so-called non-equilibrium (NEq) solvent model for vertical excitation energies against a set of experimental data for nitroaromatics (find it here), I have recently been working on the respective equilibrium variant. In a nutshell, non-equilibrium and equilibrium solvent models can be rationalized in analogy to the Franck-Condon (FC) principle:
  • The non-equilibrium case applies to vertical (i.e. very fast) processes like absorption and fluorescence. To be in accordance with the FC principle, you want to clamp the solvents nuclei, while relaxing its electronic degrees of freedom. Within a PCM, this is realized by using the optical dielectric constant (n²) instead of epsilon for a recomputation of the point charges w.r.t. the excited-state ESP. n² is nothing but the macroscopic polarizability ofa solvent at the frequency of visible light, whereas epsilon is the total polarizability (including a rearrangement of the solvent nuclei).
  • The equilibrium case applies to long-lived states, i.e. whenever you expect your systems nuclei to relax w.r.t. an excited state potential energy surface. Consequently, you should also relax the solvents nuclei, which is equivalent to recompute the surface charge for the new molecular charge distribution using the full dielectric constant just like for the ground state.
Schematic visualization of equilibrium and non-equilibirum solvation for the example of an excited-state proton transfer in quinolines. The proton transfer can be regarded as the molecules geometrical relaxation, which is accompanied by the solvent equilibration.

Although the explanation and also the equations for the non-equilibrium case are slightly more complicated due to the separation into fast (n²) and slow (epsilon) parts of the polarization, they are much simpler to implement. The reason being that n² of typical solvents is rather small one hence, one can apply perturbation theory an turn it into a correction for excitation energies. For details, see my paper.

The equilibrium case looks straightforward at first glance, but turns out much more complicated w.r.t. its implementation because of the way our excited-state methods work: We compute the Hartree-Fock (HF) ground-state wavefunction (in the form of molecular orbitals, short MOs) and subsequently use it as a basis for the calculation of excited-state wavefunctions and excitation energies with ADC (Algebraic-Diagrammatic Construction for the Polarization Propagator, a configuration-interaction type excited-state method).
Since the HF MOs contain the interaction with PCM surface charges just like they contain the interaction with the nuclei, one needs the PCM surface charges of the excited state before you do the initial HF calculation. Since this is not possible, one has to iterate between HF and ADC until the solvent field and the excited-state ESP are converged, like so:
  1. Standard HF calculation with PCM solvent model => MOs
  2. ADC calculation using HF MOs => excited-state density
  3. HF calculation in the "frozen" surface-charges for ES density=> new MOs
  4. ADC calculation with new MOs to obtain new excited-state density
  5. repeat from 3 until surface charges/energy are converged 
Eventually, I got the implementation working and the first numbers were looking promising. To check if the code does indeed work correctly, I came up with a simple toy system in which the solvated ground state is identical to an equilibrium solvated charge-transfer excited state: an asymmetrically charged, cationic ethene dimer with a distance of 1 nm:

The cationic ethene dimer as test system. The influence from the PCM is indicated by the boldness of the cavity. As soon as the iterations of the ES reaction field are converged, the system is in the same situation as in the beginning. Also, the non equilibrium situations with charge-tranfer (CT) state the in the field of the ground state (abbreviated  "0" in the scheme) (Nr. 2) and the ground state in the field of the CT state (converged Nr. 3) should be very comparable.
There is only a one practical problem: During the solvent-equilibration iterations (described above), the charge in the ground state jumps back and forth, causing the solvent-equilibration procedure to oscillate instead of converging. Obviously, the HF-SCF calculation in the frozen surface charges (point 3) of the charge-tranfer state converges to the energetically much more favorable solution with the positive charge sitting the ethene in the negatively charged cavity (No surprise, this is exactly what the SCF algorithm is supposed to do). Employing the MOs of the previous iteration step as starting point in the subsequent SCF cycles is not enough do do the trick, the other solution seems too low energetically.
How I was nevertheless able to converge the calculations using a number of tricks will be presented along with some more details on the system and preliminary results in my next post very soon.

So long!

Freitag, 9. Januar 2015

publishing in JPC

Publishing can be kind of annoying. In particular if journals outsource the last quanta of work required to convert a manuscript prepared with latex into a journal article in PDF format to the authors.
JPC recently decided to require the authors to provide references in manuscript with article titles in title case as well as some other changes. To save at least some authors from the pain of  doing this by hand or searching the internet for the tools, here they are:
1) Install the achemso package and use:
2) Add these (hopefully self-explanatory) lines in the referenced .bib file:
  ctrl-Article-Title  = "yes",
  ctrl-etal-number    = "10",
  ctrl-max-authors    = "10",
3) Use the perl script provided and described here:
to change all the articles titles in the .bib file to title case.
4) Write an angry mail to ACS and complain.
So long!