Category Archives: TD-DFT

Natural Transition Orbitals (NTOs) Gaussian


The canonical molecular orbital depiction of an electronic transition is often a messy business in terms of a ‘chemical‘ interpretation of ‘which electrons‘ go from ‘which occupied orbitals‘ to ‘which virtual orbitals‘.

Natural Transition Orbitals provide a more intuitive picture of the orbitals, whether mixed or not, involved in any hole-particle excitation. This transformation is particularly useful when working with the excited states of molecules with extensively delocalized chromophores or multiple chromophoric sites. The elegance of the NTO method relies on its simplicity: separate unitary transformations are performed on the occupied and on the virtual set of orbitals in order to get a localized picture of the transition density matrix.

[1] R. L. Martin, J. Chem. Phys., 2003, DOI:10.1063/1.1558471.

In Gaussian09:
After running a TD-DFT calculation with the keyword TD(Nstates=n) (where n = number of states to be requested) we need to take that result and launch a new calculation for the NTOs but lets take it one step at a time. As an example here’s phenylalanine which was already optimized to a minimum at the B3LYP/6-31G(d,p) level of theory. If we take that geometry and launch a new calculation with the TD(Nstates=40) in the route section we obtain the UV-Vis spectra and the output looks like this (only the first three states are shown):

Excitation energies and oscillator strengths:

Excited State 1: Singlet-A 5.3875 eV 230.13 nm f=0.0015 <S**2>=0.000
42 -> 46 0.17123
42 -> 47 0.12277
43 -> 46 -0.40383
44 -> 45 0.50838
44 -> 47 0.11008
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-KS) = -554.614073682
Copying the excited state density for this state as the 1-particle RhoCI density.

Excited State 2: Singlet-A 5.5137 eV 224.86 nm f=0.0138 <S**2>=0.000
41 -> 45 -0.20800
41 -> 47 0.24015
42 -> 45 0.32656
42 -> 46 0.10906
42 -> 47 -0.24401
43 -> 45 0.20598
43 -> 47 -0.14839
44 -> 45 -0.15344
44 -> 47 0.34182

Excited State 3: Singlet-A 5.9254 eV 209.24 nm f=0.0042 <S**2>=0.000
41 -> 45 0.11844
41 -> 47 -0.12539
42 -> 45 -0.10401
42 -> 47 0.16068
43 -> 45 -0.27532
43 -> 46 -0.11640
43 -> 47 0.16780
44 -> 45 -0.18555
44 -> 46 -0.29184
44 -> 47 0.43124

The oscillator strength is listed on each Excited State as “f” and it is a measure of the probability of that excitation to occur. If we look at the third one for this phenylalanine we see f=0.0042, a very low probability, but aside from that the following list shows what orbital transitions compose that excitation and with what energy, so the first line indicates a transition from orbital 41 (HOMO-3) to orbital 45 (LUMO); there are 10 such transitions composing that excitation, visualizing them all with canonical orbitals is not an intuitive picture, so lets try the NTO approach, we’re going to take excitation #10 for phenylalanine as an example just because it has a higher oscillation strength:

%chk=Excited State 10: Singlet-A 7.1048 eV 174.51 nm f=0.3651 <S**2>=0.000
41 -> 45 0.35347
41 -> 47 0.34685
42 -> 45 0.10215
42 -> 46 0.17248
42 -> 47 0.13523
43 -> 45 -0.26596
43 -> 47 -0.22995
44 -> 46 0.23277

Each set of NTOs for each transition must be calculated separately. First, copy you filename.chk file from the TD-DFT result to a new one and name it after the Nth state of interest as shown below (state 10 in this case). NOTE: In the route section, replace N with the number of the excitation of interest according to the results in filename.log. Run separately for each transition your interested in:

#chk=state10.chk

#p B3LYP/6-31G(d,p) Geom=AllCheck Guess=(Read,Only) Density=(Check,Transition=N) Pop=(Minimal,NTO,SaveNTO)

0 1
--blank line--

By requesting SaveNTO, the canonical orbitals in the state10.chk file are replaced with the NTOs for the 10th excitation, this makes it easier to plot since most visualizers just plot whatever set of orbitals they read in the chk file but if they find the canonical MOs then one would need to do some re-processing of them. This is much more straightforward.

Now we format our chk files into fchk with the formchk utility:

formchk -3 filename.chk filename.fchk
formchk -3 state10.chk state10.fchk

If we open filename.fchk (the file where the original TD-DFT calculation is located) with GaussView we can plot all orbitals involved in excited state number ten, those would be seven orbitals from 41 (HOMO-3) to 47 (LUMO+2) as shown in figure 1.

Figure 1. Canonical orbitals involved in the 10th excited state according to the TD-DFT calculation

If we now open state10.fchk we see that the numbers at the side of the orbitals are not their energy but their occupation number particular to this state of interest, so we only need to plot those with highest occupations, in our example those are orbitals 44 and 45 (HOMO and LUMO) which have occupations = 0.81186; you may include 43 and 46 (HOMO-1 and LUMO+1, respectively) for a much more complete description (occupations = 0.18223) but we’re still dealing with 4 orbitals instead of 7.

Figure 2. Natural Transition Orbitals for Phenylalanine. Orbital 44 (particle) and Orbital 45 (hole) exhibit the largest occupations for Excited State No. 10

The NTO transition 44 -> 45 is far easier to conceptualize than all the 10 combinations given in the canonical basis from the direct TD-DFT calculation. TD-DFT provides us with the correct transitions, NTOs just paint us a picture more readily available to the chemist mindset.

NOTE: for G09 revC and above, the %OldChk option is available, I haven’t personally tried it but using it to specify where the excitations are located and then write the NTOs of interest into a new chk file in the following way, thus eliminating the need of copying the original chk file for each state:

%OldChk=filename.chk
%chk=stateN.chk

NTOs are based on the Natural Hybrid orbitals vision by Löwdin and others, and it is said to be so straightforward that it has been re-discovered from time to time. Be that as it may, the NTO visualization provides a much clearer vision of the excitations occurring during a TD calculation.

Thanks for reading, stay home and stay safe during these harsh days everyone. Please share, rate and comment this and other posts.

The HOMO-LUMO Gap in Open Shell Calculations. Meaningful or meaningless?


The HOMO – LUMO orbitals are central to the Frontier Molecular Orbital (FMO) Theory devised by Kenichi Fukui back in the fifties. The central tenet of the FMO theory resides on the idea that most of chemical reactivity is dominated by the interaction between these orbitals in an electron donor-acceptor pair, in which the most readily available electrons of the former arise from the HOMO and will land at the LUMO in the latter. The energy difference between the HOMO and LUMO of any chemical species, known as the HOMO-LUMO gap, is a very useful quantity for describing and understanding the photochemistry and photophysics of organic molecules since most of the electronic transitions in the UV-Vis region are dominated by the electron transfer between these two frontier orbitals.

But when we talk about Frontier Orbitals we’re usually referring to their doubly occupied version; in the case of open shell calculations the electron density with α spin is separate from the one with β spin, therefore giving rise to two separate sets of singly occupied orbitals and those in turn have a α-HOMO/LUMO and β-HOMO/LUMO, although SOMO (Singly Occupied Molecular Orbital) is the preferred nomenclature. Most people will then dismiss the HOMO/LUMO question for open shell systems as meaningless because ultimately we are dealing with two different sets of molecular orbitals. Usually the approach is to work backwards when investigating the optical transitions of a, say, organic radical, e.g. by calculating the transitions with such methods like TD-DFT (Time Dependent DFT) and look to the main orbital components of each within the set of α and β densities.

To the people who have asked me this question I strongly suggest to first try Restricted Open calculations, RODFT, which pair all electrons and treat them with identical orbitals and treat the unpaired ones independently. As a consequence, RO calculations and Unrestricted calculations vary due to variational freedom. RO calculations could yield wavefunctions with small to large values of spin contamination, so beware. Or just go straight to TDDFT calculations with hybrid orbitals which include a somewhat large percentage of HF exchange and polarized basis sets, but to always compare results to experimental values, if available, since DFT based calculations are Kohn-Sham orbitals which are defined for non-interacting electrons so the energy can be biased. Performing CI or CASSCF calculations is almost always prohibitive for systems of chemical interest but of course they would be the way to go.

Mg²⁺ Needs a 5th Coordination in Chlorophylls – New paper in IJQC


Photosynthesis, the basis of life on Earth, is based on the capacity a living organism has of capturing solar energy and transform it into chemical energy through the synthesis of macromolecules like carbohydrates. Despite the fact that most of the molecular processes present in most photosynthetic organisms (plants, algae and even some bacteria) are well described, the mechanism of energy transference from the light harvesting molecules to the reaction centers are not entirely known. Therefore, in our lab we have set ourselves to study the possibility of some excitonic transference mechanisms between pigments (chlorophyll and its corresponding derivatives). It is widely known that the photophysical properties of chlorophylls and their derivatives stem from the electronic structure of the porphyrin and it is modulated by the presence of Mg but its not this ion the one that undergoes the main electronic transitions; also, we know that Mg almost never lies in the same plane as the porphyrin macrocycle because it bears a fifth coordination whether to another pigment or to a protein that keeps it in place (Figure 1).

TOC_final

Figure 1 The UV-Vis spectra of BCHl-a changes with the coordination state

During our calculations of the electronic structure of the pigments (Bacteriochlorophyll-a, BChl-a) present in the Fenna-Matthews-Olson complex of sulfur dependent bacteria we found that the Mg²⁺ ion at the center of one of these pigments could in fact create an intermolecular interaction with the C=C double bond in the phytol fragment which lied beneath the porphyrin ring.

fig3

Figure 2 Mg points ‘downwards’ upon optimization, hinting to the interaction under study

 

This would be the first time that a dihapto coordination is suggested to occur in any chlorophyll and that on itself is interesting enough but we took it further and calculated the photophysical implications of having this fifth intramolecular dihapto coordination as opposed to a protein or none for that matter. Figure 3 shows that the calculated UV-Vis spectra (calculated with Time Dependent DFT at the CAM-B3LYP functional and the cc-pVDZ, 6-31G(d,p) and 6-31+G(d,p) basis sets). A red shift is observed for the planar configuration, respect to the five coordinated species (regardless of whether it is to histidine or to the C=C double bond in the phytyl moiety).

 

Fig6

Figure 3 CAMB3LYP UV-VIS spectra. Basis set left to right cc-PVDZ, 6-31G(d,p) and 6-31+G(d,p)

Before calculating the UV-Vis spectra, we had to unambiguously define the presence of this observed interaction. To that end we calculated to a first approximation the C-Mg Wiberg bond indexes at the CAM-B3LYP/cc-pVDZ level of theory. Both values were C(1)-Mg 0.022 and C(2)-Mg 0.032, which are indicative of weak interactions; but to take it even further we performed a non-covalent interactions analysis (NCI) under the Atoms in Molecules formalism, calculated at the M062X density which yielded the presence of the expected critical points for the η²Mg-(C=C) interaction. As a control calculation we performed the same calculation for Magnoscene just to unambiguously assign these kind of interactions (Fig 4, bottom).

Fig4.jpg

Figure 4 (a), (b) NCI analysis for Mg-(C=C) interaction compared to Magnesocene (c)

This research is now available at the International Journal of Quantum Chemistry. A big shoutout and kudos to Gustavo “Gus” Mondragón for his work in this project during his masters; many more things come to him and our group in this and other research ventures.

Photosynthesis and Singlet Fission – #WATOC2017 PO1-296


If you work in the field of photovoltaics or polyacene photochemistry, then you are probably aware of the Singlet Fission (SF) phenomenon. SF can be broadly described as the process where an excited singlet state decays to a couple of degenerate coupled triplet states (via a multiexcitonic state) with roughly half the energy of the original singlet state, which in principle could be centered in two neighboring molecules; this generates two holes with a single photon, i.e. twice the current albeit at half the voltage (Fig 1).

Imagen1

Jablonski’s Diagram for SF

It could also be viewed as the inverse process to triplet-triplet annihilation. An important requirement for SF is that the two triplets to which the singlet decays must be coupled in a 1(TT) state, otherwise the process is spin-forbidden. Unfortunately (from a computational perspective) this also means that the 3(TT) and 5(TT) states are present and should be taken into account, and when it comes to chlorophyll derivatives the task quickly scales.

SF has been observed in polyacenes but so far the only photosynthetic pigments that have proven to exhibit SF are some carotene derivatives; so what about chlorophyll derivatives? For a -very- long time now, we have explored the possibility of finding a naturally-occurring, chlorophyll-based, photosynthetic system in which SF could be possible.

But first things first; The methodology: It was soon enough clear, from María Eugenia Sandoval’s MSc thesis, that TD-DFT wasn’t going to be enough to capture the whole description of the coupled states which give rise to SF. It was then that we started our collaboration with SF expert, Prof. David Casanova from the Basque Country University at Donostia, who suggested the use of Restricted Active Space – Spin Flip in order to account properly for the spin change during decay of the singlet excited state. A set of optimized bacteriochlorophyll-a molecules (BChl-a) were oriented ad-hoc so their Qy transition dipole moments were either parallel or perpendicular; the rate to which SF could be in principle present yielded that both molecules should be in a parallel Qy dipole moments configuration. When translated to a naturally-occurring system we sought in two systems: The Fenna-Matthews-Olson complex (FMO) containing 7 BChl-a molecules and a chlorosome from a mutant photosynthetic bacteria made up of 600 Bchl-d molecules (Fig 2). The FMO complex is a trimeric pigment-protein complex which lies between the antennae complex and the reaction center in green sulfur dependent photosynthetic bacteria such as P. aestuarii or C. tepidium, serving thus as a molecular wire in which is known that the excitonic transfer occurs with quantum coherence, i.e. virtually no energy loss which led us to believe SF could be an operating mechanism. So far it seems it is not present. However, for a crystallographic BChl-d dimer present in the chlorosome it could actually occur even when in competition with fluorescence.

FMO

FMO Complex. Trimer (left), monomer (center), pigments (right)

Imagen2

BChQRU chlorosome. 600 Bchl-d molecules

I will keep on blogging more -numerical and computational- details about these results and hopefully about its publication but for now I will wrap this post by giving credit where credit is due: This whole project has been tackled by our former lab member María Eugenia “Maru” Sandoval and Gustavo Mondragón. Finally, after much struggle, we are presenting our results at WATOC 2017 next week on Monday 28th at poster session 01 (PO1-296), so please stop by to say hi and comment on our work so we can improve it and bring it home!

A New Graduate Student


With pleasure I announce that last week our very own Gustavo “Gus” Mondragón became the fifth undergraduate student from my lab to defend his BSc thesis and it has to be said that he did it admirably so.

Gus has been working with us for about a year now and during this time he not only worked on his thesis calculating excited states for bacteriochlorophyl pigments but also helped us finishing some series of calculations on calix[n]arene complexes of Arsenic (V) acids, which granted him the possibility to apear as a co-author of the manuscript recently published in JIPH. Back in that study he calculated the interaction energies between a family of calix macrocycles and arsenic acid derivatives in order to develop a suitable extracting agent.

For his BSc thesis, Gus reproduced the UV-Vis absorption spectra of bacteriochlorophyll-a pigments found in the Fenna-Matthews-Olson complex of photosynthetic purple bacteria using Time Dependent Density Functional Theory (TD-DFT) with various levels of theory, with PBEPBE yielding the best results among the tried set. These calculations were performed at the crystallographic conformation and at the optimized structure, also, in vacuo results were compared to those in implicit solvent (SMD, MeOH). He will now move towards his masters where he will further continue our research on photosynthesis.

Thank you, Gustavo, for your hard work and your sense of humor. Congratulations on this step and may many more successes come your way.

 

Maru Sandoval M.Sc. – Our First Graduate Thesis


It is with great pride that I’d like to announce that for the first time we have a Masters Student graduated from this Comp.Chem. lab: María Eugenia “Maru” Sandoval-Salinas has finished her graduate studies and just last Friday defended her thesis admirably earning not only the degree of Masters of Science in Chemistry but doing so with the highest honors given by the National Autonomous University of Mexico.

Maru’s thesis is for many reasons a landmark in this lab not only because it is the first graduate thesis published from our lab but also the first document on our work about the study of Photosynthesis, a long sought after endeavor now closer to publication. It must also be said that Maru came to this lab when she was an undergraduate student five years ago when I just recently joined UNAM as a researcher fresh out of a postdoc stay. After getting her B.Sc. degree and publishing an article in JCTC (DOI: 10.1021/ct4004178) she now is about to publish more papers that I’m sure will be as highly ranked as the previous one. Thus, Maru was a pioneer in our lab giving it a vote of confidence when we had little to nothing to show for; thanks to her hard work and confidence, along with that of the students who have followed her, we managed to succeed as a consolidated research group in the field of computational chemistry.

More specifically, her thesis centered around finding a mechanism for the excitonic transference between pigments (bacteriochlorophyl-a, BChl-a) in the Fenna-Matthews-Olson (FMO) complex, a protein trimer with seven BChl-a molecules in each monomer, located between the antenna complex and the reaction center in green sulfur bacteria. Among the possible mechanisms explored were Förster’s theory, a modification to Marcus’ theory and finally we explored the possibility of Singlet Fission occurring between adjacent molecules with the help of Dr. David Casanova from the Basque Country University where Maru took a short research stay last autumn. Since nature doesn’t conform to any specific mechanism -specially in a complex arrangement such as the FMO- then it could be possible that a combination of the above might also occur but lets just wait for the papers to be published to discuss it. Calculations were performed through the TD-DFT and the C-DFT formalisms using G09 and Q-Chem; comparing experimental data in CH3OH (SMD implicit calculations with the SVWN5 functional) were undertaken previously for selection of the level of theory.

Now, after two original theses written and successfully defended, an article published in JCTC and more in process, at least five posters, a couple of oral presentations and countless hours at her desk, Maru will go pursuit a PhD abroad where I’m sure she will exceed anyone’s expectations with her work, drive, dedication and scientific curiosity. Thank you, Maru, for all your hard work and trust when this lab needed it the most, we wish you the best for you earn it. You will surely be missed.

New paper in J. Phys. Chem. C


Having a new paper out is always fun and this week we got the wonderful news from the Journal of Physical Chemistry C that a paper I co authored with Prof. Alireza Badiei at the University of Tehran in Iran and his student, who actually got us all in touch, Dr. Pezhman Zarabadi-Poor, was accepted for publication.

The paper is titled “Selective Optical Sensing of Hg(II) in Aqueous Media by H-Acid/SBA-15: A Combined Experimental and Theoretical Study“; in it we explored the fluorescence quenching mechanism for a Hg(II) complex which forms the basis of a novel selective mercury detector. Geometry optimizations were carried out at the PBE0/6-31++G** PCM level of theory (along with the aug-cc-pVDZ-PP basis set and corresponding ECP for Hg), also the electronic spectrum of both the free acid and the Hg(II) complex was calculated.

(Frontier orbitals were depicted using Chemcraft)

Higher laying orbitals for Hg(II) complex

Higher laying orbitals for Hg(II) complex

We can observe that HOMO and LUMO+1 are mainly located on the naphtalene ring allowing for the S0 -> S1 transition and back, which accounts for the molecular fluorescence. Other internal conversion processes were also assessed and discussed in the paper which accounts for the quenching effect. In short, we have obtained a full quantum description of the mechanism by which coordination of the free acid to Hg(II) alters the ligand’s electronic structure converting its emisive lowest-lying excited state to a dark state, i.e., quenching! Pretty cool stuff!

Once again thanks to both Dr. Zarabadi-Poor and Prof. Badiei for thinking about me for collaborating with them in this joint endeavor which hopefully wont be our last. A PDF copy of the article is available by direct request through this post.

Thanks for reading, sharing, rating and commenting.

%d bloggers like this: