# Monthly Archives: August 2017

## 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).

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}(*T*T) 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.

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 – Medicinal #CompChem on HIV-1

Last Friday Durbis Castillo-Pazos became officially a graduated chemist. His presentation about the* in silico* development of entry inhibtors for the HIV-1 virus was very clear and straightforward and he performed admirably during the examination for which he graduated with Honors from the Mexico State Autonomous University (UAEMex).

Ever since he came to my lab, Durbis was adamant to work in some project related to medicinal chemistry which is not really my thing. Still, we were able to take an old project related to the *in silico* design of entry inhibitors for the protein GP120 which is responsible for the entry of the HIV-1 virus into human T-cells; the very first stage of the HIV infection which leads to AIDS. The lengths to which Durbis took the project were remarkable but none of that would have been possible without the leadership of my good friend and colleague Dr. Antonio Romo from the Queretaro Autonomous University (UAQ) who not only guided us through the nuances of the field but also on the intricacies of working with Schrödinger Inc.’s software, MAESTRO.

Suffice it to say that based on a piperazine core and four thousand fragments with commercial pharmaceutical applications, Durbis built a **16.3 million** compounds library from which a few candidates are selected as potential drug molecules after several docking steps at various precision levels and molecular dynamics simulations plus QSAR related analysis. More about the details in future posts.

The knowledge gained by Durbis allowed him to become a member of the QSAR team led by Dr. Karina Martinez, at the Institute of Chemistry UNAM which provides QSAR studies to various companies who want to submit this kind of studies for regulatory purposes. Durbis has his sight abroad and has been admitted to a prestigious graduate program where he will keep seeking to improve his knowledge on medicinal chemistry. I’m sure he will succeed in anything on which he sets his mind.

## Collaborations in Inorganic Chemistry

I began my path in computational chemistry while I still was an undergraduate student, working on my thesis under professor Cea at unam, synthesizing main group complexes with sulfur containing ligands. Quite a mouthful, I know. Therefore my first calculations dealt with obtaining Bond indexed for bidentate ligands bonded to tin, antimony and even arsenic; yes! I worked with arsenic once! Happily, I keep a tight bond (pun intended) with inorganic chemists and the recent two papers published with the group of Prof. Mónica Moya are proof of that.

In the first paper, cyclic metallaborates were formed with Ga and Al but when a cycle of a given size formed with one it didn’t with the other (fig 1), so I calculated the relative energies of both analogues while compensating for the change in the number of electrons with the following equation:

Fig 1

Δ*E* = *E*(M* _{n}*B

*O*

_{x}*) –*

_{y}*nE*M +

*nE*M’ –

*E*(M’

*B*

_{n}*O*

_{x}*) Eq 1*

_{y}A seamless substitution would imply Δ*E* = 0 when changing from M to M’

The calculated Δ*E *were: Δ*E*(3/3′) = -81.38 kcal/mol; Δ*E*(4/4′) = 40.61 kcal/mol; Δ*E*(5/5′) = 70.98 kcal/mol

In all, the increased stability and higher covalent character of the Ga-O-Ga unit compared to that of the Al analogue favors the formation of different sized rings.

Additionally, a free energy change analysis was performed to assess the relative stability between compounds. Changes in free energy can be obtained easily from the thermochemistry section in the FREQ calculation from Gaussian.

This paper is published in Inorganic Chemistry under the following citation: Erandi Bernabé-Pablo, Vojtech Jancik, Diego Martínez-Otero, Joaquín Barroso-Flores, and Mónica Moya-Cabrera* “Molecular Group 13 Metallaborates Derived from M−O−M Cleavage Promoted by BH3” *Inorg. Chem*. **2017**, 56, 7890−7899

The second paper deals with heavier atoms and the bonds the formed around Yttrium complexes with triazoles, for which we calculated a more detailed distribution of the electronic density and concluded that the coordination of Cp to Y involves a high component of ionic character.

This paper is published in Ana Cristina García-Álvarez, Erandi Bernabé-Pablo, Joaquín Barroso-Flores, Vojtech Jancik, Diego Martínez-Otero, T. Jesús Morales-Juárez, Mónica Moya-Cabrera* “Multinuclear rare-earth metal complexes supported by chalcogen-based 1,2,3-triazole” *Polyhedron *135 (**2017**) 10-16

We keep working on other projects and I hope we keep on doing so for the foreseeable future because those main group metals have been in my blood all this century. Thanks and a big shoutout to Dr. Monica Moya for keeping me in her highly productive and competitive team of researchers; here is to many more years of joint work.

## All you wanted to know about Hybrid Orbitals…

#### … but were afraid to ask

#### or

#### How I learned to stop worrying and not caring that much about hybridization.

The math behind orbital hybridization is fairly simple as I’ll try to show below, but first let me give my praise once again to the formidable Linus Pauling, whose creation of this model built a bridge between quantum mechanics and chemistry; I often say Pauling was the first Quantum Chemist (Gilbert N. Lewis’ fans, please settle down). Hybrid orbitals are therefore a way to create a basis that better suits the geometry formed by the bonds around a given atom and not the result of a process in which atomic orbitals transform themselves for better sterical fitting, or like I’ve said before, the C atom in CH_{4} is sp^{3} hybridized because CH_{4} is tetrahedral and not the other way around. Jack Simmons put it better in his book:

The atomic orbitals we all know and love are the set of solutions to the Schrödinger equation for the Hydrogen atom and more generally they are solutions to the hydrogen-like atoms for which the value of *Z* in the potential term of the Hamiltonian changes according to each element’s atomic number.

Since the Hamiltonian, and any other quantum mechanical operator for that matter, is a Hermitian operator, any given linear combination of wave functions that are solutions to it, will also be an acceptable solution. Therefore, since the *2s* and *2p* valence orbitals of Carbon do not point towards the edges of a tetrahedron they don’t offer a suitable basis for explaining the geometry of methane; even more so these atomic orbitals are not degenerate and there is no reason to assume all C-H bonds in methane aren’t equal. However we can come up with a linear combination of them that might and at the same time will be a solution to the Schrödinger equation of the hydrogen-like atom.

Ok, so we need four degenerate orbitals which we’ll name *ζ _{i}* and formulate them as linear combinations of the C atom valence orbitals:

*ζ _{1}*=

*a*+

_{1}2s*b*+

_{1}2p_{x}*c*+

_{1}2p_{y}*d*

_{1}2p_{z}*ζ _{2}*=

*a*+

_{2}2s*b*+

_{2}2p_{x}*c*+

_{2}2p_{y}*d*

_{2}2p_{z}*ζ _{3}*=

*a*+

_{3}2s*b*+

_{3}2p_{x}*c*+

_{3}2p_{y}*d*

_{3}2p_{z}*ζ _{4}*=

*a*+

_{4}2s*b*+

_{4}2p_{x}*c*+

_{4}2p_{y}*d*

_{4}2p_{z}to comply with equivalency lets set *a _{1}* =

*a*=

_{2}*a*=

_{3}*a*and normalize them:

_{4}*a _{1}*

*+*

^{2}*a*

_{2}*+*

^{2}*a*

_{3}*+*

^{2}*a*

_{4}*= 1 ∴*

^{2}*a*= 1/√4

_{i}Lets take *ζ _{1}* to be directed along the

*z*axis so

*b*=

_{1}*c*= 0

_{1}*ζ _{1 }*= 1/√4(

*2s*) +

*d*

_{1}2p_{z}since *ζ _{1}* must be normalized the sum of the squares of the coefficients is equal to 1:

^{1}/_{4} + *d _{1}^{2}* = 1;

*d _{1}* =

^{√3}/

_{2}

Therefore the first hybrid orbital looks like:

*ζ _{1}* =

^{1}/

_{√4}(

*2s*) +

^{√3}/

_{2}(

*2p*)

_{z}We now set the second hybrid orbital on the xz plane, therefore *c _{2}* = 0

*ζ _{2}* =

^{1}/

_{√4}(

*2s*) +

*b*+

_{2}2p_{x}*d*

_{2}2p_{z}since these hybrid orbitals must comply with all the conditions of atomic orbitals they should also be orthonormal:

〈*ζ _{1}*|

*ζ*〉 = δ

_{2}_{1,2}= 0

^{1}/_{4} + *d _{2}*

^{√3}/

_{2}= 0

*d _{2}* = –

^{1}/

_{2√3}

our second hybrid orbital is almost complete, we are only missing the value of *b _{2}*:

*ζ _{2}* =

^{1}/

_{√4}(

*2s*) +

*b*+-

_{2}2p_{x}^{1}/

_{2√3}(

*2p*)

_{z}again we make use of the normalization condition:

^{1}/_{4} + *b _{2}^{2}* +

^{1}/

_{12}= 1;

*b*=

_{2}^{√2}/

_{√3}

Finally, our second hybrid orbital takes the following form:

*ζ _{2}* =

^{1}/

_{√4}(

*2s*) +

^{√2}/

_{√3}(

*2p*) –

_{x}^{1}/

_{√12}(

*2p*)

_{z}The procedure to obtain the remaining two hybrid orbitals is the same but I’d like to stop here and analyze the relative direction *ζ _{1}* and

*ζ*take from each other. To that end, we take the angular part of the hydrogen-like atomic orbitals involved in the linear combinations we just found. Let us remember the canonical form of atomic orbitals and explicitly show the spherical harmonic functions to which the 2s, 2px, and 2pz atomic orbitals correspond:

_{2}ψ* _{2s}* = (1/4π)

^{½}

*R*(

*r*)

ψ* _{2px}* = (3/4π)

^{½}sinθcosφ

*R*(

*r*)

ψ* _{2pz}* = (3/4π)

^{½}cosθ

*R*(

*r*)

we substitute these in *ζ _{2}* and factorize R(r) and

^{1}/

_{√(4π)}

*ζ _{2}* = (

^{R(r)}/

_{√(4π)})[

^{1}/

_{√4}+ √2 sinθcosφ –

^{√3}/

_{√12}cosθ]

We differentiate *ζ _{2}* respect to θ, and set it to zero to find the maximum value of θ respect to the z axis we get the angle between the first to hybrid orbitals

*ζ*and

_{1}*ζ*(remember that

_{2}*ζ*is projected entirely over the

_{1}*z*axis)

d*ζ _{2}*/dθ = (

^{R(r)}/

_{√(4π)})[√2 cosθ –

^{√3}/

_{√12}sinθ] = 0

sinθ/cosθ = tanθ = -√8

θ = -70.53°,

but since θ is measured from the z axis towards the xy plane this result is equivalent to the complementary angle 180.0° – 70.53° = 109.47° which is exactly the angle between the C-H bonds in methane we all know! and we didn’t need to invoke the unpairing of electrons in full orbitals, their promotion of any electron into empty orbitals nor the ‘*reorganization*‘ of said orbitals into new ones. Orbital hybridization is nothing but a mathematical tool to find a set of orbitals which comply with the experimental observation and that is the important thing here!

To summarize, you can take any number of orbitals and build any linear combination you want, in order to comply with the observed geometry. Furthermore, no matter what hybridization scheme you follow, you still take the entire orbital, you cannot take half of it because they are basis functions. That is why you should never believe that any atom exhibits something like an *sp ^{2.5}* hybridization just because their bond angles lie between 109 and 120°. Take a vector

*v*= x

*i*+y

*j*+z

*k*, even if you specify it to be

*v*= 1/2

*i*that means x = 1/2, not that you took half of the unit vector i, and it doesn’t mean you took nothing of

*j*and

*k*but rather than y = z = 0.

This was a very lengthy post so please let me know if you read it all the way through by commenting, liking, or sharing. Thanks for reading.