Posts Tagged ‘energy gap’

150,000,000 DFT calculations on 2,300,000 compounds!

Friday, July 5th, 2013

The title of this post summarises the contents of a new molecular database: www.molecularspace.org[1] and I picked up on it by following the post by Jan Jensen at www.compchemhighlights.org (a wonderful overlay journal that tracks recent interesting articles). The molecularspace project more formally is called “The Harvard Clean Energy Project: Large-scale computational screening and design of organic photovoltaics on the world community grid“. It reminds of a 2005 project by Peter Murray-Rust et al at the same sort of concept[2] (the World-Wide-Molecular-Matrix, or WWMM[3]), although the new scale is certainly impressive. Here I report my initial experiences looking through molecularspace.org

The 150,000,000 calculations are released under the the CC-BY license, which is an encouraging (open) start. One does need however to login to the site, which I was able to do using my Google credentials. Shown below is a screenshot of a typical result in a search (of Power conversion efficiency in my case).

CEPDB1

It comes in two parts, the first being the structure (given as a SMILES and 2D layout) with the principle predicted energy levels and predicted photovoltaic performance listed below that. This is then followed by what might be called an annotation with further computed/predicted properties using the algorithms applied by Chemicalize.org. This idea that a data set could accrete via semantically powerful annotations using other tools was also very much part of the concept of the WWMM (the matrix had at its heart a molecule in one dimension and a property, measured or computed in the other. The matrix is of course very sparse, which is why it needs annotation!).

It was at this point however that I started to wonder how I might add other annotations, based perhaps on other types of calculations. But thus far at least, I have not found any trace of something which I could immediately use for my own calculation; 3D coordinates specifically. Thus, the HOMO-LUMO energy gap is the key property which makes molecularspace unique and valuable (to someone working in the field of photovoltaics). But HOMO/LUMO gaps can be calculated in many different ways, and it can always be valuable to calibrate/validate the reported values against other methods. Perhaps if I continue to look, I might find these 3D coordinates (which, for 2,300,000 molecules would be a very valuable resource).  Certainly for example, should  I wish to do so, I could not at the moment readily replicate the calculation for any specific entry on the molecularspace site (which can be regarded as an essential component of scientific validation). When I use the first person, I mean of course either myself as a human or a software agent acting on my behalf (the latter having the endurance to repeat its procedures millions of times if necessary). 

The reader of this blog may have noticed that whenever I report a calculation here, I like to cite its doi (more formally its handle), which links to a digital repository. In my case, the repository certainly carries the 3D coordinates, and also the full wavefunction provided if the reader wishes other properties to be derived from it.‡ Now if molecularspace is able to provide that in the fullness of time, it truly would be an impressive resource.

But the important take-home message from molecularspace is that archiving (under a CC-BY license) the “big” data from any given research in a manner which makes it readily re-usable by others (perhaps from quite different fields of science) is now an essential requisite of doing science. And it is really nice to see good examples of this in practice!

‡ Generally, the calculations I perform for this blog are published in a DSpace repository (the original one, started in 2006[4]), and more recently in Chempound (a project by Peter Murray-Rust and colleagues which emerged out of the WWMM experiments) as well as Figshare[5]. The first and the third assign unique handles (i.e. a doi) to the data; chempound does not (and neither does molecularspace).

References

  1. J. Hachmann, R. Olivares-Amaya, S. Atahan-Evrenk, C. Amador-Bedolla, R.S. Sánchez-Carrera, A. Gold-Parker, L. Vogt, A.M. Brockway, and A. Aspuru-Guzik, "The Harvard Clean Energy Project: Large-Scale Computational Screening and Design of Organic Photovoltaics on the World Community Grid", The Journal of Physical Chemistry Letters, vol. 2, pp. 2241-2251, 2011. https://doi.org/10.1021/jz200866s
  2. P. Murray-Rust, H.S. Rzepa, J.J.P. Stewart, and Y. Zhang, "A global resource for computational chemistry", Journal of Molecular Modeling, vol. 11, pp. 532-541, 2005. https://doi.org/10.1007/s00894-005-0278-1
  3. P. Murray-Rust, S.E. Adams, J. Downing, J.A. Townsend, and Y. Zhang, "The semantic architecture of the World-Wide Molecular Matrix (WWMM)", Journal of Cheminformatics, vol. 3, 2011. https://doi.org/10.1186/1758-2946-3-42
  4. J. Downing, P. Murray-Rust, A.P. Tonge, P. Morgan, H.S. Rzepa, F. Cotterill, N. Day, and M.J. Harvey, "SPECTRa: The Deposition and Validation of Primary Chemistry Research Data in Digital Repositories", Journal of Chemical Information and Modeling, vol. 48, pp. 1571-1581, 2008. https://doi.org/10.1021/ci7004737
  5. H.S. Rzepa, "Gaussian Job Archive for CLi6", 2013. https://doi.org/10.6084/m9.figshare.739310

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π-hydrogen bonds as a function of ring size.

Saturday, January 5th, 2013

A simple correlation between a ring size and the hydrogen bonding as quantified by the O(Lp)/H-O σ* NBO interaction in that ring, indicated a 7- or 8-membered ring was preferred over smaller ones. Here is the same study, but this time using the π-electrons of an alkene as the electron donor.

pi-hbond

n  E(2), kcal/mol  O…H length, Å  Angle,°
2 0.84 2.54, 2.75 107.4, 126.7
3 1.37 2.35, 2.92 133.1, 152.9
4 2.04 2.45, 2.63 139.1, 144.5
5 1.89 2.56, 2.63 152.2, 138.9

The E(2) interaction energies between the NBO filled π-orbital localised to the alkene and the H-O σ* are significantly smaller than for O(Lp) as donors. The energy gap between the donor and acceptor orbitals is smaller for π (ΔE=0.919) than for the O…HO (0.969 au) and if one can compare these values across different localisations, then the finger must point to reduced overlap as the more probable explanation.

7pi

NBO interaction for 7-ring H-bond. Click for 3D.

So does that mean that π bonds do not form? Well take a look at this molecule:[1], which exhibits one example of a π-bond and one of a conventional O…HO bond. E(2) for the π interaction is now 6.6 kcal/mol, and the C…H distance is 2.16Å (calc, 2.1-2.2Å at its shortest, obs). 

WAK

7pi

NBO interaction for 7-ring H-bond. Click for 3D.

There are probably several reasons for this.

  1. The geometry of the scaffold enforces close proximity of the alkene and the OH group. The geometry of the scaffold results in a greater overlap of the C=C π and H-O σ* NBOs. Recollect however the H…H distance in cis-butene, a proximity that was enforced by other effects and which I argued was NOT a chemical bond.
  2. The energy gap between filled and empty NBOs is slightly reduced from 0.919 to to 0.902 au.
  3. This in turn may arise because the acceptor strength of the H-O σ* is enhanced by a knock-on effect by an additional conventional hydrogen bond the O (Lp) on this oxygen is forming to a H-O of a second molecular unit.

So we may conclude that whilst strong π H-O hydrogen bonds can be observed, they arise for the molecule shown above from a co-operation of several affects associated with the specific environment, rather than the intrinsic propensity of this type of H-bond to form strong interactions. But one more surprise (perhaps, or possibly just a further insight). The NCI (non-covalent-interactions) surface.

Non-covelent-interactions surface. Click for 3D.

Non-covalent-interactions (NCI) surface. Click for 3D.

This maps the character of the (electron) density gradients, and shows up as blue (attractive) and red (repulsive). Four different regions show up as blue. Arrow 1 is our C=C π…H-O bond. Note how adjacent to the blue region is a green-yellow one, indicating weak repulsions there (this proximity of both attractive and repulsive regions of the density was suggested to account for the confusion surrounding the  H…H interaction in cis-butene). Blue on its own however occurs in the region indicated by  arrow  2. In this, the conventional  O…H-O attraction has no associated repulsion, which may also be an explanation for why such bonds are far more common. But the surprise is arrow 3, which suggests attractive back donation from the O(Lp) to the π* empty orbital (E(2) 1.4 kcal/mol)  and arrow 4 indicates an attractive donation from the C=C π to the  C=O π* (E(2) = 0.6 kcal/mol). In this particularly rigid system, all these are largely enforced by the atom-scaffold. but it does all show how we often miss noticing the weaker interactions in molecules.

References

  1. M. Etzkorn, S.D. Smeltz-Zapata, T.B. Meyers, X. Yu, and M. Gerken, "From the anti-tricyclo[4.2.1.12,5]deca-3,7-diene framework to 4,5,6,7-tetrachloro-isoindenone derivatives", Tetrahedron Letters, vol. 51, pp. 6075-6077, 2010. https://doi.org/10.1016/j.tetlet.2010.09.045

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Hydrogen bond strength as a function of ring size.

Thursday, January 3rd, 2013

One frequently has to confront the question: will a hydrogen bond form between a suitable donor (lone pair or π) and an acceptor? One of the factors to be taken into consideration for hydrogen bonds which are part of a cycle is the ring size. Here I explore one way of quantifying the effect for the series below, n=1-5 (4-8 membered rings).h-bond

I will use the NBO approach. To remind, this reduces the wavefunction for a molecule to a set of localised orbitals, referred to as natural bond orbitals. The perturbation interaction energy E(2) between any (doubly occupied, i.e. donor) orbital and an (unoccupied) acceptor orbital establishes the strength of that interaction. For a hydrogen bond, this can be expressed as the NBO corresponding to the (in this case oxygen) lone pair (shown in orange and purple below) and the corresponding H-O σ* empty orbital (shown as red and blue below). E(2) is a function both of how close in energy this pair of orbitals is (the smaller the energy gap the better) and how well they overlap (the relevant overlap in this case is the positive one between purple and blue). This latter attribute is shown below for the series n=2,3,4,5 (n=1 does not form any discernible hydrogen bond), at the ωB97XD/6-311G(d,p) computational level.

NBO interaction for 5-ring H-bond. Click for 3D.

NBO interaction for 6-ring H-bond. Click for 3D

NBO interaction for 7-ring H-bond. Click for 3D.

NBO interaction for 8-ring H-bond. Click for 3D.

The interaction energies E(2) are collected below, together with the computed lengths. To put E(2) into context, it is around 16 kcal/mol for a strong anomeric interaction, and about 6 kcal/mol for the stereoelectronic influence in di-fluoroethane. One can see that by the time the angle subtended at the hydrogen has increased to ~150°, the interaction energy has reached a respectable value.

n  E(2), kcal/mol  O…H length, Å  Angle, °
1 ~0.0  –  81.8
2 0.75 2.294  109.7
3 3.56 1.984  139.6
4 6.24 2.017  146.5
5 8.35 1.957  153.4

So the simple trick of looking at the donor-acceptor NBO interaction in a cyclic hydrogen bond can give us a straightforward way of quantifying how the size of the ring and hence the orbital overlap (one presumes that the Lp/C-O σ* energy gap is similar for all the systems) affects the strength of the interaction. One might also explore this by looking at structures in the Cambridge crystal database. But note from the above that whilst the  E(2) energies follow ring size, this does not appear to happen for the H…O lengths! The analysis reveals that the maximum number of structures for the span 5 to 8-rings occurs at ~2.15, 1.85, 1.65 and 1.85Å respectively. 

Crystal data for 5-rings

Crystal data for 5-rings
Crystal data for 6-rings.

Crystal data for 6-rings.
Crystal data for 7-rings

Crystal data for 7-rings
Crystal data for 8-rings

Crystal data for 8-rings

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The conformation of 1,2-difluoroethane

Tuesday, April 6th, 2010

Here I offer another spin-off from writing a lecture course on conformational analysis. This is the famous example of why 1,2-difluoroethane adopts a gauche rather than antiperiplanar conformation.

The gauche and antiperiplanar conformations of 1,2-difluoroethane

One major contribution to the greater stability of the gauche is the stereoelectronic interactions, and this is best probed using the NBO (Natural Bond Orbital) approach of Weinhold (DOI: 10.1021/ja00501a009). The process is approximately described as first reducing the wavefunction down to a set of orbitals which have been localized (using appropriate algorithms) down to two or one centres (corresponding to two-centre covalent bonds, or one-centre electron lone pairs). Perturbation theory is then used to evaluate the interaction energy between any filled and any empty combination. For the molecule above, six such combinations are inspected, involving any one of the six filled C-H or C-F σ-orbitals, and the best-overlapping σ* orbital which turns out to be located on the C-H or C-F bond anti-periplanar to the filled orbital.

Filled C-H NBO orbital. Click for 3D to superimpose empty C-F anti bonding orbital.

Empty C-F antibonding NBO orbital. Click for 3D

A filled C-H orbital is shown above on the left, accompanied by an empty C-F σ* orbital on the right which is anti-periplanar to the first. This alignment allows the phases of the two orbitals to overlap maximally (blue-blue on the top, red-red beneath).

The interaction energy between this pair is determined not only by the efficacy of the overlap, but by the energy gap between the two. The smaller the gap, the better the interaction energy (referred to as E2, in kcal/mol). For the gauche conformation, the six pairs of orbitals have the following interaction energies; two σC-H/σ*C-F interactions (illustrated above), 4.9; two σC-H/σ*C-H 2.6 and two σC-F/σ*C-H 0.8 kcal/mol. For the anti-periplanar conformation, the terms are four σC-H/σ*C-H 2.5 and two σC-F/σ*C-F 1.8 kcal/mol. The two totals (16.6 vs 13.6) indicate that gauche is stabilized more by such interactions.

There is of course a bit more to this story, but I have documented the above here, since I can include an explicit (and rotatable) illustration of the orbitals involved (which  I have not seen elsewhere). If you want a recipe for generating these orbitals, go here.

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