Posts Tagged ‘Molecular orbital’

Hypervalent hydrogen?

Saturday, January 13th, 2018

I discussed the molecule the molecule CH3F2- a while back. It was a very rare computed example of a system where the added two electrons populate the higher valence shells known as Rydberg orbitals as an alternative to populating the C-F antibonding σ-orbital to produce CH3– and F–. The net result was the creation of a weak C-F “hyperbond”, in which the C-F region has an inner conventional bond, with an outer “sheath” encircling the first bond. But this system very easily dissociates to CH3– and F– and is hardly a viable candidate for experimental detection.  In an effort to “tune” this effect to see if a better candidate for such detection might be found, I tried CMe3F2-. Here is its story.

The calculation‡ is at the ωB97XD/Def2-TZVPPD/SCRF=water level (water is here used as an approximate model for a condensed environment, helping to bind the two added electrons).

  1. An NBO (Natural Bond orbital) analysis reveals a total Rydberg orbital population of 1.186e and the following bond indices; F 0.853, C 3.977, C(methyl) 4.051, H(*3) 1.332. The latter corresponds to the three methyl hydrogens aligned antiperiplanar to the C-F bond.
  2. To put this value into context, the hydrogen in the FHF– anion has an NBO H bond index of 0.724, and the bridging hydrogens in diborane only have a value of 0.988. Even the hexa-coordinate hydride system [Co6H(CO)15]– discussed in an earlier blog  has an H bond index of just 0.86. Actually, coordination of six or even higher for hydrogen is no longer rare; some 28 crystal structures of the type HM6 (M=metal) are known (it would be useful to find out if any of the other 27 such structures might have a hydrogen bond index >1).
  3. Next, the ELF analysis (Electron localisation function), analysed firstly using the excellent MultiWFN program.[1]

    This reveals an attractor basin integrating to 1.663e and located along the axis of the F-C bond and extended into the region of the three antiperiplanar methyl hydrogens. The C-F bond itself only supports a basin of 0.729e, typical of the fairly ionic C-F bond. The covalent C-Me bonds are also pretty normal, as are the other hydrogens.
  4. I also show ELF analysis using the alternative TopMod program[2]; the numerical values on this diagram are the calculated bond lengths in Å. The basin integrations are very similar to those obtained using MultiWFN.

    The Wiberg bond orders of the three H…H regions shown connected by dashed lines above are 0.154, which contributes to the bond index of >1 at these three hydrogens.
  5. The predicted 1H chemical shift of these three “hypervalent” hydrogens is +3.0 ppm, whilst the other six methyl hydrogens are at -0.87ppm.

So changing CH3F2- to CMe3F2- has dramatically changed the bonding picture that emerges, rather than a fine-tuning. The C-F is no longer a “hyperbond”, although the Rydberg occupancy of 1.186e remains unusually large. Most of the additional electrons have fled the torus surrounding the C-F bond and relocated to the exo-region of that bond where they now influence the three antiperiplanar methyl hydrogens. A two-electron-three-centre interaction if you like, but with the electron basin occupying a tetrahedral vertex rather than the triatom centroid.

I end with a challenge. Is it possible to find “real” molecules containing hydrogen where the formal bond index for at least one hydrogen exceeds 1.0 significantly, thus making it hypervalent? 

‡The calculations are all collected at FAIR doi; 10.14469/hpc/3372.

References

  1. T. Lu, and F. Chen, "Multiwfn: A multifunctional wavefunction analyzer", Journal of Computational Chemistry, vol. 33, pp. 580-592, 2011. https://doi.org/10.1002/jcc.22885
  2. S. Noury, X. Krokidis, F. Fuster, and B. Silvi, "Computational tools for the electron localization function topological analysis", Computers & Chemistry, vol. 23, pp. 597-604, 1999. https://doi.org/10.1016/s0097-8485(99)00039-x

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Posted in Hypervalency | 2 Comments »

Molecule orbitals as indicators of reactivity: bromoallene.

Thursday, September 1st, 2016

Bromoallene is a pretty simple molecule, with two non-equivalent double bonds. How might it react with an electrophile, say dimethyldioxirane (DMDO) to form an epoxide?[1] Here I explore the difference between two different and very simple approaches to predicting its reactivity. bromoallene

Both approaches rely on the properties of the reactant and use two types of molecule orbitals derived from its electronic wavefunction. The first of these is very well-known as the molecular orbital (MO), which has the property that it tends to delocalise over all the contributing atoms (the “molecule”). MOs are often used in this context; the highest energy occupied MO is thought of as being associated with the most nucleophilic (electron donating) regions of the molecule and so such a HOMO would be expected to predict the region of nucleophilic attack. The second is known as the natural bond orbital (NBO), which is evaluated in a manner that tends to localise it on bonds (the functional groups or reaction centres) and atom centres. What do these respective orbitals reveal for bromoallene? 

The MOs
HOMO, -0.3380 HOMO-1, -0.3692 au
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The NBOs
HONBO, -0.3769 HONBO-2, -0.3898
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The table above shows the energies (in Hartrees) of the four relevant orbitals. The less negative (less stable) the orbital, the more nucleophilic it is. The (heavily) delocalized HOMO is located on the C=C bond bond carrying the C-Br bond, Δ1,2 alkene, but it also has a large component on the Br. The more stable HOMO-1 is located on the C=C bond located away from the Br, the Δ2,3 alkene and also with a (different type of) component on the Br.

In contrast, the HONBO is located on the Δ2,3 alkene and it is the HONBO-2 that is on the Δ1,2 alkene. Both these orbitals have very little “leakage” onto other atoms, they are almost completely localised.

Well, now we have a problem since these two analyses lead to diametrically opposing predictions! So what does experiment say? A recent article[1] addresses this issue by isolating the initially formed epoxide from reaction with DMDO and characterising it using crystallography. But here comes the catch; such isolation only proved possible if the allene was also substituted with large sterically bulky groups such as t-butyl or adamantyl. And the isolated product was the Δ1,2 epoxide. So does that mean that the MO method was correct and the NBO method wrong? Well, not necessarily. Those large groups play an additional role via steric effects. To factor in such effects one has to look at the transition state model for the reaction rather than depending purely on the reactant properties. And the steric effects in this case appear to win out over the electronic ones.[1]

The Klopman[2]-Salem[3] equation (shown in very simplified, and original, form below for just the covalent term) casts some light on what is going on. This term is a double summation over occupied/unoccupied (donor-acceptor) orbital interactions, involving the coefficients of the orbitals (the overlap integrals in effect) in the numerator and the energy difference between the occupied/unoccupied orbital pair as denominator.

KS1

Performing such a double summation is rarely attempted; instead the equation is reduced to just one single term involving the donor of highest energy and the acceptor of lowest energy, ensuring the energy difference is a minimum and hence the term itself is (potentially) the largest in the summation. There is still the issue of the orbital coefficients, and here we get to the crux of the difference between the use of MOs and NBOs. You can see by inspection that the two π-MOs for bromoallene have different coefficients on the two atoms of interest, the two carbons of the double bond. One really has to evaluate the size of this term in the summation by using quantitative values for the respective coefficients and to very probably include the further terms in the summation for any other orbitals which also have significantly non-zero coefficients on these two atoms. But with the NBOs, the localisation procedure used to derive them has reduced the coefficients to just the carbon atoms and effectively no other atoms; all the other terms in the double summation in effect do drop out entirely. So with NBOs, the only number that matters is the energy difference between the occupied/empty orbitals (the denominator). But since the acceptor (the electrophile, DMDO in this case) is the same for both regiochemistries, things reduce even further to just comparing the donor energies for the two alternatives (Table above). The higher/less stable of these will have the greater contribution in the Klopman-Salem equation.

This little molecule teaches the important lesson that electronic and steric effects both play a role in directing reactions, and in this system they may well oppose each other. Simple interpretations based on reactant orbitals may give only a partial and even potentially misleading answer.

References

  1. D. Christopher Braddock, A. Mahtey, H.S. Rzepa, and A.J.P. White, "Stable bromoallene oxides", Chemical Communications, vol. 52, pp. 11219-11222, 2016. https://doi.org/10.1039/c6cc06395k
  2. G. Klopman, "Chemical reactivity and the concept of charge- and frontier-controlled reactions", Journal of the American Chemical Society, vol. 90, pp. 223-234, 1968. https://doi.org/10.1021/ja01004a002
  3. L. Salem, "Intermolecular orbital theory of the interaction between conjugated systems. I. General theory", Journal of the American Chemical Society, vol. 90, pp. 543-552, 1968. https://doi.org/10.1021/ja01005a001

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Real hypervalency in a small molecule.

Sunday, February 21st, 2016

Hypervalency is defined as a molecule that contains one or more main group elements formally bearing more than eight  electrons in their  valence shell. One example of a molecule so characterised was CLi6[1] where the description "“carbon can expand its octet of electrons to form this relatively stable molecule“ was used. Yet, in this latter case, the octet expansion is in fact an illusion, as indeed are many examples that are cited. The octet shell remains resolutely un-expanded. Here I will explore the tiny molecule CH3F2- where two extra electrons have been added to fluoromethane.

Two such electrons added to e.g. such a methane derivative can be in principle accommodated in two ways:

  1. The electrons on carbon could expand the octet shell by populating molecular orbitals constructed using 3s or 3p atomic orbitals (AOs) as well as the normal 2s and 2p shells. This is also the normal "explanation" for expanded octets, the assumption being that as one moves down the rows of the periodic table (e.g. P, S, Cl, etc) these shells become energetically more accessible (e.g. the 3d or 4s shell for P, S, Cl etc). In fact, for e.g. PF5, the occupancy of such  "Rydberg" shells is only ~0.2 electrons, not a significant octet expansion.
  2. The electrons can instead or as well as populate the antibonding molecular orbitals (MOs) formed from just the 2s/2p AOs. For a methane derivative, there are four bonding MOs (into which the octet of electrons are placed) and four anti-bonding MOs all constructed from the total of eight AOs. Well known examples of populating antibonding MOs are the series N≡N, O=O (singlet), F-F, Ne…Ne where the additional electrons are added to anti-bonding MOs and have the effect of reducing the bond orders from 3 to 2 to 1 to 0. And of course all core shells contain populated bonding and antibonding pairs.

Here are some ωB97XD/Def2-TZVPPD/scrf=water calculations. All these species are molecules with all-real vibrations, being stable toward dissociation to e.g. CH3– + H– or CH3– + F–.  A transition state for this latter dissocation with IRC[2] can be characterised. In all cases the energy of the highest occupied MO or NBO is -ve, meaning that the electrons are bound, at least in part due to the solvent field applied.

Molecule Wiberg CH order Wiberg CF order Natural Populations E HONBO, au dataDOI
CH42- 0.773 –

C:[core]2S(1.98)2p(3.82)3S( 0.15)4d( 0.01)

H:1S( 1.00)

-0.144CH4 [3]
CH3F2- 0.980 1.213

C:[core]2S(1.05)2p( 3.20)3S(1.26)4p( 0.01)4d( 0.01)

H:1S( 0.84)2S( 0.01)2p( 0.02)

F:[core]2S(1.88)2p( 5.61)3S( 0.30)3p( 0.04)3d( 0.01)4p( 0.01)

-0.068
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 [4]
CH2F22- 0.871 0.897

C:[core]2S(1.60)2p( 2.64)3S(0.39)3p( 0.01)4d( 0.01)

H:1S(1.19)2S( 0.06)

F:[core]2S(1.86)2p( 5.52)3S( 0.01)3p( 0.01)4p( 0.01)

-0.281
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 [5]
CF42- – 0.801

C:[core]2S(1.94)2p( 1.96)3S( 0.19)3p( 0.04)5d( 0.01)

F:[core]2S(1.89)2p( 5.54)3p( 0.01)3d( 0.02)

 

-0.148CF4 [6]
  1. CH42- shows only small Rydberg occupancy (< 0.2e), but a significantly reduced bond order for the four C-H bonds (each C-H bonding NBO also has some antibonding character for the other three CHs) and hence the molecule is not truly hypervalent.
  2. CH3F2- in contrast shows quite different behavour. The C-H bond order is almost 1 and the C-F bond order is actually >1. Of the two extra electrons, ~1.28 now occupy carbon Rydberg AOs and the fluorine also has significant Rydberg population (~0.36e). So this is a real hypervalent system, in which the total valencies exceed that expected from an octet.
  3. CH2F22- is somewhere inbetween the previous two systems. The carbon has modest Rydberg occupancy (~0.4e) but there is also significant occupation of the antibonding MOs. Both the C-H and C-F bond orders are <1.
  4. CF42- shows a further reduction in the C Rydberg occpancy (<0.2) and the C-F bond order is also reduced. This reduction in bond order is also seen in other so-called hypervalent systems such as PF5.

So of these systems, CH3F2- can be reasonably called hypervalent, whilst the others have much less such character. It does appear that there is a fine balance between placing extra electrons into Rydberg orbitals to expand the "octet" and hence valencies, and placing them in anti-bonding orbitals where the individual valencies are actually reduced. It seems that substituting methane with just one fluorine encourages population of the Rydberg orbitals, but that more fluorines encourage instead population of the antibonding orbitals. What is remarkable is that CH3F2- actually has a (small) barrier to dissociation. The challenge now is to try to design a system which has a significant Rydberg population, a low antibonding population AND is stable to dissociation; this will require some inspiration. So do not hold your breaths!

 

References

  1. H. Kudo, "Observation of hypervalent CLi6 by Knudsen-effusion mass spectrometry", Nature, vol. 355, pp. 432-434, 1992. https://doi.org/10.1038/355432a0
  2. https://doi.org/
  3. H.S. Rzepa, "C 1 H 4 -2", 2016. https://doi.org/10.14469/ch/191837
  4. H.S. Rzepa, "C 1 H 3 F 1 -2", 2016. https://doi.org/10.14469/ch/191919
  5. H.S. Rzepa, "C 1 H 2 F 2 -2", 2016. https://doi.org/10.14469/ch/191918
  6. H.S. Rzepa, "C 1 F 4 -2", 2016. https://doi.org/10.14469/ch/191916

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Quintuple bonds: resurfaced.

Sunday, January 31st, 2016

Six years ago, I posted on the nature of a then recently reported[1] Cr-Cr quintuple bond. The topic resurfaced as part of the discussion on a more recent post on NSF3, and a sub-topic on the nature of the higher order bonding in C2. The comment made a connection between that discussion and the Cr-Cr bond alluded to above. I responded briefly to that comment, but because I want to include 3D rotatable surfaces, I expand the discussion here and not in the comment.‡

Firstly, a quick update. Since the original post, quite a few Cr-Cr quintuple bonds have been reported. In searching the crystal structure database, I used the text "quintuple" as a text search term (since specifying a quintuple bond as such is not supported) along with a Boolean AND using the sub-structure Cr-Cr (with any type of bond allowed). The result is shown below. It is striking that in fact these "quintuple" bonds cluster into a set with a bond distance of ~1.74Å and another with 1.83Å. Are these valence bond isomers?

 

Now to the system shown at the top (one of the 1.74Å set). My original post discussed the results of a density functional evaluation of the properties of the electron density in the Cr-Cr region. Most striking was the value of the Laplacian ∇2ρ(r) of this density, the value of +1.45au being the largest ever reported for a pair of identical atoms. I should remind that ∇2ρ(r) is used as one measure of the character of a bond, being the balance between electronic kinetic energy density and potential energy density along a bond. But it is well recognised that the bonding between such transition metals has what is called multi-reference character; the wavefunction is not well described by just a single doubly occupied electronic configuration. More electronic configurations have to be included, and hence a MC-SCF (multi-configuration) self-consistent description of the wavefunction is needed. So as a response to the comment noted above, I decided to carry out CASSCF/6-311G(d) calculations, in which an active space of electrons and molecular orbitals is specified, and using the geometry previously obtained at the DFT level. Thus a CASSCF(8,8) calculation takes 8 electrons and evaluates all possible configurations arising from placing them into an active space of eight molecular orbitals. With metals unfortunately the active space is likely to be large, and so I decided to computed (10,10), (12,12) and (14,14) CASSCF as well to see if any convergence might occur. The last is close to the limit offered by the program. The values shown below are at the QTAIM line (bond) critical point along the Cr-Cr axis.

Active space ρ(r) ∇2ρ(r) Total energy, Hartree % of CS config Calculation DOI
8 .303 1.720 -2383.48049 63 [2]
10 .308 1.612 -2383.68830 61 [3]
12 .308 1.612 -2383.70398 60.6 [4]
14 .308 1.612 -2383.72161 59 [5]
DFT .313 1.45 – 100 [6]

From the trend above, we might safely conclude that the CASSCF active space IS convergent, at least for the density if not for the energy. Also convergent are the properties of the density such as ∇2ρ(r), and noteworthy is that the value of this property is even higher than was obtained using single-configuration DFT theory. So the claim that this system has a record such property does not change. Negative values of the Laplacian are normally taken to indicate a conventionally covalent bond, whereas +ve values show the bond has what is called charge-shift character.[7] So these Cr-Cr quintuple bonds must be amongst the most charge-shifted exemplars!

I show some surfaces (click on the image to get a rotatable model) computed from the CASSCF(14,14) density. Firstly the electron density ρ(r) itself, contoured at 0.25au, showing the high value between the chromium atoms.

Next, ∇2ρ(r) contoured at ±1.5, revealing its high value in the Cr-Cr region (blue = +ve, red = -ve) and then below at ± 0.25 which includes the covalent bonds of the ligands.

Finally, the ELF (electron localisation function) function which tries to gather the electron density into localised ELF basins (numbers are the integration of the electron density in this basin). This looks very similar to that shown previously and is striking because there is no basin in the Cr-Cr region. Instead, the localisation is along the Cr-N bonds. One might describe this as saying that the Cr-Cr region is very highly correlated.

‡It is a limitation of the WordPress system that such objects cannot be included in comments.

References

  1. C. Hsu, J. Yu, C. Yen, G. Lee, Y. Wang, and Y. Tsai, "Quintuply‐Bonded Dichromium(I) Complexes Featuring Metal–Metal Bond Lengths of 1.74 Å", Angewandte Chemie International Edition, vol. 47, pp. 9933-9936, 2008. https://doi.org/10.1002/anie.200803859
  2. H.S. Rzepa, "C 2 H 6 Cr 2 N 4", 2016. https://doi.org/10.14469/ch/191860
  3. H.S. Rzepa, "C 2 H 6 Cr 2 N 4", 2016. https://doi.org/10.14469/ch/191857
  4. H.S. Rzepa, "C 2 H 6 Cr 2 N 4", 2016. https://doi.org/10.14469/ch/191858
  5. H.S. Rzepa, "C2H6N2O2", 2016. https://doi.org/10.14469/ch/191855
  6. H.S. Rzepa, "C 2 H 6 Cr 2 N 4", 2010. https://doi.org/10.14469/ch/4156
  7. S. Shaik, D. Danovich, W. Wu, and P.C. Hiberty, "Charge-shift bonding and its manifestations in chemistry", Nature Chemistry, vol. 1, pp. 443-449, 2009. https://doi.org/10.1038/nchem.327

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Posted in General, Interesting chemistry | 6 Comments »