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The rational design of helium bondsHenry S. Rzepa*

The chemistry of helium has hitherto been confined to experimental and theoretical analysis of small molecules containingthree to five atoms in the gas phase. Here a new suggestion is made for compounds of helium deriving from a recentproposal that five-coordinate carbon might be captured as a frozen SN2 transition state. A series of logical steps, originallydiscussed as postings and comments to two blogs, led to the outcome described here of a central hypervalent atom boundon one face by a small cyclic carbon ligand, with the other free face having an interaction to a helium atom with thetopological properties of a charge-shift rather than a covalent bond. Although high-level theory predicts these heliumbonds to be quite short with relatively high stretching frequencies, the kinetic barriers to the loss of helium are predictedto be small, and are not increased by the strategy of having bulky substituents on the ring ligand.

Helium is one of only two (non-radioactive) elements for whichcrystalline derivatives are not available (the other element isNe; only crystalline clathrates of Ar and Kr are known)1.

The search for a chemistry of helium has been taking place formany decades2,3; and most of the search has focused on cationicsystems involving the interaction of a helium atom with a smallnumber of other atoms in the gas phase. Some neutral systemshave also been identified as thermodynamically metastable (thatis, with a finite but not necessarily large free energy barrier todissociation), of which HeBeO (ref. 2), HHeF (ref. 4), HeOCsF(ref. 5), HeCuF and HeAuF (ref. 6) are typical examples.

The topic of helium chemistry has recently been reviewed7. Avariety of other close (that is, shorter than the sum of the van derWaals radii) interactions to helium atoms have also been reported.Thus Frenking, Merino and colleagues have investigated theoreti-cally the nature of the interactions between pairs of helium atomstrapped in carbon cages; interatomic He–He distances as short as1.265Å have been calculated8–10. However, when liberated fromtheir endohedral confinement, these dimers immediately dissociate.Topological analyses of the electron density of these systems usingtechniques such as atoms in molecules (AIM)10,11, which seem toreveal that the He–He region resembles a bond, also serve to high-light both the controversial character of such conclusions and thegenuine difficulty in defining what a bond is to the satisfaction ofall12. The recently calculated endohedral cluster He@Mo6Cl8F8(ref. 13), although stable to loss of He, likewise seems to containno covalent He–Mo bond. In the present article, a potentially newclass of helium-bonded systems resulting from a rational designprocess is investigated, and the helium binding is analysed in thecontext of a recent proposal of a charge-shift mode of bonding byShaik and Hiberty14.

The topic of putative helium chemistry itself came to the atten-tion of the present author under relatively novel circumstances com-pared with the more conventional processes of scientific discourse15.The story starts with the recent investigation16 of whether an SN2transition state for nucleophilic substitution at carbon with trigonalbipyramidal geometry at carbon could be frozen into a stable inter-mediate (that is, the potential energy surface inverted) by judiciousselection of substituents. Computational modelling predicted thatthis would be achieved using astatine anions as both nucleophileand nucleofuge surrounding a tricyanomethyl carbocation, 1.However, given the radioactive nature of astatine, it seems unlikelythat this can be easily subjected to experimental scrutiny!

At At

NC

CN

CN

Cp Cp

NC

CN

CN Si

Mg(THF)3

n

2

X

R

R

RHe

n

X

R

R

R

9 10

R

R R

R

R

R

R

R

CR

R

R

R

R

CR

R

R

R

R

HBR

R

R

R

R

BrR

Co(CO)3R

R

R

6 7 85

1 2 3 4

Molecule 1, it was argued16, shows not only pentacoordinationbut also pentavalency at the central carbon. This article becamethe topic of a blog post by Bachrach17, and open discussion wasinvited. The present author contributed to the Bachrach blog bynoting a recent report18 that the cyclopentadienyl anion couldalso act as a nucleofuge (in the manner of a pseudo-halogen).Indeed, it transpired that replacing the astatine atoms in the originalproposal by cyclopentadienyl (Cp) anions also results in a (compu-tationally) frozen transition state 2. This observation was thendocumented on the present author’s own blog site19, where it wassuggested that this variation was perhaps more amenable to experi-mental study than coping with astatine. Further logical connectionswith observations reported in the literature followed:

† The central atom can be pared down to just a C2þ atom bearingno substituents. This idea was inspired by the report20 of thecrystal structure of a formally h5-coordinated Si2þ cation to apentamethylcyclopentadienyl (Cp*) anion 3 (R¼Me).

† This carbon analogue 4 (R¼Me) has now also been calculated tobe a stable minimum, one in which a carbon atom is hemispheri-cally coordinated to the face of the Cp* group, and which can besaid to be both pentacoordinate and pentavalent21.

Department of Chemistry, Imperial College London, South Kensington Campus, Exhibition Road, London, SW7 2AZ. *e-mail: rzepa@imperial.ac.uk

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† The highest occupied molecular orbital of 4 was found to showwhat might be termed a lone pair at the apex of the five-coordinatecarbon. Inspired by Frenking’s report22 that carbones (formallyC(0) species) have remarkably high second proton affinities, themonocation 4 was found to also readily bind a proton to form adicationic complex 5 (R¼Me), which again was calculated tobe a minimum in the potential energy surface23. This can be sum-marized by stating that Cp* can h5-coordinate a HC3þ cation togive a formally hexacoordinated and hexavalent carbon, forwhich a formal electron octet is maintained.

† Analogy to 5 was found in the report of a crystal structure of aCp* anion complex24 involving h5 coordination to a BrB2þ

cation 6 (R¼Me), in which BrB2þ is isoelectronic with HC3þ

at the coordinating atom.† There is also literature precedent for varying the size of the ring

forming the coordinating ligand. Thus the crystal structure of(aromatic) cyclobutadienyl dianion as an h4 ligand coordinatingto Mg2þ (7, R¼ SiMe3) has been reported25 as has the structure26

of a formal (aromatic) cyclopropenyl trianion h3 coordinating toCo3þ (8, R¼ Ph).

† The final logical connection required (although the logical con-nections are made here by the present author, a human, wehave argued that formally exposing the logic in journal articlesusing resource description framework (RDF) declarations mayenable such creative discovery to be capable of robotic automationin the future27) is to hypothesize that for carbon centres with (theequivalent of) unusually high second proton affinities, one mightbe able to replace (2H)2þ with the isoelectronic28 He2þ.

† One is now in a position to explore a range of possible (closed shell)systems as shown with the general motif 9, the high symmetryallowing reasonably high (predictive) levels of theory to be used.

† The advantage of using ligands such as those in 9 compared withthe small molecules noted in the introduction is that the nature ofthe R group can now be used to explore both the electronic andthe steric responses.

Results and discussionCalculations for a range of systems of general type 9 are reported inthe table in Fig. 1. For the examples with C4v symmetry (n¼ 2), theCCSD(T)/aug-cc-pVTZ procedure is viable for R¼H. The recently

developed double-hybrid density functional theory methods(B2GP-PLYP/TZVPP)29,30 offer comparable accuracy to theCCSD(T) procedure at much less computational cost, and allowvibrational modes to be realistically computed. Also included inthe table are results using the more common B3LYP/aug-cc-pVTZ method. A multi-reference calculation at the same basis setlevel (CASSCF(8,8), eight electrons in an active space of eight orbi-tals) indicates that the wavefunction is dominated (�94%) by asingle configuration, suggesting that the use of single-referencemethods is appropriate. Computed force constants are all positivefor the putative minima in the table. The shortest computedlength to the helium atom (for R¼H, X¼ C and n¼ 2) ofrC–He¼ 1.19Å is comparable to the length of a C–H bond (forcomparison, the monohelioacetylene monocation at theMP2/6-31G(d,p) level has a He–C bond length of 1.11Å)31. TheC–He stretching wavenumber of �1,022 cm21 is about half thatof a C–D bond (of equivalent reduced mass). The system forwhich R¼H, X¼ B, n¼ 1 is also neutral rather than cationic,and it has a B–He stretching wavenumber nB–He of 513 cm21.

Given the relatively short bond lengths and high stretchingfrequencies, these systems emerge as interesting candidates fortopological analysis of the electron density using the bond-critical method (atoms in molecules, AIM) of Bader11. All thesystems had bond critical points in the X–He region, andthe values of the electron density r(r) are all substantial. Thedicationic R¼H, X¼ C, n¼ 2 has r(r) 0.161, which is approachingthe values found for normal single bonds (�0.25–0.30).The value of the electronic Laplacian ∇2r(r), which describesthe electronic kinetic energy at the critical point, is large andpositive for all the systems. These characteristics (large r(r) andlarge positive ∇2r(r)) are also the properties that have been associ-ated with a type of bond known as charge-shift type, examples ofwhich cited by Hiberty and Shaik14 include the central bond in[1.1.1]propellane (r(r) 0.19, ∇2r(r) þ0.43) and the F–F bond(r(r) 0.25, ∇2r(r) þ0.58). In a X–He bond in which the X atomcarries a significant positive charge, the purely covalent X–Hecontribution can be regarded as electrostatically repulsive, whereasit is the less repulsive ionic components such as X–He2þ andHe–X2þ that stabilize the bond by their resonance with thecovalent component.

Figure 1 | A screenshot of an interactive table that compiles calculated properties for molecular compounds of helium. The interactive version of this table

and associated footnotes are available online at http://www.nature.com/nchem/journal/v2/n5/media/nchem.596_jmol.html.

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An alternative way of presenting information about the elec-tronic kinetic energy is the electron localization function (ELF) pro-cedure32,33, which derives a function related to the excess Paulikinetic energy density and which can be related to bond character-istics. In this analysis, a bond emerges as a so-called disynapticbasin, with its centroid located somewhere in the region betweentwo nuclear attractors. This basin can be integrated for the electrondensity contained within its boundaries. When this analysis is per-formed on the species reported here, clear disynaptic basins emergefor the helium region, together with further such basins linking theatom X and each carbon in the perimeter of the ligand. The inte-gration of these latter basins reveals them to correspond moreclosely to highly bent one-electron rather than two-electron bonds(see X¼H, n¼ 2). Both the AIM and the ELF procedures identifynot only charge-shift bonds to He, but also hypervalency (but notoctet expansion) for atom X.

The monocationic X¼ B, n¼ 2 seems a reasonable candidate forexploration as a potentially isolable crystalline species. This is mostlikely achievable if a non-coordinating34 anion such as B12X12

22,X¼ Cl, Br were to be used. If the anion were significantly nucleo-philic, then the highly exothermic disproportionation reaction9nþþNun– O 10–NuþHe is likely to occur and would destroythe bond to helium. Nonetheless, if a significant barrier to the dis-sociation reaction 9 � 10þHe existed, then 9 would be kineticallymetastable. The reaction path for this dissociation for 9, R¼H, X¼ B,n¼ 2 turns out to deviate substantially from a vertical take off fromthe ‘launch pad’ (Fig. 2a). The B–He distance at the transitionstate is elongated by 0.37Å and the geometry has only Cs symmetry,with a calculated free energy (DG‡) barrier of 4.4 kcal mol21 (B2GP-PLYP/TZVPP). The free energy of the overall reaction is exothermictowards helium loss by 8.3 kcal mol21 at the same level of theory.The calculated barrier seems to be both method and basis setinsensitive (4.7@B3LYP/aug-cc-pVTZ, 4.8@B3LYP/aug-cc-pV5Z),which suggests that basis-set-superposition errors are not signifi-cant. Replacing R¼H by R¼ CN decreases the free energybarrier to 1.0 kcal mol21 (B3LYP/aug-cc-pVTZ). These values aretoo small to expect any kinetic stability for such a species otherthan at very low temperatures, but there remains the possibilitythat using a large and bulky R group might feasibly increase thisbarrier. Using a standard large substituent (R¼ 2,6-diisopropyl-phenyl, DIP), the sideways trajectory is now inhibited, and thetransition state (Fig. 2b) instead corresponds to a ‘vertical lift off’by the helium (C4v symmetry). The DG‡ (B3LYP/6-311G(d,p)

barrier, however, reduces to close to zero (the positive enthalpicbarrier of þ1.7 kcal mol21 more or less matches the reductionowing to an increase in entropy, resulting in no overall freeenergy barrier). The dissociation of He from the neutral 9, R¼H,X¼ Be, n¼ 2 likewise proceeds along a vertical trajectory. ForR¼H, no transition state can be located, the potential surfacebeing endothermic to dissociation by þ5.1 kcal mol21 (B2GP-PLYP/TZVPP). For X¼ Be, n¼ 2, R¼DIP, a dissociative transitionstate can be located, but the barrier is tiny (0.4 kcal mol21) and thereaction is predicted to be exothermic overall (–8.6 kcal mol21,B3LYP/6-311G(d,p)).

ConclusionsDevising a compound containing an indisputable bond to heliumthat would be capable of characterization as a crystalline species isclearly a substantial challenge. Here an approach has been presentedthat involves creating a ‘stressed’ coordination site for the heliuminvolving hypercoordinate and hemispherically bound atoms fromthe first row. These systems are indeed predicted to interact with ahelium atom to form short contacts, and topological analysis ofthe electron density reveals these as clear-cut bonds that seem tobelong to the recently proposed charge-shift variety. This non-covalent character means that the bond stabilization is localizedon the dissociation coordinate, and this in turn may be the originof the low barriers to dissociation. This characteristic makes it diffi-cult to impart long kinetic lifetimes to these species using purelyelectronic control. Although attempts to increase this lifetimeusing large steric groups have been unsuccessful so far, thisapproach has not been fully explored, and may still succeed withother designs.

Received 11 November 2009; accepted 23 February 2010;published online 28 March 2010

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a b

1.64 Å

Figure 2 | Form (eigenvectors) of the calculated normal transition state mode (green arrows) at the B2GP-PLYP/TZVPP level for the dissociation/combination

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Additional informationThe author declares no competing financial interests. Reprints and permission informationis available online at http://npg.nature.com/reprintsandpermissions/. Correspondence andrequests for materials should be addressed to H.S.R.

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