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Aberration corrected imaging of a carbon nanotube encapsulated Lindqvist Ion and correlation with Density Functional Theory

80 kV aberration-corrected transmission electron microscopy (AC-TEM) of discrete [W6O19]2− polyoxometalate ions mounted within double walled carbon nanotubes (DWNTs) allow high precision structural studies to be performed. W atom column separations within the octahedral W6 tungsten template can be visualized with sufficient clarity that correlation with full-scale density functional theory (DFT) can be achieved. Calculations performed on the gas phase and DWNT-mounted [W6O19]2− anions show good agreement, in the latter case, with measured separations between pairs of W2 atom columns imaged within equatorial WO6 octahedra and single W atoms within axial WO6 octahedra. Structural data from the tilted chiral encapsulating DWNT was also determined simultaneously with the anion structural measurements, allowing the nanotube conformation to be addressed in the DFT calculations.


Introduction
In tandem with the burgeoning interest in a wide diversity of nanoscale structures, associated studies into single molecules are becoming more prevalent. Advances in atomic probe-type (i.e. AFM, STM or similar) [1] and electron microscopy [2,3] atomic and molecular imaging techniques are making efficient comparison between experimentally determined discrete structures and ab initio or a posteriori theory more routine. A key aspect of these investigations is the correlation of intramolecular perturbations with effects induced by the local environment. Polyoxometalate ions (POMs) are of interest in this respect as they have an extensive structure-synthetic chemistry enabling a wide variety of ordered molecular-scale cluster anions to be produced with variable charge-ordering arrangements [4]. In the present context, they provide molecular-scale heavy atom motifs with observable symmetry than can be imaged by conventional high resolution transmission electron microscopy (HRTEM) when mounted in single or double walled carbon nanotubes (i.e. SWNTs or DWNTs) or graphene oxide [5,6]. We have previously been able to image the octahedral O h symmetry Linqvist [W 6 O 19 ] 2ion in DWNTs [5] (Fig. 1(a)) by HR-TEM and have imaged the W 2 -W 2 atom column separations in the equatorial plane of the anion. A limitation of this study was that information from the corresponding axial W atom columns was blurred however a minimum requirement for an effective comparison with theory is that at least two dimensions of the anion be resolvable. We demonstrate here that it is possible to do this for individual ions by aberration corrected transmission electron microscopy (AC-TEM) and also that we are able to obtain conformational information from the nanotube simultaneously [7]. This allows us to produce trial composite anions and nanotube conformations for investigating both structural and electronic interactions between the encapsulated anion and the nanotube using DFT.

Experimental Details
The DWNTs used in this experiment were supplied by Carbon Nanotechnology Inc. [nBu 4

Results
The previous imaging study of [W 6 O 19 ] 2ions mounted within DWNTs [5] revealed that within sterically matched nanotubes with an innermost ~1.2 nm diameter SWNT the ions lie with a preferred orientation within the encapsulating cylindrical volume, specified by the van der Waals radii of the wall carbons (i.e. 0.17 nm), of diameter ca. 0.9 nm. This orientation (which is projected along the C 2 rotation axis of the anion -see Fig. 1(a)) conveniently enables W 2 -W 2 atom column pairs within the equatorial plane of the [W 6 O 19 ] 2superoctahedron, to be directly visualised by a conventional HR-TEM with an objective lens coefficient of spherical aberration, C s (alternatively, C 3 ), of 0.6 mm.
Multislice image simulation studies showed that this level of aberration blurs the image contrast from the W 2 -W 2 atom column pairs once the contribution of the equatorial terminal oxygen atoms is taken into account. Additionally, image contrast from the single atom W-W pair was blurred or missing. Fig.  1(b) shows a wider field of view image of two parallel DWNTs, one empty, one containing a discrete [W 6 O 19 ] 2anion. Comparison of a detail of the same structure anion as imaged using the 300 kV HR-TEM (C s = 0.6 mm) in Fig. 1(c) with the same structure anion using the lower voltage (i.e. 80 kV) AC-TEM (C s = 0.001 mm) imaging conditions in Fig. 1(d) shows the improvement in detail.   Fig. 4(b).
An indication of the improvement in information in the AC-TEM images can be made using line profiles through W 2 -W 2 and W-W atom column pairs in multislice image simulations for both cases (i.e. Figs. 1(e) and (f)) as shown by the extracted equatorial and axial profiles (i.e. Figs. 2(a) and (b)). As noted previously, there is a ~5% distortion in the W 2 -W 2 column separation for the more aberrated case partly due to higher C s but also to the smearing contribution of the O 3 columns on the anion periphery [5]. This distortion is reproduced in Fig. 2(a) in which the troughs of profile I corresponding to the W 2 columns are displaced ~5% with respect their expected positions. Profile II in Fig. 2(a) corresponds to the simulated W 2 -W 2 atom column pairs for the AC-TEM but with C s = 0.001 mm. In this case, the troughs are displaced ~1%, reflecting a greater confidence in the new measurements. According to profiles III and IV in Fig. 2(b), there is little distortion of the axial W-W columns in either the 300 kV or 80 kV images but the image contrast from the 300 kV image (Fig. 1(c)) is too noisy to produce a reliable measurement. In Fig.  2(c) we see that it is possible to measure the atom column spacings for both equatorial W 2 -W 2 and axial W-W separations for the 80 kV case (i.e. 0.342 and 0.477 nm respectively, precision 0.026 nm). Additionally we have also been able to resolve the wall carbon spacings on one side of the DWNT (Figs. 1(b) and (d)). Line profiles through all four walls ( Fig. 3(a) Fig. 4(a) is evidently more appropriate for comparison with the experimental case. We can also now compare both experimentally determined and DFT-optimised equatorial W 2 -W 2 and axial W-W separations. The experimental measurements for the equatorial and axial separations (i.e. 0.342 and 0.477 nm, see above) compare reasonably with the corresponding DFT optimised gas phase separations (i.e. 0.333 and 0.471 nm, respectively) and optimised [W 6 O 19 ] 2-@(12,6) SWNT separations (i.e. 0.331 and 0.471 nm, respectively) [7].