Gas phase molecule testing

Now that the cage fragment has been successfully described, we can test how well CSFF described a gas phase cage. CC1 was used for this set of calculations, since its core structure was common to all of the cage molecules (CC1–CC4). Additionally, all cage structures have the same carbon atom types in the n=..c..c..n= link between the imine groups (CC1: ethylene, CC2: methylethylene and CC3: 1,2-cyclohexyl). Figure 3.8 shows a comparison for the minimisations

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RMS

1

N

E

_E

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of the original base FF, PCFF, the new updated FF, CSFF, and that of a cage taken from the crystal structure. It was clear that the planarity of the cage faces was more accurately reproduced using CSFF, and this was because the potential parameters required to describe the planarity of the cages was absent in PCFF. As CSFF seemed to be performing well, CC1, CC2 and CC3 were compared to higher level calculations, to see whether the FF was transferable. Each cage was optimised using DFT (B3LYP/6-31G(d,p)) within the Gaussian03 package.16 _Figure

3.8 also displays the overlay of the three cage structures obtained from the crystal structure with the structures obtained via optimisation using DFT and optimisation when using CSFF. It was evident that CSFF represents the cage accurately and this superimposition of the three indicates that the cage was well represented. This gave a molecular similarity greater than 96% based on the Field method, with an average RMS atom distance of 0.2 Å. This was similar to the B3LYP/6-31G(d,p) optimised structures that had an average molecular similarity of 98% and an average RMS distance of 0.1 Å. So although the averaged DFT structures were slightly more accurate, CSFF allows the use of molecular mechanical MD and this was computationally far less expensive than ab initio MD, thus making the use of CSFF far more efficient when looking at a cage in the gas phase.

Figure 3.8 – Figure comparing the three cages, CC1, CC2 and CC3 (left to right), when taken straight from the crystallographic X-ray structure (red), minimised with CSFF (blue), minimised using DFT B3LYP calculations with a 6- 31G(d,p) basis set (green) superimposed on top of one another. On average, the cages minimised using the higher level density functional theory had a 98% similarity, whereas when the cages were minimised using CSFF there was a greater than 97% similarity to the crystal data. The average RMS atom distance was 0.1 Å and 0.2 Å respectively.

As molecular flexibility was a key factor and might influence host-guest behaviour as well as gas sorption properties, it was important to make sure that CSFF was describing the flexibility of the cages reasonably. From a design perspective, these ultramicroporous cages must strike a balance between being flexible enough to allow guest movement within the voids while being rigid enough to be

shape persistent, and therefore not collapse to a denser form. Empirically speaking, the imine cages were clearly less rigid than comparably-sized molecules such as C60, which can be treated as a rigid unit in MD simulations,19

but more rigid than many organic polymer chains.20 _{Therefore, the dynamic}

characteristics of the cages were analysed, paying particular attention to the molecular flexibility. The FF has been fitted to potential curves opposed to basic minima, consequently it would be expected to be able to perform the dynamics successfully, as the potential can oscillate at the bottom of the potential energy well.

Gas phase MD simulations were carried out for CC1, CC2 and CC3 using the Discover module in Materials Studio17 _{for 1 ns using an NVT ensemble at 298 K}

sampled every 0.5 ps using the cage structure from the respective crystal structure model. For simplicity, only one positional isomer of CC2 was used; an explanation for this can be found in Appendix A.1.1 _{In reality, the crystal}

structure for CC2 contained greater disorder due to positional isomers based on placement of the vertex methyl groups. A number of structural parameters for these cage molecules were monitored during the MD simulations, specifically around the diamine vertices: these include the C-N-C angle, the N-C-C angle, and the N-C-C-N torsion angle. These parameters were then compared to the experimental crystallographic data.1 _{Since the vertices for CC2 are asymmetric,}

the angle parameters behave slightly differently and hence these have been separated into C-N-C(Me), C-N-C, N-C-C(Me) and N-C(Me)-C.

When analysing the gas phase MD results, data taken directly from crystal structures may not act as a perfect benchmark as the packing forces were no longer present. However, all values seem to be in reasonable agreement at 298 K. Therefore it was unsurprising that the averages seen in Figure 3.9 deviate slightly. It was prudent to compare DFT to the FF to see how accurately the shape of the cage was being maintained. It was evident that for all three cages, the shape was being upheld. Only one conformer was considered and no interconversion was observed.21

Figure 3.9 – Gas phase MD results showing a) CC1 C-N-C angle, CC2 C-N-C(Me) angle, CC2 C-N-C angle, and CC3 C-N-C angle, b) CC1 N-C-C angle, CC2 N-C- (Me)-C angle, CC2 N-C-C(Me) angle and CC3 N-C-C angle and c) the N-C-C-N dihedral for CC1, CC2 and CC3. The red line indicates the static crystallographic value. Simulation proceeded for 1 ns using an NVT ensemble at 298 K sampled every 0.5 ps.