Testing existing FFs

To see whether any off-the-shelf FFs were capable of describing our cages, three well-known FFs were used to minimise the cage structures, and several internal degrees of freedom were evaluated. Initial tests showed that generalised FFs, such as the Universal force field9 _{(UFF), the polymer consistent force field}

(PCFF),10 _{and COMPASS,}11,12 _{do not accurately simulate the structures; Table 3.1.}

FF Used C-N-C (°) N-C-C (°) N-C-C-N (°) Similarity

(%)

RMS atom distance (Å) Crystal

Structure 115.50 108.84 69.48 Target Target

Universal 123.31 110.00 62.67 98.80 0.073

Compass 122.01 116.67 112.74 93.01 0.237

PCFF 117.75 117.07 62.67 98.73 0.078

Table 3.1 – CC1 was minimised in the gas phase using a variety of generic FFs and compared to the X-ray crystal structure data. For similarity and RMS atom distance, hydrogens have been omitted.

As an example, a comparison of the optimised structures of a cage of CC1 in the gas phase from each FF with the initial crystal structure geometry is given in Table 3.1. The Universal FF overestimates the C-N-C angle for the imine group by around 8°, and shows a root mean squared (RMS) distance between the optimised and reference structure of 0.073 Å. The COMPASS FF shows a similar overestimation of the C-N-C angle for the imine group and the N-C-C-N torsion was over 40° greater than that experimentally observed, resulting in an RMS distance between calculated and observed structures of 0.237 Å. PCFF does give the C-N-C angle for the imine group to within 3°, but the N-C-C angle associated with the imine group was significantly over estimated. Even so, the RMS distance of atoms in the PCFF10 _{structure from the experimental structure was only 0.078}

Å. In particular, the planarity of the region around the phenyl rings of the cages, which depends on conjugation with the imine groups,1 _{was poorly represented,}

Figure 3.1 – Figure showing the similarity to crystal structure (red) post FF minimisation (blue) using a) UFF, b) PCFF and, c) COMPASS FF.

PCFF10 _{lacked an accurate parameterisation of the imine group in the}

environment found in these cage materials. Nonetheless, PCFF did describe the porous cage molecules more accurately than the other off-the-shelf FFs we tested, and so we decided to use this as the basis for a new, bespoke FF that would accurately describe a range of discrete porous imine cage molecules.

Table 3.2 – Table listing the lattice parameters and number of molecules used for all MD simulations.

The main issue seems to be the imine functionality, which is directly attached to an aromatic ring. For example, Figure 3.2 shows a whole subset of different molecules parameterised within the COMPASS FF. Here, it was evident that benzene has been accurately parameterised, as well as alkanes, amines, and amides; imines, though, were omitted. This would explain why the aromatic region of the system seems to be well produced, while the imine regions were not. UFF was fitted for a wide range of functional groups; unstrained and uncongested hydrocarbons, saturated ethers and phosphines, alkenes, silanes, saturated amines, aromatic systems, and simple unconjugated multiple bond containing compounds such as nitriles, ketones, and imines.9 _{However, like the}

COMPASS FF, the planarity of the phenyl ring in combination with an imine bond Cell Parameters System Supercell size a / Å b / Å c / Å α / ° β / ° ϒ / ° Density (g/cm3₎ No. atoms CC1α 4 x 4 x 2 51.24 43.64 73.62 90.00 97.49 90.00 1.03 13824 CC1β 4 x 2 x 4 84.92 42.46 42.48 90.00 90.00 120.00 0.93 10368 CC2 4 x 4 x 4 75.08 75.08 43.68 90.00 90.00 120.00 0.87 16128 CC3 2 x 2 x 2 49.60 49.60 49.60 90.00 90.00 90.00 0.97 10752 CC4 2 x 2 x 4 47.85 47.85 43.83 90.00 90.00 120.00 0.95 7200 CC1α, CC3 2 x 2 x 2 48.55 48.55 48.55 90.00 90.00 90.00 0.89 8832 Benzene 3 x 3 x 3 21.86 27.60 20.06 90.00 90.00 90.00 1.16 1296 Aniline 2 x 8 x 4 43.64 46.94 33.55 90.00 101.01 90.00 1.17 7168

was not present in the parameterisation criteria. Although this was also true of PCFF, it was a useful starting point as it has been used to accurately simulate polymers and organic materials and hence we can develop the additional PCFF parameters through FF fitting to density functional theory (DFT) reference data for the absent functionalities.

Figure 3.2 – Parameterisation precedence tree for COMPASS FF. The parameterisation starts from the top and all parameters determined at one level were fixed and transferred as many times as possible to the next level. Figure taken from reference 12.

The aim of this FF was to accurately describe CC1, CC2, and CC3. The only difference between these cges was the functionality of the vertices, meaning an unfunctionalised 108-atom cage core (CC1) acts as a good description of all three cages. Therefore, ab initio data was fitted to describe this cage core and the accuracy for the other cages can be subsequently analysed to see whether this assumption was appropriate.

When using MD, it was important to use a system that was large enough so that periodic boundaries do not affect the results. Therefore, supercells of crystal structures were generally used. The CC1α unit cell has dimensions a = 12.81 Å, b = 10.91 Å, c = 24.54 Å, α= 90.00°, β= 97.49° and γ= 90.00°. This was used to generate a 4 × 4 × 2 supercell which contains 128 cages with a total of 13,824 atoms. As this system consists of 128 identical cages, one was extracted and

studied to see if there were any degrees of symmetry within the molecule. It was clear that a 24 atom fragment was repeated around the cage system four times and this describes all the intramolecular parameters required to describe a whole cage. This meant that only 34 intramolecular potentials could describe the whole cage system. To validate this assumption, after the fragment was fully parameterised, a whole cage was minimised and the accuracy of the FF tested by comparing to single crystal structure data. This procedure is shown is Figure 3.3.

Figure 3.3 – A 4 x 4 x 2 supercell of the crystal structure of CC1α; containing 13.824 atoms. This contains a 108 atom repeat unit; this was a single cage. A common fragment of 24 atoms was identified within a single cage and this was extracted from the crystal structure. This fragment was then used to fit the parameters required for the intramolecular degrees of freedom. The 24-atom fragment highlighted four times in the single cage to show how it was constantly repeated across the cage core.