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The repulsion potential had to be derived using the charge distribution of a smaller benzodioxoboryl derivative, as 1 is too large for our computational resources. The benzodioxoboryl derivative 2 (Figure 4.4) was chosen from the CSD, as it provides a similar bonding environment for the oxyboryl group.

New Models for intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui

4 Blind Crystal Structure Prediction 63 H9 H11 £4 ,0 5 P7 0 3 H8‘ _H12 0 6 0 2 H10

Figure 4.4 Diagram of the benzodioxoboryl derivative with labelling o f atoms, used for the potential derivation (Scheme 2).

The structure of 2 was optimised at the MP2 level with the 6-3IG** basis set, using the program suite CADPAC [56] (See Table 4.1 for optimised geometry parameters).

Ab initio structure Bond lengths / Â Bi...Cé 1.541 B1... O2 1.390 B1... O5 1.390 O5. . .C4 1.383 O2...C3 1.383 C3. . .C4 1.342 C4. . .H9 1.074 C3...H8 1.074 Cg. ..C7 1.343 C5. .. H10 1.084 C7...H11 1.082 C7.. .Hi2 1.081 Angles / " Hg C3 O2 118 H9 C4 O5 118 C3 C4 C5 1 1 0 O2 C3 C4 1 1 0 B1 O2 C3 105 O5 B| O2 1 1 0 C4 O5 B] 105 O5 B] Cg 125 B, C6 C7 1 2 2 Hio Cg C7 119 Cô C7 Hi] 1 2 1 Cg C7 Hi2 1 2 2

Table 4.1 Molecular geometry parameters for scheme 2 ab initio optimised structure. Note all other torsion angles < 1®. See Figure 4.4 for numbering of atoms.

This charge density was re-expressed in terms of atom-centred Gaussian multipoles using the program GMUL3 [54,116]. The standard GMUL simplification of exponents procedure was used to represent the core of the atomic charge densities. This GMUL procedure defines the splitting up of the repulsion between atoms. The atom-centred Gaussian representation of the molecular charge density at each relative orientation of the two molecules was then used to calculate:

(a) the total molecular overlap Sp{R,Q.) (defined through Equation (2.36) and (2.37)) using GMUL3,

= KS^ = kIp, ( r ) p , (r)d^ r (4.4)

New Models for intermolecular Repulsion and their Application to van der W aals Com plexes and Crystals of Organic Molecules

Helen H.Y. Tsui August 2001

4 Blind Crystal Structure Prediction___________________________________________________ W

U ^ { R , a ) = K S ^ { R , a ) (4.5) (b) each atom-atom contribution SU- .Q* ) (Equation (2.43)) using GMUL3, and

U „ , = K S f,{R ^.Q ,,) (4.6) i s A , k e B

(c) the analytical expansion of each atom-atom overlap, using GMUL3 [116]

(4.7) where the coefficients depend on the atom-atom separation, and are the non-normalised set of orthogonal orientation dependent functions developed by Stone [64], with = 1.

The anisotropic contributions to the overlap were assumed to be negligible and so only isotropic S-function coefficients C% were considered. The set of isotropic S-function coefficients C% for each type of atom-atom overlap were analysed to obtain the isotropic atom-atom model of form

s^^ =exp(-a,^/?,.^) by a linear regression of the negative logarithm of C% over the interatomic separation R using the spreadsheet program EXCEL [174]. This procedure can provide model repulsion potentials. However, the derivation of both the and a^^ parameters from the isotropic overlap coefficient does not allow the opportunity for the neglected anisotropic terms to be absorbed into the model potential [69,104]. The analytical expression of the overlap of two atomic charge distributions, given by GMUL [116] using a partial wave expansion, treats the region around each atom in the direction of the intramolecular bonds on equal footing to the intermolecular contact region. Thus the isotropic coefficient is unlikely to be the optimum isotropic coefficient for the intermolecular repulsion. An alternative to the above method to obtain the 5,^ parameters is to fit them over a range of atom-atom overlaps that can be calculated using the program GMUL. Ideally, a large number of dimer geometries would be required. Hence the parameters were obtained by fitting to the total atom-atom overlaps (b) for orientations in the intermolecular contact region, assuming that the exponents for the model isotropic overlap were accurately obtained from the isotropic coefficient. Thus the coefficients required to model the total overlap (and hence repulsion with the addition of X ) were determined.

For the quickly 'estimated' model potential, the atoms B,, 0%, C3 and Hg in 2 were used to give the 7 types of atom-atom pairs required to sample all repulsion potentials involving B and O. The overlaps were calculated at 19 geometries of the benzodioxoboryl derivative (2) dimer, designed to sample these contacts (See Figure 4.5 and Table 4.4). All the atom-atom overlaps with a separation

within ± 1 Â of the sum of the van der Waals radii for the atoms (B = 1.5 Â, O = 1.4 Â, C = 1.8 Â and H = 1.2 Â) were used in the analysis, so at least 5 overlaps were used in the derivation of each pair of coefficients. We excluded all data except those points for which:

0.005 > S'* > 0.00005 (X-X pairs) 0.005 > S'* > 0.00001 (X-H pairs) 0.005 > S;* > 0.000005 (H-H pairs)

New Models for Intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui

4 Blind Crystal Structure Prediction___________________________________________________ ^ It is necessary to discard the many uninteresting larger separations to prevent them from dominating the fitting. Note 5^ is in a.u. (

The derivation of the completely non-empirical repulsive potential was performed with emphasis on assessing and developing the method, rather than speed. For the non-empirical potential, the atom- atom overlaps were calculated from 230 geometries for the benzodioxoboryl derivative (2) dimer. Most of these configurations were randomly generated within the repulsive region of the potential surface (defined such that the estimated maximum atom-atom repulsive energy was less than ICX) kJ/mol), with the addition of some stacking configurations to specifically sample the B ...B , C ...C interactions, etc. This guaranteed a minimum of 10 atom-atom overlap values corresponding to the distance range used in the analysis of isotropic coefficients calculations for each atom-atom pair. Two methods of fitting the pre-exponential parameters were considered. For the 'estimated' potential, the were determined by fitting directly to the atom-atom overlaps by least squares using LINEST in EXCEL [174]. However, the fitting of the natural logarithm of the overlaps, ln5p , to In 5,^ , with fixed, using SOLVER in EXCEL [174], gave a slightly better weighting to the errors and was used for the final non-empirical potential. Parameters were derived separately for the different C, H and O atoms, and when there appeared to be no significant difference between the parameters, then the data sets were combined for the final fitting.