Clase principal

The experim ental crystal structure was used to provide the m olecular model and also to test the non- em pirical potential. Since so m uch o f 1 is hydrocarbon, the em pirically fitted hydrocarbon param eters in the 'estim ated' potential should give a reasonable reproduction o f the crystal structure. Indeed, the successful prediction [32] o f the crystal structure o f 1 ju st assum ed that the boron param eters were those o f an sp^ carbon. H ence, the crystal structure is a much m ore severe test o f the overlap potential m ethod when it is used consistently for all interactions. H ence we attem pted the construction o f a com plete non-em pirical repulsion model and validate by using the sam e crystal structure. The resulting potential is tabulated in T able 4.10, and contrasted with the em pirically fitted potential o f W illiam s [75,76,166].

The C . . . C repulsion is steeper for the non-em pirical potential and the total H ...H potential is a lot softer (m ainly reflecting the greater dispersion coefficients) than the em pirically fitted (or com bining rule generated) potentials (See F igure 4.13 and T able 4.10). If we com pare the B ...B repulsion, we can see there is a significant difference, as expected from W illiam s' em pirically m odelled repulsion. O ur B ...B repulsion is derived using a m olecule that has sim ilar environm ent as the blind test m olecule, whereas W illiam s' repulsion is fitted using a range o f borane crystals [166].

N e w M odels for Interm olecular Repulsion and their Application to van d er W a a ls C o m p le x e s and Crystals of O rg anic M olecules

H e len H .Y . Tsui August 2001

4 Blind Crystal Structure Prediction 79 B...B R / Â B ...0 R / Â 0...0 18 13 8 3 •2 Â R / B...C B...H C ...O R / Â g LU H ...0 H...H 13 8 3 2 R / Â C ...C C...H

Figure 4.13 Graphs o f repulsion-dispersion energy for each atom-atom pairs using the 'estimated', non-empirical and Williams' models.

N o te red lines d e n o te 'e stim a te d ' m o d el, blue lines d e n o te n o n -e m p irica l m odel a n d green lines d e n o te W illia m 's m odel.

N e w M odels fo r Interm o lecu lar R ep u lsio n and their Application to van d e r W a a ls C o m p lex es and Crystals of O rg a n ic M olecules

H e le n H .Y . Tsui A ugust 2001

4 Blind Crystal Structure Prediction 80

'estimated' non-empirical Williams*

Atom pairs A . Q

«.X

A .

c..

a..

Ax Q B...B 4.21 424361 3739.9 4.21 462505 5485.2 3.42 391404 4911.6 B ...0 4.84 3997253 1859.7 4.84 4111103 2263.7 3.69 300099 2349.2 0 ...0 5.31 13944948 1035.7 5.31 15762121 1174.8 3.96 230094 1123.6 B...C 4.10 335210 1939.3 4.12 1018089 3252.1 3.51 380444 3461.7 B...H 4.33 86122 922.2 4.35 118465 1101.7 3.58 68455 818.5 C ...0 4.61 14925612 1050.4 4.59 5774961 1516.0 3.78 291696 1655.7 H...0 4.95 621741 511.6 4.99 776928 490.8 3.85 52486 391.5 C...C 3.60* 369743* 2439.8* 4.01 1889878 2060.5 3.60 369743 2439.8 H...H 3.74* 11971* 136.4* 4.31 16256 227.3 3.74 11971 136.4 C...H 3.67* 66530* 576.9* 4.04 149195 681.3 3.67 66530 576.9

Table 4.10 Repulsion-dispersion potential parameters used in conjunction with the distributed multipole electrostatic model.

^The William's potential was taken from the literature [75,76,166], assuming that these potentials were transferable and could be used in combination with using the relationships a,^ = - (A,Aor ) ^ > ^ik = *Also used Williams' empirical potentials. in  ‘, in kJ/mol and in kJ/mol ®.

Table 4.11 shows the errors in the reproduction of the crystal structure of 1 with variations on the non-empirical model. The large changes in the dispersion through using either Ketelar's polarizabilities [169] (which give a very low value for carbon) or using Halgren's [172] expression for produces potentials with a rather large error in the b parameter, and smaller lattice energies. Using the more modem atomic polarizabilities, with and scaling the dispersion, as suggested by Mooij [93], improves the b parameter considerably, though somewhat at the expense of the other parameters and volume.

The effects upon changing values of K are shown in Table 4.11, to test the sensitivity of the repulsion to K . Increasing the repulsion by varying K, the proportionality constant makes small differences to the structure, though much larger changes to the total lattice energy. However, the structural reproductions of many of these non-empirical potentials are quite acceptable, and not significantly worse than the other potentials, which are based on a large body of empirical fitting. The predicted lattice energies would be discriminated more between the variations in dispersion coefficients, but unfortunately, no estimates are available for 1.

New Models for Intermolecular Repulsion and their Application to van der W aals Complexes and Crystals of Organic Molecules

Helen H.Y. Tsui August 2001

4 Blind Crystal Structure Prediction_______________________________________ 81

Dispersion model K Uiatt(expt.)“ Uiatt(min) / Differences from experimental crystal structure in

/ kJ/mol kJ/mol _{L V ol Aa A6 Ac A^ r.m.s.} % erroi^ S-K (Ketelaar) 8.48 -99.6 -103.4 2.70 -1.73 5.16 -0.40 1.05 3.15 S-K (Miller) N, 8.48 -107.2 -110.1 1.84 -1.63 4.69 -0.90 1.04 2.92 S-K (Miller) 8.48 -75.9 -82.0 6.24 -0.60 7.05 0.00 0.81 4.09 S-K (Mooij) 8.48 -149.3 -153.1 -3.08 -2.94 2.16 -1.98 1.37 2.40 Effect o f variation o f K S-K (Mooij) N, 7.50 -157.8 -165.0 -5.93 -3.63 0.74 -2.75 1.69 2.67 S-K (Mooij) N, 8.00 -153.5 -158.6 -4.44 -3.27 1.49 -2.35 1.53 2.48 S-K (Mooij) 8.50 -149.1 -152.9 -3.03 -2.92 2.19 -1.97 1.37 2.39 S-K (Mooij) /V„ 9.00 -144.8 -147.8 -1.70 -2.60 2.84 -1.61 1.22 2.41 S-K (Mooij) 9.50 -140.5 -143.2 -0.45 -2.30 3.44 -1.27 1.08 2.50

C om parison with m odel d e riv e d fr o m W illia m s’ p a ra m eters(See Table 4.10)

Williams -121.5 -123.3 2.47 1.31 3.16 -1.78 0.91 2.23

Table 4.11 Errors in the reproduction of the crystal structure of 1 (2-(2-phenylethenyl)-1,3,2-benzodioxaborole) using variations on a non-empirical potential with a distributed multipole electrostatic model potential.

The Slater-Kirkwood dispersion model [51] used the polarizabilities and/or scaling in brackets [93,169,170], and either the valence N, or effective (Equation (4.3)) number of electrons. “Lattice energy at experimental crystal parameters and corresponding '’minimum, "’r.m.s. % error is calculated over 3 cell lengths. ^ K is the proportionality constant between the repulsion energy and the overlap given here in atomic units ( ).

4.7 Discussion

Blind crystal structure prediction is a difficult challenge since there was a deadline for the submission of the possible crystal structures for the investigated system. Therefore all the steps carried out were performed to the best possible within the time limit. The time factor played an important role in this study, limiting the possibility of improvements to some of the procedures. Our rigid-body assumption has introduced error right from the beginning. More work was needed for the MOLPAK search as both the planar and non-planar geometries were searched. The other procedure that was also affected by the time factor was the derivation of new repulsion and dispersion potentials for boron and oxygen involved atom-atom pairs. There was not enough time to test the reliability and accuracy of the new repulsion and dispersion parameters, and there were no suitable existing boron parameters available. Also, there was not enough time to perform the overlap model on the investigated system, so we assumed that the benzodioxyboryl derivative we used in the overlap model has similar environments to the investigated system.

When the experimental results were released, we knew that our predictions were unsuccessful as we had used the incorrect molecular geometry. Nevertheless, the space group of the experimental crystal structure was predicted correctly to be P 2 ,/ c , and closer observation showed similarities between the experimental crystal structure and the predicted structures. First of all, the herringbone arrangements can be seen in all of them and secondly the inverted dimer motif can be visualised in all crystal structures. In order to check whether the force fields used in the predictions is reliable or not, the experimental crystal structure was minimised in DMAREL with the estimated' model potential. The minimised experimental crystal structure show that it is very close when compared with the

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

4 Blind Crystal Structure Prediction___________________________________________________ 8^ experimental structure, in both ceil parameters and lattice energy. This indicates that the new boron potential seem to be adequate for the crystal structure prediction.

This study is the second example of the use of the overlap model to provide repulsion parameters for an organic molecule. It extends the methodology developed for the small symmetric molecule of oxalic acid [101], to an application for a larger molecule 1, where the overlap analysis of a smaller organic model molecule 2 was necessary. Nevertheless, the methodology is appealing in that the transferability assumptions required are far more reasonable than those used in the empirical derivation of potential parameters. It is also not necessary to assume combining rules relating hetero- and homo-atomic interaction parameters, which have no real justification for repulsion parameters [95]. The main appeal of the method is that it does not require any experimental data.

The success of the estimated' potential for modelling the intermolecular interactions that determine the crystal structure shows that the method is very suitable for providing estimates of "missing" parameters. The non-empirical potential provides a more stringent test of the method. This potential has been constructed without any reference to experimental data (except tabulated atomic polarizabilities), and, yet, is as satisfactory for crystal structure modelling as the model constructed from carefully fitted empirical potentials. There are still many uncertainties in the potential, such as the effect of basis sets and electron correlation, the omission of anisotropic terms and the method of deriving K , so Table 4.10 should not be taken as a definitive set of parameters. The main weakness in the non-empirical model is in the estimates of the dispersion coefficients C,^ . The plausible, but large variations in C^^ values have a small effect on the structure reproduction, but produce major variations in the predicted lattice energy. Further investigations into the possible derivation of the atom-atom dispersion coefficients from the wavefunctions of organic molecules should improve our ability to predict these coefficients in the future. The success of this non-empirical potential, along with that of the oxalic acid potential [101], does encourage us to further develop this systematic approach to constructing potentials from the charge distributions of the molecules.

The original application of the 'estimated' potential, the attempted crystal structure prediction of 1, has been a partial success. The CCDC blind test workshop [32] proved most illuminating in defining the progress that has been made towards reliable methods of predicting the crystal structures of organic molecules. The results and analysis presented here for 1 illustrate a major problem in predicting the crystal structures of flexible molecules. A small change in a torsion angle (in range 0 - 19 °) has a major effect on the crystal packing and cell parameters, but the internal energy changes by less than 1 kJ/mol. The changes in the lattice energy with conformation are somewhat larger, but the balance is so subtle that it is a considerable achievement for our estimated' potential that the global minimum in the combined lattice and internal energy does occur for the correct crystal and molecular structure. Therefore, the prediction of crystal structures of flexible molecules not only involves an extremely demanding search of conformational and crystal structure space, but also relies on an accurate balance between the inter- and intramolecular forces. The methodology developed here should help in improving the realism of the intermolecular potentials. In conclusion, blind crystal structure prediction is a highly challenging task, but provided the method used is based on firm theoretical footing; there is great prospect in overcoming such a challenge.

New Models for Intermolecular Repulsion and tfieir Application to van d er W aals Helen H.Y. Tsui

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