Results from the GMUL analysis

The overlap model allows one to determine the exponential repulsion parameter a and pre-exponential A separately for N —H and N---0, without the problem of the correlation of parameters which often necessitates the assumption of combining rules in empirical fits. The parameters a and A are determined directly from linear regression of the negative natural logarithm of the isotropic coefficient C^o on the interatomic distance, as summarised in table VI-2. Although these fits are excellent, they are not exact, as expected from the limited accuracy of the tail of the wavefunction. As the basis set gets better, the behaviour of the isotropic coefficient is more closely approximated by an exponential {e~^), and so the slope-derived a

should be more accurate. The different wavefunctions used for methylcyanide show that both «NO and values are sensitive to basis set, and the slightly larger DZP basis set gives a values in better agreement with those used in an empirical repulsion- dispersion potential^'* that successfully predicts the crystal structures of a range of polar and hydrogen bonded molecular crystals 2.233 ao~\ «no = 2.048 ao~'). It is important to note that the N —O parameters are more sensitive both to the basis set

VI. Use o f molecular overlap to p red ict repulsion in N - H —O

used and to the environment of the nitrogen atom, so that these can be expected to be less transferable than the N - H parameters.

Overall the overlap model gives reasonable estimates for the coefficient a,

which often is ill-determined in fits to experimental data because of correlation with the pre-exponential factor, but it is clear that it will be necessary to use high quality wavefunctions. In this comparison with a potential energy surface, the errors due to basis set will not cancel completely, and the exponent for the pyridine N---Q is probably too large because of the limited quality of the basis set.

VI. 4.3.2. Anisotropic repulsion parameters

The anisotropy (^'-function) coefficients for the N --H and N---0 interactions for both complexes are shown in figure VI-4. As the symmetry of the environment around the interacting atoms dictates the number of non zero coefficients, it was expected that there would be fewer important coefficients for the N —H than the N —0 interaction, and for the methylcyanide-methanol than the pyridine-methanol case. In the methylcyanide case it is rather clear that three coefficients (Cioi^^, Con°°) dominate the N--H anisotropy. In the pyridine case, there is less of a natural break in the series, so it is debatable whether we need 3 (Con®^, €303°°, Cioi^®), or six

C40/®, €404"'*^ in addition) coefficients to describe the N--H anisotropy. For the N --0

the cutoff is even less obvious, with five (Coii®"\ €303^^, CioiT Cq2 2~^), ten

(C404''", C404'', C,2i \ CoiiT C202* ''in addition) or thirteen (C022'"', C404""", C033' ' in

addition) coefficients being above different cutoff thresholds for pyridine, and only a small gap between the top four (CioiT €202^^, Con^"\ €022^^^) and other anisotropy

coefficients for methylcyanide. It is clear that in the N —0 case there is a problem of convergence, most particularly in the h values, which is associated with the asymmetrical bonding environment around the oxygen atom in methanol. It is worth noting that for the description of the N--H anisotropy the same Co/^ term (referring to the anisotropy on the H atom) is important in the description o f the N —H interaction between methanol and two very different molecules, methylcyanide and pyridine, confirming our expectation, that the difference in the anisotropies would stem primarily from the terms involving the nitrogen atoms. There are significant differences in the dominant Cjoj”° terms (anisotropy on the N atom) for the N - H

VI. Use o f molecular overlap to p red ict repulsion in N---H—O

interaction in methylcyanide-methanol and pyridine-methanol, reflecting their different charge distributions. In both systems the Cioi^^ is large, a fact obviously related to the extend of the charge density in the z-direction due to the lone pair on the nitrogen atom. However, the other dominant Cjoj®° coefficient is the for the methylcyanide complex and the €303°” for the pyridine one, clearly reflecting the

different bonding environments of the nitrogen atom in the two complexes.

VI. 4.3.3. Omission o f small coefficients and its effect on the model

The effects of omitting ^-functions with smaller coefficients can be tested by comparing how well the various analytical models predict the individual N - H and N —0 overlaps. For the N —H interaction in the pyridine-methanol complex, the correlation between the expansion model (equation VI: 10) and calculated N -H overlap increases from 0.9862, when only the isotropic term is used to 0.9966, when six anisotropic terms are added. The correlation is actually worse (0.9734), if only the first three largest anisotropic terms are used than if they are left out, indicating that an anisotropic model will only do better than the isotropic, if enough terms are added to model the anisotropy correctly. As expected, the addition of more terms results in better correlation of the model with the calculated N --0 overlap, with a 13-term expansion (0.9929) being better than a 10-term (0.9699), and a 5-term (0.9359) being fairly poor in contrast with the correlation for the isotropic prediction (0.9894). Once again the isotropic prediction is better than an anisotropic, where a lot of terms have been neglected, though this may be because the anisotropy in this system is fairly small. These correlations were evaluated using the pre-exponential coefficient A

obtained from the intercept of the plot of isotropic coefficient versus interatomic distance. As we shall see, some of the error of neglecting ^'-functions may be absorbed by fitting the pre-exponential coefficient to the calculated atom-atom overlaps, as this leads to a better agreement between the calculated and the analytical model overlap. This improvement is possible because only a limited part of the region around each atom is sampled in the intermolecular potential energy surface, and so many omitted S

functions may have the same sign in the intermolecular region, although they are, of course, orthogonal for integration over all orientations in space.

VI. Use o f molecular overlap to p red ict repulsion in N - H —O

VI. 4.3.4. The neglect o f variation o f with interatomic separation

A further approximation in the analytic model, the neglect of the variation of the relative anisotropic coefficients with separation, is also seen from figure VI-4 to be a significant approximation at short separations. For example the C/q, for the N —H overlap, and for both methylcyanide and pyridine, almost doubles in the range of interatomic distances examined. If we define Cooo^° to be unit (since we are not interested in the absolute value of the overlap), this is equivalent to a change of the fraction Cioi^VCooo^” from the 1.95 Â separation o f up to approximately 10% of the isotropic coefficient. It is worth noting that a much smaller ^-dependence was observed in the early work of Wheatley and Price^^ on ( ^2)2, (€12)2 and (p2)2. Hence,

the use of the coefficients at the normal hydrogen bond length will introduce errors into the model repulsive wall, which will be larger at shorter separations.