Bond Polar Parameters

Within the framework of the bond polarization the shift components of the unpolarized bond and the parameter Aai giving the polarization influence on the chemical shift are determined empirically from solving a set of linear equations 1 for a number of substances where both the chemical shift tensor and the molecular structure are known. The bond polarization energies Vai are calculated as effect of surrounding net atomic charges qx on atomic hybrids %. With the bond polarity parameter the polarization energy can be calculated. 

The origin of equations 1 and 2 was explained in more detail in (6). The calibration of the bond polarization parameters for, 3C chemical shift tensors for C(sp3/sp2)-C, C(sp3/sp2)-H, C(sp3/sp2)-0, and C(sp3)-N o-bonds as well as C(sp2)-C and C(sp2)-0 71-bonds was described in detail in (5). Structural data and tensorial single crystal, 3C NMR data of 20 crystalline substances including sugars, polycyclic aromatic compounds, and amino acids were used in this calculation. 

The bond polarity parameter jam affects remarkably (in the first order) only the diagonal density matrix elements the off-diagonal ones acquire the corrections of the second order in /im. 

The important question of the stability of the perturbation expansion to changes in hybridization and the bond polarity parameter is discussed by Jordan et a/.152 The method has been extended to radicals with a well localized odd electron153 and to some excited states.154 A similar ab initio treatment has been developed but can only be applied to small molecules.155 In a paper dealing with calculation of n.m.r. coupling constants, Dennis and Malrieu make some use of INDO terms rather than CNDO.156 A complete derivation of the PCILO equations using diagramatic techniques has been given recently by Kvasnicka.157... 

Because of the inclusion of Dewar-type as well as the Kekul6-type structures in the Lewis structure resonance scheme, the increased-valence structures are more stable than are the familiar Kekule-type Lewis structures from which they are derived, provided that the one-electron bond polarity parameters, are chosen variationally. Therefore as discussed already in Section 8, a better (i.e. lower energy) VB description of the bonding may be obtained when increased-valence structures rather than only the component Kekul6-type structures, are used to provide VB representions of electronic structure. 

The intensity parameters employed, tmrned bond polar parameters (BPP), represent derivatives of die Cartesian components of the molecular dipole moment with respect to the variables Ar, A0 ( and A<. These form two types of parametric matrices for each bond ... 

The solution of the inverse intensity problem, which in this formulation implies die evaluation of bond polar parameters from experimental dipole moment derivatives with respect to normal coordinates, can only be performed fm a molecule possessing higfrer symmetry. The situation in this respect is the same as in the alternative theoretical formulations. The requirement is that the direction of the vibrational transition dipole is fixed by symmetry. In odier words, there should be only one non>zero element in each colunm of the Pq matrix [Eq. (3.1)]. Again, all calculations are considerably simplified if the dp/dQi derivatives are first transformed into dipole moment derivatives with respect to internal symmetry coordinates. The determination of the elements of P(, can then be realized using die following general expression, in matrix notation... 

The values of bond polar parameters obtained using Eqs. (4.123) and (4.126) depend on the specific orientation of the reference Cartesian system with reflect to which the analysis is performed. In order to compare parameter values in differoit molecules it is necessary to convert the initially obtained sets into values corresponding to a local bond axis system. The transformation from a molecular (x, y, z) to a bond system (xg, y, Zg) is achieved by applying the following relations ... 

Application of Eq. (4.126) produces die following equations relating dp/dSj to bond polar parameters ... 

The C=0 and C=S bonds have much greater parameter values reflecting the higher polarity of these bonds. Very good linear correlations between C-H bond polar parameters and halogen electronegativities have been found for the series of methyl haUdes [48]. 

An intriguing point to consider in relation to die data presented in Table 4.10 is the transferability of parameters between molecules having die same type of bonds in a similar environment. In the methyl halide series die variation of dpx /dr. H and dpxQ/d6( H is substantial and the quantities are, evidendy, not transferable between these molecules. This finding is in contrast to the overall similarity of the force fields of methyl halides [24]. The variations of bond polar parameters in these molecules illustrate clearly the high sensitivity of infiared band intensities to structural variations. The SPxq/3tc h parameter values for C P -H bonds in ethylene, allene and benzene are... 

Bond polar parameters for carbon-halogen bonds in some organic molecules ... 

Table 4.11 contains bond polar parameter values for carbon-halogen bonds determined from experimental infrared intensities in halomethanes and carbonyl halides. As emphasized before, bond polar parameters are not directly related to the equilibrium charge distribution and, therefore, any relationship between the magnitude or sign of diese quantities and the actual polarity of valence bonds may only be qualitative. It should also be pointed out that parameter values are dependent on the accuracy of experimental measurements and the force fields employed. 

In analyzing the data presented in Table 4.11 some general trends are found and wordi discussing. It can be seen that the magnitude of bond polar parameters for C-F, C-Cl, C-Br and C-I bonds is much higher than for the respective quantities of C-H and C-C bonds (Table 4.10). It may safely be concluded that carbon-halogen bonds arc much more polar than the C-H and C-C bonds, in accord with expectations. If we sinvey the relative magnitudes of dp /dtQ x parameters for flie different... 

We went into some detail in discussing bond polar parameter values in different molecules since only such an analysis can reveal the physical significance of diese molecular quantities. Let us emphasize here, that no approximations in transforming the... 

E. Prediction of Vibrationai Absorption Intensities by Transferring Bond Polar Parameters... 

The transfer of intensity parameters between molecules for quantitative intensity predictions encounters various problems that need care l consideration. As already emphasized in tius section, due to the very high sensitivity of intensities to structural changes transferability properties of intensity parameters are expected to be much less pronounced compared to other molecular quantities. Secondly, certain parameters will be dependent on the particular site symmetry of the chemical bonds or atoms considered. Additional complications can arise if rotational correction terms are to be calculated. Predictions by transfer of parameters should, therefore, only be attempted for closely related molecules, such as homologous series. Bond polar parameters have been used in predicting intensities in intiared spectra in fluorinated methanes [144], alltylacetylenes [145] and medium-size n-alkanes [143]. In Fig. 4.8 the predicted infrared spectra of different conformers of n-pentane using bond polar parameters from n-butane are presented [143]. In more quantitative terms the predicted intensities are compared with the experimental values in Table 4.12. As can be seen from Table 4.12, the agreement between calculated and observed intensities is quite satisfactory. 

The relationship between atomic polar tensors and bond polar parameters has also been analyzed by Galabov et al. [100,124]. Multiplying both sides of the equation Ps - Rs = Pb V Ags [Eq. (4.126)] by a symmetrized B matrix we obtain... 

Making use of equation (4.14) die following relation expressing atomic polar tensors in terms of bond polar parameters is obtained... 

The semiclassical theories described so far are aimed mostly at interpreting the experimentally determined vibrational absorption intensities of molecules in terms of quantities associated with the charge distribution and dynamics. Fewer attempts have been made for quantitative predictions of intensities based on transferable intensity parameters. Successful predictions are difficult to achieve because transferability properties are not so well expressed as in the case of force constants. This is determined by a number of factors (1) the high sensitivity of vibrational intensities associated with particular modes to changes in molecular environment (2) the physical limitations of the approximate point-charge models and (3) mathematical difficulties in applying non-approximate models such as polar tensors or bond polar parameters for larger molecules. 

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