Ionic bond dipole moment

When the adjacency between a pair of atoms i-j is represented by a bond weight (for example, -> bond order, force constant, ionic character, - dipole moment, -> bond distances or its inverse) and/or each atom is represented by some - atomic properties such as atomic numbers, several weighted-vertex adjacency matrices called atom connectivity matrices ACM can be defined [Spialter, 1963 Spialter, 1964a Spialter, 1964b] and their entries are ... 

However, it turns out that this quantity is a rather poor indicator of the bond ionicity, as the system hardly behaves like a classical dipole consisting of two point charges, which is also illustrated by the fact that Mo depends strongly on cluster size. A much better indicator of the bond polarity is contained in the quantities M/, M2, and Ms. For all systems studied, Mj w -1.4 to -1.6, and Ms and M3 are small, and furthermore the cluster size dependence of these quantities is much less than that of Mq. (This points to a general property of cluster calculations already alluded to in Section 111.1 whereas absolute quantities may depend sensitively on cluster size, trends and slopes of trend curves show a much weaker cluster size dependence.) This linear behavior is consistent with an ionic bond where the slope. Mi, is related to the extent of ionicity. The dipole moment of two point charges +q and -q will be = -qx r and d/j/dr = M/ = -q. Hence for an ideal fully ionic halide bond, the curve is expected to be a straight line with slope M, = -l. 

In addition to the in situ electronegativity of atom A, EIa, there is also the question of in situ bond polarity across the bond AB in a molecule. At first, one would expect this to be IEa — IEb, but bond polarity is the ionic component (bond dipole moment) of the AB bond, and thus the covalent component must be subtracted out. So the bond polarity index, BPIab, must be defined as... 

Although the S—O bond lengths in sulphoxides and sulphones seem to indicate that these are covalent double bonds, the dipole moments of these compounds obtained by calculation or by experimental measurements support the semipolar single-bond character in these compounds, and they should be represented as S - O, with about 66% ionic character14,15. 

It is then shown that (excepting the rare-earth ions) the magnetic moment of a non-linear molecule or complex ion is determined by the number of unpaired electrons, being equal to ms = 2 /S(S + 1), in which 5 is half that number. This makes it possible to determine from magnetic data which eigenfunctions are involved in bond formation, and so to decide between electron-pair bonds and ionic or ion-dipole bonds for various complexes. It is found that the transition-group elements almost without exception form electron-pair bonds with CN, ionic bonds with F, and ion-dipole bonds with H2O with other groups the bond type varies. 

The quantum mechanical argument used in deriving the original electronegativity scale involved the amount of ionic character of a normal covalent bond A—B, and it was evident that the amount of ionic character and accordingly the value of the electric dipole moment of the bond would be closely correlated with the difference Ax = xA — xB of the two atoms A and B. In the first edition of The Nature of the Chemical Bond (1939) the following equation was advanced ... 

The observed value of the electric dipole moment of the molecule is 0.297 D, which corresponds to 0.24 D for the moment of the bond. The value of tr, 6.67 D, leads to 3.60% as the contribution of each of the two structures of type 6 to the ground state of the molecule. The ionic character corresponding to Ax = 0.5 is 6.06% from Equation 1-1, which gives bond moment 0.41 D, which would lie close to the straight line in Figure 1-3. 

Having shown that the weighting coefficient (A) of the term giving the contribution of an ionic structure to the molecular wave function is related to the dipole moment of the molecule, it is logical to expect that equations could be developed that relate the ionic character of a bond to the electronegativities of the atoms. Two such equations that give the percent ionic character of the bond in terms of the electronegativities of the atoms are... 

Calculate the percent of ionic character in the X-Y bond. If the X-Y bond length is 142 pm, what is the dipole moment of XY ... 

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