Bond moments

In stead, the electrostatic con tribn tion conies from definin g a set of bond dipole moments associated woth polar bonds. These bond moments are defined in the m m psir.LxL(dbf) file along with the bond stretching parameters and are given in units of Debyes. The cen ter of th e dipole Is defined to be th e m Idpoint of the bond an d two dipoles p. and pj. separated by Rjj. as shown beltnv ... 

The angles ot, p, and x relate to the orientation of the dipole nionient vectors. The geonieti y of interaction between two bonds is given in Fig. 4-16, where r is the distance between the centers of the bonds. It is noteworthy that only the bond moments need be read in for the calculation because all geometr ic features (angles, etc.) can be calculated from the atomic coordinates. A default value of 1.0 for dielectric constant of the medium would normally be expected for calculating str uctures of isolated molecules in a vacuum, but the actual default value has been increased 1.5 to account for some intramolecular dipole moment interaction. A dielectric constant other than the default value can be entered for calculations in which the presence of solvent molecules is assumed, but it is not a simple matter to know what the effective dipole moment of the solvent molecules actually is in the immediate vicinity of the solute molecule. It is probably wrong to assume that the effective dipole moment is the same as it is in the bulk pure solvent. The molecular dipole moment (File 4-3) is the vector sum of the individual dipole moments within the molecule. 

All bonds between equal atoms are given zero values. Because of their symmetry, methane and ethane molecules are nonpolar. The principle of bond moments thus requires that the CH3 group moment equal one H—C moment. Hence the substitution of any aliphatic H by CH3 does not alter the dipole moment, and all saturated hydrocarbons have zero moments as long as the tetrahedral angles are maintained. 

Charge asymmetry can be associated with a particular bond in a molecule and gives rise to what is called a bond dipole moment or, simply, bond moment. One use of bond moments is that they can be transferred, to a fair degree of approximation, from one molecule to another. In this way the dipole moment of a molecule can sometimes be estimated from a vector sum... 

The BF3 molecule, shown in Figure 4.18(i), is now seen to have /r = 0 because it belongs to the point group for which none of the translational symmetry species is totally symmetric. Alternatively, we can show that /r = 0 by using the concept of bond moments. If the B-F bond moment is /Tgp and we resolve the three bond moments along, say, the direction of one of the B-F bonds we get... 

If it seems obvious on looking at the BF3 molecule in Figure 4.18(i) that it has no dipole moment then what we are doing in coming to that conclusion is a rapid, mental resolution of bond moments. 

The molecule tran5 -l,2-difluoroethylene, in Figure 4.18(h), belongs to the C2 , point group in which none of the translational symmetry species is totally symmetric therefore the molecule has no dipole moment. Arguments using bond moments would reach the same conclusion. 

NF3 is a colourless, odourless, thermodynamically stable gas (mp —206.8°, bp —129.0°, AG29g — 83.3kJmol ). The molecule is pyramidal with an F-N-F angle of 102.5°, but the dipole moment (0.234 D) is only one-sixth of that of NH3 (1.47 D) presumably because the N-F bond moments act in the opposite direction to that of the lone-pair moment ... 

Nevertheless, Murrell, Kettle, and Tedder conclude in their book on valence theory57 that there is no correlation between the electric dipole moment of a bond and the electronegativity difference. They have plotted the values of the electric dipole moments of eight bonds against the difference in the values of the Mulliken electronegativity (see Figure 1-2). (The bond moments for OH, NH, PH, NF, and PF are calculated from the... 

Figure 1-2. Bond moments m of some bonds plotted against the difference in Mul-liken electronegativity of the bonded atoms. (Redrawn from Reference 57, p.359.)...

Values of the bond moments (in debye units) for the eight bonds shown in Figure 1-2 are given in Table 1-2. In Figure 1-3 the large circles represent... 

Figure 1-3. Bond moments /i plotted against the difference in the original electronegativity values large circles represent bond moments for the bonds displayed in Figure 1-1.

Equation 1-1 with Ax = 1 for N—F leads to 22.1% ionic character and bond moment 1.46 D, a little above the straight line in Figure 1-3. Let us assume that the contribution of the pure covalent structure 1 has the value of 47.2%, calculated from the value 77.9% for each bond (22.1% ionic character). Since the three structures of type 2 contribute 3 X 2.74% = 8.2%, the structures of type 3 contribute the remainder, 44.6%. This value leads to 14.9% for the amount of double-bond character of each of the bonds in the NF3 molecule, close to the value 15% for CHF3, CC1F3, and C1F3 calculated from the shortening of the bond length,59 which is by 0.05 A. 

For PF3 the observed value of the bond moment with the same calculation yields 10.5% for each of the type 2 structures, a total of 31.5% for these struc-... 

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. 

The electric dipole moments in units 1 X 10 18 e. s. u. of these molecules and their derivatives by hydrogenation measured19 in benzene solution are the following furan, 0.670 2,5-di-hydrofuran, 1.53 tetrahydrofuran, 1.68 pyrrole, 1.80 pyrroline, 1.42 pyrrolidine, 1.57 thiophene, 0.54 and tetrahydrothiophene, 1.87. We now give a very rough interpretation of these quantities based on the bond moments given... 

The dipole moment is a property of the molecule that results from charge separations like those discussed above. However, it is not possible to measure the dipole moment of an individual bond within a molecule we can measure only the total moment of the molecule, which is the vectorial sum of the individual bond moments. " These... 

Figure 2.6 The dipole moment of the water molecule can be resolved into two OH bond moments. This does not give the true value of the bond moments because this procedure ignores the atomic dipoles.

Figure 2.7 The dipole moments of the symmetrical SF6 and CCI4 molecules are zero because the vector sum of the bond moments is zero. In contrast the dipole moment of POCI3 is not zero because the molecule is less symmetrical and the vector sum of the three Cl bond moments is not equal and opposite to the CO bond moment.

Figure 2.5 Bond moments and the resulting dipole moments of water and ammonia.

For molecules that have several polar bonds, a rough approximation of the overall dipole moment can be made by considering the bond moments as vectors and finding the vector sum. Consider the water molecule, which has the structure... 

Table 6.2 Bond Moments for Some Types of Polar Bonds. ...

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