Gallup G.A. - Valence Bond Methods, Theory and applications (CUP, 2002)
.pdf12.3 Dipole moments of CO, BF, and BeNe |
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The curves for CO and BF show the form typical of these systems as is emphasized
in Ref. [53]. In our discussion of LiF in Section 8.3 we emphasized how the nature of a wave function could change from ionic to covalent with a change in internuclear
distance. Here again we appear to have the “signature” of this sort of phenomenon:
the change of sign of the moment at internuclear distances around 1.0–1.5 A |
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strongly |
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suggests the interplay of two effects where the winning one changes fairly rapidly |
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with distance. On the other hand the sign of BeNe does not change and this suggests |
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that one of these effects is absent in this molecule. |
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From the signs on the moments and our work in Chapters 2 and 8 we interpret |
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these curves as follows (for the interpretation of the signs the reader is reminded |
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that all three of our systems are oriented with the |
less |
electronegative |
atom in |
the |
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positive |
z-direction). |
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1. At internuclear distances intermediate, but greater than equilibrium, the familiar ideas of |
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electronegativity win out, and the more electronegative atom has an excess of negative |
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−0.70|e |. |
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charge. |
At the maxima the charge on O in CO is around |
−0.29|e | and o |
n F in BF |
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It is not surprising that in BF the effect is larger. No legitimate argument would suggest |
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that Ne has any sort of negative ion propensity, and we do not see a maximum in that |
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curve. |
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2. When systems are pushed together, nonbonded electrons, on the other hand, tend to |
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retreat toward the system that has the more diffuse orbitals. In this case that is C, B, or |
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Be. Since the nonbonded electrons are generally in orbitals less far out, this effect occurs |
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at closer distances and, according to our calculations, wins out at equilibrium distances |
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for CO and BF. This is the only effect for BeNe, and the moment is in the same direction |
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at all of the distances we show. This retreat of electrons is definitely a result of the Pauli |
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exclusion principle. |
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Both sorts of physical effects tend to fall off exponentially as the distance between |
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the atoms increases – the dipole moment must go to zero asymptotically. A close |
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examination of the CO results shows that the moment goes to very small negative |
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values again around 4.0 A |
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. Whether this is real is difficult to decide without further |
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calculations. It might be that the Pauli exclusion effect wins again at these distances, |
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the result might be different for a still larger basis. Also, Gaussian basis functions |
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can cause troubles at larger distances because individually they really fall off much |
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too rapidly with distance. |
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12.3.2 |
Difficulties with the STO3G basis |
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We also calculated the dipole moment functions for CO, BF, and BeNe with an |
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STO3G basis, and it can be seen in |
Fig. 12.2 that there are real |
difficulties |
with |
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the minimal basis. We have argued that the numerical value and sign of the electric |
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182 13 Methane, ethane and hybridization
constant. Using the methods of Chapter 5, we may write |
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T |
h R in terms of standard |
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tableaux functions: |
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1 |
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h |
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h |
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h |
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T h R |
12 |
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b |
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1 s b |
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2 pa x |
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1 s a |
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h |
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1 s a |
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h |
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1 s |
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= |
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h z |
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− |
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1 s b |
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+ |
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1 s b |
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5 |
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2 p x |
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2 p x |
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1 sa |
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1 s a |
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1 sa a |
2 p |
x |
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h |
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h a |
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h |
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h b |
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h z |
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1 s b |
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x |
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2 p |
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2 p x |
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9 |
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1 sa |
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2 pb x |
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1 sa a |
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zp |
x |
. (13.5) |
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h |
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1 s |
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h b |
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h b |
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h b |
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2 p x |
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h z |
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1 s b |
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We see immediately that |
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T |
1 |
AO , the standard tableaux function invariant to the hybrid |
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angles, is actually the largest term in |
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T |
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h R |
, but not overwhelmingly so. The others |
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all depend on the hybrid angles and, therefore, so does |
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1 |
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T |
h R . We may also note that |
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T 1h R |
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1 |
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using hybrid orbitals |
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has a lower energy by |
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≈3 eV, but, as seen from Table 13.1, |
≈3 eV. |
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the full calculation, with either sort of basis, is still more stable by another |
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The calculated value of the dipole moment is 0.6575 D for this basis with the |
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charge positive at the H-atom end of the bonds. |
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CH |
3 |
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Adding an H atom to CH |
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2 |
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might be expected to do little more than regularize the |
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hybrids we gave in Eq. (13.2), converting them to a canonical |
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sp 2 |
set. With this we |
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expect a planar doublet system. Whether the molecule is really planar is difficult |
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to judge from qualitative considerations. Calculations and experiment bear out the |
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planarity, however. |
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A full valence orbital VB calculation in this basis involves 784 standard tableaux |
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functions, of which only 364 are involved in 68 |
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2 |
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2 |
A |
2 |
symmetry functions. For CH |
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we present the results in terms |
of |
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sp |
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hybrids. This |
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no effect |
on |
the energy, |
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of course. We show the principal standard tableaux functions in Table 13.5. The |
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molecule is oriented with the |
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C |
3 -axis along the |
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z -axis and one of the H atoms on the |
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x -axis. The three trigonal hybrids are oriented towards the H atoms. The “ |
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x ” sub- |
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script on the orbital symbols in Table 13.5 indicates the functions on the |
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x -axis, the |
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“a ” subscript those 120 |
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◦ from the first set, and the “ |
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b ” subscript those 240 |
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◦ from the |
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first set. |
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