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Heteroatoms single and multiple bonds

We now consider molecules isoelectronic to ethane, ethylene, and acetylene containing heteroatoms instead of carbons. As shown in Figure 5.21, the molecules ethane, hydrazine, hydrogen peroxide, and fluorine are isoelectronic to each other; as are ethylene, diimide, and singlet oxygen; and acetylene and dinitrogen.

Figure 5.21: Gallery of heteroatom single, double, and triple bonds.

We find that bonds between heteroatoms are too strong and too short (Figure 5.22). For example, while we calculate ethane to have a bond dissociation energy of 140 kcal/mol vs 90 kcal/mol exact, and a bond length of 1.53 $ \mathrm{\AA}$ versus 1.53 $ \mathrm{\AA}$ exact, we calculate $ \mathrm{F_{2}}$ to have a bond dissociation energy of 275 kcal/mol vs 38 kcal/mol exact, and a bond length of 1.05 $ \mathrm{\AA}$ versus 1.35 $ \mathrm{\AA}$ exact. One possibility is that eFF does not have sufficient repulsion between lone pairs. In both the single and double bonds, increasing the nuclear charge causes the bond joining the atoms to become weaker, due in part to the greater repulsion between lone pairs as the bond length shrinks.

Figure 5.22: Bonds between heteroatoms are too strong and too short, possibly due to insufficient repulsion between lone pairs.

This logic does not extend to $ \mathrm{N_{2}}$, where the lone pairs are directed away from each other -- the triple bond in $ \mathrm{N_{2}}$ is more than 100 kcal/mol stronger than the triple bond in acetylene. eFF also predicts that the $ \mathrm{N_{2}}$ bond should be especially strong, but with a bond dissociation energy only 42 kcal/mol stronger than in acetylene.

Triplet oxygen is another unusual case -- it is analogous to $ \mathrm{F_{2}}$, but with two fewer lone pair electrons it is able to form two two-center three-electron bonds with a combined strength of 163 kcal/mol, which is 125 kcal/mol stronger than the $ \mathrm{F_{2}}$ bond. It is difficult to tell whether eFF can capture these effects; eFF predicts that the $ \mathrm{O_{2}}$ triplet bond is 20 kcal/mol weaker than the bond in $ \mathrm{F_{2}}$, but it is not clear how this value would change if lone pairs were made to be more repulsive.

To test our hypothesis that lone pairs do not repel strongly enough in eFF, we compute the interaction energy of two neon atoms (Figure 5.23), and compare it to the Hartree-Fock interaction energy, which serves as an accurate estimate of exchange repulsion. We find that eFF significantly underestimates the neon-neon repulsion. In $ \mathrm{F_{2}}$, eFF finds that the lone pairs repel each other with an energy of $ \sim$0.25 hartrees. If we assume that the fluorine atoms should repel each other as the neon atoms do, we conclude that the bond length should be larger by $ \sim$0.3 $ \mathrm{\AA}$, which matches the discrepancy between eFF and exact bond lengths. Other contributions, such as the change in electron size upon binding, and the effects of $ p$ versus $ s$ character on Pauli repulsion, were found to be minimal.

Figure 5.23: Repulsion between neon atoms in eFF is too small.

We conclude that the Pauli repulsion between lone pairs is too small and that it is necessary that this issue be corrected before simulations with heteroatoms can be accurate. Once lone pair-lone pair interactions are properly described, a wide range of organic reactions could be studied using eFF.


next up previous contents
Next: Van der Waals dimers Up: Results and discussion Previous: Carbon-carbon single and multiple   Contents
Julius 2008-04-29