next up previous contents
Next: Carbon-carbon single and multiple Up: Results and discussion Previous: Atom ionization potentials and   Contents

Atom hydrides

We optimize with eFF a series of atom hydrides $ \mathrm{AH_{n}}$, where A = carbon, nitrogen, oxygen, and fluorine, and $ \mathrm{n}=1-4$ (Figure 5.6). In all cases, we have selected the spin state corresponding to the most stable known ground state geometry. We find very good agreement with known bond lengths and angles (Figure 5.7) and moderately good agreement with known bond dissociation energies $ \mathrm{AH_{n}} \rightarrow \mathrm{AH_{n-1}} + \mathrm{H}$ (Figure 5.8). We reproduce (1) the shrinking of bond lengths with increasing Z, (2) the larger bond angles in $ \mathrm{CH_{2}}$ and $ \mathrm{CH_{3}}$ versus $ \mathrm{NH_{2}}$ and $ \mathrm{NH_{3}}$, and (3) the fact that bonds to nitrogen are weaker due to the special stability of the nitrogen half-filled $ p$ shell.

Figure 5.6: eFF describes both open-shell and closed-shell atom hydrides properly.

Figure 5.7: Atom hydride bond lengths and angles.

Figure 5.8: Atom hydride bond dissociation energies.

It is encouraging that eFF can describe both radical species and closed-shell species correctly, and at the same level of accuracy. This bodes well for the application of eFF to processes where radical species are present, for example in combustion or oxidation reactions. The closed-shell molecules $ \mathrm{CH_{4}}$, $ \mathrm{NH_{3}}$, $ \mathrm{OH_{2}}$, and FH are isoelectronic with each other, and we find that in these geometries, electrons spin pair with each other. In the open-shell molecules, bond pair electrons are spin paired, but lone pair electrons separate from each other as they do in the free atoms.

Just as $ \mathrm{CH_{4}}$, $ \mathrm{NH_{3}}$, $ \mathrm{OH_{2}}$, and FH are isoelectronic with each other, the molecules $ \mathrm{CH_{3}}$, $ \mathrm{NH_{2}}$, and $ \mathrm{OH}$ are isoelectronic as well, as are the molecules $ \mathrm{CH_{2}}$ and NH. These similarities are reflected in the correspondence of electron arrangements as shown in Figure 5.6. We see, for example, that we can transform OH(d) to $ \mathrm{NH_{2} (d)}$ by decreasing the nuclear charge by one and adding a proton, which brings two opposite spin electrons together, and leaves three electrons as lone pair electrons.

It is evident that the nuclei in atom hydrides are in the correct positions, but what about the bond pair and lone pair electrons? Their positions are not directly observable quantities, but we can get some sense of where electrons should be by finding the average position of Boys localized electrons using a density functional theory calculation (B3LYP/6-311g**). For the molecules $ \mathrm{CH_{4}}$, $ \mathrm{NH_{3}}$, $ \mathrm{OH_{2}}$, FH, and Ne, we find that the distance between bond pair electrons and the central nucleus matches those found with DFT, as do the angles between lone pair electrons (Figures 5.9 and 5.10).

Figure 5.9: Measuring electron-nuclear distances and the angle between lone pairs.

Figure 5.10: Comparison of eFF electron positions versus B3LYP localized orbital positions. There is good agreement, except that eFF lone pairs are further away from the nucleus than B3LYP lone pairs.

However, we find that eFF lone pair electrons are about $ \sim$0.2 bohr further away from the nucleus than they are in DFT. This trend is made further visible if we plot the electron densities of the lone pairs along the electron-center/nuclear-center axis, comparing eFF to DFT (Figure 5.11). In the density functional theory calculation, both the bond pair and the lone pair have a planar node, and are shifted asymmetrically in one direction, with the degree of shift greater in the bond pair than in the lone pair.

Figure 5.11: Electron densities along lone pairs and bond pairs; a comparison between eFF electron densities and B3LYP localized orbital electron densities.

The eFF wavefunction in contrast has no planar node, but is centered in a way that roughly overlaps the wavefunction on the ``bonding side'' of the node. This results in good overlap between eFF and DFT wavefunctions in the case of the bond pair, where the ``bonding lobe'' dominates; but worse overlap in the case of the lone pair, where there is substantial electron density on both sides of the planar node.

In other words, eFF may not describe properly the fact that lone pairs have density on both sides of the nucleus. This does not affect bonding in atom hydrides, but it does make the dipole moment of atom hydrides too high (e.g., FH dipole moment of 2.76 D versus 1.90 D exact; $ \mathrm{OH_{2}}$ dipole moment of 3.27 D versus 1.86 D exact; Figure 5.3), which causes problems in describing intermolecular interactions, as we shall see later. It may also account for the $ \mathrm{CH_{2}}$ singlet-triplet splitting having the wrong sign (singlet found to be 11 kcal/mol more stable than the triplet, when it should be 9.4 kcal/mol less stable [5]).

Table 5.3: Contributions to the dipole moment of hydrogen fluoride.
  dipole (debye)
contribution eFF DFT
nuclei 4.20 4.41
$ \mathbf{d_{bp \cdot nuc} - d_{lp \cdot nuc}}$ -0.68 -1.79
$ \theta_{lp \cdot lp} - 109.5^{o}$ -0.76 -0.72
total 2.76 1.90

By optimizing the ionization potentials of high-spin atoms, we have been able to obtain accurate geometries and bond dissociation energies for atom hydrides. We have had the benefit of optimizing the proton-p-character spline to achieve this goal, but it is surprising that optimizing one polynomial creates an agreement that persists over such a range of molecules. By making comparisons to DFT localized orbitals, we find that the bonding electrons are in the locations we would expect, and that the lone pairs, though ``lopsided'' do make the correct angles with each other. With the caveat that lone range electrostatics is not properly described due to the too-high dipole moments of atom hydrides, we move on to consider other types of bonds.

next up previous contents
Next: Carbon-carbon single and multiple Up: Results and discussion Previous: Atom ionization potentials and   Contents
Julius 2008-04-29