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Too-small sterics cause other problems

We found by studying the interaction energy of neon dimer that Pauli repulsions between valence electrons on different atoms were underestimated, which caused bonds between heteroatoms to be too strong, and hydrogen bonds to be too strong as well. We show in this section that this effect causes problems in other systems as well, including systems that were previously well-described by the old version of eFF.

Cyclic alkanes with more than three carbons are nonplanar, and the old eFF reproduced well the magnitude of key dihedral angles measuring the twist of cycloalkanes out of planarity. The new eFF does slightly worse, making cyclobutane, cyclopentane, and cyclohexane more planar than they should be (Table 5.4). This is likely a consequence of the too-small barrier to ethane rotation discussed previously (1.6 kcal/mol versus 3 kcal/mol exact). We find that other intermediate range steric interactions are underestimated as well (Table 5.5), including the gauche versus trans butane interaction (0.4 versus 0.9 kcal/mol B3LYP), and the 1,3-diaxial interaction (3.3 kcal/mol versus 5.9 kcal/mol B3LYP).

Table 5.4: New eFF makes cyclic alkanes slightly more planar than they should be.
  key dihedral (degrees)
  old eFF new eFF B3LYP
cyclobutane 0.3 0.0 18.0
cyclopentane -21.5 -18.9 -33.2
cyclohexane (chair) 57.7 50.6 56.6
cyclohexane (twist-boat) -34.0 -27.1 -32.3

Table 5.5: New eFF underestimates the magnitude of intermediate range steric repulsions.
      $ \mathrm{\Delta E}$ (kcal/mol)
system energy of relative to old eFF new eFF B3LYP
ethane eclipsed staggered 2.1 1.6 2.7
butane gauche trans 1.6* 0.4 0.9
cyclohexane twist-boat chair 4.7 4.3 6.3
1,3-dimethyl-cyclohexane ax-ax eq-eq 5.8 3.3 5.9
  ax-eq eq-eq 2.7 0.7 2.1
decalin cis trans 12.1 1.1 3.2
2-pentene major minor 5.5 5.2 4.6

The old eFF was used to study the dynamics of hydrogen plasmas, but the new eFF is no longer useful for that purpose, because it improperly stabilizes triangular and tetrahedral clusters of hydrogen atoms (triangular $ \mathrm{H_{3}}$ is 28 kcal/mol more stable than $ \mathrm {H_{2}}$ + H, and tetrahedral $ \mathrm{H_{4}}$ is 28 kcal/mol more stable than $ \mathrm{H_{2} + H_{2}}$). This is a clear consequence of insufficient Pauli repulsion between s-like electrons.

Figure 5.26: The new eFF creates spurious stable minima corresponding to unphysical arrangements of hydrogen atoms.

We have been curious to study bonding in electron-rich solids, and were delighted to find that the new eFF could optimize a cluster of twelve boron atoms in an icosaheral arrangement (Figure 5.27). Such an icosahedral arrangement mirrors the units found in $ \alpha$-boron solid, and it was not possible to obtain such a structure with the old eFF. With the new eFF, the boron-boron distances are nearly identical to those found with B3LYP (1.677 $ \mathrm{\AA}$ versus 1.673 $ \mathrm{\AA}$ B3LYP), and a slight shear distortion is also reproduced.

Figure 5.27: Icosahedral boron cluster $ B_{12}$ is stable with the new eFF, and matches a B3LYP optimized geometry well; however an amorphous boron-centered structure is found to be even more stable.

However, we also discover with the new eFF a boron-centered amorphous jumble of atoms 600 kcal/mol more stable than the icosahedral structure; such a structure does not have any special stability according to B3LYP. It is possible to destabilize this structure by adjusting other parameters in the eFF, and to obtain stable structures for $ \mathrm{B_{12}}$, larger boron hydrides, and carboranes; but we would prefer to stay with a single set of parameters that treated all systems consistently.

Based on the above results, it is not possible to unequivocally recommend the new eFF over the old eFF, even though the new eFF describes with higher accuracy atoms, molecules with lone pairs, atom hydrides, and single and double bonds.

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