Understanding Bonding in H-H
From WikidChem
Contents |
Overview
These slides show the total electron density around two bonded hydrogen atoms, as well as the electron density due to bonding. This "difference density" is derived from subtracting the electron density of two separate hydrogen atoms (1s) from the calculated total electron density around a H2 molecule. Various calculations are used in each slide to get a more accurate bond energy.
[edit]Slide 5
The first thing to notice on this slide is that the two electron density contours are scaled to different densities. The difference density is thus much smaller than the total electron density, indicating the relatively small distortion caused by bonding. If you approximate molecular orbitals as the sum of atomic orbitals:
(1/sqrt2)*(A+B)
where A and B are atomic 1s orbital functions, you can get the first electron density map by squaring this formula, which is basically squaring psi.
The density difference map takes this total electron density and subtracts at every point the average electron density of two, unbonded H atoms, created by (1/2)*(A^2+B^2). This is analogous to the X ray difference graphs. The resulting formula is A*B, the electron density due to bonding or overlap.
Although the calculated total electron energy is 92.9% of measured electron energy in an H2 molecule, most of this is from the actual H atoms themselves, rather than their bond. The calculated bond energy of 52% is a better indicator of the difference density map's accuracy. Since the calculated energy is so low compared to the experimental one, we need to tweak the total electron density calculation to yield a higher bond energy.
[edit]Slide 6
The first method used to change the total electron density is to "spread" psi out, or increase the area under the graph farther from the nucleus. This would create more electron overlap between the two atoms, increasing the bond energy. Psi is spread out near the ends by optimizing the exponential function e^-p/2 .
While this method does yield greater bond energy, it creates inaccuracies near the nucleus by decreasing the electron density there. Also, it increases electron density on both sides of the nucleus, which is accurate for the side involved in bonding, but not accurate for the outer side not involved in bonding.
[edit]Slide 7
To increase electron density on the side of the atom involved in bonding, hybrid orbitals are created by adding small amounts of 2s and 2p to the 1s orbital. This creates an asymmetrical electron distribution, so that more electrons overlap between the atoms, and calculated bond energy is increased to a higher percentage of actual energy. Also, there are fewer electrons on the outer sides of the atoms, which is consistent with reality.
[edit]Slide 8
This slide is the same as Slide 7, except that an experimentally determined Correlation Energy is added to the electron density map to increase calculated bond energy.
