Sunday, February 7, 2010

I'm positive

fig4-2
Figure 4.2. 0.002 au isodensity surface with superimposed electrostatic potential of (a) Li+, (b) Na+, and (c) K+ ion. The maximum potential value is 0.8 au, and the level of theory is B3LYP/6-31G(d).
From Molecular Modeling Basics CRC Press, May 2010.

Here is an example of how computational chemistry can be used to enhance teaching at the general chemistry level.

Why does the ionization energy decrease on from Li to Na to K? That's the same as asking why the electron affinities decrease on going from Li+ to Na+ to K+.

Figure 4.2 show the ions colored by how positive they are at the surface (i.e. the electrostatic potential superimposed on the 0.002 isodensity surface). The darker the
color the more positive the ion, and it is clear that the Li+ ion is “more positive” than Na+, which is more positive than K+. Thus, more energy should be released when adding an electron to Li+ compared to Na+, and hence more energy is needed to remove an electron from Li
compared to Na (and similarly for K).

The reason why Li+ is “more positive” than Na+ or, more accurately, why the potential on the 0.002 au isodensity surface is more positive for Li+ than for Na+, is that the former is a smaller ion than the latter, so the surface is closer to the +1 charge at the center of the ion.

fig4-4
Figure 4.4. 0.002 au isodensity surface with superimposed electrostatic potential of (a) Li+, (b) Ne+, and (c) Na+ ion. The maximum potential value is 0.8 au, and the level of theory is B3LYP/6-31G(d).
From Molecular Modeling Basics CRC Press, May 2010.

This rationalization is, of course, only qualitative and is is not predictive of the ionization energies among different groups. For example, based on Figure 4.4 one would expect that Ne would have roughly the same ionization potential as Na, which is not true at all.

When making these figures it is very important to get the relative sizes of the ions correct, but this can be difficult since each image can be zoomed to an arbitrary size. The screencast below shows how to control this in MacMolPlt using the Manual Windows Parameter window.

The same point can also be made with a "quick-and-dirty" electrostatic potential, as shown in this interactive figure. Here the electrostatic potential is due to a plus one charge centered at the atom (rather than the nuclear charge and the electron density) and the surfaces are the spheres defined by empirical ionic radii. The Jmol script can be found here, and the mol2 files here, here, and here.

Click on the picture for an interactive version
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