Chemical Bonding and Electron Density in H2+
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This Demonstration considers the fundamental behavior of the chemical bond using the hydrogen molecule-ion 
as an example. We plot the bonding and antibonding potential energy curves and the electron probability distribution for both bonding and antibonding orbitals. These plots are generated using approximate solutions of the Schrödinger equation.
Contributed by: Nicholas Barresi, Edward Hu and Kailey Lashbrook (January 2024)
Open content licensed under CC BY-NC-SA
Snapshots
Details
This Demonstration shows potential energy curves of the bonding and antibonding orbitals as functions of 
, the distance between the two protons. At smaller 
, repulsion dominates since the repulsion of the two protons is greater than the attraction between the individual protons and the electron. In the antibonding orbital, the repulsion always dominates. The potential energy is at a minimum at 
and a stable bond is formed. At this point, attraction between the electron and the protons leads to a bonding molecular orbital.
Use the "
" slider to adjust the distance between the two protons. The range of 
is 0.001 Å to 2 Å. The particles interact too weakly at longer distances; at shorter distances, the repulsion between protons dominates. The electron probability densities are shown for both the bonding and repulsive states as you vary 
. Both the antibonding orbital and the bonding orbital are plotted to show the possibility of the electron being in both. These results are found from approximate solutions of the Schrödinger equation.
Reference
[1] A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Mineola, NY: Dover Publications, 1996.
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