27: The Chemical Bond in Diatomic Molecules
- Page ID
- 416117
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In this chapter we will see a couple of examples of how the concept and mathematics of quantum mechanics can be applied to understand the chemical bond in molecules. We will start from the simplest molecule, the \(\mathrm{H}_2^+\) molecular ion, and then we will move on to the simplest two-electron bond in the hydrogen molecule. To simplify the notation in this chapter, we will move away from S.I. units and use a set tailored for molecules, called atomic units (a.u.). This set of units is built by setting \(\hbar=e=m_e=a_0=1\). As an example of the simplification that a.u. allows, the energy eigenvalues of the hydrogen atom, Equation 21.8, simply becomes \(E_n=-\dfrac{1}{2n^2}\) in the a.u. of energy, which are called Hartrees.
- 27.1: The Chemical Bond in the Hydrogen Molecular Cation
- This system has only one electron, but since its geometry is not spherical (figure 28.1.1), the TISEq cannot be solved analytically as for the hydrogen atom.
- 27.2: The Chemical Bond in the Hydrogen Molecule
- We can now examine the formation of the two-electron chemical bond in the H2 molecule.