# Why are bonding orbitals more stable?

##### 1 Answer

**Bonding orbitals minimize the nuclear repulsion energy.**

Let us consider the following equation which describes the energy of a quantum mechanical system via the Particle-in-a-Box model for the helium atom:

The first two terms indicate kinetic energy. Let's ignore that since that is not our focus.

The **1-electron terms** describe the coulombic attractions of each individual electron to the nucleus of the atom, whereas the **2-electron term** describes the coulombic repulsions between the pairwise electron interactions in the atom. (*Note: this term is why solving for the exact ground-state energy of helium is impossible*)

You can tell from the equation that to maintain the equality, if the third and/or fourth term increases, the sixth term decreases (if it changes), and if the third and/or fourth term decreases, the sixth term increases (if it changes). The fifth term changes randomly.

Using the **Born-Oppenheimer Approximation**, the nuclei stay still, and so if the electrons move, interactions between the electrons change (2-electron term) and interactions between the nucleus and electron changes (1-electron terms).

The point is, the more nuclear repulsion, the higher in energy the molecular orbital is.

**Bonding orbitals minimize the nuclear repulsion energy.**