Molecular Orbitals  Contents -  The Quantum Mechanical Origin

The Molecular Orbital Approximation

The atomic orbitals for the Hydrogen atom: the 1s orbital is

$$1s_H=\frac{1}{\sqrt{\pia_0^3}}\exp(-r/a_0)$$ (9)

 We use units such that distances are measured in bohr(a₀). Thus

$${\rm 1s}_H\sim e^{-r}\ \ \ \ \ (\sim '{\rm behaves\ like}')$$ (10)

 Similarly the 2s and 2p orbitals are

$${\rm 2s}_H\sim (2-r)e^{-r/2}$$ (11)

$${\rm 2p}_{xH}\sim xe^{-r/2}$$ (12)

$${\rm 2p}_{yH}\sim ye^{-r/2}$$ (13)

$${\rm 2p}_{zH}\sim ze^{-r/2}$$ (14)

 We sketch these orbitals as follows
    For atoms larger than H, atomic orbitals have the same form but they are a different size. For example for Oxygen:

$${\rm 1s}_O\sim e^{-8r}$$ (15)

 The notation 1s,2s... implies that atomic orbitals are normalised.    
 Molecular Orbitals  Contents -  The Quantum Mechanical Origin

1998-09-23