The simplest Molecule

The Atomic Orbital Model gives the chance to understand in a simple way the main properties of simple molecules: Assume two separate atoms with their own electron orbitals¹³ When they get closer to each other both electrons start to 'orbit' both atomic cores. Thus the two electron system has to be solved. And due to the electrons being Fermions they tend to be as independent as possible. In addition the two electron electric potential is repulsive. Both is the chance of the Atomic orbital model where the two-particle wavefunction $\vert\psi_{1,2}\!>$after having been represented by single particle wavefunction of an electron in the joint potential,

$$\vert\psi_{1,2}\!> = \sum_{1,2}^{\infty,\infty} \begin{vmatri... ...\\ \vert\phi_2\!> & \vert\phi_2\!> \\ \end{vmatrix} \quad .$$ (8)

Each of the terms in the sum are Slater determinants in space representation

$$( (\!x\vert (\!x^{'}\vert) \quad (\vert\phi_1\!>\vert\phi_2\!>) = \phi_1(x') \phi_2(x)$$ (9)