The simple example of the molecule AB allows laying some essential bases of the chemical bond, through the linear combination of atomic orbitals (LCAO) method. We consider the system formed by two ionic cores A and B and an electron whose position is denoted by r. The Hamiltonian of the system writes: H=T+VA+VB, where T=(2/2m)2,VA=KZAe2/(rRA) and VB=KZBe2/(rRB). We are looking for a solution to Schrdinger's equation H=E, considering =(r) as a linear combination of atomic orbitals A and B, of energies EA and EB : =cAA+cBB, where (T+VA)A=EAA and (T+VB)B=EBB. Using Dirac notation, one has: H>=E>(),with>=cAA+cBB>. 1) Projecting () on