Let E 1 ( R ) and E 2 ( R ) two different electronic potential curves. If they intersect at some point, then the functions E 1 ( R ) and E 2 ( R ) will have neighbouring values near this point. To decide whether such an intersection can occur, it is convenient to put the problem as follows. Suppose at some internuclear distance R c the values E 1 ( R C ) and E 2 ( R C ) are close, but distinct (as shown in the figure). Then it is to be examined whether or E 1 ( R ) and E 2 ( R ) can be made to intersect by the modification R C → → R C + Δ Δ R . The energies E 1 ( 0 ) = E 1 ( R C ) and E 2 ( 0 ) = E 2 ( R C ) are eigenvalues of the Hamiltonian H 0 = H ( R C ) . The corresponding orthonormal electronic eigenstates will be denoted by | Φ Φ 1 ( 0 ) ⟩ and | Φ Φ 2 ( 0 ) ⟩ and are assumed to be real. The Hamiltonian now becomes H ≡ ≡ H ( R C + Δ Δ R ) = H 0 + H ′ , where H ′ = ∂ ∂ H 0 ∂ ∂ R C Δ Δ R is the small perturbation operator (though it is a degenerate case, so ordinary method of perturbation won't work). setting H i j ′ = ⟨ Φ Φ i ( 0 ) | H ′ | Φ Φ j ( 0 ) ⟩ ; i , j = 1 , 2 , it can be deduced that in order for E 1 ( R ) and E 2 ( R ) to be equal at the point R C + Δ Δ R the following two conditions are required to be fulfilled: