To combine successfully arbitrary atoms A and B with the LCAO approach Ψ = c_{A}Φ_{A} + c_{B}Φ_{B}, the wave functions
An example is depicted in the figure on the left, where Φ_{A} is an sAO and Φ_{B} is an p_{x}AO. Axis x is assumed to be orthogonal to the axis of the molecule AB which is in accordance with a convention saying that the molecule's axis points in direction z.
The figure illustrates that, due to contrary signs of the wave function in both lobes of the p_{x} orbital, the integral S = ∫Φ_{A}Φ_{B}dτ = 0. Obviously, combinations of an In case the integral ∫Φ_{A}Φ_{B}dτ is zero, the pair of wave functions Φ_{A} and Φ_{B} are said to be orthogonal. As shown above, different symmetry with respect to a plane that contains both nuclei causes wave functions to be orthogonal. 

The integral ∫Φ_{A}Φ_{B}dτ disappears due to symmetry as for any volume element dτ_{1} there is a respective element dτ_{2}. The integrand delivers identical, but contrarily signed values for such pairs of volume elements. 
The following table classifies combinations of s, p and dtype atomic orbitals in view of the LCAO molecular orbital approach.





















^{#} To obtain the combinations for p_{y} und d_{yz} orbitals, substitute all indices x by indices y and vice versa in the respective row 
In later chapters, examples for combinations of one atomic orbital Φ_{A} with two or more orbitals Φ_{B} of atom B are presented. Again, possible partner orbitals are found in column "combines with Φ_{B}". As we regard axis z as molecular axis, preferable dorbitals are d_{xy},
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