[Quantum Chemistry] Generalized wave function in covalent bonding

[Mayhem]

Is there a general expression for the wave function $\psi$, which describes the electronic properties of an arbitrary covalent bond? For example is it equal to some sort of trigonometric expression?

 

[DrClaude]

No. I guess the closest you could get are the molecular orbitals of H₂⁺, but even they don't have a simple analytical expression.