# Why must basis sets used in computations be non-orthogonal?

While constructing basis sets for calculations using Hartree Fock, the basis set must be non-orthogonal. And because of this, we go through many steps to put the overlap and density matrices in the 'right' basis. (See Modern Quantum Chemistry (Szabo and Ostlund) or David Sherill's notes online).

My question is: why must this basis be non-orthogonal?

• Besides the existing answers, it's important to note that the 'many steps' you mention are there so you can handle non-orthogonal bases, but the formalism works perfectly fine if your basis happens to be orthogonal already. – Emilio Pisanty Jul 21 '17 at 23:12