For HF, the LCAO-MO, $\Psi $=c_H$\Psi $_H +c_F$\Psi $_F,has c_H = c_F.

Question

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In the Linear Combination of Atomic Orbitals-Molecular Orbital (LCAO-MO) theory for HF, the coefficients $c_{_{H_{}}}$ and $c_{_{F_{}}}$ represent the contributions of the hydrogen and fluorine atomic orbitals, respectively, to the molecular orbital. Given the difference in electronegativity and atomic size between hydrogen and fluorine, it's unlikely these coefficients would be equal, as they reflect how much each atom's orbitals contribute to the bonding and anti-bonding molecular orbitals.

For HF, the LCAO-MO Ψ\Psi Ψ =CH Ψ\Psi Ψ H +CF Ψ\Psi Ψ

For HF, the LCAO-MO $\Psi$ =C_H $\Psi$ _H +C_F $\Psi$