# Canonical Restricted Open-shell Hartree–Fock equation

In Frank Jensen's Introduction to Computational Chemistry ($$\mathrm{2^{nd}}$$ edition), on page 99, it says:

For an ROHF wave function, it is not possible to choose a unitary transformation that makes the matrix of Lagrange multipliers in eq. (3.41) diagonal, and orbital energies from an ROHF (Restricted Open-shell Hartree–Fock) wave function are consequently not uniquely defined and cannot be equated to ionization potentials by a Koopmans-type argument.

Here ROHF eq. (3.41) is the non canonical Hartree-Fock equation:

$$F_i\phi_i=\sum\lambda_{ij}\phi_j$$

But in ATTILA SZABO, NEIL S. OSTLUND's Modern Quantum Chemestry, they prove that the Hartree-Fock equation can always be put into the canonical form:

$$F_i\phi_i=\lambda_{i}\phi_i$$

What am I misunderstanding here?

• I'm guessing that "restricted open-shell" part is important. Mar 5 '19 at 10:56
• ATTILA SZABO, NEIL S. OSTLUND showed that there is a basis where the hartree-fock equation has the form $F_i\phi_i=\lambda_{i}\phi_i$ that is, it does not work for every basis , only for a kind special of basis , so there is no issue in the two statements Mar 5 '19 at 12:50