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:


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:


What am I misunderstanding here?

  • 1
    $\begingroup$ I'm guessing that "restricted open-shell" part is important. $\endgroup$ – Buck Thorn Mar 5 '19 at 10:56
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    $\begingroup$ 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 $\endgroup$ – amilton moreira Mar 5 '19 at 12:50

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