Return to Question

Koopmans' theorem says that the energy of the HOMO of the Hartree-Fock orbitals is equal to the first ionization energy of whatever system is being studied. This is only approximate because it assumes no changes in the orbitals in the ionic state, no relativistic effects, and no electron correlation. Ignoring those approximations, there is another feature of this which I don't understand.

The wavefunction as determined using HF can be unitarily transformed so that the total energy and wavefunction are preserved, but the "orbitals" themselves are not. Under many of these transformations, I assume that the orbital energies change. Is this true? If it is true, I assume Koopmans' theorem is still valid, but is now more complicated so that the ionization energy is some combination of orbital energies. Can anyone expand on this and let me know if my thinking is correct?

Also, what is it that is so special about the Hartree-Fock orbitals that Koopmans' Theorem has such a simple interpretation, while, if what I say above is true, it seems to be quite convoluted for other sets of orbitals?

As a note, I asked a question which more or less contained this question, but was a bit broader. The question I'm asking right now is the question I am really more interested in having answered.

You can find that other question here: Observability of Orbitals and Orbital Energies

Koopmans' theorem says that the energy of the HOMO of the Hartree-Fock orbitals is equal to the first ionization energy of whatever system is being studied. This is only approximate because it assumes no changes in the orbitals in the ionic state, no relativistic effects, and no electron correlation. Ignoring those approximations, there is another feature of this which I don't understand.

The wavefunction as determined using HF can be unitarily transformed so that the total energy and wavefunction are preserved, but the "orbitals" themselves are not. Under many of these transformations, I assume that the orbital energies change. Is this true? If it is true, I assume Koopmans' theorem is still valid, but is now more complicated so that the ionization energy is some combination of orbital energies. Can anyone expand on this and let me know if my thinking is correct?

Also, what is it that is so special about the Hartree-Fock orbitals that Koopmans' Theorem has such a simple interpretation, while, if what I say above is true, it seems to be quite convoluted for other sets of orbitals?

As a note, I asked a question which more or less contained this question, but was a bit broader. The question I'm asking right now is the question I am really more interested in having answered.

You can find that other question here: Observability of Orbitals and Orbital Energies

Koopmans' theorem says that the energy of the HOMO of the Hartree-Fock orbitals is equal to the first ionization energy of whatever system is being studied. This is only approximate because it assumes no changes in the orbitals in the ionic state, no relativistic effects, and no electron correlation. Ignoring those approximations, there is another feature of this which I don't understand.

The wavefunction as determined using HF can be unitarily transformed so that the total energy and wavefunction are preserved, but the "orbitals" themselves are not. Under many of these transformations, I assume that the orbital energies change. Is this true? If it is true, I assume Koopmans' theorem is still valid, but is now more complicated so that the ionization energy is some combination of orbital energies. Can anyone expand on this and let me know if my thinking is correct?

As a note, I asked a question which more or less contained this question, but was a bit broader. This is the question I am really more interested in having answered.

You can find that other question here: Observability of Orbitals and Orbital Energies

Koopmans' theorem says that the energy of the HOMO of the Hartree-Fock orbitals is equal to the first ionization energy of whatever system is being studied. This is only approximate because it assumes no changes in the orbitals in the ionic state, no relativistic effects, and no electron correlation. Ignoring those approximations, there is another feature of this which I don't understand.

The wavefunction as determined using HF can be unitarily transformed so that the total energy and wavefunction are preserved, but the "orbitals" themselves are not. Under many of these transformations, I assume that the orbital energies change. Is this true? If it is true, I assume Koopmans' theorem is still valid, but is now more complicated so that the ionization energy is some combination of orbital energies. Can anyone expand on this and let me know if my thinking is correct?

Also, what is it that is so special about the Hartree-Fock orbitals that Koopmans' Theorem has such a simple interpretation, while, if what I say above is true, it seems to be quite convoluted for other sets of orbitals?

As a note, I asked a question which more or less contained this question, but was a bit broader. The question I'm asking right now is the question I am really more interested in having answered.

You can find that other question here: Observability of Orbitals and Orbital Energies