# Natural orbitals

## Summary

To produce state-average natural orbitals, run

```
qp_run save_natorb file.ezfio
```

The MOs will be replaced, so the two-electron integrals and the wave function are invalidated as well.

## Extracting natural orbitals

Once obtained the near FCI wave function, one can obtain many quantities related to it. One of these quantities are the natural orbitals which have the property of diagonalizing the one-body density matrix:

\[\rho_{ij} = \delta_{ij}\]

where the element of the one-body density matrix \(\rho_{ij}\) is defined as:

\[\rho_{ij} = \langle \Psi | \left( a^{\dagger}_{j,\alpha} a_{i,\alpha} + a^{\dagger}_{j,\beta} a_{i,\beta} \right) | \Psi \rangle\]

These orbitals are in general known to be better than the usual HF MOs as they are obtained from a correlated wave function. To use these orbitals for future calculations, one has to replace the current MOs by the natural orbitals. To do so, just run:

```
qp_run save_natorb file.ezfio
```

## Hands on

Important

As the MOs are changed, for the sake of coherence of future
calculations, the save_natorb program *automatically removes the
current wave function* stored in the EZFIO database and replaces
it by a single Slater determinant corresponding to a HF occupation
of the new spin orbitals. Also, all the keywords to read the one-
and two-electron integrals on the MO basis are set to `None`

in
order to be sure to avoid reading integrals incompatible with the
current set of MOs.

See also

The documentation of the save_natorb program.