# 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 Onquantities related to it. e of these quantities are the natural Onorbitals which have the properties of diagonalizing the one-body Ondensity matrix:

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

where the element of the one-body density matrix \(\rho_{ij}\) is define 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.