**System details**

Compound | Sodium Tetramer |

Formula | Na_{4} |

CAS Number | 39297-86-4 |

**Ground state input**

Pseudopotential(s) | SG15^{[01]} () |

## Dielectric Screening

The dielectric matrix of Sodium Tetramer (Na_{4}) is computed in WEST by iterative diagonalization, see Fig. 2 of Ref. [02].
The eigenvalues of the symmetrized irreducible polarizability for Sodium Tetramer (Na_{4}) are reported in Fig. 1.
Results were obtained using the program `wstat.x`

of the WEST package.

**Fig. 1** - Eigenvalues of the symmetrized irreducible polarizability for Sodium Tetramer (Na_{4}). The calculations were performed with the PBE exchange-correlation functional.

## Spectral Function

The G_{0}W_{0} spectral function of Sodium Tetramer (Na_{4}) is computed in WEST with full frequency integration.
Results were obtained using the program `wfreq.x`

of the WEST package.

**Fig. 2** - G_{0}W_{0} HOMO spectral function of Sodium Tetramer (Na_{4}). The calculations were performed with the PBE exchange-correlation functional.

## Vertical Ionization Potential (VIP)

## Vertical Electron Affinity (VEA)

### Legend

- AE: All Electron
- AC: Analytic Continuation
- EXP: Experimental value, if marked in parentheses the ionization potential is not vertical
- FA: Fully Analytic
- FF-CD: Full Frequency integration w/ Contour Deformation
- FF-RA: Full Frequency integration along the Real Axis
- Full: Full solution of the quasiparticle (QP) eq.
- Linear: Solution of the linearized quasiparticle (QP) eq.
- LO: Localized Orbitals
- PSP: Pseudopotential
- PW: Plane Waves
- XC: Exchange and Correlation

### References

*Optimization algorithm for the generation of ONCV pseudopotentials*, Comput. Phys. Comm. 196, 36 (2015).

*Large Scale GW calculations*, J. Chem. Theory Comput. 11, 2680 (2015).

*GW100: Benchmarking G*, J. Chem. Theory Comput. 11, 5665 (2015).

_{0}W_{0}for Molecular Systems*GW100: A Plane Wave Perspective for Small Molecules*, J. Chem. Theory Comput. 13, 635 (2017).