# Generalization of the concepts of seniority number and ionicity

## TL;DR

This paper introduces generalized concepts of seniority number and ionicity that count partially and fully occupied shells in orbital space, enabling refined hierarchical classification of wave functions.

## Contribution

It develops generalized seniority and ionicity numbers with associated Hermitian operators, enhancing the hierarchy of configuration interaction spaces.

## Key findings

- Hierarchies of CI spaces are refined using GSNs.
- Application demonstrated on buckminsterfullerene molecule.
- Generalized concepts extend traditional seniority and ionicity ideas.

## Abstract

We present generalized versions of the concepts of seniority number and ionicity. These generalized numbers count respectively the partially occupied and fully occupied shells for any partition of the orbital space into shells. The Hermitian operators whose eigenspaces correspond to wave functions of definite generalized seniority or ionicity values are introduced. The generalized seniority numbers (GSNs) afford to establish refined hierarchies of configuration interaction (CI) spaces within those of fixed ordinary seniority. Such a hierarchy is illustrated on the buckminsterfullerene molecule.