Linear scaling computation of excited states

Ab initio molecular orbital calculations are usually limited to smalland medium-size molecular systems. The obstacle lies in the rapid increase of computational cost as the systems become larger and more complex. For the ground state, a number of linear scaling computational methods are proposed. Here the locality of the ground state density matrix was the key to achieve the linear scaling computation. However, the linear scaling computation for excited states is a much more difficult task, since the excited state density matrix is more delocalized compared with the ground state one. Several linear scaling calculations based on the noninteracting electron models have been proposed.