The energy, orbitals and electric properties of the ozone molecule with ensemble density functional theory

Abstract

For a molecule with a complicated electronic structure, the solution of the Kohn–Sham equations of density functional theory (DFT) may require the use of an ensemble density matrix rather than a pure-state density matrix. In this paper, we first outline how an ensemble density matrix may be parameterised in a form, which ensures that all occupation numbers are between zero and two and that the total number of electrons is constant. A previously developed method for the optimisation of both orbitals and occupation numbers is summarised, and a time-independent linear response method for ensemble densities is developed. The optimisation and linear response methods are applied to the energy, dipole moment and static polarisability of the ground state of ozone at various bond angles. When comparing the results of pure-state and ensemble DFT calculations, it is found that the latter gives better agreement with wave-function methods and in particular provides smooth and differentiable potential and property curves.

Keywords:

• ensemble DFT
• fractional occupation numbers
• response theory
• polarisabilities

Acknowledgements

It is with pleasure the authors congratulate Trygve Helgaker on his 60th birthday. JO would like to express his gratitude for many years of collaborations and friendship. The authors acknowledge and thank for support from the Lundbeck Foundation to the Lundbeck Foundation Centre for Theoretical Chemistry. The research was also supported by a grant from the Danish Research Council, FNU.