Excitation energies from Görling–Levy perturbation theory along the range-separated adiabatic connection

ABSTRACT

A Görling–Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh–Schrödinger (RS)-based perturbation theory this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionisation energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.

KEYWORDS:

• Density-functional theory
• range separation
• adiabatic connection
• perturbation theory
• excitation energies

Acknowledgments

This work was supported by the Norwegian Research Council through the CoE Centre for Theoretical and Computational Chemistry (CTCC) Grant No. 179568/V30 and through the European Research Council under the European Union Seventh Framework Program through the Advanced Grant ABACUS, ERC Grant Agreement No. 267683. Andrew M. Teale gratefully acknowledges support from the Royal Society University Research Fellowship scheme and the Engineering and Physical Sciences Research Council (EPSRC), Grant No. EP/M029131/1.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Engineering and Physical Sciences Research Council [grant number EP/M029131/1]; FP7 Ideas: European Research Council, Advanced Grant ABACUS [ERC Grant Agreement No. 267683]; Norwegian Research Council through the Centres of Excellence scheme, project number 1179568/V30 262695; and European Research Council under the European Union Seventh Framework Program through the Advanced Grant ABACUS [ERC Grant Agreement No. 267683].