Jump to main content
Jump to site search
Access to RSC content Close the message box

Continue to access RSC content when you are not at your institution. Follow our step-by-step guide.

Variational Calculations of Excited States Via Direct Optimization of Orbitals in DFT


A direct optimization method for obtaining excited electronic states using density functionals is presented. It involves selective convergence on saddle points on the energy surface representing the variation of the energy as a function of the electronic degrees of freedom, thereby avoiding convergence to a minimum and corresponding variational collapse to the ground electronic state. The method is based on an exponential transformation of the molecular orbitals, making it possible to use efficient quasi-Newton optimization approaches. Direct convergence on a target nth-order saddle point is guided by an appropriate preconditioner for the optimization as well as the maximum overlap method. Results of benchmark calculations of 52 excited states of molecules indicate that the method is more robust than a standard self-consistent field (SCF) approach especially when degenerate or quasi-degenerate orbitals are involved. The method can overcome challenges arising from rearrangement of closely spaced orbitals in a charge-transfer excitation of the nitrobenzene molecule, a case where the SCF fails to converge. The formulation of the method is general and can be applied to non-unitary invariant functionals, such as self-interaction corrected functionals.

Back to tab navigation

Supplementary files

Article information

16 May 2020
01 Jun 2020
First published
02 Jun 2020

Faraday Discuss., 2020, Accepted Manuscript
Article type

Variational Calculations of Excited States Via Direct Optimization of Orbitals in DFT

G. Levi, A. V. Ivanov and H. Jonsson, Faraday Discuss., 2020, Accepted Manuscript , DOI: 10.1039/D0FD00064G

Social activity

Search articles by author