Orthogonality Constrained Density Functional Theory for Electronic Excited States

• Published in: The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory Vol. 117; no. 32; pp. 7378 - 7392
• Main Authors: Evangelista, Francesco A, Shushkov, Philip, Tully, John C
• Format: Journal Article
• Language: English
• Published: Washington, DC American Chemical Society 15.08.2013
• Subjects: Adiabatic flow; Atomic and molecular physics; Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations); Computation; Density functional theory; Electronic structure of atoms, molecules and their ions: theory; Electronics; Exact sciences and technology; Excitation; Ground state; Mathematical analysis; Orthogonality; Physics; Adiabatic approximation; Algorithms; Ground states; Transition energy; Electronically excited state; Density functional method; Excitation; Excited states; Charge transfer
• ISSN: 1089-5639; 1520-5215; 1520-5215
• DOI: 10.1021/jp401323d

We report a novel scheme for computing electronic excitation energies within the framework of density functional theory (DFT) based on a time-independent variational formulation of DFT. The excited state density functional is recast as a Kohn–Sham functional, which is further simplified by an adiabatic approximation of the exchange-correlation functional. Under the adiabatic approximation, the minimization of the excited state Kohn–Sham functional is shown to be equivalent to a ground state DFT computation augmented with orthogonality constraints with respect to the ground state Kohn–Sham determinant. An algorithm for the optimization of the energy subject to orthogonality constraints, which does not suffer from variational collapse, is described and implemented. A benchmark test set containing 28 organic molecules ( Schreiber M. J. Chem. Phys. 2008, 128, 134110 ) was used to assess the quality of the excitation energies obtained. Two novel approaches to spin-adapt the resulting excitation energies are discussed and found to provide results with error metrics similar to those of time-dependent DFT. Similarities and differences with respect to other time-independent DFT approaches are highlighted and some of the advantages of our schemeincluding the ability to correctly describe charge-transfer excitationsare critically assessed.