Obtaining Hartree–Fock and density functional theory doubly excited states with Car–Parrinello density matrix search

Double-core excitations in formamide can be probed by X-ray double-quantum-coherence spectroscopy

The attosecond, time-resolved X-ray double-quantum-coherence four-wave mixing signals of formamide at the nitrogen and oxygen K-edges are simulated using restricted excitation window time-dependent density functional theory and the excited core hole approximation. These signals, induced by core exciton coupling, are particularly sensitive to the level of treatment of electron correlation, thus providing direct experimental signatures of electron and core-hole many-body effects and a test of electronic structure theories.

Double excitations from modified Hartree Fock subsequent minimization scheme

Doubly excited states have nowadays become important in technological applications, e.g., in increasing the efficiency of solar cells and therefore, their description using ab initio methods is a great theoretical challenge as double excitations cannot be described by linear response theories based on a single Slater determinant. In the present work we extend our recently developed Hartree-Fock (HF) approximation for calculating singly excited states [M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem. 113, 690 (2013)] in order to allow for the calculation of doubly excited states. We describe the double excitation as two holes in the subspace spanned from the occupied HF orbitals and two particles in the subspace of virtual HF orbitals. A subsequent minimization of the energy results to the determination of the spin orbitals of both the holes and the particles in the occupied and virtual subspaces, respectively. We test our method, for various atoms, H2 and polyene molecules which are known to have excitations presenting a significant double excitation character. Importantly, our approach is computationally inexpensive.

Doubly, triply, and multiply excited states from a constrained optimized effective potential method

This article further develops and applies a constrained optimized effective potential (COEP) approach for the practical calculations of doubly and multiply excited states of atoms and molecules. The COEP method uses the time-independent theory of pure excited states and implements a simple asymptotic projection method to take orthogonality constraints into account. We show that, in contrast with the common time-dependent density functional method, the COEP methodology is capable of treating doubly, triply, and multiply excited states and can be easily applied to both atoms and molecules. In particular, doubly excited energies of each state are calculated through a constrained minimization procedure including constraints that make its Slater determinantal functions orthogonal to those of the ground and all lower-lying doubly excited states. The performance of the proposed method is examined by calculations of doubly excited state energies for the He atom and H(2) molecule at exchange-only and exchange-correlation level of approximation.