Natural excitation orbitals from linear response theories: Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory

Abstract

Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In contrast, in a basis of natural orbitals (NOs) or Hartree-Fock orbitals, excitations often employ many orbitals and are accordingly hard to characterize. We demonstrate that it is possible in these cases to transform to natural excitation orbitals (NEOs) which resemble very closely the KS orbitals and afford the same simple description of excitations. The desired transformation has been obtained by diagonalization of a submatrix in the equations of linear response time-dependent 1-particle reduced density matrix functional theory (LR-TDDMFT) for the NO transformation, and that of a submatrix in the linear response time-dependent Hartree-Fock (LR-TDHF) equations for the transformation of HF orbitals. The corresponding submatrix is already diagonal in the KS basis in the LR-TDDFT equations. While the orbital shapes of the NEOs afford the characterization of the excitations as (mostly) simple orbital-to-orbital transitions, the orbital energies provide a fair estimate of excitation energies.

Charge Transfer Excitations with Range Separated Functionals Using Improved Virtual Orbitals

“…It is known, that excitations calculated by linear response time dependent HFT need a large linear combination of single particle excitations (i.e. a high number of unoccupied states), while excitations calculated by lrT-DDFT using the kernels of local functionals can often be described by an individual excitation [94,95]. The twelve unoccupied states that are used in the lrTDDFT calculations for the Na 2 -NaCl-system presented in fig.…”

Bond-breaking excitations with diverging coupling matrix of response density functional theory from highest-level functionals

“…Moreover, the present methodological strategy can also be applied to tackle another problem of adiabatic TDDFT, the lack of double excitations. Based on the recent unified description of TDDFT, time-dependent Hartree-Fock (TDHF) theory, and time-dependent density matrix functional theory (TDDMFT) [26], the consistent differentiation of the properly chosen GKS functional can produce the following response matrix diagonalization problem [ √ ED…”

“…the antihermiticity of which is required to ensure orthogonality of the perturbed orbitals. The orbital changes (8) induce the change in the electron-electron interaction which, in a general case, is represented with the following matrix equation [10,26] δv ef f ai (t) = jb K ai,jb δU bj (t).…”

“…Then, the adiabatic coupling matrix K is obtained with further orbital differentiation of (12), so K ai,jb are expressed through the projected orbital derivatives of v ee ai as follows [10,26]…”

On the time evolution of fermionic occupation numbers

“…Unfortunately, time-dependent extensions of the theory of the one-body reduced density matrix suffer from various shortcomings. Save for two-electron systems, the current status of the theory does not allow the fermionic occupation numbers to evolve in time [21][22][23][24] . To understand the problem it is worth recalling that the Schrödinger equation leads to the a) Electronic mail: carlos.benavides-riveros@physik.uni-halle.de BBGKY hierarchy, whose equation for γ(t) is 25 :…”