Excitation energies with time-dependent density matrix functional theory: Singlet two-electron systems

Abstract

Time-dependent density functional theory in its current adiabatic implementations exhibits three striking failures: ͑a͒ Totally wrong behavior of the excited state surface along a bond-breaking coordinate, ͑b͒ lack of doubly excited configurations, affecting again excited state surfaces, and ͑c͒ much too low charge transfer excitation energies. We address these problems with time-dependent density matrix functional theory ͑TDDMFT͒. For two-electron systems the exact exchange-correlation functional is known in DMFT, hence exact response equations can be formulated. This affords a study of the performance of TDDMFT in the TDDFT failure cases mentioned ͑which are all strikingly exhibited by prototype two-electron systems such as dissociating H 2 and HeH + ͒. At the same time, adiabatic approximations, which will eventually be necessary, can be tested without being obscured by approximations in the functional. We find the following: ͑a͒ In the fully nonadiabatic ͑-dependent, exact͒ formulation of linear response TDDMFT, it can be shown that linear response ͑LR͒-TDDMFT is able to provide exact excitation energies, in particular, the first order ͑linear response͒ formulation does not prohibit the correct representation of doubly excited states; ͑b͒ within previously formulated simple adiabatic approximations the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; ͑c͒ an adiabatic approximation is formulated in which also the double excitations are fully accounted for.

Oscillator strengths of electronic excitations with response theory using phase including natural orbital functionals

“…This is corroborated by the results of Ref. 17, which demonstrate that the NOs 109 and 110 (in the numbering by decreasing occupation) are important in the low-lying excitations of H 2 at 5.0 Bohr. Furthermore, the NOs are solutions to a one-particle equation, such as the HF and KS orbitals, but the electronic "potential" is not the customary exchange or exchange-correlation potential but it is obtained according to Gilbert 36 as the functional derivative δW/δγ (r, r ) of the electron-electron interaction energy W .…”

“…17,[19][20][21][22] It can be proven 17,21,22 that an adiabatic TD-DMFT with a functional 0 [γ 0 ] produces an incorrect zero response of the NO occupations, δn(ω) = 0. This makes it impossible to describe diagonal double excitations of the type (φ i ) 2 → (φ a ) 2 , which entail a response in the occupation numbers (diagonal elements of the 1RDM).…”

“…12,17,18 In this theory, the first-order reduced density matrix (1RDM) γ (r, r , ω) is chosen as the …”

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

“…(14) and (A1) with the one-electron elements {h pq } replaced with {h μ pq } and the full-range two-electron integrals { pq|rs } replaced with their long-range counterparts pq|rs μ defined in Eq. (47).…”

Spectrum for Nonmagnetic Mott Insulators from Power Functional within Reduced Density Matrix Functional Theory

“…In practice, however, the correlation energy is an unknown functional of the 1-RDM and must be approximated. Although there are several known approximations for the xc energy functional [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], the most promising for extended systems is the power functional [14,15] where the xc energy reads…”