Linear-response time-dependent density-functional theory with pairing fields

Abstract

Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies (van Aggelen et al. Phys. Rev. A, 88, 030501 (2013)) and N ± 2 excitation energies (Yang, et al. J.Chem. Phys.). So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing elds with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing eld for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justi es the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

First order nonadiabatic coupling matrix elements between excited states: Implementation and application at the TD-DFT and pp-TDA levels

“…Loosely speaking, Kohn-Sham orbitals and eigenvalues can also be used here, for pp-RPA can in a way be viewed as an extension of TD-DFT for a pairing field. 38 Since the reference |0⟩ and the target states have different numbers of electrons, the quantities γ˜0 I pq and hence g ξ 0I are naturally zero. However, the fo-NACME g ξ IJ between two N-electron states are accessible by pp-TDA.…”

Nature of ground and electronic excited states of higher acenes

“…In contrast, the molecular orbital based on Kohn-Sham DFT is more intuitive and has been argued to be very suitable for qualitative chemical applications (91)(92)(93). Although, strictly speaking, the transitional amplitude of pp-RPA only describes the pairing density response to a pairing field (82), it can also be perceived that pp-RPA combines seamlessly a DFT description of the N−2 core electrons and a CI wave-function description of the outermost two electrons. It is thus possible to use molecular orbitals to reveal the nature of an excitation.…”

“…It was later further extended to describing excitations (81)(82)(83)(84). For excited states calculation, it starts from a two-electron deficient (N−2) system described with DFT correlation, then recovers a series of neutral states by adding back two explicitly correlated electrons.…”

The Chronus Quantum software package

“…In general, the columns of the eigenvectors T represent the transition density pertaining to the transition energies of the corresponding diagonal element of Ω . ChronusQ supports residue calculations using two different approximations of the quantum propagator, namely, ph‐RPA and pp‐RPA . Both HF and KS reference wave functions may be used for either of these propagator approximations.…”