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Time-dependent density-functional theory (TDDFT) is deemed to be a formally rigorous way of dealing with the time-evolution of a many-electron system at the level of electron densities rather than the underlying wavefunctions, which in turn provides an, in principle, exact density-based approach to the treatment of electron excitations in atoms and molecules. This claim has not remained unchallenged, and a detailed account of the relevant criticism is given in this paper. In view of our analysis one has to face the conclusion that there is currently no valid justification for TDDFT, and expectations of finding a remedy here are hardly justified., Comment: 38 pages

Adapting a veritable many-body method to a system of non-interacting particles (NIP), while being trivial from a physical point of view, can be of interest with regard to methodological aspects. In this article we study the NIP versions of the bi-orthogonal (BCC) and unitary (UCC) coupled-cluster methods both for the ground state and generalized excitations. The essential simplification here is that the cluster operator is confined to single (or $p$-$h$) excitations. For the ground state, specifically the CC amplitude equations, the NIP versions illustrate the enormous complexity of the UCC approach as compared to the BCC concept. In the treatment of excitations, on the other hand, the UCC outperforms the BCC method, as the UCC secular matrix is block-diagonal with respect to the excitation classes, e.g., $1h$ (one-hole), $2h$-$1p$ (two-hole-one particle), $\dots$ excitations of $N\!-\!1$ particles. Moreover, the UCC basis states are essentially equivalent with the states used in the ADC/ISR (algebraic-diagrammatic construction/intermediate state representation) approach, whose NIP version has been discussed in a recent paper [J. Schirmer, arXiv:2309.15721].

This article presents an alternative formulation of quasi-degenerate perturbation theory (QDPT). The development results by simplifying established many-body (MB) techniques to systems of non-interacting particles (NIP). While the physical information of a NIP system is fully equivalent with that of the underlying one-particle system, NIP adaptions of MB schemes can acquire useful new roles in the one-particle context. In particular, the algebraic-diagrammatic construction (ADC) approach to the particle-detachment part of the electron propagator, turns into a new formalism of QDPT for the original one-particle system, establishing a diagrammatic perturbation theory for the matrix elements of the effective hamiltonian and the associated effective eigenvector coefficients (EEC). Using the NIP-ADC procedure explicit QDPT expansions are derived through third order. Alternatively, the intermediate state representation (ISR), underlying the ADC approach, allows one to construct the effective secular quantities directly from successive orders in the PT expansions of the NIP ground state and ground-state energy. Moreover, exact closed-form expressions can be derived for the effective hamiltonian and the EEC matrix in terms of 'target state' eigenvectors and eigenvalues of the one-particle system. These results are fully consistent with corresponding expressions derived within the QDPT context. The NIP approach to QDPT is not confined to actual particles but applies to arbitrary quantum systems. Any quantum system can be seen as formally constituting a "hyper-particle" giving rise to a system of non-interacting hyper-particles. The NIP adaptions of the biorthogonal coupled-cluster (BCC) and unitary coupled-cluster (UCC) methods are briefly discussed as well.

We present an algebraic, nondiagrammatic derivation of finite-temperature second-order many-body perturbation theory [FT-MBPT(2)], using techniques and concepts accessible to theoretical chemical physicists. We give explicit expressions not just for the grand potential but particularly for the mean energy of an interacting many-electron system. The framework presented is suitable for computing the energy of a finite or infinite system in contact with a heat and particle bath at finite temperature and chemical potential. FT-MBPT(2) may be applied if the system, at zero temperature, may be described using standard (i.e., zero-temperature) second-order many-body perturbation theory [ZT-MBPT(2)] for the energy. We point out that in such a situation, FT-MBPT(2) reproduces, in the zero-temperature limit, the energy computed within ZT-MBPT(2). In other words, the difficulty that has been referred to as the Kohn--Luttinger conundrum, does not occur. We comment, in this context, on a "renormalization" scheme recently proposed by Hirata and He., Comment: To appear in Chem. Phys. (2016)

We report detailed results on ionization in metallic quantum--dot (QD) nanorings described by the extended Hubbard model at half filling obtained by exact numerical diagonalization. In spite of very strong electron correlations, the ionization spectra are astonishingly scarce. We attribute this scarcity to a hidden quasi--symmetry, generalizing thereby similar results on optical absorption recently reported [I. Baldea and L. S. Cederbaum, \prb {\bf 75}, 125323 (2007); {\bf 77}, 165339 (2008)]. Numerical results indicate that this hidden quasi--symmetry of the extended Hubbard model does not evolve into a true (hidden) symmetry but remains a quasi--symmetry in the case of the restricted Hubbard model as well. Based on the observation on the number of significant ionization signals per each spatial symmetry, we claim the existence of a one--to--one map between the relevant ionization signals of the correlated half-filled nanorings and the one-hole and two-hole--one-particle processes possible in the noninteracting case. Similar to the case of optical absorption, numerous avoided crossings (anticrossings) are present in the ionization spectra, which often involve more than two states. The present results demonstrate that ionization could be a useful tool to study electron correlations in metallic QD--nanoarrays, providing information that is complementary to optical absorption.