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This contribution reports the study of a set of molecular electronic-structure reorganization representations related to light-induced electronic transitions, modeled in the framework of time-dependent density-functional response theory.…

This chapter gives an introduction to qualitative and quantitative topological analyses of molecular electronic transitions. Among the possibilities for qualitatively describing how the electronic structure of a molecule is reorganized upon…

The calculation of molecular excited states is critically important to decipher a plethora of molecular properties. In this manuscript, we develop an equation of motion formalism on top of a bi-exponentially parametrized ground state…

In this work we describe the rank-reduced variant of the equation-of-motion coupled cluster theory with complete inclusion of single, double, and triple excitations. The advantage of the proposed formalism in comparison with the canonical…

Variational calculations of excited electronic states are carried out by finding saddle points on the surface that describes how the energy of the system varies as a function of the electronic degrees of freedom. This approach has several…

We initiate the recently proposed $\boldsymbol{w}$-ensemble one-particle reduced density matrix functional theory ($\boldsymbol{w}$-RDMFT) by deriving the first functional approximations and illustrate how excitation energies can be…

The formalism to calculate excited state properties from the $GW$-Bethe-Salpeter equation (BSE) method is introduced, providing convenient access to excited state absorption, excited state circular dichroism, and excited state optical…

The quantum equation-of-motion (qEOM) method with singles and doubles has been suggested to study electronically excited states while it fails to predict the excitation energies dominated by double excitations. In this work, we present an…

The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional…

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we introduce a novel equation-of-motion (EOM)…

The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…

In [Phys. Rev. Lett. 127, 023001 (2021)] a reduced density matrix functional theory (RDMFT) has been proposed for calculating energies of selected eigenstates of interacting many-fermion systems. Here, we develop a solid foundation for this…

We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave…

A summary is presented of the properties of the coefficient matrices formed by expanding the two-body reduced density matrix in a complete set of two-electron wave functions. Calculating the relationship between the many electron wave…

This paper analyses the GW method for finite electronic systems. In a first step, we provide a mathematical framework for the usual one-body operators that appear naturally in many-body perturbation theory. We then discuss the GW equations…

We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a…

In this work, we establish a general theory of phase transitions and quantum entanglement in the equilibrium state at arbitrary temperatures. First, we derived a set of universal functional relations between the matrix elements of two-body…

Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining…

With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced-density matrix (one-matrix). The eigenvalues of the one-matrix, which represent the…

There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the equivalent…