Exchange-correlation entropy from the generalized thermal adiabatic connection.

Warm dense matter is a highly energetic phase characterized by strong correlations, thermal effects, and quantum mechanical electrons. Thermal density functional theory is commonly used in simulations of this challenging phase, driving the development of temperature-dependent approximations to the exchange-correlation free energy. Approaches using the adiabatic connection formula are well known at zero temperature and have been recently leveraged at non-zero temperatures as well.

Møller-Plesset and Density-Fixed Adiabatic Connections for a Model Diatomic System at Different Correlation Regimes.

In recent years, adiabatic connection (AC) interpolations developed within density functional theory (DFT) have been found to provide good performances in the calculation of interaction energies when used with Hartree-Fock (HF) ingredients. The physical and mathematical reasons for such unanticipated performance have been clarified, to some extent, by studying the strong-interaction limit of the Møller-Plesset (MP) AC. In this work, we calculate both the MP and the DFT AC integrand for the asymmetric Hubbard dimer, which allows for a systematic investigation of different correlation regimes by varying two simple parameters in the Hamiltonian: the external potential, Δ, and the interaction strength, .

Good Vibrations: Calculating Excited-State Frequencies Using Ground-State Self-Consistent Field Models.

The use of Δ-self-consistent field (SCF) approaches for studying excited electronic states has received a renewed interest in recent years. In this work, the use of this scheme for calculating excited-state vibrational frequencies is examined. Results from Δ-SCF calculations for a set of representative molecules are compared with those obtained using configuration interaction with single substitutions (CIS) and time-dependent density functional theory (TD-DFT) methods.

Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test case study.

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree-Fock (HF) and Kohn-Sham (KS) states as analytical functions of the external potential, Δv, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, Δv} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the "traditional" correlation energy, i.

Comparison of Linear Response Theory, Projected Initial Maximum Overlap Method, and Molecular Dynamics-Based Vibronic Spectra: The Case of Methylene Blue.

The simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited electronic states. In this report, we show that the utilization of such a procedure within an adiabatic linear response (LR) theory framework may lead to state mixings and a breakdown of the Born-Oppenheimer approximation, resulting in a poor description of absorption spectra.

Approximate bounds and temperature dependence of adiabatic connection integrands for the uniform electron gas.

Thermal density functional theory is commonly used in simulations of warm dense matter, a highly energetic phase characterized by substantial thermal effects and by correlated electrons demanding quantum mechanical treatment. Methods that account for temperature dependence, such as Mermin-Kohn-Sham finite-temperature density functional theory and free energy density functional theory, are now employed with more regularity and available in many standard code packages. However, approximations from zero-temperature density functional theory are still often used in temperature-dependent simulations using thermally weighted electronic densities as an input to exchange-correlation functional approximations, a practice known to miss temperature-dependent effects in the exchange-correlation free energy of these systems.

Using projection operators with maximum overlap methods to simplify challenging self-consistent field optimization.

Maximum overlap methods are effective tools for optimizing challenging ground- and excited-state wave functions using self-consistent field models such as Hartree-Fock and Kohn-Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user-defined initial guess of the target wave function. In this work, a projection operator framework is defined and used to provide a metric for non-aufbau orbital selection in maximum-overlap-methods.

Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory.

A very specific ensemble of ground and excited states is shown to yield an exact formula for any excitation energy as a simple correction to the energy difference between orbitals of the Kohn-Sham ground state. This alternative scheme avoids either the need to calculate many unoccupied levels as in time-dependent density functional theory (TDDFT) or the need for many self-consistent ensemble calculations. The symmetry-eigenstate Hartree-exchange (SEHX) approximation yields results comparable to standard TDDFT for atoms.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem.

The van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. This produces a natural method for generating new thermal exchange-correlation approximations.

DFT: A Theory Full of Holes?

This article is a rough, quirky overview of both the history and present state of the art of density functional theory. The field is so huge that no attempt to be comprehensive is made. We focus on the underlying exact theory, the origin of approximations, and the tension between empirical and nonempirical approaches.

Excitations and benchmark ensemble density functional theory for two electrons.

A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived.