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 (SEHX), is derived. Exact conditions that are proven include the signs of the correlation energy components, the virial theorem for both exchange and correlation, and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.Comment: 15 pages, supplemental material pd

Exploring Foundations of Time-Independent Density Functional Theory for Excited-States

Based on the work of Gorling and that of Levy and Nagy, density-functional formalism for many Fermionic excited-states is explored through a careful and rigorous analysis of the excited-state density to external potential mapping. It is shown that the knowledge of the ground-state density is a must to fix the mapping from an excited-state density to the external potential. This is the excited-state counterpart of the Hohenberg-Kohn theorem, where instead of the ground-state density the density of the excited-state gives the true many-body wavefunctions of the system. Further, the excited-state Kohn-Sham system is defined by comparing it's non-interacting kinetic energy with the true kinetic energy. The theory is demonstrated by studying a large number of atomic systems.Comment: submitted to J. Chem. Phy

Local-density approximation for exchange energy functional in excited-state density functional theory

An exchange energy functional is proposed and tested for obtaining a class of excited-state energies using density functional formalism. The functional is the excited-state counterpart of the local-density approximation functional for the ground state. It takes care of the state dependence of the energy functional and leads to highly accurate excitation energies

A correction for the Hartree-Fock density of states for jellium without screening

We revisit the Hartree-Fock (HF) calculation for the uniform electron gas, or jellium model, whose predictions—divergent derivative of the energy dispersion relation and vanishing density of states (DOS) at the Fermi level—are in qualitative disagreement with experimental evidence for simple metals. Currently, this qualitative failure is attributed to the lack of screening in the HF equations. Employing Slater’s hyper-Hartree-Fock (HHF) equations, derived variationally, to study the ground state and the excited states of jellium, we find that the divergent derivative of the energy dispersion relation and the zero in the DOS are still present, but shifted from the Fermi wavevector and energy of jellium to the boundary between the set of variationally optimised and unoptimised HHF orbitals. The location of this boundary is not fixed, but it can be chosen to lie at arbitrarily high values of wavevector and energy, well clear from the Fermi level of jellium. We conclude that, rather than the lack of screening in the HF equations, the well-known qualitative failure of the ground-state HF approximation is an artifact of its nonlocal exchange operator. Other similar artifacts of the HF nonlocal exchange operator, not associated with the lack of electronic correlation, are known in the literature

Foundations of self-consistent particle-rotor models and of self-consistent cranking models

The Kerman-Klein formulation of the equations of motion for a nuclear shell model and its associated variational principle are reviewed briefly. It is then applied to the derivation of the self-consistent particle-rotor model and of the self-consistent cranking model, for both axially symmetric and triaxial nuclei. Two derivations of the particle-rotor model are given. One of these is of a form that lends itself to an expansion of the result in powers of the ratio of single-particle angular momentum to collective angular momentum, that is essentual to reach the cranking limit. The derivation also requires a distinct, angular-momentum violating, step. The structure of the result implies the possibility of tilted-axis cranking for the axial case and full three-dimensional cranking for the triaxial one. The final equations remain number conserving. In an appendix, the Kerman-Klein method is developed in more detail, and the outlines of several algorithms for obtaining solutions of the associated non-linear formalism are suggested.Comment: 29 page

Imaging cervical cytology with scanning near-field optical microscopy (SNOM) coupled with an IR-FEL

Cervical cancer remains a major cause of morbidity and mortality among women, especially in the developing world. Increased synthesis of proteins, lipids and nucleic acids is a pre-condition for the rapid proliferation of cancer cells. We show that scanning near-field optical microscopy, in combination with an infrared free electron laser (SNOM-IR-FEL), is able to distinguish between normal and squamous low-grade and high-grade dyskaryosis, and between normal and mixed squamous/glandular pre-invasive and adenocarcinoma cervical lesions, at designated wavelengths associated with DNA, Amide I/II and lipids. These findings evidence the promise of the SNOM-IR-FEL technique in obtaining chemical information relevant to the detection of cervical cell abnormalities and cancer diagnosis at spatial resolutions below the diffraction limit (?0.2 \ensuremathμm). We compare these results with analyses following attenuated total reflection Fourier-transform infrared (ATR-FTIR) spectroscopy; although this latter approach has been demonstrated to detect underlying cervical atypia missed by conventional cytology, it is limited by a spatial resolution of ~3 \ensuremathμm to 30 \ensuremathμm due to the optical diffraction limit

Response function analysis of excited-state kinetic energy functional constructed by splitting k-space

Over the past decade, fundamentals of time independent density functional theory for excited state have been established. However, construction of the corresponding energy functionals for excited states remains a challenging problem. We have developed a method for constructing functionals for excited states by splitting k-space according to the occupation of orbitals. In this paper we first show the accuracy of kinetic energy functional thus obtained. We then perform a response function analysis of the kinetic energy functional proposed by us and show why method of splitting the k-space could be the method of choice for construction of energy functionals for excited states.Comment: 11 page

Thermal Density Functional Theory in Context

This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by illustrating some of its key reformulations. The basics of DFT for thermal ensembles are explained in this context, as are tools useful for analysis and development of approximations. We close by discussing some key ideas relating thermal DFT and the ground state. This review emphasizes thermal DFT's strengths as a consistent and general framework.Comment: Submitted to Spring Verlag as chapter in "Computational Challenges in Warm Dense Matter", F. Graziani et al. ed