Foundations Of Density Functional Theory Research Articles

Giant values obtained for first hyperpolarizabilities of methyl orange: a DFT investigation

Advances in photonics and optoelectronics depend on proposing new materials with well-defined nonlinear optics properties. Based on the foundations of density functional theory, this work presents a systematic investigation of linear and nonlinear optical properties of methyl orange, a well-known azo dye. Structural changes from alkaline to acidic structures drastically boost all investigated properties. For instance, the material dipole polarizability starts from an isotropic condition ( $$\alpha _{\mathrm{iso}}>\varDelta \alpha $$ ) to an anisotropic behavior ( $$\alpha _{\mathrm{iso}}<\varDelta \alpha $$ ). The first hyperpolarizabilities are also strongly tuned varying from 18.9 $$\times\, 10^{-30}$$ to 171.7 $$\times\, 10^{-30}$$ esu. A careful analysis of frontier molecular orbitals indicates proper wide-bandgap semiconductor energy gap (3.22 eV) and associates the highest hyperpolarizabilities to the lowest energy gap, which means semiconductor molecules with intense nonlinear optical activity.

Chapter 6 - Generalized Kohn–Sham Density Functional Theory via Effective Action Formalism

Publisher Summary This chapter examines the foundation of density functional theory. Density functional theory allows studying the ground state properties of the many-body system in terms of the expectation value of the particle-density operator. It offers the possibility of finding the ground state energy by minimizing the energy functional that depends on the density only. In general, it is possible to imagine a description of a many-body system in terms of the expectation value of any other suitable operator. Such a description can be presented via the effective action formalism, thus leading to a generalized density-functional theory–a theory that allows a description of many-body systems in terms of the expectation value of any suitable operator. Density-functional theory relies on the theorem of Hohenberg and Kohn, which shows that there exists a unique description of a many-body system in terms of the expectation value of the particle-density operator. In the framework of the effective action formalism, the proof of existence was given only in a diagrammatic sense and was tailored to the particular features of the particle-density based description of a nonrelativistic many-electron system. The chapter presents a different resolution of this issue. Constructed are the first few orders of the exchange-correlation functional, there are comments on the local density approximation, and discussion on the results as compared to other methods. The chapter discusses effective action functional, generalized Kohn–Sham theory via the inversion method, Kohn–Sham density-functional theory, time-dependent probe, one-electron propagators, excitation energies, and theorems involving functionals W [J] and T [Q]. Kohn–Sham theory has been derived. This formulation is specifically geared towards practical calculations of the ground and excited properties of real systems. This can be applied to various many-body systems for constructing Kohn–Sham like descriptions in terms of the expectation value of any general operator.

Coarse-grained V representability

The unsolved problem of determining which densities are ground state densities of an interacting electron system in some external potential is important to the foundations of density functional theory. A coarse-grained version of this ensemble V-representability problem is shown to be thoroughly tractable. Averaging the density of an interacting electron system over the cells of a regular partition of space produces a coarse-grained density. It is proved that every strictly positive coarse-grained density is coarse-grained ensemble V representable: there is a unique potential, constant over each cell of the partition, which has a ground state with the prescribed coarse-grained density. For a system confined to a box, the (coarse-grained) Lieb [Int. J. Quantum Chem. 24, 243 (1983)] functional is also shown to be Gâteaux differentiable. All results extend to open systems.

DEGENERATE GASES UNDER HARMONIC CONFINEMENT IN ONE DIMENSION: RIGOROUS RESULTS IN THE IMPENETRABLE-BOSONS/SPIN-POLARIZED-FERMIONS LIMIT

Developments in the realization and study of ultracold atomic gases inside elongated magnetic traps and atom waveguides have stimulated calculations of equilibrium properties and excitation spectra for mesoscopic clouds of hard-core bosons and of spin-polarized fermions moving under an external harmonic potential in one dimension. A rigorous correspondence exists between the wave functions of these two types of system, allowing a number of exact results to be obtained. The main theoretical techniques and results are reviewed in this article, with emphasis on their relevance in regard to tests of the Thomas–Fermi approximation for confined Fermi fluids and to the foundations of density functional theory for inhomogeneous quantum systems.

Macroscopic polarization from electronic wave functions

The dipole moment of any finite and neutral system, having a square-integrable wave function, is a well-defined quantity. The same quantity is ill-defined for an extended system, whose wave function invariably obeys periodic (Born–von Kármán) boundary conditions. Despite this fact, macroscopic polarization is a theoretically accessible quantity, for either uncorrelated or correlated many-electron systems: in both cases, polarization is a rather “exotic” observable. For an uncorrelated—either Hartree–Fock or Kohn–Sham—crystalline solid, polarization has been expressed and computed as a Berry phase of the Bloch orbitals (since 1993). The case of a correlated and/or disordered system received a definitive solution only very recently (1998): This latest development allows us to present here the whole theory from a novel, and very general, viewpoint. The modern theory of polarization is even relevant to the foundations of density functional theory in extended systems. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 599–606, 1999

Macroscopic polarization from electronic wave functions

The dipole moment of any finite and neutral system, having a square-integrable wavefunction, is a well defined quantity. The same quantity is ill-defined for an extended system, whose wavefunction invariably obeys periodic (Born-von Karman) boundary conditions. Despite this fact, macroscopic polarization is a theoretically accessible quantity, for either uncorrelated or correlated many-electron systems: in both cases, polarization is a rather exotic observable. For an uncorrelated-either Hartree-Fock or Kohn-Sham-crystalline solid, polarization has been expressed and computed as a Berry phase of the Bloch orbitals (since 1993). The case of a correlated and/or disordered system received a definitive solution only very recently (1998): this latest development allows us present here the whole theory from a novel, and very general, viewpoint. The modern theory of polarization is even relevant to the foundations of density functional theory in extended systems.

Density Functional Theory through Legendre Transformation

Theoretical foundation of density functional theory in terms of field theoretical Legendre trans­ formation is presented. The ground state energy is first written as a functional of local probe coupled to the density operator. The density functional is then defined by the functional Legendre transformation, which leads to a systematic formulation of density functional theory. Excitation spectrum is also determined within the same formalism in a unified way. The diagrammatic evaluation is most conveniently done by using auxiliary field method. Several generalizations of the formalism and extension to the case other than the density operator are also discussed. The density functional theory is now one.of the most commonly used methods in discussing various many particle systems. 1 l In this formalism the energy of the system is written as a functional of the density which is a function of single variable x instead of N coordinates X1 ~ XN of N particles. In spite of the usefulness, its theoretical formulation is rather involved and sometimes difficult to achieve a system­ atic approximation scheme. The purpose of this paper is to present a clear formulation of the density func­ tional theory in terms of full use of the Legendre transformation applied to the quantum system, especially to the system described by the second quantized field theory. 2 l It presents a theoretical basis of the density functional formalism which is both exact and systematic. These can be achieved by a straightforward application of our technique called on-shell expansion. The discussion is organized as follows: 1. Ground state 2. Excited states 3. Generalization to the case other than the density operator 4. Finite temperature case (equilibrium and non-equilibrium), etc. They are all formulated in terms of the field theoretical Legendre transformation in a unified way. We have in mind, in the following, atomic system with N electrons but the arguments can be applied to any many particle system with minor modifications. The essential feature of the formulation of the density functional theory in terms of Legendre transformation is the following. In the usual approach the ground state wave function lf! is used to connect the potential v and the density n;