Density functional theory formalism

Tran, F. Weber. J. Wesolowski. T.A. Theoretical study of the benzene dimer by the density-functional-theory formalism based on electron-density partitioning. Helv. Chim. Acta 2001, 84 (6), 1489-1503. 

Higuchi, M. Higuchi, K. Arbitrary choice of basic variables in density functional theory formalism. Phys. Rev. B 2004, 69,035113. 

Bylaska E, Tsemekhman K, Govind N and Valiev M 2011 Large-scale plane-wave-based density-functional theory formalism, parallelization, and applications. Computational methods for large systems electronic structure approaches for biotechnology and rmnotechnology. Wiley, Hoboken pp. 77-116. 

Fischer-type carbene complexes, generally characterized by the formula (CO)5M=C(X)R (M=Cr, Mo, W X=7r-donor substitutent, R=alkyl, aryl or unsaturated alkenyl and alkynyl), have been known now for about 40 years. They have been widely used in synthetic reactions [37,51-58] and show a very good reactivity especially in cycloaddition reactions [59-64]. As described above, Fischer-type carbene complexes are characterized by a formal metal-carbon double bond to a low-valent transition metal which is usually stabilized by 7r-acceptor substituents such as CO, PPh3 or Cp. The electronic structure of the metal-carbene bond is of great interest because it determines the reactivity of the complex [65-68]. Several theoretical studies have addressed this problem by means of semiempirical [69-73], Hartree-Fock (HF) [74-79] and post-HF [80-83] calculations and lately also by density functional theory (DFT) calculations [67, 84-94]. Often these studies also compared Fischer-type and... 

In this volume dedicated to Yngve Ohm we feel it is particularly appropriate to extend his ideas and merge them with the powerful practical and conceptual tools of Density Functional Theory (6). We extend the formalism used in the TDVP to mixed states and consider the states to be labeled by the densities of electronic space and spin coordinates. (In the treatment presented here we do not explicitly consider the nuclei but consider them to be fixed. Elsewhere we shall show that it is indeed straightforward to extend our treatment in the same way as Ohm et al. and obtain equations that avoid the Bom-Oppenheimer Approximation.) In this article we obtain a formulation of exact equations for the evolution of electronic space-spin densities, which are equivalent to the Heisenberg equation of motion for the electtons in the system. Using the observation that densities can be expressed as quadratic expansions of functions, we also obtain exact equations for Aese one-particle functions. 

Gross, E. K. U., Oliveira, L. N., Kohn, W., 1988b, Density-Functional Theory for Ensembles of Fractionally Occupied States. I. Basic Formalism , Phys. Rev. A, 37, 2809. 

From the early advances in the quantum-chemical description of molecular electron densities [1-9] to modem approaches to the fundamental connections between experimental electron density analysis, such as crystallography [10-13] and density functional theories of electron densities [14-43], patterns of electron densities based on the theory of catastrophes and related methods [44-52], and to advances in combining theoretical and experimental conditions on electron densities [53-68], local approximations have played an important role. Considering either the formal charges in atomic regions or the representation of local electron densities in the structure refinement process, some degree of approximate transferability of at least some of the local structural features has been assumed. 

Group 2 complexes are formally electron deficient and conformationally floppy only small energies (often only 1-2 kcal mol-1) are required to alter their geometries by large amounts (e.g., bond angles by 20° or more). In such cases, the inclusion of electron-correlation effects becomes critical to an accurate description of the molecules structures. Both HF/MP2 and density functional theory (DFT) methods have been applied to organoalkaline earth compounds. DFT approaches, which implicitly incorporate electron correlation in a computationally efficient form, are generally the more widely used. Molecular orbital calculations that successfully reproduce bent... 

The inherent problems associated with the computation of the properties of solids have been reduced by a computational technique called Density Functional Theory. This approach to the calculation of the properties of solids again stems from solid-state physics. In Hartree-Fock equations the N electrons need to be specified by 3/V variables, indicating the position of each electron in space. The density functional theory replaces these with just the electron density at a point, specified by just three variables. In the commonest formalism of the theory, due to Kohn and Sham, called the local density approximation (LDA), noninteracting electrons move in an effective potential that is described in terms of a uniform electron gas. Density functional theory is now widely used for many chemical calculations, including the stabilities and bulk properties of solids, as well as defect formation energies and configurations in materials such as silicon, GaN, and Agl. At present, the excited states of solids are not well treated in this way. 

FORMAL FOUNDATIONS OF DENSITY FUNCTIONAL THEORY FOR TIME-DEPENDENT ELECTRIC AND MAGNETIC FIELDS... 

Density functional theory was originally formalized for the ground state [1]. It is valid for the lowest energy state in each symmetry class [2,3]. To calculate excitation energies, Slater [4] introduced the transition state method, which proved to be a reasonably good one to calculate excitation energies. 

There are other noteworthy single excited-state theories. Gorling developed a stationary principle for excited states in density functional theory [41]. A formalism based on the integral and differential virial theorems of quantum mechanics was proposed by Sahni and coworkers for excited state densities [42], The local scaling approach of Ludena and Kryachko has also been generalized to excited states [43]. 

The density functional theory (DFT) [32] represents the major alternative to methods based on the Hartree-Fock formalism. In DFT, the focus is not in the wavefunction, but in the electron density. The total energy of an n-electron system can in all generality be expressed as a summation of four terms (equation 4). The first three terms, making reference to the noninteracting kinetic energy, the electron-nucleus Coulomb attraction and the electron-electron Coulomb repulsion, can be computed in a straightforward way. The practical problem of this method is the calculation of the fourth term Exc, the exchange-correlation term, for which the exact expression is not known. 

This survey of theoretical methods for a qualitative description of homogeneous catalysis would not be complete without a mention to the Hartree-Fock-Slater, or Xot, method [36]. This approach, which can be formulated as a variation of the LDA DFT, was well known before the formal development of density functional theory, and was used as the more accurate alternative to extended Hiickel in the early days of computational transition metal chemistry. 

---