Density-based Hartree-Fock theory

Geometrical Derivatives and Magnetic Properties in Atomic-orbital Density-based Hartree-Fock Theory. 

Formally, this expansion may be obtained from the BCH expansion of exp(—X)A exp(X) by padding X with S everywhere except next to A. The theory of nonunitary transformations is used in the development of density-based Hartree-Fock theory in Section 10.7. 

The remainder of Section 10.8 consists of two parts. In Section 10.8.2, we discuss the implementation of Newton s method within the framework of density-based Hartree-Fock theory, in particular the transformation of trial vectors (10.8.8). Next, in Sections 10.8.3-10.8.8, we consider Newton s method in orbital-based Hartree-Fock theory. The orbital-based treatment is more general than the density-based one in that it enables us to treat more general Hartree-Fock states, thus preparing us for the multiconfigurational states of MCSCF theory in Chapter 12. 

In density-based Hartree-Fock theory, the Newton iterations are established by minimizing the second-order energy (10.8.1) obtained by truncating (10.7.77) at second order in X ... 

Density functional theory (DFT),32 also a semi-empirical method, is capable of handling medium-sized systems of biological interest, and it is not limited to the second row of the periodic table. DFT has been used in the study of some small protein and peptide surfaces. Nevertheless, it is still limited by computer speed and memory. DFT offers a quantum mechanically based approach from a fundamentally different perspective, using electron density with an accuracy equivalent to post Hartree-Fock theory. The ideas have been around for many years,33 34 but only in the last ten years have numerous studies been published. DFT, compared to ab initio... 

Li, J. Cramer, and Truhlar, D. G. 1999. Application of a Universal Solvation Model to Nucleic Acid Bases. Comparison of Semiempirical Molecular Orbital Theory, Ab Initio, Hartree-Fock Theory, and Density Functional Theory , Biophys. Chem.. 78, 147. 

An alternative to Hartree-Fock theory is density-functional (DF) theory in which certain elements in the Hamiltonian are evaluated at fixed points directly from the electron densities at those points. This can circumvent the need for calculating the enormous numbers of electron-electron repulsion integrals encountered in Hartree-Fock calculations. We here briefly describe density-functional theory based upon reviews by von Barth (1986) and Srivastava and Weaire (1987). 

Over the decade 1995-2005, ab initio quantum chemistry has become an important tool in studying imidazole derivatives. Two highly productive approaches are often utilized for the calculations the wave function-based methods (e.g., Hartree-Fock theory and second-order Moller-Plesset perturbation theory (MP2)) and the density functional theory (DFT) based methods (e.g., gradient-corrected (BLYP) and hybrid (B3LYP) methods). 

Various density-functional theory based descriptors were probed with success by Arulmozhiraja and Morita [155]. In 2005, Hirokawa and coworkers employed Hartree-Fock theory, which identifies the polarization as a key parameter for QSAR on AhR binding [156]. Wang et al. extended their work to include polybrominated compounds and reached a cross-validated r2 of 0.580 and 0.680 using CoMFA and CoMSIA, respectively [157], Zheng and coworkers [158] employed radial basis function neural networks and obtained... 

Accounting for relativistic effects in computational organotin studies becomes complicated, because Hartree-Fock (HF), density functional theory (DFT), and post-HF methods such as n-th order Mpller-Plesset perturbation (MPn), coupled cluster (CC), and quadratic configuration interaction (QCI) methods are non-relativistic. Relativistic effects can be incorporated in quantum chemical methods with Dirac-Hartree-Fock theory, which is based on the four-component Dirac equation. " Unformnately the four-component Flamiltonian in the all-electron relativistic Dirac-Fock method makes calculations time consuming, with calculations becoming 100 times more expensive. The four-component Dirac equation can be approximated by a two-component form, as seen in the Douglas-Kroll (DK) Hamiltonian or by the zero-order regular approximation To address the electron cor-... 

In the last few years, methods based on Density Functional Theory have gained steadily in popularity. The best DFT methods achieve significantly greater accuracy than Hartree-Fock theory at only a modest increase in cost (far less than MP2 for medium-size and larger molecular systems). They do so by including some of the effects of electron correlation much less expensively than traditional correlated methods. 

As indicated before, the ab initio electronic-structure theory of solid-state materials has largely profited from density-functional theory (DFT), and the performance of DFT has turned out well even when the one of its molecular quantum-chemical competitors - Hartree-Fock theory - has been weakest, namely for metallic materials. For these, and also for covalent materials, DFT is a very reasonable choice. On the other hand, ionic compounds (with both metals and nonmetals present) are often discussed using only the ionic model, on which most of Section 1.2 was based, and the quantum-mechanical approach is not considered at all, at least in introductory textbooks. Nonetheless, let us see, as a first instructive example, how a t5q)ical ionic material can be described and understood by the ionic and the quantum-chemical (DFT and HF) approaches, and let us also analyze the strengths and weaknesses. 

The broken-symmetry approach was developed within the framework of unrestricted Hartree-Fock theory or spin-polarized density functional theory, i.e., Xa theory. " It is based on the assumption that the energy difference between the singlet and triplet states resulting from the interaction between two 5 = 1/2 spin centers is given by ... 

The Amsterdam Density Functional package (ADF) is software for first-principles electronic structure calculations (quantum chemistry). ADF is often used in the research areas of catalysis, inorganic and heavy-element chemistry, biochemistry, and various types of spectroscopy. ADF is based on density functional theory (DFT) (see Chapter 2.39), which has dominated quantum chemistry applications since the early 1990s. DFT gives superior accuracy to Hartree-Fock theory and semi-empirical approaches, especially for transition-metal compounds. In contrast to conventional correlated post-Hartree-Fock methods, it enables accurate treatment of systems with several hundreds of atoms (or several thousands with QM/MM)." ... 

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