Density functional theories methods development

In a complementary development, very rapid, if inexact, evaluations of a PES are now possible through the density functional theory methods developed by Hohenberg and Kohn [31], Kohn and Sham [32], Lee et al. [33a], Parr and Yong [33b], and Becke [34], for which Kohn shared in the 1998 Nobel Prize in Chemistry. 

Jursic, B. S., 1996, Computing Transition State Structures With Density Functional Theory Methods in Recent Developments and Applications of Modem Density Functional Theory, Seminario, J. M. (ed.), Elsevier, Amsterdam. 

John Slater, bom Oak Park, Illinois, 1900. Ph.D. Harvard, 1923. Professor of physics, Harvard, 1924-1930 MIT 1930-1966 University of Florida at Gainesville, 1966-1976. Author of 14 textbooks, contributed to solid-state physics and quantum chemistry, developed X-alpha method (early density functional theory method). Died Sanibel Island, Florida, 1976. 

A mode coupling theory is recently developed [135] which goes beyond the time-dependent density functional theory method. In this theory a projection operator formalism is used to derive an expression for the coupling vertex projecting the fluctuating transition frequency onto the subspace spanned by the product of the solvent self-density and solvent collective density modes. The theory has been applied to the case of nonpolar solvation dynamics of dense Lennard-Jones fluid. Also it has been extended to the case of solvation dynamics of the LJ fluid in the supercritical state [135],... 

Before any computational study on molecular properties can be carried out, a molecular model needs to be established. It can be based on an appropriate crystal structure or derived using any technique that can produce a valid model for a given compound, whether or not it has been prepared. Molecular mechanics is one such technique and, primarily for reasons of computational simplicity and efficiency, it is one of the most widely used technique. Quantum-mechanical modeling is far more computationally intensive and until recently has been used only rarely for metal complexes. However, the development of effective-core potentials (ECP) and density-functional-theory methods (DFT) has made the use of quantum mechanics a practical alternative. This is particularly so when the electronic structures of a small number of compounds or isomers are required or when transition states or excited states, which are not usually available in molecular mechanics, are to be investigated. However, molecular mechanics is still orders of magnitude faster than ab-initio quantum mechanics and therefore, when large numbers of... 

During the last 10-20 years, a large number of efficient theoretical methods for the calculation of linear and nonlinear optical properties have been developed— this development includes semi-empirical, highly correlated ab initio, and density functional theory methods. Many of these approaches will be reviewed in later chapters of this book, and applications will be given that illustrate the merits and limitations of theoretical studies of linear and nonlinear optical processes. It will become clear that theoretical studies today can provide valuable information in Are search for materials with specific nonlinear optical properties. First, there is the possibility to screen classes of materials based on cost and time effective calculations rather then labor intensive synthesis and characterization work. Second, there is Are possibility to obtain a microscopic understanding for the performance of the material—one can investigate the role of individual transition channels, dipole moments, etc., and perform systematic model Improvements by inclusion of the environment, relativistic effects, etc. 

Density Functional Theory Methods In parallel to the development of ab initio theory, it was theorized that all molecular properties could be described as a function of the electron density [24]. By using mathematical functions, called functionals, to describe the electron density, a new theoretical approach, density functional theory (DFT), was developed. In 1965, Kohn and Sham [25] produced a set of equations that demonstrated how to determine a self-consistent density from DFT decomposition of the Schrodinger equation ... 

Density functional theory (DFT), developed within solid state physics, is based on the theorem of Hohenberg and Kohn that the ground state energy of a system depends on the electron density. It can be applied to calculations performed either with localised basis sets or by combination of plane waves. Both approaches have been applied to microporous solids, although the plane wave methods have been used more commonly. The SIESTA code, for example,permits DFT calculations using localised basis sets as does GAUSSIAN. 

Pulay demonstrated that analytic first derivatives with respect to geometric parameters can be calculated easily and efficiently for HF energies. Derivatives of correlated methods followed a number of years after SCF derivatives [4, 5]. Extensions of the SCF derivatives to density functional theory methods were straightforward. In the three decades since Pulay s article, hundreds of papers on energy derivatives have been published, and all can trace their roots back to his paper. Energy derivatives have become so useful for calculating molecular structures and properties that, almost universally, first derivatives are formulated and coded soon after a new theoretical method is developed for the energy. 

Much effort is currently devoted to developing more economical quantum-chemical methods for biopolymers. Semiempirical techniques are very inaccurate (even compared to force fields) for description of molecular interactions [12d,e]. More promising are the Density Functional Theory methods [14]. A high quality DFT method can provide, for some applications, results comparable to those obtained by good quality, traditional ab initio techniques. However, high quality DFT techniques are still costly. Furthermore, no DFT method currently works for dispersion-controlled interactions [12b, 15]... 

Janetzko, F., Koster, A. M., 8c Salahub, D. R. (2008). Development of the cyclic cluster model formalism for Kohn-Sham auxiliary density functional theory methods. Journal of Chemical Physics, 128, 024102. 

Density functional theory (DFT) has become very popular in recent years. This is justified based on the pragmatic observation that it is less computationally intensive than other methods with similar accuracy. This theory has been developed more recently than other ah initio methods. Because of this, there are classes of problems not yet explored with this theory, making it all the more crucial to test the accuracy of the method before applying it to unknown systems. 

An important conceptual, or even philosophical, difference between the orbital/wavefunction methods and the density functional methods is that, at least in principle, the density functional methods do not appeal to orbitals. In the former case the theoretical entities are completely unobservable whereas electron density invoked by density functional theories is a genuine observable. Experiments to observe electron densities have been routinely conducted since the development of X-ray and other diffraction techniques (Coppens, 2001).18... 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

It is a truism that in the past decade density functional theory has made its way from a peripheral position in quantum chemistry to center stage. Of course the often excellent accuracy of the DFT based methods has provided the primary driving force of this development. When one adds to this the computational economy of the calculations, the choice for DFT appears natural and practical. So DFT has conquered the rational minds of the quantum chemists and computational chemists, but has it also won their hearts To many, the success of DFT appeared somewhat miraculous, and maybe even unjust and unjustified. Unjust in view of the easy achievement of accuracy that was so hard to come by in the wave function based methods. And unjustified it appeared to those who doubted the soundness of the theoretical foundations. There has been misunderstanding concerning the status of the one-determinantal approach of Kohn and Sham, which superficially appeared to preclude the incorporation of correlation effects. There has been uneasiness about the molecular orbitals of the Kohn-Sham model, which chemists used qualitatively as they always have used orbitals but which in the physics literature were sometimes denoted as mathematical constructs devoid of physical (let alone chemical) meaning. 

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