Density-functional theory going beyond

In order to fully understand such technologically important phenomena as near-equilibrium crystal growth and homogeneous nucleation, it is necessary to have detailed information as to the microscopic properties of the equilibrium interface between a crystal and its melt. Unfortunately, there is an almost total lack of experimental data on such systems as the interface lies between two condensed phases of similar density, making study difficult. Thus, computational methods, such as computer simulation or density functional theory, go beyond their usual roles in the interpretation of experimental data and become important in determining the generic phenomenology of such systems. 

Recent calculations of hyperfine parameters using pseudopotential-density-functional theory, when combined with the ability to generate accurate total-energy surfaces, establish this technique as a powerful tool for the study of defects in semiconductors. One area in which theory is not yet able to make accurate predictions is for positions of defect levels in the band structure. Methods that go beyond the one-particle description are available but presently too computationally demanding. Increasing computer power and/or the development of simplified schemes will hopefully... 

The study of behavior of many-electron systems such as atoms, molecules, and solids under the action of time-dependent (TD) external fields, which includes interaction with radiation, has been an important area of research. In the linear response regime, where one considers the external held to cause a small perturbation to the initial ground state of the system, one can obtain many important physical quantities such as polarizabilities, dielectric functions, excitation energies, photoabsorption spectra, van der Waals coefficients, etc. In many situations, for example, in the case of interaction of many-electron systems with strong laser held, however, it is necessary to go beyond linear response for investigation of the properties. Since a full theoretical description based on accurate solution of TD Schrodinger equation is not yet within the reach of computational capabilities, new methods which can efficiently handle the TD many-electron correlations need to be explored, and time-dependent density functional theory (TDDFT) is one such valuable approach. 

Finally, can we dare to ask what is the future of first-principle MD It would be hard to be highly predictive. However we would like to quote the following directions of research QM/MM methods to treat quantum systems in an environment [92-94,225,226,269-272], Gaussian basis sets [23,30,38, 63,110,172] or Gaussian augmented plane waves methods [168] in search for order N methods [273,274] etc. Also, in order to go beyond Density Functional Theory, Quantum-Monte Carlo techniques are very attractive [119]. Some of these topics are already well-advanced and are discussed here in this book. 

Current approximations to density functional theory are not equally successful for all materials. While its formulation is general, there are some materials for which the EDA and GGA do not seem to be adequate. Examples include the transition metal oxides, and presumably transition metal bearing silicates as well. The problem is that the strongly localized Coulomb repulsion between d electrons does not seem to be adequately represented. As a consequence, FeO wustite is predicted to be a metal in LDA and GGA, whereas experimental observations find an insulator. Despite this failure, it is interesting to note that the structural and elastic properties of FeO are well reproduced by LDA (Isaak et al. 1993). In any case, the complete understanding of Mott insulators will require new advances in theory. These will need to go beyond such developments as the LDA+U method which has yielded considerable insight but adds the local Coulomb repulsion (U parameter) in an ad hoc manner (Mazin and Anisimov 1997). 

In ab initio methods the HER approximation is used for build-up of initial estimate for and which have to be further improved by methods of configurational interaction in the complete active space (CAS) [39], or by Mpller-Plesset perturbation theory (MPn) of order n, or by the coupled clusters [40,41] methods. In fact, any reasonable result within the ab initio QC requires at least minimal involvement of electron correlation. All the technical tricks invented to go beyond the HFR calculation scheme in terms of different forms of the trial wave function or various perturbative procedures represent in fact attempts to estimate somehow the second term of Eq. (5) - the cumulant % of the two-particle density matrix. 

Abstract In this chapter we review recent advances which have been achieved in the theoretical description and understanding of polyelectrolyte solutions. We will discuss an improved density functional approach to go beyond mean-field theory for the cell model and an integral equation approach to describe stiff and flexible polyelectrolytes in good solvents and compare some of the results to computer simulations. Then we review some recent theoretical and numerical advances in the theory of poor solvent polyelectrolytes. At the end we show how to describe annealed polyelectrolytes in the bulk and discuss their adsorption properties. 

Up to this point, all the analysis of nucleation presented has been based on the classical nucleation theory of Section II. To go beyond it, and indeed to begin to test its validity, a new approach is needed. In this section we summarize the results of a recent density functional approach to nucleation, and show that the results differ in quantitative detail but not in overall character from the predictions of the classical theory. 

Markovian pair conditional probability density with the basic concepts of the catastrophe theory, he succeeded in introducing new Markovian ELF classes which generalize the previous Becke-Edgecombe definition. Going beyond the actual interpretation of ELF as the error in electron locahzation, this new approach provides a quantum step-function indicating where the electrons are trapped rather than where they have peaks of spatial density. 

A number of attempts have been made to incorporate the effect of composition fluctuations [86-88] in theories involving neutral polymers. Here, we present systematic one-loop expansion to go beyond the saddle-point approximation described in the previous section. In order to carry out the loop expansion, it is advantageous to use Hubbard-Stratonovich transformation to get rid of redundant functional integrals over collective density variables (q in Eq. (6.85)) and use Eq. (6.81) as the starting point for the partition function with the explicitly known normalization constants except A,. Saddle-point approximation within this formalism now requires taking functional derivatives with respect to fields only. 

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