Density Functional Theory motivation

To motivate the form of orbital-based g-density functional theory, it is useful to start with the familiar case of 1-density functional theory, where the orbital representation is well established [55]. 

All three areas will be addressed here. The application of classical density functional theory has led to some of the most important recent theoretical advances in SFE and these have been the subject of several authoritative review articles [10-16]. On the other hand, we know of no recent comprehensive review addressing theoretical approaches other than density functional theories (DFT) and the other two subject areas, particularly the last one, and it was this that motivated us to write this chapter. We hope that the somewhat broader coverage of molecular modeling research in SFE given in this chapter will be of benefit to researchers new to the field. We should mention that this Chapter is written from a perspective that is more strongly influenced by liquid-state statistical mechanics than by solid-state theory. The interests of the authors in the problem at hand are an outgrowth of their previous work on phase equilibrium in fluids and fluid mixtures. 

Abstract This chapter discusses descriptions of core-ionized and core-excited states by density functional theory (DFT) and by time-dependent density functional theory (TDDFT). The core orbitals are analyzed by evaluating core-excitation energies computed by DFT and TDDFT their orbital energies are found to contain significantly larger self-interaction errors in comparison with those of valence orbitals. The analysis justifies the inclusion of Hartree-Fock exchange (HFx), capable of reducing self-interactions, and motivates construction of hybrid functional with appropriate HFx portions for core and valence orbitals. The determination of the HFx portions based on a first-principle approach is also explored and numerically assessed. 

Computations in the gas-phase Theoretical modeling is typically performed by organometallic chemists using the framework of pervasive density functional theory (DFT). The vast majority of these quantum chemical calculations are traditionally performed in the gas-phase (vacuum) and quite frequently by using simplified molecular models. The most typical motivation for this is "to reduce computational time."... 

This chapter is devoted to orbital-dependent exchange-correlation (xc) functionals, a concept that has attracted more and more attention during the last ten years. After a few preliminary remarks, which clarify the scope of this review and introduce the basic notation, some motivation will be given why such implicit density functionals are of definite interest, in spite of the fact that one has to cope with additional complications (compared to the standard xc-functionals). The basic idea of orbital-dependent xc-functionals is then illustrated by the simplest and, at the same time, most important functional of this type, the exact exchange of density functional theory (DFT for a review see e.g. [1], or the chapter by J. Perdew and S. Kurth in this volume). 

Kohn and Sham later proved that Slater s intuitively motivated suggestion can be justified theoretically and procedures which combine the orbital-based Hartree kinetic functional with density-based exchange-correlation functionals are now called Kohn-Sham density functional theories. They are shown as family 3 in Figure 1. 

The forcefields discussed in Section 2.1 use energy functions which do not take into account quantum effects. Many important processes are intrinsically quantum mechanical, and thus cannot be modelled classically. SA has been used in con-juction with density functional theory, the Schrodinger equation, chemical reaction dynamics, electronic structure studies, and to optimize linear and nonlinear parameters in trial wave functions. This is important because quantum effects are often embedded in an essentially classical system. This has motivated mixing the classical fields with the quantum potentials in simulations known as quantum mechanic/molecular mechanic hybrids. Including quantum effects is important in the study of enzyme reactions, and proton and electron transport studies. 

Density functional theory (DPT) offers the opportunity to calculate the energies of nuclear configurations of polyatomic systems with an increasing efficiency. Direct dynamics , where the energies of the nuclear configurations are calculated as they are reached by a trajectory, promise to bypass the need for a PES in rate calculations. However, chemists need more general and structure-motivated methods to interpret and predict reactivity. Semi-anpirical methods may play a significant role in this respect, because they offer a simple, accurate and structure-related approach to chemical reactivity. 

The interesting properties of the hypergolic ILs have motivated a theoretical studies based on Density Functional Theory (Gao et al, 2007, b. Zhang et al., 2010). Heats of formation coupled with densities can be used further for predicting the detonation pressures and velocities and specific impulses of energetic salts for the rational design of hypergolic ILs. 

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