DFT approach

For a recent critical evaluation of situations where current DFT approaches experience difficulties, see Davidson E R 1998 How robust is present-day DFT ... 

The siipercell plane wave DFT approach is periodic in tliree dimensions, which has some disadvantages (i) thick vacuum layers are required so the slab does not interact with its images, (ii) for a tractably sized unit cell, only high adsorbate coverages are modelled readily and (iii) one is limited in accuracy by the fonn of the... 

Density functional theory-based methods ultimately derive from quantum mechanics research from the 1920 s, especially the Thomas-Fermi-Dirac model, and from Slater s fundamental work in quantum chemistry in the 1950 s. The DFT approach is based upon a strategy of modeling electron correlation via general functionals of the electron density. 

It has been shown that ab initio total energy DFT approach is a suitable tool for studies of phase equilibria at low temperatures and high pressures even when small energy differences of the order of 0.01 eV/mol are involved. The constant pressure optimization algorithm that has been developed here allows for the calculation of the equation of state for complex structures and for the study of precursor effects related to phase transitions. 

Peter Gill has recently given a more accurate as well as more witty account of what he regards as the demise of the DFT approach (Gill, 2001). 

In summary, the combined experimental (NIS, IR- and Raman-spectroscopy) and computational (DFT) approach has enabled the identification of the vibrational modes that contribute most to the entropic driving force for SCO transition. 

Glaesemann, K. R., Gordon, M. S., 1998, Investigation of a Grid-Free Density Functional Theory (DFT) Approach , J. Chem. Phys., 108, 9959. 

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... 

In conclusion, the DFT approach, even in a two-component scheme, is generally not applicable to treat lanthanides. 

There have been extensive computer simulations and liquid state theories, and a good understanding of these systems is now available. The majority of work has focused on simple hard-chain systems, and the depletion and enhancement effects in these systems are well understood and there are several theories that are in quantitative agreement with computer simulations. In contrast, there has been relatively little attention focused on the effect of wall-fluid and fluid-fluid attractions on the behavior of confined polymers. Only the simplest of DFT approaches has been attempted, and the results are promising although the quantitative performance leaves a lot to be desired. 

In the following text we present a very short synopsis both of the DFT approach and the ab initio molecular dynamics (AIMD) method that can by no means be considered as an introduction to the use of the computational tools based on them. The interested reader will find exhaustive treatment of these arguments elsewhere in this book (Chapter 1). 

Kohn and Sham provided a further contribution to make the DFT approach useful for practical calculations, by introducing the concept of fictitious non-interacting electrons with the same density as the true interacting electrons [8]. Non-interacting electrons are described by orthonormal single-particle wavefunctions y/i (r) and their density is given by ... 

The term Exc[p] is called the exchange-correlation energy functional and represents the main problem in the DFT approach. The exact form of the functional is unknown, and one must resort to approximations. The local density approximation (LDA), the first to be introduced, assumed that the exchange and correlation energy of an electron at a point r depends on the density at that point, instead of the density at all points in space. The LDA was not well accepted by the chemistry community, mainly because of the difficulty in correctly describing the chemical bond. Other approaches to Exc[p] were then proposed and enable satisfactory prediction of a variety of observables [9]. 

Note that, in the limit that the time dependence is turned off, the TD-DFT approach correctly reduces to the usual time-independent DFT one, as VS vanishes, Equations 8.17, 8.22, and 8.23 are identically satisfied, and Equation 8.15 will reduce to the time-independent kinetic energy of an /V-electron system. 

In Section 8.4.2, we considered the problem of the reduced dynamics from a standard DFT approach, i.e., in terms of single-particle wave functions from which the (single-particle) probability density is obtained. However, one could also use an alternative description which arises from the field of decoherence. Here, in order to extract useful information about the system of interest, one usually computes its associated reduced density matrix by tracing the total density matrix p, (the subscript t here indicates time-dependence), over the environment degrees of freedom. In the configuration representation and for an environment constituted by N particles, the system reduced density matrix is obtained after integrating pt = T) (( over the 3N environment degrees of freedom, rk Nk, ... 

The paper of Parr and Bartolotti is prescient in many ways [1], It defines the shape function and describes its meaning. It notes the previously stated link to Levy s constrained search. It establishes the importance of the shape function in resolving ambiguous functional derivatives in the DFT approach to chemical reactivity—the subdiscipline of DFT that Parr has recently begun to call chemical DFT [6-9]. Indeed, until the recent resurgence of interest in the shape function, the Parr-Bartolotti paper was usually cited because of its elegant and incisive analysis of the electronic chemical potential [10],... 

Details on the numerical evaluation of the descriptors will be given in the individual cases but in most cases a computational DFT approach is used, with a hybrid functional of the B3LYP type [32]. Condensation of f(r) or sir) is done with conventional population analysis techniques (Mulliken [33], Natural Population Analysis (NPA) [34]) or with the Hirshfeld technique [35], often used by our group [36]. 

The activity of CMe2-bridged Zr(II) and Hf(II) boratabenzene cationic complexes toward ethylene trimerization has been explored computationally using a gradient-corrected DFT approach the Zr species was calculated to be a highly efficient catalyst, exceeding the efficiency of the corresponding Cp system.108... 

Semiempirical parameterizations require reliable experimental or theoretical reference data and are impeded by the lack, of such data. Such problems do not occur in ab initio or DFT approaches. 

The DFT approach, on the other hand, focuses on the density, which is... 

In the near future, quantum chemistry will inevitably forge a union between the WT and DFT approaches, as these are two different approaches to the same problem and this union will, hopefully, offer the best of both worlds. In the following, I will attempt to point the way that this will possibly be accomplished. However, to do so, we need to pay more attention to some of the pertinent mathematical structure of the theories. 

The DFT approach (for an excellent introduction, see Parr and Yang 1989) is different and somewhat simpler. The electron density p(r) has been recognized to be a feature that uniquely determines all properties of the electronic ground state (1st Hohenberg-Kohn theorem). Instead of minimizing E with respect to coefficients of the wave function as in HF, E is minimized with respect to the electron density p... 

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