The Density Functional Theory DFT

The pseudopotential density-functional technique is used to calculate total energies, forces on atoms and stress tensors as described in Ref. 13 and implemented in the computer code CASTEP. CASTEP uses a plane-wave basis set to expand wave-functions and a preconditioned conjugate gradient scheme to solve the density-functional theory (DFT) equations iteratively. Brillouin zone integration is carried out via the special points scheme by Monkhorst and Pack. The nonlocal pseudopotentials in Kleynman-Bylander form were optimized in order to achieve the best convergence with respect to the basis set size. 5... 

Quantum-chemical calculations which utilize the density functional theory (DFT) are now perhaps amongst the most frequently performed because of their relatively low cost and high accuracy. Structural results obtained from DFT based methods are often as good as those derived from MP2 calculations. It is well documented that DFT methods, especially those involving hybrid functionals such as B3LYP, B3P86 and B3PW91, yield reliable... 

A group of investigators recently suggested that the density-functional theory (DFT), which calculates IR and Raman spectra, is a useful tool for direct characterization of the structures of diamondoids with increasing complexity [66]. They applied DFT to calculate Raman spectra whose frequencies and relative intensities were shown to be in excellent agreement with the experimental Raman spectra for C26H30, thus providing direct vibrational proof of its existence. 

Currently, the density functional theory (DFT) method has become the method of choice for the study of reaction mechanism with transition-metals involved. Gradient corrected DFT methods are of particular value for the computational modeling of catalytic cycles. They have been demonstrated in numerous applications for several elementary processes, to be able to provide quantitative information of high accuracy concerning structural and energetic properties of the involved key species and also to be capable of treating large model systems.30... 

It is seen from this comparison that the geometrical parameters obtained by the IPM and by the density functional theory (DFT) methods are close. It is enough to multiply re by 1.44 to obtain the same C H O distance for the TS calculated by the DFT method. The following parametric equations were proposed for the estimation of the C—H, O—H, and C—O distances in the reaction center of TS for reactions ROO + RH in the IPM method [34,35],... 

An alternative approach to conventional methods is the density functional theory (DFT). This theory is based on the fact that the ground state energy of a system can be expressed as a functional of the electron density of that system. This theory can be applied to chemical systems through the Kohn-Sham approximation, which is based, as the Hartree-Fock approximation, on an independent electron model. However, the electron correlation is included as a functional of the density. The exact form of this functional is not known, so that several functionals have been developed. 

In addition to conventional ab initio methods, techniques based on the density functional theory (DFT) have also been used to study the Diels-Alder reaction between butadiene and ethylene97-99. With these kinds of methods, a concerted mechanism through a symmetric transition state is also predicted. Several kinds of density functionals have been used. The simplest one is based on the Local Density Approach (LDA), in which all the potentials depend only on the density. More sophisticated functionals include a dependence on the gradient of the density, such as that of Becke, Lee, Yang and Parr (BLYP). 

The three main approaches based on the single-particle density are the density functional theory (DFT), quantum fluid dynamics (QFD), and studying the properties of a system through local quantities in 3D space. In this chapter, we present simple discussions on certain conceptual and methodological aspects of the single-particle density for details, the reader may consult the references listed at the end of this chapter. 

The density functional theory (DFT) [32] represents the major alternative to methods based on the Hartree-Fock formalism. In DFT, the focus is not in the wavefunction, but in the electron density. The total energy of an n-electron system can in all generality be expressed as a summation of four terms (equation 4). The first three terms, making reference to the noninteracting kinetic energy, the electron-nucleus Coulomb attraction and the electron-electron Coulomb repulsion, can be computed in a straightforward way. The practical problem of this method is the calculation of the fourth term Exc, the exchange-correlation term, for which the exact expression is not known. 

Fig. 5 A proposed mechanism for enhanced emission (or AIEE) in solid-state organic dye nanoparticles. The dye considered here is trans-biphenylethylene (CN-MBE) compound. The geometry is optimized by the density functional theory (DFT) calculation at the B3LYP/6-31G level. Molecular distortion such as twisting and/or subsequent planarization causes prevention of radiationless processes along with specific aggregation such as the /-aggregate in the nanoparticles...

Because of these difficulties, great interest arose in the last decade in methods free of such limitations, based on the density functional theory (DFT). The DFT equations contain terms that evaluate—already at the SCF level—a significant amount (ca. 70%) of the correlation energy. On the other hand, very accurate DFT methods require calculation of much fewer integrals (n ) than ab initio, which is why they have been widely used in theoretical studies of large systems. The DFT [2] is based upon Hohenberg-Kohn (HK) theorems, which legitimize the use of electron density as a basis variable [22]. 

The oxime-induced reactivation of organophosphorus-inhibited AChE has been modeled recently through the Density Functional Theory (DFT) approach. Two possible computed reactivation pathways of Sarin-inhibited AChE adduct by formoximate anion are shown in Scheme The two-step mechanism (Scheme 7B) is favored by the authors. 

Vibrational frequencies of 1,4-benzodioxin using the density functional theory (DFT) method, as well as the conventional HF and MM3 force-field methods, were calculated to evaluate the frequency prediction capability of each computational method and get a better understanding of the vibrational spectra . 

In this paper we present preliminary results of an ab-initio study of quantum diffusion in the crystalline a-AlMnSi phase. The number of atoms in the unit cell (138) is sufficiently small to permit computation with the ab-initio Linearized Muffin Tin Orbitals (LMTO) method and provides us a good starting model. Within the Density Functional Theory (DFT) [15,16], this approach has still limitations due to the Local Density Approximation (LDA) for the exchange-correlation potential treatment of electron correlations and due to the approximation in the solution of the Schrodinger equation as explained in next section. However, we believe that this starting point is much better than simplified parametrized tight-binding like s-band models. 

The choice of the exchange correlation functional in the density functional theory (DFT) calculations is not very important, so long as a reasonable double-zeta basis set is used. In general, the parameterized model will not fit the quantum mechanical calculations well enough for improved DFT calculations to actually produce better-fitted parameters. In other words, the differences between the different DFT functionals will usually be small relative to the errors inherent in the potential model. A robust way to fit parameters is to use the downhill simplex method in the parameter space. Having available an initial set of parameters, taken from an analogous ion, facilities the fitting processes. 

The paper is organized as follows. A complete description of the theoretical methods used is given in Section 2 considering, in the different subsections, the Density Functional Theory (DFT) (Section 2.1), the A self-consistent (A-SCF) approach (Section 2.1.1), and the Many-Body perturbation theory (Section 2.2) through the GW (Section 2.2.1) and the Bethe-Salpeter (Section 2.2.2) methods. 

The above experimental developments represent powerful tools for the exploration of molecular structure and dynamics complementary to other techniques. However, as is often the case for spectroscopic techniques, only interactions with effective and reliable computational models allow interpretation in structural and dynamical terms. The tools needed by EPR spectroscopists are from the world of quantum mechanics (QM), as far as the parameters of the spin Hamiltonian are concerned, and from the world of molecular dynamics (MD) and statistical thermodynamics for the simulation of spectral line shapes. The introduction of methods rooted into the Density Functional Theory (DFT) represents a turning point for the calculations of spin-dependent properties [7],... 

The density functional theory (DFT) [7,8] is now widely used in studying both infinite bulk crystalline materials and finite atoms, molecules, and clusters. In principle, the ground-state total energy as well as the electron density itself in interacting many-electron systems is accurately described in DFT. Therefore, the geometry optimization by minimizing the total energy should also be accurate in DFT as well. The electronic band structure is, on the other hand, a very useful but approximate physical concept based on the quasiparticle theory for inter-... 

Another approach closely related to the ab initio methods that has gained increasing prominence in recent years is the density functional theory (DFT). This method bypasses the determination of the wavefunction electronic probability density p directly and then calculates the energy of the system from p. 

The HSAB principle can be considered as a condensed statement of a very large amount of experimental information, but cannot be labelled a law, since a quantitative definition of the intuitive concepts of chemical hardness (T ) and softness (S) was lacking. This problem was solved when the hardness found an exact, and also an operational, definition in the framework of the Density Functional Theory (DFT) by Parr and co-workers [2], In this context, the hardness is defined as the second order derivative of energy with respect to the number of electrons and has the meaning of resistance to change in the number of electrons. The softness is the inverse of the hardness [3]. Moreover, these quantities are defined in their local version [4, 5] as response functions [6] and have found a wide application in the chemical reactivity theory [7],... 

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