Dreizler RM, Gross EKU (1990) Density functional theory. An approach to the quantum many-body problem. Springer, Berlin Heidelberg New York 226 Danny Porath et al.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(2.25) ffl xc (n) and ffl xc (n ; n Gamma ) are well known and several parametrizations in terms of the electron density exist. In this work the parametrizations of Hedin and Lundquist [26] and von Barth and Hedin are used, 25] an extensive compilation of alternative forms can be found in Ref. [27]. Both LDA and LSDA are easily justifiable only in the limit of slowly varying densities. In contrast, they have been used successfully to describe many ground state properties even when the condition of slowly varying densities is not fullfilled. For magnetic systems the correct description of ....

....the correct description of the size of the magnetic moments in the ferromagnetic 3d transition metals Fe, Co, and Ni is one of the great successes of density functional theory and LDA LSDA. The desire to understand the success of LDA has generated a large body of literature and is reviewed in Ref. [27]. For the calculation of magnetocrystalline anisotropy the direction of magnetization is fixed by the direction of the exchange field, b(r) e ffiE xc ffim(r) 2.26) Two calculations with different magnetization directions, e 1 and e 2 , are performed and the MAE at zero temperature is ....

R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer, Berlin, 1990).

....more complicated and nonlinear problems and results in important physical e#ects [7, ch.4] the most prominent of which being the reduction of the bandgap to which we confine our analysis here. We include into our kp model a Hartree potential and, motivated by the Density Functional Formalism [8], an exchange correlation potential. As can be seen from the thin lines in Fig. 7 the quantum confined carriers exhibit di#erent localization behaviour in the Quantum Well, which is due to the di#erent band o#sets, Luttinger parameters and the presence of strain. In e#ect, an electrostatic ....

R. M. Dreizler and E. K. U. Gross. Density Functional Theory. Springer--Verlag, Berlin, 1990.

....Finally, we draw some conclusions. 2 Basics of Quantum Chemistry This section is to be seen as a short user s guide for an expert at control theory that would be curious of knowing more on the models of Quantum Chemistry. A more general and comprehensive introduction can be found for instance in [13, 18, 21, 27, 29, 35]. For the theoretical background coming from Quantum Mechanics, we refer to [20, 26] e.g. We only give here a brief overview of the stationary models, without getting into the details nor in the rigorous foundations. The time dependent models will be the topic of Section 4. Let us anticipate on ....

....of this exact problem have been developped and numerically simulated. Basically, the models of Quantum Chemistry that approximate (3) 4) range in two classes : the class of the Density Functional Theory (DFT) models, and that of the Hartree Fock (HF) type models. The idea of the DFT (see [13, 21, 27, 29]) is to replace problem (3) 4) by a problem set on the electronic density # = N # IR 3(N 1) # e 2 (x, x 2 , x N ) dx 2 dx N , 6) which has the advantage to be a function of only 3 variables instead of 3N.Next,one approximates the energy by a functional of this density # (whence ....

[Article contains additional citation context not shown here]

R.M. Dreizler and E.K.U. Gross, Density functional theory, SpringerVerlag, 1990.

....equation turns into Schrodinger s equation. The exchange correlation energy E xc can be decomposed further into exchange and correlation energy, E xc = E x E c , where E x is defined as the Kohn Sham exchange energy computed from the single particle density matrix of the exact Kohn Sham orbitals [21]. Obviously, E x = GammaE H , and therefore E c = 0. In Table 1.1, we show the numerical values for the various terms in (1.1) for the hydrogen atom. The energies have been calculated with the self consistent electron number densities n(r) Similar results have been published previously [21, ....

....[21] Obviously, E x = GammaE H , and therefore E c = 0. In Table 1.1, we show the numerical values for the various terms in (1.1) for the hydrogen atom. The energies have been calculated with the self consistent electron number densities n(r) Similar results have been published previously [21, 22], but not for self consistent densities. For comparison, we also show the exact analytic results in Table 1.1. The GGA PW91 functional not only gives a much better agreement for the total energy than LSDA, but also the individual terms are closer to the exact values. Further, the separation ....

[Article contains additional citation context not shown here]

R. Dreizler and E. Gross, Density Functional Theory (Springer-Verlag, Berlin, 1990).

....the nucleon fields, as in the Skyrme interaction. While there are no explicit pions in the Skyrme force, direct pion contributions largely average to zero for the bulk properties of nuclei and the e#ects of pion loops can be approximately absorbed into a general density functional for the energy [11,12]. Thus the nucleon terms should dominate the physics of closed shell nuclei. The signature of the underlying short range physics should be the size of the coe#cients of the e#ective lagrangian. However, it is not obvious that a Hartree Fock energy functional fit directly to finite nuclei should ....

R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer, Berlin, 1990)

....the limit of inhomogeneous system with slowly varying density is disscussed. There are however other representations for gradient corrections. In the limit of the inhomogeneous system with slowly varying density it is reasonable to assume that the energy density corresponding to the functional [115] G[ae] Z dr g(r; ae] B.20) may be represented in terms of a gradient expansion: g( ae] g 00 (ae(r) g 22 (ae(r) rae(r) 2 [g 42 (ae(r) 4ae(r) 2 g 43 (ae(r) 4ae(r) rae(r) 2 g 44 (ae(r) rae(r) 2 (rae(r) 2 ] B.21) where the zero term g 00 is the LDA ....

R. M. Dreizler E. K. U. Gross, Density Functional Theory, (Springer-Verlag, Berlin, 1990).

.... 5=3 Gamma Z R 3 ( X k2 1 jx Gamma kj )ae(x)dx 1 2 Z Z R 3 ThetaR 3 ae(x)ae(y) jx Gamma yj dxdy: 2) The TFW (and as well as the TF) model belongs to a large class of models that is today identified as the models arising in Density Functional Theory: we refer the reader to [14, 41] for an introduction to the general features and the physical foundations of such models. Mathematically, it is a well known fact that the problem (1) 2) has a unique minimizing density, denoted by ae (see E.H. Lieb [29] R. Benguria, H. Br ezis E.H. Lieb [5] or P. L. Lions [35] and that, ....

R.M. Dreizler & E.K.U. Gross, Density functional theory, SpringerVerlag, 1990.

....phonon frequencies at the Brillouin zone center can be estimated. The efficiency of the method is demonstrated for silicon test systems. 1 Introduction Ab initio computations of the total energy within the framework of density functional theory (DFT) and the local density approximation (LDA) [1] have been successful in predicting the structural properties of materials [3] At zero temperature and pressure, the structural parameters are determined by moving the constituting atoms to positions where the energy E is minimal. This can be done much more efficiently if the forces on the atoms ....

R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer Verlag, Berlin, 1990)

.... Alternatively, one can consider this expansion at the level of an energy functional or effective action [21] In such a formulation of the relativistic nuclear many body problem, the central object is an energy functional of scalar and vector densities (or more generally, vector four currents) [22 24]. Extremization of the functional gives rise to Dirac equations for occupied orbitals with local scalar and vector potentials, not only in the Hartree approximation, but in the general case as well. Rather than work solely with the densities, one can introduce auxiliary variables corresponding to ....

R. M. Dreizler and E. K. U. Gross, Density functional theory (Springer, Berlin, 1990).

No context found.

R. M. Dreizler and E. K. U. Gross, Density Functional Theory, (Springer, Berlin, 1990).

No context found.

Dreizler RM, Gross EKU (1990) Density functional theory. An approach to the quantum many-body problem. Springer, Berlin Heidelberg New York 226 Danny Porath et al.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC