Local spin density approximation method

LORG (localized orbital-local origin) technique for removing dependence on the coordinate system when computing NMR chemical shifts LSDA (local spin-density approximation) approximation used in more approximate DFT methods for open-shell systems LSER (linear solvent energy relationships) method for computing solvation energy... 

We have used the multisublattice generalization of the coherent potential approximation (CPA) in conjunction with the Linear-MufRn-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed for the local spin density approximation (LSDA) the Vosko-Wilk-Nusair parameterization". 

The muffin-tin potential around each atom in the unit cell has been calculated in the framework of the Local-Spin-Density-Approximation using the ASW method. The ASW method uses the atomic sphere approximation (ASA), i.e. for each atom a sphere radius is chosen such that the sum of the volumes of all the overlapping spheres equals the unit cell volume. The calculation yields the expected ferromagnetic coupling between Cr and Ni. From the self-consistent spin polarized DOS, partial and total magnetic moment per formula unit can be computed. The calculated total magnetic moment is 5.2 pg in agreement with the experimental value (5.3 0.1 e calculations presented here have been performed... 

Table4.4 Spectroscopic properties for Au2 q= -1,0, + 1) using ab-initio (Hartree Fock, HF, second-order Moller-Plesset, MP2, and coupled cluster, CCSD(T)) and DFT (local spin-density approximation, LSDA, Perdew-Wang CCA, PW91, and Becke three-parameter Lee-Yang-Parr functional, B3LYP) methods at the RPPA level of theory.

Table 8 summarizes the results of the calculations of the C2h symmetric chair and the C2v symmetric boat transition structures [83]. The local spin density approximation predicts a tight transition structure, comparable to the one obtained by the MP2(fc)/6-31G method, but fails to reproduce the experimental activation energies [84], The use of the gradient-corrected BLYP functional yields loose, aromatic-type transition structures and improved activation energies for the chair transition structures. The activation energy for the boat transition structure is, however, too low by 9-10 kcal/mol as compared to the experimental value of 44.7 kcal/mol [85]. The activation energies for the chair and the boat transition structures obtained by the Becke 3LYP method are in... 

This can be extended to the local spin density approximation (LSDA) for those cases where the a and p densities are not equal. Slater s X method is a scaled form of Eq. (1.52), and often the terms LSDA and Slater are used interchangeably. 

The cornerstone of the field (the "Hartree-Fock" of Density Functional Theory) is the Local Density Approximation (LDA) also called the Local (Spin) Density (LSD) method Here the basic information on electron correlation, how electrons avoid each other, is taken from the uniform density electron gas Essentially exact calculations exist for this system (the Quantum Monte Carlo work of Ceperley and Alder) and this information from the homogeneous model is folded into the inhomogeneous case through the energy integral ... 

The earliest class of DFT methods is known as local (electron) density approximation (LDA) methods in the case that the total electron density is decomposed into individual spin densities for +1 /2 and -1/2 spin we refer to these methods as local spin density approximation (LSDA) methods. In these methods the total molecular XC energy is evaluated by integration on a numerical grid of the electron density, and the energy is a function of only the specific value of the density at each point, hence the local density ... 

Density Functional theory [4] (DFT) has been widely recognized as a powerful alternative computational method to traditional ab initio schemes, particularly in studies of transition metal complexes where large size of basis set and an explicit treatment of electron correlation are required. The local spin density approximation [5] (LDA) is the most frequently applied approach within the families of approximate DFT schemes. It has been used extensively in studies on solids and molecules. Most properties obtained by the LDA scheme are in better agreement with experiments [4a] than data estimated by ab initio calculations at the Hartree-Fock level. However, bond energies are usually overestimated by LDA. Thus, gradient or nonlocal corrections [6] have been introduced to rectify the shortcomings in the LDA. The non-... 

The LDA and the Local Spin Density approximation (LSD), when spin is considered, have been successful in determining molecular structure and many one-electron properties or expectation values. It is very well known now that the LDA and LSD underbind core electrons and overbind atoms in a molecule. Energies are not as good as those obtained by correlated ab initio methods, although the relative energies of isomers and activation barriers which do not involve bond-breaking can be quite accurate. It was observed,... 

Better results than with the LDA are obtained by an elaboration of the LDA in which electrons of a and spin in the uniform electron gas are assigned different spatial KS orbitals and from which different electron density functions and follow. This unrestricted LDA method (cf. UHF, section 5.2.3.6e) is called the local spin density approximation, LSDA, and has the advantages that it can handle systems with one or more unpaired electrons, like radicals, and systems in which electrons are becoming unpaired, such as molecules far from their equilibrium geometries even for ordinary molecules it appears to be more forgiving toward the use of (necessarily) inexact xcfunctionals [37], For species in which all the electrons are securely paired, the LSDA is equivalent to the LDA. Like and its functional derivative... 

As was discussed, infrared and raman spectra for organometallic systems can typically be computed to within 5% of the experiment. Unlike adsorption energy predictions, structure and vibrational frequencies are fairly insensitive to differences in the DFT methods (local vs. nonlocal spin density). Even some of the earliest reported local-spin-density approximation (LDA) DFT calculations which ignored adsorbate and surface relaxation predicted frequencies to within 10 percent of the measured values. For example, Ushio et al. have shown that LDA calculations for formate on small Nia clusters (frozen at its bulk atomic positions) provide very good agreement with experimental HREELS studies on Ni(lll) [72]. Unlike adsorption energy predictions, structure and vibrational frequencies are fairly insensitive to gradient-corrections. 

We have recently succeeded in calculating the d< fect energies in metals, such as I-I (I=iinpiirily), P-1 (P=probe), V-I (V=vacancy) in.fraction energies(IE s). The calculations apply the Korringa-Kohn-Rostoker (KKR) Gieen s function method for impurities and are based on the local-spin-density approximation (LSDA) for density-functional (heory. The nice agreement of calculated results foi P-I IE s with available accurate measured values seems to demonstrate the accuracy of our calculations. It was also shown that the Monte Carlo simulations based on the calculated I-I IE s reproduce very well the measured values of temperature-concentration dependence for the solid solubility limit of impurities in metals. 

The different densities for different spins" case (analogous to DODS in HF theory) for which the two spatial densities must be retained and used separately. This method will generate the closed-shell case if the system is, indeed, actually spin-paired. This is often called the Local Spin Density Approximation (LSD) for obvious reasons. 

As most of the electronic structure simulation methods, we start with the Born-Oppenheimer approximation to decouple the ionic and electronic degrees of freedom. The ions are treated classically, while the electrons are described by quantum mechanics. The electronic wavefunctions are solved in the instantaneous potential created by the ions, and are assumed to evolve adiabatically during the ionic dynamics, so as to remain on the Born-Oppenheimer surface. Beyond this, the most basic approximations of the method concern the treatment of exchange and correlation (XC) and the use of pseudopotentials. XC is treated within Kohn-Sham DFT [3]. Both the local (spin) density approximation (LDA/LSDA) [16] and the generalized gradients approximation (GGA) [17] are implemented. The pseudopotentials are standard norm-conserving [18, 19], treated in the fully non-local form proposed by Kleinman and Bylander [20]. 

At the same time, the LDA gave an a posteriori justification of the old Xa method by Slater, because the latter is a special LDA variant without correlation. The corresponding spin-dependent version of the LDA is called a local spin-density approximation (LSDA or LSD or just spin-polarized LDA), and even now when people talk of LDA functionals, they always refer to its generalized form for systems with (potentially) unpaired spins. Among the most influential LDA parametrizations, the one of von Barth and Hedin (BH) [154] and the one of Vosko, Wilk and Nusair (VWN) [155] are certainly worth mentioning. The latter is based on the very accurate Monte Carlo-type calculations of Ceperley and Alder [156] for the uniform electron gas, as indicated above. 

A common feature of all pseudopotential methods is that the parameters depend on the employed method, i.e. the potential derived for e.g. the Local Spin Density Approximation (LSDA) functional (Section 6.5.1) is different from that derived from a generalized gradient functional such as Perdew-Burke-Ernzerhof (PBE) (Section 6.5.2). In practice, the difference is relatively small and pseudopotentials optimized for one functional are often used for other functionals without re-optimization. 

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