Density approximations for exchange and

Theoretical calculations were performed with the linear muffin tin orbital (LMTO) method and the local density approximation for exchange and correlation. This method was used in combination with supercell models containing up to 16 atoms to calculate the DOS. The LMTO calculations are run self consistently and the DOS obtained are combined with the matrix elements for the transitions from initial to final states as described in detail elsewhere (Botton et al., 1996a) according to the method described by Vvedensky (1992). A comparison is also made between spectra calculated for some of the B2 compounds using the Korringa-Kohn-Rostoker (KKR) method. 

We have performed ground state total-energy calculations using the pseudopotential plane-wave method based on density-functional theory in the local density approximation for exchange and correlationThe Vanderbilt ultrasoft pseudopotentials were used ... 

Fig. 1 Asymptotic structure coefficients as(j8), c ks,xG ) crw03), a CS), and aKS gOS) as fimction of barrier height parameter )S =VW/eF, where W is the barrier height and eF the Fermi energy. Corresponding values of the Wigner-Seitz radius rs for jellium and structureless-pseudopotential models over the metallic range of densities are also given. The relationship between rs and ff is via self-consistent calculations in the local density approximation for exchange-correlation.

Fig.1.4. Self-consistent energy-band structure for bcc tungsten obtained by the LMTO method within the atomic-sphere approximation (ASA) using local-density theory for exchange and correlation. Relativistic effects are included except spin-orbit coupling which is neglected...

The electron diffraction study was complemented by an all-electron theoretical calculation of Lu, Wei, and Zunger (LWZ) (1992), using the local density approximation for the exchange and correlation terms in the Hamiltonian. They find agreement within x0.6% between the calculated and dynamic structure factor values for the lowest three reflections, (100), (110), and (111). But for (200), with sin 0/A = 0.3464 A-1, the discrepancy is as large as 1.7%. The discrepancy is attributed to insufficiently accurate knowledge of the temperature factors in this diatomic crystal, which affect the derivation of the X-ray structure factor from the electron diffraction measurement, as well as the calculation of the dynamic theoretical structure factors needed for the comparison with experiment. For the monoatomic Si crystal for which the B values are well known, the agreement is... 

The time-dependent density functional theory [38] for electronic systems is usually implemented at adiabatic local density approximation (ALDA) when density and single-particle potential are supposed to vary slowly both in time and space. Last years, the current-dependent Kohn-Sham functionals with a current density as a basic variable were introduced to treat the collective motion beyond ALDA (see e.g. [13]). These functionals are robust for a time-dependent linear response problem where the ordinary density functionals become strongly nonlocal. The theory is reformulated in terms of a vector potential for exchange and correlations, depending on the induced current density. So, T-odd variables appear in electronic functionals as well. 

J. P. Perdew, in Electronic Structure of Solids 91, P. Ziesche and H. Eschrig, Eds., Akademie Verlag, Berlin, 1991. Unified Theory for Exchange and Correlation. Beyond the Local Density Approximation. 

However, in the second set of data, reporting scans of the PES for a limited set of small molecules, it appears that the geometries obtained are satisfactory. Moreover, the nature of the technique used for the determination of Exc, namely the use of a "senior" Exe functional, or the use of the virial theorem, as well as the use of a line integration (not reported here), leads to quite similar geometries. This point is in accord with a similar conclusion obtained by van Gisbergen et ol. in their frequency-dependent polarizabilities [75] they choose to use a "mixed scheme" where a different approximation for fxc and Vxc were used, whereas fxc is the functional derivative of the exchange-correlation potential Vxc, with respect to the time-dependent density. 

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