LDA

In a number of classic papers Hohenberg, Kohn and Sham established a theoretical framework for justifying the replacement of die many-body wavefiinction by one-electron orbitals [15, 20, 21]. In particular, they proposed that die charge density plays a central role in describing the electronic stnicture of matter. A key aspect of their work was the local density approximation (LDA). Within this approximation, one can express the exchange energy as... 

This expression is an example of how is given as a local density functional approximation (LDA). The tenn local means that the energy is given as a fiinctional (i.e. a fiinction of p) which depends only on p(r) at the points in space, but not on p r) at more than one point in space. 

More advanced teclmiques take into account quasiparticle corrections to the DFT-LDA eigenvalues. Quasiparticles are a way of conceptualizing the elementary excitations in electronic systems. They can be detennined in band stmcture calculations that properly include the effects of exchange and correlation. In the... 

LDA, these effects are modelled by the exchange-correlation potential In order to more accurately... 

The pseudopotential is derived from an all-electron SIC-LDA atomic potential. The relaxation correction takes into account the relaxation of the electronic system upon the excitation of an electron [44]- The authors speculate that ... the ability of the SIRC potential to produce considerably better band structures than DFT-LDA may reflect an extra nonlocality in the SIRC pseudopotential, related to the nonlocality or orbital dependence in the SIC all-electron potential. In addition, it may mimic some of the energy and the non-local space dependence of the self-energy operator occurring in the GW approximation of the electronic many body problem [45]. 

Perhaps the most sophisticated embeddmg scheme for describmg metal surfaces to date is the LDA-based... 

Anisimov V I, Aryasetiawan F and Liechtenstein A I 1997 First-principles calculations of the electronic structure and spectra of strongly correlated systems The LDA+U method J. Phys. Condens Matters 767... 

Shiok A B, Lieohtenstein A i and Piokett W E 1999 impiementation of the LDA+U method using the fuii-potentiai iinearized augmented piane-wave basis Phys. Rev. B 60 10 763... 

The local density approximation (LDA) is the oldest and simplest of the functional types stiU in use. It is based on the idea of a imiform electron gas, a homogeneous... 

Ester Enolates- Esters are susceptible to substitution by the base, even LDA can be problematic. Use very hindered non-nucleophillic base (Li isopropylcyclohexyl amide)... 

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