Beyond LSDA

Plutonium has physical properties which cannot be accounted for within the local density-functional approximations. It undergoes a very large lattice expansion (a - 5) at 600 K, but the L(S)DA cannot predict this. The reason is that this scheme cannot describe correlations sufficiently accurately. The / states are itinerant in the light actinides but localized in the 

The orbital polarization scheme has been applied to several systems (see references above) where it improved the agreement between theory and experiment. A recent application to americium was reported by Soderlind et al.,[110] who examined structural changes of Am under pressure. The results were consistent with a high-pressure phase with delocalized 5/ electrons and a low-pressure phase with localized and non-bonding 5/ states, a Mott transition. 

A different approach to treat correlation effects which are not well described within the LSDA consists in incorporating self-interaction corrections (SIC) [111-114] in electron structure methods for solids, Svane et al. [115-120]. In the Hartree-Fock (HF) theory the electron-electron interactions are usually divided into two contributions, the Coulomb term and the exchange term although they both are Coulomb interactions. The separation though, is convenient because simplifications of self-consistent-field calculations can be obtained by including in both terms the interaction of the electron itself. In the HF theory this has no influence on the solutions because these selfinteractions in the Coulomb and exchange terms exactly cancel each other. However, when the exchange term is treated 

Here a labels the orbitals, and the sum in eq. (66) runs over the occupied states. U[na] is the Haxtree term for a single state or and 4.] 

The SIC-LSDA treats localized and delocalized states on equal footing, and by comparing total energies corresponding to different distributions of electrons in a shell on localized resp. delocalized states the energetically most favorable configuration can be selected.[119] 

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Despite the fact that p in a molecule is not a slowly varying function of position, the LSDA works surprisingly well for calculating molecular equilibrium geometries, vibrational frequencies, and dipole moments, even for transition-metal compounds, where Hartree-Fock calculations often give poor results. (For detailed results, see Chapter 17.) However, calculated LSDA molecular atomization energies are very inaccurate. Accurate dissociation energies require functionals that go beyond LSDA. 

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]. 

Our calculations go beyond all the earlier work because SIC-LSDA treats all the f-states on equal footing and the KKR-CPA allows for a consistent description of spin and valence disorder. Johansson et al. (1995) used a binary pseudo-alloy concept, but needed one adjustable parameter to put on a common energy scale both the y-phase, described by LSDA with one f-state included into the core, and the a-phase, described by the standard LSD approximation, with all the f-states treated as valence bands. Svane (1996) performed SIC-LSD calculations using a supercell geometry which limited him to the study of a few concentrations only. 

The LDA and LSDA are based on the uniform-electron-gas model, which is appropriate for a system where p varies slowly with position. The integrand in the expression (16.52) for is a function of only p, and the integrand in is a function of only p and p. Functionals that go beyond the LSDA aim to correct the LSDA for the variation of electron density with position. A common way to do this is by including the gradients [Eq. (5.30)] of p and p in the integrand. Thus... 

The first DFT calculations on GC and AT base pairs recently appeared. Calculations were carried out within the LSDA using the VWN parameterization. Calculations beyond the LSDA were also performed using Becke s gradient-corrected exchange functionaP and Perdew s gradient-corrected correlation functional. The results from these calculations are listed in Tables 6 and 7, along with those from HF and MP2 calculations. ... 

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