GW correlation effects on plutonium quasiparticle energies: changes in crystal-field splitting Page: 4 of 10
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VH(r) _ dr2 (r . (5)
r -r'
The single-particle density n(r) is calculated as n(r) ~i f_ t dwG (r, r, w)e2"w In
addition to this mapping of G --> G, one can also generate an excellent effective
potential from G that makes it possible to approximately do the inverse mapping
of G -> G [3]. The QSGW is a method to specify this (nearly) optimal mapping
of G -> G , so that G -> G -> G0 --> ... can be iterated to self-consistency
[3, 5]. At self-consistency the quasiparticle energies of G coincide with those of
G. Thus QSGW is a self-consistent perturbation theory, where the self-consistency
condition is constructed to minimize the size of the perturbation. The QSGW
method is parameter-free, and independent of basis set as well as the LDA starting
point [2, 3, 5]. We have previously shown that QSGW reliably describes a wide
range of spd [3, 4, 6, 7, 10], and rare-earth [9] systems. We have also applied the
method to calculate the electronic structure of a-uranium [8].
Our version of the QSGW method is based upon the Full Potential Linear Muffin
Tin Orbital (FP-LMTO) method [11], which makes no approximation for the shape
of the crystal potential. The smoothed LMTO basis [3] includes orbitals with l <
Imax = 6; both 7p and 6p as well as both 5f and 6f are included in the basis. The
6f orbitals are added as a local orbital [3], which is confined to the augmentation
sphere and has no envelope function. The 7p orbital is added as a kind of extended
'local orbital,' the 'head' of which is evaluated at an energy far above Fermi level
[3] and instead of making the orbital vanish at the augmentation radius a smooth
Hankel 'tail' is attached to the orbital. For our calculations we use the fcc Pu
lattice with the following lattice constants a=4.11 A (which corresponds to 90%
of the a-Pu equillibriurm volume), 4.26 A (at the a-Pu equilibrium volume), 4.64
A (at the b-Pu equilibrium volume) and 4.79 A (at 110% of the 8-Pu equilibrium
volume).
3. Results
8 8
(a) (b) 40 (c)
4 4
-3 -2 0I 0 I 2
L -X L X EE (eV) 2 3
Figure 1. (color online). (a) The QSGW energy bands (or quasi-particle energies) for b-Pu along two
symmetry directions (left panel), compared to (b) the LDA energy bands (right panel); the Mulliken
weights of the f orbitals are presented in red (dark gray), for s orbitals in black and for d orbitals in blue
(light gray). (c) Comparison of the total density of states (DOS) for QSGW, red (dark gray) solid line,
and LDA, blue (light gray) dashed line. The Fermi energy is set at zero.
In Fig.1 we compare the QSGW one-particle electronic structure of 3-Pu with
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Albers, Robert C; Chantis, Athanasios N; Svane, Axel & Christensen, Niels E. GW correlation effects on plutonium quasiparticle energies: changes in crystal-field splitting, article, January 1, 2009; [New Mexico]. (https://digital.library.unt.edu/ark:/67531/metadc929752/m1/4/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.