Wave-function-basedab initiomethod for metals: Application of the incremental scheme to magnesium

Abstract

We apply ab initio quantum-chemical methods to calculate correlation effects on cohesive properties of Mg, thereby extending the method of increments to metallic systems. Metals require special treatment because of two distinct features. Since the conduction bands are only partially filled, we cannot construct well localized orbitals from them. Furthermore we must deal properly with charge screening which obviously is a correlation effect. A starting point for treatment of the many-body correlation effects in solids is a reliable Hartree-Fock self-consistent-field (HF SCF) result for the infinite system. In the case of Mg the HF cohesive energy of the solid is significantly underestimated with respect to the experimental value. Summing up all correlation contributions, we obtain nearly 100 % of the difference between the experimental and HF cohesive energies. Ignoring the correlations, HF model gives rather good agreement with experiment of one lattice parameter (c), but incorrect value for c/a ratio because of too large lattice constant a. Application of the method of increments allows us not only to improve the HF values, giving deviation by about 1 % from experimental values, but also to explain the reason for these changes.

Correlation energies for small magnesium clusters in comparison with bulk magnesium

“…Via an embedding scheme, we can guarantee localization in metallic systems and can mimic the metallic band structure within finite fragments of the solid (details can be found in [7]). Thus far we have applied the method of increments successfully to mercury [8][9][10] and magnesium [11], where, in both cases, the ground-state properties such as cohesive energy, lattice constants and bulk modulus agree very well with the experimental values. We have obtained reliable results especially for mercury, where DFT approaches fail.…”

“…When considering solid Mg, it can be assumed that the requirement is not met since Á" 12 > Á" 13 , where r 12 ¼ 3:197 Å and r 12 ¼ 3:209 , A > r 12 (table 1). However, as already reported [11], this is a consequence of the crystal symmetry and is due to the better interaction between the 3p orbitals of Mg 1 and Mg 3 compared with Mg 1 and Mg 2 , which makes the correlation effects stronger in the first case. In general, Á" AB extracted from embedded clusters decreases rapidly with distance, and can be fitted to ÀB=r 4:8 (see figure 3).…”

“…(i) In the first approach the dimer is surrounded by 26 Mg atoms in the solid structure, and are described using large-core PP and minimal basis sets and kept frozen during the correlation calculation. This is the approach that was employed for the magnesium and mercury calculations [8][9][10][11].…”

“…We calculated correlation energies for 47 four-body embedded clusters [11]: the selection criterion for the four-site clusters is that, for each atom, at least one can be found that is not further away than the first-neighbour shell (3.209 Å ). The general trend is similar to that for the three-body case: the largest contributions arise for the compact geometries, whereas the longer the distance between the first and fourth atom, the smaller the contribution of the corresponding cluster.…”

The method of increments—a wavefunction-based ab initio correlation method for solids

“…But of course a combination of the method of increments with the local correlation method of Pulay is possible to reduce the computational effort even further [31,32]. The focus of this review lies on the method of increments and its application to ground-state properties of various material classes: From insulators [33][34][35][36][37] over semiconductors [20,21,[38][39][40][41][42] to metals [22,43,44], from strongly bound ionic or covalent systems to weakly bound van der Waals solids [45][46][47], from large molecules [31,48] over polymers [49][50][51][52][53][54][55][56] to three-dimensional solids, from weakly correlated systems to strongly correlated ones such as transition-metal oxides [57,58] and rare-earth nitrides and oxides [59][60][61]. The generalisation to metals is discussed for the example of solid mercury [44,62] and the inclusion of multi-reference treatments for strongly correlated systems is presented for a one-dimensional lithium chain [43].…”