Representation of electronic structures in crystals in terms of highly localized quasiatomic minimal basis orbitals

A method is presented for expressing electronic orbital states of a periodic solid in terms of a minimal basis set of localized quasiatomic orbitals. While spanning exactly the same occupied subspace as the orbitals determined by a fully converged first-principles calculation with a large basis set, the minimal-basis orbitals from this work are highly localized on atoms and exhibit shapes close to orbitals of the isolated atom. They are also shown to be useful for analyzing chemical bonding in periodic systems. All of these features are found for insulating as well as metallic solids.

Figure 1

(a) $s$-like and (b) $p$-like QUAMBOs in diamond Si in the (110) plane; (c) $s$-like and (d) $p$-like QUAMBOs in fcc Al in the (100) plane. The contour step is $0.015{\mathrm{\AA }}^{-3∕2}$ and the outmost line has the value of $0.01{\mathrm{\AA }}^{-3∕2}$.

Figure 2

Profiles of the $s$- and $p_z$-like QUAMBOs in diamond Si and fcc Al along the $z$ axis, compared with the corresponding free-atom orbitals. Orbital amplitude is in ${\mathrm{\AA }}^{-3∕2}$.

Figure 3

Electronic density of states of (a) diamond Si and (b) fcc Al obtained by using the QUAMBOs as basis set, compared with those from the original LDA calculations using the PW basis set.

Figure 4

The matrix elements $M_{i0,jn}$, defined by Eq. (8), between the origin atom and its various neighbors for diamond Si and fcc Al.