Fusion of the LAPW and LMTO methods: The augmented plane wave plus muffin-tin orbital method

We present a full potential linearized method to solve the one-body problem, for example in the local density approximation. A mixed basis of augmented plane waves and generalized muffin-tin orbitals (MTOs) are used for the eigenfunctions. Since MTOs efficiently describe low-energy and localized states, the mixed basis is dramatically more efficient than the linearized augmented plane wave method for a given tolerance. GaAs, MnAs, ${\text{SrTiO}}_3$, Cu, and the ${\text{O}}_2$ dimer are used as illustrations.

Figure 1

(Color online) Deviation $\Delta E$ from fully converged total energy/atom, in mRy vs total number of basis functions $N_{\text{b}}^{\Gamma }$ at $\Gamma$. Data are drawn on a $\text{log}\Delta E-\text{log}1/N_{\text{b}}^{\Gamma }$ scale. Each curve corresponds to a fixed $\text{MTO}+\text{local}$ orbital basis (see Table ). The basis is enlarged by increasing the PW energy cutoff $E_{\text{MAX}}^{\text{APW}}$. Data is shown for three periodic crystals and the ${\text{O}}_2$ dimer. Dashed-dot lines with circles are the closest to a pure LAPW basis (null in Table ); solid lines with diamonds correspond to the hyperminimal LMTO basis in Table ; dashed lines with squares employ a minimal LMTO set (small in Table ); finally, solid lines with circles contain the most LMTO’s (large in Table ), corresponding to a standard LMTO calculation. The rightmost points in the minimal and large basis set cases correspond to all-LMTO basis sets. GaAs panel inset: ${\Gamma }_1{\text{-X}}_3$ transition between the conduction band minimum and second conduction band at $X$. (The large basis is not shown because it is converged to $<0.01\text{eV}$ without APWs.)

Figure 2

(Color online) Energy bands for Cu, in eV. Fermi level at zero. Top left: large LMTO basis of Table , without APWs. Red depicts $4d$ orbital character, significant between 25 and 50 eV; green depicts $5sp$ orbital character. The state near 55 eV at $\Gamma$ is mostly $\text{Cu}5s$. Top right: converged ‘large’ basis with APWs. Bottom figures show RMS deviation (eV) relative to fully converged (Ref. 10) bands as a function of the PW cutoff energy $E_{\text{MAX}}^{\text{APW}}$, in the following energy windows: (left) $-10<E_k<30\text{eV}$; (middle) $-10<E_k<50\text{eV}$; (right) $-10<E_k<100\text{eV}$. Light lines: null basis of Table ; dark lines: large basis.