Transferability of the Slater-Koster tight-binding scheme from an environment-dependent minimal-basis perspective

Tight-binding Hamiltonian and overlap matrix elements are calculated from the first-principles using the recently developed quasiatomic minimal basis orbitals (QUAMBOs). By decomposing the matrix elements into the hopping and overlap parameters through the Slater-Koster scheme, the transferability of the commonly used two-center approximation in tight-binding parametrization is examined. The analysis results provide very useful insight into the dependence of tight-binding hopping and on-site parameters on the bonding environment of the systems.

Figure 1

Nonorthogonal $s$- and $p$-like QUAMBOs in Si (a) diamond structure in the (110) plane for three bond lengths 1.95, 2.35, and $2.75\mathrm{\AA }$, and (b) fcc structure in the (100) plane for three bond lengths 2.34, 2.74, and $3.14\mathrm{\AA }$.

Figure 2

Electronic density of states of diamond Si obtained by using the QUAMBOs as basis set, compared with those from the corresponding LDA calculations using the PW basis set.

Figure 3

Overlap integrals as a function of interatomic distance for Si in the diamond, SC, and fcc structures.

Figure 4

Nonorthogonal tight-binding hopping integrals for Si as a function of interatomic distance in the diamond, SC, and fcc structures obtained by decomposing the QUAMBO-based effective one-electron Hamiltonian according to the Slater-Koster tight-binding scheme.

Figure 5

Orthogonal $s$- and $p$-like QUAMBOs in Si (a) diamond structure in the (110) plane for three bond lengths 1.95, 2.35, and $2.75\mathrm{\AA }$, and (b) fcc structure in the (100) plane for three bond lengths 2.34, 2.74, and $3.14\mathrm{\AA }$.

Figure 6

Orthogonal tight-binding hopping integrals for Si as a function of interatomic distances in the diamond, SC, and fcc structures obtained by decomposing the QUAMBO-based effective one-electron Hamiltonian according to the Slater-Koster tight-binding scheme.

Figure 7

Hamiltonian diagonal matrix elements for (a) nonorthogonal and (b) orthogonal QUAMBOs as a function of bond length in Si diamond-, SC-, and fcc-like clusters (${\mathrm{Si}}_{47}{\mathrm{H}}_{60}$, ${\mathrm{Si}}_{57}{\mathrm{H}}_{56}$, and ${\mathrm{Si}}_{55}$).