Tight-binding bond parameters for dimers across the periodic table from density-functional theory

We obtain parameters for nonorthogonal and orthogonal tight-binding (TB) models from two-atomic molecules for all combinations of elements of period 1 to 6 and group 3 to 18 of the periodic table. The TB bond parameters for 1711 homoatomic and heteroatomic dimers show clear chemical trends. In particular, using our parameters we compare to the rectangular $d$-band model, the reduced $sp$ TB model, as well as canonical TB models for $sp$- and $d$-valent systems, which have long been used to gain qualitative insight into the interatomic bond. The transferability of our dimer-based TB bond parameters to bulk systems is discussed exemplarily for the bulk ground-state structures of Mo and Si. Our dimer-based TB bond parameters provide a well-defined and promising starting point for developing refined TB parametrizations and for making the insight of TB available for guiding materials design across the periodic table.

Figure 1

TB and DFT eigenvalues as a function of distance for the Si dimer (top) and the Mo dimer (bottom).

Figure 2

Matrix elements of nonorthogonal TB Hamiltonian matrix, overlap matrix, and on-site levels obtained by downfolding and orthogonal TB Hamiltonian matrix for Si (top) and Mo (bottom) dimer. Symbols correspond to the matrix elements from downfolding, solid lines are interpolations using Eqs. (11) and (12).

Figure 3

Bond integrals $ss\sigma$ of orthogonal TB models across period $3p$ (left) and period $4d$ (right).

Figure 4

Inverse decay length ${\lambda }_0$ of the $ss\sigma$ matrix elements of orthogonal TB models across the periods of the $sp$-valent (left) and $sd$-valent (right) homoatomic dimers.

Figure 5

Inverse decay length ${\lambda }_0$ for $ss\sigma$ and orthogonal TB models across homoatomic and heteroatomic dimers.

Figure 6

Bond integral $sp\sigma$ and reduced TB approximation for Si (left) and across the $sp$-block (right) at a fixed interatomic distance of $R=2.5\AA$.

Figure 7

Bond integrals of homoatomic dimers compared to canonical TB models, $sp$-valent (left), and $d$-valent (right). Horizontal lines correspond to the canonical TB models. Right panel: sSolid lines: Eq. (17); dashed lines: Eq. (18).

Figure 8

Comparison of TB matrix elements of Hamiltonian $H$ (left) and overlap $S$ (right) of the Si-Si dimer obtained from downfolding, NRL-TB and DFTB. The sign of the $sp\sigma$ matrix element for DFTB was changed for easier comparison.

Figure 9

Electronic DOS (states/eV) of Si in the diamond structure (left) and Mo in the body-centered cubic structure (right) as obtained from DFT and from TB with the dimer TB bond parameters.