^{1,a)}, Vincent Meunier

^{1,2}and Robert J. Harrison

^{1,3}

### Abstract

We describe the occurrence of computational artifacts when the principal layer method is used in combination with the cluster approximation for the calculation of electronic transportproperties of nanostructures. For a one-dimensional gold chain, we observe an unphysical band in the band structure. The artificial band persists for large principal layers and for large buffer sizes. We demonstrate that the assumption of equality between Hamiltonian elements of neighboring layers is no longer valid and that a discontinuity is introduced in the potential at the layer transition. The effect depends on the basis set. When periodic boundary conditions are imposed and the -space sampling is converged, the discontinuity disappears and the principal layer method can be correctly applied by using a linear combination of atomic orbitals as basis set.

This research was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basis Energy Sciences, U.S. Department of Energy, under Contract No. DE-AC05-00OR22725 with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC, and, in part, by ORNL Laboratory Directed Research and Development Funds.

INTRODUCTION

METHOD AND IMPLEMENTATION

RESULTS AND DISCUSSION

CONCLUSION

### Key Topics

- Gold
- 30.0
- Band structure
- 18.0
- Lead
- 12.0
- Density functional theory
- 9.0
- Basis sets
- 7.0

## Figures

Typical input structure for the quantum chemical code of a gold chain where a gap is introduced.

Typical input structure for the quantum chemical code of a gold chain where a gap is introduced.

Conductance of gold chain, dotted-dashed line denotes Fermi energy. (a) Bulk calculation for different principal layer sizes, LANL2DZ-nw basis set. (b) Conductor calculation for different gap sizes in atomic distances (ad), principal layer size six atoms, LANL2DZ-nw basis set. (c) Conductor calculation for different gap sizes in atomic distances (ad), principal layer size six atoms, LANL2DZ-cry basis set.

Conductance of gold chain, dotted-dashed line denotes Fermi energy. (a) Bulk calculation for different principal layer sizes, LANL2DZ-nw basis set. (b) Conductor calculation for different gap sizes in atomic distances (ad), principal layer size six atoms, LANL2DZ-nw basis set. (c) Conductor calculation for different gap sizes in atomic distances (ad), principal layer size six atoms, LANL2DZ-cry basis set.

Band structure of a gold chain, the Fermi level is indicated by a dashed-dotted line. (a) Periodic CRYSTAL calculation, six atoms in unit cell, LANL2DZ-nw. (b) Principal layer method, six atoms in principal layer, LANL2DZ-nw; arrows mark unphysical band. (c) Principal layer method, six atoms in principal layer, LANL2DZ-cry. For transport-based calculations, the bands are represented by dots on the energy grid. This is due to the fact that in that case the bands are expressed as rather than since is an input parameter of the Green’s function approach. It follows that some bands might look dotted when the band is flat since step sizes in energy are finite.

Band structure of a gold chain, the Fermi level is indicated by a dashed-dotted line. (a) Periodic CRYSTAL calculation, six atoms in unit cell, LANL2DZ-nw. (b) Principal layer method, six atoms in principal layer, LANL2DZ-nw; arrows mark unphysical band. (c) Principal layer method, six atoms in principal layer, LANL2DZ-cry. For transport-based calculations, the bands are represented by dots on the energy grid. This is due to the fact that in that case the bands are expressed as rather than since is an input parameter of the Green’s function approach. It follows that some bands might look dotted when the band is flat since step sizes in energy are finite.

Hamiltonian projected onto the basis function along a 24 atom gold chain, finite-size NWCHEM calculation: Upper panel LANL2DZ-nw and lower panel LANL2DZ-cry. The inset panels enlarge the scale for the Hamiltonian elements along atoms 7–18a. (a) Principal layer approximation by replicating values from atoms 7–12 for atoms 13–18. (b) Hamiltonian elements from NWCHEM calculation. (c) Hamiltonian elements from CRYSTAL calculation.

Hamiltonian projected onto the basis function along a 24 atom gold chain, finite-size NWCHEM calculation: Upper panel LANL2DZ-nw and lower panel LANL2DZ-cry. The inset panels enlarge the scale for the Hamiltonian elements along atoms 7–18a. (a) Principal layer approximation by replicating values from atoms 7–12 for atoms 13–18. (b) Hamiltonian elements from NWCHEM calculation. (c) Hamiltonian elements from CRYSTAL calculation.

## Tables

Largest absolute values of the NWCHEM Hamiltonian in a.u. and overlap matrix elements between the next nearest neighbors for different principal layer sizes and basis sets.

Largest absolute values of the NWCHEM Hamiltonian in a.u. and overlap matrix elements between the next nearest neighbors for different principal layer sizes and basis sets.

Largest absolute values of the differences between the NWCHEM Hamiltonian elements in a.u. of a principal layer and its neighbor and potential differences at layer transition in a.u. measured as the absolute value of the difference between the NWCHEM Hamiltonian projected onto the function of the first and the last atom in the principal layer for different principal layer sizes, buffer sizes, and basis sets.

Largest absolute values of the differences between the NWCHEM Hamiltonian elements in a.u. of a principal layer and its neighbor and potential differences at layer transition in a.u. measured as the absolute value of the difference between the NWCHEM Hamiltonian projected onto the function of the first and the last atom in the principal layer for different principal layer sizes, buffer sizes, and basis sets.

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