Analysis of a capped carbon nanotube by linear-scaling density-functional theory.

The apex region of a capped (5,5) carbon nanotube (CNT) has been modelled with the DFT package ONETEP, using boundary conditions provided by a classical calculation with a conducting surface in place of the CNT. Results from the DFT solution include the Fermi level and the physical distribution and energies of individual orbitals for the CNT tip. Application of an external electric field changes the orbital number of the highest occupied molecular orbital (HOMO) and consequently changes its distribution on the CNT

Role of spin in the calculation of Hubbard U and Hund's J parameters from first principles

The density functional theory (DFT)+$U$ method is a pragmatic and effective approach for calculating the ground-state properties of strongly-correlated systems, and linear response calculations are widely used to determine the requisite Hubbard parameters from first principles. We provide a detailed treatment of spin within this linear response approach, demonstrating that the conventional Hubbard $U$ formula, unlike the conventional DFT+$U$ corrective functional, incorporates interactions that are off-diagonal in the spin indices and places greater weight on one spin channel over the other. We construct alternative definitions for Hubbard and Hund's parameters that are consistent with the contemporary DFT+$U$ functional, expanding upon the minimum-tracking linear response method. This approach allows Hund's $J$ and spin-dependent $U$ parameters to be calculated with the same ease as for the standard Hubbard $U$. Our methods accurately reproduce the experimental band gap, local magnetic moments, and the valence band edge character of manganese oxide, a canonical strongly-correlated system. We also apply our approach to a complete series of transition-metal complexes [M(H$_2$O)$_6$]$^{n+}$ (for M = Ti to Zn), showing that Hubbard corrections on oxygen atoms are necessary for preserving bond lengths, and demonstrating that our methods are numerically well-behaved even for near-filled subspaces such as in zinc. However, spectroscopic properties appear beyond the reach of the standard DFT+$U$ approach. Collectively, these results shed new light on the role of spin in the calculation of the corrective parameters $U$ and $J$, and point the way towards avenues for further development of DFT+$U$-type methods

Example input/output files for "Role of spin in the calculation of Hubbard U and Hund’s J parameters from first principles"

This repository contains example input and output ONETEP files for linear response calculations and DFT+U+J calculations on manganese oxide (MnO) and hexahydrated transition metal complexes ([M(H2O)6]n+, for M = Ti to Zn and n = 2 and/or 3). Specifically, the repository contains: mno/ input (*.dat) and output (*.onetep) files for a typical DFT+U+J calculation on MnO, as well as the requisite pseudopotentials (Mn and O) hexaaqua/optimised_structures/ atomic coordinates of hexahydrated transition metals as optimised using the PBE exchange-correlation functional hexaaqua/pseudopotentials/ all pseudopotentials used for the hexahydrated transition metal complexes (Ti to Zn, as well as O and H) hexaaqua/linear_response_calculations/ input/output files from linear response calculations on [Cr(H2O)6]3+ hexaaqua/dft+u_calculations/ input/output files for DFT+U+J calculation on [Zn(H2O)6]2+ and a README file. These calculations are representative of those performed in the associated publication