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Register a new userSmart local orbitals for efficient calculations within density functional theory and beyond
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Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs which provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.
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Linear scaling methods for density-functional theory (DFT) simulations are formulated in terms of localised orbitals in real-space, rather than the delocalised eigenstates of conventional approaches. In local-orbital methods, relative to conventional DFT, desirable properties can be lost to some extent, such as the translational invariance of the total energy of a system with respect to small displacements and the smoothness of the potential energy surface. This has repercussions for calculating accurate ionic forces and geometries. In this work we present results from textsc{onetep}, our linear scaling method based on localised orbitals in real-space. The use of psinc functions for the underlying basis set and on-the-fly optimisation of the localised orbitals results in smooth potential energy surfaces that are consistent with ionic forces calculated using the Hellmann-Feynman theorem. This enables accurate geometry optimisation to be performed. Results for surface reconstructions in silicon are presented, along with three example systems demonstrating the performance of a quasi-Newton geometry optimisation algorithm: an organic zwitterion, a point defect in an ionic crystal, and a semiconductor nanostructure.
A globally-adaptive curvilinear coordinate formalism is shown to be easily convertible to a class of curvilinear transformations locally optimized around atom sites by a few parameters. Parameter transferability is established for a demanding test case, and the results of the two methods are shown to be comparable. Computational efficiencies realized in the local method are discussed.
We present an efficient, linear-scaling implementation for building the (screened) Hartree-Fock exchange (HFX) matrix for periodic systems within the framework of numerical atomic orbital (NAO) basis functions. Our implementation is based on the localized resolution of the identity approximation by which two-electron Coulomb repulsion integrals can be obtained by only computing two-center quantities -- a feature that is highly beneficial to NAOs. By exploiting the locality of basis functions and efficient prescreening of the intermediate three- and two-index tensors, one can achieve a linear scaling of the computational cost for building the HFX matrix with respect to the system size. Our implementation is massively parallel, thanks to a MPI/OpenMP hybrid parallelization strategy for distributing the computational load and memory storage. All these factors add together to enable highly efficient hybrid functional calculations for large-scale periodic systems. In this work we describe the key algorithms and implementation details for the HFX build as implemented in the ABACUS code package. The performance and scalability of our implementation with respect to the system size and the number of CPU cores are demonstrated for selected benchmark systems up to 4096 atoms.
Density functional theory (DFT) calculations are used to investigate the electronic and magnetic structures of a two-dimensional (2D) monolayer Li$_{2}$N. It is shown that bulk Li$_{3}$N is a non-magnetic semiconductor. The non-spinpolarized DFT calculations show that $p$ electrons of N in 2D Li$_{2}$N form a narrow band at the Fermi energy $E_{rm{F}}$ due to a low coordination number, and the density of states at the Fermi energy ($g(E_{rm{F}}$)) is increased as compared with bulk Li$_{3}$N. The large $g(E_{rm{F}}$) shows instability towards magnetism in Stoners mean field model. The spin-polarized calculations reveal that 2D Li$_{2}$N is magnetic without intrinsic or impurity defects. The magnetic moment of 1.0,$mu_{rm{B}}$ in 2D Li$_{2}$N is mainly contributed by the $p_{z}$ electrons of N, and the band structure shows half-metallic behavior. {Dynamic instability in planar Li$_{2}$N monolayer is observed, but a buckled Li$_{2}$N monolayer is found to be dynamically stable.} The ferromagnetic (FM) and antiferromagnetic (AFM) coupling between the N atoms is also investigated to access the exchange field strength. {We found that planar (buckled) 2D Li$_{2}$N is a ferromagnetic material with Curie temperature $T_{c}$ of 161 (572) K.}
The accurate description of the optical spectra of insulators and semiconductors remains an important challenge for time-dependent density-functional theory (TDDFT). Evidence has been given in the literature that TDDFT can produce bound as well as continuum excitons for specific systems, but there are still many unresolved basic questions concerning the role of dynamical exchange and correlation (xc). In particular, the role of the long spatial range and the frequency dependence of the xc kernel $f_{rm xc}$ for excitonic binding are still not very well explored. We present a minimal model for excitons in TDDFT, consisting of two bands from a one-dimensional Kronig-Penney model and simple approximate xc kernels, which allows us to address these questions in a transparent manner. Depending on the system, it is found that adiabatic xc kernels can produce a single bound exciton, and sometimes two bound excitons, where the long spatial range of $f_{rm xc}$ is not a necessary condition. It is shown how the Wannier model, featuring an effective electron-hole interaction, emerges from TDDFT. The collective, many-body nature of excitons is explicitly demonstrated.
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