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Register a new userDaubechies wavelets as a basis set for density functional pseudopotential calculations
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Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances and an excellent efficiency for parallel calculations.
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We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of DFT calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the contracted basis functions for closely related environments, e.g. in geometry optimizations or combined calculations of neutral and charged systems.
The constrained electron density method of embedding a Kohn-Sham system in a substrate system (first described by P. Cortona, Phys. Rev. B {bf 44}, 8454 (1991) and T.A. Wesolowski and A. Warshel, J. Phys. Chem {bf 97}, 8050 (1993)) is applied with a plane-wave basis and both local and non-local pseudopotentials. This method divides the electron density of the system into substrate and embedded electron densities, the sum of which is the electron density of the system of interest. Coupling between the substrate and embedded systems is achieved via approximate kinetic energy functionals. Bulk aluminium is examined as a test case for which there is a strong interaction between the substrate and embedded systems. A number of approximations to the kinetic-energy functional, both semi-local and non-local, are investigated. It is found that Kohn-Sham results can be well reproduced using a non-local kinetic energy functional, with the total energy accurate to better than 0.1 eV per atom and good agreement between the electron densities.
A new method is presented for obtaining all-electron results from a pseudopotential calculation. This is achieved by carrying out a localised calculation in the region of an atomic nucleus using the embedding potential method of Inglesfield [J.Phys. C {bf 14}, 3795 (1981)]. In this method the core region is emph{reconstructed}, and none of the simplifying approximations (such as spherical symmetry of the charge density/potential or frozen core electrons) that previous solutions to this problem have required are made. The embedding method requires an accurate real space Green function, and an analysis of the errors introduced in constructing this from a set of numerical eigenstates is given. Results are presented for an all-electron reconstruction of bulk aluminium, for both the charge density and the density of states.
Recent experiments demonstrate the synthesis of 2D black arsenic exhibits excellent electronic and transport properties for nanoscale device applications. Herein, we study by first principle calculations density functional theory together with non equilibrium Greens function methods, the structural, electronic, adsorption strength, charge transfer, and transport properties of five gas molecules CO, CO2, NO, NO2, and NH3 on a monolayer of black arsenic. Our findings suggest optimum sensing performance of black arsenic that can even surpass that of other 2D material such as graphene. Further, we note the optimum adsorption sites for all the five gas molecules on the black arsenic and significant charge transfer between the gas molecules and black arsenic are responsible for optimum adsorption strength. Particularly, the significant charger transfer is a sign that the interaction between the target gas molecule and nanoscale device is sufficient to yield noticeable changes in the electronic transport properties. As a proof of principle, we have examined the sensitivity of a modeled nano-scale device towards CO, CO2, NO, NO2, and NH3 gas molecules, indicating that it is indeed possible to reliably detect all the five gas molecules. Thus, based on all these findings, such as sensitivity and selectivity to all the five gas molecules adsorption make black arsenic a promising material as an optimum gas sensor nano-scale device.
We present algorithms to numerically evaluate Daubechies wavelets and scaling functions to high relative accuracy. These algorithms refine the suggestion of Daubechies and Lagarias to evaluate functions defined by two-scale difference equations using splines; carefully choosing amongst a family of rapidly convergent interpolators which effectively capture all the smoothness present in the function and whose error term admits a small asymptotic constant. We are also able to efficiently compute derivatives, though with a smoothness-induced reduction in accuracy. An implementation is provided in the Boost Software Library.
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