Query: Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

Candidate papers:

abstract: We present a detailed description and comparison of algorithms for performing ab initio quantum mechanical calculations using pseudopotentials and a plane wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density functional theory, (b) iterative methods for the diagonalization of the Kohn Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order Natoms2 scaling even for relatively large systems, (c) efficient Broyden like and Pulay like mixing methods for the charge density including a new special 'preconditioning' optimized for a plane wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab initio molecular dynamics package) The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
author_names: Georg Kresse

Jurgen Furthmuller
title: Efficiency of ab initio total energy calculations for metals and semiconductors using a plane wave basis set
year: 1996

abstract: We present an efficient scheme for calculating the Kohn Sham ground state of metallic systems using pseudopotentials and a plane wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order \mathit{N}}_{\mathrm{atoms}{3} operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special `metric' and a special `preconditioning' optimized for a plane wave basis set will be introduced. Scaling of the method will be discussed in detail for non self consistent and self consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order \mathit{N}}_{\mathrm{atoms}{2} scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach \mathit{N}}_{\mathrm{atoms} We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package) The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. \textcopyright{ 1996 The American Physical Society.
title: Efficient iterative schemes for ab initio total energy calculations using a plane wave basis set.
venue: Physical review. B, Condensed matter
year: 1996

abstract: We present a novel real space formalism for ab initio electronic structure calculations. We use localized non orthogonal functions that are expressed in terms of a basis set that is equivalent to a plane wave basis. As a result, advantages of the plane wave approach also apply to our method: its applicability to any lattice symmetry, and systematic basis set improvement via the kinetic energy cut off parameter. The localization of our functions enables the use of fast Fourier transforms over small regions of the simulation cell to calculate the total energy with efficiency and accuracy. With just one further variational approximation, namely the truncation of the density matrix, the calculation may be performed with a cost that scales linearly with system size for insulating systems.
author_names: Arash A Mostofi

Chris-Kriton Skylaris

Peter D Haynes

Mike C Payne
title: Total energy calculations on a real space grid with localized functions and a plane wave basis
year: 2002

abstract: Plane wave basis sets offer many advantages in ab initio molecular dynamics due to their efficiency and simplicity. In combination with hybrid density functionals, they become computationally expensive due to the evaluation of the Hartree Fock exchange energy. The computational cost can be significantly reduced by screening the Kohn Sham orbital products after localizing the orbitals in real space. However, such a procedure introduces apparent errors in the wavefunctions and nuclear forces resulting in unstable dynamics. It is shown here that a noise stabilized dynamics approach can overcome this problem and at the same time permits using insufficiently converged wavefunctions for evaluating atomic forces. In this way, we achieve significant speed up even for a small system containing about 100 atoms. After benchmarking the accuracy and efficiency of this approach, we use it in combination with well sliced metadynamics to compute the free energy barrier of formamide hydrolysis in alkaline aqueous medium. These results provide insight into the error of the Perdew Burke Ernzerhof functional in predicting the free energy barrier for hydrolysis reactions in water.
author_names: Sagarmoy Mandal

Jayashrita Debnath

Bernd Meyer

Nisanth N Nair
title: Enhanced sampling and free energy calculations with hybrid functionals and plane waves for chemical reactions.
venue: The Journal of chemical physics
year: 2018

abstract: We present a new technique aimed at preventing plane wave based total energy and stress calculations from the effect of abrupt changes in basis set size. This scheme relies on the interpolation of energy as a function of the number of plane waves, and on a scaling hypothesis that allows to perform the interpolation for a unique reference volume. From a theoretical point of view, the new method is compared to those already proposed in the literature, and its more rigorous derivation is emphasized. From a practical point of view, we illustrate the importance of the correction on different materials (Si, BaTiO 3 and He) corresponding to different types of bonding, and to different k point samplings and cutoff energies. Then, we compare the different approaches for the calculation of a 0 B 0 and B 0 in bulk silicon.
author_names: Philippe Ghosez

Jean-Christophe Charlier
title: A Scaling Hypothesis for Corrections to Total Energy and Stress in Plane wave Based Ab Initio Calculations Typeset Using Revt E X
year: 1995

abstract: Lithium oxide (Li2O) has been suggested as a suitable breeder blanket material for fusion reactors. Li+ vacancies are created by neutron irradiation, forming bulk defect complex whose extra character is experimentally unclear. We present a theoretical study of Li2O using density functional theory (DFT) with a plane wave basis set. The generalized gradient approximation (GGA) and local density approximation (LDA) were used for exchange and correlation. Here we address the total energy for defect free, cation defect, cation vacancy and vacancy formation energy in Li2O crystal in anti fluorite structure.Lithium oxide (Li2O) has been suggested as a suitable breeder blanket material for fusion reactors. Li+ vacancies are created by neutron irradiation, forming bulk defect complex whose extra character is experimentally unclear. We present a theoretical study of Li2O using density functional theory (DFT) with a plane wave basis set. The generalized gradient approximation (GGA) and local density approximation (LDA) were used for exchange and correlation. Here we address the total energy for defect free, cation defect, cation vacancy and vacancy formation energy in Li2O crystal in anti fluorite structure.
author_names: V P Saleel Ahammad Saleel

D S Vijaya Chitra

Kasinadar Veluraja

R D Eithiraj
title: Ab initio calculation for cation vacancy formation energy in anti fluorite structure
year: 2018

abstract: We introduced two methods to correct the singularity in the calculation of long range Hartree Fock (HF) exchange for long range corrected density functional theory (LC DFT) calculations in plane wave basis sets. The first method introduces an auxiliary function to cancel out the singularity. The second method introduces a truncated long range Coulomb potential, which has no singularity. We assessed the introduced methods using the LC BLYP functional by applying it to isolated systems of naphthalene and pyridine. We first compared the total energies and the HOMO energies of the singularity corrected and uncorrected calculations and confirmed that singularity correction is essential for LC DFT calculations using plane wave basis sets. The LC DFT calculation results converged rapidly with respect to the cell size as the other functionals, and their results were in good agreement with the calculated results obtained using Gaussian basis sets. LC DFT succeeded in obtaining accurate orbital energies and excitation energies. We next applied LC DFT with singularity correction methods to the electronic structure calculations of the extended systems, Si and SiC. We confirmed that singularity correction is important for calculations of extended systems as well. The calculation results of the valence and conduction bands by LC BLYP showed good convergence with respect to the number of k points sampled. The introduced methods succeeded in overcoming the singularity problem in HF exchange calculation. We investigated the effect of the singularity correction on the excitation state calculation and found that careful treatment of the singularities is required compared to ground state calculations. We finally examined the excitonic effect on the band gap of the extended systems. We calculated the excitation energies to the first excited state of the extended systems using a supercell model at the G point and found that the excitonic binding energy, supposed to be small for inorganic semiconductors, was quite large. Our findings suggest that more investigation on the effect of the excitonic binding energy on band gaps is necessary.
author_names: Yukio Kawashima

Kimihiko Hirao
title: Singularity Correction for Long Range Corrected Density Functional Theory with Plane Wave Basis Sets.
venue: The journal of physical chemistry. A
year: 2017

abstract: We report the results of pressure induced semiconductor metal phase transition of the semiconducting chalcogenide compound KPSe6 under high pressure using the ab initio methods. The ground state energy calculations were performed within density functional theory and the generalized gradient approximation using the pseudopotential method with plane wave basis sets. The projector augmented wave (PAW) pseudopotentials were used in our calculation. The optimized lattice parameters were found from total energy calculations as 13 Bohr, 1.6 Bohr, and 1.8 Bohr for cell dimensions one, two, and three, respectively, which are in good agreement with experimental calculations. At zero pressure, the material portrayed a semiconducting property with a direct bandgap of 1.7 eV. As we subjected the material to pressure, the band gap was observed to reduce until it disappeared. The phase transition from the semiconductor to metal was found to occur at ~45 GPa, implying that the material underwent metallization as pressure was increased further.
author_names: P J Jomo

Calford O Otieno

P W O Nyawere
title: Ab Initio High Pressure Study of Semiconductor Metal Phase Transition of the Chalcogenide Compound KPSe6
year: 2020

abstract: We propose a unique scheme to construct fully optimized atomic basis sets for density functional calculations. The shapes of the radial functions are optimized by minimizing the spillage of the wavefunctions between the atomic orbital calculations and the converged plane wave results for dimer systems. The quality of the bases can be systematically improved by increasing the size of the bases within the same framework. We show that the spillage can describe the convergency of the total energy very well and the cutoff radii of the atomic orbitals are extremely important for the quality of the atomic orbitals. The scheme is easy to implement and very flexible. We have performed extensive tests of this scheme for a wide variety of systems, including semiconductors, oxides, metals, clusters, etc. The results show that the obtained atomic bases are very satisfactory for both accuracy and transferability.
author_names: Mohan Chen

Guangcan Guo

Lixin He
title: Systematically improvable optimized atomic basis sets for ab initio calculations.
venue: Journal of physics. Condensed matter an Institute of Physics journal
year: 2010

abstract: We present a detailed study of the adsorption of CO on Cu, Rh, and Pt (111) surfaces in top and hollow sites. The study has been performed using the local density approximation, the gradient corrected functional PBE, and the hybrid Hartree Fock density functionals PBE0 and HSE03 within the framework of generalized Kohn Sham density functional theory using a plane wave basis set. As expected, the local density approximation and generalized gradient approximation functionals show a tendency to favor the hollow sites, at variance with experimental findings that give the top site as the most stable adsorption site. The PBE0 and HSE03 functionals reduce this tendency. In fact, they predict the correct adsorption site for Cu and Rh but fail for Pt. However, even in this case, the hybrid functional destabilizes the hollow site by $50\phantom{\rule{0.3em}{0ex}\mathrm{meV} compared to the PBE functional. The results of the total energy calculations are presented along with an analysis of the projected density of states.
author_names: Alessandro Stroppa

Konstantinos Termentzidis

Joachim A Paier

Georg Kresse

J Hafner
title: CO adsorption on metal surfaces: A hybrid functional study with plane wave basis set
year: 2007