Introducing PROFESS: A new program for orbital-free density functional theory calculations

We present PROFESS (PRinceton Orbital-Free Electronic Structure Software), a new software package that performs orbital-free density functional theory (OF-DFT) calculations. OF-DFT is a first principles quantum mechanics method primarily for condensed matter that can be made to scale linearly with system size. We describe the implementation of energy, force, and stress functionals and the methods used to optimize the electron density under periodic boundary conditions. All electronic energy and potential terms scale linearly while terms involving the ions exhibit quadratic scaling in our code. Despite the latter scaling, the program can treat tens of thousands of atoms with quantum mechanics on a single processor, as we demonstrate here. Limitations of the method are also outlined, the most serious of which is the accuracy of state-of-the-art kinetic energy functionals, which limits the applicability of the method to main group elements at present.

Program summary

Program title: PROFESSCatalogue identifier: AEBN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 35 933No. of bytes in distributed program, including test data, etc.: 329 924Distribution format: tar.gzProgramming language: Fortran 90Computer: Intel with ifort; AMD Opteron with pathf90Operating system: LinuxRAM: Problem dependent, but 2 GB is sufficient for up to 10,000 ionsClassification: 7.3External routines: FFTW (http://www.fftw.org), MINPACK-2Nature of problem: Given a set of coordinates describing the initial ion positions under periodic boundary conditions, recovers the ground state energy, electron density, ion positions, and cell lattice vectors predicted by orbital-free density functional theory. Except for computation of the ion-ion and ion-electron terms, all other terms are effectively linear scaling. Up to ∼10,000 ions may be included in the calculation on just a single processor.Solution method: Computes energies as described in text; minimizes this energy with respect to the electron density, ion positions, and cell lattice vectors.Restrictions: PROFESS cannot use nonlocal (such as ultrasoft) pseudopotentials. Local pseudopotential files for aluminum, magnesium, silver, and silicon are available upon request. Also, due to the current state of the kinetic energy functionals, PROFESS is only reliable for main group metals and some properties of semiconductors.Running time: Problem dependent: the test example provided with the code takes less than a second to run. Timing results for large scale problems are given in the paper.References:[1] Y.A. Wang, N. Govind, E.A. Carter, Phys. Rev. B 58 (1998) 13465;  Y.A. Wang, N. Govind, E.A. Carter, Phys. Rev. B 64 (2001) 129901 (erratum).[2] S.C. Watson, E.A. Carter, Comput. Phys. Comm. 128 (2000) 67.     

Optimal Fourier filtering of a function that is strictly confined within a sphere

We present an alternative method to filter a distribution, that is strictly confined within a sphere of given radius rc, so that its Fourier transform is optimally confined within another sphere of radius kc. In electronic structure methods, it can be used to generate optimized pseudopotentials, pseudocore charge distributions, and pseudo atomic orbital basis sets.     

Efficient first-principles calculations of the electronic structure of periodic systems

We have recently presented a real-space method for electronic-structure calculations of periodic systems that is based on the Hohenberg-Kohn-Sham density-functional theory. The method allows the computation of electronic properties of periodic systems in the spirit of traditional plane-wave approaches. In addition, it can be implemented efficiently on parallel computers. Here we will show that the method's inherent parallelism, in conjunction with a newly designed approach for solving the Kohn-Sham equations, enables the accurate study of the ionic and electronic properties of periodic systems containing thousands of atoms from first principles.     

Computation of Maximally Localized Wannier Functions using a simultaneous diagonalization algorithm

We show that a simultaneous diagonalization algorithm used in signal processing applications can be used in the context of electronic structure calculations to efficiently compute Maximally Localized Wannier Functions (MLWFs). Applications to calculations of MLWFs in molecular and solid systems demonstrate the efficiency of the approach. We also present and discuss a parallel version of the algorithm. An extension of the concept of MLWF to generalized minimum spread wavefunctions is proposed.     

JuNoLo - Jülich nonlocal code for parallel post-processing evaluation of vdW-DF correlation energy

Nowadays the state of the art Density Functional Theory (DFT) codes are based on local (LDA) or semilocal (GGA) energy functionals. Recently the theory of a truly nonlocal energy functional has been developed. It has been used mostly as a post-DFT calculation approach, i.e. by applying the functional to the charge density calculated using any standard DFT code, thus obtaining a new improved value for the total energy of the system. Nonlocal calculation is computationally quite expensive and scales as N² where N is the number of points in which the density is defined, and a massively parallel calculation is welcome for a wider applicability of the new approach. In this article we present a code which accomplishes this goal.

Program summary

Program title: JuNoLoCatalogue identifier: AEFM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 176 980No. of bytes in distributed program, including test data, etc.: 2 126 072Distribution format: tar.gzProgramming language: Fortran 90Computer: any architecture with a Fortran 90 compilerOperating system: Linux, AIXHas the code been vectorised or parallelized?: Yes, from 1 to 65536 processors may be used.RAM: depends strongly on the problem's size.Classification: 7.3External routines:• FFTW (http://www.tw.org/)• MPI (http://www.mcs.anl.gov/research/projects/mpich2/ or http://www.lam-mpi.org/)Nature of problem: Obtaining the value of the nonlocal vdW-DF energy based on the charge density distribution obtained from some Density Functional Theory code.Solution method: Numerical calculation of the double sum is implemented in a parallel F90 code. Calculation of this sum yields the required nonlocal vdW-DF energy.Unusual features: Binds to virtually any DFT program.Additional comments: Excellent parallelization features.Running time: Depends strongly on the size of the problem and the number of CPUs used.     

Linear-scaling density-functional theory with tens of thousands of atoms: Expanding the scope and scale of calculations with ONETEP

ONETEP is an ab initio electronic structure package for total energy calculations within density-functional theory. It combines ‘linear scaling’, in that the total computational effort scales only linearly with system size, with ‘plane-wave’ accuracy, in that the convergence of the total energy is systematically improvable in the manner typical of conventional plane-wave pseudopotential methods. We present recent progress on improving the performance, and thus in effect the feasible scope and scale, of calculations with ONETEP on parallel computers comprising large clusters of commodity servers. Our recent improvements make calculations of tens of thousands of atoms feasible, even on fewer than 100 cores. Efficient scaling with number of atoms and number of cores is demonstrated up to 32,768 atoms on 64 cores.     

yambo: An ab initio tool for excited state calculations

yambo is an ab initio code for calculating quasiparticle energies and optical properties of electronic systems within the framework of many-body perturbation theory and time-dependent density functional theory. Quasiparticle energies are calculated within the GW approximation for the self-energy. Optical properties are evaluated either by solving the Bethe-Salpeter equation or by using the adiabatic local density approximation. yambo is a plane-wave code that, although particularly suited for calculations of periodic bulk systems, has been applied to a large variety of physical systems. yambo relies on efficient numerical techniques devised to treat systems with reduced dimensionality, or with a large number of degrees of freedom. The code has a user-friendly command-line based interface, flexible I/O procedures and is interfaced to several publicly available density functional ground-state codes.

Program summary

Program title:yamboCatalogue identifier: AEDH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDH_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU General Public Licence v2.0No. of lines in distributed program, including test data, etc.: 149 265No. of bytes in distributed program, including test data, etc.: 2 848 169Distribution format: tar.gzProgramming language: Fortran 95, CComputer: any computer architecture, running any flavor of UNIXOperating system: GNU/Linux, AIX, Irix, OS/XHas the code been vectorised or parallelized?: YesRAM: 10-1000 MbytesClassification: 7.3, 4.4, 7.2External routines:

•

BLAS (http://www.netlib.org/blas/)

•

LAPACK (http://www.netlib.org/lapack/)

•

MPI (http://www-unix.mcs.anl.gov/mpi/) is optional.

•

BLACS (http://www.netlib.org/scalapack/) is optional.

•

SCALAPACK (http://www.netlib.org/scalapack/) is optional.

•

FFTW (http://www.fftw.org/) is optional.

•

netCDF (http://www.unidata.ucar.edu/software/netcdf/) is optional.

Nature of problem: Calculation of excited state properties (quasiparticles, excitons, plasmons) from first principles.Solution method: Many body perturbation theory (Dyson equation, Bethe Salpeter equation) and time-dependent density functional theory. Quasiparticle approximation. Plasmon-pole model for the dielectric screening. Plane wave basis set with norm conserving pseudopotentials.Unusual features: During execution, yambo supplies estimates of the elapsed and remaining time for completion of each runlevel. Very friendly shell-based user-interface.Additional comments:yambo was known as “SELF” prior to GPL release. It belongs to the suite of codes maintained and used by the European Theoretical Spectroscopy Facility (ETSF) [1].Running time: The typical yambo running time can range from a few minutes to some days depending on the chosen level of approximation, and on the property and physical system under study.References:[1] The European Theoretical Spectroscopy Facility, http://www.etsf.eu.     

The solution of stationary ODE problems in quantum mechanics by Magnus methods with stepsize control

In solid state physics the solution of the Dirac and Schrödinger equation by operator splitting methods leads to differential equations with oscillating solutions for the radial direction. For standard time integrators like Runge-Kutta or multistep methods the stepsize is restricted approximately by the length of the period. In contrast the recently developed Magnus methods allow stepsizes that are substantially larger than one period. They are based on a Lie group approach and incorporate exponential functions and matrix commutators. A stepsize control is implemented and tested. As numerical examples eigenvalue problems for the radial Schrödinger equation and the radial Dirac equation are solved. Further, phase shifts for scattering solutions for hydrogen atoms and copper are computed.     

SaX: An open source package for electronic-structure and optical-properties calculations in the GW approximation

We present here SaX (Self-energies and eXcitations), a plane-waves package aimed at electronic-structure and optical-properties calculations in the GW framework, namely using the GW approximation for quasi-particle properties and the Bethe-Salpeter equation for the excitonic effects. The code is mostly written in FORTRAN90 in a modern style, with extensive use of data abstraction (i.e. objects). SaX employs state of the art techniques and can treat large systems. The package is released with an open source license and can be also download from http://www.sax-project.org/.

Program summary

Program title: SaX (Self-energies and eXcitations)Catalogue identifier: AEDF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDF_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenseNo. of lines in distributed program, including test data, etc.: 779 771No. of bytes in distributed program, including test data, etc.: 4 894 755Distribution format: tar.gzProgramming language: FORTRAN, plus some C utilitiesComputer: Linux PC, Linux clusters, IBM-SP5Operating system: Linux, AixHas the code been vectorised or parallelized?: YesRAM: depending on the system complexityClassification: 7.3External routines: Message-Passing Interface (MPI) to perform parallel computations. ESPRESSO (http://www.quantum-espresso.org)Nature of problem: SaX is designed to calculate the electronic band-structure of semiconductors, including quasi-particle effects and optical properties including excitonic effects.Solution method: The electronic band-structure is calculated using the GW approximation for the self-energy operator. The optical properties are calculated solving the Bethe-Salpeter equation in the GW approximation. The wavefunctions are expanded on a plane-waves basis set, using norm-conserving pseudopotentials.Restrictions: Many objects are non-local matrix represented in plane wave basis sets. The memory required by the program in the allocation of such objects increases with the increase of the simulation cell volume. Other quantities are built calculating electronic transitions, so that the computational time increase with their number, and scales as , where Nv and Nc are the number of valence and conduction bands implied in the transition and Nk is the number of special k vectors. Symmetries are not exploited yet. Finally, metallic systems cannot be studied yet.Unusual features: SaX is written using FORTRAN90 in an object-oriented way. Thus, it is easy to add new features and to reuse the code.Running time: The 3 examples, contained in the distribution file, each take only a few seconds to run. For systems of interest, the run may take a number of days with a typical memory allocation of 1600 Mb per processor.     

Generating relativistic pseudo-potentials with explicit incorporation of semi-core states using APE, the Atomic Pseudo-potentials Engine

We present a computer package designed to generate and test norm-conserving pseudo-potentials within Density Functional Theory. The generated pseudo-potentials can be either non-relativistic, scalar relativistic or fully relativistic and can explicitly include semi-core states. A wide range of exchange-correlation functionals is included.

Program summary

Program title: Atomic Pseudo-potentials Engine (APE)Catalogue identifier: AEAC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAC_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 88 287No. of bytes in distributed program, including test data, etc.: 649 959Distribution format: tar.gzProgramming language: Fortran 90, CComputer: any computer architecture, running any flavor of UNIXOperating system: GNU/LinuxRAM: <5 MbClassification: 7.3External routines: GSL (http://www.gnu.org/software/gsl/)Nature of problem: Determination of atomic eigenvalues and wave-functions using relativistic and nonrelativistic Density-Functional Theory. Construction of pseudo-potentials for use in ab-initio simulations.Solution method: Grid-based integration of the Kohn-Sham equations.Restrictions: Relativistic spin-polarized calculations are not possible. The set of exchange-correlation functionals implemented in the code does not include orbital-dependent functionals.Unusual features: The program creates pseudo-potential files suitable for the most widely used ab-initio packages and, besides the standard non-relativistic Hamann and Troullier-Martins potentials, it can generate pseudo-potentials using the relativistic and semi-core extensions to the Troullier-Martins scheme. APE also has a very sophisticated and user-friendly input system.Running time: The example given in this paper (Si) takes 10 s to run on a Pentium IV machine clocked at 2 GHz.     

Recursion method for electronic structure calculations

We present a new recursion method based on the Trotter formula for the electronic structure calculations of molecules or solids. The proposed method has the feature to be more effective at high temperatures in contrast with direct calculations methods (real space or plane waves methods).     

A web-deployed interface for performing ab initio molecular dynamics, optimization, and electronic structure in Fireball

Fireball is an ab initio technique for fast local orbital simulations of nanotechnological, solid state, and biological systems. We have implemented a convenient interface for new users and software architects in the platform-independent Java language to access Fireball's unique and powerful capabilities. The graphical user interface can be run directly from a web server or from within a larger framework such as the Computational Science and Engineering Online (CSE-Online) environment or the Distributed Analysis of Neutron Scattering Experiments (DANSE) framework. We demonstrate its use for high-throughput electronic structure calculations and a multi-100 atom quantum molecular dynamics (MD) simulation.

Program summary

Program title: FireballUICatalogue identifier: AECF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECF_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 279 784No. of bytes in distributed program, including test data, etc.: 12 836 145Distribution format: tar.gzProgramming language: JavaComputer: PC and workstationOperating system: The GUI will run under Windows, Mac and Linux. Executables for Mac and Linux are included in the package.RAM: 512 MBWord size: 32 or 64 bitsClassification: 4.14Nature of problem: The set up and running of many simulations (all of the same type), from the command line, is a slow process. But most research quality codes, including the ab initio tight-binding code FIREBALL, are designed to run from the command line. The desire is to have a method for quickly and efficiently setting up and running a host of simulations.Solution method: We have created a graphical user interface for use with the FIREBALL code. Once the user has created the files containing the atomic coordinates for each system that they are going to run a simulation on, the user can set up and start the computations of up to hundreds of simulations.Running time: 3 to 5 minutes on a 2 GHz Pentium IV processor.     

Reply to Comment on “Ewald summation technique for one-dimensional charge distributions”

We explain why the methods in Langridge, Hart and Crampin [Comput. Phys. Commun. 134 (2001) 78] suffice for the evaluation of the lattice sums entering the Madelung matrix describing multipole interactions in systems with one-dimensional translational periodicity.     

wannier90: A tool for obtaining maximally-localised Wannier functions

We present wannier90, a program for calculating maximally-localised Wannier functions (MLWF) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimising the total spread of the MLWF in real space. This is done in the space of unitary matrices that describe rotations of the Bloch bands at each k-point. As a result, wannier90 is independent of the basis set used in the underlying calculation to obtain the Bloch states. Therefore, it may be interfaced straightforwardly to any electronic structure code. The locality of MLWF can be exploited to compute band-structure, density of states and Fermi surfaces at modest computational cost. Furthermore, wannier90 is able to output MLWF for visualisation and other post-processing purposes. Wannier functions are already used in a wide variety of applications. These include analysis of chemical bonding in real space; calculation of dielectric properties via the modern theory of polarisation; and as an accurate and minimal basis set in the construction of model Hamiltonians for large-scale systems, in linear-scaling quantum Monte Carlo calculations, and for efficient computation of material properties, such as the anomalous Hall coefficient. wannier90 is freely available under the GNU General Public License from http://www.wannier.org/.

Program summary

Program title: wannier90Catalogue identifier: AEAK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 556 495No. of bytes in distributed program, including test data, etc.: 5 709 419Distribution format: tar.gzProgramming language: Fortran 90, perlComputer: any architecture with a Fortran 90 compilerOperating system: Linux, Windows, Solaris, AIX, Tru64 Unix, OSXRAM: 10 MBWord size: 32 or 64Classification: 7.3External routines:

•

BLAS (http://www/netlib.org/blas).

•

LAPACK (http://www.netlib.org/lapack).

Both available under open-source licenses.Nature of problem: Obtaining maximally-localised Wannier functions from a set of Bloch energy bands that may or may not be entangled.Solution method: In the case of entangled bands, the optimally-connected subspace of interest is determined by minimising a functional which measures the subspace dispersion across the Brillouin zone. The maximally-localised Wannier functions within this subspace are obtained by subsequent minimisation of a functional that represents the total spread of the Wannier functions in real space. For the case of isolated energy bands only the second step of the procedure is required.Unusual features: Simple and user-friendly input system. Wannier functions and interpolated band structure output in a variety of file formats for visualisation.Running time: Test cases take 1 minute.References:

[1] 

N. Marzari, D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56 (1997) 12847.

[2] 

I. Souza, N. Marzari, D. Vanderbilt, Maximally localized Wannier functions for entangled energy bands, Phys. Rev. B 65 (2001) 035109.

     

Rapid iterative method for electronic-structure eigenproblems using localised basis functions

Eigenproblems resulting from the use of localised basis functions (typically Gaussian or Slater type orbitals) in density functional electronic-structure calculations are often solved using direct linear algebra. A full implementation is presented built around an iterative method known as ‘residual minimisation—direct inversion of the iterative subspace’ (RM-DIIS) to be used to solve many similar eigenproblems in a self-consistency cycle. The method is more efficient than direct methods and exhibits superior scaling on parallel supercomputers.     

State estimation by orthogonal expansion of probability distributions

A recursive estimation scheme suitable for real-time implementation is derived for a class of nolinear systems and observations expressed as nonlinear functions in discrete time, corrupted by a non-Gaussian mutually correlated random white noise sequence. The probability densities are expanded as a Gram-Charlier series and a Gauss-Hermite quadrature formula is used for computing the expectations. In the multidimensional case an expansion about a density of mutually independent Gaussian variables is used instead of a general multidimensional Gaussian density, which may result in a poorer performance in linear systems with Gaussian noise. However, in the case of nonlinear systems and non-Gaussian noise, the computational simplifications which result, outweigh the impairment in performance if any. A computational example is included.     

改进的多分量多项式相位信号参数估计

乘积高阶模糊函数（PHAF）是以分析多分量多项式相位信号（mc-PPS）而提出来的,但实际上它抑制交叉项的能力有限,仍然难以实现mc-PPS估计。逐次滤波方法是抑制交叉项的有力工具,但存在着分量间的误差扩散;松弛法（RELAX）采用循环迭代方式,对串行估计中的误差扩散有着较强的抑制能力,将二者结合起来提出来了迭代松弛PHAF方法。通过分析被估计信号参数变化时的性能表明改进后的PHAF具有较好的鲁棒性：减少了估计盲区,具有更好的估计精度,具有较低的信噪比（SNR）门限。这些性能由mc-PPS仿真例子所验证。     

Linear optical properties of solids within the full-potential linearized augmented planewave method

We present a scheme for the calculation of linear optical properties by the all-electron full-potential linearized augmented planewave (LAPW) method. A summary of the theoretical background for the derivation of the dielectric tensor within the random-phase approximation is provided. The momentum matrix elements are evaluated in detail for the LAPW basis, and the interband as well as the intra-band contributions to the dielectric tensor are given. As an example the formalism is applied to Aluminum. The program is available as a module within the WIEN2k code.