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.     

Issues and challenges in orbital-free density functional calculations

Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudopotential calculations and, if the latter, construction of the pseudopotential. Another is the stability, speed, and accuracy of solution algorithms. Underlying both is the fundamental issue of satisfactory quality of the approximate functionals (kinetic energy and exchange–correlation). We address both computational issues and illustrate them by some comparative performance testing of our recently developed modified-conjoint generalized gradient approximation kinetic energy functionals. Comparisons are given for atoms, diatomic molecules, and some simple solids.     

A scaling theory for linear systems

In this paper we develop a theory of scaling for rational (transfer) functions in terms of transformation groups. In particular, we identify two different four-parameter scaling groups which play natural roles in studying linear systems and investigate the effect of scaling on Fisher information and related statistical measures in system identification. The scalings considered include change of time scale, feedback, exponential scaling, magnitude scaling, etc. The scaling action of the groups studied in this paper is tied to the geometry of transfer functions in a rather strong way as becomes apparent in our examination of the invariants of scaling. As a result, the scaling process also provides new insight into the parameterization question for rational functions.     

A program to generate a basis set adaptive radial quadrature grid for density functional theory

We present an automatic quadrature routine (AQR) which generates an atomic basis set adaptive radial quadrature grid for the numerical evaluation of molecular integrands in density functional theory. Unlike the popular radial grids that are tuned to a particular class of integrands and rely on a fixed selection of points, our grid adapts itself automatically to the atomic shell structure of any radial integrand and determines the best number of quadrature points that provides user specified accuracy. We evaluate the performance of our radial grid on various tight, diffuse, and noble gas atom radial integrands. We conclude that the radial quadrature grid generated by our AQR is generally comparable to and sometimes better than the best ranked popular radial grids in efficiency and reliability.     

Plato: A localised orbital based density functional theory code

The Plato package allows both orthogonal and non-orthogonal tight-binding as well as density functional theory (DFT) calculations to be performed within a single framework. The package also provides extensive tools for analysing the results of simulations as well as a number of tools for creating input files. The code is based upon the ideas first discussed in Sankey and Niklewski (1989) [1] with extensions to allow high-quality DFT calculations to be performed. DFT calculations can utilise either the local density approximation or the generalised gradient approximation. Basis sets from minimal basis through to ones containing multiple radial functions per angular momenta and polarisation functions can be used. Illustrations of how the package has been employed are given along with instructions for its utilisation.

Program summary

Program title: PlatoCatalogue identifier: AEFC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_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.: 219 974No. of bytes in distributed program, including test data, etc.: 1 821 493Distribution format: tar.gzProgramming language: C/MPI and PERLComputer: Apple Macintosh, PC, Unix machinesOperating system: Unix, Linux and Mac OS XHas the code been vectorised or parallelised?: Yes, up to 256 processors testedRAM: Up to 2 Gbytes per processorClassification: 7.3External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTWNature of problem: Density functional theory study of electronic structure and total energies of molecules, crystals and surfaces.Solution method: Localised orbital based density functional theory.Restrictions: Tight-binding and density functional theory only, no exact exchange.Unusual features: Both atom centred and uniform meshes available. Can deal with arbitrary angular momenta for orbitals, whilst still retaining Slater–Koster tables for accuracy.Running time: Test cases will run in a few minutes, large calculations may run for several days.     

Libxc: A library of exchange and correlation functionals for density functional theory

The central quantity of density functional theory is the so-called exchange–correlation functional. This quantity encompasses all non-trivial many-body effects of the ground-state and has to be approximated in any practical application of the theory. For the past 50 years, hundreds of such approximations have appeared, with many successfully persisting in the electronic structure community and literature. Here, we present a library that contains routines to evaluate many of these functionals (around 180) and their derivatives.Program summaryProgram title: LIBXCCatalogue identifier: AEMU_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU Lesser General Public License version 3No. of lines in distributed program, including test data, etc.: 87455No. of bytes in distributed program, including test data, etc.: 945365Distribution format: tar.gzProgramming language: C with Fortran bindings.Computer: All.Operating system: All.RAM: N.A.Classification: 7.3, 16.1.Nature of problem: Evaluation of the exchange–correlation energy functional and its derivatives. This is a fundamental part of any atomic, molecular, or solid-state code that uses density-functional theory.Solution method: The values of the energy functional and its derivatives are given in a real grid of mesh points.Running time: Typically much smaller than the remainder of the electronic structure code. The running time has a natural linear scaling with the number of grid points.     

乙炔基双二茂铁丙烷衍生物的密度泛函理论研究

为揭示取代基对金属有机化合物乙炔基双二茂铁丙烷电子结构的影响,采用密度泛函理论方法模拟计算了乙炔基双二茂铁丙烷及其2个衍生物苯炔基双二茂铁丙烷及二茂铁炔基双二茂铁丙烷的电子结构、前线轨道、电离能(IP)以及电子亲和势(EA),并讨论了取代基对化合物能级和能隙的影响。计算结果表明,电子在基态与激发态间的跃迁,主要是发生在双二茂铁丙烷和乙炔基苯或乙炔基二茂铁之间。取代基为苯基时化合物最高占据轨道(HOMO)能级降低量小于最低空轨道(LUMO)能级降低量,因此二者之间的能隙总体降低。取代基为二茂铁基时化合物HOMO能级增加,LUMO能级降低,从而使HOMO-LUMO能隙降低。结合化合物6-苯炔基双二茂铁丙烷电子亲和势最大以及化合物6-二茂铁炔基双二茂铁丙烷电离能最小,可见苯基取代使炔基双二茂铁丙烷类化合物电子传输能力增强,而二茂铁基取代则可以使该类化合物的空穴传输能力增强,这使炔基双二茂铁丙烷类化合物在功能导电材料方面具有较好的应用前景。     

Accurate finite element method for atomic calculations based on density functional theory and Hartree–Fock method

An accurate finite element method is developed for atomic calculations based on density functional theory (DFT) within local density approximation (LDA) and Hartree–Fock (HF) method. The radial wave functions are expanded by cubic Hermite spline functions on a uniform mesh for , and all the associated integrals are analytically evaluated in conjunction with fitting procedures of the Hartree and the exchange–correlation potentials to the same cubic Hermite spline functions using a set of recurrence formulas. The total energy of atoms systematically converges from above, and the error algebraically decays as the mesh spacing decreases. When the mesh spacing d is taken to be , the total energy for an atom of atomic number Z can be calculated within error of ¹⁰−7 hartree for both the LDA and HF methods. The equal applicability of the method to DFT and the HF method with a similar degree of high accuracy enables the method to be a reliable platform for development of new functionals in DFT such as hybrid functionals.     

POLYRATE: A general computer program for variational transition state theory and semiclassical tunneling calculations of chemical reaction rates

We present a computer program for calculating rate constants of gas-phase chemical reactions involving one or two reactants with a total of three to ten atoms. The program accepts information about the potential energy surface in the form of either an analytic potential energy function or a sequence of geometries, energies, gradients and second (or higher) derivative matrices at points along the reaction path. In the former case the program itself calculates the reaction pathe and the sequence of derivative matrices. From this information the program calculates the rate constant for quantized internal degrees of freedom and classical reaction-path motion by variational transition state theory (VTST). The probabilities for tunneling and nonclassical reflection are estimated by semiclassical methods and incorporated by a transmission coefficient, which for thermal reactions is based on the ground state. There are several options for including the effects of anharmonicity in the independent-normal-mode approximation, and the reaction-path curvature may be included in the tunneling calculation by the small-curvature approximation. The article also presents test calculations illustrating the use of new reaction-path interpolation and extrapolation procedures which should be useful in conjunction with VTST calculations based on ab initio gradients and Hessian calculations.     

金属卟啉与咪唑及吡啶轴向配位作用的密度泛函理论研究

为了考察金属卟啉与含氮杂环化合物之间的轴向配位作用,本文采用密度泛函理论方法研究了中心金属分别为铁、锰、钴的3种金属卟啉与咪唑及吡啶2种轴向配体之间形成的配位络合物,从几何结构、相互作用能方面考察了配位络合物的稳定性、并从电荷和前线分子轨道能级方面解释了所形成配位络合物稳定性的差异。计算结果表明,具有不同中心金属离子的卟啉与不同轴向配体之间的配位作用也不同,卟啉中心金属的正电性越强,其与咪唑及吡啶所形成的配位络合物越稳定。3种金属卟啉中,铁卟啉中心金属具有较多的正电荷,更易与咪唑或吡啶发生轴向配位作用形成稳定的配位络合物。与吡啶相比,咪唑与金属卟啉之间的配位作用更强,形成的配位络合物更稳定。     

NBI: A fortran program for molecular mechanics calculations on a microcomputer

A FORTRAN program for simple molecular mechanics calculations under the rigid-rotor approximation is presented. The program uses a potential energy function built up from cosine-type functions, for torsional terms, and modified Buckingham functions plus a Coulombic term, for non-bonded interaction. Although no automatic parameter optimization is implemented, “manual” parameter improvements can be performed very easily.     

Structures and spectroscopic properties of nonperipherally and peripherally substituted metal-free phthalocyanines: a substitution effect study based on density functional theory calculations

The molecular structures, molecular orbitals, atomic charges, electronic absorption spectra, and infrared (IR) and Raman spectra of a series of substituted metal-free phthalocyanine compounds with four (1, 3, 5, 7) or eight (2, 4, 6, 8) methoxyl (1, 2, 5, 6) or methylthio groups (3, 4, 7, 8) on the nonperipheral (1-4) or peripheral positions (5-8) of the phthalocyanine ring are studied by density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations. The calculated structural parameters and simulated electronic absorption and IR spectra are compared with the X-ray crystallography structures and the experimentally observed electronic absorption and IR spectra of the similar molecules, and good agreement between the calculated and experimental results is found. The substitution of the methoxyl or methylthio groups at the nonperipheral positions of the phthalocyanine ring has obvious effects on the molecular structure and spectroscopic properties of the metal-free phthalocyanine. Nonperipheral substitution has a more significant influence than peripheral substitution. The substitution effect increases with an increase in the number of substituents. The methylthio group shows more significant influence than the methoxyl group, despite the stronger electron-donating property of the methoxyl group than the methylthio group. The octa-methylthio-substituted metal-free phthalocyanine compounds have nonplanar structures whose low-lying occupied molecular orbitals and electronic absorption spectra are significantly changed by the substituents. The present systematical study will be helpful for understanding the relationship between structures and properties in phthalocyanine compounds and designing phthalocyanines with typical properties.     

Lambda-hoisting: A transformation technique for fully lazy evaluation of functional programs

Lambda-hoisting is a technique for transforming functional programs into ones suitable for fully lazy evaluation. The proposed method has a great advantage in generating efficient code for conventional computers. The basic idea of lambda-hoisting is described with remarks on similar techniques, and a simple algorithm is presented in a formal way.     

A model for semiconductor quantum dot molecule based on the current spin density functional theory

Based on the current spin density functional theory, a theoretical model of three vertically aligned semiconductor quantum dots is proposed and numerically studied. This quantum dot molecule (QDM) model is treated with realistic hard-wall confinement potential and external magnetic field in three-dimensional setting. Using the effective-mass approximation with band nonparabolicity, the many-body Hamiltonian results in a cubic eigenvalue problem from a finite difference discretization. A self-consistent algorithm for solving the Schrödinger-Poisson system by using the Jacobi-Davidson method and GMRES is given to illustrate the Kohn-Sham orbitals and energies of six electrons in the molecule with some magnetic fields. It is shown that the six electrons residing in the central dot at zero magnetic field can be changed to such that each dot contains two electrons with some feasible magnetic field. The Förster-Dexter resonant energy transfer may therefore be generated by two individual QDMs. This may motivate a new paradigm of Fermionic qubits for quantum computing in solid-state systems.     

A Lyapunov theory for linear time-delay systems

Some relationships between a Lyapunov based stability test and linear control system models with time delays are explored. The main result is a generalization of the result that if (A, B) is a reachable pair of matrices, then squareAis a stability matrix if and only if there is a positive-definite matrixKsuch thatAK + KA' = - BB'.     

micrOMEGAs 2.0: A program to calculate the relic density of dark matter in a generic model

micrOMEGAs 2.0 is a code which calculates the relic density of a stable massive particle in an arbitrary model. The underlying assumption is that there is a conservation law like R-parity in supersymmetry which guarantees the stability of the lightest odd particle. The new physics model must be incorporated in the notation of CalcHEP, a package for the automatic generation of squared matrix elements. Once this is done, all annihilation and coannihilation channels are included automatically in any model. Cross-sections at v=0, relevant for indirect detection of dark matter, are also computed automatically. The package includes three sample models: the minimal supersymmetric standard model (MSSM), the MSSM with complex phases and the NMSSM. Extension to other models, including non-supersymmetric models, is described.

Program summary

Title of program:micrOMEGAs2.0Catalogue identifier:ADQR_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADQR_v2_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputers for which the program is designed and others on which it has been tested:PC, Alpha, Mac, SunOperating systems under which the program has been tested:UNIX (Linux, OSF1, SunOS, Darwin, Cygwin)Programming language used:C and FortranMemory required to execute with typical data:17 MB depending on the number of processes requiredNo. of processors used:1Has the code been vectorized or parallelized:noNo. of lines in distributed program, including test data, etc.:91 778No. of bytes in distributed program, including test data, etc.:1 306 726Distribution format:tar.gzExternal routines/libraries used:noCatalogue identifier of previous version:ADQR_v1_3Journal reference of previous version:Comput. Phys. Comm. 174 (2006) 577Does the new version supersede the previous version:yesNature of physical problem:Calculation of the relic density of the lightest stable particle in a generic new model of particle physics.Method of solution: In numerically solving the evolution equation for the density of dark matter, relativistic formulae for the thermal average are used. All tree-level processes for annihilation and coannihilation of new particles in the model are included. The cross-sections for all processes are calculated exactly with CalcHEP after definition of a model file. Higher-order QCD corrections to Higgs couplings to quark pairs are included.Reasons for the new version:There are many models of new physics that propose a candidate for dark matter besides the much studied minimal supersymmetric standard model. This new version not only incorporates extensions of the MSSM, such as the MSSM with complex phases, or the NMSSM which contains an extra singlet superfield but also gives the possibility for the user to incorporate easily a new model. For this the user only needs to redefine appropriately a new model file.Summary of revisions:

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Possibility to include in the package any particle physics model with a discrete symmetry that guarantees the stability of the cold dark matter candidate (LOP) and to compute the relic density of CDM.

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Compute automatically the cross-sections for annihilation of the LOP at small velocities into SM final states and provide the energy spectra for final states.

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For the MSSM with input parameters defined at the GUT scale, the interface with any of the spectrum calculator codes reads an input file in the SUSY Les Houches Accord format (SLHA).

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Implementation of the MSSM with complex parameters (CPV-MSSM) with an interface to CPsuperH to calculate the spectrum.

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Routine to calculate the electric dipole moment of the electron in the CPV-MSSM.

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In the NMSSM, new interface compatible with NMHDECAY2.1.

Typical running time:0.2 secUnusual features of the program:Depending on the parameters of the model, the program generates additional new code, compiles it and loads it dynamically.     

A new method for solving an arbitrary fully fuzzy linear system

In this paper, We propose a simple and practical method (that works only for triangular fuzzy numbers) to solve an arbitrary fully fuzzy linear system (FFLS) in the form $\widetilde{A}\otimes \widetilde{x}=\widetilde{b},$ where $\widetilde{A}_{n \times n}$ is a fuzzy matrix, $\widetilde{x}$ and $\widetilde{b}$ are n × 1 fuzzy vectors. The idea of the presented method is constructed based on the extending 0-cut and 1-cut solution of original fully fuzzy linear systems (FFLS). We also define a fuzzy solution of FFLS and establish the necessary and sufficient conditions for the uniqueness of a fuzzy solution.     

CO在贵金属Pt(111)表面吸附的密度泛函理论研究

采用密度泛函理论研究CO在Pt(111)表面的吸附位和活化机理。研究采用三维周期结构取代以往的团簇模型,消除金属表面结构选择对计算结果的影响。结果表明,CO在不同的表面活性位吸附后C-O键有不同程度的增长,即C-O键均不同程度地削弱,从而活化CO分子。经比较吸附能、化学键参数和CO重叠布居数,发现在顶位、桥位、hcp空穴位和fcc空穴位4个吸附位中,fcc空穴位是CO的最佳活性位。通过考察原子轨道电子变化,分析CO在Pt(111)表面的吸附活化机理,得到了CO分子在Pt(111)表面吸附的σ／π键作用机理。     

FEXPAC: a program for linear discriminant classification

A new program for feature extraction and two-class classification utilizing the Fisher linear discriminant function model has been developed. It is intended as a tool in multivariate data analysis, and is especially suited for the design and storage of linear classifiers from training data sets.     

Structures and properties of 1,8,15,22-tetrasubstituted phthalocyaninato zinc and nickel complexes: Substitution and axially coordination effects study based on density functional theory calculations

On the basis of the density functional theory (DFT) calculation of ZnPc (1), Zn[Pc(α-OC₅H₁₁)₄] (2), Ni[Pc(α-OC₅H₁₁)₄] (3), and Zn[Pc(α-OC₅H₁₁)₄]·H₂O (4), the effects of non-peripheral substitution, different transition metals, and axial water coordination on the molecular structure, molecular orbital, atomic charge, infrared (IR) spectrum, and electronic absorption spectrum were investigated. The calculation results reveal that bulky 3-pentyloxy groups at the non-peripheral positions of the phthalocyanine ring evince great changes in structure and properties: they deflect the isoindole units, lift the frontier molecular orbitals, alter the atomic charge distribution, shift the bands of IR and electronic absorption spectra, etc. Though the central metal can shorten or lengthen the bond length, its effect on the electronic structure and properties of the phthalocyanine complex is very limited. Axial coordination significantly enhances the non-planarity of the phthalocyanine ring and, thus, alters the electronic structure, which is important for the formation of novel dimeric supramolecular structures through intermolecular hydrogen bonds. In addition, the calculated structures of 3 as well as the simulated IR and electronic absorption spectra of 4 were compared with the experimental data and showed good agreement.