The two-electron atomic systems. S-states

A simple Mathematica program for computing the S-state energies and wave functions of two-electron (helium-like) atoms (ions) is presented. The well-known method of projecting the Schrödinger equation onto the finite subspace of basis functions was applied. The basis functions are composed of the exponentials combined with integer powers of the simplest perimetric coordinates. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of results and computation time depend on the basis size. The precise energy values of 7-8 significant figures along with the corresponding wave functions can be computed on a single processor within a few minutes. The resultant wave functions have a simple analytical form consisting of elementary functions, that enables one to calculate the expectation values of arbitrary physical operators without any difficulties.

Program summary

Program title: TwoElAtom-SCatalogue identifier: AEFK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFK_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.: 10 185No. of bytes in distributed program, including test data, etc.: 495 164Distribution format: tar.gzProgramming language: Mathematica 6.0; 7.0Computer: Any PCOperating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux SUSE 11.0RAM:?¹⁰⁹ bytesClassification: 2.1, 2.2, 2.7, 2.9Nature of problem: The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or other physical attributes from quantum mechanical calculations.Solution method: The S-wave function is expanded into a triple basis set in three perimetric coordinates. Method of projecting the two-electron Schrödinger equation (for atoms/ions) onto a subspace of the basis functions enables one to obtain the set of homogeneous linear equations F.C=0 for the coefficients C of the above expansion. The roots of equation det(F)=0 yield the bound energies.Restrictions: First, the too large length of expansion (basis size) takes the too large computation time giving no perceptible improvement in accuracy. Second, the order of polynomial Ω (input parameter) in the wave function expansion enables one to calculate the excited nS-states up to n=Ω+1 inclusive.Additional comments: The CPC Program Library includes “A program to calculate the eigenfunctions of the random phase approximation for two electron systems” (AAJD). It should be emphasized that this fortran code realizes a very rough approximation describing only the averaged electron density of the two electron systems. It does not characterize the properties of the individual electrons and has a number of input parameters including the Roothaan orbitals.Running time: ∼10 minutes (depends on basis size and computer speed)     

Revised and extended Utilities for the Ratip package

During the last years, the Ratip package has been found useful for calculating the excitation and decay properties of free atoms. Based on the (relativistic) multiconfiguration Dirac-Fock method, this program is used to obtain accurate predictions of atomic properties and to analyze many recent experiments. The daily work with this package made an extension of its Utilities [S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163] desirable in order to facilitate the data handling and interpretation of complex spectra. For this purpose, we make available an enlarged version of the Utilities which mainly supports the comparison with experiment as well as large Auger computations. Altogether 13 additional tasks have been appended to the program together with a new menu structure to improve the interactive control of the program.

Program summary

Title of program: RATIPCatalogue identifier: ADPD_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADPD_v2_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneReference in CPC to previous version: S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163Catalogue identifier of previous version: ADPDAuthors of previous version: S. Fritzsche, Department of Physics, University of Kassel, Heinrich-Plett-Strasse 40, D-34132 Kassel, GermanyDoes the new version supersede the original program?: yesComputer for which the new version is designed and others on which it has been tested: IBM RS 6000, PC Pentium II-IVInstallations: University of Kassel (Germany), University of Oulu (Finland)Operating systems: IBM AIX, Linux, UnixProgram language used in the new version: ANSI standard Fortran 90/95Memory required to execute with typical data: 300 kBNo. of bits in a word: All real variables are parameterized by a selected kind parameter and, thus, can be adapted to any required precision if supported by the compiler. Currently, the kind parameter is set to double precision (two 32-bit words) as used also for other components of the Ratip package [S. Fritzsche, C.F. Fischer, C.Z. Dong, Comput. Phys. Comm. 124 (2000) 341; G. Gaigalas, S. Fritzsche, Comput. Phys. Comm. 134 (2001) 86; S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163; S. Fritzsche, J. Elec. Spec. Rel. Phen. 114-116 (2001) 1155]No. of lines in distributed program, including test data, etc.:231 813No. of bytes in distributed program, including test data, etc.: 3 977 387Distribution format: tar.gzip fileNature of the physical problem: In order to describe atomic excitation and decay properties also quantitatively, large-scale computations are often needed. In the framework of the Ratip package, the Utilities support a variety of (small) tasks. For example, these tasks facilitate the file and data handling in large-scale applications or in the interpretation of complex spectra.Method of solution: The revised Utilities now support a total of 29 subtasks which are mainly concerned with the manipulation of output data as obtained from other components of the Ratip package. Each of these tasks are realized by one or several subprocedures which have access to the corresponding modules of the main components. While the main menu defines seven groups of subtasks for data manipulations and computations, a particular task is selected from one of these group menus. This allows to enlarge the program later if technical support for further tasks will become necessary. For each selected task, an interactive dialog about the required input and output data as well as a few additional information are printed during the execution of the program.Reasons for the new version: The requirement for enlarging the previous version of the Utilities [S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163] arose from the recent application of the Ratip package for large-scale radiative and Auger computations. A number of new subtasks now refer to the handling of Auger amplitudes and their proper combination in order to facilitate the interpretation of complex spectra. A few further tasks, such as the direct access to the one-electron matrix elements for some given set of orbital functions, have been found useful also in the analysis of data.Summary of revisions: extraction and handling of atomic data within the framework of Ratip. With the revised version, we now ‘add’ another 13 tasks which refer to the manipulation of data files, the generation and interpretation of Auger spectra, the computation of various one- and two-electron matrix elements as well as the evaluation of momentum densities and grid parameters. Owing to the rather large number of subtasks, the main menu has been divided into seven groups from which the individual tasks can be selected very similarly as before.Typical running time: The program responds promptly for most of the tasks. The responding time for some tasks, such as the generation of a relativistic momentum density, strongly depends on the size of the corresponding data files and the number of grid points.Unusual features of the program: A total of 29 different tasks are supported by the program. Starting from the main menu, the user is guided interactively through the program by a dialog and a few additional explanations. For each task, a short summary about its function is displayed before the program prompts for all the required input data.     

Interval type-2 fuzzy membership function generation methods for pattern recognition

Type-2 fuzzy sets (T2 FSs) have been shown to manage uncertainty more effectively than T1 fuzzy sets (T1 FSs) in several areas of engineering [4], [6], [7], [8], [9], [10], [11], [12], [15], [16], [17], [18], [21], [22], [23], [24], [25], [26], [27] and [30]. However, computing with T2 FSs can require undesirably large amount of computations since it involves numerous embedded T2 FSs. To reduce the complexity, interval type-2 fuzzy sets (IT2 FSs) can be used, since the secondary memberships are all equal to one [21]. In this paper, three novel interval type-2 fuzzy membership function (IT2 FMF) generation methods are proposed. The methods are based on heuristics, histograms, and interval type-2 fuzzy C-means. The performance of the methods is evaluated by applying them to back-propagation neural networks (BPNNs). Experimental results for several data sets are given to show the effectiveness of the proposed membership assignments.     

Numerical solving of the vibrational time-independent Schrödinger equation in one and two dimensions using the variational method

A program package for variational solving of the time-independent Schrödinger equation (SE) in one and two dimensions is described. The first part of the the program package includes the fitting program (FIT) with which the ab initio or DFT calculated points are fitted to a computationally inexpensive functional form. Proper fitting of the potential energy surface is crucial for the quality of the results. The second part of the package consists of a program for variational solving of the SE (2DSCHRODINGER) using either a shifted Gaussian basis set or the rectangular basis set proposed by Balint-Kurti and coworkers [J. Chem. Phys. 91 (1989) 3571]. The third part of the program package consists of the calculation of the expectation values, IR and Raman spectra XPECT), and the visualization of results (PLOT). The program package is applied to study a quantum harmonic oscillator and an intramolecular, strong hydrogen bond in picolinic acid N-oxide. For the former system analytical solutions exist, while for the latter system a comparison with the experimental data is made. The advantages and disadvantages of the applied methods are discussed.     

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials.

Program summary

Program title: KANTBPCatalogue identifier: ADZH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_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.: 4224No. of bytes in distributed program, including test data, etc.: 31 232Distribution format: tar.gzProgramming language: FORTRAN 77Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IVOperating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XPRAM: depends on (a) the number of differential equations; (b) the number and order of finite-elements; (c) the number of hyperradial points; and (d) the number of eigensolutions required. Test run requires 30 MBClassification: 2.1, 2.4External routines: GAULEG and GAUSSJ [W.H. Press, B.F. Flanery, S.A. Teukolsky, W.T. Vetterley, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986]Nature of problem: In the hyperspherical adiabatic approach [J. Macek, J. Phys. B 1 (1968) 831-843; U. Fano, Rep. Progr. Phys. 46 (1983) 97-165; C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142], a multi-dimensional Schrödinger equation for a two-electron system [A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Comm. 90 (1995) 311-339] or a hydrogen atom in magnetic field [M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352] is reduced by separating the radial coordinate ρ from the angular variables to a system of second-order ordinary differential equations which contain potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite-element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions for such systems of coupled differential equations.Solution method: The boundary problems for coupled differential equations are solved by the finite-element method using high-order accuracy approximations [A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns (E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. The generalized algebraic eigenvalue problem (A−EB)F=λDF with respect to pair unknowns (λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDLT factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials described in [Yu. A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361; O. Chuluunbaatar, A.A. Gusev, S.Y. Larsen, S.I. Vinitsky, J. Phys. A 35 (2002) L513-L525; N.P. Mehta, J.R. Shepard, Phys. Rev. A 72 (2005) 032728-1-11; O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269]. For this benchmark model the needed analytical expressions for the potential matrix elements and first-derivative coupling terms, their asymptotics and asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system.Restrictions: The computer memory requirements depend on:

•

(a) the number of differential equations;

•

(b) the number and order of finite-elements;

•

(c) the total number of hyperradial points; and

•

(d) the number of eigensolutions required.

Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMSC (when solving the scattering problem) that evaluate the asymptotics of the radial wave functions at the right boundary point in case of a boundary condition of the third type, respectively.Running time: The running time depends critically upon:

•

(a) the number of differential equations;

•

(b) the number and order of finite-elements;

•

(c) the total number of hyperradial points on interval [0,ρmax]; and

•

(d) the number of eigensolutions required.

The test run which accompanies this paper took 28.48 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.     

On ERI sorting for SIMD execution of large-scale Hartree-Fock SCF

Given the resurgent attractiveness of single-instruction-multiple-data (SIMD) processing, it is important for high-performance computing applications to be SIMD-capable. The Hartree-Fock SCF (HF-SCF) application, in it's canonical form, cannot fully exploit SIMD processing. Prior attempts to implement Electron Repulsion Integral (ERI) sorting functionality to essentially “SIMD-ify” the HF-SCF application have met frustration because of the low throughput of the sorting functionality. With greater awareness of computer architecture, we discuss how the sorting functionality may be practically implemented to provide high-performance. Overall system performance analysis, including memory locality analysis, is also conducted, and further emphasises that a system with ERI sorting is capable of very high throughput. We discuss two alternative implementation options, with one immediately accessible software-based option discussed in detail. The impact of workload characteristics on expected performance is also discussed, and it is found that in general as basis set size increases the potential performance of the system also increases. Consideration is given to conventional CPUs, GPUs, FPGAs, and the Cell Broadband Engine architecture.     

DAMQT: A package for the analysis of electron density in molecules

DAMQT is a package for the analysis of the electron density in molecules and the fast computation of the density, density deformations, electrostatic potential and field, and Hellmann-Feynman forces. The method is based on the partition of the electron density into atomic fragments by means of a least deformation criterion. Each atomic fragment of the density is expanded in regular spherical harmonics times radial factors, which are piecewise represented in terms of analytical functions. This representation is used for the fast evaluation of the electrostatic potential and field generated by the electron density and nuclei, as well as for the computation of the Hellmann-Feynman forces on the nuclei. An analysis of the atomic and molecular deformations of the density can be also carried out, yielding a picture that connects with several concepts of the empirical structural chemistry.

Program summary

Program title: DAMQT1.0Catalogue identifier: AEDL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDL_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPLv3No. of lines in distributed program, including test data, etc.: 278 356No. of bytes in distributed program, including test data, etc.: 31 065 317Distribution format: tar.gzProgramming language: Fortran90 and C++Computer: AnyOperating system: Linux, Windows (Xp, Vista)RAM: 190 MbytesClassification: 16.1External routines: Trolltech's Qt (4.3 or higher) (http://www.qtsoftware.com/products), OpenGL (1.1 or higher) (http://www.opengl.org/), GLUT 3.7 (http://www.opengl.org/resources/libraries/glut/).Nature of problem: Analysis of the molecular electron density and density deformations, including fast evaluation of electrostatic potential, electric field and Hellmann-Feynman forces on nuclei.Solution method: The method of Deformed Atoms in Molecules, reported elsewhere [1], is used for partitioning the molecular electron density into atomic fragments, which are further expanded in spherical harmonics times radial factors. The partition is used for defining molecular density deformations and for the fast calculation of several properties associated to density.Restrictions: The current version is limited to 120 atoms, 2000 contracted functions, and lmax=5 in basis functions. Density must come from a LCAO calculation (any level) with spherical (not Cartesian) Gaussian functions.Unusual features: The program contains an OPEN statement to binary files (stream) in file GOPENMOL.F90. This statement has not a standard syntax in Fortran 90. Two possibilities are considered in conditional compilation: Intel's ifort and Fortran2003 standard. This latter is applied to compilers other than ifort (gfortran uses this one, for instance).Additional comments: The distribution file for this program is over 30 Mbytes and therefore is not delivered directly when download or e-mail is requested. Instead a html file giving details of how the program can be obtained is sent.Running time: Largely dependent on the system size and the module run (from fractions of a second to hours).References: [1] J. Fernández Rico, R. López, I. Ema, G. Ramírez, J. Mol. Struct. (Theochem) 727 (2005) 115.     

Analogue evolutionary brain computer interfaces [Application Notes]

The keyboard is a device that, with its many switches, provides us with an interface that is reliable but also very unnatural. The mouse is only slightly less primitive, being an electro-mechanical transducer of musculoskeletal movement. Both have been with us for decades, yet they are unusable for people with severe musculoskeletal disorders and are themselves known causes of work-related upperlimb and back disorders, both hugely widespread problems [1], [2]. It will be a major contribution to computer interface technology one day to be able to replace mouse and keyboard with Brain-Computer Interfaces (BCIs) capable of directly interpreting the desires and intentions of computer users.     

KANTBP 2.0: New version of a program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

A FORTRAN 77 program for calculating energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach is presented. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with homogeneous boundary conditions: (i) the Dirichlet, Neumann and third type at the left and right boundary points for continuous spectrum problem, (ii) the Dirichlet and Neumann type conditions at left boundary point and Dirichlet, Neumann and third type at the right boundary point for the discrete spectrum problem. The resulting system of radial equations containing the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite element method. As a test desk, the program is applied to the calculation of the reaction matrix and radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field. This version extends the previous version 1.0 of the KANTBP program [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675].

Program summary

Program title: KANTBPCatalogue identifier: ADZH_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v2_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.: 20 403No. of bytes in distributed program, including test data, etc.: 147 563Distribution format: tar.gzProgramming language: FORTRAN 77Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IVOperating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XPRAM: This depends on

1.

the number of differential equations;

2.

the number and order of finite elements;

3.

the number of hyperradial points; and

4.

the number of eigensolutions required.

The test run requires 2 MBClassification: 2.1, 2.4External routines: GAULEG and GAUSSJ [2]Nature of problem: In the hyperspherical adiabatic approach [3-5], a multidimensional Schrödinger equation for a two-electron system [6] or a hydrogen atom in magnetic field [7-9] is reduced by separating radial coordinate ρ from the angular variables to a system of the second-order ordinary differential equations containing the potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions of the continuum spectrum for such systems of coupled differential equations on finite intervals of the radial variable ρ∈[ρmin,ρmax]. This approach can be used in the calculations of effects of electron screening on low-energy fusion cross sections [10-12].Solution method: The boundary problems for the coupled second-order differential equations are solved by the finite element method using high-order accuracy approximations [13]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns (E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [14]. The generalized algebraic eigenvalue problem (A−EB)F=λDF with respect to pair unknowns (λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDLT factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [14]. As a test desk, the program is applied to the calculation of the reaction matrix and corresponding radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field described in [9] on finite intervals of the radial variable ρ∈[ρmin,ρmax]. For this benchmark model the required analytical expressions for asymptotics of the potential matrix elements and first-derivative coupling terms, and also asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system.Restrictions: The computer memory requirements depend on:

1.

the number of differential equations;

2.

the number and order of finite elements;

3.

the total number of hyperradial points; and

4.

the number of eigensolutions required.

Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Section 3 and [1] for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should also supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMS0 and ASYMSC (when solving the scattering problem) which evaluate asymptotics of the radial wave functions at left and right boundary points in case of a boundary condition of the third type for the above problems.Running time: The running time depends critically upon:

1.

the number of differential equations;

2.

the number and order of finite elements;

3.

the total number of hyperradial points on interval [ρmin,ρmax]; and

4.

the number of eigensolutions required.

The test run which accompanies this paper took 2 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.References:[1] O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675; http://cpc.cs.qub.ac.uk/summaries/ADZHv10.html.[2] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986.[3] J. Macek, J. Phys. B 1 (1968) 831-843.[4] U. Fano, Rep. Progr. Phys. 46 (1983) 97-165.[5] C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142.[6] A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Commun. 90 (1995) 311-339.[7] M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352.[8] O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, L.A. Melnikov, V.V. Serov, S.I. Vinitsky, J. Phys. A 40 (2007) 11485-11524.[9] O. Chuluunbaatar, A.A. Gusev, V.P. Gerdt, V.A. Rostovtsev, S.I. Vinitsky, A.G. Abrashkevich, M.S. Kaschiev, V.V. Serov, Comput. Phys. Commun. 178 (2007) 301 330; http://cpc.cs.qub.ac.uk/summaries/AEAAv10.html.[10] H.J. Assenbaum, K. Langanke, C. Rolfs, Z. Phys. A 327 (1987) 461-468.[11] V. Melezhik, Nucl. Phys. A 550 (1992) 223-234.[12] L. Bracci, G. Fiorentini, V.S. Melezhik, G. Mezzorani, P. Pasini, Phys. Lett. A 153 (1991) 456-460.[13] A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Commun. 85 (1995) 40-64.[14] K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982.     

FRODO: a MuPAD program to calculate matrix elements between contracted wavefunctions

A symbolic program performing the Formal Reduction of Density Operators (FRODO) has been developed in the MuPAD computer algebra system with the purpose of evaluating the matrix elements of the electronic Hamiltonian between internally contracted functions in a complete active space (CAS) scheme. The program is illustrated making use of two meaningful examples.

Program summary

Title of program:FRODOCatalogue identifier:ADVYProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVYProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer:Any computer on which the MuPAD computer algebra system can be installedOperating systems under which the program has been tested:LinuxProgramming language used:MuPAD vs. 2.5.3 for LinuxNo. of lines in distributed program, including test data, etc.:3939No. of bytes in distributed program, including test data, etc.:19 661Distribution format:tar.gzNature of physical problem: In order to improve on the CAS-SCF wavefunction one can resort to multireference perturbation theory or configuration interaction based on internally contracted functions (ICF) which are obtained by application of the excitation operators to the reference CAS-SCF wavefunction. The formulation of such matrix elements is quite cumbersome and a computer algebra system like MuPAD appears ideally suited to perform such a task.Method of solution: The method adopted consists in successively eliminating all occurrences of inactive orbital indices (core and virtual) from the products of excitation operators which appear in the definition of the ICF's and in the electronic Hamiltonian expressed in the second quantization formalism.Restrictions due to the complexity of the problem: The program is limited to no more than doubly excited ICF's.     

Atomic self-consistent-field program by the basis set expansion method: Columbus version

A revised and extended (Columbus) version of the Chicago atomic self-consistent-field (Hartree-Fock) program of 1963 is described. Its principal present use is in developing Gaussian basis sets for molecular calculations. Complete memory allocation (using Fortran 90) has been added as well as improved integral formulas and efficient and simple programming features. Energy-expression coefficients have been added sufficient to treat the ground states of all atoms to the extent that Russell-Saunders (LS) coupling applies. Excited states with large angular-momentum orbitals can be treated. Relativistic effects can be included to the extent possible with relativistic effective core potentials. A review of earlier work is included.

Program summary

Program title: atmscfCatalogue identifier: ADVRProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVRProgram available from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming language: Fortran 90Computer: Sun, SGI, PCOperating system: Solaris, Irix, LinuxRAM: 10 MbytesNo. of lines in distributed program, including test data, etc.: 2113No. of bytes in distributed program, including test data, etc.: 15 379Distribution format: tar.gzNature of problem: Energies and wave functions, at the Hartree-Fock levelSolution method: Expansions in Gaussian or Slater functions. Iterative minimization of the total energy. Optimization of exponential parameters. Used frequently for developing Gaussian basis sets for molecular useRunning time: Typical 30 s per calculation     

ERI sorting for emerging processor architectures

Electron Repulsion Integrals (ERIs) are a common bottleneck in ab initio computational chemistry. It is known that sorted/reordered execution of ERIs results in efficient SIMD/vector processing. This paper shows that reconfigurable computing and heterogeneous processor architectures can also benefit from a deliberate ordering of ERI tasks. However, realizing these benefits as net speedup requires a very rapid sorting mechanism. This paper presents two such mechanisms. Included in this study are analytical, simulation-based, and experimental benchmarking approaches to consider five use cases for ERI sorting, i.e. SIMD processing, reconfigurable computing, limited address spaces, instruction cache exploitation, and data cache exploitation. Specific consideration is given to existing cache-based processors, FPGAs, and the Cell Broadband Engine processor. It is proposed that the analyses conducted in this work should be built upon to aid the development of software autotuners which will produce efficient ab initio computational chemistry codes for a variety of computer architectures.     

An improved version of ISICS: a program for calculating K-, L- and M-shell cross sections from PWBA and ECPSSR theory using a personal computer

The C program, ISICS [Z. Liu, S.J. Cipolla, Comput. Phys. Comm. 97 (1996) 315-330], which calculates ionization and X-ray production cross-sections using PWBA and ECPSSR theory, has been enhanced to include new options, correct some minor flaws, and to make the program more versatile.

Program summary

Title of program: ISICSCatalog identifier: ADDS_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADDS_v2_0Program available from: CPC Program Library, Queen's University of Belfast, N. IrelandOperating system under which the program has been tested: WINDOWS XPProgram language used: CComputer: 80486 or higher-level PCsNo. of lines in distributed program, including test data, etc.: 5343No. of bytes in distributed program, including test data, etc.: 151 838Distribution format: tar.gzCatalogue identifier of previous version: ADDSJournal reference of previous version: Comput. Phys. Comm. 97 (1996) 315-330Does the new version supersede the previous version: YesNature of the physical problem: Ionization and X-ray production cross-section calculations for ion-atom collisions.Reasons for new version: Increased functionality and new options.Summary of revisions: Option for the united-atom approximation for binding-energy correction; easier inputting of updated atomic parameters; extension of projectile energy down to eV range; accounting for DHS wave function in K-shell ionization; other miscellaneous changes.Method of solution: Numerical integration of form factor using a logarithmic transform and Gaussian quadrature, plus exact integration limits.Restrictions on the complexity of the problem: The consumed CPU time increases with the atomic shell (K, L, M), but execution is still very fast.Typical running time: No change from previous version.Unusual features of the program: No     

基于有阶为7的自同构的二元双偶编码[56,28,12]的研究

编码纠错、检错是计算机应用中最重要的操作手段之一，双偶编码在其中有着重要作用，但目前对长度较大的编码却研究甚少，尤其在对编码分类问题的研究中遇到较大困难。针对此问题，本文给出了所有有阶为7的自同构的二元极大双偶编码[56，28，12]，在等价关系下有499种这样的编码，从而使这类编码得到彻底解决。     

An application of the interpolating scaling functions to wave packet propagation

The wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an equidistantly spaced grid. They have compact support of the size determined by the order of the underlying interpolating polynomial. In this basis the potential energy matrix is diagonal. The kinetic energy matrix is sparse, and in the 1D case, has a band-diagonal structure. An important future of the basis is that matrix elements of a Hamiltonian are exactly computed by means of simple algebraic transformations efficiently implemented numerically. Therefore, the number of grid points and the order of the underlying interpolating polynomial can easily be varied allowing one to approach the accuracy of pseudospectral methods in a regular manner, similar to the high order finite difference methods. The results for the calculation of the H+H₂ collinear collision shows that the ISF provide one with an accurate and efficient representation for use in wave packet propagation method.