×

Dftatom: a robust and general Schrödinger and Dirac solver for atomic structure calculations. (English) Zbl 1286.81010

Summary: A robust and general solver for the radial Schrödinger, Dirac, and Kohn-Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge-Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of \(10^{-8}\) Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number \(Z=1-92\) are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, dftatom, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.

MSC:

81-04 Software, source code, etc. for problems pertaining to quantum theory
82-04 Software, source code, etc. for problems pertaining to statistical mechanics
49S05 Variational principles of physics
81V45 Atomic physics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
82D20 Statistical mechanics of solids

Software:

Dftatom
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Martin, R. M., Electronic Structure: Basic Theory and Practical Methods (2005), Cambridge University Press
[2] Wilson, B.; Sonnad, V.; Sterne, P.; Isaacs, W., J. Quant. Spectrosc. Radiat. Transfer, 99, 658 (2006)
[3] Butler, W. H.; Dederichs, P. H.; Gonis, A.; Weaver, R. L., Application of Multiple Scattering Theory to Materials Science (1992), Materials Research Society: Materials Research Society Pittsburg, Penn.
[4] Skriver, H. L., The LMTO Method (1984), Springer: Springer Berlin
[5] Singh, D. J.; Nordstrom, L., Planewaves, Pseudopotentials, and the LAPW Method (2006), Springer: Springer New York
[6] Artacho, E., J. Phys.: Condens. Matter., 20 (2008), 2nd Workshop on Theory Meets Industry, Erwin Schrodinger Inst, Vienna, Austria, Jun 12-14, 2007
[7] Blöchl, P. E., Phys. Rev. B, 50, 17953 (1994)
[8] Marsman, M.; Kresse, G., J. Chem. Phys., 125 (2006)
[9] Vackář, J.; Šimůnek, A., Phys. Rev. B, 67 (2003)
[10] Desclaux, J. P.; Mayers, D. F.; O’Brien, F., J. Phys. B: At. Mol. Opt. Phys., 4, 631 (1971)
[11] Hamann, D. R., Phys. Rev. B, 40, 2980 (1989)
[12] Jonsson, P.; He, X.; Froese Fischer, C.; Grant, I. P., Comput. Phys. Comm., 177, 597 (2007)
[13] Froese Fischer, C., Comput. Phys. Comm., 64, 431 (1991)
[14] Tackett, A. R.; Holzwarth, N. A.W.; Matthews, G. E., Comput. Phys. Comm., 135, 348 (2001)
[15] Jia, W., Comput. Phys. Comm., 184, 9 (2013)
[17] Pask, J. E.; Sterne, P. A., Modelling Simul. Mater. Sci. Eng., 13, R71 (2005)
[18] Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P., Numerical Recipes: The Art of Scientific Computing (2007), Cambridge University Press: Cambridge University Press New York · Zbl 1132.65001
[19] Cayford, J.; Fimple, W.; Unger, D.; White, S., J. Comput. Phys., 16, 259 (1974)
[20] Tobin, F. L.; Hinze, J., J. Chem. Phys., 63, 1034 (1975)
[21] Biegler-König, F.; Hinze, J., J. Comput. Phys., 67, 290 (1986)
[22] Andrae, D.; Hinze, J., Int. J. Quantum Chem., 63, 65 (1997)
[23] Andrae, D.; Reiher, M.; Hinze, J., Int. J. Quantum Chem., 76, 473 (2000)
[24] Andrae, D.; Brodbeck, R.; Hinze, J., Int. J. Quantum Chem., 82, 227 (2001)
[25] Fischer, C. F.; Zatsarinny, O., Comput. Phys. Comm., 180, 879 (2009)
[26] Grant, I. P., J. Phys. B: At. Mol. Opt. Phys., 42 (2009)
[27] Kotochigova, S.; Levine, Z. H.; Shirley, E. L.; Stiles, M. D.; Clark, C. W., Phys. Rev. A, 55, 191 (1997)
[31] Strange, P., Relativistic Quantum Mechanics (1998), Cambridge University Press
[32] Zabloudil, J.; Hammerling, R.; Szunyogh, L.; Weinberger, P., Electron Scattering in Solid Matter (2005), Springer-Verlag: Springer-Verlag Berlin
[33] Grant, I. P., J. Phys. B: At. Mol. Opt. Phys., 41, 1 (2008)
[34] Oulne, M., Int. Rev. Phys., 4, 349 (2010)
[35] Vosko, S. H.; Wilk, L.; Nusair, M., Can. J. Phys., 58 (1980)
[36] MacDonald, A. H.; Vosko, S. H., J. Phys. C, 12 (1979)
[37] Ridley, E. C., Proc. Cambridge Philos. Soc., 51, 702 (1955)
[38] Douglas, A. S., Proc. Cambridge Philos. Soc., 52, 636 (1955)
[39] Hartree, D. R., The Calculation of Atomic Structures (1957), John Wiley & Sons, Inc.: John Wiley & Sons, Inc. New York
[40] Mayers, D. F., Proc. R. Soc. Lond. Ser. A, 241, 93 (1957)
[41] Torrance, C. C., Phys. Rev., 46, 388 (1934)
[42] Yost, W. J., Phys. Rev., 58, 557 (1940)
[43] Cohen, E. R.; Taylor, B. N., Rev. Modern Phys., 59, 1121 (1987)
[45] Kolos, W.; Wolniewicz, L., J. Chem. Phys., 50, 3228 (1969)
[46] Lin, C. S., J. Chem. Phys., 60, 4660 (1974)
[47] Connerade, J. P.; Dolmatov, V. K., J. Phys. B: At. Mol. Opt. Phys., 31, 3557 (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.