Abstract
We show how to implement a Full Potential Multiple Scattering (fpms) code based on a real-space FPMS theory valid for both continuum and bound states, under conditions for space partitioning that are less restrictive than those applied so far. This theory is free from the need to expand cell shape functions in spherical harmonics or to use rectangular matrices. Tests of the program show that it is able to reproduce with very good accuracy known solutions of the Schrödinger equation. Applications to the spectroscopy of low dimensional systems, such as one-dimensional (1D) chain like systems, 2D layered systems and 3D diamond structure systems, where the Muffin-Tin approximation is known to give very poor results, show a remarkable improvement toward the agreement with experiments. The default mode of the code uses superimposed atomic charge densities, which works satisfactorily in most of the applications, but with help of the es2ms interface, incorporated in the program, one can also use self-consistent charge densities derived from the vasp program. The program is also incorporated in the photoelectron diffraction code msspec and parallelized for energy point.
Keywords
- MS Theory
- Photoelectron Diffraction
- Rectangular Matrices
- Ballistic Electron Emission Microscopy
- Radial Mesh Points
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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J. Korringa, Physica 13, 392–400 (1947)
W. Kohn, N. Rostoker, Phys. Rev. 94, 1111–1120 (1954)
J.C. Slater, K.H. Johnson, Phys. Rev. B 5, 844–853 (1972)
D. Dill, J.L. Dehmer, J. Chem. Phys. 61, 692–699 (1974)
K. Hatada, K. Hayakawa, M. Benfatto, C.R. Natoli, Phys. Rev. B 76, 060102R1–4 (2007)
K. Hatada, K. Hayakawa, M. Benfatto, C.R. Natoli, J. Phys.: Condens. Matter 21, 104206 (2009)
K. Hatada, K. Hayakawa, M. Benfatto, C.R. Natoli, J. Phys.: Condens. Matter 22, 185501 (2010)
J. Xu, P. Krüger, C.R. Natoli, K. Hayakawa, Z. Wu, K. Hatada, Phys. Rev. B 92, 125408–1–11 (2015)
O.K. Andersen, Phys. Rev. B 12, 3060–3083 (1975)
A.R. Williams, J.W. van Morgan, J. Phys. C: Solid State Phys. 7, 37–60 (1974)
N. Papanikolau, R. Zeller, P.H. Dederich, J. Phys.: Condens. Matter 14, 2799–2823 (2002)
A. Gonis, W.H. Butler, Multiple Scattering in Solids (Springer Science & Business Media, New York, 2012)
G. Breit, H.A. Bethe, Phys. Rev. 93, 888–890 (1954)
L.F. Canto, M.S. Hussein, Scattering Theory of Molecules, Atoms and Nuclei (World Scientific, Singapore, 2013)
W.H. Butler, A. Gonis, X.G. Zhang, Phys. Rev. B 45, 11527–11541 (1992)
D. Sebilleau, R. Gunnella, Z.-Y. Wu, S. Di Matteo, C.R. Natoli, J. Phys.: Condens. Matter 18, R175–R230 (2006)
V.I. Lebedev, Comput. Math. Math. Phys. 15, 44–51 (1975)
X.G. Wang, T. Carrington Jr., J. Theor. Comput. Chem. 4, 599–608 (2003)
M. Abramowitz, I.N. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Goverment Printing Office, Washington, 1972)
A.D. Becke, J. Chem. Phys. 88, 2547–2553 (1988)
V.F. Brastev, Atomic Wavefunctions (Nauka, Moscow, 1966)
S. Flügge, Practical Quantum Mechanics, Springer study edn. (Springer, Berlin, 1974), problem 22, p. 42
M. Benfatto, C.R. Natoli, A. Bianconi, J. Garcia, A. Marcelli, M. Fanfoni, I. Davoli, Phys. Rev. B 34, 5774–5781 (1986)
F.G. Tricomi, Integral Equations (Courier Dover Publications, New York, 1985)
R.G. Newton, Scattering Theory of Waves and Particles, 2nd edn. (Courier Dover Publications, New York, 2002)
A. Gonis, W.H. Butler, Multiple Scattering in Solids (Springer, New York, 2000), and references therein
E.T. Whittaker, G.N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1965)
R.V. Vedrinskii, A.A. Novakovich, Phys. Met. Metallogr. 39, 7–15 (1975)
D. Pacilé, M. Papagno, A.F. Rodríguez, M. Grioni, L. Papagno, Ç.Ö. Girit, J.C. Meyer, G.E. Begtrup, A. Zettl, Phys. Rev. Lett. 101, 066806 (2008)
K. Hatada, J. Xu, K. Hayakawa, C.R. Natoli (2005), https://www.lnf.infn.it/theory/CondensedMatter/fpms.html
G. Subías, J. Herrero-Martín, J. García, J. Blasco, C. Mazzoli, K. Hatada, S. Di Matteo, C.R. Natoli, Phys. Rev. B 75, 235101 (2007)
X. Junqing, C.R. Natoli, P. Krüger, K. Hayakawa, D. Sébilleau, L. Song, K. Hatada, Comput. Phys. Commun. 203, 331–338 (2016)
G. Kresse, D. Joubert, Phys. Rev. B 59, 1758–1775 (1999)
K. Hayakawa, K. Hatada, S. Della Longa, P. D’Angelo, M. Benfatto, AIP Conf. Proc. 882, 111–113 (2007)
K. Hatada, K. Hayakawa, unpublished 2011
D. Sébilleau, C. Natoli, G.M. Gavaza, H. Zhao, F. Da Pieve, K. Hatada, Comput. Phys. Commun. 182, 2567–2579 (2011)
OpenGL, Opengl 4.0 specification (2013), http://www.opengl.org/registry/doc/glspec40.core.20100311.pdf
Message P Forum, Mpi: a message-passing interface standard, Technical report, Knoxville, TN, USA (1994)
E. Anderson, Z. Bai, J. Dongarra, A. Greenbaum, A. McKenney, J. Du Croz, S. Hammerling, J. Demmel, C. Bischof, D. Sorensen, in Proceedings of the 1990 ACM/IEEE Conference on Supercomputing, Supercomputing’90, Los Alamitos, CA, USA (IEEE Computer Society Press, 1990), pp. 2–11
L.S. Blackford, J. Demmel, J. Dongarra, I. Duff, S. Hammarling, G. Henry, M. Heroux, L. Kaufman, A. Lumsdaine, A. Petitet, R. Pozo, K. Remington, R.C. Whaley, ACM Trans. Math. Softw. 28, 135–151 (2002)
G. Rossi, M. Calizzi, V. Di Cintio, S. Magkos, L. Amidani, L. Pasquini, F. Boscherini, J. Phys. Chem. C 120, 7457–7466 (2016)
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Hatada, K., Natoli, C.R. (2018). Real Space Full Potential Multiple Scattering Theory. In: Sébilleau, D., Hatada, K., Ebert, H. (eds) Multiple Scattering Theory for Spectroscopies. Springer Proceedings in Physics, vol 204. Springer, Cham. https://doi.org/10.1007/978-3-319-73811-6_3
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