Applicability of the DFT Augmented Symmetry Approach to Simulations of the Chromium-based Rings : Cross-validation Using the PBE Functional

• Autorzy: Wojciechowski M. , Brzostowski B. , Kamieniarz G.

Identyfikatory

DOI

10.12921/cmst.2016.22.02.006

• Języki publikacji: EN

Abstrakty

EN

We present comprehensive convergence and accuracy tests for predictions of the augmented symmetry approach suggested to reduce computational complexity of the DFT calculations for molecular rings. Using the PBE functional, we demonstrate the numerical stability of magnetic couplings, magnetic moments and the HOMO-LUMO gaps with respect to the size of the basic parameters RKM, the number of k-points and types of the unit cells as well as to the presence of full or absence of any point group symmetry. We show that both the performance and the final results are equal to those obtained for the standard approaches but the computing time is significantly lower. We conclude that the value RKM = 3:0 and a single k-point in the irreducible Brillouin zone are enough to reach the uncertainty of magnetic couplings of the order of 0:1 meV and a distortion resulting from the approach is irrelevant as far as the magnetic properties are concerned.

Słowa kluczowe

EN

molecular magnets; chromium nanorings; density functional theory

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2016
• Tom: Vol. 22, No. 2
• Strony: 109--121
• Opis fizyczny: Bibliogr. 43 poz., rys.

Twórcy

autor

Wojciechowski M.

• Institute of Physics, University of Zielona Góra, Prof. Szafrana 4a, 65-516 Zielona Góra, Poland

autor

Brzostowski B.

• Institute of Physics, University of Zielona Góra, Prof. Szafrana 4a, 65-516 Zielona Góra, Poland

autor

Kamieniarz G.

• Faculty of Physics, A. Mickiewicz University Umultowska 85, 61-614 Poznań, Poland

Bibliografia

• [1] M. Wojciechowski, B. Brzostowski, G. Kamieniarz, Augmented Symmetry Approach to the DFT Simulations of the Chromium-Based Rings, in: R. Wyrzykowski et al. (ed.) Parallel Processing and Applied Mathematics, 11th International Conference PPAM 2015, Berlin Heidelberg Springer-Verlag, p. 321-331, 2016.
• [2] D. M. Tomecka, V. Bellini, F. Troiani, F. Manghi, G. Kamieniarz, M. Affronte, Ab initio study of a chain model of the Cr8 molecular magnet, Phys. Rev. B 77 224401 (2008).
• [3] V. Corradini, F. Moro, R. Biagi, V. De Renzi, U. del Pennino, V. Bellini, S. Carretta, P. Santini, V. A. Milway, G. Timco, R. E. P. Winpenny, M. Affronte, Successful grafting of isolated molecular Cr7Ni rings on Au(111) surface, Phys. Rev. B 79, 144419 (2009).
• [4] V. Bellini, M. Affronte, A density-functional study of heterometallic Cr-based molecular rings, J. Phys. Chem. B 114, 14797 (2010).
• [5] J. van Slageren, R. Sessoli, D. Gatteschi, A. A. Smith, M. Helliwell, R. E. P. Winpenny, A. Cornia, A.-L. Barra, A. G. M. Jansen, E. Rentschler, G. Timco, Magnetic anisotropy of the antiferromagnetic ring Cr8F8Piv16, Chem. Eur. J. 8, 277 (2002).
• [6] F. K. Larsen, E. J. L. McInnes, H. E. Mkami, J. Overgaard, S. Piligkos, G. Rajaraman, E. Rentschler, A. A. Smith, G. M. Smith, V. Boote, M. Jennings, G. A. Timco, R. E. P.Winpenny, Synthesis and characterization of heterometallic Cr7M wheels, Angew. Chem. Int. Ed. 42, 101 (2003).
• [7] C. R. Groom, I. J. Bruno, M. P. Lightfoot, S. C. Ward, The Cambridge Structural Database, Acta Cryst. B72, 171 (2016).
• [8] T. ´ Slusarski, B. Brzostowski, D. M. Tomecka, G. Kamieniarz, Application of the package SIESTA to linear models of a molecular chromium-based ring, Acta Phys. Pol. A. 118, 967 (2010).
• [9] V. Bellini, A. Olivieri, F. Manghi, Density-functional study of the Cr8 antiferromagnetic ring, Phys. Rev. B 73, 184431 (2006).
• [10] P. Hohenberg, W. Kohn, Inhomogeneous Electron Gas, Phys. Rev. 136, 864 (1964).
• [11] W. Kohn, L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140, A1133 (1965).
• [12] P. Blaha, K. Schwarz, G. H. K. Madsen, D. Kvasnicka, J. Luitz, WIEN2k: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties, Karlheinz Schwarz, Techn. Universität, Wien (1999).
• [13] E. Sjöstedt, L. Nordström, D. J. Singh, An alternative way of linearizing the augmented plane-wave method, Solid State Commun. 114, 15 (2000).
• [14] G. K. H. Madsen, P. Blaha, K. Schwarz, E. Sjöstedt, L. Nordström, Efficient linearization of the augmented plane-wave method, Phys. Rev. B 64, 195134 (2001).
• [15] O. K. Andersen, Linear methods in band theory, Phys. Rev. B 12, 3060 (1975).
• [16] D. J. Singh, Planewaves Pseudopotentials and the LAPW Method, Kluwer Academic Publishers, Boston (1994).
• [17] J. P. Desclaux, Hartree Fock Slater self consistent field calculations, Comp. Phys. Commun. 1, 216 (1969).
• [18] D. D. Koelling, B. N. Harmon, A technique for relativistic spin-polarised calculations, J. Phys. C: Sol. St. Phys. 10, 3107 (1977).
• [19] J. C. Slater, Wave Functions in a Periodic Potential, Phys. Rev. 51, 846 (1937).
• [20] M. Wojciechowski, B. Brzostowski, G. Kamieniarz, DFT estimation of exchange coupling constant of Cr8 molecular ring using the hybrid functional B3LYP, Acta Phys. Pol. A. 127, 407 (2015).
• [21] J. P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
• [22] M. L. Baker, T. Guidi, S. Carretta, J. Ollivier, H. Mutka, H. U. Güdel, G. A. Timco, E. J. L. McInnes, G. Amoretti, R. E. P. Winpenny, P. Santini, Spin dynamics of molecular nanomagnets unravelled at atomic scale by four-dimensional inelastic neutron scattering, Nat. Phys. 8, 906 (2012).
• [23] M. Antkowiak, P. Kozłowski, G. Kamieniarz, G. A. Timco, F. Tuna, R. E. P. Winpenny, Detection of ground states in frustrated molecular rings by in-field local magnetization profiles, Phys. Rev. B 87, 184430 (2013).
• [24] L. Kronik, T. Stein, S. Refaely-Abramson, R. Baer, Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals, J. Chem. Theory Comput. 8, 1515 (2012).
• [25] B. Brzostowski, M. Wojciechowski, G. Kamieniarz, Fundamental gaps in Cr8, Cr7Ni and Cr7Cd molecules, Acta Phys. Pol. A. 126, 234 (2014).
• [26] H. Mera, K. Stokbro, Using Kohn-Sham density functional theory to describe charged excitations in finite systems, Phys. Rev. B 79, 125109 (2009).
• [27] X. Andrade, A. Aspuru-Guzik, Prediction of the Derivative Discontinuity in Density Functional Theory from an Electrostatic Description of the Exchange and Correlation Potential, Phys. Rev. Lett. 107, 183002 (2011).
• [28] L. J. Noodleman, Valence bond description of antiferromagnetic coupling in transition metal dimers, Chem. Phys. 74, 5737 (1981).
• [29] G. Kamieniarz, P. Kozłowski, M. Antkowiak, P. Sobczak, T. ´ Slusarski, D. M. Tomecka, A. Barasiński, B. Brzostowski,A. Drzewiński, A. Bieńko, J. Mroziński, Anisotropy, geometric structure ńd frustration effects in molecule-based nanomagnets, Acta Phys. Pol. A. 121, 992 (2012).
• [30] P. Blaha, K. Schwarz, G. H. K. Madsen, D. Kvasnicka, J. Luitz, WIEN2k User’s Guide; revision 14.2 (Release 10/15/2014), www.wien2k.at/reg_user/textbooks/.
• [31] P. Blaha, K. Schwarz, J. Luitz, WIEN2k: Frequently asked Questions, www.wien2k.at/reg_user/faq/.
• [32] S. Piligkos, H. Weihe, E. Bill, F. Neese, H. E. Mkami, G. M. Smith, D. Collison, G. Rajaraman, G. A. Timco, R. E. P. Winpenny, E. J. L. McInnes, EPR Spectroscopy of a Family of CrIII 7MII (M = Cd, Zn, Mn, Ni) Wheels: Studies of Isostructural Compounds with Different Spin Ground States, Chem. Eur. J. 15, 3152 (2009).
• [33] B. Brzostowski, R. Lema´nski, T. ´ Slusarski, D. Tomecka, G. Kamieniarz, Chromium-based rings within the DFT and Falicov-Kimball model approach, J. Nanopart. Res. 15, 1528 (2013).
• [34] B. Brzostowski, T. ´ Slusarski, G. Kamieniarz, DFT study of octanuclear molecular chromium-based ring using new pseudopotential parameters, Acta Phys. Pol. A. 121, 1115 (2012).
• [35] B. Brzostowski, M. Wojciechowski, R. Lemański, G. Kamieniarz, DFT and Falicov-Kimball model approach to Cr9 molecular ring, Acta Phys. Pol. A. 126, 270 (2014).
• [36] M. Wojciechowski, B. Brzostowski, R. Lemański,G. Kamieniarz, Mapping of the DFT spin configuration energies of Cr8Cd molecular ring onto the energy structure of Falicov-Kimball model, Acta Phys. Pol. A. 127, 410 (2015).
• [37] V. Bellini, D.M. Tomecka, B. Brzostowski, M.Wojciechowski, F. Troiani, F. Manghi, M. Affronte, DFT study of the Cr8 molecular magnet within chain-model approximations, in: R. Wyrzykowski et al. (ed.) Parallel Processing and Applied Mathematics, 10th International Conference PPAM 2013, Berlin Heidelberg Springer-Verlag, p. 428-437, 2014.
• [38] M. L. Baker, G. A. Timco, S. Piligkos, J. S. Mathieson, H. Mutka, F. Tuna, P. Kozłowski, M. Antkowiak, T. Guidi, T. Gupta, H. Rath, R. J. Woolfson, G. Kamieniarz, R. G. Pritchard, H. Weihe, L. Cronin, G. Rajaraman, D. Collison, E. J. L. McInnes, R. E. P. Winpenny, A classification of spin frustration in molecular magnets from a physical study of large odd-numbered-metal, odd electron rings, Proc. Natl. Acad. Sci. U.S.A. 109, 19113 (2012).
• [39] P. Christian, G. Rajaraman, A. Harrison, J. J. W. McDouall, J. T. Rafterya, R. E. P. Winpenny, Structural, magnetic and DFT studies of a hydroxide-bridged Cr8 wheel, Dalton Trans. 10, 1511 (2004).
• [40] S. Carretta, J. van Slageren, T. Guidi, E. Liviotti, C. Mondelli, D. Rovai, A. Cornia, A. L. Dearden, F. Carsughi, M. Affronte, C. D. Frost, R. E. P. Winpenny, D. Gatteschi, G. Amoretti, R. Caciuffo, Microscopic spin Hamiltonian of a Cr8 antiferromagnetic ring from inelastic neutron scattering, Phys. Rev. 67, 094405 (2003).
• [41] R. Caciuffo, T. Guidi, G. Amoretti, S. Carretta, E. Liviotti, P. Santini, C. Mondelli, G. Timco, C. A. Muryn, R. E. P. Winpenny, Spin dynamics of heterometallic Cr7M wheels (M=Mn, Zn, Ni) probed by inelastic neutron scattering, Phys. Rev. 71, 174407 (2005).
• [42] A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98, 5648 (1993).
• [43] C. Lee,W. Yang, R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37, 785 (1988).

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.