Abstract
We suggest an augmented symmetry approach to reduce the computational complexity of the DFT electronic structure calculations based on the Wien2k package and to extend its applicability to the studies of heterogeneous ring-shape molecular nanomagnets. The approach is tested for the reference chromium-based rings \({\mathrm{Cr}_8}\), \({\mathrm{Cr}_7\mathrm{Cd}}\) and \({\mathrm{Cr}_7\mathrm{Ni}}\), and a good agreement with the results of the previous standard studies is reached with the substantial gain in the computing time.
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References
van Slageren, J., Sessoli, R., Gatteschi, D., Smith, A.A., Helliwell, M., Winpenny, R.E.P., Cornia, A., Barra, A.-L., Jansen, A.G.M., Rentschler, E., Timco, G.: Magnetic anisotropy of the antiferromagnetic ring [Cr_8F_8Piv_16]. Chem. Eur. J. 8, 277 (2002)
Larsen, F.K., McInnes, E.J.L., Mkami, H.E., Overgaard, J., Piligkos, S., Rajaraman, G., Rentschler, E., Smith, A.A., Smith, G.M., Boote, V., Jennings, M., Timco, G.A., Winpenny, R.E.P.: Synthesis and characterization of heterometallic {Cr_7M} wheels. Angew. Chem. Int. Ed. 42, 101 (2003)
Christian, P., Rajaraman, G., Harrison, A., McDouall, J.J.W., Rafterya, J.T., Winpenny, R.E.P.: Structural, magnetic and DFT studies of a hydroxide-bridged {Cr_8} wheel. Dalton Trans. 10, 1511 (2004)
Bellini, V., Affronte, M.: A density-functional study of heterometallic Cr-based molecular rings. J. Phys. Chem. B 114, 14797 (2010)
Brzostowski, B., Ślusarski, T., Kamieniarz, G.: DFT study of octanuclear molecular chromium-based ring using new pseudopotential parameters. Acta Phys. Pol. A. 121, 1115 (2012)
Wojciechowski, M., Brzostowski, B., Kamieniarz, G.: DFT estimation of exchange coupling constant of Cr_8 molecular ring using the hybrid functional B3LYP. Acta Phys. Pol. A. 127, 407 (2015)
Kamieniarz, G., Kozłowski, P., Antkowiak, M., Sobczak, P., Ślusarski, T., Tomecka, D.M., Barasiński, A., Brzostowski, B., Drzewiński, A., Bieńko, A., Mroziński, J.: Anisotropy, geometric structure and frustration effects in molecule-based nanomagnets. Acta Phys. Pol. A. 121, 992 (2012)
Brzostowski, B., Lemański, R., Ślusarski, T., Tomecka, D., Kamieniarz, G.: Chromium-based rings within the DFT and Falicov-Kimball model approach. J. Nanopart. Res. 15, 1528 (2013)
Brzostowski, B., Wojciechowski, M., Lemański, R., Kamieniarz, G., Timco, G.A., Tuna, F., Winpenny, R.E.P.: DFT and Falicov-Kimball model approach to Cr9 molecular ring. Acta Phys. Pol. A. 126, 270 (2014)
Wojciechowski, M., Brzostowski, B., Lemański, R., Kamieniarz, G.: 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)
Bellini, V., Tomecka, D.M., Brzostowski, B., Wojciechowski, M., Troiani, F., Manghi, F., Affronte, M.: DFT study of the Cr8 molecular magnet within chain-model approximations. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) PPAM 2013, Part II. LNCS, vol. 8385, pp. 428–437. Springer, Heidelberg (2014)
Tomecka, D.M., Bellini, V., Troiani, F., Manghi, F., Kamieniarz, G., Affronte, M.: Ab initio study on a chain model of the Cr_8 molecular magnet. Phys. Rev. B 77, 224401 (2008)
Ślusarski, T., Brzostowski, B., Tomecka, D.M., Kamieniarz, G.: Application of the package SIESTA to linear models of a molecular chromium-based ring. Acta Phys. Pol. A. 118, 967 (2010)
Brzostowski, B., Wojciechowski, M., Kamieniarz, G.: Fundamental gaps in Cr_8, Cr_7Ni and Cr_7 molecules. Acta Phys. Pol. A. 126, 234 (2014)
Ślusarski, T., Brzostowski, B., Tomecka, D., Kamieniarz, G.: Electronic structure and magnetic properties of a molecular octanuclear chromium-based ring. J. Nanosci. Nanotechnol. 11, 9080 (2011)
Bellini, V., Olivieri, A., Manghi, F.: Density-functional study of the Cr_8 antiferromagnetic ring. Phys. Rev. B 73, 184431 (2006)
Blaha, P., Schwarz, K., Madsen, G.H.K., Kvasnicka, D., Luitz, J.: WIEN2k: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties, Karlheinz Schwarz, Techn., Universität Wien (1999)
Sjöstedt, E., Nordström, L., Singh, D.J.: An alternative way of linearizing the augmented plane-wave method. Solid State Commun. 114, 15 (2000)
Madsen, G.K.H., Blaha, P., Schwarz, K., Sjöstedt, E., Nordström, L.: Efficient linearization of the augmented plane-wave method. Phys. Rev. B 64, 195134 (2001)
Baker, M.L., Timco, G.A., Piligkos, S., Mathieson, J.S., Mutka, H., Tuna, F., Kozłowski, P., Antkowiak, M., Guidi, T., Gupta, T., Rath, H., Woolfson, R.J., Kamieniarz, G., Pritchard, R.G., Weihe, H., Cronin, L., Rajaraman, G., Collison, D., McInnes, E.J.L., Winpenny, R.E.P.: 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)
Andersen, O.K.: Linear methods in band theory. Phys. Rev. B 12, 3060 (1975)
Singh, D.J.: Planewaves Pseudopotentials and the LAPW Method. Kluwer Academic Publishers, Boston (1994)
Slater, J.C.: Wave functions in a periodic potential. Phys. Rev. 51, 846 (1937)
Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996)
Baker, M.L., Guidi, T., Carretta, S., Ollivier, J., Mutka, H., Güdel, H.U., Timco, G.A., McInnes, E.J.L., Amoretti, G., Winpenny, R.E.P., Santini, P.: Spin dynamics of molecular nanomagnets unravelled at atomic scale by four-dimensional inelastic neutron scattering. Nat. Phys. 8, 906 (2012)
Antkowiak, M., Kozłowski, P., Kamieniarz, G., Timco, G.A., Tuna, F., Winpenny, R.E.P.: Detection of ground states in frustrated molecular rings by in-field local magnetization profiles. Phys. Rev. B 87, 184430 (2013)
Soler, J.M., Artacho, E., Gale, J.D., García, A., Junquera, J., Ordejón, P., Sánchez-Portal, D.: The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 14, 2745 (2002)
Noodleman, L.J.: Valence bond description of antiferromagnetic coupling in transition metal dimers. Chem. Phys. 74, 5737 (1981)
Ruiz, E., Cano, J., Alvarez, S., Alemany, P.: Broken symmetry approach to calculation of exchange coupling constants for homobinuclear and heterobinuclear transition metal complexes. J. Comput. Chem. 20, 1391 (1999)
Acknowledgments
One of the authors (M.W.) was supported by the European Union scholarship No. DFS.VI.052.4.62.8.2013 from Human Capital Programme, sub-measure 8.2.2, priority VIII, funded from EFS and the Lubusz Voivodeship budget. Calculations were performed on computing servers in the Institute of Physics at University of Zielona Góra. We also acknowledge access to the HPC resources in PSNC Poznań (Poland) and those available within the DECI program by PRACE-3IP project (FP7 RI-312763) in Nicosia (Cyprus).
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Wojciechowski, M., Brzostowski, B., Kamieniarz, G. (2016). Augmented Symmetry Approach to the DFT Simulations of the Chromium-Based Rings. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. Lecture Notes in Computer Science(), vol 9574. Springer, Cham. https://doi.org/10.1007/978-3-319-32152-3_30
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DOI: https://doi.org/10.1007/978-3-319-32152-3_30
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