{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T06:49:27Z","timestamp":1773384567300,"version":"3.50.1"},"reference-count":87,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T00:00:00Z","timestamp":1676592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"DAAD financial support","award":["91645341"],"award-info":[{"award-number":["91645341"]}]},{"name":"IDEA-AISBL-Bruxelles","award":["91645341"],"award-info":[{"award-number":["91645341"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We conducted a systematic investigation using state-of-the-art techniques on the electronic and optical properties of two crystals of alkaline earth metal fluorides, namely rutile MgF2 and cubic SrF2. For these two crystals of different symmetry, we present density functional theory (DFT), many-body perturbation theory (MBPT), and Bethe\u2013Salpeter equation (BSE) calculations. We calculated a variety of properties, namely ground-state energies, band-energy gaps, and optical absorption spectra with the inclusion of excitonic effects. The quantities were obtained with a high degree of convergence regarding all bulk electronic and optical properties. Bulk rutile MgF2 has distinguished ground-state and excited-state properties with respect to the other cubic fluoride SrF2 and the other members of the alkaline earth metal fluoride family. The nature of the fundamental gaps and estimates of the self-energy and excitonic effects for the two compounds are presented and discussed in detail. Our results are in good accordance with the measurements and other theoretical\u2013computational data. A comparison is made between the excitation and optical properties of bulk rutile MgF2, cubic SrF2, and the corresponding clusters, for which calculations have recently been published, confirming strong excitonic effects in finite-sized systems.<\/jats:p>","DOI":"10.3390\/sym15020539","type":"journal-article","created":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T02:57:22Z","timestamp":1676602642000},"page":"539","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Electronic and Optical Properties of Alkaline Earth Metal Fluoride Crystals with the Inclusion of Many-Body Effects: A Comparative Study on Rutile MgF2 and Cubic SrF2"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9746-3025","authenticated-orcid":false,"given":"Giancarlo","family":"Cappellini","sequence":"first","affiliation":[{"name":"Department of Physics, University of Cagliari, CNR-IOM SLACS and ETSF, Cittadella Universitaria di Monserrato, Strada Prov.le Monserrato-Sestu, Km 0.700, Monserrato, 09042 Cagliari, Italy"}]},{"given":"J\u00fcrgen","family":"Furthm\u00fcller","sequence":"additional","affiliation":[{"name":"Institute f\u00fcr Festk\u00f6rpertheorie und -Optik, Friedrich-Schiller-Universit\u00e4t Jena, and ETSF, Max-Wien-Platz 1, D-07743 Jena, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3294-6082","authenticated-orcid":false,"given":"Friedhelm","family":"Bechstedt","sequence":"additional","affiliation":[{"name":"Institute f\u00fcr Festk\u00f6rpertheorie und -Optik, Friedrich-Schiller-Universit\u00e4t Jena, and ETSF, Max-Wien-Platz 1, D-07743 Jena, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4920-2370","authenticated-orcid":false,"given":"Silvana","family":"Botti","sequence":"additional","affiliation":[{"name":"Institute f\u00fcr Festk\u00f6rpertheorie und -Optik, Friedrich-Schiller-Universit\u00e4t Jena, and ETSF, Max-Wien-Platz 1, D-07743 Jena, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1103\/PhysRevB.5.662","article-title":"Far-Ultraviolet Reflectance Spectra and the Electronic Structure of Ionic Crystals","volume":"5","author":"Rubloff","year":"1972","journal-title":"Phys. Rev. B"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1107\/S0365110X65000361","article-title":"Crystal structures, 2nd edition. Vol. 1, by R. W. G. Wyckoff","volume":"18","author":"Zemann","year":"1965","journal-title":"Acta Crystallogr."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bechstedt, F. (2015). Many-Body Approach to Electronic Excitations, Springer.","DOI":"10.1007\/978-3-662-44593-8"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Bhushan, B. (2012). Encyclopedia of Nanotechnology, Springer.","DOI":"10.1007\/978-90-481-9751-4"},{"key":"ref_5","unstructured":"Bertoni, C.M., Cappellini, G., Finocchi, F., and Monachesi, P. (2015). Physics of Solid Surfaces, Springer."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"15665","DOI":"10.1103\/PhysRevB.56.15665","article-title":"Ab initio study of point defects in CdF2","volume":"56","author":"Mattila","year":"1997","journal-title":"Phys. Rev. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"8367","DOI":"10.1088\/0953-8984\/18\/35\/021","article-title":"Ab initio calculations of the BaF2 bulk and surface F centers","volume":"18","author":"Shi","year":"2006","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"055501","DOI":"10.1088\/0953-8984\/22\/5\/055501","article-title":"The atomic and electronic structure of CaF2 and BaF2 crystals with H centers: A hybrid DFT calculation study","volume":"22","author":"Jia","year":"2010","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1103\/PhysRev.50.1057","article-title":"Optical Constants of Fluorite in the Extreme Ultraviolet","volume":"50","author":"Tousey","year":"1936","journal-title":"Phys. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4529","DOI":"10.1103\/PhysRevB.13.4529","article-title":"Temperature and pressure dependences of the dielectric properties of PbF2and the alkaline-earth fluorides","volume":"13","author":"Samara","year":"1976","journal-title":"Phys. Rev. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1103\/PhysRevB.32.1301","article-title":"Satellites in X-ray photoelectron spectroscopy of insulators. I. Multielectron excitations in CaF2, SrF2, and BaF2","volume":"32","author":"Scrocco","year":"1985","journal-title":"Phys. Rev. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1372","DOI":"10.1103\/PhysRevB.33.1372","article-title":"Laser spectroscopy of ion-size effects on point-defect equilibria in PbF2:Eu3+","volume":"33","author":"Weesner","year":"1986","journal-title":"Phys. Rev. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5972","DOI":"10.1103\/PhysRevB.33.5972","article-title":"Fundamental absorption edge of PbF2 and Cd1-xPbxF2 crystals","volume":"33","author":"Kosacki","year":"1986","journal-title":"Phys. Rev. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"14837","DOI":"10.1103\/PhysRevB.58.14837","article-title":"Effect of hydrostatic pressure on the crystal structure and superionic behavior of lead (II) fluoride","volume":"58","author":"Hull","year":"1998","journal-title":"Phys. Rev. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"15731","DOI":"10.1103\/PhysRevB.61.15731","article-title":"Optical spectra and electronic structures of lead halides","volume":"61","author":"Fujita","year":"2000","journal-title":"Phys. Rev. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"241102\u20131","DOI":"10.1103\/PhysRevB.64.241102","article-title":"Intrinsic birefringence in calcium fluoride and barium fluoride","volume":"64","author":"Burnett","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1744","DOI":"10.1080\/22221751.2020.1796529","article-title":"Rapid inactivation of SARS-CoV-2 with deep-UV LED irradiation","volume":"9","author":"Inagaki","year":"2020","journal-title":"Emerg. Microbes Infect."},{"key":"ref_18","first-page":"Doc08","article-title":"Ultraviolet irradiation doses for coronavirus inactivation - review and analysis of coronavirus photoinactivation studies","volume":"15","author":"Hessling","year":"2020","journal-title":"GMS Hyg. Infect. Control."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Kowalski, W. (2009). Ultraviolet Germicidal Irradiation Handbook, Springer.","DOI":"10.1007\/978-3-642-01999-9"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/BF01314577","article-title":"Principles of selective inactivation of viral genome","volume":"68","author":"Budowsky","year":"1981","journal-title":"Arch. Virol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1700497","DOI":"10.1002\/pssb.201700497","article-title":"Optical Properties of Free and Si(001)-Adsorbed Pyrimidinic Nucleobases","volume":"255","author":"Molteni","year":"2017","journal-title":"Phys. Status Solidi (b)"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"05437\u20131","DOI":"10.1103\/PhysRevB.95.075437","article-title":"Optical properties of organically functionalized silicon surfaces: Uracil-like nucleobases on Si(001)","volume":"95","author":"Molteni","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1140\/epjb\/e2011-10382-1","article-title":"Electronic structure of fluorides: General trends for ground and excited state properties","volume":"81","author":"Cadelano","year":"2011","journal-title":"Eur. Phys. J. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"125501","DOI":"10.1088\/0953-8984\/26\/12\/125501","article-title":"One- and two-particle effects in the electronic and optical spectra of barium fluoride","volume":"26","author":"Cadelano","year":"2014","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"075203\u20131","DOI":"10.1103\/PhysRevB.87.075203","article-title":"Electronic and optical properties of cadmium fluoride: The role of many-body effects","volume":"87","author":"Cappellini","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1140\/epjb\/e2009-00313-2","article-title":"A practical first-principles band-theory approach to the study of correlated materials","volume":"71","author":"Filippetti","year":"2009","journal-title":"Eur. Phys. J. B"},{"key":"ref_27","first-page":"27","article-title":"The LDA-1\/2 technique: Recent Developments","volume":"Volume 1566","author":"Ferreira","year":"2013","journal-title":"Proceedings of the 31st International Conference on the Physics of Semiconductors (ICPS)"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"365501","DOI":"10.1088\/1361-648X\/aad654","article-title":"Electronic properties of fluorides by approximated quasiparticle DFT-1\/2 and PSIC methods: BaF2, CaF2 and CdF2 as test cases","volume":"30","author":"Matusalem","year":"2018","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1002\/pssb.2220530218","article-title":"Spectra of Electronic Excitations in CaF2, SrF2, and BaF2 in the 8 to 150 eV Range","volume":"53","author":"Frandon","year":"1972","journal-title":"Phys. Status Solidi (b)"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1088\/0022-3719\/13\/9\/028","article-title":"UPS and XPS spectra of CdF2 and SrF2 and interpretation of optical properties of these compounds","volume":"13","author":"Raisin","year":"1980","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"12597","DOI":"10.1103\/PhysRevB.43.12597","article-title":"Electronic structure of fluorite-type compounds and mixed crystals","volume":"43","author":"Christensen","year":"1991","journal-title":"Phys. Rev. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1140\/epjb\/e2005-00301-6","article-title":"Structural, electronic and optical properties of fluorite-type compounds","volume":"47","author":"Khenata","year":"2005","journal-title":"Eur. Phys. J. B"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.nima.2005.01.188","article-title":"Time-resolved luminescent VUV-spectroscopy of pure and doped by rare earth ions crystals of strontium fluoride","volume":"543","author":"Ivanovskikh","year":"2005","journal-title":"Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers, Detect. Assoc. Equip."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"17","DOI":"10.4028\/p-wd48sx","article-title":"The Highly Efficient Inorganic SrF2:Gd3+,Eu3+ Phosphor for Mercury Free Fluorescence Lamps","volume":"1171","author":"Jaiswal","year":"2022","journal-title":"Adv. Mater. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5691","DOI":"10.1088\/0022-3719\/13\/31\/010","article-title":"Self-consistent energy band structure of magnesium fluoride using the LCAO method","volume":"13","author":"Chaney","year":"1980","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"515","DOI":"10.2478\/s11534-010-0101-1","article-title":"Ab initio calculations of the atomic and electronic structure of MgF2 (011) and (111) surfaces","volume":"9","author":"Vassilyeva","year":"2011","journal-title":"Open Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"085602(5pp)","DOI":"10.1088\/0953-8984\/24\/8\/085602","article-title":"Quasiparticle band structures and optical properties of magnesium fluoride","volume":"24","author":"Yi","year":"2012","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"13268","DOI":"10.1021\/acsomega.0c01317","article-title":"Electronic and Optical Properties of Small Metal Fluoride Clusters","volume":"5","author":"Cappellini","year":"2020","journal-title":"ACS Omega"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1950","DOI":"10.1021\/jp994339n","article-title":"Unusual Dimer Structures of the Heavier Alkaline Earth Dihalides: A Density Functional Study","volume":"104","author":"Levy","year":"2000","journal-title":"J. Phys. Chem. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"9267","DOI":"10.1021\/jp046682k","article-title":"CaF2 As a Quasilinear Molecule: The Vibrational-Rotational Energy Levels Predicted by Ab Initio Quantum Chemistry Approach","volume":"108","author":"Koput","year":"2004","journal-title":"J. Phys. Chem. A"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.comptc.2014.05.007","article-title":"A theoretical study of structural and electronic properties of alkaline-earth fluoride clusters","volume":"1043","author":"Pandey","year":"2014","journal-title":"Comput. Theor. Chem."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2093","DOI":"10.1063\/1.1672304","article-title":"Geometry and Vibrational Spectra of Alkaline-Earth Dihalides. II. CaF2, SrF2, and BaF2","volume":"51","author":"Calder","year":"1969","journal-title":"J. Chem. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/0927-0256(96)00008-0","article-title":"Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set","volume":"6","author":"Kresse","year":"1996","journal-title":"Comput. Mater. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"11169","DOI":"10.1103\/PhysRevB.54.11169","article-title":"Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set","volume":"54","author":"Kresse","year":"1996","journal-title":"Phys. Rev. B"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1941","DOI":"10.1088\/0953-8984\/1\/11\/002","article-title":"Universal features of the equation of state of solids","volume":"1","author":"Vinet","year":"1989","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"136406\u20131","DOI":"10.1103\/PhysRevLett.100.136406","article-title":"Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces","volume":"100","author":"Perdew","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","unstructured":"Aroyo, M.I. (2021). Teaching Edition of International Tables for Crystallography: Crystallographic Symmetry, IUCr\/Wilet."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3865","DOI":"10.1103\/PhysRevLett.77.3865","article-title":"Generalized Gradient Approximation Made Simple","volume":"77","author":"Perdew","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"085108\u20131","DOI":"10.1103\/PhysRevB.72.085108","article-title":"Functional designed to include surface effects in self-consistent density functional theory","volume":"72","author":"Armiento","year":"2005","journal-title":"Phys. Rev. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"5048","DOI":"10.1103\/PhysRevB.23.5048","article-title":"Self-interaction correction to density-functional approximations for many-electron systems","volume":"23","author":"Perdew","year":"1981","journal-title":"Phys. Rev. B"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"134110\u20131","DOI":"10.1103\/PhysRevB.64.134110","article-title":"X-ray diffraction and theoretical studies of the high-pressure structures and phase transitions in magnesium fluoride","volume":"64","author":"Haines","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1007\/BF00726988","article-title":"Thermal expansion of strontium fluoride","volume":"4","author":"Subhadra","year":"1985","journal-title":"J. Mater. Sci. Lett."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"A1366","DOI":"10.1103\/PhysRev.136.A1366","article-title":"Elastic Constants of Strontium Fluoride between 4.2 and 300 \u00b0K","volume":"136","author":"Gerlich","year":"1964","journal-title":"Phys. Rev."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"A796","DOI":"10.1103\/PhysRev.139.A796","article-title":"New Method for Calculating the One-Particle Green\u2019s Function with Application to the Electron-Gas Problem","volume":"139","author":"Hedin","year":"1965","journal-title":"Phys. Rev."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"10159","DOI":"10.1103\/PhysRevB.37.10159","article-title":"Self-energy operators and exchange-correlation potentials in semiconductors","volume":"37","author":"Godby","year":"1988","journal-title":"Phys. Rev. B"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1016\/0038-1098(92)90476-P","article-title":"An efficient method for calculating quasiparticle energies in semiconductors","volume":"84","author":"Bechstedt","year":"1992","journal-title":"Solid State Commun."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1103\/RevModPhys.74.601","article-title":"Electronic excitations: Density-functional versus many-body Green\u2019s-function approaches","volume":"74","author":"Onida","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"325902","DOI":"10.1088\/1361-648X\/ab15d0","article-title":"Many-body perturbation theory calculations using the yambo code","volume":"31","author":"Sangalli","year":"2019","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"3764","DOI":"10.1103\/PhysRevB.53.3764","article-title":"Generalized Kohn-Sham schemes and the band-gap problem","volume":"53","author":"Seidl","year":"1996","journal-title":"Phys. Rev. B"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1877","DOI":"10.1002\/pssb.200945074","article-title":"Ab-initio theory of semiconductor band structures: New developments and progress","volume":"246","author":"Bechstedt","year":"2009","journal-title":"Phys. Status Solidi (b)"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"5069","DOI":"10.1021\/acs.jctc.9b00322","article-title":"Large-Scale Benchmark of Exchange\u2013Correlation Functionals for the Determination of Electronic Band Gaps of Solids","volume":"15","author":"Borlido","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"8207","DOI":"10.1063\/1.1564060","article-title":"Hybrid functionals based on a screened Coulomb potential","volume":"118","author":"Heyd","year":"2003","journal-title":"J. Chem. Phys."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"224106\u20131","DOI":"10.1063\/1.2404663","article-title":"Influence of the exchange screening parameter on the performance of screened hybrid functionals","volume":"125","author":"Krukau","year":"2006","journal-title":"J. Chem. Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"241201\u20131","DOI":"10.1103\/PhysRevB.84.241201","article-title":"G0W0 band gap of ZnO: Effects of plasmon-pole models","volume":"84","author":"Stankovski","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"9892","DOI":"10.1103\/PhysRevB.47.9892","article-title":"Model dielectric function for semiconductors","volume":"47","author":"Cappellini","year":"1993","journal-title":"Phys. Rev. B"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"085307\u20131","DOI":"10.1103\/PhysRevB.67.085307","article-title":"Efficient (N2) method to solve the Bethe-Salpeter equation","volume":"67","author":"Schmidt","year":"2003","journal-title":"Phys. Rev. B"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"081102\u20131","DOI":"10.1103\/PhysRevB.86.081102","article-title":"Unified description of ground and excited states of finite systems: The self-consistentGWapproach","volume":"86","author":"Caruso","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"2125","DOI":"10.1016\/j.physb.2010.01.118","article-title":"Ab initio calculations of MgF2 (001) and (011) surface structure","volume":"405","author":"Vassilyeva","year":"2010","journal-title":"Phys. B Cond. Matt."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"980","DOI":"10.1016\/j.commatsci.2008.02.012","article-title":"Ab initio calculations for SrF2 with F- and M-centers","volume":"43","author":"Jia","year":"2008","journal-title":"Comp. Mat. Sci."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"8444","DOI":"10.1021\/jp104437n","article-title":"First-Principles Calculations for the H Center in SrF2 Crystals","volume":"114","author":"Yue","year":"2010","journal-title":"J. Phys. Chem. A"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/j.commatsci.2013.09.010","article-title":"First principle study of MF2 ( M=Mg, Ca, Sr, Ba, Ra) compounds","volume":"81","author":"Jibran","year":"2014","journal-title":"Comp. Mater. Sci."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"375501","DOI":"10.1088\/0953-8984\/21\/37\/375501","article-title":"Luminescence of singlet self-trapped excitons in MgF2","volume":"21","author":"Kolobanov","year":"2009","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.nimb.2015.08.002","article-title":"Stabilization of primary mobile radiation defects in MgF2 crystals","volume":"374","author":"Lisitsyn","year":"2016","journal-title":"Nucl. Instruments Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms"},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Shishkin, M., and Kresse, G. (2007). Self-consistent GW calculations for semiconductors and insulators. Phys. Rev. B, 75.","DOI":"10.1103\/PhysRevB.75.235102"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"1840","DOI":"10.1021\/acs.jpclett.9b03423","article-title":"Accurate Absolute and Relative Core-Level Binding Energies from GW","volume":"11","author":"Golze","year":"2020","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"7570","DOI":"10.1021\/acs.jctc.2c00617","article-title":"Benchmark of GW Methods for Core-Level Binding Energies","volume":"18","author":"Li","year":"2022","journal-title":"J. Chem. Theory Comput."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"6637","DOI":"10.1021\/acs.jctc.2c00686","article-title":"Combining Renormalized Singles GW Methods with the Bethe\u2013Salpeter Equation for Accurate Neutral Excitation Energies","volume":"18","author":"Li","year":"2022","journal-title":"J. Chem. Theory Comput."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Eglitis, R.I., Purans, J., and Jia, R. (2021). Comparative Hybrid Hartree-Fock-DFT Calculations of WO2-Terminated Cubic WO3 as Well as SrTiO3, BaTiO3, PbTiO3 and CaTiO3 (001) Surfaces. Crystals, 11.","DOI":"10.3390\/cryst11040455"},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Botti, S., and Marques, M.A.L. (2013). Strong Renormalization of the Electronic Band Gap due to Lattice Polarization in the GW Formalism. Phys. Rev. Lett., 110.","DOI":"10.1103\/PhysRevLett.110.226404"},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Lambrecht, W.R.L., Bhandari, C., and van Schilfgaarde, M. (2017). Lattice polarization effects on the screened Coulomb interaction W of the GW approximation. Phys. Rev. Mater., 1.","DOI":"10.1103\/PhysRevMaterials.1.043802"},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Cao, H., Yu, Z., Lu, P., and Wang, L.W. (2017). Fully converged plane-wave-based self-consistent GW calculations of periodic solids. Phys. Rev. B, 95.","DOI":"10.1103\/PhysRevB.95.035139"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"4619","DOI":"10.1103\/PhysRevB.16.4619","article-title":"Electronic energy bands in the fluorite structure: CaF2 and CdF2","volume":"16","author":"Albert","year":"1977","journal-title":"Phys. Rev. B"},{"key":"ref_83","unstructured":"Fox, M. (2001). Optical Properties of Solids, Oxford University Press."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1103\/PhysRev.52.191","article-title":"The Structure of Electronic Excitation Levels in Insulating Crystals","volume":"52","author":"Wannier","year":"1937","journal-title":"Phys. Rev."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"195212\u20131","DOI":"10.1103\/PhysRevB.70.195212","article-title":"Many-body effects in the electronic spectra of cubic boron nitride","volume":"70","author":"Satta","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"125203\u20131","DOI":"10.1103\/PhysRevB.86.125203","article-title":"Speeding up the solution of the Bethe-Salpeter equation by a double-grid method and Wannier Wannier interpolation","volume":"86","author":"Kammerlander","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"16654","DOI":"10.1021\/acsomega.0c01516","article-title":"Time-Dependent Density Functional Theory Investigation on the Electronic and Optical Properties of Poly-C,Si,Ge-acenes","volume":"5","author":"Mocci","year":"2020","journal-title":"ACS Omega"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/539\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:39:13Z","timestamp":1760121553000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,17]]},"references-count":87,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["sym15020539"],"URL":"https:\/\/doi.org\/10.3390\/sym15020539","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,17]]}}}