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Their transferability to periodic materials, however, cannot be assessed reliably without a genuinely periodic Hamiltonian, Brillouin-zone sampling, and symmetry-aware crystal calculations. We present a periodic implementation of the second-generation geometry, frequency, and noncovalent interaction parametrization of extended tight binding (GFN2-xTB) in CP2K. The central theoretical ingredient is a multipolar Ewald formulation for the self-consistent shell charges, atomic dipoles, and quadrupoles of GFN2-xTB, together with analytical forces and stress contributions for geometry optimization, cell optimization, and molecular dynamics. For the ranking of ice polymorphs in the DMC-ICE13 data set, periodic GFN2-xTB on a converged 33k-point mesh improves the relative polymorph energies over GFN1-xTB, reducing the mean absolute error from 8.01 to 3.46 kJ mol\u20131. Because GFN1-xTB and GFN2-xTB differ in several coupled, jointly parametrized terms, this whole-model comparison does not isolate the contribution of multipolar electrostatics. For the LC10 set of cubic covalent and ionic solids, GFN2-xTB yields valid equation-of-state minima for all ten systems, with lattice-constant and cohesive-energy mean absolute errors of 0.062 \u00c5 and 1.30 eV per atom, respectively. Periodic GFN2-xTB is evaluated for molecular crystal lattice energies and cell parameters using the X23b data set. Using native Bloch 23-mesh cell optimization with full symmetry reduction, followed by a 33-mesh energy evaluation on the optimized cells, periodic GFN2-xTB gives a mean absolute lattice-energy error of 14.09 kJ mol\u20131 and a mean absolute relaxed-cell volume error of 5.84% for the full X23b relaxed-cell set. The benchmarks position periodic GFN2-xTB as an efficient electronic structure level for screening, pre-optimization, and large exploratory simulations. This work creates the foundation for periodic anisotropic electrostatics in the extended tight-binding framework and their efficient application in CP2K.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c01034","type":"journal-article","created":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T15:02:15Z","timestamp":1788879735000},"page":"9688-9699","source":"Crossref","is-referenced-by-count":1,"title":["Periodic GFN2-\n                    <i>x<\/i>\n                    TB in CP2K:\nMultipolar Ewald Electrostatics, k-Point Sampling, and Transferability\nBenchmarks for Solids"],"prefix":"10.1021","volume":"22","author":[{"given":"Vahideh","family":"Alizadeh","sequence":"first","affiliation":[{"name":"Center for Advanced Systems Understanding (CASUS) , Conrad-Schiedt-Stra\u00dfe 20 , ,","place":["Go\u0308rlitz, Germany, 02826"]},{"name":"Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstra\u00dfe 400 , ,","place":["Dresden, Germany, 01328"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9982-0556","authenticated-orcid":true,"given":"Johann","family":"Pototschnig","sequence":"additional","affiliation":[{"name":"Center for Advanced Systems Understanding (CASUS) , Conrad-Schiedt-Stra\u00dfe 20 , ,","place":["Go\u0308rlitz, Germany, 02826"]},{"name":"Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstra\u00dfe 400 , ,","place":["Dresden, Germany, 01328"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leopold M.","family":"Seidler","sequence":"additional","affiliation":[{"name":"Universita\u0308t Bonn , , Beringstra\u00dfe 4 , ,","place":["Bonn, Germany, 53115"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7809-771X","authenticated-orcid":true,"given":"Sebastian","family":"Ehlert","sequence":"additional","affiliation":[{"name":"Microsoft Research , , Karl-Liebknecht-Str. 32 , ,","place":["Berlin, Germany, 10178"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5471-2407","authenticated-orcid":true,"given":"Thomas D.","family":"Ku\u0308hne","sequence":"additional","affiliation":[{"name":"Center for Advanced Systems Understanding (CASUS) , Conrad-Schiedt-Stra\u00dfe 20 , ,","place":["Go\u0308rlitz, Germany, 02826"]},{"name":"Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstra\u00dfe 400 , ,","place":["Dresden, Germany, 01328"]},{"name":"Technische Universita\u0308t Dresden , , Helmholtzstra\u00dfe 10 , ,","place":["Dresden, Germany, 01069"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,8]]},"reference":[{"key":"2026092209071332800_cit1","doi-asserted-by":"publisher","first-page":"4899","DOI":"10.1021\/ja00457a004","article-title":"Ground States of Molecules. 38. 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