P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Phys. Rev. 136, B864-B871 (1964). 10.1103/physrev.136.b864
X. Gonze, J.-M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.-M. Rignanese, L. Sindic, M. Verstraete, G. Zérah, F. Jollet, M. Torrent, A. Roy, M. Mikami, P. Ghosez, J.-Y. Raty, and D. C. Allan, "First-principles computation of material properties: The ABINIT software project," Comput. Mater. Sci. 25, 478-492 (2002). 10.1016/s0927-0256(02)00325-7
X. Gonze, G.-M. Rignanese, M. Verstraete, J.-M. Beuken, Y. Pouillon, R. Caracas, F. Jollet, M. Torrent, G. Zerah, M. Mikami, P. Ghosez, M. Veithen, J.-Y. Raty, V. Olevano, F. Bruneval, L. Reining, R. Godby, G. Onida, D. Hamann, and D. Allan, "A brief introduction to the ABINIT software package," Z. Kristallogr.-Cryst. Mater. 220, 558-562 (2005). 10.1524/zkri.220.5.558.65066
X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Côté, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D. R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M. J. T. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.-M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M. J. Verstraete, G. Zérah, and J. W. Zwanziger, "ABINIT: First-principles approach to material and nanosystem properties," Comput. Phys. Commun. 180, 2582-2615 (2009). 10.1016/j.cpc.2009.07.007
X. Gonze, F. Jollet, F. Abreu Araujo, D. Adams, B. Amadon, T. Applencourt, C. Audouze, J.-M. Beuken, J. Bieder, A. Bokhanchuk, E. Bousquet, F. Bruneval, D. Caliste, M. Côté, F. Dahm, F. Da Pieve, M. Delaveau, M. Di Gennaro, B. Dorado, C. Espejo, G. Geneste, L. Genovese, A. Gerossier, M. Giantomassi, Y. Gillet, D. R. Hamann, L. He, G. Jomard, J. Laflamme Janssen, S. Le Roux, A. Levitt, A. Lherbier, F. Liu, I. Lukačević, A. Martin, C. Martins, M. J. T. Oliveira, S. Poncé, Y. Pouillon, T. Rangel, G.-M. Rignanese, A. H. Romero, B. Rousseau, O. Rubel, A. A. Shukri, M. Stankovski, M. Torrent, M. Van Setten, B. Van Troeye, M. J. Verstraete, D. Waroquiers, J. Wiktor, B. Xu, A. Zhou, and J. W. Zwanziger, "Recent developments in the ABINIT software package," Comput. Phys. Commun. 205, 106-131 (2016). 10.1016/j.cpc.2016.04.003
M. P. Teter and M. C. Payne, "Apparatus and methods for predicting physical and chemical properties of materials," (August 22, 2000).
R. M. Martin, Electronic Structure (Cambridge University Press, 2004).
S. Baroni, P. Giannozzi, and A. Testa, "Green's-function approach to linear response in solids," Phys. Rev. Lett. 58, 1861-1864 (1987). 10.1103/physrevlett.58.1861
X. Gonze and J.-P. Vigneron, "Density-functional approach to nonlinear-response coefficients of solids," Phys. Rev. B 39, 13120-13128 (1989). 10.1103/physrevb.39.13120
P. Giannozzi, S. de Gironcoli, P. Pavone, and S. Baroni, "Ab initio calculation of phonon dispersions in semiconductors," Phys. Rev. B 43, 7231 (1991). 10.1103/physrevb.43.7231
G. Onida, L. Reining, and A. Rubio, "Electronic excitations: Density-functional versus many-body Green's-function approaches," Rev. Mod. Phys. 74, 601-659 (2002). 10.1103/revmodphys.74.601
R. M. Martin, L. Reining, and D. M. Ceperley, Interacting Electrons. Theory and Computational Approaches (Cambrige University Press, Cambridge, 2016).
A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, "Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions," Rev. Mod. Phys. 68, 13-125 (1996). 10.1103/revmodphys.68.13
G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, "Electronic structure calculations with dynamical mean-field theory," Rev. Mod. Phys. 78, 865-951 (2006). 10.1103/revmodphys.78.865
B. Amadon, F. Jollet, and M. Torrent, "γ and β cerium: LDA + U calculations of ground-state parameters," Phys. Rev. B 77, 155104 (2008). 10.1103/physrevb.77.155104
B. Amadon and B. Dorado, "A unified and efficient theory for the structural properties of actinides and phases of plutonium," J. Phys.: Condens. Matter 30, 405603 (2018). 10.1088/1361-648x/aadc7a
X. Gonze, B. Amadon, G. Antonius, F. Arnardi, L. Baguet, J.-M. Beuken, J. Bieder, F. Bottin, J. Bouchet, E. Bousquet, N. Brouwer, F. Bruneval, G. Brunin, T. Cavignac, J.-B. Charraud, W. Chen, M. Côté, S. Cottenier, J. Denier, G. Geneste, P. Ghosez, M. Giantomassi, Y. Gillet, O. Gingras, D. R. Hamann, G. Hautier, X. He, N. Helbig, N. Holzwarth, Y. Jia, F. Jollet, W. Lafargue-Dit-Hauret, K. Lejaeghere, M. A. Marques, A. Martin, C. Martins, H. P. Miranda, F. Naccarato, K. Persson, G. Petretto, V. Planes, Y. Pouillon, S. Prokhorenko, F. Ricci, G.-M. Rignanese, A. H. Romero, M. M. Schmitt, M. Torrent, M. J. van Setten, B. V. Troeye, M. J. Verstraete, G. Zérah, and J. W. Zwanziger, "The abinit project: Impact, environment and recent developments," Comput. Phys. Commun. 248, 107042 (2020). 10.1016/j.cpc.2019.107042
A. Georges, "Strongly correlated electron materials: Dynamical mean-field theory and electronic structure," AIP Conf. Proc. 715, 3 (2004). 10.1063/1.1800733
B. Amadon, "A self-consistent DFT + DMFT scheme in the projector augmented wave method: Applications to cerium, Ce2O3 and Pu2O3 with the Hubbard I solver and comparison to DFT + U," J. Phys.: Condens. Matter 24, 075604 (2012). 10.1088/0953-8984/24/7/075604
B. Amadon, "First-principles DFT+DMFT calculations of structural properties of actinides: Role of Hund's exchange, spin-orbit coupling, and crystal structure," Phys. Rev. B 94, 115148 (2016). 10.1103/physrevb.94.115148
B. Amadon, F. Lechermann, A. Georges, F. Jollet, T. O. Wehling, and A. I. Lichtenstein, "Plane-wave based electronic structure calculations for correlated materials using dynamical mean-field theory and projected local orbitals," Phys. Rev. B 77, 205112 (2008). 10.1103/physrevb.77.205112
P. Werner, A. Comanac, L. de Medici, M. Troyer, and A. J. Millis, "Continuous-time solver for quantum impurity models," Phys. Rev. Lett. 97, 076405 (2006). 10.1103/physrevlett.97.076405
J. Bieder and B. Amadon, "Thermodynamics of the α-γ transition in cerium from first principles," Phys. Rev. B 89, 195132 (2014). 10.1103/physrevb.89.195132
D. Bergeron and A.-M. S. Tremblay, "Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation," Phys. Rev. E 94, 023303 (2016). 10.1103/physreve.94.023303
O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko, L. Messio, and P. Seth, "TRIQS: A toolbox for research on interacting quantum systems," Comput. Phys. Commun. 196, 398-415 (2015). 10.1016/j.cpc.2015.04.023
P. Seth, I. Krivenko, M. Ferrero, and O. Parcollet, "TRIQS/CTHYB: A continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impurity problems," Comput. Phys. Commun. 200, 274-284 (2016). 10.1016/j.cpc.2015.10.023
B. Amadon, T. Applencourt, and F. Bruneval, "Screened Coulomb interaction calculations: cRPA implementation and applications to dynamical screening and self-consistency in uranium dioxide and cerium," Phys. Rev. B 89, 125110 (2014). 10.1103/physrevb.89.125110
F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, "Frequency-dependent local interactions and low-energy effective models from electronic structure calculations," Phys. Rev. B 70, 195104 (2004). 10.1103/physrevb.70.195104
F. Aryasetiawan, K. Karlsson, O. Jepsen, and U. Schönberger, "Calculations of Hubbard U from first-principles," Phys. Rev. B 74, 125106 (2006). 10.1103/physrevb.74.125106
J.-B. Morée and B. Amadon, "First-principles calculation of Coulomb interaction parameters for lanthanides: Role of self-consistence and screening processes," Phys. Rev. B 98, 205101 (2018). 10.1103/physrevb.98.205101
B. Amadon and A. Gerossier, "Comparative analysis of models for the α-γ phase transition in cerium: A DFT+DMFT study using Wannier orbitals," Phys. Rev. B 91, 161103 (2015). 10.1103/physrevb.91.161103
O. Gingras, R. Nourafkan, A.-M. S. Tremblay, and M. Côté, "Superconducting symmetries of Sr2RuO4 from first-principles electronic structure," Phys. Rev. Lett. 123, 217005 (2019). 10.1103/physrevlett.123.217005
X. Gonze, "First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugate-gradient algorithm," Phys. Rev. B 55, 10337-10354 (1997). 10.1103/physrevb.55.10337
X. Gonze and C. Lee, "Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory," Phys. Rev. B 55, 10355-10368 (1997). 10.1103/physrevb.55.10355
R. Resta, "Macroscopic polarization in crystalline dielectrics: The geometric phase approach," Rev. Mod. Phys. 66, 899-915 (1994). 10.1103/revmodphys.66.899
R. W. Nunes and X. Gonze, "Berry-phase treatment of the homogeneous electric field perturbation in insulators," Phys. Rev. B 63, 155107 (2001). 10.1103/physrevb.63.155107
I. Souza, J. Íñiguez, and D. Vanderbilt, "First-principles approach to insulators in finite electric fields," Phys. Rev. Lett. 89, 117602 (2002). 10.1103/physrevlett.89.117602
J. W. Zwanziger, J. Galbraith, Y. Kipouros, M. Torrent, M. Giantomassi, and X. Gonze, "Finite homogeneous electric fields in the projector augmented wave formalism: Applications to linear and nonlinear response," Comput. Mater. Sci. 58, 113-118 (2012). 10.1016/j.commatsci.2012.01.028
J. W. Zwanziger, "Computation of Mössbauer isomer shifts from first principles," J. Phys.: Condens. Matter 21, 195501 (2009). 10.1088/0953-8984/21/19/195501
J. W. Zwanziger and M. Torrent, "First-principles calculation of electric field gradients in metals, semiconductors, and insulators," Appl. Magn. Reson. 33, 447-456 (2008). 10.1007/s00723-008-0080-1
J. W. Zwanziger, "First-principles study of the nuclear quadrupole resonance parameters and orbital ordering in LaTiO3," Phys. Rev. B 79, 033112 (2009). 10.1103/physrevb.79.033112
M. Torrent, F. Jollet, F. Bottin, G. Zérah, and X. Gonze, "Implementation of the projector augmented-wave method in the ABINIT code: Application to the study of iron under pressure," Comput. Mater. Sci. 42, 337-351 (2008). 10.1016/j.commatsci.2007.07.020
G. Kresse and D. Joubert, "From ultrasoft pseudopotentials to the projector augmented-wave method," Phys. Rev. B 59, 1758-1775 (1999). 10.1103/physrevb.59.1758
P. E. Blöchl, "Projector augmented-wave method," Phys. Rev. B 50, 17953-17979 (1994). 10.1103/physrevb.50.17953
M. Profeta, F. Mauri, and C. J. Pickard, "Accurate first principles prediction of 17O NMR parameters in SiO2: Assignment of the zeolite ferrierite spectrum," J. Am. Chem. Soc. 125, 541-548 (2003). 10.1021/ja027124r
A. Honma, "Dipolar lattice-sums with applications to the exciton bands of anthracene crystal and the crystal field due to point charges," J. Phys. Soc. Jpn. 42, 1129-1135 (1977). 10.1143/jpsj.42.1129
M. J. Puska and R. M. Nieminen, "Theory of positrons in solids and on solid surfaces," Rev. Mod. Phys. 66, 841-897 (1994). 10.1103/revmodphys.66.841
E. Boroński and R. M. Nieminen, "Electron-positron density-functional theory," Phys. Rev. B 34, 3820-3831 (1986). 10.1103/physrevb.34.3820
F. Tuomisto and I. Makkonen, "Defect identification in semiconductors with positron annihilation: Experiment and theory," Rev. Mod. Phys. 85, 1583-1631 (2013). 10.1103/revmodphys.85.1583
M. J. Puska, A. P. Seitsonen, and R. M. Nieminen, "Electron-positron Car-Parrinello methods: Self-consistent treatment of charge densities and ionic relaxations," Phys. Rev. B 52, 10947-10961 (1995). 10.1103/physrevb.52.10947
B. Barbiellini, M. J. Puska, T. Torsti, and R. M. Nieminen, "Gradient correction for positron states in solids," Phys. Rev. B 51, 7341-7344 (1995). 10.1103/physrevb.51.7341
B. Barbiellini, M. J. Puska, T. Korhonen, A. Harju, T. Torsti, and R. M. Nieminen, "Calculation of positron states and annihilation in solids: A density-gradient-correction scheme," Phys. Rev. B 53, 16201-16213 (1996). 10.1103/physrevb.53.16201
J. Wiktor, G. Jomard, and M. Torrent, "Two-component density functional theory within the projector augmented-wave approach: Accurate and self-consistent computations of positron lifetimes and momentum distributions," Phys. Rev. B 92, 125113 (2015). 10.1103/physrevb.92.125113
J. Wiktor, G. Jomard, M. Torrent, and M. Bertolus, "Electronic structure investigation of energetics and positron lifetimes of fully relaxed monovacancies with various charge states in 3 C-SiC and 6 H-SiC," Phys. Rev. B 87, 235207 (2013). 10.1103/physrevb.87.235207
J. Wiktor, X. Kerbiriou, G. Jomard, S. Esnouf, M.-F. Barthe, and M. Bertolus, "Positron annihilation spectroscopy investigation of vacancy clusters in silicon carbide: Combining experiments and electronic structure calculations," Phys. Rev. B 89, 155203 (2014). 10.1103/physrevb.89.155203
J. Wiktor, G. Jomard, and M. Bertolus, "Electronic structure calculations of positron lifetimes in SiC: Self-consistent schemes and relaxation effect," Nucl. Instrum. Methods Phys. Res., Sect. B 327, 63-67 (2014). 10.1016/j.nimb.2013.09.050
J. Wiktor, M.-F. Barthe, G. Jomard, M. Torrent, M. Freyss, and M. Bertolus, "Coupled experimental and DFT + U investigation of positron lifetimes in UO2," Phys. Rev. B 90, 184101 (2014). 10.1103/physrevb.90.184101
J. Wiktor, G. Jomard, M. Torrent, and M. Bertolus, "First-principles calculations of momentum distributions of annihilating electron-positron pairs in defects in UO2," J. Phys.: Condens. Matter 29, 035503 (2016). 10.1088/1361-648x/29/3/035503
S. Hagiwara, Y. Suzuki, and K. Watanabe, "Spin-polarized annihilation lifetime of positron of d ferromagnetism in gallium nitride: A two-component density functional theory simulation," Appl. Phys. Express 9, 041001 (2016). 10.7567/apex.9.041001
A. Marinopoulos, "Positron lifetimes of bare and hydrogenated zirconium vacancies in cubic yttria-stabilized zirconia: An ab initio study," J. Phys.: Condens. Matter 31, 315503 (2019). 10.1088/1361-648x/ab1d18
S. Hagiwara and K. Watanabe, "Positron states at Li-and O-adsorbed Fe (001) ferromagnetic surfaces studied by two-component density functional theory," J. Phys. Soc. Jpn. 85, 114703 (2016). 10.7566/jpsj.85.114703
W. Humphrey, A. Dalke, and K. Schulten, "VMD: Visual molecular dynamics," J. Mol. Graphics 14, 33-38 (1996). 10.1016/0263-7855(96)00018-5
D. R. Hamann, X. Wu, K. M. Rabe, and D. Vanderbilt, "Metric tensor formulation of strain in density-functional perturbation theory," Phys. Rev. B 71, 035117 (2005). 10.1103/physrevb.71.035117
X. Gonze, P. Ghosez, and R. W. Godby, "Density-polarization functional theory of the response of a periodic insulating solid to an electric field," Phys. Rev. Lett. 74, 4035-4038 (1995). 10.1103/physrevlett.74.4035
M. Veithen, X. Gonze, and P. Ghosez, "Nonlinear optical susceptibilities, Raman efficiencies, and electro-optic tensors from first-principles density functional perturbation theory," Phys. Rev. B 71, 125107 (2005). 10.1103/physrevb.71.125107
G. Placzek, Marx Handbuch Der Radiologie (Akademische Ver-lagsgesellschaft, Leipzig, 1934).
M. Cardona and G. Güntherodt, Light Scattering in Solids II (Springer, 1982).
P. Brüesch, Phonons: Theory and Experiments II (Springer, 1986).
W. D. Johnston, "Nonlinear optical coefficients and the Raman scattering efficiency of LO and TO phonons in acentric insulating crystals," Phys. Rev. B 1, 3494-3503 (1970). 10.1103/physrevb.1.3494
M. Veithen, X. Gonze, and P. Ghosez, "First-principles study of the electro-optic effect in ferroelectric oxides," Phys. Rev. Lett. 93, 187401 (2004). 10.1103/physrevlett.93.187401
K. Miwa, "Prediction of Raman spectra with ultrasoft pseudopotentials," Phys. Rev. B 84, 094304 (2011). 10.1103/physrevb.84.094304
B. Lafuente, R. Downs, H. Yang, and N. Stone, "The power of databases: The RRUFF project," in Highlights in Mineralogical Crystallography (Walter de Gruyter GmbH, 2016), pp. 1-29, http://rruff.info/(sample id. R040031).
S. A. Prosandeev, U. Waghmare, I. Levin, and J. Maslar, "First-order Raman spectra of AB 1/2 ′ B 1/2 ″ O3 double perovskites," Phys. Rev. B 71, 214307 (2005). 10.1103/physrevb.71.214307
R. Caracas and R. E. Cohen, "Theoretical determination of the Raman spectra of MgSiO3 perovskite and post-perovskite at high pressure," Geophys. Res. Lett. 33, L12S05, https://doi.org/10.1029/2006gl025736 (2006). 10.1029/2006gl025736
P. Hermet, M. Veithen, and P. Ghosez, "First-principles calculations of the nonlinear optical susceptibilities and Raman scattering spectra of lithium niobate," J. Phys.: Condens. Matter 19, 456202 (2007). 10.1088/0953-8984/19/45/456202
P. Hermet, M. Veithen, and P. Ghosez, "Raman scattering intensities in BaTiO3 and PbTiO3 prototypical ferroelectrics from density functional theory," J. Phys.: Condens. Matter 21, 215901 (2009). 10.1088/0953-8984/21/21/215901
H. Djani, P. Hermet, and P. Ghosez, "First-principles characterization of the P 21 ab ferroelectric phase of aurivillius Bi2WO6," J. Phys. Chem. C 118, 13514 (2014). 10.1021/jp504674k
P. Hermet and P. Ghosez, "First-principles study of the dynamical and nonlinear optical properties of urea single crystals," Phys. Chem. Chem. Phys. 12, 835-843 (2010). 10.1039/b917347a
N. A. Pike, A. Dewandre, B. Van Troeye, X. Gonze, and M. J. Verstraete, "Vibrational and dielectric properties of the bulk transition metal dichalcogenides," Phys. Rev. Mater. 2, 063608 (2018). 10.1103/physrevmaterials.2.063608
N. A. Pike, A. Dewandre, B. Van Troeye, X. Gonze, and M. J. Verstraete, "Vibrational and dielectric properties of the monolayer transition metal dichalcogenides," Phys. Rev. Mater. 3, 074009 (2019). 10.1103/physrevmaterials.3.074009
R. Caracas, "Database of computed Raman and infrared spectra and other physical properties of minerals," http://www.wurm.info, 26 November 2019.
D. Sando, P. Hermet, J. Allibe, J. Bourderionnet, S. Fusil, C. Carrétéro, E. Jacquet, J.-C. Mage, D. Dolfi, A. Barthélémy, P. Ghosez, and M. Bibes, "Linear electro-optic effect in multiferroic BiFeO3 thin films," Phys. Rev. B 89, 195106 (2014). 10.1103/physrevb.89.195106
M. Veithen and P. Ghosez, "Temperature dependence of the electro-optic tensor and refractive indices of BaTiO3 from first principles," Phys. Rev. B 71, 132101 (2005). 10.1103/physrevb.71.132101
X. Wu, D. Vanderbilt, and D. R. Hamann, "Systematic treatment of displacements, strains, and electric fields in density-functional perturbation theory," Phys. Rev. B 72, 035105 (2005). 10.1103/physrevb.72.035105
R. D. King-Smith and D. Vanderbilt, "Theory of polarization of crystalline solids," Phys. Rev. B 47, 1651-1654 (1993). 10.1103/physrevb.47.1651
D. R. Hamann, K. M. Rabe, and D. Vanderbilt, "Generalized-gradient-functional treatment of strain in density-functional perturbation theory," Phys. Rev. B 72, 033102 (2005). 10.1103/physrevb.72.033102
A. Martin, M. Torrent, and R. Caracas, "Projector augmented-wave formulation of response to strain and electric-field perturbation within density functional perturbation theory," Phys. Rev. B 99, 094112 (2019). 10.1103/physrevb.99.094112
S. Grimme, "Semiempirical GGA-type density functional constructed with a long-range dispersion correction," J. Comput. Chem. 27, 1787-1799 (2006). 10.1002/jcc.20495
S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, "A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu," J. Chem. Phys. 132, 154104 (2010). 10.1063/1.3382344
H. Rydberg, M. Dion, N. Jacobson, E. Schröder, P. Hyldgaard, S. I. Simak, D. C. Langreth, and B. I. Lundqvist, "Van der Waals density functional for layered structures," Phys. Rev. Lett. 91, 126402 (2003). 10.1103/physrevlett.91.126402
M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, "Van der Waals density functional for general geometries," Phys. Rev. Lett. 92, 246401 (2004). 10.1103/physrevlett.92.246401
A. Tkatchenko and M. Scheffler, "Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data," Phys. Rev. Lett. 102, 073005 (2009). 10.1103/physrevlett.102.073005
A. M. Reilly and A. Tkatchenko, "van der Waals dispersion interactions in molecular materials: beyond pairwise additivity," Chem. Sci. 6, 3289-3301 (2015). 10.1039/c5sc00410a
B. Van Troeye, M. Torrent, and X. Gonze, "Interatomic force constants including the DFT-D dispersion contribution," Phys. Rev. B 93, 144304 (2016). 10.1103/physrevb.93.144304
B. Van Troeye, M. J. van Setten, M. Giantomassi, M. Torrent, G.-M. Rignanese, and X. Gonze, "First-principles study of paraelectric and ferroelectric CsH2PO4 including dispersion forces: Stability and related vibrational, dielectric, and elastic properties," Phys. Rev. B 95, 024112 (2017). 10.1103/physrevb.95.024112
C. P. Romao, "Anomalous thermal expansion and chiral phonons in BiB3O6," Phys. Rev. B 100, 060302 (2019). 10.1103/physrevb.100.060302
M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, Oxford, 1954).
R. Resta, "Towards a bulk theory of flexoelectricity," Phys. Rev. Lett. 105, 127601 (2010). 10.1103/physrevlett.105.127601
J. Hong and D. Vanderbilt, "First-principles theory of frozen-ion flexoelectricity," Phys. Rev. B 84, 180101(R) (2011). 10.1103/physrevb.84.180101
J. Hong and D. Vanderbilt, "First-principles theory and calculation of flexoelectricity," Phys. Rev. B 88, 174107 (2013). 10.1103/physrevb.88.174107
M. Stengel, "Flexoelectricity from density-functional perturbation theory," Phys. Rev. B 88, 174106 (2013). 10.1103/physrevb.88.174106
M. Stengel, "Microscopic response to inhomogeneous deformations in curvilinear coordinates," Nat. Commun. 4, 2693 (2013). 10.1038/ncomms3693
M. Stengel, "Surface control of flexoelectricity," Phys. Rev. B 90, 201112(R) (2014). 10.1103/physrevb.90.201112
M. Stengel and D. Vanderbilt, "First-principles theory of flexoelectricity," in Flexoelectricity in Solids From Theory to Applications, edited by A. K. Tagantsev and P. V. Yudin (World Scientific Publishing Co., Singapore, 2016), Chap. 2, pp. 31-110.
M. Stengel and D. Vanderbilt, "Quantum theory of mechanical deformations," Phys. Rev. B 98, 125133 (2018). 10.1103/physrevb.98.125133
A. Schiaffino, C. E. Dreyer, D. Vanderbilt, and M. Stengel, "Metric-wave approach to flexoelectricity within density-functional perturbation theory," Phys. Rev. B 99, 085107 (2019). 10.1103/physrevb.99.085107
C. E. Dreyer, M. Stengel, and D. Vanderbilt, "Current-density implementation for calculating flexoelectric coefficients," Phys. Rev. B 98, 075153 (2018). 10.1103/physrevb.98.075153
M. Royo and M. Stengel, "First-principles theory of spatial dispersion: Dynamical quadrupoles and flexoelectricity," Phys. Rev. X 9, 021050 (2019). 10.1103/physrevx.9.021050
R. M. Martin, "Piezoelectricity," Phys. Rev. B 5, 1607-1613 (1972). 10.1103/physrevb.5.1607
F. Giustino, "Electron-phonon interactions from first principles," Rev. Mod. Phys. 89, 015003 (2017). 10.1103/revmodphys.89.015003
P. B. Allen, "New method for solving Boltzmann's equation for electrons in metals," Phys. Rev. B 17, 3725-3734 (1978). 10.1103/physrevb.17.3725
S. Y. Savrasov and D. Y. Savrasov, "Electron-phonon interactions and related physical properties of metals from linear-response theory," Phys. Rev. B 54, 16487-16501 (1996). 10.1103/physrevb.54.16487
B. Xu and M. J. Verstraete, "First principles explanation of the positive Seebeck coefficient of lithium," Phys. Rev. Lett. 112, 196603 (2014). 10.1103/physrevlett.112.196603
P. B. Allen and V. Heine, "Theory of the temperature dependence of electronic band structures," J. Phys. C: Solid State Phys. 9, 2305-2312 (1976). 10.1088/0022-3719/9/12/013
P. B. Allen and M. Cardona, "Temperature dependence of the direct gap of Si and Ge," Phys. Rev. B 27, 4760-4769 (1983). 10.1103/physrevb.27.4760
S. Poncé, G. Antonius, P. Boulanger, E. Cannuccia, A. Marini, M. Côté, and X. Gonze, "Verification of first-principles codes: Comparison of total energies, phonon frequencies, electron-phonon coupling and zero-point motion correction to the gap between ABINIT and QE/Yambo," Comput. Mater. Sci. 83, 341-348 (2014). 10.1016/j.commatsci.2013.11.031
G. Antonius, S. Poncé, P. Boulanger, M. Côté, and X. Gonze, "Many-body effects on the zero-point renormalization of the band structure," Phys. Rev. Lett. 112, 215501 (2014). 10.1103/physrevlett.112.215501
G. Antonius, S. Poncé, E. Lantagne-Hurtubise, G. Auclair, X. Gonze, and M. Côté, "Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure," Phys. Rev. B 92, 085137 (2015). 10.1103/physrevb.92.085137
S. Poncé, Y. Gillet, J. Laflamme Janssen, A. Marini, M. Verstraete, and X. Gonze, "Temperature dependence of the electronic structure of semiconductors and insulators," J. Chem. Phys. 143, 102813 (2015). 10.1063/1.4927081
S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, "Phonons and related crystal properties from density-functional perturbation theory," Rev. Mod. Phys. 73, 515-562 (2001). 10.1103/revmodphys.73.515
J. P. Nery, P. B. Allen, G. Antonius, L. Reining, A. Miglio, and X. Gonze, "Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to the full first-principles theory and the Fröhlich polaron," Phys. Rev. B 97, 115145 (2018). 10.1103/physrevb.97.115145
F. Brown-Altvater, G. Antonius, T. Rangel, M. Giantomassi, C. Draxl, X. Gonze, S. G. Louie, and J. B. Neaton, "Band gap renormalization, carrier mobilities, and the electron-phonon self-energy in crystalline naphthalene," Phys. Rev. B (to be published).
A. Eiguren and C. Ambrosch-Draxl, "Wannier interpolation scheme for phonon-induced potentials: Application to bulk MgB2, W, and the (1 × 1) H-covered W(110) surface," Phys. Rev. B 78, 045124 (2008). 10.1103/physrevb.78.045124
P. Vogl, "Microscopic theory of electron-phonon interaction in insulators or semiconductors," Phys. Rev. B 13, 694-704 (1976). 10.1103/physrevb.13.694
C. Verdi and F. Giustino, "Fröhlich electron-phonon vertex from first principles," Phys. Rev. Lett. 115, 176401 (2015). 10.1103/physrevlett.115.176401
J. Sjakste, N. Vast, M. Calandra, and F. Mauri, "Wannier interpolation of the electron-phonon matrix elements in polar semiconductors: Polar-optical coupling in GaAs," Phys. Rev. B 92, 054307 (2015). 10.1103/physrevb.92.054307
X. Gonze, P. Boulanger, and M. Côté, "Theoretical approaches to the temperature and zero-point motion effects on the electronic band structure," Ann. Phys. 523, 168-178 (2010). 10.1002/andp.201000100
Y.-H. Chan, G. Antonius, and S. G. Louie, "Polaron spectral properties in ZnO and SrTiO3 from first principles," (unpublished).
S. Ponce, E. R. Margine, and F. Giustino, "Towards predictive many-body calculations of phonon-limited carrier mobilities in semiconductors," Phys. Rev. B 97, 121201(R) (2018). 10.1103/physrevb.97.121201
G. K. H. Madsen, J. Carrete, and M. J. Verstraete, "BoltzTraP2, a program for interpolating band structures and calculating semi-classical transport coefficients," Comput. Phys. Commun. 231, 140-145 (2018). 10.1016/j.cpc.2018.05.010
J. Deslippe, G. Samsonidze, D. A. Strubbe, M. Jain, M. L. Cohen, and S. G. Louie, "BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures," Comput. Phys. Commun. 183, 1269-1289 (2012). 10.1016/j.cpc.2011.12.006
Z. Li, G. Antonius, M. Wu, F. H. da Jornada, and S. G. Louie, "Electron-phonon coupling from ab initio linear-response theory within the GW method: Correlation-enhanced interactions and superconductivity in Ba1-xKxBiO3," Phys. Rev. Lett. 122, 186402 (2019). 10.1103/physrevlett.122.186402
G. M. Rignanese, J. P. Michenaud, and X. Gonze, "Ab initio study of the volume dependence of dynamical and thermodynamical properties of silicon," Phys. Rev. B 53, 4488-4497 (1996). 10.1103/physrevb.53.4488
G. Leibfried and W. Ludwig, "Theory of anharmonic effects in crystals, "in Solid State Physics Vol. 12 (Academic Press, New York, 1961), pp. 275-444.
A. A. Maradudin and A. E. Fein, "Scattering of neutrons by anharmonic crystal," Phys. Rev. 128, 2589 (1962). 10.1103/physrev.128.2589
T. Barron and M. Klein, Dynamical Properties of Solids: Volume 1. Crystalline Solids, Fundamentals (North Holland, Amsterdam, 1974), p. 391.
P. Brüesch, Phonons: Theory and Experiments I (Springer-Verlag, Berlin, Heidelberg, 1982).
D. C. Wallace, Thermodynamics of Crystals (Dover, New York, 1997).
D. C. Wallace, Statistical Physics of Crystals and Liquids (World Scientific Publishing Company, Singapore, 2003).
A. Togo, F. Oba, and I. Tanaka, "First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressure," Phys. Rev. B 78, 134106 (2008). 10.1103/physrevb.78.134106
A. Carreras, A. Togo, and I. Tanaka, "Dynaphopy: A code for extracting phonon quasiparticles from molecular dynamics simulations," Comput. Phys. Commun. 221, 221 (2017). 10.1016/j.cpc.2017.08.017
T. Tadano, Y. Gohda, and S. Tsuneyuki, "Anharmonic force constants extracted from first-principles molecular dynamics: Applications to heat transfer simulations," J. Phys. Condens. Matter 26, 225012 (2014). 10.1088/0953-8984/26/22/225402
I. Errea, M. Calandra, and F. Mauri, "First-principles theory of anharmonicity and the inverse isotope effect in superconducting palladium-hydride compounds," Phys. Rev. Lett. 111, 177002 (2013). 10.1103/physrevlett.111.177002
L. J. Nelson, G. L. W. Hart, F. Zhou, and V. Ozolins, "Compressive sensing as a paradigm for building physics models," Phys. Rev. B 87, 035125 (2013). 10.1103/physrevb.87.035125
A. Glensk, B. Grabowski, T. Hickel, and J. Neugebauer, "Breakdown of the Arrhenius law in describing vacancy formation energies: The importance of local anharmonicity revealed by ab initio thermodynamics," Phys. Rev. X 4, 011018 (2014). 10.1103/physrevx.4.011018
C. Toher, J. J. Plata, O. Levy, M. de Jong, M. Asta, M. B. Nardelli, and S. Curtarolo, "High-throughpout computational screening of thermal conductivity, Debye temperature, and Grüneisen parameters using a quasiharmonic Debye model," Phys. Rev. B 90, 174107 (2014). 10.1103/physrevb.90.174107
K. Esfarjani and H. T. Stokes, "Method to extract anharmonic force constants from first principles calculations," Phys. Rev. B 77, 144112 (2008). 10.1103/physrevb.77.144112
O. Hellman, I. A. Abrikosov, and S. I. Simak, "Lattice dynamics of anharmonic solids from first principles," Phys. Rev. B 84, 180301(R) (2011). 10.1103/physrevb.84.180301
O. Hellman, P. Steneteg, I. A. Abrikosov, and S. I. Simak, "Temperature dependent effective potential method for accurate free energy calculations of solids," Phys. Rev. B 87, 104111 (2013). 10.1103/physrevb.87.104111
O. Hellman and I. A. Abrikosov, "Temperature-dependent effective third-order interatomic force constants from first principles," Phys. Rev. B 88, 144301 (2013). 10.1103/physrevb.88.144301
C. Lee and X. Gonze, "Ab initio calculation of the thermodynamic properties and atomic temperature factors SiO2 α-quartz and stishovite," Phys. Rev. B 51, 8610-8613 (1995). 10.1103/physrevb.51.8610
J. Shiomi, K. Esfarjani, and G. Chen, "Thermal conductivity of half-Heusler compounds from first-principles calculations," Phys. Rev. B 84, 104302 (2011). 10.1103/physrevb.84.104302
C. H. Lee and C. K. Gan, "Anharmonic interatomic force constants and thermal conductivity from Grüneisen parameters: An application to graphene," Phys. Rev. B 96, 035105 (2017). 10.1103/physrevb.96.035105
J. Bouchet and F. Bottin, "Thermal evolution of vibrational properties of α-U," Phys. Rev. B 92, 174108 (2015). 10.1103/physrevb.92.174108
A. Dewaele, V. Stutzmann, J. Bouchet, F. Bottin, F. Occelli, and M. Mezouar, "High pressure-temperature phase diagram and equation of state of titanium," Phys. Rev. B 91, 134108 (2015). 10.1103/physrevb.91.134108
J. Bouchet and F. Bottin, "High-temperature and high-pressure phase transitions in uranium," Phys. Rev. B 95, 054113 (2017). 10.1103/physrevb.95.054113
B. Dorado, F. Bottin, and J. Bouchet, "Phonon spectra of plutonium at high temperatures," Phys. Rev. B 95, 104303 (2017). 10.1103/physrevb.95.104303
J. Bouchet, F. Bottin, V. Recoules, F. Remus, G. Morard, R. M. Bolis, and A. Benuzzi-Mounaix, "Ab initio calculations of the B1-B2 phase transition in MgO," Phys. Rev. B 99, 094113 (2019). 10.1103/physrevb.99.094113
F. Bottin, J. Bouchet, and J. Bieder, "a-tdep: Temperature dependent effective potential for abinit. Thermodynamic properties using second and third order interatomic force constants," Comput. Phys. Commun (submitted) (2019).
M. J. Verstraete, M. Torrent, F. Jollet, G. Zérah, and X. Gonze, "Density functional perturbation theory with spin-orbit coupling: Phonon band structure of lead," Phys. Rev. B 78, 045119 (2008). 10.1103/physrevb.78.045119
J. E. Peralta, G. E. Scuseria, and M. J. Frisch, "Noncollinear magnetism in density functional calculations," Phys. Rev. B 75, 125119 (2007). 10.1103/physrevb.75.125119
D. Hobbs, G. Kresse, and J. Hafner, "Fully unconstrained noncollinear magnetism within the projector augmented-wave method," Phys. Rev. B 62, 11556-11570 (2000). 10.1103/physrevb.62.11556
J. Kubler, K. H. Hock, J. Sticht, and A. R. Williams, "Density functional theory of non-collinear magnetism," J. Phys. F: Met. Phys. 18, 469 (1988). 10.1088/0305-4608/18/3/018
F. Ricci, S. Prokhorenko, M. Torrent, M. J. Verstraete, and E. Bousquet, "Density functional perturbation theory within noncollinear magnetism," Phys. Rev. B 99, 184404 (2019). 10.1103/physrevb.99.184404
Note that the meaning of ixcrot was unfortunately inverted in Ref. 166 with respect to the actual implementation.
S. Y. Savrasov, "Linear response calculations of spin fluctuations," Phys. Rev. Lett. 81, 2570-2573 (1998). 10.1103/physrevlett.81.2570
K. Cao, H. Lambert, P. G. Radaelli, and F. Giustino, "Ab initio calculation of spin fluctuation spectra using time-dependent density functional perturbation theory, plane waves, and pseudopotentials," Phys. Rev. B 97, 024420 (2018). 10.1103/physrevb.97.024420
M. Pajda, J. Kudrnovský, I. Turek, V. Drchal, and P. Bruno, "Ab initio calculations of exchange interactions, spin-wave stiffness constants, and Curie temperatures of Fe, Co, and Ni," Phys. Rev. B 64, 174402 (2001). 10.1103/physrevb.64.174402
Y. Gillet, M. Giantomassi, and X. Gonze, "Efficient on-the-fly interpolation technique for Bethe-Salpeter calculations of optical spectra," Comput. Phys. Commun. 203, 83-93 (2016). 10.1016/j.cpc.2016.02.008
Y. Gillet, M. Giantomassi, and X. Gonze, "First-principles study of excitonic effects in Raman intensities," Phys. Rev. B 88, 094305 (2013). 10.1103/physrevb.88.094305
Y. Gillet, S. Kontur, M. Giantomassi, C. Draxl, and X. Gonze, "Ab initio approach to second-order resonant Raman scattering including exciton-phonon interaction," Sci. Rep. 7, 7344 (2017). 10.1038/s41598-017-07682-y
Y. Gillet, "Ab initio study of Raman and optical spectra of crystalline materials and their temperature dependence," Ph.D. thesis, Université catholique de Louvain, Louvain-la-neuve, Belgium, 2017.
A. Marini, "Ab initio finite-temperature excitons," Phys. Rev. Lett. 101, 106405 (2008). 10.1103/physrevlett.101.106405
G. E. Jellison and F. A. Modine, "Optical functions of silicon between 1.7 and 4.7 eV at elevated temperatures," Phys. Rev. B 27, 7466 (1983). 10.1103/physrevb.27.7466
K. F. Garrity, J. W. Bennett, K. M. Rabe, and D. Vanderbilt, "Pseudopotentials for high-throughput DFT calculations," Comput. Mater. Sci. 81, 446-452 (2014). 10.1016/j.commatsci.2013.08.053
K. Lejaeghere, G. Bihlmayer, T. Björkman, P. Blaha, S. Blügel, V. Blum, D. Caliste, I. E. Castelli, S. J. Clark, A. Dal Corso, S. de Gironcoli, T. Deutsch, J. K. Dewhurst, I. Di Marco, C. Draxl, M. Dułak, O. Eriksson, J. A. Flores-Livas, K. F. Garrity, L. Genovese, P. Giannozzi, M. Giantomassi, S. Goedecker, X. Gonze, O. Grånäs, E. K. U. Gross, A. Gulans, F. Gygi, D. R. Hamann, P. J. Hasnip, N. A. W. Holzwarth, D. Iuşan, D. B. Jochym, F. Jollet, D. Jones, G. Kresse, K. Koepernik, E. Küçükbenli, Y. O. Kvashnin, I. L. M. Locht, S. Lubeck, M. Marsman, N. Marzari, U. Nitzsche, L. Nordström, T. Ozaki, L. Paulatto, C. J. Pickard, W. Poelmans, M. I. J. Probert, K. Refson, M. Richter, G.-M. Rignanese, S. Saha, M. Scheffler, M. Schlipf, K. Schwarz, S. Sharma, F. Tavazza, P. Thunström, A. Tkatchenko, M. Torrent, D. Vanderbilt, M. J. van Setten, V. Van Speybroeck, J. M. Wills, J. R. Yates, G.-X. Zhang, and S. Cottenier, "Reproducibility in density functional theory calculations of solids," Science 351, aad3000 (2016). 10.1126/science.aad3000
F. Jollet, M. Torrent, and N. Holzwarth, "Generation of projector augmented-wave atomic data: A 71 element validated table in the XML format," Comput. Phys. Commun. 185, 1246-1254 (2014). 10.1016/j.cpc.2013.12.023
N. A. W. Holzwarth, A. R. Tackett, and G. E. Matthews, "A projector augmented wave (PAW) code for electronic structure calculations, Part I: Atompaw for generating atom-centered functions," Comput. Phys. Commun. 135, 329-347 (2001). 10.1016/s0010-4655(00)00244-7
PAW-XML, XML specification for atomic PAW datasets, https://esl.cecam.org/Paw-xml, 26 November 2019.
L. G. Ferreira, M. Marques, and L. K. Teles, "Approximation to density functional theory for the calculation of band gaps of semiconductors," Phys. Rev. B 78, 125116 (2008). 10.1103/physrevb.78.125116
M. J. van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G.-M. Rignanese, "The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table," Comput. Phys. Commun. 226, 39-54 (2018). 10.1016/j.cpc.2018.01.012
S. G. Louie, S. Froyen, and M. L. Cohen, "Nonlinear ionic pseudopotentials in spin-density-functional calculations," Phys. Rev. B 26, 1738-1742 (1982). 10.1103/physrevb.26.1738
M. Teter, "Additional condition for transferability in pseudopotentials," Phys. Rev. B 48, 5031-5041 (1993). 10.1103/physrevb.48.5031
D. R. Hamann, "Optimized norm-conserving Vanderbilt pseudopotentials," Phys. Rev. B 88, 085117 (2013). 10.1103/physrevb.88.085117
A. García, M. J. Verstraete, Y. Pouillon, and J. Junquera, "The psml format and library for norm-conserving pseudopotential data curation and interoperability," Comput. Phys. Commun. 227, 51-71 (2018). 10.1016/j.cpc.2018.02.011
X. Gonze, C.-O. Almbladh, A. Cucca, D. Caliste, C. Freysoldt, M. Marques, V. Olevano, Y. Pouillon, and M. Verstraete, "Specification of an extensible and portable file format for electronic structure and crystallographic data," Comput. Mater. Sci. 43, 1056-1065 (2008). 10.1016/j.commatsci.2008.02.023
D. Caliste, Y. Pouillon, M. J. Verstraete, V. Olevano, and X. Gonze, "Sharing electronic structure and crystallographic data with ETSF_IO," Comput. Phys. Commun. 179, 748-758 (2008). 10.1016/j.cpc.2008.05.007
M. Giantomassi et al., Abipy project, https://github.com/abinit/abipy.
A. Jain, S. P. Ong, W. Chen, B. Medasani, X. Qu, M. Kocher, M. Brafman, G. Petretto, G.-M. Rignanese, G. Hautier, D. Gunter, and K. A. Persson, "FireWorks: A dynamic workflow system designed for high-throughput applications," Concurrency Comput.: Pract. Exper. 27, 5037-5059 (2015). 10.1002/cpe.3505
G. Petretto, X. Gonze, G. Hautier, and G.-M. Rignanese, "Convergence and pitfalls of density functional perturbation theory phonons calculations from a high-throughput perspective," Comput. Mater. Sci. 144, 331-337 (2018). 10.1016/j.commatsci.2017.12.040
G. Petretto, S. Dwaraknath, H. P. C. Miranda, D. Winston, M. Giantomassi, M. J. van Setten, X. Gonze, K. A. Persson, G. Hautier, and G.-M. Rignanese, "High-throughput density-functional perturbation theory phonons for inorganic materials," Sci. Data 5, 180065 (2018). 10.1038/sdata.2018.65
A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, "The materials project: A materials genome approach to accelerating materials innovation," APL Mater. 1, 011002 (2013). 10.1063/1.4812323
S. K. Kurtz and T. T. Perry, "A powder technique for the evaluation of nonlinear optical materials," J. Appl. Phys. 39, 3798-3813 (1968). 10.1063/1.1656857
J. M. Rondinelli and E. Kioupakis, "Predicting and designing optical properties of inorganic materials," Annu. Rev. Mater. Res. 45, 491-518 (2015). 10.1146/annurev-matsci-070214-021150
I. Petousis, D. Mrdjenovich, E. Ballouz, M. Liu, D. Winston, W. Chen, T. Graf, T. D. Schladt, K. A. Persson, and F. B. Prinz, "High-throughput screening of inorganic compounds for the discovery of novel dielectric and optical materials," Sci. Data 4, 160134 (2017). 10.1038/sdata.2016.134
F. Naccarato, F. Ricci, J. Suntivich, G. Hautier, L. Wirtz, and G.-M. Rignanese, "Searching for materials with high refractive index and wide band gap: A first-principles high-throughput study," Phys. Rev. Mater. 3, 044602 (2019). 10.1103/physrevmaterials.3.044602
L. Hedin, "New method for calculating the one-particle Green's function with application to the electron-gas problem," Phys. Rev. 139, A796-A823 (1965). 10.1103/physrev.139.a796
M. J. van Setten, M. Giantomassi, X. Gonze, G.-M. Rignanese, and G. Hautier, "Automation methodologies and large-scale validation for GW: Towards high-throughput GW calculations," Phys. Rev. B 96, 155207 (2017). 10.1103/physrevb.96.155207
M. Giantomassi, M. Stankovski, R. Shaltaf, M. Grüning, F. Bruneval, P. Rinke, and G.-M. Rignanese, "Electronic properties of interfaces and defects from many-body perturbation theory: Recent developments and applications," Phys. State Solidi B 248, 275-289 (2011). 10.1002/pssb.201046094
T. Rangel, D. Caliste, L. Genovese, and M. Torrent, "A wavelet-based projector augmented-wave (PAW) method: Reaching frozen-core all-electron precision with a systematic, adaptive and localized wavelet basis set," Comput. Phys. Commun. 208, 1-8 (2016). 10.1016/j.cpc.2016.06.012
L. Genovese, A. Neelov, S. Goedecker, T. Deutsch, S. A. Ghasemi, A. Willand, D. Caliste, O. Zilberberg, M. Rayson, A. Bergman, and R. Schneider, "Daubechies wavelets as a basis set for density functional pseudopotential calculations," J. Chem. Phys. 129, 014109 (2008). 10.1063/1.2949547
X.-G. Xiong and T. Yanai, "Projector augmented wave method incorporated into Gauss-type atomic orbital based density functional theory," J. Chem. Theory Comput. 13, 3236-3249 (2017). 10.1021/acs.jctc.7b00404
ATOMPAW, Atompaw atomic datasets, http://users.wfu.edu/natalie/papers/pwpaw/PAWDatasets.html, 26 November 2019.
GPAW, GPAW atomic PAW setups, https://wiki.fysik.dtu.dk/gpaw/setups/setups.html, 07 June 2019.
S. Lehtola, C. Steigemann, M. J. T. Oliveira, and M. A. L. Marques, "Recent developments in libxc-A comprehensive library of functionals for density functional theory," SoftwareX 7, 1-5 (2018). 10.1016/j.softx.2017.11.002
J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized gradient approximation made simple," Phys. Rev. Lett. 77, 3865 (1996). 10.1103/PhysRevLett.77.3865
Y. Zhang and W. Yang, "Comment on: Generalized gradient approximation made simple," Phys. Rev. Lett. 80, 890 (1998). 10.1103/PhysRevLett.80.890
