Susi Lehtola, Frank Blockhuys, and Christian Van Alsenoy. An overview of self-consistent field calculations within finite basis sets. Molecules, 2020. doi:10.3390/molecules25051218.


Attila Szabo and Neil S Ostlund. Modern quantum chemistry: introduction to advanced electronic structure theory. Courier Corporation, 2012.


Susi Lehtola. Assessment of initial guesses for self-consistent field calculations. Superposition of atomic potentials: simple yet efficient. J. Chem. Theory Comput., 15:1593, 2019. doi:10.1021/acs.jctc.8b01089.


J. Almlöf, K. Faegri Jr., and K. Korsell. Principles for a direct scf approach to lcao–mo ab-initio calculations. Journal of Computational Chemistry, 3(3):385–399, 1982. doi:


J. H. Van Lenthe, R. Zwaans, H. J. J. Van Dam, and M. F. Guest. Starting scf calculations by superposition of atomic densities. Journal of Computational Chemistry, 27(8):926–932, 2006. doi:


Susi Lehtola. Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals. Phys. Rev. A, 101:012516, 2020. doi:10.1103/PhysRevA.101.012516.


Péter Pulay. Convergence acceleration of iterative sequences. The case of SCF iteration. Chem. Phys. Lett., 73:393, 1980. doi:10.1016/0009-2614(80)80396-4.


P. Pulay. Improved SCF convergence acceleration. J. Comput.. Chem., 3:556, 1982. doi:10.1002/jcc.540030413.


Konstantin N. Kudin, Gustavo E. Scuseria, and Eric Cancès. A black-box self-consistent field convergence algorithm: One step closer. J. Chem. Phys., 116(19):8255, 2002. doi:10.1063/1.1470195.


Xiangqian Hu and Weitao Yang. Accelerating self-consistent field convergence with the augmented Roothaan–Hall energy function. J. Chem. Phys., 132:054109, 2010. doi:10.1063/1.3304922.


Qiming Sun. Co-iterative augmented Hessian method for orbital optimization. arXiv preprint arXiv:1610.08423, 2016.


Qiming Sun, Jun Yang, and Garnet Kin-Lic Chan. A general second order complete active space self-consistent-field solver for large-scale systems. Chem. Phys. Lett., 683:291, 2017. doi:10.1016/j.cplett.2017.03.004.


Rolf Seeger and John A. Pople. Self-consistent molecular orbital methods. XVIII. Constraints and stability in Hartree–Fock theory. J. Chem. Phys., 66:3045, 1977. doi:10.1063/1.434318.


Per-Olov Löwdin. On the nonorthogonality problem. Adv. Quantum Chem., 5:185, 1970. doi:10.1016/S0065-3276(08)60339-1.


Susi Lehtola. Curing basis set overcompleteness with pivoted cholesky decompositions. J. Chem. Phys., 151(24):241102, 2019. doi:10.1063/1.5139948.


Susi Lehtola. Accurate reproduction of strongly repulsive interatomic potentials. Phys. Rev. A, 101:032504, 2020. doi:10.1103/PhysRevA.101.032504.


Kenneth G Dyall. Interfacing relativistic and nonrelativistic methods. iv. one-and two-electron scalar approximations. The Journal of Chemical Physics, 115(20):9136–9143, 2001.


W. Kohn and L. J. Sham. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev., 140:A1133, 1965.


J. P. Perdew and K. Schmidt. Jacob's Ladder of Density Functional Approximations for the Exchange-Correlation Energy. AIP Conf. Proc., 577:1, 2001.


A Seidl, A. Görling, P. Vogl, J. A. Majewski, and M. Levy. Generalized Kohn-Sham Schemes and the Band-Gap Problem. Phys. Rev. B, 53:3764, 1996.


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, 2018.


U. Ekström, L. Visscher, R. Bast, A. J. Thorvaldsen, and K. Ruud. Arbitrary-Order Density Functional Response Theory from Automatic Differentiation. J. Chem. Theory Comput., 6:1971, 2010.


S. Grimme, J. Antony, S. Ehrlich, and H. Krieg. A Consistent and Accurate \textit ab initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys., 132:154104, 2010.


O. A. Vydrov and T. Van Voorhis. Nonlocal van der Waals Density Functional: The Simpler the Better. J. Chem. Phys., 133:244103, 2010.


Zhichen Pu, Hao Li, Ning Zhang, Hong Jiang, Yiqin Gao, Yunlong Xiao, Qiming Sun, Yong Zhang, and Sihong Shao. Noncollinear density functional theory. Physical Review Research, 5(1):013036, 2023.


C. Møller and M. S. Plesset. Note on an approximation treatment for many-electron systems. Phys. Rev., 46:618, Oct 1934. doi:10.1103/PhysRev.46.618.


J. A. Pople, R. Krishnan, H. B. Schlegel, and J. S. Binkley. Derivative studies in hartree-fock and møller-plesset theories. Int. J. Quantum Chem., 16:225, 1979. doi:10.1002/qua.560160825.


N. C. Handy, R. D. Amos, J. F. Gaw, J. E. Rice, and E. D. Simandiras. The elimination of singularities in derivative calculations. Chem. Phys. Lett., pages 151, 1985. doi:10.1016/0009-2614(85)87031-7.


Y. Yamaguchi and H. F. Schaefer III. Analytic Derivative Methods in Molecular Electronic Structure Theory: A New Dimension to Quantum Chemistry and its Applications to Spectroscopy, chapter Fundamentals and Theory, pages 325. John Wiley & Sons, Ltd., 2011. doi:10.1002/9780470749593.hrs006.


Tianyu Zhu and Garnet Kin-Lic Chan. All-electron gaussian-based g0w0 for valence and core excitation energies of periodic systems. J. Chem. Theory Comput., 17(2):727–741, 2021.


P. J. Knowles and N. C. Handy. A new determinant-based full configuration interaction method. Chem. Phys. Lett., 111(4):315, 1984. doi:10.1016/0009-2614(84)85513-X.


Attila Szabo and Neil S Ostlund. Modern quantum chemistry: introduction to advanced electronic structure theory. Courier Corporation, 2012.


T. Helgaker, P. Jørgensen, and J. Olsen. Configuration-Interaction Theory, chapter 11, pages 523. John Wiley & Sons, Ltd, 2000. doi:10.1002/9781119019572.ch11.


Y. Osamura, Y. Yamaguchi, and H. F. Schaefer III. Generalization of analytic energy derivatives for configuration interaction wave functions. Theoret. Chim. Acta, 72(2):71, 1987. doi:10.1007/BF00528133.


Y. Yamaguchi and H. F. Schaefer III. Analytic Derivative Methods in Molecular Electronic Structure Theory: A New Dimension to Quantum Chemistry and its Applications to Spectroscopy, chapter Fundamentals and Theory, pages 325. John Wiley & Sons, Ltd., 2011. doi:10.1002/9780470749593.hrs006.


J. Schirmer, L. S. Cederbaum, and O. Walter. New approach to the one-particle Green's function for finite Fermi systems. Phys. Rev. A, 28(3):1237–1259, 1983.


J. Schirmer, A. B. Trofimov, and G. Stelter. A non-Dyson third-order approximation scheme for the electron propagator. J. Chem. Phys., 109(12):4734, 1998. doi:10.1063/1.477085.


A. B. Trofimov and J. Schirmer. Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach. J. Chem. Phys., 123(14):144115, October 2005. doi:10.1063/1.2047550.


S. Banerjee and A. Yu. Sokolov. Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green's function implementation. J. Chem. Phys., 151(22):224112, December 2019. doi:10.1063/1.5131771.


S. Banerjee and A. Yu. Sokolov. Efficient implementation of the single-reference algebraic diagrammatic construction theory for charged excitations: Applications to the TEMPO radical and DNA base pairs. J. Chem. Phys., 154(7):074105, January 2021. doi:10.1063/5.0040317.


C. M. Oana and A. I. Krylov. Dyson orbitals for ionization from the ground and electronically excited states within equation-of-motion coupled-cluster formalism: Theory, implementation, and examples. J. Chem. Phys., 127(23):234106, December 2007. doi:10.1063/1.2805393.


Oliver J. Backhouse, Max Nusspickel, and George H. Booth. Wave function perspective and efficient truncation of renormalized second-order perturbation theory. J. Chem. Theory Comput., 16(2):1090–1104, 2020. doi:10.1021/acs.jctc.9b01182.


Oliver J. Backhouse and George H. Booth. Efficient excitations and spectra within a perturbative renormalization approach. J. Chem. Theory Comput., 16(10):6294–6304, 2020. doi:10.1021/acs.jctc.0c00701.


Trygve Helgaker, Poul Jorgensen, and Jeppe Olsen. Molecular Electronic-Structure Theory. Wiley, 2013. ISBN 9781118531471.


Esqc lectures 2019. URL:


Qiming Sun, Jun Yang, and Garnet Kin-lic Lic Chan. A general second order complete active space self-consistent-field solver for large-scale systems. Chemical Physics Letters, 683:291–299, 2017. arXiv:1610.08394, doi:10.1016/j.cplett.2017.03.004.


Celestino Angeli, Renzo Cimiraglia, S Evangelisti, T Leininger, and J-P Malrieu. Introduction of n-electron valence states for multireference perturbation theory. J. Chem. Phys., 114(23):10252–10264, 2001. doi:10.1063/1.1361246.


Celestino Angeli, Renzo Cimiraglia, and Jean-Paul Malrieu. N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant. Chem. Phys. Lett., 350(3-4):297–305, 2001. doi:10.1016/S0009-2614(01)01303-3.


Celestino Angeli, Renzo Cimiraglia, and Jean-Paul Malrieu. N-electron valence state perturbation theory: a spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants. J. Chem. Phys., 117(20):9138–9153, 2002. doi:10.1063/1.1515317.


Sheng Guo, Mark A Watson, Weifeng Hu, Qiming Sun, and Garnet Kin-Lic Chan. N-electron valence state perturbation theory based on a density matrix renormalization group reference function, with applications to the chromium dimer and a trimer model of poly (p-phenylenevinylene). J. Chem. Theory Comput., 12(4):1583–1591, 2016. doi:10.1021/acs.jctc.5b01225.


Andreas Dreuw and Martin Head-Gordon. Single-reference ab initio methods for the calculation of excited states of large molecules. Chemical reviews, 105(11):4009–4037, 2005.


So Hirata and Martin Head-Gordon. Time-dependent density functional theory within the tamm–dancoff approximation. Chemical Physics Letters, 314(3-4):291–299, 1999.


Patrick J Lestrange, Franco Egidi, and Xiaosong Li. The consequences of improperly describing oscillator strengths beyond the electric dipole approximation. The Journal of chemical physics, 143(23):234103, 2015.


Brett I. Dunlap. Robust and variational fitting. Phys. Chem. Chem. Phys., 2:2113–2116, 2000. doi:10.1039/B000027M.


Florian Weigend, Andreas Köhn, and Christof Hättig. Efficient use of the correlation consistent basis sets in resolution of the identity mp2 calculations. J. Chem. Phys., 116:3175–3183, 2002. doi:10.1063/1.1445115.


Arnim Hellweg, Christof Hättig, Sebastian Höfener, and Wim Klopper. Optimized accurate auxiliary basis sets for ri-mp2 and ri-cc2 calculations for the atoms rb to rn. Theor. Chem. Acc., 117:587–597, 2007. doi:10.1007/s00214-007-0250-5.


Florian Weigend, Marco Häser, Holger Patzelt, and Reinhart Ahlrichs. Ri-mp2: optimized auxiliary basis sets and demonstration of efficiency. Chem. Phys. Lett., 294:143–152, 1998. doi:10.1016/S0009-2614(98)00862-8.


Florian Weigend. A fully direct ri-hf algorithm: implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency. Phys. Chem. Chem. Phys., 4:4285–4291, 2002. doi:10.1039/B204199P.


Florian Weigend. Accurate coulomb-fitting basis sets for h to rn. Phys. Chem. Chem. Phys., 8:1057–1065, 2006. doi:10.1039/B515623H.


Joachim Paier, Robin Hirschl, Martijn Marsman, and Georg Kresse. The perdew–burke–ernzerhof exchange-correlation functional applied to the g2-1 test set using a plane-wave basis set. J. Chem. Phys., 122(23):234102, 2005. doi:10.1063/1.1926272.


Peter Broqvist, Audrius Alkauskas, and Alfredo Pasquarello. Hybrid-functional calculations with plane-wave basis sets: effect of singularity correction on total energies, energy eigenvalues, and defect energy levels. Phys. Rev. B, 80:085114, Aug 2009. doi:10.1103/PhysRevB.80.085114.


Ravishankar Sundararaman and T. A. Arias. Regularization of the coulomb singularity in exact exchange by wigner-seitz truncated interactions: towards chemical accuracy in nontrivial systems. Phys. Rev. B, 87:165122, Apr 2013. doi:10.1103/PhysRevB.87.165122.


James Spencer and Ali Alavi. Efficient calculation of the exact exchange energy in periodic systems using a truncated coulomb potential. Phys. Rev. B, 77:193110, May 2008. doi:10.1103/PhysRevB.77.193110.


Qiming Sun, Timothy C. Berkelbach, James D. McClain, and Garnet Kin-Lic Chan. Gaussian and plane-wave mixed density fitting for periodic systems. J. Chem. Phys., 147(16):164119, 2017. doi:10.1063/1.4998644.


Joost VandeVondele, Matthias Krack, Fawzi Mohamed, Michele Parrinello, Thomas Chassaing, and Jürg Hutter. Quickstep: fast and accurate density functional calculations using a mixed gaussian and plane waves approach. Comput. Phys. Commun., 167(2):103 – 128, 2005. doi:10.1016/j.cpc.2004.12.014.


Thomas D. Kühne, Marcella Iannuzzi, Mauro Del Ben, Vladimir V. Rybkin, Patrick Seewald, Frederick Stein, Teodoro Laino, Rustam Z. Khaliullin, Ole Schütt, Florian Schiffmann, Dorothea Golze, Jan Wilhelm, Sergey Chulkov, Mohammad Hossein Bani-Hashemian, Valéry Weber, Urban Borštnik, Mathieu Taillefumier, Alice Shoshana Jakobovits, Alfio Lazzaro, Hans Pabst, Tiziano Müller, Robert Schade, Manuel Guidon, Samuel Andermatt, Nico Holmberg, Gregory K. Schenter, Anna Hehn, Augustin Bussy, Fabian Belleflamme, Gloria Tabacchi, Andreas Glöβ, Michael Lass, Iain Bethune, Christopher J. Mundy, Christian Plessl, Matt Watkins, Joost VandeVondele, Matthias Krack, and Jürg Hutter. Cp2k: an electronic structure and molecular dynamics software package - quickstep: efficient and accurate electronic structure calculations. J. Chem. Phys., 152(19):194103, 2020. doi:10.1063/5.0007045.


James McClain, Qiming Sun, Garnet Kin-Lic Chan, and Timothy C. Berkelbach. Gaussian-based coupled-cluster theory for the ground-state and band structure of solids. J. Chem. Theory Comput., 13(3):1209–1218, 2017. doi:10.1021/acs.jctc.7b00049.


Hong-Zhou Ye and Timothy C. Berkelbach. Fast periodic gaussian density fitting by range separation. arXiv preprint arXiv:2102.02989, 2021.


Feliciano Giustino. Electron-phonon interactions from first principles. Rev. Mod. Phys., 89:015003, 2017.


J. M. Foster and S. F. Boys. Canonical Configurational Interaction Procedure. Rev. Mod. Phys., 32(2):300–302, 1960.


N. Marzari and D. Vanderbilt. Maximally Localized Generalized Wannier Functions for Composite Energy Bands. Phys. Rev. B, 56(20):12847–12865, 1997.


János Pipek and Paul G. Mezey. A fast intrinsic localization procedure applicable for ab-initio and semiempirical linear combination of atomic orbital wave functions. J. Chem. Phys., 90(9):4916, 1998.


Susi Lehtola and Hannes Jónsson. Pipek–mezey orbital localization using various partial charge estimates. Journal of chemical theory and computation, 10(2):642–649, 2014.


Clyde Edmiston and Klaus Ruedenberg. Localized Atomic and Molecular Orbitals. Rev. Mod. Phys., 35(3):457–464, 1963.


Francesco Aquilante, Thomas Bondo Pedersen, Alfredo Sánchez de Merás, and Henrik Koch. Fast noniterative orbital localization for large molecules. J. Chem. Phys., 125(17):174101, 2006. doi:10.1063/1.2360264.


Per-Olov Löwdin. On the Non-Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals. J. Chem. Phys., 18(3):365, 1950.


Qiming Sun and Garnet Kin-Lic Chan. Exact and optimal quantum mechanics/molecular mechanics boundaries. J. Chem. Theory Comput., 10:3784, 2014.


Alan E. Reed, Robert B. Weinstock, and Frank Weinhold. Natural population analysis. J. Chem. Phys., 83(2):735–746, 1985.


Gerald Knizia. Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts. J. Chem. Theory Comput., 9(11):4834–4843, 2013.


Richard A. Friesner. Solution of self-consistent field electronic structure equations by a pseudospectral method. Chem. Phys. Lett., 116:39–43, 1985. doi:10.1016/0009-2614(85)80121-4.


Frank Neese, Frank Wennmohs, Andreas Hansen, and Ute Becker. Efficient, approximate and parallel Hartree-Fock and hybrid DFT calculations. A 'chain-of-spheres' algorithm for the Hartree-Fock exchange. Chem. Phys., 356:98, 2009. doi:10.1016/j.chemphys.2008.10.036.


Róbert Izsák and Frank Neese. An overlap fitted chain of spheres exchange method. J. Chem. Phys., 135:144105, 2011. doi:10.1063/1.3646921.