List of published papers and other sources (books, theses) documenting the development of various features of DIRAC, some interesting applications and various related references.

Reference entries are sorted alphabetically according to the first author’s family name with the year of the publishing. If the first author has several publications in the same year, characters in alphabetical order - “a”, “b”, “c”, etc. - are added after the year.

Please always provide each citation entry with its permanent URL-link. The best web-link is the DOI web identity, used almost for all peer-reviewed papers. For books we recommend to resort to semi-permanent links, like the publisher’s web-site, or the popular Google-Books web-space.

References availability

All references are also available for download as one (big) file in the popular BibTex format. Please keep them in the alphabetical order as described above.


Hans Agren, Paul S. Bagus, and Björn O. Roos. Symmetry adapted versus symmetry broken wavefunctions: the 1s core level ions of O$^+_2$. Chem. Phys. Lett., 82(3):505–510, 1981. doi:10.1016/0009-2614(81)85429-2.


Adel Almoukhalalati, Avijit Shee, and Trond Saue. Nuclear size effects in vibrational spectra. Phys. Chem. Chem. Phys., 18:15406–15417, 2016. doi:10.1039/C6CP01913G.


Claudio Amovilli, Vincenzo Barone, Roberto Cammi, Eric Cancès, Maurizio Cossi, Benedetta Mennucci, Christian S. Pomelli, and Jacopo Tomasi. Recent Advances in the Description of Solvent Effects with the Polarizable Continuum Mode. In Per-Olov Löwdin, editor, Advances in Quantum Chemistry, Vol 32: Quantum Systems in Chemistry and Physics, Part II, volume 32 of Advances in Quantum Chemistry, pages 227 – 261. Academic Press, 1998. doi:10.1016/S0065-3276(08)60416-5.


G. A. Aucar, T. Saue, L. Visscher, and H. J. Aa. Jensen. On the origin and contribution of the diamagnetic term in four-component relativistic calculations of magnetic properties. J. Chem. Phys., 110(13):6208–6218, 1999. doi:10.1063/1.479181.


Gustavo Adolfo Aucar and Ignacio Agustín Aucar. Recent developments in absolute shielding scales for nmr spectroscopy. In Graham A. Webb, editor, Annual Rep. on NMR Spect., volume 96, chapter 3, pages 77–141. Academic Press, 2019. doi:10.1016/bs.arnmr.2018.08.001.


Ignacio Agustín Aucar and Anastasia Borschevsky. Relativistic study of parity-violating nuclear spin-rotation tensors. J. Chem. Phys., 155(13):134307, 2021. doi:10.1063/5.0065487.


Ignacio Agustín Aucar, Sergio Santiago Gómez, Claudia Gloria Giribet, and Gustavo Adolfo Aucar. The role of spin dependent terms on the relationship among nuclear spin-rotation and nmr magnetic shielding tensors. J. Phys. Chem. Lett., 7:5188–5192, 2016. doi:10.1021/acs.jpclett.6b02361.


Ignacio Agustín Aucar, Sergio Santiago Gómez, Claudia Gloria Giribet, and Martín César Ruiz de Azúa. Theoretical study of the relativistic molecular rotational g-tensor. J. Chem. Phys., 141:194103, 2014. doi:10.1063/1.4901422.


Ignacio Agustín Aucar, Sergio Santiago Gómez, Martín César Ruiz de Azúa, and Claudia Gloria Giribet. Theoretical study of the nuclear spin-molecular rotation coupling for relativistic electrons and non-relativistic nuclei. J. Chem. Phys., 136:204119, 2012. doi:10.1063/1.4721627.


Paul S. Bagus and Henry F. Schaefer. Direct near-hartree-fock calculations on the 1s hole states of NO$^+$. J. Chem. Phys., 55(3):1474–1475, 1971. doi:10.1063/1.1676248.


Paul S. Bagus and Henry F. Schaefer. Localized and delocalized 1s hole states of the O$_2^+$ molecular ion. J. Chem. Phys., 56(1):224–226, 1972. doi:10.1063/1.1676850.


Jon Baker. Techniques for geometry optimization: A comparison of cartesian and natural internal coordinates. J. Comput. Chem., 14(9):1085–1100, 1993. doi:10.1002/jcc.540140910.


Radovan Bast, Hans Jørgen Aa. Jensen, and Trond Saue. Relativistic adiabatic time-dependent density functional theory using hybrid functionals and noncollinear spin magnetization. Int. J. Quantum Chem., 109(10):2091–2112, 2009. doi:10.1002/qua.22065.


Radovan Bast, Anton Koers, Andre Severo Pereira Gomes, Miroslav Iliaš, Lucas Visscher, Peter Schwerdtfeger, and Trond Saue. Analysis of parity violation in chiral molecules. Physical Chemistry Chemical Physics, 13:864–876, 2011. doi:10.1039/C0CP01483D.


Radovan Bast, Peter Schwerdtfeger, and Trond Saue. Parity nonconservation contribution to the nuclear magnetic resonance shielding constants of chiral molecules: A four-component relativistic study. J. Chem. Phys., 125(6):064504, 2006. doi:10.1063/1.2218333.


Alfred Bauder, Andreas Beil, David Luckhaus, Franz Müller, and Martin Quack. Combined high resolution infrared and microwave study of bromochlorofluoromethane. The Journal of chemical physics, 106(18):7558–7570, 1997.


Charles W. Bauschlicher. The construction of modified virtual orbitals (MVOs) which are suited for configuration interaction calculations. J. Chem. Phys., 72(2):880–885, 1980. doi:10.1063/1.439243.


A. D. Becke. A multicenter numerical integration scheme for polyatomic molecules. J. Chem. Phys., 88(4):2547–2553, 1988. doi:10.1063/1.454033.


A. D. Becke. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A, 38:3098–3100, Sep 1988. doi:10.1103/PhysRevA.38.3098.


S.F. Boys and F. Bernardi. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol. Phys., 19(4):553–566, 1970. doi:10.1080/00268977000101561.


D.B. Chesnut. Ab Initio Calculations of NMR Chemical Shielding. In G.A. Webb, editor, Annual Reports on NMR Spectroscopy, volume 29 of Annual Reports on NMR Spectroscopy, pages 71 – 122. Academic Press, 1994. doi:10.1016/S0066-4103(08)60131-3.


O. Christiansen, T. M. Nymand, and K. V. Mikkelsen. A theoretical study of the electronic spectrum of water. Chem. Phys. Lett., 113(3):8101–, 2000. doi:10.1063/1.1316035.


Sonia Coriani and Henrik Koch. Communication: x-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework. J. Chem. Phys., 143(18):181103, 2015. doi:10.1063/1.4935712.


M. Denis, M. Nørby, H. J. Aa. Jensen, A. S. P. Gomes, M. K. Nayak, S. Knecht, and T. Fleig. Theoretical study on ThF$^+$, a prospective system in search of time-reversal violation. New J. Phys., 17:043005, 2015. doi:10.1088/1367-2630/17/4/043005.


P. A. M. Dirac. The Quantum Theory of the Electron. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 117(778):610–624, 1928. doi:10.1098/rspa.1928.0023.


P. A. M. Dirac. Note on Exchange Phenomena in the Thomas Atom. Mathematical Proceedings of the Cambridge Philosophical Society, 26:376–385, 7 1930. doi:10.1017/S0305004100016108.


S. Dubillard, J.-B. Rota, T. Saue, and K. Faegri. Bonding analysis using localized relativistic orbitals: Water, the ultrarelativistic case and the heavy homologues H2X (X=Te, Po, eka-Po). J. Chem. Phys., 124(15):154307, 2006. doi:10.1063/1.2187001.


Thom H. Dunning. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys., 90(2):1007–1023, 1989. doi:10.1063/1.456153.


K. G. Dyall, I. P. Grant, C. T. Johnson, F. A. Parpia, and E. P. Plummer. Grasp: a general-purpose relativistic atomic structure program. Comput. Phys. Commun., 55(3):425 – 456, 1989. doi:10.1016/0010-4655(89)90136-7.


Kenneth G. Dyall. An exact separation of the spin-free and spin-dependent terms of the Dirac-Coulomb-Breit Hamiltonian. J. Chem. Phys., 100(3):2118–2127, 1994. doi:10.1063/1.466508.


Kenneth G. Dyall and Knut Faegri. Introduction to Relativistic Quantum Chemistry. Oxford University Press, 4 2007. ISBN 9780195140866.


Ulf Ekström, Patrick Norman, and Antonio Rizzo. Four-component Hartree-Fock calculations of magnetic-field induced circular birefringence-Faraday effect-in noble gases and dihalogens. J. Chem. Phys., 122(7):074321, 2005. doi:10.1063/1.1849167.


Ephraim Eliav, Marius J. Vilkas, Yasuyuki Ishikawa, and Uzi Kaldor. Extrapolated intermediate Hamiltonian coupled-cluster approach: Theory and pilot application to electron affinities of alkali atoms. J. Chem. Phys., 122(22):224113, 2005. doi:10.1063/1.1929727.


Walter C. Ermler, Yoon S. Lee, Phillip A. Christiansen, and Kenneth S. Pitzer. Ab initio effective core potentials including relativistic effects. A procedure for the inclusion of spin-orbit coupling in molecular wavefunctions. Chem. Phys. Lett., 81(1):70 – 74, 1981. doi:10.1016/0009-2614(81)85329-8.


T. Fleig and M. K. Nayak. Electron electric-dipole-moment interaction constant for HfF$^+$ from relativistic correlated all-electron theory. Phys. Rev. A, 88:032514, 2013. doi:10.1103/PhysRevA.88.032514.


T. Fleig and M. K. Nayak. Electron electric dipole moment and hyperfine interaction constants for ThO. J. Mol. Spectrosc., 300:16, 2014. doi:10.1016/j.jms.2014.03.017.


T. Fleig, M. K. Nayak, and M. G. Kozlov. TaN, a molecular system for probing P,T-violating hadron physics. Phys. Rev. A, 93:012505, 2016. doi:10.1103/PhysRevA.93.012505.


T. Fleig and L. Visscher. Large-scale electron correlation calculations in the framework of the spin-free dirac formalism: the Au$_2$ molecule revisited. Chem. Phys., 311(1–2):113 – 120, 2005. Relativistic Effects in Heavy-Element Chemistry and Physics. In Memoriam Bernd A. Hess (1954–2004). doi:10.1016/j.chemphys.2004.10.003.


Timo Fleig. Wave Function Based Relativistic Multi-Reference Electron Correlation Methods. PhD thesis, Habilitation, Heinrich Heine University Düsseldorf, 2006. Development and Application to Atomic and Molecular Properties. URL:


Timo Fleig, Hans Jørgen Aa. Jensen, Jeppe Olsen, and Lucas Visscher. The generalized active space concept for the relativistic treatment of electron correlation. III. Large-scale configuration interaction and multiconfiguration self-consistent-field four-component methods with application to UO$_2$. J. Chem. Phys., 124(10):104106, 2006. doi:10.1063/1.2176609.


Timo Fleig, Jeppe Olsen, and Christel M. Marian. The generalized active space concept for the relativistic treatment of electron correlation. I. Kramers-restricted two-component configuration interaction. J. Chem. Phys., 114(11):4775–4790, 2001. doi:


Timo Fleig, Jeppe Olsen, and Lucas Visscher. The generalized active space concept for the relativistic treatment of electron correlation. II. Large-scale configuration interaction implementation based on relativistic 2- and 4-spinors and its application. J. Chem. Phys., 119(6):2963–2971, 2003. doi:10.1063/1.1590636.


O. Fossgaard, O. Gropen, E. Eliav, and T. Saue. Bonding in the homologous series CsAu, CsAg, and CsCu studied at the 4-component density functional theory and coupled cluster levels. J. Chem. Phys., 119(18):9355–9363, 2003. doi:10.1063/1.1615953.


O. Fossgaard, O. Gropen, M. Corral Valero, and T. Saue. On the performance of four-component relativistic density functional theory: Spectroscopic constants and dipole moments of the diatomics HX and XY (X,Y=F, Cl, Br, and I). J. Chem. Phys., 118(23):10418–10430, 2003. doi:10.1063/1.1574317.


Knut Fægri and Trond Saue. Diatomic molecules between very heavy elements of group 13 and group 17: A study of relativistic effects on bonding. J. Chem. Phys., 115(6):2456–2464, 2001. doi:10.1063/1.1385366.


Konstantin Gaul and Robert Berger. Quasi-relativistic study of nuclear electric quadrupole coupling constants in chiral molecules containing heavy elements. Molecular Physics, 118(19-20):e1797199, 2020.


Andrew T. B. Gilbert, Nicholas A. Besley, and Peter M. W. Gill. Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM). J. Phys. Chem. A, 112(50):13164–13171, 2008. doi:10.1021/jp801738f.


Andre Severo Pereira Gomes and Christoph R. Jacob. Quantum-chemical embedding methods for treating local electronic excitations in complex chemical systems. Annual Reports on the Progress of Chemistry Section C, 108:222–277, 2012. doi:10.1039/C2PC90007F.


Andre Severo Pereira Gomes, Christoph R. Jacob, and Lucas Visscher. Calculation of local excitations in large systems by embedding wave-function theory in density-functional theory. Physical Chemistry Chemical Physics, 10:5353–5362, 2008. doi:10.1039/B805739G.


M. Grüning, O. V. Gritsenko, S. J. A. van Gisbergen, and E. J. Baerends. Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region. J. Chem. Phys., 114(2):652–660, 2001. doi:10.1063/1.1327260.


Loic Halbert, Marta Lopez Vidal, Avijit Shee, Sonia Coriani, and Andre Severo Pereira Gomes. Relativistic EOM-CCSD for core-excited and core-ionized state energies based on the 4-component Dirac-Coulomb(-Gaunt) Hamiltonian. unpublished, 2021. doi:10.1021/acs.jctc.0c01203.


Tracy P. Hamilton and Peter Pulay. Direct inversion in the iterative subspace (DIIS) optimization of open-shell, excited-state, and small multiconfiguration SCF wave functions. J. Chem. Phys., 84(10):5728–5734, 1986. doi:10.1063/1.449880.


Erik Donovan Hedegård, Radovan Bast, Jacob Kongsted, Jógvan Magnus Haugaard Olsen, and Hans Jørgen Aa. Jensen. Relativistic Polarizable Embedding. J. Chem. Theory Comput., 13(6):2870–2880, 2017. doi:10.1021/acs.jctc.7b00162.


Erik Donovan Hedegård and Markus Reiher. Polarizable Embedding Density Matrix Renormalization Group. J. Chem. Theory Comput., 12(9):4242–4253, 2016. doi:10.1021/acs.jctc.6b00476.


T. Helgaker, P. Jørgensen, and J. Olsen. Molecular Electronic Structure Theory. John Wiley & Sons, Ltd, Chichester, 2000.


Benjamin Helmich-Paris and Lucas Visscher. Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators. J. Comput. Phys., 321:927 – 931, 2016. doi:10.1016/


Johan Henriksson, Patrick Norman, and Hans Jørgen Aa. Jensen. Two-photon absorption in the relativistic four-component Hartree-Fock approximation. J. Chem. Phys., 122(11):114106, 2005. doi:10.1063/1.1869469.


Johan Henriksson, Trond Saue, and Patrick Norman. Quadratic response functions in the relativistic four-component Kohn–Sham approximation. J. Chem. Phys., 128(2):024105, 2008. doi:10.1063/1.2816709.


Roald Hoffmann. An Extended Huckel Theory. I. Hydrocarbons. J. Chem. Phys., 39(6):1397–1412, 1963. doi:10.1063/1.1734456.


Sebastian Höfener, André Severo Pereira Gomes, and Lucas Visscher. Solvatochromic shifts from coupled-cluster theory embedded in density functional theory. J. Chem. Phys., 139(10):104106, 2013. doi:10.1063/1.4820488.


Sebastian Höfener, André Severo Pereira Gomes, and Lucas Visscher. Molecular properties via a subsystem density functional theory formulation: A common framework for electronic embedding. J. Chem. Phys., 136(4):044104, 2012. doi:10.1063/1.3675845.


Hisayoshi Iikura, Takao Tsuneda, Takeshi Yanai, and Kimihiko Hirao. A long-range correction scheme for generalized-gradient-approximation exchange functionals. J. Chem. Phys., 115(8):3540–3544, 2001. doi:10.1063/1.1383587.


M. Iliaš, T. Saue, T. Enevoldsen, and H. J. Aa. Jensen. Gauge origin independent calculations of nuclear magnetic shieldings in relativistic four-component theory. J. Chem. Phys., 131:124119, 2009. doi:10.1063/1.3240198.


Miroslav Iliaš, Hans Jørgen Aa. Jensen, Radovan Bast, and Trond Saue. Gauge origin independent calculations of molecular magnetisabilities in relativistic four-component theory. Mol. Phys., 111(9-11):1373–1381, 2013. doi:10.1080/00268976.2013.798436.


Miroslav Iliaš, Hans Jørgen Aa. Jensen, Vladimir Kellö, Björn O. Roos, and Miroslav Urban. Theoretical study of PbO and the PbO anion. Chem. Phys. Lett., 408(4–6):210 – 215, 2005. doi:10.1016/j.cplett.2005.04.027.


Miroslav Iliaš, Vladimír Kellö, Lucas Visscher, and Bernd Schimmelpfennig. Inclusion of mean-field spin–orbit effects based on all-electron two-component spinors: Pilot calculations on atomic and molecular properties. J. Chem. Phys., 115(21):9667–9674, 2001. doi:10.1063/1.1413510.


Miroslav Iliaš and Trond Saue. An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation. J. Chem. Phys., 126(6):064102, 2007. doi:10.1063/1.2436882.


Miroslav Iliaš and Miroslav Dobruck\'y. Grid Computing with Relativistic Quantum Chemistry Software. Journal of Grid Computing, 12(4):681–690, 2014. doi:10.1007/s10723-014-9309-4.


Christoph R. Jacob, S. Maya Beyhan, Rosa E. Bulo, Andre Severo Pereira Gomes, Andreas W. Gatz, Karin Kiewisch, Jetze Sikkema, and Lucas Visscher. PyADF A scripting framework for multiscale quantum chemistry. J. Comput. Chem., 32(10):2328–2338, 2011. doi:10.1002/jcc.21810.


Christoph R. Jacob and Johannes Neugebauer. Subsystem density-functional theory. Wiley Interdisciplinary Reviews: Computational Molecular Science, 4(4):325–362, 2014. doi:10.1002/wcms.1175.


J. Jarvie, W. Willson, J. Doolittle, and C. Edmiston. Tetrahedral methane without $2s\rightarrow 2p$ promotion and hybridization: Direct calculation of the effects of promotion and hybridization in CH$_4$, NH$_3$, H$_2$O and H$_2$S. J. Chem. Phys., 59:3020, 1973. doi:10.1063/1.1680438.


Hans Jørgen Aa. Jensen, Kenneth G. Dyall, Trond Saue, and Knut Fægri. Relativistic four-component multiconfigurational self-consistent-field theory for molecules: Formalism. J. Chem. Phys., 104(11):4083–4097, 1996. doi:10.1063/1.471644.


Hans Jørgen Aa. Jensen, Poul Jørgensen, Hans Ågren, and Jeppe Olsen. Second-order Møller-Plesset perturbation theory as a configuration and orbital generator in multiconfiguration self-consistent field calculations. J. Chem. Phys., 88(6):3834–3839, 1988. doi:10.1063/1.453884.


Thomas W. Keal and David J. Tozer. The exchange-correlation potential in Kohn–Sham nuclear magnetic resonance shielding calculations. J. Chem. Phys., 119(6):3015–3024, 2003. doi:10.1063/1.1590634.


Jensen Knecht, Repisky, Ruud, and Saue. Genuine relativistic quantum chemistry with exact two-component Hamiltonians: The easy way to infinite-order two-electron spin-orbit corrections. in preparation, 2014.


S. Knecht and T. Saue. X2Cmod: A modular code for Exact-Two-Component Hamiltonian Transformations. 2010-2013 with contributions from M. Ilias, H. J. Aa. Jensen and M. Repisky, 2010.


Stefan Knecht, Samuel Fux, Robert van Meer, Lucas Visscher, Markus Reiher, and Trond Saue. Mossbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury. Theor. Chem. Acc., 129(3-5):631–650, 2011. doi:10.1007/s00214-011-0911-2.


Stefan Knecht, Hans Jøgen Aa. Jensen, and Timo Fleig. Large-scale parallel configuration interaction. I. Nonrelativistic and scalar-relativistic general active space implementation with application to (Rb–Ba)+. J. Chem. Phys., 128(1):014108, 2008. doi:10.1063/1.2805369.


Stefan Knecht, Hans Jørgen Aa. Jensen, and Timo Fleig. Large-scale parallel configuration interaction. II. Two- and four-component double-group general active space implementation with application to BiH. J. Chem. Phys., 132(1):014108, 2010. doi:10.1063/1.3276157.


Stefan Knecht, Örs Legeza, and Markus Reiher. Communication: Four-component density matrix renormalization group. J. Chem. Phys., 140(4):041101, 2014. doi:10.1063/1.4862495.


Stefan Knecht, Michal Repisky, H. J. Aa. Jensen, and Trond Saue. Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple. J. Chem. Phys., 157:114106, 2022. doi:10.1063/5.0095112.


Stefan R. Knecht. Parallel Relativistic Multiconfiguration Methods: New Powerful Tools for Heavy-Element Electronic-Structure Studies. PhD thesis, Mathematisch-Naturwissenschaftliche Fakultät, Heinrich-Heine-Universität Düsseldorf, 2009. URL:


Gerald Knizia. Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts. J. Chem. Theory Comput., 9(11):4834–4843, 2013. doi:10.1021/ct400687b.


J. Kongsted, A. Osted, K. V. Mikkelsen, and O. Christiansen. Dipole and quadrupole moments of liquid water calculated within the coupled cluster/molecular mechanics method. Chem. Phys. Lett., 364(3-4):379–386, 2002. doi:10.1016/S0009-2614(02)01286-1.


Ossama Kullie and Trond Saue. Range-separated density functional theory: A 4-component relativistic study of the rare gas dimers He2, Ne2, Ar2, Kr2, Xe2, Rn2 and Uuo2. Chemical Physics, 395(0):54 – 62, 2012. Recent Advances and Applications of Relativistic Quantum Chemistry. doi:10.1016/j.chemphys.2011.06.024.


Werner Kutzelnigg. Chemical Bonding in Higher Main Group Elements. Angewandte Chemie International Edition in English, 23(4):272–295, 1984. doi:10.1002/anie.198402721.


Jon K. Laerdahl, Trond Saue, and Knut Faegri Jr. Direct relativistic MP2: properties of ground state CuF, AgF and AuF. Theor. Chem. Acc., 97(1-4):177–184, 1997. doi:10.1007/s002140050251.


Jon K. Laerdahl and Peter Schwerdtfeger. Fully relativistic ab initio calculations of the energies of chiral molecules including parity-violating weak interactions. Phys. Rev. A, 60:4439–4453, Dec 1999. doi:10.1103/PhysRevA.60.4439.


Arie Landau, Ephraim Eliav, Yasuyuki Ishikawa, and Uzi Kaldor. Mixed-sector intermediate Hamiltonian Fock-space coupled cluster approach. J. Chem. Phys., 121(14):6634–6639, 2004. doi:10.1063/1.1788652.


Chengteh Lee, Weitao Yang, and Robert G. Parr. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B, 37:785–789, Jan 1988. doi:10.1103/PhysRevB.37.785.


Yoon S. Lee, Walter C. Ermler, and Kenneth S. Pitzer. Abinitio effective core potentials including relativistic effects. I. Formalism and applications to the Xe and Au atoms. J. Chem. Phys., 67(12):5861–5876, 1977. doi:10.1063/1.434793.


Helene Lefebvre-Brion. CECAM-ORSAY Documentation for Molecular Calculations – 1970. February 2021. URL:, doi:10.5281/zenodo.4527848.


Susi Lehtola, Lucas Visscher, and Eberhard Engel. Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets. J. Chem. Phys., 152:144105, 2020. arXiv:2002.02587, doi:10.1063/5.0004046.


Patrick J. Lestrange, Franco Egidi, and Xiaosong Li. The consequences of improperly describing oscillator strengths beyond the electric dipole approximation. J. Chem. Phys., 143(23):234103, 2015. doi:10.1063/1.4937410.


Roland Lindh, Per-Ake Malmqvist, and Laura Gagliardi. Molecular integrals by numerical quadrature. I. Radial integration. Theor. Chem. Acc., 106(3):178–187, 2001. doi:10.1007/s002140100263.


Nanna Holmgaard List, Timothé Romain Léo Melin, Martin van Horn, and Trond Saue. Beyond the electric-dipole approximation in simulations of x-ray absorption spectroscopy: Lessons from relativistic theory. J. Chem. Phys., 152(18):184110, 2020. doi:10.1063/5.0003103.


Jean-Marc Lévy-Leblond. Nonrelativistic particles and wave equations. Communications in Mathematical Physics, 6(4):286–311, 1967. doi:10.1007/BF01646020.


Markus Mayer, Oliver D. Häberlen, and Notker Rösch. Relevance of relativistic exchange-correlation functionals and of finite nuclei in molecular density-functional calculations. Phys. Rev. A, 54:4775–4782, Dec 1996. doi:10.1103/PhysRevA.54.4775.


B. Mennucci and R. Cammi. Front Matter, pages i–xv. John Wiley & Sons, Ltd, 2007. doi:10.1002/9780470515235.fmatter.


Yuji Mochizuki and Hiroshi Tatewaki. On the electronic structure of CmF$_n$ (n=1–4) by all-electron Dirac–Hartree–Fock calculations. J. Chem. Phys., 118(20):9201–9207, 2003. doi:10.1063/1.1568075.


R. S. Mulliken. Electronic Population Analysis on LCAO MO Molecular Wave Functions. I. J. Chem. Phys., 23(10):1833–1840, 1955. doi:10.1063/1.1740588.


Malaya K. Nayak and Rajat K. Chaudhuri. Ab initio calculation of p,t-odd effects in ybf molecule. Chem. Phys. Lett., 419(1):191 – 194, 2006. doi:


Malaya K. Nayak, Rajat K. Chaudhuri, and B. P. Das. Ab initio calculation of the electron-nucleus scalar-pseudoscalar interaction constant $w_s$ in heavy polar molecules. Phys. Rev. A, 75:022510, Feb 2007. doi:10.1103/PhysRevA.75.022510.


Malaya K. Nayak and B. P. Das. Relativistic configuration-interaction study of the nuclear-spin-dependent parity-nonconserving electron-nucleus interaction constant $w_\text A$ in baf. Phys. Rev. A, 79:060502, Jun 2009. doi:10.1103/PhysRevA.79.060502.


Egon S. Nielsen, Poul Jørgensen, and Jens Oddershede. Transition moments and dynamic polarizabilities in a second order polarization propagator approach. J. Chem. Phys., 73(12):6238–6246, 1980. doi:10.1063/1.440119.


Patrick Norman. A perspective on nonresonant and resonant electronic response theory for time-dependent molecular properties. Physical Chemistry Chemical Physics, 13:20519–20535, 2011. doi:10.1039/C1CP21951K.


Patrick Norman and Hans Jørgen Aa. Jensen. Quadratic response functions in the time-dependent four-component Hartree-Fock approximation. J. Chem. Phys., 121(13):6145–6154, 2004. doi:10.1063/1.1785774.


Patrick Norman Norman and Hans Jørgen Aa. Jensen. Phosphorescence parameters for platinum (II) organometallic chromophores: A study at the non-collinear four-component Kohn-Sham level of theory. Chem. Phys. Lett., 531():229 – 235, 2012. doi:10.1016/j.cplett.2012.02.012.


Malgorzata Olejniczak, Radovan Bast, Trond Saue, and Magdalena Pecul. A simple scheme for magnetic balance in four-component relativistic Kohn-Sham calculations of nuclear magnetic resonance shielding constants in a Gaussian basis. J. Chem. Phys., 136(1):014108, 2012. doi:10.1063/1.3671390.


Jeppe Olsen, Poul Jørgensen, and Jack Simons. Passing the one-billion limit in full configuration-interaction (FCI) calculations. Chem. Phys. Lett., 169(6):463 – 472, 1990. doi:10.1016/0009-2614(90)85633-N.


Jógvan Magnus Olsen, Ke\k stutis Aidas, and Jacob Kongsted. Excited states in solution through polarizable embedding. J. Chem. Theory Comput., 6(12):3721–3734, 2010. doi:10.1021/ct1003803.


Jógvan Magnus Haugaard Olsen and Jacob Kongsted. Molecular properties through polarizable embedding. In Advances in Quantum Chemistry, pages 107–143. 2011. doi:10.1016/b978-0-12-386013-2.00003-6.


Y. C. Park, I. S. Lim, and Y. S. Lee. Two-Component Spin-orbit Effective Core Potential Calculations with an All-electron Relativistic Program DIRAC. Bulletin of the Korean Chemical Society, 33(3):803 – 808, 2012. doi:10.5012/bkcs.2012.33.3.803.


Michael J. G. Peach, Peter Benfield, Trygve Helgaker, and David J. Tozer. Excitation energies in density functional theory: An evaluation and a diagnostic test. J. Chem. Phys., 128(4):044118, 2008. doi:10.1063/1.2831900.


Magdalena Pecul, Trond Saue, Kenneth Ruud, and Antonio Rizzo. Electric field effects on the shielding constants of noble gases: A four-component relativistic Hartree-Fock study. J. Chem. Phys., 121(7):3051–3057, 2004. doi:10.1063/1.1771635.


Daoling Peng and Markus Reiher. Local relativistic exact decoupling. J. Chem. Phys., 136(24):244108, 2012. doi:10.1063/1.4729788.


John P. Perdew and Wang Yue. Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. Phys. Rev. B, 33:8800–8802, Jun 1986. doi:10.1103/PhysRevB.33.8800.


Markus Pernpointner. The relativistic polarization propagator for the calculation of electronic excitations in heavy systems. J. Chem. Phys., 140:084108, 2014. doi:10.1063/1.4865964.


Markus Pernpointner and Lucas Visscher. Parallelization of four-component calculations. II. Symmetry-driven parallelization of the 4-Spinor CCSD algorithm. J. Comput. Chem., 24(6):754–759, 2003. doi:10.1002/jcc.10215.


Markus Pernpointner, Lucas Visscher, and Alexander B. Trofimov. Four-component polarization propagator calculations of electron excitations: spectroscopic implications of spin–orbit coupling effects. J. Chem. Theory Comput., 14:1510–1522, 2018. doi:10.1021/acs.jctc.7b01056.


J. Pipek and P. G. Mezey. A fast intrinsic localization procedure applicable for \it ab initio and semiempirical linear combination of atomic orbital wave functions. J. Chem. Phys., 90:4916, 1989. doi:10.1063/1.456588.


P. Pulay. Improved SCF convergence acceleration. J. Comput. Chem., 3(4):556–560, 1982. doi:10.1002/jcc.540030413.


Péter Pulay. Convergence acceleration of iterative sequences. the case of SCF iteration. Chem. Phys. Lett., 73(2):393 – 398, 1980. doi:10.1016/0009-2614(80)80396-4.


Markus Reiher and Alexander Wolf. Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science. Wiley-VCH, 1 edition, 2 2009. ISBN 9783527312924.


P. Salek, T. Helgaker, and T. Saue. Linear response at the 4-component relativistic density functional level: Application to the frequency-dependent dipole polarizability of Hg, AuH and PtH$_2$ . Chem. Phys., 311:187, 2005. doi:10.1016/j.chemphys.2004.10.011.


T. Saue, K. Faegri, T. Helgaker, and O. Gropen. Principles of direct 4-component relativistic SCF: application to caesium auride. Mol. Phys., 91(5):937–950, 1997. doi:10.1080/002689797171058.


T. Saue and H. J. Aa. Jensen. Quaternion symmetry in relativistic molecular calculations: I. The Dirac-Fock method. J. Chem. Phys., 111:6211, 1999. doi:10.1063/1.479958.


T. Saue and H. J. Aa. Jensen. Quaternion symmetry of the Dirac equation. In Mathematical Models and Methods for Ab Initio Quantum Chemistry, volume 74 of Lecture Notes in Chemistry, pages 227–246. Springer Berlin Heidelberg, 2000. doi:10.1007/978-3-642-57237-1_11.


T. Saue and H. J. Aa. Jensen. Linear response at the 4-component relativistic level: Application to the frequency-dependent dipole polarizabilities of the coinage metal dimers. J. Chem. Phys., 118(2):522–536, 2003. doi:10.1063/1.1522407.


Trond Saue. Chapter 7 Post Dirac-Hartree-Fock methods—properties. In Peter Schwerdtfeger, editor, Relativistic Electronic Structure Theory, volume 11 of Theoretical and Computational Chemistry, pages 332 – 400. Elsevier, 2002. doi:10.1016/S1380-7323(02)80033-4.


Trond Saue. Relativistic Hamiltonians for Chemistry: A Primer. ChemPhysChem, 12(17):3077–3094, 2011. doi:10.1002/cphc.201100682.


Trond Saue and Trygve Helgaker. Four-component relativistic Kohn-Sham theory. J. Comput. Chem., 23(8):814–823, 2002. doi:10.1002/jcc.10066.


P. R. T. Schipper, O. V. Gritsenko, S. J. A. van Gisbergen, and E. J. Baerends. Molecular calculations of excitation energies and (hyper)polarizabilities with a statistical average of orbital model exchange-correlation potentials. J. Chem. Phys., 112(3):1344–1352, 2000. doi:10.1063/1.480688.


Avijit Shee, Trond Saue, Lucas Visscher, and Andre Severo Pereira Gomes. Equation-of-Motion Coupled-Cluster Theory based on the 4-component Dirac-Coulomb(-Gaunt) Hamiltonian. J. Chem. Phys., 145(17):174113, 2018. doi:10.1063/1.5053846.


Avijit Shee, Lucas Visscher, and Trond Saue. Analytic one-electron properties at the 4-component relativistic coupled cluster level with inclusion of spin-orbit coupling. J. Chem. Phys., 145(18):184107, 2016. doi:10.1063/1.4966643.


Kai Siegbahn. E. S. C. A. applied to free molecules. North-Holland Pub. Co. Amsterdam, 1969. ISBN 0-7204-0160-7.


Jetze Sikkema, Lucas Visscher, Trond Saue, and Miroslav Ilias. The molecular mean-field approach for correlated relativistic calculations. J. Chem. Phys., 131(12):124116, 2009. doi:10.1063/1.3239505.


Pascale Soulard, Pierre Asselin, Arnaud Cuisset, Juan Ramon Aviles Moreno, Thérèse R Huet, Denis Petitprez, Jean Demaison, Teresa B Freedman, Xiaolin Cao, Laurence A Nafie, and others. Chlorofluoroiodomethane as a potential candidate for parity violation measurements. Physical Chemistry Chemical Physics, 8(1):79–92, 2006.


Richard E. Stanton and Stephen Havriliak. Kinetic balance: A partial solution to the problem of variational safety in Dirac calculations. J. Chem. Phys., 81(4):1910–1918, 1984. doi:10.1063/1.447865.


R. G. Stone, J. M. Pochan, and W. H. Flygare. Zeeman Studies Including the Molecular \it g Values, Magnetic Susceptibilities, and Molecular Quadrupole Moments in Phosphorous and Nitrogen Trifluorides and Phosphoryl, Thionyl, and Sulfuryl Fluorides. Inorg. Chem., 8:2647, 1969. doi:10.1021/ic50082a021.


Akio Takatsuka, Seiichiro Ten-no, and Wolfgang Hackbusch. Minimax approximation for the decomposition of energy denominators in Laplace-transformed Møller–Plesset perturbation theories. J. Chem. Phys., 129(4):044112, 2008. doi:10.1063/1.2958921.


J. Thyssen and H. J. Aa. Jensen. Average-of-configurations SCF manuscript. unpublished, 1998.


Jørn Thyssen. Development and Applications of Methods for Correlated Relativistic Calculations of Molecular Properties. PhD thesis, University of Southern Denmark, 2001. URL:


Jørn Thyssen, Timo Fleig, and Hans Jørgen Aa. Jensen. A direct relativistic four-component multiconfiguration self-consistent-field method for molecules. J. Chem. Phys., 129(3):034109, 2008. doi:10.1063/1.2943670.


Jacopo Tomasi, Benedetta Mennucci, and Roberto Cammi. Quantum Mechanical Continuum Solvation Models. Chemical Reviews, 105(8):2999–3094, 2005. PMID: 16092826. doi:10.1021/cr9904009.


Jacopo Tomasi and Maurizio Persico. Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent. Chemical Reviews, 94(7):2027–2094, 1994. doi:10.1021/cr00031a013.


David J. Tozer and Nicholas C. Handy. Improving virtual Kohn-Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities. J. Chem. Phys., 109(23):10180–10189, 1998. doi:10.1063/1.477711.


J. H. Van Lenthe, R. Zwaans, H. J. J. Van Dam, and M. F. Guest. Starting SCF calculations by superposition of atomic densities. J. Comput. Chem., 27(8):926–932, 2006. doi:10.1002/jcc.20393.


S. Varga, E. Engel, W.-D. Sepp, and B. Fricke. Systematic study of the ib diatomic molecules cu$_2$, ag$_2$, and au$_2$ using advanced relativistic density functionals. Phys. Rev. A, 59:4288–4294, Jun 1999. doi:10.1103/PhysRevA.59.4288.


S. Varga, B. Fricke, H. Nakamatsu, T. Mukoyama, J. Anton, D. Geschke, A. Heitmann, E. Engel, and Baştug T. Four-component relativistic density functional calculations of heavy diatomic molecules. J. Chem. Phys., 112(8):3499–3506, 2000. doi:10.1063/1.480934.


Sebastien Villaume, Trond Saue, and Patrick Norman. Linear complex polarization propagator in a four-component Kohn-Sham framework. J. Chem. Phys., 133(6):064105, 2010. doi:10.1063/1.3461163.


L. Visscher and K.G. Dyall. Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions. Atomic Data and Nuclear Data Tables, 67(2):207 – 224, 1997. doi:10.1006/adnd.1997.0751.


L. Visscher, O. Visser, P. J. C. Aerts, H. Merenga, and W. C. Nieuwpoort. Relativistic quantum chemistry: the MOLFDIR program package. Comput. Phys. Commun., 81(1 - 2):120 – 144, 1994. doi:10.1016/0010-4655(94)90115-5.


Lucas Visscher. Approximate molecular relativistic Dirac-Coulomb calculations using a simple Coulombic correction. Theor. Chem. Acc., 98(2-3):68–70, 1997. doi:10.1007/s002140050280.


Lucas Visscher. The Dirac equation in quantum chemistry: Strategies to overcome the current computational problems. J. Comput. Chem., 23(8):759–766, 2002. doi:10.1002/jcc.10036.


Lucas Visscher, Ephraim Eliav, and Uzi Kaldor. Formulation and implementation of the relativistic Fock-space coupled cluster method for molecules. J. Chem. Phys., 115(21):9720–9726, 2001. doi:10.1063/1.1415746.


Lucas Visscher, Thomas Enevoldsen, Trond Saue, Hans Jørgen Aagaard Jensen, and Jens Oddershede. Full four-component relativistic calculations of NMR shielding and indirect spin-spin coupling tensors in hydrogen halides. J. Comput. Chem., 20(12):1262–1273, 1999. doi:10.1002/(SICI)1096-987X(199909)20:12<1262::AID-JCC6>3.0.CO;2-H.


Lucas Visscher, Thomas Enevoldsen, Trond Saue, and Jens Oddershede. Molecular relativistic calculations of the electric field gradients at the nuclei in the hydrogen halides. J. Chem. Phys., 109(22):9677–9684, 1998. doi:10.1063/1.477637.


Lucas Visscher, Timothy J. Lee, and Kenneth G. Dyall. Formulation and implementation of a relativistic unrestricted coupled-cluster method including noniterative connected triples. J. Chem. Phys., 105(19):8769–8776, 1996. doi:10.1063/1.472655.


Lucas Visscher and Trond Saue. Approximate relativistic electronic structure methods based on the quaternion modified Dirac equation. J. Chem. Phys., 113(10):3996–4002, 2000. doi:10.1063/1.1288371.


O. Visser, L. Visscher, P. J. C. Aerts, and W. C. Nieuwpoort. Molecular open shell configuration interaction calculations using the Dirac-Coulomb Hamiltonian: The f6-manifold of an embedded EuO6(9-) cluster. J. Chem. Phys., 96(4):2910–2919, 1992. doi:10.1063/1.461987.


S. H. Vosko, L. Wilk, and M. Nusair. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Canadian Journal of Physics, 58(8):1200–1211, 1980. doi:10.1139/p80-159.


Steven E. Wheeler and K. N. Houk. Through-Space Effects of Substituents Dominate Molecular Electrostatic Potentials of Substituted Arenes. J. Chem. Theory Comput., 5(9):2301–2312, 2009. doi:10.1021/ct900344g.


G.R. Wight, C.E. Brion, and M.J. Van Der Wiel. K-shell energy loss spectra of 2.5 keV electrons in N2 and CO. J. Electron. Spectrosc. Relat. Phenom., 1(5):457 – 469, 1972. doi:10.1016/0368-2048(72)80016-1.


Takeshi Yanai, David P Tew, and Nicholas C Handy. A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem. Phys. Lett., 393(1-3):51 – 57, 2004. doi:10.1016/j.cplett.2004.06.011.


Xiang Yuan. Molecular properties in the linear response regime and beyond with relativistic coupled-cluster. PhD thesis, VU E-Publishing, 2024. URL:, doi:10.5463/thesis.505.


Xiang Yuan, Loïc Halbert, Johann Valentin Pototschnig, Anastasios Papadopoulos, Sonia Coriani, Lucas Visscher, and André Severo Pereira Gomes. Formulation and implementation of frequency-dependent linear response properties with relativistic coupled cluster theory for gpu-accelerated computer architectures. Journal of Chemical Theory and Computation, 20(2):677–694, January 2024. URL:, doi:10.1021/acs.jctc.3c00812.


Xiang Yuan, Loïc Halbert, Lucas Visscher, and André Severo Pereira Gomes. Frequency-dependent quadratic response properties and two-photon absorption from relativistic equation-of-motion coupled cluster theory. Journal of Chemical Theory and Computation, 19(24):9248–9259, December 2023. URL:, doi:10.1021/acs.jctc.3c01011.


Roberto Di Remigio, Radovan Bast, Luca Frediani, and Trond Saue. Four-Component Relativistic Calculations in Solution with the Polarizable Continuum Model of Solvation: Theory, Implementation, and Application to the Group 16 Dihydrides H2X (X = O, S, Se, Te, Po). J. Phys. Chem. A, 119(21):5061–5077, 2015. PMID: 25412410. doi:10.1021/jp507279y.


Piet Th. van Duijnen and Marcel Swart. Molecular and Atomic Polarizabilities: Thole's Model Revisited. J. Phys. Chem. A, 102(14):2399–2407, 1998. doi:10.1021/jp980221f.


Martin van Horn, Trond Saue, and Nanna Holmgaard List. Probing chirality across the electromagnetic spectrum with the full semi-classical light-matter interaction. J. Chem. Phys., 156:054113, 2022. doi:10.1063/5.0077502.


E. van Lenthe, E. J. Baerends, and J. G. Snijders. Relativistic total energy using regular approximations. J. Chem. Phys., 101(11):9783–9792, 1994. doi:10.1063/1.467943.


E. van Lenthe, J. G. Snijders, and E. J. Baerends. The zero-order regular approximation for relativistic effects: The effect of spin-orbit coupling in closed shell molecules. J. Chem. Phys., 105(15):6505–6516, 1996. doi:10.1063/1.472460.


Joost N. P. van Stralen, Lucas Visscher, Christoffer Vaaben Larsen, and Hans Jørgen Aa. Jensen. First-order MP2 molecular properties in a relativistic framework. Chemical Physics, 311(1-2):81–95, 2005. Relativistic Effects in Heavy-Element Chemistry and Physics. In Memoriam Bernd A. Hess (1954-2004). doi:10.1016/j.chemphys.2004.10.018.