**I. Hartree-Fock theory**

`D.R. Hartree, The wave mechanics of an atom with a non-Coulomb central field. Part I. Theory and methods, Proc. Cambridge Phil. Soc. 24, 89 (1928)`

`V. Fock, Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems, Z. Phys. 61, 126-148 (1930)`

Roothaan-Hall equations

`C.C.J. Roothaan, New developments in molecular orbital theory, Rev. Mod. Phys. 23, 69 (1951)`

`G.G. Hall, The molecular orbital theory of chemical valency VIII. A method of calculating ionization potentials, Proc. Roy. Soc. A205, 541-552 (1951) `

unrestricted HF (UHF)

`J.A. Pople and R.K. Nesbet, Self‐consistent orbitals for radicals, J. Chem. Phys. 22, 571-572 (1954)`

restricted open-shell HF (ROHF)

`C.C.J. Roothaan, Self-consistent field theory for open shells of electronic systems, Rev. Mod. Phys. 32, 179 (1960)`

two-configurational SCF (TCSCF)

`A.C. Wahl and G. Das, The method of optimized valence configurations: A reasonable application of the multiconfiguration self-consistent-field technique to the quantitative description of chemical bonding, Adv. Quant. Chem. 5, 261-296 (1970)`

`F.W. Bobrowicz and W.A. Goddard, The self-consistent field equations for generalized valence bond and open-shell Hartree—Fock wave functions, in `*Modern Theoretical Chemistry*, Ed.: H.F. Schaefer III (Plenum, New York, 1977) Vol. 3, p. 79

complete-active space SCF (CASSCF)

`B.O. Roos, P.R. Taylor and P.E.M. Siegbahn, A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach, Chem. Phys. 48, 1157-173 (1980)`

`K. Ruedenberg, M. W. Schmidt, M. M. Gilbert, and S. T. Elbert, Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model, Chem. Phys. 71, 41-49 (1982)`

`H.J.Aa. Jensen and P. Jørgensen, A direct approach to second‐order MCSCF calculations using a norm extended optimization scheme, J. Chem. Phys. 80, 1204-1214 (1980)`

`F. Lipparini and J. Gauss, Cost-effective treatment of scalar relativistic effects for multireference systems: A CASSCF implementation based on the spin-free Dirac–Coulomb Hamiltonian, J. Chem. Theor. Comp. 12, 4284-4295 (2016); implementation in CFour`

`T. Nottoli, F. Lipparini and J. Gauss, Second-Order CASSCF Algorithm with the Cholesky Decomposition of the Two-Electron Integrals, J. Chem. Theor. Comp. 17, 6819-6831 (2021); implementation in CFour using Cholesky decomposition`

convergence acceleration in SCF (DIIS)

`P. Pulay, Improved SCF convergence acceleration, J. Comp. Chem. 3, 556-560 (1982)`

**II. Many-body-perturbation theory (Møller-Plesset perturbation theory)**

review articles

`R.J. Bartlett, Many-body perturbation theory and coupled cluster theory for electron correlation in molecules, Ann. Rev. Phys. Chem.32, 359-401 (1981)`

`D. Cremer, Møller–Plesset perturbation theory, in Encyclopedia of Computational Chemistry, Eds.: P.v.R. Schleyer et al., (Wiley, 1998), p. 1706 `

Møller-Plesset Hamiltonian

`C. Møller and M.S. Plesset, Note on an approximation treatment for many-electron systems, Phys. Rev. 46, 618 (1934)`

many-body perturbation theory (also known as Møller-Plesset perturbation theory)

`R.J. Bartlett and D.M. Silver, Pair-correlation energies in sodium hydride with many-body perturbation theory, Phys. Rev. A10, 1927 (1974)`

`R.J. Bartlett and D.M. Silver, Many‐body perturbation theory applied to electron pair correlation energies. I. Closed‐shell first‐row diatomic hydrides, J. Chem. Phys. 62, 3258-3268 (1975)`

`R.J. Bartlett and D.M. Silver, Many‐body perturbation theory applied to electron pair correlation energies. II. Closed‐shell second‐row diatomic hydrides, J. Chem. Phys. 64, 4578-4586 (1976)`

`R.J. Bartlett and I. Shavitt, Comparison of high-order many-body perturbation theory and configuration interaction for H2O, Chem. Phys. Lett. 50, 190-198 (1977)`

`J.A. Pople, J.S. Binkley, and R. Seeger, Theoretical models incorporating electron correlation, Int. J. Quant. Chem. Symp. 10, 1-19 (1976)`

`R. Krishnan and J.A. Pople, Approximate fourth‐order perturbation theory of the electron correlation energy, Int. J. Quant. Chem. 14, 91-100 (1978) (MP4(SDQ)`

`R. Krishnan, M.J. Frisch, and J.A. Pople, Contribution of triple substitutions to the electron correlation energy in fourth order perturbation theory, J. Chem. Phys. 72, 4244-4245 (1980)`

ROHF-MBPT/ROHF-MP

`W.J. Lauderdale, J.F. Stanton, J. Gauss, J.D. Watts, and R.J. Bartlett, Many-body perturbation theory with a restricted open-shell Hartree—Fock reference, Chem. Phys. Lett. 187, 21-28 (1991)`

`W.J. Lauderdale, J.F. Stanton, J. Gauss, J.D. Watts, and R.J. Bartlett, Restricted open‐shell Hartree–Fock‐based many‐body perturbation theory: Theory and application of energy and gradient calculations, J. Chem. Phys. 97, 6606-6620 (1992)`

see also

` P.J. Knowles, J.S. Andrews, R.D. Amos, N.C. Handy, and J.A. Pople, Restricted Møller—Plesset theory for open-shell molecules, Chem. Phys. Lett. 186, 130-136 (1991)`

**III. Coupled-Cluster Theory**

book

`I. Shavitt and R.J. Bartlett, `*Many-Body Methods in Chemistry and Physics*, (Cambridge University Press, Cambridge, 2009)

review articles

`R.J. Bartlett, Coupled-cluster approach to molecular structure and spectra: a step toward predictive quantum chemistry, J. Phys. Chem. 93, 1697-1708 (1989)`

`R.J. Bartlett and J.F. Stanton, Applications of Post‐Hartree—Fock Methods: A Tutorial, Rev. Comp. Chem. 5, 65 (1994)`

`T.J. Lee and G.E. Scuseria, in `*Quantum Mechanical Electronic Structure Calculations*, Ed.: S.R. Langhoff, (Kluwer, Dordrecht, 1995), p. 47

`R.J. Bartlett, in `*Modern Electronic Structure Theory*, Ed.: D.R. Yarkony (World Scientific, Singapore, 1995), p. 1047

`J. Gauss, Coupled‐cluster Theory, in Encyclopedia of Computational Chemistry, Eds.: P.v.R. Schleyer et al. (Wiley, New York, 1998)), p. 615`

`T.D. Crawford and H.F. Schaefer III, An Introduction to Coupled Cluster Theory for Computational Chemists, Rev. Comp. Chem. 14, 33 (2000)`

`R.J. Bartlett and M. Musiał, Coupled-cluster theory in quantum chemistry, Rev. Mod. Phys. 79, 291 (2007)`

original formulation of CC theory by Čížek

`J. Čížek, On the correlation problem in atomic and molecular systems. Calculation of wavefunction components in Ursell‐type expansion using quantum‐field theoretical methods, J. Chem. Phys. 45, 4256 (1966)`

`J. Čížek, On the use of the cluster expansion and the technique of diagrams in calculations of correlation effects in atoms and molecules, Adv. Chem. Phys. 14, 35 (1966)`

actual implementation and CC approximations:

CCD

`R.J. Bartlett and G.D. Purvis III, Many‐body perturbation theory, coupled‐pair many‐electron theory, and the importance of quadruple excitations for the correlation problem, Int. J. Quantum Chem. 14, 561-581 (1978)`

`J.A. Pople, R. Krishnan, H.B. Schlegel, and J.S. Binkley, Electron correlation theories and their application to the study of simple reaction potential surfaces, Int. J. Quantum Chem.14, 545-560 (1978)`

CCSD

`G.D.Purvis III and R.J.Bartlett, A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples, J. Chem. Phys. 76, 1910-1918 (1982)`

for more recent implementations, see

`G.E. Scuseria, A.C. Scheiner, T.J. Lee, J.E. Rice, and H.F. Schaefer III, The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results, J. Chem. Phys. 86, 2881-2890 (1987)`

`J.F. Stanton, J. Gauss, J.D. Watts, and R.J. Bartlett, A direct product decomposition approach for symmetry exploitation in many‐body methods. I. Energy calculations, J. Chem. Phys. 94, 4334-4345 (1991); implementation in CFour`

`C. Hampel, K.A. Peterson, and H.-J. Werner, A comparison of the efficiency and accuracy of the quadratic configuration interaction (QCISD), coupled cluster (CCSD), and Brueckner coupled cluster (BCCD) methods, Chem. Phys. Letters 190, 1-12 (1992)`

CCSDT-1

`Y.S. Lee, S.A. Kucharski, and R.J. Bartlett, A coupled cluster approach with triple excitations, J. Chem. Phys. 81, 5906-5912 (1984)`

CCSDT-2 and CCSDT-3

`J. Noga, R.J. Bartlett, and M. Urban, Towards a full CCSDT model for electron correlation. CCSDT-n models, Chem. Phys. Letters 134, 126-132 (1987)`

CCSD+T(CCSD)

`M. Urban, J. Noga, S.J. Cole, and R.J. Bartlett, Towards a full CCSDT model for electron correlation, J. Chem. Phys. 83, 4041-4046 (1985)`

CCSD(T)

`K. Raghavachari, G.W. Trucks, J.A. Pople and M. Head-Gordon, A fifth-order perturbation comparison of electron correlation theories, Chem. Phys. Lett. 157, 479-483 (1989)`

`R.J. Bartlett, J.D. Watts, S.A. Kucharski, and J. Noga, Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods, Chem. Phys. Lett. 165, 513-522 (1990)`

`J.F. Stanton, Why CCSD(T) works: a different perspective, Chem. Phys. Letters 281, 130-134 (1997); a posteriori rationalization of CCSD(T)`

CCSD(T)_Lambda

`T.D. Crawford and J.F. Stanton, Investigation of an asymmetric triple‐excitation correction for coupled‐cluster energies, Int. J. Quant. Chem. 70, 601-611 (1998) `

`S.A. Kucharski and R.J. Bartlett, Noniterative energy corrections through fifth-order to the coupled cluster singles and doubles method, J. Chem. Phys. 108, 5243-5254 (1998)`

CCSD(T-n)

`J.J. Eriksen, K. Kristensen, T. Kjærgaard, P. Jørgensen, and J. Gauss, A Lagrangian framework for deriving triples and quadruples corrections to the CCSD energy, J. Chem. Phys. 140, 064108 (2014); theory`

`J.J. Eriksen, P. Jørgensen, and J. Gauss, On the convergence of perturbative coupled cluster triples expansions: Error cancellations in the CCSD(T) model and the importance of amplitude relaxation, J. Chem. Phys. 142, 014102 (2015); implementation for closed-shell systems up to n=4`

CCn hierarchy

CC2

`O. Christiansen, H. Koch, and P. Jørgensen, The second-order approximate coupled cluster singles and doubles model CC2, Chem. Phys. Letters 243, 409-418 (1995)`

CC3

`H. Koch, O. Christiansen, P. Jørgensen, A.M. Sanchez de Merás, T. Helgaker, The CC3 model: An iterative coupled cluster approach including connected triples, J. Chem. Phys. 106, 1808-1818 (1997)`

CCSDT

`J. Noga and R.J. Bartlett, The full CCSDT model for molecular electronic structure, J. Chem. Phys. 86, 7041-7050 (1987), Erratum J. Chem. Phys. 89, 3401 (1988)`

`G.E. Scuseria and H.F. Schaefer III, A new implementation of the full CCSDT model for molecular electronic structure, Chem. Phys. Letters 152, 382-386 (1988)`

`J.D. Watts and R.J. Bartlett, The coupled‐cluster single, double, and triple excitation model for open‐shell single reference functions, J. Chem. Phys. 93, 6104-6105 (1990); UHF implementation`

for the parallel CCSDT-1, CCSDT-2, CCSDT-3, CCSDT-4, CC3, and CCSDT implementation in CFOUR , see:

`E. Prochnow, M.E. Harding and J. Gauss, Parallel Calculation of CCSDT and Mk-MRCCSDT Energies, J. Chem. Theor. Comp. 6, 2339-2347 (2010)`

CCSDTQ

`S.A. Kucharski and R.J. Bartlett, Recursive intermediate factorization and complete computational linearization of the coupled-cluster single, double, triple, and quadruple excitation equations, Theor. Chim. Acta 80, 387-405 (1991)`

`N. Oliphant and L. Adamowicz, Coupled‐cluster method truncated at quadruples, J. Chem. Phys. 95, 6645-6651 (1991)`

`S.A. Kucharski and R.J. Bartlett, The coupled‐cluster single, double, triple, and quadruple excitation method, J. Chem. Phys. 97, 4282-4288 (1992) `

`D.A. Matthews and J.F. Stanton, Non-orthogonal spin-adaptation of coupled cluster methods: A new implementation of methods including quadruple excitations, J. Chem. Phys. 142, 064108 (2015)`

CCSDT[Q]

`S.A. Kucharski and R.J. Bartlett, Coupled-cluster methods that include connected quadruple excitations, T4: CCSDTQ-1 and Q(CCSDT), Chem. Phys. Letters 158, 550-555 (1989)`

CCSDT(Q)

`Y.J. Bomble, J.F. Stanton, M. Kállay, and J. Gauss, Coupled-cluster methods including noniterative corrections for quadruple excitations, J. Chem. Phys. 123, 054101 (2005)`

`M. Kállay and J. Gauss, Approximate treatment of higher excitations in coupled-cluster theory, J. Chem. Phys. 123, 214105 (2005) `

`M. Kállay and J. Gauss, Approximate treatment of higher excitations in coupled-cluster theory. II. Extension to general single-determinant reference functions and improved approaches for the canonical Hartree–Fock case, J. Chem. Phys. 129, 144101 (2008); CCSDT(Q) for ROHF, CCSDT(Q) variants A and B`

CCSDT(Q-n) methods

`J.J. Eriksen, K. Kristensen, T. Kjærgaard, P. Jørgensen, and J. Gauss, A Lagrangian framework for deriving triples and quadruples corrections to the CCSD energy, J. Chem. Phys. 140, 064108 (2014); theory`

`J.J. Eriksen, D.A. Mattehws, P. Jørgensen, and J. Gauss, The performance of non-iterative coupled cluster quadruples models, J. Chem. Phys. 143, 041101 (2015); implementation for closed-shell systems up to n=4`

general CC

`M. Kállay and P.R. Surján, Higher excitations in coupled-cluster theory, J. Chem. Phys. 115, 2945-2954 (2001)`

`J. Olsen, The initial implementation and applications of a general active space coupled cluster method, J. Chem. Phys. 113, 7140-7148 (2000)`

`S. Hirata, Tensor Contraction Engine: Abstraction and Automated Parallel Implementation of Configuration-Interaction, Coupled-Cluster, and Many-Body Perturbation Theories, J. Phys. Chem. A 107, 9887-9897 (2003)`

ROHF and QRHF-CC methods

CCSD

`M. Rittby and R.J. Bartlett, An open-shell spin-restricted coupled cluster method: application to ionization potentials in nitrogen, J. Phys. Chem. 92, 3033-3036 (1988)`

CCSD(T)

`J. Gauss, W.J. Lauderdale, J.F. Stanton, J.D. Watts, R.J. Bartlett, Analytic energy gradients for open-shell coupled-cluster singles and doubles (CCSD) calculations using restricted open-shell Hartree—Fock (ROHF) reference functions, Chem. Phys. Letters 182, 207-215 (1991)`

`J.D. Watts, J. Gauss, and R.J. Bartlett, Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients, J. Chem. Phys. 98, 8718-8733 (1993)`

partially-spin-adapted CC methods

`P.J. Knowles, C.Hampel, and H.-J. Werner, Coupled cluster theory for high spin, open shell reference wave functions, J. Chem. Phys. 99, 5219-5227 (1993); Erratum J. Chem. Phys. 112, 3106-3107 (2000)`

`P. Neogrády, M. Urban, and I. Hubač, Spin adapted restricted Hartree–Fock reference coupled cluster theory for open shell systems, J. Chem. Phys. 100, 3706-3716 (1994) `

`P.G. Szalay and J. Gauss, Spin-restricted open-shell coupled-cluster theory, J. Chem. Phys. 107, 9028-9038 (1997)`

spin-restricted CC methods

`P.G. Szalay and J. Gauss, Spin-restricted open-shell coupled-cluster theory, J. Chem. Phys. 107, 9028-9038 (1997)`

`P.G. Szalay and J. Gauss, Spin-restricted open-shell coupled-cluster theory for excited states, J. Chem. Phys. 112, 4027-4036 (1999)`

`I. Berente, P.G. Szalay, and J. Gauss, Spin-restricted coupled-cluster theory with triple excitations, J. Chem. Phys. 117, 7872-7881 (2003)`

spin-adapted CC methods

`M. Heckert, O. Heun, J. Gauss, and P.G. Szalay, Towards a spin-adapted coupled-cluster theory for high-spin open-shell states, J. Chem. Phys. 124, 124105 (2006)`

unitary group based spin-adapted CC methods using a combinatoric open-shell CC ansatz

`D. Datta and D. Mukherjee, A compact spin‐free combinatoric open‐shell coupled cluster theory applied to single‐reference doublets, Int. J. Quantum Chem. 108, 2211-2222 (2008)`

`D. Datta and D. Mukherjee, An explicitly spin-free compact open-shell coupled cluster theory using a multireference combinatoric exponential ansatz: Formal development and pilot applications, J. Chem. Phys. 131 044124 (2009)`

`D. Datta and J. Gauss, A non-antisymmetric tensor contraction engine for the automated implementation of spin-adapted coupled cluster approaches, J. Chem. Theory Comput. 9, 2639-2653 (2013); implementation in CFour`

Brueckner CC methods

`R.A. Chiles and C.E. Dykstra, An electron pair operator approach to coupled cluster wave functions. Application to He2, Be2, and Mg2 and comparison with CEPA methods, J. Chem. Phys. 74, 4544-4556 (1981)`

`J.F. Stanton, J. Gauss, and R.J. Bartlett, On the choice of orbitals for symmetry breaking problems with application to NO3, J. Chem. Phys. 97, 5554-5559 (1992)`

orbital-optimized CC

`G.E. Scuseria and H.F. Schaefer III, The optimization of molecular orbitals for coupled cluster wavefunctions, Chem. Phys. Lett. 142, 354-358 (1987)`

QCISD and QCISD(T)

`J.A. Pople, M. Head-Gordon, and K. Raghavachari, Quadratic configuration interaction. A general technique for determining electron correlation energies, J. Chem. Phys. 87, 5968-5975 (1987)`

unitary CC (UCC) methods

` R.J. Bartlett, S.A. Kucharski, and J. Noga, Alternative coupled-cluster ansätze II. The unitary coupled-cluster method, Chem. Phys. Lett. 155, 133-140 (1989)`

`J.D. Watts, G.W. Trucks, and R.J. Bartlett, The unitary coupled-cluster approach and molecular properties. Applications of the UCC(4) method, Chem. Phys. Lett. 157, 359 (1989)`

`J. Liu, D.A. Matthews, and L. Cheng, Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version, J. Chem. Theory Comput. 18, 2281-2291 (2022)`

Mukherjee's Multireference CC method (Mk-MRCC)

`U.S. Mahapatra, B. Datta, and D. Mukherjee, A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications, J. Chem. Phys. 101, 6171 (1999)`

`F.A. Evangelista, W.D. Allen, and H.F. Schaefer III, Coupling term derivation and general implementation of state-specific multireference coupled cluster theories, J. Chem. Phys. 127, 024102 (2007)`

`F.A. Evangelista, A.D. Simmonett, W.D. Allen, H.F. Schaefer III, and J. Gauss, Triple excitations in state-specific multireference coupled cluster theory: Application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems, J. Chem. Phys. 128, 124104 (2008)`

`F.A. Evangelista, E. Prochnow, J. Gauss, and H.F. Schaefer III, Perturbative triples corrections in state-specific multireference coupled cluster theory, J. Chem. Phys. 132, 074107 (2010)`

for the parallel Mk-MRCCSDT implementation in CFOUR , see:

`E. Prochnow, M.E. Harding, and J. Gauss, Parallel Calculation of CCSDT and Mk-MRCCSDT Energies, J. Chem. Theor. Comp. 6, 2339 (2010)`

two-component CCSD and CCSD(T) approaches with spin-orbit coupling

`F. Wang, J. Gauss, and C. van Wüllen, Closed-shell coupled-cluster theory with spin-orbit coupling, J. Chem. Phys. 129, 064113 (2008)`