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Quantum Chemical Methods

I. Hartree-Fock theory

original Papers
D.R. Hartree, Proc. Cambridge Phil. Soc. 24, 89 (1928)
V. Fock, Z. Phys. 61, 126 (1930)

Roothaan-Hall equations
C.C.J. Roothaan, Rev. Mod. Phys. 23, 69 (1951)
G.G. Hall, Proc. Roy. Soc. A205, 541 (1951)

unrestricted HF (UHF)
J.A. Pople and R.K. Nesbet, J. Chem. Phys. 22, 571 (1954)

restricted open-shell HF (ROHF)
C.C.J. Roothaan, Rev. Mod. Phys. 32, 179 (1960)

two-configurational SCF (TCSCF)
A.C. Wahl and G. Das, Adv. Quant. Chem. 5, 261 (1970)
F.W. Bobrowicz and W.A. Goddard, in Modern Theoretical Chemistry, Ed.: H.F. Schaefer III (Plenum, New York, 1977) Vol. 3, p. 79

complete-active space SCF (CASSCF)
H.J.Aa. Jensen and P. Jørgensen, J. Chem. Phys. 80, 1204 (1980)
F. Lipparini and J. Gauss, J. Chem. Theor. Comp. 12, 4284 (2016); implementation in CFour

convergence acceleration in SCF (DIIS)
P. Pulay, J. Comp. Chem. 3, 556 (1982)

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

review articles
R.J. Bartlett, Ann. Rev. Phys. Chem.32, 359 (1981)
D. Cremer, 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, Phys. Rev. 46, 618 (1934)

many-body perturbation theory (also known as Møller-Plesset perturbation theory)
R.J. Bartlett and D.M. Silver, Phys. Rev. A10, 1927 (1974)
R.J. Bartlett and D.M. Silver, J. Chem. Phys. 62, 3258 (1975)
R.J. Bartlett and D.M. Silver, J. Chem. Phys. 64, 4578 (1976)
R.J. Bartlett and I. Shavitt, Chem. Phys. Lett. 50, 190 (1977)
J.A. Pople, J.S. Binkley, and R. Seeger, Int. J. Quant. Chem. Symp. 10, 1 (1976)
R. Krishnan and J.A. Pople, Int. J. Quant. Chem. 14, 91 (1978) (MP4(SDQ)
R. Krishnan, M.J. Frisch, and J.A. Pople, J. Chem. Phys. 72, 4244 (1980)

ROHF-MBPT/ROHF-MP
W.J. Lauderdale, J.F. Stanton, J. Gauss, J.D. Watts, and R.J. Bartlett, Chem. Phys. Lett. 187, 21 (1991)
W.J. Lauderdale, J.F. Stanton, J. Gauss, J.D. Watts, and R.J. Bartlett, J. Chem. Phys. 97, 6606 (1992)

see also
P.J. Knowles, J.S. Andrews, R.D. Amos, N.C. Handy, and J.A. Pople, Chem. Phys. Lett. 186, 130 (1991)

III. Coupled-Cluster Theory

book
I. Shavitt and R.J. Bartlett, Many-Body Methods in Chemistry and Physics, (Cambridge Molecular Science, Cambridge, 2009)

review articles
R.J. Bartlett, J. Phys. Chem. 93, 1697 (1989)
R.J. Bartlett and J.F. Stanton, 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, 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, Rev. Comp. Chem. 14, 33 (2000)
R.J. Bartlett and M. Musial, Rev. Mod. Phys. 79, 291 (2007)

original formulation of CC theory by Cizek
J. Cizek, J. Chem. Phys. 45, 4256 (1966)
J. Cizek, Adv. Chem. Phys. 14, 35 (1966)

actual implementation and CC approximations:

CCD
R.J. Bartlett and G.D. Purvis III, Int. J. Quantum Chem. 14, 561 (1978)
J.A. Pople, R. Krishnan, H.B. Schlegel, and J.S. Binkley, Int. J. Quantum Chem.14, 545 (1978)

CCSD
G.D.Purvis III and R.J.Bartlett, J. Chem. Phys. 76, 1910 (1982)

for more recent implementations, see
G.E. Scuseria, A.C. Scheiner, T.J. Lee, J.E. Rice, and H.F. Schaefer III, J. Chem. Phys. 86, 2881 (1987)
J.F. Stanton, J. Gauss, J.D. Watts, and R.J. Bartlett, J. Chem. Phys. 94, 4334 (1991); implementation in CFour
C. Hampel, K.A. Peterson, and H.-J. Werner, Chem. Phys. Letters 190, 1 (1992)

CCSDT-1
Y.S. Lee, S.A. Kucharski, and R.J. Bartlett, J. Chem. Phys. 81, 5906 (1984)

CCSDT-2 and CCSDT-3
J. Noga, R.J. Bartlett, and M. Urban, Chem. Phys. Letters 134, 126 (1987)

CCSD+T(CCSD)
M. Urban, J. Noga, S.J. Cole, and R.J. Bartlett, J. Chem. Phys. 83, 4041 (1985)

CCSD(T)
K. Raghavachari, G.W. Trucks, J.A. Pople and M. Head-Gordon, Chem. Phys. Lett. 157, 479 (1989)
R.J. Bartlett, J.D. Watts, S.A. Kucharski, and J. Noga, Chem. Phys. Lett. 165, 513 (1990)
J.F. Stanton, Chem. Phys. Letters 281, 130 (1997); a posteriori rationalization of CCSD(T)

CCSD(T)_Lambda
T.D. Crawford and J.F. Stanton, Int. J. Quant. Chem. 70, 601 (1998)
S.A. Kucharski and R.J. Bartlett, J. Chem. Phys. 108, 5243 (1998)

CCSD(T-n)
J.J. Eriksen, K. Kristensen, T. Kjæegaard, P. Jørgensen, and J. Gauss, J. Chem. Phys. 140, 064108 (2014); theory
J.J. Eriksen, P. Jørgensen, and J. Gauss, 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, Chem. Phys. Letters 243, 409 (1995)

CC3
H. Koch, O. Christiansen, P. Jørgensen, A.M. Sanchez de Meras, T. Helgaker, J. Chem. Phys. 106, 1808 (1997)

CCSDT
J. Noga and R.J. Bartlett, J. Chem. Phys. 86, 7041 (1987), Erratum J. Chem. Phys. 89, 3401 (1988)
G.E. Scuseria and H.F. Schaefer III, Chem. Phys. Letters 152, 382 (1988)
J.D. Watts and R.J. Bartlett, J. Chem. Phys. 93, 6104 (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, J. Chem. Theor. Comp. 6, 2339 (2010)

CCSDTQ
S.A. Kucharski and R.J. Bartlett, Theor. Chim. Acta 80, 387 (1991)
N. Oliphant and L. Adamowicz, J. Chem. Phys. 95, 6645 (1991)
S.A. Kucharski and R.J. Bartlett, J. Chem. Phys. 97, 4282 (1992)

CCSDT[Q]
S.A. Kucharski and R.J. Bartlett, Chem. Phys. Letters 158, 550 (1989)

CCSDT(Q)
Y.J. Bomble, J.F. Stanton, M. Kállay, and J. Gauss, J. Chem. Phys. 123, 054101 (2005)
M. Kállay and J. Gauss, J. Chem. Phys. 123, 214105 (2005)
M. Kállay and J. Gauss, 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. Kjaeregaard, P. Jørgensen, and J. Gauss, J. Chem. Phys. 140, 064108 (2014); theory
J.J. Eriksen, D.A. Mattehws, P. Jørgensen, and J. Gauss, J. Chem. Phys. 143, 041101 (2015); implementation for closed-shell systems up to n=4

general CC
M. Kállay and P.R. Surján, J. Chem. Phys. 115, 2945 (2001)
J. Olsen, J. Chem. Phys. 113, 7140 (2000)
S. Hirata, J. Phys. Chem. A 107, 9887 (2003)

ROHF and QRHF-CC methods

CCSD
M. Rittby and R.J. Bartlett, J. Phys. Chem. 92, 3033 (1988)

CCSD(T)
J. Gauss, W.J. Lauderdale, J.F. Stanton, J.D. Watts, R.J. Bartlett, Chem. Phys. Letters 182, 207 (1991)
J.D. Watts, J. Gauss, and R.J. Bartlett, J. Chem. Phys. 98, 8718 (1993)

partially-spin-adapted CC methods
P.J. Knowles, C.Hampel, and H.-J. Werner, J. Chem. Phys. 99, 5219 (1993); Erratum J. Chem. Phys. 112, 3106 (2000)
P. Neogrady, M. Urban, and I. Hubac, J. Chem. Phys. 100, 3706 (1994)
P.G. Szalay and J. Gauss, J. Chem. Phys. 107, 9028 (1997)

spin-restricted CC methods
P.G. Szalay and J. Gauss, J. Chem. Phys. 107, 9028 (1997)
P.G. Szalay and J. Gauss, J. Chem. Phys. 112, 4027 (1999)
I. Berente, P.G. Szalay, and J. Gauss, J. Chem. Phys. 117, 7872 (2003)

spin-adapted CC methods
M. Heckert, O. Heun, J. Gauss, and P.G. Szalay, J. Chem. Phys. 124, 124105 (2006)

Brueckner CC methods
R.A. Chiles and C.E. Dykstra, J. Chem. Phys. 74, 4544 (1981)
J.F. Stanton, J. Gauss, and R.J. Bartlett, J. Chem. Phys. 97, 5554 (1992)

orbital-optimized CC
G.E. Scuseria and H.F. Schaefer III, Chem. Phys. Lett. 142, 354 (1987)

QCISD and QCISD(T)
J.A. Pople, M. Head-Gordon, and K. Raghavachari, J. Chem. Phys. 87, 5968 (1987)

unitary CC (UCC) methods
R.J. Bartlett, S.A. Kucharski, and J. Noga, Chem. Phys. Lett. 155, 133 (1989)
J.D. Watts, G.W. Trucks, and R.J. Bartlett, Chem. Phys. Lett. 157, 359 (1989)

Mukherjee's Multireference CC method (Mk-MRCC)

U.S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 101, 6171 (1999)
F.A. Evangelista, W.D. Allen, and H.F. Schaefer III, J. Chem. Phys. 127, 024102 (2007)
F.A. Evangelista, A.D. Simmonett, W.D. Allen, H.F. Schaefer III, and J. Gauss, J. Chem. Phys. 128, 124104 (2008)
F.A. Evangelista, E. Prochnow, J. Gauss, and H.F. Schaefer III, J. Chem. Phys. 132, 074107 (2010)

for the parallel Mk-MRCCSDT implementation in CFOUR , see:
E. Prochnow, M.E. Harding, and J. Gauss, 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, J. Chem. Phys. 129, 064113 (2008)

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CFOUR is partially supported by the U.S. National Science Foundation.