An up-to-date overview of the CFOUR program system is given. After providing a brief outline of the evolution of the program since its inception in 1989, a comprehensive presentation is given of its well-known capabilities for high-level coupled-cluster theory and its application to molecular properties. Subsequent to this generally well-known background information, much of the remaining content focuses on lesser-known capabilities of CFOUR, most of which have become available to the public only recently or will become available in the near future. Each of these new features is illustrated by a representative example, with additional discussion targeted to educating users as to classes of applications that are now enabled by these capabilities. Finally, some speculation about future directions is given, and the mode of distribution and support for CFOUR are outlined.

1.
J. F.
Stanton
,
J.
Gauss
,
L.
Cheng
,
M. E.
Harding
,
D. A.
Matthews
, and
P. G.
Szalay
, CFOUR, Coupled-Cluster techniques for Computational Chemistry, a quantum-chemical program package, with contributions from
A. A.
Auer
,
R. J.
Bartlett
,
U.
Benedikt
,
C.
Berger
,
D. E.
Bernholdt
,
Y. J.
Bomble
,
O.
Christiansen
,
F.
Engel
,
R.
Faber
,
M.
Heckert
,
O.
Heun
,
M.
Hilgenberg
,
C.
Huber
,
T.-C.
Jagau
,
D.
Jonsson
,
J.
Jusélius
,
T.
Kirsch
,
K.
Klein
,
W. J.
Lauderdale
,
F.
Lipparini
,
T.
Metzroth
,
L. A.
Mück
,
D. P.
O’Neill
,
D. R.
Price
,
E.
Prochnow
,
C.
Puzzarini
,
K.
Ruud
,
F.
Schiffmann
,
W.
Schwalbach
,
C.
Simmons
,
S.
Stopkowicz
,
A.
Tajti
,
J.
Vázquez
,
F.
Wang
,
J. D.
Watts
and the integral packages MOLECULE (
J.
Almlöf
and
P. R.
Taylor
), PROPS (
P. R.
Taylor
), ABACUS (
T.
Helgaker
,
H. J. Aa.
Jensen
,
P.
Jørgensen
, and
J.
Olsen
), and ECP routines by
A. V.
Mitin
and
C.
van Wüllen
. For the current version, see http://www.cfour.de.
2.
G. D.
Purvis
 III
and
R. J.
Bartlett
, “
ACES, a program to perform MBPT and CC calculations
,” in
Quantum Theory Project
(
University of Florida
,
Gainesville, FL
,
1977
).
3.
R. J.
Bartlett
, “
Many-body perturbation theory and coupled cluster theory for electron correlation in molecules
,”
Annu. Rev. Phys. Chem.
32
,
359
401
(
1981
).
4.
I.
Shavitt
and
R. J.
Bartlett
,
Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory
(
Cambridge University Press
,
2009
).
5.
J.
Gauss
,
J. F.
Stanton
, and
R. J.
Bartlett
, “
Coupled-cluster open-shell analytic gradients—Implementation of the direct product decomposition approach in energy gradient calculations
,”
J. Chem. Phys.
95
,
2623
2638
(
1991
).
6.
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 calculation
,”
J. Chem. Phys.
94
,
4334
4345
(
1991
).
7.
J.
Almlöf
, “
The MOLECULE integral program
,” Technical Report No. 74-09 (
University of Stockholm Institute of Physics
,
1974
).
8.
P. R.
Taylor
, “VPROPS: A program for the evaluation of one-electron property integrals over Gaussians.”
9.
J. W.
Moskowitz
and
L. C.
Snyder
, “
POLYATOM: A general computer program for ab initio calculations
,” in
Methods of Electronic Structure Theory
, Modern Theoretical Chemistry Vol. 3, edited by
H. F.
Schaefer
 III
(
Springer
,
Boston
,
1977
), pp.
387
411
.
10.
T.
Helgaker
,
H. J. Aa.
Jensen
,
P.
Jørgensen
,
J.
Olsen
, and
P. R.
Taylor
, ABACUS: A Gaussian integral and integral derivative program.
11.
J. D.
Watts
,
J. F.
Stanton
,
J.
Gauss
, and
R. J.
Bartlett
, “
A coupled-cluster study of the ground state of C3+.
,”
J. Chem. Phys.
94
,
4320
4327
(
1991
).
12.
J. F.
Stanton
,
J.
Gauss
, and
R. J.
Bartlett
, “
Potential nonrigidity of the NO3 radical
,”
J. Chem. Phys.
94
,
4084
4087
(
1991
).
13.
J. F.
Stanton
,
J.
Gauss
,
R. J.
Bartlett
,
T.
Helgaker
,
P.
Jørgensen
,
H. J. Aa.
Jensen
, and
P. R.
Taylor
, “
Interconversion of diborane(4) isomers
,”
J. Chem. Phys.
97
,
1211
1216
(
1992
).
14.
J. F.
Stanton
,
J.
Gauss
,
J. D.
Watts
,
W. J.
Lauderdale
, and
R. J.
Bartlett
, “
The ACES II program system
,”
Int. J. Quantum Chem.
44
,
879
894
(
1992
).
15.
V.
Lotrich
,
N.
Flocke
,
M.
Ponton
,
A. D.
Yau
,
A.
Perera
,
E.
Deumens
, and
R. J.
Bartlett
, “
Parallel implementation of electronic structure energy, gradient and Hessian calculations
,”
J. Chem. Phys.
128
,
194104
(
2008
).
16.
J.
Gauss
,
J. F.
Stanton
,
M. E.
Harding
, and
P. G.
Szalay
, “
Coupled cluster techniques for computational chemistry
,” in
Invited Lecture at the 8th WATOCMmeeting in Sydney, Australia
,
2008
.
17.
J.
Gauss
, “
Calculation of NMR chemical shifts at second-order many-body perturbation theory using gauge-including atomic orbitals
,”
Chem. Phys. Lett.
191
,
614
620
(
1992
).
18.
J.
Gauss
, “
Effects of electron correlation in the calculation of nuclear magnetic resonance chemical shifts
,”
J. Chem. Phys.
99
,
3629
3643
(
1993
).
19.
J.
Gauss
, “
GIAO-MBPT(3) and GIAO-SDQ-MBPT(4) calculations of nuclear magnetic shielding constants
,”
Chem. Phys. Lett.
229
,
198
203
(
1994
).
20.
J.
Gauss
and
J. F.
Stanton
, “
Gauge-invariant calculation of nuclear magnetic shielding constants at the coupled–cluster singles and doubles level
,”
J. Chem. Phys.
102
,
251
253
(
1995
).
21.
J.
Gauss
and
J. F.
Stanton
, “
Coupled-cluster calculations of nuclear magnetic resonance chemical shifts
,”
J. Chem. Phys.
103
,
3561
3578
(
1995
).
22.
J.
Gauss
and
J. F.
Stanton
, “
Perturbative treatment of triple excitations in coupled-cluster calculations of nuclear magnetic shielding constants
,”
J. Chem. Phys.
104
,
2574
2583
(
1996
).
23.
J.
Gauss
, “
Analytic second derivatives for the full coupled-cluster singles, doubles, and triples model: Nuclear magnetic shielding constants for BH, HF, CO, N2, N2O, and O3
,”
J. Chem. Phys.
116
,
4473
4776
(
2002
).
24.
J. F.
Stanton
and
R. J.
Bartlett
, “
The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties
,”
J. Chem. Phys.
98
,
7029
7039
(
1993
).
25.
J. F.
Stanton
, “
Many-body methods for excited state potential energy surfaces. I. General theory of energy gradients for the equation-of-motion coupled-cluster method
,”
J. Chem. Phys.
99
,
8840
8847
(
1993
).
26.
J. F.
Stanton
and
J.
Gauss
, “
Analytic energy gradients for the equation-of-motion coupled-cluster method: Implementation and application to the HCN/HNC system
,”
J. Chem. Phys.
100
,
4695
4698
(
1994
).
27.
J. F.
Stanton
and
J.
Gauss
, “
Analytic energy derivatives for ionized states described by the equation-of-motion coupled cluster method
,”
J. Chem. Phys.
101
,
8938
8944
(
1994
).
28.
J. F.
Stanton
and
J.
Gauss
, “
A simple correction to final state energies of doublet radicals described by equation-of-motion coupled cluster theory in the singles and doubles approximation
,”
Theor. Chem. Acc.
93
,
303
313
(
1996
).
29.
D. A.
Matthews
and
J. F.
Stanton
, “
A new approach to approximate equation-of-motion coupled cluster with triple excitations
,”
J. Chem. Phys.
145
,
124102
(
2016
).
30.
J.
Gauss
and
J. F.
Stanton
, “
Analytic CCSD(T) second derivatives
,”
Chem. Phys. Lett.
276
,
70
77
(
1997
).
31.
P. G.
Szalay
,
J.
Gauss
, and
J. F.
Stanton
, “
Analytic UHF-CCSD(T) second derivatives: Implementation and application to the calculation of the vibration-rotation interaction constants of NCO and NCS
,”
Theor. Chem. Acc.
100
,
5
11
(
1998
).
32.
J.
Gauss
and
J. F.
Stanton
, “
Analytic first and second derivatives for the CCSDT-n (n = 1 – 3) models: A first step towards the efficient calculation of CCSDT properties
,”
Phys. Chem. Chem. Phys.
2
,
2047
2059
(
2000
).
33.
J. F.
Stanton
and
J.
Gauss
, “
Analytic second derivatives in high-order many-body perturbation and coupled-cluster theories: Computational considerations and applications
,”
Int. Rev. Phys. Chem.
19
,
61
96
(
2000
).
34.
J. F.
Stanton
,
C. L.
Lopreore
, and
J.
Gauss
, “
The equilibrium structure and fundamental vibrational frequencies of dioxirane
,”
J. Chem. Phys.
108
,
7190
7196
(
1998
).
35.
C.
Puzzarini
,
J. F.
Stanton
, and
J.
Gauss
, “
Quantum-chemical calculation of spectroscopic parameters for rotational spectroscopy
,”
Int. Rev. Phys. Chem.
29
,
273
367
(
2010
).
36.
P. G.
Szalay
and
J.
Gauss
, “
Spin-restricted open-shell coupled-cluster theory
,”
J. Chem. Phys.
107
,
9028
9038
(
1997
).
37.
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
).
38.
J.
Gauss
,
K.
Ruud
, and
T.
Helgaker
, “
Perturbation-dependent atomic orbitals for the calculation of spin-rotation constants and rotational g tensors
,”
J. Chem. Phys.
105
,
2804
2812
(
1996
).
39.
J.
Gauss
and
D.
Sundholm
, “
Coupled-cluster calculations of spin-rotation constants
,”
Mol. Phys.
91
,
449
458
(
1997
).
40.
J.
Gauss
,
M.
Kállay
, and
F.
Neese
, “
Calculation of electronic g-tensors using coupled cluster theory
,”
J. Phys. Chem. A
113
,
111541
(
2009
).
41.
G.
Tarczay
,
P. G.
Szalay
, and
J.
Gauss
, “
First-principles calculation of electron spin-rotation tensors
,”
J. Phys. Chem. A
114
,
9246
9252
(
2010
).
42.
M.
Kállay
,
P. R.
Nagy
,
Z.
Rolik
,
D.
Mester
,
G.
Samu
,
J.
Csontos
,
J.
Csóka
,
B. P.
Szabó
,
L.
Gyevi-Nagy
,
I.
Ladjánszki
,
L.
Szegedy
,
B.
Ladóczki
,
K.
Petrov
,
M.
Farkas
,
P. D.
Mezei
, and
B.
Hégely
, MRCC, a quantum chemical program. See also
Z.
Rolik
,
L.
Szegedy
,
I.
Ladjánszki
,
B.
Ladóczki
, and
M.
Kállay
,
J. Chem. Phys.
139
,
094105
(
2013
), as well as: www.mrcc.hu.
43.
M.
Kállay
,
P. R.
Nagy
,
D.
Mester
,
Z.
Rolik
,
G.
Samu
,
J.
Csontos
,
J.
Csóka
,
P. B.
Szabó
,
L.
Gyevi-Nagy
,
B.
Hégely
,
I.
Ladjánszki
,
L.
Szegedy
,
B.
Ladóczki
,
K.
Petrov
,
M.
Farkas
,
P. D.
Mezei
, and
Á.
Ganyecz
, “
The MRCC program system: Accurate quantum chemistry from water to proteins
,”
J. Chem. Phys.
152
,
074107
(
2020
).
44.
M.
Kállay
and
P. R.
Surján
, “
Higher excitations in coupled-cluster theory
,”
J. Chem. Phys.
115
,
2945
2954
(
2001
).
45.
M.
Kállay
,
J.
Gauss
, and
P. G.
Szalay
, “
Analytic first derivatives for general coupled-cluster and configuration interaction models
,”
J. Chem. Phys.
119
,
2991
3004
(
2003
).
46.
M.
Kállay
and
J.
Gauss
, “
Analytic second derivatives for general coupled-cluster and configuration-interaction models
,”
J. Chem. Phys.
120
,
6841
6848
(
2004
).
47.
M.
Kállay
and
J.
Gauss
, “
Calculation of excited-state properties using general coupled-cluster and configuration-interaction models
,”
J. Chem. Phys.
121
,
9257
9269
(
2004
).
48.
J.
Gauss
,
A.
Tajti
,
M.
Kállay
,
J. F.
Stanton
, and
P. G.
Szalay
, “
Analytic calculation of the diagonal Born–Oppenheimer correction within configuration-interaction and coupled-cluster theory
,”
J. Chem. Phys.
125
,
144111
(
2006
).
49.
A.
Tajti
,
P. G.
Szalay
, and
J.
Gauss
, “
Perturbative treatment of the electron-correlation contribution to the diagonal Born–Oppenheimer correction
,”
J. Chem. Phys.
127
,
014102
(
2007
).
50.
T.
Ichino
,
J.
Gauss
, and
J. F.
Stanton
, “
Quasidiabatic states described by coupled-cluster theory
,”
J. Chem. Phys.
130
,
174105
(
2011
).
51.
A.
Tajti
and
P. G.
Szalay
, “
Analytic evaluation of the nonadiabatic coupling vector between excited states using equation-of-motion coupled-cluster theory
,”
J. Chem. Phys.
131
,
124104
(
2009
).
52.
S.
Stopkowicz
and
J.
Gauss
, “
Relativistic corrections to electrical first-order properties using direct perturbation theory
,”
J. Chem. Phys.
129
,
164119
(
2008
).
53.
S.
Stopkowicz
and
J.
Gauss
, “
Direct perturbation theory in terms of energy derivatives: Fourth-order relativistic corrections at the Hartree–Fock level
,”
J. Chem. Phys.
134
,
064114
(
2011
).
54.
S.
Stopkowicz
and
J.
Gauss
, “
Fourth-order relativistic corrections to electrical properties using direct perturbation theory
,”
J. Chem. Phys.
134
,
204106
(
2011
).
55.
L.
Cheng
and
J.
Gauss
, “
Analytical evaluation of first-order electrical properties based on the spin-free Dirac–Coulomb Hamiltonian
,”
J. Chem. Phys.
134
,
244112
(
2011
).
56.
L.
Cheng
and
J.
Gauss
, “
Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian
,”
J. Chem. Phys.
135
,
084114
(
2011
).
57.
L.
Cheng
and
J.
Gauss
, “
Analytic second derivatives for the spin-free exact two-component theory
,”
J. Chem. Phys.
135
,
244104
(
2011
).
58.
L.
Cheng
,
S.
Stopkowicz
, and
J.
Gauss
, “
Analytic energy derivatives in relativistic quantum chemistry
,”
Int. J. Quantum Chem.
114
,
1108
1127
(
2014
).
59.
J.
Liu
and
L.
Cheng
, “
An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling
,”
J. Chem. Phys.
148
,
144108
(
2018
).
60.
A.
Asthana
,
J.
Liu
, and
L.
Cheng
, “
Exact two-component equation-of-motion coupled-cluster singles and doubles method using atomic mean-field spin-orbit integrals
,”
J. Chem. Phys.
150
,
074102
(
2019
).
61.
A.
Köhn
,
M.
Hanauer
,
L. A.
Mück
,
T.-C.
Jagau
, and
J.
Gauss
, “
State-specific multireference coupled-cluster theory
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
3
,
176
197
(
2013
).
62.
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
).
63.
D. A.
Matthews
,
J.
Vazquéz
, and
J. F.
Stanton
, “
Calculated stretching overtone levels and Darling–Dennison resonances in water: A triumph of simple theoretical approaches
,”
Mol. Phys.
105
,
19
22
(
2007
).
64.
D. A.
Matthews
and
J. F.
Stanton
, “
Quantitative analysis of Fermi resonances by harmonic derivatives of perturbation theory corrections
,”
Mol. Phys.
107
,
213
222
(
2009
).
65.
M. E.
Harding
,
T.
Metzroth
,
J.
Gauss
, and
A. A.
Auer
, “
Parallel calculation of CCSD and CCSD(T) analytic first and second derivatives
,”
J. Chem. Theory Comput.
4
,
64
74
(
2008
).
66.
E.
Prochnow
,
M. E.
Harding
, and
J.
Gauss
, “
Parallel calculation of CCSDT and Mk-MRCCSDT energies
,”
J. Chem. Theory Comput.
6
,
2339
2347
(
2010
).
67.
I. M.
Mills
, “
Vibration-rotation structure in asymmetric- and symmetric-top molecules
,” in
Molecular Spectroscopy: Modern Research
, edited by
K. N.
Rao
and
C. W.
Mathews
(
Academic Press
,
New York
,
1972
), pp.
115
140
.
68.
M.
Heckert
,
M.
Kállay
,
D. P.
Tew
,
W.
Klopper
, and
J.
Gauss
, “
Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory
,”
J. Chem. Phys.
125
,
044108
(
2006
).
69.
J.
Jusélius
,
D.
Sundholm
, and
J.
Gauss
, “
Calculation of current densities using gauge-including atomic orbitals
,”
J. Chem. Phys.
121
,
3952
3963
(
2004
).
70.
M.
Barbatti
,
G.
Granucci
,
M.
Persico
,
M.
Ruckenbauer
,
M.
Vazdar
,
M.
Eckert-Maksić
, and
H.
Lischka
, “
The on-the-fly surface-hopping program system NEWTON-X: Application to ab initio simulation of the nonadiabatic photodynamics of benchmark systems
,”
J. Photochem. Photobiol. A
190
,
228
240
(
2007
).
71.
M.
Barbatti
,
M.
Ruckenbauer
,
F.
Plasser
,
J.
Pittner
,
G.
Granucci
,
M.
Persico
, and
H.
Lischka
, “
Newton-X: A surface-hopping program for nonadiabatic molecular dynamics
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
4
,
26
33
(
2014
).
72.
M.
Barbatti
,
G.
Granucci
,
M.
Ruckenbauer
,
F.
Plasser
,
R.
Crespo-Otero
,
J.
Pittner
,
M.
Persico
, and
H.
Lischka
, NEWTON-X: A package for Newtonian dynamics close to the crossing Seam (v. 2.2). Available via the internet at www.newtonx.org (
2018
).
73.
M.
Hanauer
and
A.
Köhn
, “
Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly
,”
J. Chem. Phys.
134
,
204111
(
2011
).
74.
F.
Lipparini
,
T.
Kirsch
,
A.
Köhn
, and
J.
Gauss
, “
Internally contracted multireference coupled cluster calculations with a spin-free Dirac-Coulomb Hamiltonian: Application to the monoxides of titanium, zirconium, and hafnium
,”
J. Chem. Theory Comput.
13
,
3171
3184
(
2017
).
75.
A. I.
Krylov
, “
Equation-of-motion coupled-cluster methods for open-shell and electronically excited species: The Hitchhiker’s guide to Fock space
,”
Annu. Rev. Phys. Chem.
59
,
433
462
(
2008
).
76.
P. G.
Szalay
and
R. J.
Bartlett
, “
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The reader is doubtless also aware of another popular class of elaborated triples correction, specifically those based on the completely renormalized (CR) class of methods (see, e.g., Ref. 442). Indeed, the CR-CC(2,3) method is among the most popular methods other than CCSD(T) that is used for this purpose, but CFOUR does not yet have an implementation of this method.

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