Fe(II)–porphyrin complexes exhibit a diverse range of electronic interactions between the metal and macrocycle. Herein, the incremental full configuration interaction method is applied to the entire space of valence orbitals of a Fe(II)–porphyrin model using a modest basis set. A novel visualization framework is proposed to analyze individual many-body contributions to the correlation energy, providing detailed maps of this complex’s highly correlated electronic structure. This technique is used to parse the numerous interactions of two low-lying triplet states (3A2g and 3Eg) and to show that strong metal d–d and macrocycle π–π orbital interactions preferentially stabilize the 3A2g state. d–π interactions, on the other hand, preferentially stabilize the 3Eg state and primarily appear when correlating six electrons at a time. Ultimately, the Fe(II)–porphyrin model’s full set of 88 valence electrons are correlated in 275 orbitals, showing the interactions up to the 4-body level, which covers the great majority of correlations in this system.

1.
J. A.
Pople
, “
Nobel lecture: Quantum chemical models
,”
Rev. Mod. Phys.
71
,
1267
1274
(
1999
).
2.
R. A.
Friesner
, “
Ab initio quantum chemistry: Methodology and applications
,”
Proc. Natl. Acad. Sci. U. S. A.
102
,
6648
6653
(
2005
).
3.
J.
Řezáč
and
P.
Hobza
, “
Benchmark calculations of interaction energies in noncovalent complexes and their applications
,”
Chem. Rev.
116
,
5038
5071
(
2016
).
4.
P. J.
Knowles
and
N. C.
Handy
, “
A new determinant-based full configuration interaction method
,”
Chem. Phys. Lett.
111
,
315
321
(
1984
).
5.
J.
Olsen
,
B. O.
Roos
,
P.
Jørgensen
, and
H. J. A.
Jensen
, “
Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces
,”
J. Chem. Phys.
89
,
2185
2192
(
1988
).
6.
J.
Olsen
,
P.
Jørgensen
, and
J.
Simons
, “
Passing the one-billion limit in full configuration-interaction (FCI) calculations
,”
Chem. Phys. Lett.
169
,
463
472
(
1990
).
7.
M. J.
Bearpark
,
F.
Ogliaro
,
T.
Vreven
,
M.
Boggio-Pasqua
,
M. J.
Frisch
,
S. M.
Larkin
,
M.
Morrison
, and
M. A.
Robb
, “
CASSCF calculations for photoinduced processes in large molecules: Choosing when to use the RASSCF, ONIOM, and MMVB approximations
,”
J. Photochem. Photobiol., A
190
,
207
227
(
2007
).
8.
S.
Vancoillie
,
H.
Zhao
,
V. T.
Tran
,
M. F. A.
Hendrickx
, and
K.
Pierloot
, “
Multiconfigurational second-order perturbation theory restricted active space (RASPT2) studies on mononuclear first-row transition-metal systems
,”
J. Chem. Theory Comput.
7
,
3961
3977
(
2011
).
9.
G.
Li Manni
,
D.
Ma
,
F.
Aquilante
,
J.
Olsen
, and
L.
Gagliardi
, “
SplitGAS method for strong correlation and the challenging case of Cr2
,”
J. Chem. Theory Comput.
9
,
3375
3384
(
2013
).
10.
R.
Olivares-Amaya
,
W.
Hu
,
N.
Nakatani
,
S.
Sharma
,
J.
Yang
, and
G. K.-L.
Chan
, “
The ab-initio density matrix renormalization group in practice
,”
J. Chem. Phys.
142
,
034102
(
2015
).
11.
J.
Ivanic
and
K.
Ruedenberg
, “
Identification of deadwood in configuration spaces through general direct configuration interaction
,”
Theor. Chem. Acc.
106
,
339
351
(
2001
).
12.
J.
Ivanic
and
K.
Ruedenberg
, “
Deadwood in configuration spaces. II. Singles + doubles and singles + doubles + triples + quadruples spaces
,”
Theor. Chem. Acc.
107
,
220
228
(
2002
).
13.
L.
Bytautas
and
K.
Ruedenberg
, “
A priori identification of configurational deadwood
,”
Chem. Phys.
356
,
64
75
(
2009
).
14.
D.
Herebian
,
K. E.
Wieghardt
, and
F.
Neese
, “
Analysis and interpretation of metal-radical coupling in a series of square planar nickel complexes: Correlated ab initio and density functional investigation of [Ni(LISQ)2] [LISQ=3,5-di-tert-butyl-o-diiminobenzosemiquinonate(1-)]
,”
J. Am. Chem. Soc.
125
,
10997
11005
(
2003
).
15.
J. P.
Malrieu
,
R.
Caballol
,
C. J.
Calzado
,
C.
De Graaf
, and
N.
Guihéry
, “
Magnetic interactions in molecules and highly correlated materials: Physical content, analytical derivation, and rigorous extraction of magnetic Hamiltonians
,”
Chem. Rev.
114
,
429
492
(
2014
).
16.
N. J.
Mayhall
and
M.
Head-Gordon
, “
Computational quantum chemistry for multiple-site Heisenberg spin couplings made simple: Still only one spin-flip required
,”
J. Phys. Chem. Lett.
6
,
1982
1988
(
2015
).
17.
N. J.
Mayhall
, “
Using higher-order singular value decomposition to define weakly coupled and strongly correlated clusters: The n-body Tucker approximation
,”
J. Chem. Theory Comput.
13
,
4818
4828
(
2017
).
18.
N.
Orms
and
A. I.
Krylov
, “
Singlet-triplet energy gaps and the degree of diradical character in binuclear copper molecular magnets characterized by spin-flip density functional theory
,”
Phys. Chem. Chem. Phys.
20
,
13127
13144
(
2018
).
19.
N.
Orms
,
D. R.
Rehn
,
A.
Dreuw
, and
A. I.
Krylov
, “
Characterizing bonding patterns in diradicals and triradicals by density-based wave function analysis: A uniform approach
,”
J. Chem. Theory Comput.
14
,
638
648
(
2018
).
20.
A. E.
Rask
and
P. M.
Zimmerman
, “
Toward full configuration interaction for transition-metal complexes
,”
J. Phys. Chem. A
125
,
1598
1609
(
2021
).
21.
D.
Ma
,
G.
Li Manni
, and
L.
Gagliardi
, “
The generalized active space concept in multiconfigurational self-consistent field methods
,”
J. Chem. Phys.
135
,
044128
(
2011
).
22.
S.
Keller
,
K.
Boguslawski
,
T.
Janowski
,
M.
Reiher
, and
P.
Pulay
, “
Selection of active spaces for multiconfigurational wavefunctions
,”
J. Chem. Phys.
142
,
244104
(
2015
).
23.
R. E.
Thomas
,
Q.
Sun
,
A.
Alavi
, and
G. H.
Booth
, “
Stochastic multiconfigurational self-consistent field theory
,”
J. Chem. Theory Comput.
11
,
5316
5325
(
2015
).
24.
G.
Li Manni
,
S. D.
Smart
, and
A.
Alavi
, “
Combining the complete active space self-consistent field method and the full configuration interaction quantum Monte Carlo within a super-CI framework, with application to challenging metal-porphyrins
,”
J. Chem. Theory Comput.
12
,
1245
1258
(
2016
).
25.
S. R.
White
, “
Density matrix formulation for quantum renormalization groups
,”
Phys. Rev. Lett.
69
,
2863
2866
(
1992
).
26.
G. K.-L.
Chan
and
M.
Head-Gordon
, “
Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group
,”
J. Chem. Phys.
116
,
4462
4476
(
2002
).
27.
G. K.-L.
Chan
,
M.
Kállay
, and
J.
Gauss
, “
State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve
,”
J. Chem. Phys.
121
,
6110
6116
(
2004
).
28.
S. R.
White
, “
Density matrix renormalization group algorithms with a single center site
,”
Phys. Rev. B
72
,
180403(R)
(
2005
).
29.
U.
Schollwöck
, “
The density-matrix renormalization group
,”
Rev. Mod. Phys.
77
,
259
315
(
2005
).
30.
K. H.
Marti
,
I. M.
Ondík
,
G.
Moritz
, and
M.
Reiher
, “
Density matrix renormalization group calculations on relative energies of transition metal complexes and clusters
,”
J. Chem. Phys.
128
,
014104
(
2008
).
31.
T.
Yanai
,
Y.
Kurashige
,
D.
Ghosh
, and
G. K.-L.
Chan
, “
Accelerating convergence in iterative solution for large-scale complete active space self-consistent-field calculations
,”
Int. J. Quantum Chem.
109
,
2178
2190
(
2009
).
32.
G. K.-L.
Chan
and
S.
Sharma
, “
The density matrix renormalization group in quantum chemistry
,”
Annu. Rev. Phys. Chem.
62
,
465
481
(
2011
).
33.
T.
Zhang
and
F. A.
Evangelista
, “
A deterministic projector configuration interaction approach for the ground state of quantum many-body systems
,”
J. Chem. Theory Comput.
12
,
4326
4337
(
2016
).
34.
A. A.
Holmes
,
N. M.
Tubman
, and
C. J.
Umrigar
, “
Heat-bath configuration interaction: An efficient selected configuration interaction algorithm inspired by heat-bath sampling
,”
J. Chem. Theory Comput.
12
,
3674
3680
(
2016
).
35.
S.
Sharma
,
A. A.
Holmes
,
G.
Jeanmairet
,
A.
Alavi
, and
C. J.
Umrigar
, “
Semistochastic heat-bath configuration interaction method: Selected configuration interaction with semistochastic perturbation theory
,”
J. Chem. Theory Comput.
13
,
1595
1604
(
2017
).
36.
J. E. T.
Smith
,
B.
Mussard
,
A. A.
Holmes
, and
S.
Sharma
, “
Cheap and near exact CASSCF with large active spaces
,”
J. Chem. Theory Comput.
13
,
5468
5478
(
2017
).
37.
J. B.
Schriber
and
F. A.
Evangelista
, “
Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy
,”
J. Chem. Phys.
144
,
161106
(
2016
).
38.
C.
Daday
,
S.
Smart
,
G. H.
Booth
,
A.
Alavi
, and
C.
Filippi
, “
Full configuration interaction excitations of ethene and butadiene: Resolution of an ancient question
,”
J. Chem. Theory Comput.
8
,
4441
4451
(
2012
).
39.
D.
Cleland
,
G. H.
Booth
, and
A.
Alavi
, “
Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo
,”
J. Chem. Phys.
132
,
041103
(
2010
).
40.
G. H.
Booth
and
A.
Alavi
, “
Approaching chemical accuracy using full configuration-interaction quantum Monte Carlo: A study of ionization potentials
,”
J. Chem. Phys.
132
,
174104
(
2010
).
41.
J. S.
Spencer
,
N. S.
Blunt
, and
W. M. C.
Foulkes
, “
The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method
,”
J. Chem. Phys.
136
,
054110
(
2012
).
42.
N. M.
Tubman
,
J.
Lee
,
T. Y.
Takeshita
,
M.
Head-Gordon
, and
K. B.
Whaley
, “
A deterministic alternative to the full configuration interaction quantum Monte Carlo method
,”
J. Chem. Phys.
145
,
044112
(
2016
).
43.
C. J.
Stein
and
M.
Reiher
, “
Automated selection of active orbital spaces
,”
J. Chem. Theory Comput.
12
,
1760
1771
(
2016
).
44.
J. E.
Deustua
,
J.
Shen
, and
P.
Piecuch
, “
Converging high-level coupled-cluster energetics by Monte Carlo sampling and moment expansions
,”
Phys. Rev. Lett.
119
,
223003
(
2017
).
45.
K. D.
Vogiatzis
,
D.
Ma
,
J.
Olsen
,
L.
Gagliardi
, and
W. A.
de Jong
, “
Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations
,”
J. Chem. Phys.
147
,
184111
(
2017
).
46.
J. E.
Deustua
,
I.
Magoulas
,
J.
Shen
, and
P.
Piecuch
, “
Communication: Approaching exact quantum chemistry by cluster analysis of full configuration interaction quantum Monte Carlo wave functions
,”
J. Chem. Phys.
149
,
151101
(
2018
).
47.
Y.
Garniron
,
A.
Scemama
,
E.
Giner
,
M.
Caffarel
, and
P. F.
Loos
, “
Selected configuration interaction dressed by perturbation
,”
J. Chem. Phys.
149
,
064103
(
2018
).
48.
P.-F.
Loos
,
M.
Boggio-Pasqua
,
A.
Scemama
,
M.
Caffarel
, and
D.
Jacquemin
, “
Reference energies for double excitations
,”
J. Chem. Theory Comput.
15
,
1939
1956
(
2019
).
49.
P.-F.
Loos
,
F.
Lipparini
,
M.
Boggio-Pasqua
,
A.
Scemama
, and
D.
Jacquemin
, “
A mountaineering strategy to excited states: Highly accurate energies and benchmarks for medium sized molecules
,”
J. Chem. Theory Comput.
16
,
1711
1741
(
2020
).
50.
C. W.
Bauschlicher
and
S. R.
Langhoff
, “
Full configuration-interaction study of the ionic-neutral curve crossing in LiF
,”
J. Chem. Phys.
89
,
4246
4254
(
1988
).
51.
M. M.
Khusniyarov
,
T.
Weyhermüller
,
E.
Bill
, and
K.
Wieghardt
, “
Tuning the oxidation level, the spin state, and the degree of electron delocalization in homo- and heteroleptic bis(α-diimine)iron complexes
,”
J. Am. Chem. Soc.
131
,
1208
1221
(
2008
).
52.
H. R.
Leverentz
,
K. A.
Maerzke
,
S. J.
Keasler
,
J. I.
Siepmann
, and
D. G.
Truhlar
, “
Electrostatically embedded many-body method for dipole moments, partial atomic charges, and charge transfer
,”
Phys. Chem. Chem. Phys.
14
,
7669
7678
(
2012
).
53.
N. S.
Blunt
,
G. H.
Booth
, and
A.
Alavi
, “
Density matrices in full configuration interaction quantum Monte Carlo: Excited states, transition dipole moments, and parallel distribution
,”
J. Chem. Phys.
146
,
244105
(
2017
).
54.
B. O.
Roos
,
P.
Linse
,
P. E. M.
Siegbahn
, and
M. R. A.
Blomberg
, “
A simple method for the evaluation of the second-order-perturbation energy from external double-excitations with a CASSCF reference wavefunction
,”
Chem. Phys.
66
,
197
207
(
1982
).
55.
K.
Andersson
,
P.-Å.
Malmqvist
,
B. O.
Roos
,
A. J.
Sadlej
, and
K.
Wolinski
, “
Second-order perturbation theory with a CASSCF reference function
,”
J. Phys. Chem.
94
,
5483
5488
(
1990
).
56.
K.
Andersson
,
P.-Å.
Malmqvist
, and
B. O.
Roos
, “
Second-order perturbation theory with a complete active space self-consistent field reference function
,”
J. Chem. Phys.
96
,
1218
1226
(
1992
).
57.
K.
Andersson
and
B. O.
Roos
, “
Multiconfigurational second-order perturbation theory: A test of geometries and binding energies
,”
Int. J. Quantum Chem.
45
,
591
607
(
1993
).
58.
N.
Forsberg
and
P.-Å.
Malmqvist
, “
Multiconfiguration perturbation theory with imaginary level shift
,”
Chem. Phys. Lett.
274
,
196
204
(
1997
).
59.
J.
Finley
,
P.-Å.
Malmqvist
,
B. O.
Roos
, and
L.
Serrano-Andrés
, “
The multi-state CASPT2 method
,”
Chem. Phys. Lett.
288
,
299
306
(
1998
).
60.
K.
Pierloot
, “
The CASPT2 method in inorganic electronic spectroscopy: From ionic transition metal to covalent actinide complexes∗
,”
Mol. Phys.
101
,
2083
2094
(
2003
).
61.
G.
Ghigo
,
B. O.
Roos
, and
P.-Å.
Malmqvist
, “
A modified definition of the zeroth-order Hamiltonian in multiconfigurational perturbation theory (CASPT2)
,”
Chem. Rev. Lett.
396
,
142
149
(
2004
).
62.
K.
Pierloot
and
S.
Vancoillie
, “
Relative energy of the high-(5T2g) and low-(1A1g) spin states of [Fe(H2O)6]2+, [Fe(NH3)6]2+, and [Fe(bpy)3]2+: CASPT2 versus density functional theory
,”
J. Chem. Phys.
125
,
124303
(
2006
).
63.
K.
Pierloot
and
S.
Vancoillie
, “
Relative energy of the high-(5T2g) and low-(1A1g) spin states of the ferrous complexes [Fe(L)(NHS4)]: CASPT2 versus density functional theory
,”
J. Chem. Phys.
128
,
034104
(
2008
).
64.
P.-Å.
Malmqvist
,
K.
Pierloot
,
A. R. M.
Shahi
,
C. J.
Cramer
, and
L.
Gagliardi
, “
The restricted active space followed by second-order perturbation theory method: Theory and application to the study of CuO2 and Cu2O2 systems
,”
J. Chem. Phys.
128
,
204109
(
2008
).
65.
S.
Vancoillie
,
H.
Zhao
,
M.
Radoń
, and
K.
Pierloot
, “
Performance of CASPT2 and DFT for relative spin-state energetics of heme models
,”
J. Chem. Theory Comput.
6
,
576
582
(
2010
).
66.
P.
Paulay
, “
A perspective on the CASPT2 method
,”
Int. J. Quantum Chem.
111
,
3273
3279
(
2011
).
67.
S.
Guo
,
M. A.
Watson
,
W.
Hu
,
Q.
Sun
, and
G. K.-L.
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
,
1583
1591
(
2016
).
68.
K.
Pierloot
,
Q. M.
Phung
, and
A.
Domingo
, “
Spin state energetics in first-row transition metal complexes: Contribution of (3s3p) correlation and its description by second- order perturbation theory
,”
J. Chem. Theory Comput.
13
,
537
553
(
2017
).
69.
S.
Guo
,
Z.
Li
, and
G. K.-L.
Chan
, “
A perturbative density matrix renormalization group algorithm for large active spaces
,”
J. Chem. Theory Comput.
14
,
4063
4071
(
2018
).
70.
N. M.
Tubman
,
C. D.
Freeman
,
D. S.
Levine
,
D.
Hait
,
M.
Head-Gordon
, and
K. B.
Whaley
, “
Modern approaches to exact diagonalization and selected configuration interaction with the adaptive sampling CI method
,”
J. Chem. Theory Comput.
16
,
2139
2159
(
2020
).
71.
J. W.
Park
, “
Second-order orbital optimization with large active spaces using adaptive sampling configuration interaction (ASCI) and its application to molecular geometry optimization
,”
J. Chem. Theory Comput.
17
,
1522
1534
(
2021
).
72.
C.
Angeli
,
R.
Cimiraglia
,
S.
Evangelisti
,
T.
Leininger
, and
J.-P.
Malrieu
, “
Introduction of n-electron valence states for multireference perturbation theory
,”
J. Chem. Phys.
114
,
10252
(
2001
).
73.
C.
Angeli
,
R.
Cimiraglia
, and
J.-P.
Malrieu
, “
N-electron valence state perturbation theory: A fast implementation of the strongly contracted variant
,”
Chem. Phys. Lett.
350
,
297
305
(
2001
).
74.
C.
Angeli
,
R.
Cimiraglia
, and
J.-P.
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
,
9138
9153
(
2002
).
75.
C.
Angeli
,
S.
Borini
,
M.
Cestari
, and
R.
Cimiraglia
, “
A quasidegenerate formulation of the second order n-electron valence state perturbation theory approach
,”
J. Chem. Phys.
121
,
4043
4049
(
2004
).
76.
C.
Angeli
,
S.
Borini
,
A.
Cavallini
,
M.
Cestari
,
R.
Cimiraglia
,
L.
Ferrighi
, and
M.
Sparta
, “
Developments in the n-electron valence state perturbation theory
,”
Int. J. Quantum Chem.
106
,
686
691
(
2006
).
77.
C.
Angeli
,
B.
Bories
,
A.
Cavallini
, and
R.
Cimiraglia
, “
Third-order multireference perturbation theory: The n-electron valence state perturbation-theory approach
,”
J. Chem. Phys.
124
,
054108
(
2006
).
78.
C.
Angeli
,
M.
Pastore
, and
R.
Cimiraglia
, “
New perspectives in multireference perturbation theory: The n-electron valence state approach
,”
Theor. Chem. Acc.
117
,
743
754
(
2007
).
79.
N. J.
Mayhall
and
M.
Head-Gordon
, “
Increasing spin-flips and decreasing cost: Perturbative corrections for external singles to the complete active space spin flip model for low-lying excited states and strong correlation
,”
J. Chem. Phys.
141
,
044112
(
2014
).
80.
G.
Li Manni
and
A.
Alavi
, “
Understanding the mechanism stabilizing intermediate spin states in Fe(II)-porphyrin
,”
J. Phys. Chem. A
122
,
4935
4947
(
2018
).
81.
G.
Li Manni
,
D.
Kats
,
D. P.
Tew
, and
A.
Alavi
, “
Role of valence and semicore electron correlation on spin gaps in Fe(II)-porphyrins
,”
J. Chem. Theory Comput.
15
,
1492
(
2019
).
82.
H.
Stoll
and
H.
Preuß
, “
On the direct calculation of localized HF orbitals in molecule clusters, layers and solids
,”
Theor. Chim. Acta
46
,
11
21
(
1977
).
83.
H.
Stoll
, “
The correlation energy of crystalline silicon
,”
Chem. Phys. Lett.
191
,
548
552
(
1992
).
84.
H.
Stoll
, “
Correlation energy of diamond
,”
Phys. Rev. B
46
,
6700
6704
(
1992
).
85.
K.
Rościszewski
,
B.
Paulus
,
P.
Fulde
, and
H.
Stoll
, “
Ab initio calculation of ground-state properties of rare-gas crystals
,”
Phys. Rev. B
60
,
7905
7910
(
1999
).
86.
B.
Paulus
,
K.
Rosciszewski
,
N.
Gaston
,
P.
Schwerdtfeger
, and
H.
Stoll
, “
Convergence of the ab initio many-body expansion for the cohesive energy of solid mercury
,”
Phys. Rev. B
70
,
165106
(
2004
).
87.
L.
Bytautas
and
K.
Ruedenberg
, “
The range of electron correlation between localized molecular orbitals. A full configuration interaction analysis for the NCCN molecule
,”
J. Phys. Chem. A
114
,
8601
8612
(
2010
).
88.
D.
Koch
,
E.
Fertitta
, and
B.
Paulus
, “
Calculation of the static and dynamical correlation energy of pseudo-one-dimensional beryllium systems via a many-body expansion
,”
J. Chem. Phys.
145
,
024104
(
2016
).
89.
J. S.
Boschen
,
D.
Theis
,
K.
Ruedenberg
, and
T. L.
Windus
, “
Correlation energy extrapolation by many-body expansion
,”
J. Phys. Chem. A
121
,
836
844
(
2017
).
90.
P. M.
Zimmerman
, “
Incremental full configuration interaction
,”
J. Chem. Phys.
146
,
104102
(
2017
).
91.
P. M.
Zimmerman
, “
Strong correlation in incremental full configuration interaction
,”
J. Chem. Phys.
146
,
224104
(
2017
).
92.
P. M.
Zimmerman
, “
Singlet-triplet gaps through incremental full configuration interaction
,”
J. Phys. Chem. A
121
,
4712
4720
(
2017
).
93.
J. J.
Eriksen
,
F.
Lipparini
, and
J.
Gauss
, “
Virtual orbital many-body expansions: A possible route towards the full configuration interaction limit
,”
J. Phys. Chem. Lett.
8
,
4633
4639
(
2017
).
94.
J. J.
Eriksen
and
J.
Gauss
, “
Many-body expanded full configuration interaction. I. Weakly correlated regime
,”
J. Chem. Theory Comput.
14
,
5180
5191
(
2018
).
95.
J. J.
Eriksen
and
J.
Gauss
, “
Many-body expanded full configuration interaction. II. Strongly correlated regime
,”
J. Chem. Theory Comput.
15
,
4873
4884
(
2019
).
96.
J. J.
Eriksen
and
J.
Gauss
, “
Generalized many-body expanded full configuration interaction theory
,”
J. Phys. Chem. Lett.
10
,
7910
7915
(
2019
).
97.
J. J.
Eriksen
and
J.
Gauss
, “
Ground and excited state first-order properties in many-body expanded full configuration interaction theory
,”
J. Chem. Phys.
153
,
154107
(
2020
).
98.
J. J.
Eriksen
,
T. A.
Anderson
,
J. E.
Deustua
,
K.
Ghanem
,
D.
Hait
,
M. R.
Hoffmann
,
S.
Lee
,
D. S.
Levine
,
I.
Magoulas
,
J.
Shen
,
N. M.
Tubman
,
K. B.
Whaley
,
E.
Xu
,
Y.
Yao
,
N.
Zhang
,
A.
Alavi
,
G. K.-L.
Chan
,
M.
Head-Gordon
,
W.
Liu
,
P.
Piecuch
,
S.
Sharma
,
S. L.
Ten-no
,
C. J.
Umrigar
, and
J.
Gauss
, “
The ground state electronic energy of benzene
,”
J. Phys. Chem. Lett.
11
,
8922
8929
(
2020
).
99.
J. J.
Eriksen
and
J.
Gauss
, “
Incremental treatments of the full configuration interaction problem
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
11
,
e1525
(
2021
).
100.
J. J.
Eriksen
, “
The shape of full configuration interaction to come
,”
J. Phys. Chem. Lett.
12
,
418
432
(
2021
).
101.
L.
González
,
D.
Escudero
, and
L.
Serrano-Andrés
, “
Progress and challenges in the calculation of electronic excited states
,”
ChemPhysChem
13
,
28
51
(
2012
).
102.
Q. M.
Phung
,
M.
Feldt
,
J. N.
Harvey
, and
K.
Pierloot
, “
Toward highly accurate spin state energetics in first-row transition metal complexes: A combined CASPT2/CC approach
,”
J. Chem. Theory Comput.
14
,
2446
2455
(
2018
).
103.
Q. M.
Phung
,
C.
Martín-Fernández
,
J. N.
Harvey
, and
M.
Feldt
, “
Ab initio calculations for spin-gaps of non-heme iron complexes
,”
J. Chem. Theory Comput.
15
,
4297
4304
(
2019
).
104.
M.
Feldt
,
Q. M.
Phung
,
K.
Pierloot
,
R. A.
Mata
, and
J. N.
Harvey
, “
Limits of coupled-cluster calculations for non-heme iron complexes
,”
J. Chem. Theory Comput.
15
,
922
937
(
2019
).
105.
P. M.
Zimmerman
,
A. R.
Molina
, and
P.
Smereka
, “
Orbitals with intermediate localization and low coupling: Spanning the gap between canonical and localized orbitals
,”
J. Chem. Phys.
143
,
014106
(
2015
).
106.
J.
Gerratt
,
D. L.
Cooper
,
P. B.
Karadakov
, and
M.
Raimondi
, “
Modern valence bond theory
,”
Chem. Soc. Rev.
26
,
87
100
(
1997
).
107.
J.
Cullen
, “
Generalized valence bond solutions from a constrained coupled cluster method
,”
Chem. Phys.
202
,
217
229
(
1996
).
108.
T.
Van Voorhis
and
M.
Head-Gordon
, “
Two-body coupled cluster expansions
,”
J. Chem. Phys.
115
,
5033
5040
(
2001
).
109.
G. J. O.
Beran
,
B.
Austin
,
A.
Sodt
, and
M.
Head-Gordon
, “
Unrestricted perfect pairing: The simplest wave-function-based model chemistry beyond mean field
,”
J. Phys. Chem. A
109
,
9183
9192
(
2005
).
110.
K. V.
Lawler
,
D. W.
Small
, and
M.
Head-Gordon
, “
Orbitals that are unrestricted in active pairs for generalized valence bond coupled cluster
,”
J. Phys. Chem. A
114
,
2930
2938
(
2010
).
111.
D. W.
Small
and
M.
Head-Gordon
, “
A fusion of the closed-shell coupled cluster singles and doubles method and valence- bond theory for bond breaking
,”
J. Chem. Phys.
137
,
114103
(
2012
).
112.
S.
Saebo
and
P.
Pulay
, “
Local treatment of electron correlation
,”
Annu. Rev. Phys. Chem.
44
,
213
236
(
1993
).
113.
Q.
Ma
,
M.
Schwilk
,
C.
Köppl
, and
H.-J.
Werner
, “
Scalable electron correlation methods. IV. Parallel explicitly correlated local coupled cluster with pair natural orbitals (PNO-LCCSD-F12)
,”
J. Chem. Theory Comput.
13
,
4871
4896
(
2017
).
114.
M. C.
Clement
,
J.
Zhang
,
C. A.
Lewis
,
C.
Yang
, and
E. F.
Valeev
, “
Optimized pair natural orbitals for the coupled cluster methods
,”
J. Chem. Theory Comput.
14
,
4581
4589
(
2018
).
115.
F.
Menezes
,
D.
Kats
, and
H.-J.
Werner
, “
Local complete active space second-order perturbation theory using pair natural orbitals (PNO-CASPT2)
,”
J. Chem. Phys.
145
,
124115
(
2016
).
116.
D.
Kats
and
H.-J.
Werner
, “
Multi-state local complete active space second-order perturbation theory using pair natural orbitals (PNO-MS-CASPT2)
,”
J. Chem. Phys.
150
,
214107
(
2019
).
117.
M.
Saitow
and
T.
Yanai
, “
A multireference coupled-electron pair approximation combined with complete-active space perturbation theory in local pair-natural orbital framework
,”
J. Chem. Phys.
152
,
114111
(
2020
).
118.
F.
Neese
,
A.
Hansen
, and
D. G.
Liakos
, “
Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis
,”
J. Chem. Phys.
131
,
064103
(
2009
).
119.
J.
Pipek
and
P. G.
Mezey
, “
A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions
,”
J. Chem. Phys.
90
,
4916
4926
(
1989
).
120.
F. W.
Bobrowicz
and
W. A.
Goddard
,
Methods of Electronic Structure Theory
(
Plenum
,
New York
,
1977
), p.
79
.
121.
E.
Epifanovsky
,
A. T. B.
Gilbert
,
X.
Feng
,
J.
Lee
,
Y.
Mao
,
N.
Mardirossian
,
P.
Pokhilko
,
A. F.
White
,
M. P.
Coons
,
A. L.
Dempwolff
,
Z.
Gan
,
D.
Hait
,
P. R.
Horn
,
L. D.
Jacobson
,
I.
Kaliman
,
J.
Kussmann
,
A. W.
Lange
,
K. U.
Lao
,
D. S.
Levine
,
J.
Liu
,
S. C.
McKenzie
,
A. F.
Morrison
,
K. D.
Nanda
,
F.
Plasser
,
D. R.
Rehn
,
M. L.
Vidal
,
Z.-Q.
You
,
Y.
Zhu
,
B.
Alam
,
B. J.
Albrecht
,
A.
Aldossary
,
E.
Alguire
,
J. H.
Andersen
,
V.
Athavale
,
D.
Barton
,
K.
Begam
,
A.
Behn
,
N.
Bellonzi
,
Y. A.
Bernard
,
E. J.
Berquist
,
H. G. A.
Burton
,
A.
Carreras
,
K.
Carter-Fenk
,
R.
Chakraborty
,
A. D.
Chien
,
K. D.
Closser
,
V.
Cofer-Shabica
,
S.
Dasgupta
,
M.
De Wergifosse
,
J.
Deng
,
M.
Diedenhofen
,
H.
Do
,
S.
Ehlert
,
P.-T.
Fang
,
S.
Fatehi
,
Q.
Feng
,
T.
Friedhoff
,
J.
Gayvert
,
Q.
Ge
,
G.
Gidofalvi
,
M.
Goldey
,
J.
Gomes
,
C. E.
González-Espinoza
,
S.
Gulania
,
A. O.
Gunina
,
M. W. D.
Hanson-Heine
,
P. H. P.
Harbach
,
A.
Hauser
,
M. F.
Herbst
,
M.
Hernández Vera
,
M.
Hodecker
,
Z. C.
Holden
,
S.
Houck
,
X.
Huang
,
K.
Hui
,
B. C.
Huynh
,
M.
Ivanov
,
Á.
Jász
,
H.
Ji
,
H.
Jiang
,
B.
Kaduk
,
S.
Kähler
,
K.
Khistyaev
,
J.
Kim
,
G.
Kis
,
P.
Klunzinger
,
Z.
Koczor-Benda
,
J. H.
Koh
,
D.
Kosenkov
,
L.
Koulias
,
T.
Kowalczyk
,
C. M.
Krauter
,
K.
Kue
,
A.
Kunitsa
,
T.
Kus
,
I.
Ladjánszki
,
A.
Landau
,
K. V.
Lawler
,
D.
Lefrancois
,
S.
Lehtola
,
R. R.
Li
,
Y.-P.
Li
,
J.
Liang
,
M.
Liebenthal
,
H.-H.
Lin
,
Y.-S.
Lin
,
F.
Liu
,
K.-Y.
Liu
,
M.
Loipersberger
,
A.
Luenser
,
A.
Manjanath
,
P.
Manohar
,
E.
Mansoor
,
S. F.
Manzer
,
S.-P.
Mao
,
A. V.
Marenich
,
T.
Markovich
,
S.
Mason
,
S. A.
Maurer
,
P. F.
McLaughlin
,
M. F. S. J.
Menger
,
J.-M.
Mewes
,
S. A.
Mewes
,
P.
Morgante
,
J. W.
Mullinax
,
K. J.
Oosterbaan
,
G.
Paran
,
A. C.
Paul
,
S. K.
Paul
,
F.
Pavošević
,
Z.
Pei
,
S.
Prager
,
E. I.
Proynov
,
Á.
Rák
,
E.
Ramos-Cordoba
,
B.
Rana
,
A. E.
Rask
,
A.
Rettig
,
R. M.
Richard
,
F.
Rob
,
E.
Rossomme
,
T.
Scheele
,
M.
Scheurer
,
M.
Schneider
,
N.
Sergueev
,
S. M.
Sharada
,
W.
Skomorowski
,
D. W.
Small
,
C. J.
Stein
,
Y.-C.
Su
,
E. J.
Sundstrom
,
Z.
Tao
,
J.
Thirman
,
G. J.
Tornai
,
T.
Tsuchimochi
,
N. M.
Tubman
,
S. P.
Veccham
,
O.
Vydrov
,
J.
Wenzel
,
J.
Witte
,
A.
Yamada
,
K.
Yao
,
S.
Yeganeh
,
S. R.
Yost
,
A.
Zech
,
I. Y.
Zhang
,
X.
Zhang
,
Y.
Zhang
,
D.
Zuev
,
A.
Aspuru-Guzik
,
A. T.
Bell
,
N. A.
Besley
,
K. B.
Bravaya
,
B. R.
Brooks
,
D.
Casanova
,
J.-D.
Chai
,
S.
Coriani
,
C. J.
Cramer
,
G.
Cserey
,
A. E.
Deprince
,
R. A.
Distasio
,
A.
Dreuw
,
B. D.
Dunietz
,
T. R.
Furlani
,
W. A.
Goddard
,
S.
Hammes-Schiffer
,
T.
Head-Gordon
,
W. J.
Hehre
,
C.-P.
Hsu
,
T.-C.
Jagau
,
Y.
Jung
,
A.
Klamt
,
J.
Kong
,
D. S.
Lambrecht
,
W.
Liang
,
N. J.
Mayhall
,
C. W.
McCurdy
,
J. B.
Neaton
,
C.
Ochsenfeld
,
J. A.
Parkhill
,
R.
Peverati
,
V. A.
Rassolov
,
Y.
Shao
,
L. V.
Slipchenko
,
T.
Stauch
,
R. P.
Steele
,
J. E.
Subotnik
,
A. J. W.
Thom
,
A.
Tkatchenko
,
D. G.
Truhlar
,
T.
Van Voorhis
,
T. A.
Wesolowski
,
K. B.
Whaley
,
H. L.
Woodcock
,
P. M.
Zimmerman
,
S.
Faraji
,
P. M. W.
Gill
,
M.
Head-Gordon
,
J. M.
Herbert
, and
A. I.
Krylov
, “
Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package
,”
J. Chem. Phys.
155
,
084801
(
2021
).
122.
P. M.
Zimmerman
and
A. E.
Rask
, “
Evaluation of full valence correlation energies and gradients
,”
J. Chem. Phys.
150
,
244117
(
2019
).
123.
D.-K.
Dang
and
P. M.
Zimmerman
, “
Fully variational incremental CASSCF
,”
J. Chem. Phys.
154
,
014105
(
2021
).
124.
P. C.
Hariharan
and
J. A.
Pople
, “
The influence of polarization functions on molecular orbital hydrogenation energies
,”
Theor. Chim. Acta
28
,
213
222
(
1973
).
125.
M.
Feyereisen
,
G.
Fitzgerald
, and
A.
Komornicki
, “
Use of approximate integrals in ab initio theory. An application in MP2 energy calculations
,”
Chem. Phys. Lett.
208
,
359
363
(
1993
).
126.
F.
Weigend
,
M.
Häser
,
H.
Patzelt
, and
R.
Ahlrichs
, “
RI-MP2: Optimized auxiliary basis sets and demonstration of efficiency
,”
Chem. Phys. Lett.
294
,
143
152
(
1998
).
127.
J. R.
Sams
and
T. B.
Tsin
, “
Electronic ground state of iron in octamethyltetrabenzporphyriniron(II), a new square planar ferrous porphyrin
,”
Chem. Phys. Lett.
25
,
599
601
(
1974
).
128.
J.
Oláh
and
J. N.
Harvey
, “
No bonding to heme groups: DFT and correlated ab initio calculations
,”
J. Phys. Chem. A
113
,
7338
7345
(
2009
).
129.
M.
Radoń
, “
Spin-state energetics of heme-related models from DFT and coupled cluster calculations
,”
J. Chem. Theory Comput.
10
,
2306
2321
(
2014
).
130.
A.
Antalík
,
D.
Nachtigallová
,
R.
Lo
,
M.
Matoušek
,
J.
Lang
,
Ö.
Legeza
,
J.
Pittner
,
P.
Hobza
, and
L.
Veis
, “
Ground state of the Fe(II)-porphyrin model system corresponds to quintet: A DFT and DMRG-based tailored CC study
,”
Phys. Chem. Chem. Phys.
22
,
17033
17037
(
2020
).
131.
P.
Golub
,
A.
Antalik
,
L.
Veis
, and
J.
Brabec
, “
Machine learning-assisted selection of active spaces for strongly correlated transition metal systems
,”
J. Chem. Theory Comput.
17
,
6053
6072
(
2021
).
132.
P.
Beran
,
M.
Matoušek
,
M.
Hapka
,
K.
Pernal
, and
L.
Veis
, “
Density matrix renormalization group with dynamical correlation via adiabatic connection
,”
J. Chem. Theory Comput.
17
,
7575
7585
(
2021
).

Supplementary Material

You do not currently have access to this content.