In this paper, we study the nuclear gradients of heat bath configuration interaction self-consistent field (HCISCF) wave functions and use them to optimize molecular geometries for various molecules. We show that HCISCF nuclear gradients are fairly insensitive to the size of the “selected” variational space, which allows us to reduce the computational cost without introducing significant errors. The ability of the HCISCF to treat larger active spaces combined with the flexibility for users to control the computational cost makes the method very attractive for studying strongly correlated systems, which require a larger active space than possible with a complete active space self-consistent field. Finally, we study the realistic catalyst, Fe(PDI), and highlight some of the challenges this system poses for density functional theory (DFT). We demonstrate how HCISCF can clarify the energetic stability of geometries obtained from DFT when the results are strongly dependent on the functional. We also use the HCISCF gradients to optimize geometries for this species and study the adiabatic singlet–triplet gap. During geometry optimization, we find that multiple near-degenerate local minima exist on the triplet potential energy surface.
REFERENCES
1.
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
, 157
(1980
).2.
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
).3.
P. Å.
Malmqvist
, A.
Rendell
, and B. O.
Roos
, “The restricted active space self-consistent-field method, implemented with a split graph unitary group approach
,” J. Phys. Chem.
94
, 5477
–5482
(1990
).4.
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
); arXiv:1707.04346.5.
P.
Celani
and H.-J.
Werner
, “Multireference perturbation theory for large restricted and selected active space reference wave functions
,” J. Chem. Phys.
112
, 5546
–5557
(2000
).6.
T.
Fleig
, J.
Olsen
, and C. 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
, 4775
–4790
(2001
).7.
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
).8.
S. R.
White
, “Density matrix formulation for quantum renormalization groups
,” Phys. Rev. Lett.
69
, 2863
–2866
(1992
).9.
S. R.
White
, “Density-matrix algorithms for quantum renormalization groups
,” Phys. Rev. B
48
, 10345
(1993
).10.
G.
Fano
, F.
Ortolani
, and L.
Ziosi
, “The density matrix renormalization group method. Application to the PPP model of a cyclic polyene chain
,” J. Chem. Phys.
108
, 9246
–9252
(1998
); arXiv:9803071 [cond-mat].11.
S. R.
White
and R. L.
Martin
, “Ab initio quantum chemistry using the density matrix renormalization group
,” J. Chem. Phys.
110
, 4127
(1999
).12.
U.
Schollwöck
, “The density-matrix renormalization group
,” Rev. Mod. Phys.
77
, 259
–315
(2005
); arXiv:0409292 [cond-mat].13.
S.
Szalay
, M.
Pfeffer
, V.
Murg
, G.
Barcza
, F.
Verstraete
, R.
Schneider
, and Ö.
Legeza
, “Tensor product methods and entanglement optimization for ab initio quantum chemistry
,” Int. J. Quantum Chem.
115
, 1342
–1391
(2015
); arXiv:1412.5829.14.
U.
Schollwöck
, “The density-matrix renormalization group in the age of matrix product states
,” Ann. Phys.
326
, 96
–192
(2011
); arXiv:1008.3477.15.
S.
Daul
, I.
Ciofini
, C.
Daul
, and S. R.
White
, “Quantum chemistry using the density matrix renormalization group
,” J. Chem. Phys.
115
, 6815
–6821
(2001
).16.
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
).17.
G.
Moritz
and M.
Reiher
, “Construction of environment states in quantum-chemical density-matrix renormalization group calculations
,” J. Chem. Phys.
124
, 034103
(2006
).18.
D.
Zgid
and M.
Nooijen
, “Obtaining the two-body density matrix in the density matrix renormalization group method
,” J. Chem. Phys.
128
, 144115
(2008
).19.
H. G.
Luo
, M. P.
Qin
, and T.
Xiang
, “Optimizing Hartree-Fock orbitals by the density-matrix renormalization group
,” Phys. Rev. B
81
, 235129
(2010
); arXiv:1002.1287.20.
K. H.
Marti
and M.
Reiher
, “The density matrix renormalization group algorithm in quantum chemistry
,” Z. Phys. Chem.
224
, 583
–599
(2010
).21.
G. K.-L.
Chan
and S.
Sharma
, “The density matrix renormalization group in quantum chemistry
,” Annu. Rev. Phys. Chem.
62
, 465
–481
(2011
).22.
Y.
Kurashige
and T.
Yanai
, “Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: Theory and application to the study of chromium dimer
,” J. Chem. Phys.
135
, 094104
(2011
).23.
S.
Sharma
and G. K.-L.
Chan
, “Spin-adapted density matrix renormalization group algorithms for quantum chemistry
,” J. Chem. Phys.
136
, 124121
(2012
).24.
S.
Sharma
, K.
Sivalingam
, F.
Neese
, and G. K.-L.
Chan
, “Low-energy spectrum of iron–sulfur clusters directly from many-particle quantum mechanics
,” Nat. Chem.
6
, 927
(2014
); arXiv:1408.5080.25.
Y.
Kurashige
, G. K.-L.
Chan
, and T.
Yanai
, “Entangled quantum electronic wavefunctions of the Mn4CaO5 cluster in photosystem II
,” Nat. Chem.
5
, 660
(2013
).26.
S.
Wouters
, T.
Bogaerts
, P.
Van Der Voort
, V.
Van Speybroeck
, and D.
Van Neck
, “Communication: DMRG-SCF study of the singlet, triplet, and quintet states of oxo-Mn(Salen)
,” J. Chem. Phys.
140
, 241103
(2014
).27.
S.
Keller
and M.
Reiher
, “Spin-adapted matrix product states and operators
,” J. Chem. Phys.
144
, 134101
(2016
).28.
Y.
Kurashige
, “Multireference electron correlation methods with density matrix renormalization group reference functions
,” Mol. Phys.
112
, 1485
–1494
(2014
).29.
T.
Yanai
, Y.
Kurashige
, W.
Mizukami
, J.
Chalupský
, T. N.
Lan
, and M.
Saitow
, “Density matrix renormalization group for ab initio calculations and associated dynamic correlation methods: A review of theory and applications
,” Int. J. Quantum Chem.
115
, 283
–299
(2015
).30.
J.
Ivanic
and K.
Ruedenberg
, “Identification of deadwood in configuration spaces through general direct configuration interaction
,” Theor. Chem. Acc.
106
, 339
–351
(2001
).31.
B.
Huron
, J. P.
Malrieu
, and P.
Rancurel
, “Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth-order wavefunctions
,” J. Chem. Phys.
58
, 5745
–5759
(1973
).32.
R. J.
Buenker
and S. D.
Peyerimhoff
, “Individualized configuration selection in CI calculations with subsequent energy extrapolation
,” Theor. Chim. Acta
35
, 33
–58
(1974
).33.
F. A.
Evangelista
, J. P.
Daudey
, and J. P.
Malrieu
, “Convergence of an improved CIPSI algorithm
,” Chem. Phys.
75
, 91
–102
(1983
).34.
R. J.
Harrison
, “Approximating full configuration interaction with selected configuration interaction and perturbation theory
,” J. Chem. Phys.
94
, 5021
–5031
(1991
).35.
M. M.
Steiner
, W.
Wenzel
, K. G.
Wilson
, and J. W.
Wilkins
, “The efficient treatment of higher excitations in CI calculations. A comparison of exact and approximate results
,” Chem. Phys. Lett.
231
, 263
–268
(1994
).36.
W.
Wenzel
, M. M.
Steiner
, and K. G.
Wilson
, “Multireference basis-set reduction
,” Int. J. Quantum Chem.
60
, 1325
–1330
(1996
).37.
F.
Neese
, “A spectroscopy oriented configuration interaction procedure
,” J. Chem. Phys.
119
, 9428
–9443
(2003
).38.
M. L.
Abrams
and C. D.
Sherrill
, “Important configurations in configuration interaction and coupled-cluster wave functions
,” Chem. Phys. Lett.
412
, 121
–124
(2005
).39.
L.
Bytautas
and K.
Ruedenberg
, “A priori identification of configurational deadwood
,” Chem. Phys.
356
, 64
–75
(2009
).40.
F. A.
Evangelista
, “A driven similarity renormalization group approach to quantum many-body problems
,” J. Chem. Phys.
141
, 054109
(2014
).41.
P. J.
Knowles
, “Compressive sampling in configuration interaction wavefunctions
,” Mol. Phys.
113
, 1655
–1660
(2015
).42.
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
); arXiv:1603.08063.43.
W.
Liu
and M. R.
Hoffmann
, “ICI: Iterative CI toward full CI
,” J. Chem. Theory Comput.
12
, 1169
–1178
(2016
).44.
M.
Caffarel
, T.
Applencourt
, E.
Giner
, and A.
Scemama
, “Using CIPSI nodes in diffusion Monte Carlo
,” ACS Symp. Ser.
1234
, 15
–46
(2016
); arXiv:1607.06742.45.
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
); arXiv:1603.02686.46.
Y.
Garniron
, A.
Scemama
, P.-F.
Loos
, and M.
Caffarel
, “Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory
,” J. Chem. Phys.
147
, 034101
(2017
).47.
N. M.
Tubman
, D. S.
Levine
, D.
Hait
, M.
Head-Gordon
, and K. B.
Whaley
, “An efficient deterministic perturbation theory for selected configuration interaction methods
,” arXiv:1808.02049 (2018
).48.
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
); arXiv:1807.00821.49.
D. S.
Levine
, D.
Hait
, N. M.
Tubman
, S.
Lehtola
, K. B.
Whaley
, and M.
Head-Gordon
, “CASSCF with extremely large active spaces using the adaptive sampling configuration interaction method
,” J. Chem. Theory Comput.
16
, 2340
–2354
(2020
); arXiv:1912.08379.50.
G. H.
Booth
, A. J. W.
Thom
, and A.
Alavi
, “Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in slater determinant space
,” J. Chem. Phys.
131
, 054106
(2009
).51.
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
).52.
F. R.
Petruzielo
, A. A.
Holmes
, H. J.
Changlani
, M. P.
Nightingale
, and C. J.
Umrigar
, “Semistochastic projector Monte Carlo method
,” Phys. Rev. Lett.
109
, 230201
(2012
); arXiv:1207.6138v2.53.
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
); arXiv:1510.03635.54.
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
).55.
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
); arXiv:1610.06660v2.56.
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
); arXiv:1708.07544.57.
B. F. E.
Curchod
and T. J.
Martínez
, “Ab initio nonadiabatic quantum molecular dynamics
,” Chem. Rev.
118
, 3305
–3336
(2018
).58.
R.
Guareschi
and C.
Filippi
, “Ground- and excited-state geometry optimization of small organic molecules with quantum Monte Carlo
,” J. Chem. Theory Comput.
9
, 5513
–5525
(2013
).59.
F.
Liu
, Y.
Kurashige
, T.
Yanai
, and K.
Morokuma
, “Multireference ab initio density matrix renormalization group (DMRG)-CASSCF and DMRG-CASPT2 study on the photochromic ring opening of spiropyran
,” J. Chem. Theory Comput.
9
, 4462
–4469
(2013
).60.
W.
Hu
and G. K.-L.
Chan
, “Excited-state geometry optimization with the density matrix renormalization group, as applied to polyenes
,” J. Chem. Theory Comput.
11
, 3000
–3009
(2015
); arXiv:1502.07731.61.
E.
Maradzike
, G.
Gidofalvi
, J. M.
Turney
, H. F.
Schaefer
, and A. E.
DePrince
, “Analytic energy gradients for variational two-electron reduced-density-matrix-driven complete active space self-consistent field theory
,” J. Chem. Theory Comput.
13
, 4113
–4122
(2017
).62.
Y.
Ma
, S.
Knecht
, and M.
Reiher
, “Multiconfigurational effects in theoretical resonance Raman spectra
,” ChemPhysChem
18
, 384
–393
(2017
).63.
A. W.
Schlimgen
and D. A.
Mazziotti
, “Analytical gradients of variational reduced-density-matrix and wavefunction-based methods from an overlap-reweighted semidefinite program
,” J. Chem. Phys.
149
, 164111
(2018
).64.
M.
Dash
, S.
Moroni
, A.
Scemama
, and C.
Filippi
, “Perturbatively selected configuration-interaction wave functions for efficient geometry optimization in quantum Monte Carlo
,” J. Chem. Theory Comput.
14
, 4176
–4182
(2018
); arXiv:1804.09610.65.
M.
Dash
, J.
Feldt
, S.
Moroni
, A.
Scemama
, and C.
Filippi
, “Excited states with selected configuration interaction-quantum Monte Carlo: Chemically accurate excitation energies and geometries
,” J. Chem. Theory Comput.
15
, 4896
–4906
(2019
).66.
L.
Freitag
, Y.
Ma
, A.
Baiardi
, S.
Knecht
, and M.
Reiher
, “Approximate analytical gradients and nonadiabatic couplings for the state-average density matrix renormalization group self-consistent-field method
,” J. Chem. Theory Comput.
15
, 6724
–6737
(2019
); arXiv:1905.01558.67.
J. W.
Park
, “Second-order orbital optimization with large active space using adaptive sampling configuration interaction (ASCI) and its application to molecular geometry optimization
,” J. Chem. Theory Comput.
17
, 1522
–1534
(2021
).68.
J. W.
Park
, “Near-exact CASSCF-level geometry optimization with a large active space using adaptive sampling configuration interaction self-consistent field corrected with second-order perturbation theory (ASCI-SCF-PT2)
,” J. Chem. Theory Comput.
17
, 4092
–4104
(2021
).69.
Q.
Sun
, “Libcint: An efficient general integral library for Gaussian basis functions
,” J. Comput. Chem.
36
, 1664
–1671
(2015
); arXiv:1412.0649.70.
Q.
Sun
, J.
Yang
, and G. K.-L.
Chan
, “A general second order complete active space self-consistent-field solver for large-scale systems
,” Chem. Phys. Lett.
683
, 291
–299
(2017
); arXiv:1610.08394.71.
Q.
Sun
, T. C.
Berkelbach
, N. S.
Blunt
, G. H.
Booth
, S.
Guo
, Z.
Li
, J.
Liu
, J. D.
McClain
, E. R.
Sayfutyarova
, S.
Sharma
, S.
Wouters
, and G. K. L.
Chan
, “PySCF: The python-based simulations of chemistry framework
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
, e1340
(2018
); arXiv:1701.08223.72.
Q.
Sun
, X.
Zhang
, S.
Banerjee
, P.
Bao
, M.
Barbry
, N. S.
Blunt
, N. A.
Bogdanov
, G. H.
Booth
, J.
Chen
, Z.-H.
Cui
, J. J.
Eriksen
, Y.
Gao
, S.
Guo
, J.
Hermann
, M. R.
Hermes
, K.
Koh
, P.
Koval
, S.
Lehtola
, Z.
Li
, J.
Liu
, N.
Mardirossian
, J. D.
McClain
, M.
Motta
, B.
Mussard
, H. Q.
Pham
, A.
Pulkin
, W.
Purwanto
, P. J.
Robinson
, E.
Ronca
, E. R.
Sayfutyarova
, M.
Scheurer
, H. F.
Schurkus
, J. E. T.
Smith
, C.
Sun
, S.-N.
Sun
, S.
Upadhyay
, L. K.
Wagner
, X.
Wang
, A.
White
, J. D.
Whitfield
, M. J.
Williamson
, S.
Wouters
, J.
Yang
, J. M.
Yu
, T.
Zhu
, T. C.
Berkelbach
, S.
Sharma
, A. Y.
Sokolov
, and G. K.-L.
Chan
, “Recent developments in the PySCF program package
,” J. Chem. Phys.
153
, 024109
(2020
); arXiv:2002.12531.73.
M. A.
Ortuño
and C. J.
Cramer
, “Multireference electronic structures of Fe-pyridine(diimine) complexes over multiple oxidation states
,” J. Phys. Chem. A
121
, 5932
–5939
(2017
).74.
S. C. E.
Stieber
, C.
Milsmann
, J. M.
Hoyt
, Z. R.
Turner
, K. D.
Finkelstein
, K.
Wieghardt
, S.
Debeer
, and P. J.
Chirik
, “Bis(imino)pyridine iron dinitrogen compounds revisited: Differences in electronic structure between four- and five-coordinate derivatives
,” Inorg. Chem.
51
, 3770
–3785
(2012
).75.
P. S.
Epstein
, “The Stark effect from the point of view of Schroedinger’s quantum theory
,” Phys. Rev.
28
, 695
–710
(1926
).76.
R. K.
Nesbet
, “Configuration interaction in orbital theories
,” Proc. R. Soc. London, Ser. A
230
, 312
–321
(1955
).77.
Y.
Garniron
, T.
Applencourt
, K.
Gasperich
, A.
Benali
, A.
Ferté
, J.
Paquier
, B.
Pradines
, R.
Assaraf
, P.
Reinhardt
, J.
Toulouse
, P.
Barbaresco
, N.
Renon
, G.
David
, J.-P.
Malrieu
, M.
Véril
, M.
Caffarel
, P.-F.
Loos
, E.
Giner
, and A.
Scemama
, “Quantum package 2.0: An open-source determinant-driven suite of programs
,” J. Chem. Theory Comput.
15
, 3591
–3609
(2019
); arXiv:1902.08154.78.
J.
Li
, M.
Otten
, A. A.
Holmes
, S.
Sharma
, and C. J.
Umrigar
, “Fast semistochastic heat-bath configuration interaction
,” J. Chem. Phys.
149
, 214110
(2018
); arXiv:1809.04600.79.
Y.
Yamaguchi
and H. F.
Schaefer
, “Analytic derivative methods in molecular electronic structure theory: A new dimension to quantum chemistry and its applications to spectroscopy
,” in Handbook of High-Resolution Spectroscopy
(John Wiley & Sons
, 2011
), pp. 325
–362
.80.
N. C.
Handy
and H. F.
Schaefer
, “On the evaluation of analytic energy derivatives for correlated wave functions
,” J. Chem. Phys.
81
, 5031
–5033
(1984
).81.
M. J.
Frisch
, G. W.
Trucks
, H. B.
Schlegel
, G. E.
Scuseria
, M. A.
Robb
, J. R.
Cheeseman
, G.
Scalmani
, V.
Barone
, G. A.
Petersson
, H.
Nakatsuji
, X.
Li
, M.
Caricato
, A. V.
Marenich
, J.
Bloino
, B. G.
Janesko
, R.
Gomperts
, B.
Mennucci
, H. P.
Hratchian
, J. V.
Ortiz
, A. F.
Izmaylov
, J. L.
Sonnenberg
, D.
Williams-Young
, F.
Ding
, F.
Lipparini
, F.
Egidi
, J.
Goings
, B.
Peng
, A.
Petrone
, T.
Henderson
, D.
Ranasinghe
, V. G.
Zakrzewski
, J.
Gao
, N.
Rega
, G.
Zheng
, W.
Liang
, M.
Hada
, M.
Ehara
, K.
Toyota
, R.
Fukuda
, J.
Hasegawa
, M.
Ishida
, T.
Nakajima
, Y.
Honda
, O.
Kitao
, H.
Nakai
, T.
Vreven
, K.
Throssell
, J. A. J.
Montgomery
, J. E.
Peralta
, F.
Ogliaro
, M. J.
Bearpark
, J. J.
Heyd
, E. N.
Brothers
, K. N.
Kudin
, V. N.
Staroverov
, T. A.
Keith
, R.
Kobayashi
, J.
Normand
, K.
Raghavachari
, A. P.
Rendell
, J. C.
Burant
, S. S.
Iyengar
, J.
Tomasi
, M.
Cossi
, J. M.
Millam
, M.
Klene
, C.
Adamo
, R.
Cammi
, J. W.
Ochterski
, R. L.
Martin
, K.
Morokuma
, O.
Farkas
, J. B.
Foresman
, and D. J.
Fox
, “Gaussian 16 Revision C.01 Release Notes,” 2016
.82.
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
).83.
L.-P.
Wang
and C.
Song
, “Geometry optimization made simple with translation and rotation coordinates
,” J. Chem. Phys.
144
, 214108
(2016
).84.
T. H.
Dunning
, “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
,” J. Chem. Phys.
90
, 1007
–1023
(1989
).85.
J. P.
Perdew
, M.
Ernzerhof
, and K.
Burke
, “Rationale for mixing exact exchange with density functional approximations
,” J. Chem. Phys.
105
, 9982
–9985
(1996
).86.
C.
Adamo
and V.
Barone
, “Toward reliable density functional methods without adjustable parameters: The PBE0 model
,” J. Chem. Phys.
110
, 6158
–6170
(1999
).87.
S.
Keller
, K.
Boguslawski
, T.
Janowski
, M.
Reiher
, and P.
Pulay
, “Selection of active spaces for multiconfigurational wavefunctions
,” J. Chem. Phys.
142
, 244104
(2015
).88.
J. M.
Bofill
and P.
Pulay
, “The unrestricted natural orbital-complete active space (UNO-CAS) method: An inexpensive alternative to the complete active space-self-consistent-field (CAS-SCF) method
,” J. Chem. Inf. Model.
90
, 3637
(1989
).89.
P.
Pulay
, “Convergence acceleration of iterative sequences. The case of SCF iteration
,” Chem. Phys. Lett.
73
, 393
–398
(1980
).90.
X.
Hu
and W.
Yang
, “Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function
,” J. Chem. Phys.
132
, 054109
(2010
).91.
W.
Kabsch
, “A discussion of the solution for the best rotation to relate two sets of vectors
,” Acta Crystallogr., Sect. A: Found. Crystallogr.
32
, 922
–923
(1976
).92.
J. C.
Kromann
, “RMSD,” 2020
.93.
A. W.
Schlimgen
and D. A.
Mazziotti
, “Static and dynamic electron correlation in the ligand noninnocent oxidation of nickel dithiolates
,” J. Phys. Chem. A
121
, 9377
–9384
(2017
).94.
D. A.
Kreplin
, P. J.
Knowles
, and H.-J.
Werner
, “Second-order MCSCF optimization revisited. I. Improved algorithms for fast and robust second-order CASSCF convergence
,” J. Chem. Phys.
150
, 194106
(2019
).95.
Y.
Yao
and C. J.
Umrigar
, “Orbital optimization in selected configuration interaction methods
,” J. Chem. Theory Comput.
17
, 4183
–4194
(2021
); arXiv:2104.02587.96.
Y.
Zhao
and D. G.
Truhlar
, “A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions
,” J. Chem. Phys.
125
, 194101
(2006
).97.
Y.
Zhao
and D. G.
Truhlar
, “The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: Two new functionals and systematic testing of four M06-class functionals and 12 other function
,” Theor. Chem. Acc.
120
, 215
–241
(2008
).98.
H. S.
Yu
, X.
He
, S. L.
Li
, and D. G.
Truhlar
, “MN15: A Kohn-Sham global-hybrid exchange-correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions
,” Chem. Sci.
7
, 5032
–5051
(2016
).99.
J. W.
Mullinax
, E.
Epifanovsky
, G.
Gidofalvi
, and A. E.
DePrince
, “Analytic energy gradients for variational two-electron reduced-density matrix methods within the density fitting approximation
,” J. Chem. Theory Comput.
15
, 276
–289
(2019
).100.
P. M.
Zimmerman
and A. E.
Rask
, “Evaluation of full valence correlation energies and gradients
,” J. Chem. Phys.
150
, 244117
(2019
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
