In large-scale quantum-chemical calculations, the electron-repulsion integral (ERI) tensor rapidly becomes the bottleneck in terms of memory and disk space. When an external finite magnetic field is employed, this problem becomes even more pronounced because of the reduced permutational symmetry and the need to work with complex integrals and wave function parameters. One way to alleviate the problem is to employ a Cholesky decomposition (CD) to the complex ERIs over gauge-including atomic orbitals. The CD scheme establishes favorable compression rates by selectively discarding linearly dependent product densities from the chosen basis set while maintaining a rigorous and robust error control. This error control constitutes the main advantage over conceptually similar methods such as density fitting, which relies on employing pre-defined auxiliary basis sets. We implemented the use of the CD in the framework of finite-field (ff) Hartree–Fock and ff second-order Møller–Plesset perturbation theory (MP2). Our work demonstrates that the CD compression rates are particularly beneficial in calculations in the presence of a finite magnetic field. The ff-CD-MP2 scheme enables the correlated treatment of systems with more than 2000 basis functions in strong magnetic fields within a reasonable time span.
REFERENCES
1.
M.
Häser
and R.
Ahlrichs
, “Improvements on the direct SCF method
,” J. Comput. Chem.
10
, 104
–111
(1989
).2.
D. S.
Lambrecht
and C.
Ochsenfeld
, “Multipole-based integral estimates for the rigorous description of distance dependence in two-electron integrals
,” J. Chem. Phys.
123
, 184101
(2005
).3.
D. S.
Lambrecht
and C.
Ochsenfeld
, “Erratum: `Multipole-based integral estimates for the rigorous description of distance dependence in two-electron integrals' [J. Chem. Phys. 123, 184101 (2005)]
,” J. Chem. Phys.
136
, 149901
(2012
).4.
V.
Dyczmons
, “No N4-dependence in the calculation of large molecules
,” Theor. Chim. Acta
28
, 307
–310
(1973
).5.
T.
Helgaker
, P.
Jørgensen
, and J.
Olsen
, Molecular Electronic-Structure Theory
(John Wiley & Sons Ltd.
, Chichester, England
, 2013
).6.
L.
Greengard
and V.
Rokhlin
, “A fast algorithm for particle simulations
,” J. Comput. Phys.
73
, 325
–348
(1987
).7.
C. A.
White
, B. G.
Johnson
, P. M. W.
Gill
, and M.
Head-Gordon
, “The continuous fast multipole method
,” Chem. Phys. Lett.
230
, 8
–16
(1994
).8.
F.
Neese
, “Some thoughts on the scope of linear scaling self-consistent field electronic structure methods
,” in Linear-Scaling Techniques in Computational Chemistry and Physics
, edited by R.
Zaleśny
, M. G.
Papadopoulos
, P. G.
Mezey
, and J.
Leszczynski
(Springer
, The Netherlands
, 2011
), Chap. 11, pp. 227
–261
.9.
J. L.
Whitten
, “Coulombic potential energy integrals and approximations
,” J. Chem. Phys.
58
, 4496
–4501
(1973
).10.
O.
Vahtras
, J.
Almlöf
, and M. W.
Feyereisen
, “Integral approximations for LCAO-SCF calculations
,” Chem. Phys. Lett.
213
, 514
–518
(1993
).11.
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
).12.
F.
Aquilante
and T. B.
Pedersen
, “Quartic scaling evaluation of canonical scaled opposite spin second-order Møller–Plesset correlation energy using Cholesky decompositions
,” Chem. Phys. Lett.
449
, 354
–357
(2007
).13.
S.
Reine
, E.
Tellgren
, A.
Krapp
, T.
Kjærgaard
, T.
Helgaker
, B.
Jansik
, S.
Høst
, and P.
Salek
, “Variational and robust density fitting of four-center two-electron integrals in local metrics
,” J. Chem. Phys.
129
, 104101
(2008
).14.
F.
Aquilante
, L.
Gagliardi
, T. B.
Pedersen
, and R.
Lindh
, “Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency
,” J. Chem. Phys.
130
, 154107
(2009
).15.
T. B.
Pedersen
, F.
Aquilante
, and R.
Lindh
, “Density fitting with auxiliary basis sets from Cholesky decompositions
,” Theor. Chem. Acc.
124
, 1
–10
(2009
).16.
E. G.
Hohenstein
, R. M.
Parrish
, and T. J.
Martínez
, “Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory
,” J. Chem. Phys.
137
, 044103
(2012
).17.
R. M.
Parrish
, E. G.
Hohenstein
, T. J.
Martínez
, and C. D.
Sherrill
, “Tensor hypercontraction. II. Least-squares renormalization
,” J. Chem. Phys.
137
, 224106
(2012
).18.
E. G.
Hohenstein
, R. M.
Parrish
, C. D.
Sherrill
, and T. J.
Martínez
, “Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions
,” J. Chem. Phys.
137
, 221101
(2012
).19.
R. M.
Parrish
, C. D.
Sherrill
, E. G.
Hohenstein
, S. I. L.
Kokkila
, and T. J.
Martínez
, “Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction
,” J. Chem. Phys.
140
, 181102
(2014
).20.
F. H.
Bangerter
, M.
Glasbrenner
, and C.
Ochsenfeld
, “Low-scaling tensor hypercontraction in the Cholesky molecular orbital basis applied to second-order Møller–Plesset perturbation theory
,” J. Chem. Theory Comput.
17
, 211
–221
(2021
).21.
D. A.
Matthews
, “Improved grid optimization and fitting in least squares tensor hypercontraction
,” J. Chem. Theory Comput.
16
, 1382
–1385
(2020
).22.
N. H. F.
Beebe
and J.
Linderberg
, “Simplifications in the generation and transformation of two-electron integrals in molecular calculations
,” Int. J. Quantum Chem.
12
, 683
–705
(1977
).23.
H.
Koch
, A.
Sánchez de Merás
, and T. B.
Pedersen
, “Reduced scaling in electronic structure calculations using Cholesky decompositions
,” J. Chem. Phys.
118
, 9481
–9484
(2003
).24.
S. D.
Folkestad
, E. F.
Kjønstad
, and H.
Koch
, “An efficient algorithm for Cholesky decomposition of electron repulsion integrals
,” J. Chem. Phys.
150
, 194112
(2019
).25.
C. C. J.
Roothaan
, “New developments in molecular orbital theory
,” Rev. Mod. Phys.
23
, 69
–89
(1951
).26.
J. A.
Pople
and R. K.
Nesbet
, “Self-consistent orbitals for radicals
,” J. Chem. Phys.
22
, 571
–572
(1954
).27.
C.
Møller
and M. S.
Plesset
, “Note on an approximation treatment for many-electron systems
,” Phys. Rev.
46
, 618
–622
(1934
).28.
E.
Epifanovsky
, D.
Zuev
, X.
Feng
, K.
Khistyaev
, Y.
Shao
, and A. I.
Krylov
, “General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks
,” J. Chem. Phys.
139
, 134105
(2013
).29.
F.
Aquilante
, T. B.
Pedersen
, R.
Lindh
, B. O.
Roos
, A.
Sánchez de Merás
, and H.
Koch
, “Accurate ab initio density fitting for multiconfigurational self-consistent field methods
,” J. Chem. Phys.
129
, 024113
(2008
).30.
F.
Aquilante
, P.-Å.
Malmqvist
, T. B.
Pedersen
, A.
Ghosh
, and B. O.
Roos
, “Cholesky decomposition-based multiconfiguration second-order perturbation theory (CD-CASPT2): Application to the spin-state energetics of CoIII(diiminato)(NPh)
,” J. Chem. Theory Comput.
4
, 694
–702
(2008
).31.
T.
Nottoli
, J.
Gauss
, and F.
Lipparini
, “A black-box, general purpose quadratic self-consistent field code with and without Cholesky decomposition of the two-electron integrals
,” Mol. Phys.
119
, e1974590
(2021
).32.
T.
Nottoli
, J.
Gauss
, and F.
Lipparini
, “Second-order CASSCF algorithm with the Cholesky decomposition of the two-electron repulsion integrals
,” J. Chem. Theory Comput.
17
, 6819
–6831
(2021
).33.
F.
Aquilante
, R.
Lindh
, and T. B.
Pedersen
, “Analytic derivatives for the Cholesky representation of the two-electron integrals
,” J. Chem. Phys.
129
, 034106
(2008
).34.
J.
Boström
, V.
Veryazov
, F.
Aquilante
, T. B.
Pedersen
, and R.
Lindh
, “Analytical gradients of the second-order Møller-Plesset energy using Cholesky decompositions
,” Int. J. Quantum Chem.
114
, 321
–327
(2013
).35.
M. G.
Delcey
, T. B.
Pedersen
, F.
Aquilante
, and R.
Lindh
, “Analytical gradients of the state-average complete active space self-consistent field method with density fitting
,” J. Chem. Phys.
143
, 044110
(2015
).36.
X.
Feng
, E.
Epifanovsky
, J.
Gauss
, and A. I.
Krylov
, “Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks
,” J. Chem. Phys.
151
, 014110
(2019
).37.
S.
Burger
, F.
Lipparini
, J.
Gauss
, and S.
Stopkowicz
, “NMR chemical shift computations at second-order Møller–Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals
,” J. Chem. Phys.
155
, 074105
(2021
).38.
M.
Glasbrenner
, S.
Vogler
, and C.
Ochsenfeld
, “Efficient low-scaling computation of NMR shieldings at the second-order Møller–Plesset perturbation theory level with Cholesky-decomposed densities and an attenuated Coulomb metric
,” J. Chem. Phys.
155
, 224107
(2021
).39.
E. I.
Tellgren
, A.
Soncini
, and T.
Helgaker
, “Nonperturbative ab initio calculations in strong magnetic fields using London orbitals
,” J. Chem. Phys.
129
, 154114
(2008
).40.
E. I.
Tellgren
, S. S.
Reine
, and T.
Helgaker
, “Analytical GIAO and hybrid-basis integral derivatives: Application to geometry optimization of molecules in strong magnetic fields
,” Phys. Chem. Chem. Phys.
14
, 9492
(2012
).41.
K. K.
Lange
, E. I.
Tellgren
, M. R.
Hoffmann
, and T.
Helgaker
, “A paramagnetic bonding mechanism for diatomics in strong magnetic fields
,” Science
337
, 327
(2012
).42.
J. W.
Furness
, J.
Verbeke
, E. I.
Tellgren
, S.
Stopkowicz
, U.
Ekström
, T.
Helgaker
, and A. M.
Teale
, “Current density functional theory using meta-generalized gradient exchange-correlation functionals
,” J. Chem. Theory Comput.
11
, 4169
–4181
(2015
).43.
R. D.
Reynolds
and T.
Shiozaki
, “Fully relativistic self-consistent field under a magnetic field
,” Phys. Chem. Chem. Phys.
17
, 14280
–14283
(2015
).44.
S.
Stopkowicz
, J.
Gauss
, K. K.
Lange
, E. I.
Tellgren
, and T.
Helgaker
, “Coupled-cluster theory for atoms and molecules in strong magnetic fields
,” J. Chem. Phys.
143
, 074110
(2015
).45.
F.
Hampe
and S.
Stopkowicz
, “Equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields
,” J. Chem. Phys.
146
, 154105
(2017
).46.
S.
Reimann
, A.
Borgoo
, E. I.
Tellgren
, A. M.
Teale
, and T.
Helgaker
, “Magnetic-field density-functional theory (BDFT): Lessons from the adiabatic connection
,” J. Chem. Theory Comput.
13
, 4089
–4100
(2017
).47.
T. J. P.
Irons
, J.
Zemen
, and A. M.
Teale
, “Efficient calculation of molecular integrals over London atomic orbitals
,” J. Chem. Theory Comput.
13
, 3636
–3649
(2017
).48.
S.
Reimann
, A.
Borgoo
, J.
Austad
, E. I.
Tellgren
, A. M.
Teale
, T.
Helgaker
, and S.
Stopkowicz
, “Kohn–Sham energy decomposition for molecules in a magnetic field
,” Mol. Phys.
117
, 97
–109
(2018
).49.
R. D.
Reynolds
, T.
Yanai
, and T.
Shiozaki
, “Large-scale relativistic complete active space self-consistent field with robust convergence
,” J. Chem. Phys.
149
, 014106
(2018
).50.
S.
Sen
and E. I.
Tellgren
, “Non-perturbative calculation of orbital and spin effects in molecules subject to non-uniform magnetic fields
,” J. Chem. Phys.
148
, 184112
(2018
).51.
S.
Sun
, D. B.
Williams-Young
, T. F.
Stetina
, and X.
Li
, “Generalized Hartree–Fock with nonperturbative treatment of strong magnetic fields: Application to molecular spin phase transitions
,” J. Chem. Theory Comput.
15
, 348
–356
(2019
).52.
F.
Hampe
and S.
Stopkowicz
, “Transition-dipole moments for electronic excitations in strong magnetic fields using equation-of-motion and linear response coupled-cluster theory
,” J. Chem. Theory Comput.
15
, 4036
–4043
(2019
).53.
S.
Sen
, K. K.
Lange
, and E. I.
Tellgren
, “Excited states of molecules in strong uniform and nonuniform magnetic fields
,” J. Chem. Theory Comput.
15
, 3974
–3990
(2019
).54.
S.
Lehtola
, M.
Dimitrova
, and D.
Sundholm
, “Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields
,” Mol. Phys.
118
, e1597989
(2019
).55.
S.
Sun
, D.
Williams-Young
, and X.
Li
, “An ab initio linear response method for computing magnetic circular dichroism spectra with nonperturbative treatment of magnetic field
,” J. Chem. Theory Comput.
15
, 3162
–3169
(2019
).56.
F.
Hampe
, N.
Gross
, and S.
Stopkowicz
, “Full triples contribution in coupled-cluster and equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields
,” Phys. Chem. Chem. Phys.
22
, 23522
–23529
(2020
).57.
F. A.
Bischoff
, “Structure of the H3 molecule in a strong homogeneous magnetic field as computed by the Hartree-Fock method using multiresolution analysis
,” Phys. Rev. A
101
, 053413
(2020
).58.
A.
Pausch
and W.
Klopper
, “Efficient evaluation of three-centre two-electron integrals over London orbitals
,” Mol. Phys.
118
, e1736675
(2020
).59.
T. J. P.
Irons
, G.
David
, and A. M.
Teale
, “Optimizing molecular geometries in strong magnetic fields
,” J. Chem. Theory Comput.
17
, 2166
–2185
(2021
).60.
T.
Culpitt
, L. D. M.
Peters
, E. I.
Tellgren
, and T.
Helgaker
, “Ab initio molecular dynamics with screened Lorentz forces. I. Calculation and atomic charge interpretation of Berry curvature
,” J. Chem. Phys.
155
, 024104
(2021
).61.
L. D. M.
Peters
, T.
Culpitt
, L.
Monzel
, E. I.
Tellgren
, and T.
Helgaker
, “Ab initio molecular dynamics with screened Lorentz forces. II. Efficient propagators and rovibrational spectra in strong magnetic fields
,” J. Chem. Phys.
155
, 024105
(2021
).62.
P.
Schmelcher
and L. S.
Cederbaum
, “Crossings of potential-energy surfaces in a magnetic field
,” Phys. Rev. A
41
, 4936
–4943
(1990
).63.
F.
London
, “Théorie quantique des courants interatomiques dans les combinaisons aromatiques
,” J. Phys. Radium
8
, 397
–409
(1937
).64.
F.
Aquilante
, R.
Lindh
, and T. B.
Pedersen
, “Unbiased auxiliary basis sets for accurate two-electron integral approximations
,” J. Chem. Phys.
127
, 114107
(2007
).65.
G. L.
Stoychev
, A. A.
Auer
, and F.
Neese
, “Automatic generation of auxiliary basis sets
,” J. Chem. Theory Comput.
13
, 554
–562
(2017
).66.
S.
Lehtola
, “Straightforward and accurate automatic auxiliary basis set generation for molecular calculations with atomic orbital basis sets
,” J. Chem. Theory Comput.
17
, 6886
(2021
).67.
J.
Gauss
, F.
Lipparini
, S.
Burger
, S.
Blaschke
, M.-P.
Kitsaras
, and S.
Stopkowicz
, The Mainz INTegral package MINT, Johannes Gutenberg-Universität Mainz
, 2021
.68.
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
, S.
Blaschke
, Y. J.
Bomble
, S.
Burger
, O.
Christiansen
, D.
Datta
, F.
Engel
, R.
Faber
, J.
Greiner
, M.
Heckert
, O.
Heun
, M.
Hilgenberg
, C.
Huber
, T.-C.
Jagau
, D.
Jonsson
, J.
Jusélius
, T.
Kirsch
, K.
Klein
, G. M.
Kopper
, W. J.
Lauderdale
, F.
Lipparini
, T.
Metzroth
, L. A.
Mück
, D. P.
O’Neill
, T.
Nottoli
, 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.69.
D. A.
Matthews
, L.
Cheng
, M. E.
Harding
, F.
Lipparini
, S.
Stopkowicz
, T.-C.
Jagau
, P. G.
Szalay
, J.
Gauss
, and J. F.
Stanton
, “Coupled-cluster techniques for computational chemistry: The CFOUR program package
,” J. Chem. Phys.
152
, 214108
(2020
).70.
L. E.
McMurchie
and E. R.
Davidson
, “One- and two-electron integrals over cartesian Gaussian functions
,” J. Comput. Phys.
26
, 218
–231
(1978
).71.
P.
Pulay
, “Convergence acceleration of iterative sequences. The case of SCF iteration
,” Chem. Phys. Lett.
73
, 393
–398
(1980
).72.
P.
Pulay
, “Improved SCF convergence acceleration
,” J. Comput. Chem.
3
, 556
–560
(1982
).73.
OpenMP Architecture Review Board, OpenMP application program interface version 4.5, 2015; last accessed 4 July 2021.
74.
T. H.
Dunning
, Jr., “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
,” J. Chem. Phys.
90
, 1007
–1023
(1989
).75.
R. A.
Kendall
, T. H.
Dunning
, Jr., and R. J.
Harrison
, “Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions
,” J. Chem. Phys.
96
, 6796
–6806
(1992
).76.
A.
Schäfer
, H.
Horn
, and R.
Ahlrichs
, “Fully optimized contracted Gaussian basis sets for atoms Li to Kr
,” J. Chem. Phys.
97
, 2571
–2577
(1992
).77.
F.
Aquilante
, L.
Boman
, J.
Boström
, H.
Koch
, R.
Lindh
, A.
Sánchez de Merás
, and T. B.
Pedersen
, “Cholesky decomposition techniques in electronic structure theory
,” in Linear-Scaling Techniques in Computational Chemistry and Physics
, edited by R.
Zaleśny
, M. G.
Papadopoulos
, P. G.
Mezey
, and J.
Leszczynski
(Springer
, The Netherlands
, 2011
), Chap. 13, pp. 301
–343
.78.
LONDON, a quantum-chemistry program for plane-wave/GTO hybrid basis sets and finite magnetic field calculations by
E.
Tellgren
(primary author), T.
Helgaker
, A.
Soncini
, K. K.
Lange
, A. M.
Teale
, U.
Ekström
, S.
Stopkowicz
, J. H.
Austad
, and S.
Sen
, see londonprogram.org for more information.79.
A. R.
Hoy
and P. R.
Bunker
, “A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule
,” J. Mol. Spectrosc.
74
, 1
–8
(1979
).80.
L.
Boman
, H.
Koch
, and A.
Sánchez de Merás
, “Method specific Cholesky decomposition: Coulomb and exchange energies
,” J. Chem. Phys.
129
, 134107
(2008
).81.
S.
Thomas
, F.
Hampe
, S.
Stopkowicz
, and J.
Gauss
, “Complex ground-state and excitation energies in coupled-cluster theory
,” Mol. Phys.
119
, e1968056
(2021
).82.
Extrapolation of the HF energy to the basis set limit yields an error of 1.7 · 10−4 Eh with respect to the unc-aug-cc-pV5Z basis set.
83.
M.-P.
Kitsaras
and S.
Stopkowicz
, “Exploiting symmetry in quantum-chemical calculations a finite magnetic field: Abelian complex groups
” (unpublished) (2021
).84.
E. I.
Tellgren
, T.
Helgaker
, and A.
Soncini
, “Non-perturbative magnetic phenomena in closed-shell paramagnetic molecules
,” Phys. Chem. Chem. Phys.
11
, 5489
(2009
).85.
G.
Monaco
, L. T.
Scott
, and R.
Zanasi
, “Magnetic euripi in corannulene
,” J. Phys. Chem. A
112
, 8136
–8147
(2008
).86.
C.
Ochsenfeld
, S. P.
Brown
, I.
Schnell
, J.
Gauss
, and H. W.
Spiess
, “Structure assignment in the solid state by the coupling of quantum chemical calculations with NMR experiments: A columnar hexabenzocoronene derivative
,” J. Am. Chem. Soc.
123
, 2597
–2606
(2001
).87.
M.
Häser
, J.
Almlöf
, and G. E.
Scuseria
, “The equilibrium geometry of C60 as predicted by second-order (MP2) perturbation theory
,” Chem. Phys. Lett.
181
, 497
–500
(1991
).88.
S.
Itoyama
, K.
Doitomi
, T.
Kamachi
, Y.
Shiota
, and K.
Yoshizawa
, “Possible peroxo state of the dicopper site of particulate methane monooxygenase from combined quantum mechanics and molecular mechanics calculations
,” Inorg. Chem.
55
, 2771
–2775
(2016
).89.
A. D.
Becke
, “A new mixing of Hartree–Fock and local density-functional theories
,” J. Chem. Phys.
98
, 1372
–1377
(1993
).90.
P. J.
Stephens
, F. J.
Devlin
, C. F.
Chabalowski
, and M. J.
Frisch
, “Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields
,” J. Phys. Chem.
98
, 11623
–11627
(1994
).91.
TURBOMOLE V7.5.1 2021, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007; available from https://www.turbomole.org.
92.
S. G.
Balasubramani
, G. P.
Chen
, S.
Coriani
, M.
Diedenhofen
, M. S.
Frank
, Y. J.
Franzke
, F.
Furche
, R.
Grotjahn
, M. E.
Harding
, C.
Hättig
, A.
Hellweg
, B.
Helmich-Paris
, C.
Holzer
, U.
Huniar
, M.
Kaupp
, A.
Marefat Khah
, S.
Karbalaei Khani
, T.
Müller
, F.
Mack
, B. D.
Nguyen
, S. M.
Parker
, E.
Perlt
, D.
Rappoport
, K.
Reiter
, S.
Roy
, M.
Rückert
, G.
Schmitz
, M.
Sierka
, E.
Tapavicza
, D. P.
Tew
, C.
van Wüllen
, V. K.
Voora
, F.
Weigend
, A.
Wodyński
, and J. M.
Yu
, “TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations
,” J. Chem. Phys.
152
, 184107
(2020
).93.
G. B.
Bacskay
, “A quadratically convergent Hartree–Fock (QC-SCF) method. Application to closed shell systems
,” Chem. Phys.
61
, 385
–404
(1981
).94.
G. B.
Bacskay
, “A quadratically convergent Hartree-Fock (QC-SCF) method. Application to open shell orbital optimization and coupled perturbed Hartree-Fock calculations
,” Chem. Phys.
65
, 383
–396
(1982
).95.
S.
Stopkowicz
, “Perspective: Coupled cluster theory for atoms and molecules in strong magnetic fields
,” Int. J. Quantum Chem.
118
, e25391
(2018
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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