We present pyflosic, an open-source, general-purpose python implementation of the Fermi–Löwdin orbital self-interaction correction (FLO-SIC), which is based on the python simulation of chemistry framework (pyscf) electronic structure and quantum chemistry code. Thanks to pyscf, pyflosic can be used with any kind of Gaussian-type basis set, various kinds of radial and angular quadrature grids, and all exchange-correlation functionals within the local density approximation, generalized-gradient approximation (GGA), and meta-GGA provided in the libxc and xcfun libraries. A central aspect of FLO-SIC is the Fermi-orbital descriptors, which are used to estimate the self-interaction correction. Importantly, they can be initialized automatically within pyflosic; they can also be optimized within pyflosic with an interface to the atomic simulation environment, a python library that provides a variety of powerful gradient-based algorithms for geometry optimization. Although pyflosic has already facilitated applications of FLO-SIC to chemical studies, it offers an excellent starting point for further developments in FLO-SIC approaches, thanks to its use of a high-level programming language and pronounced modularity.
REFERENCES
1.
Q.
Sun
, “Libcint: An efficient general integral library for Gaussian basis functions
,” J. Comput. Chem.
36
, 1664
(2015
); arXiv:1412.0649.2.
J.
Kim
, A. D.
Baczewski
, T. D.
Beaudet
, A.
Benali
, M. C.
Bennett
, M. A.
Berrill
, N. S.
Blunt
, E. J. L.
Borda
, M.
Casula
, D. M.
Ceperley
et al., “QMCPACK: An open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids
,” J. Phys.: Condens. Matter
30
, 195901
(2018
); arXiv:1802.06922.3.
S.
Lehtola
, C.
Steigemann
, M. J. T.
Oliveira
, and M. A. L.
Marques
, “Recent developments in LIBXC—A comprehensive library of functionals for density functional theory
,” SoftwareX
7
, 1
(2018
).4.
M. F.
Herbst
, M.
Scheurer
, T.
Fransson
, D. R.
Rehn
, and A.
Dreuw
, “adcc: A versatile toolkit for rapid development of algebraic–diagrammatic construction methods
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
(in press); arXiv:1910.07757.5.
P.
Koval
, M.
Barbry
, and D.
Sánchez-Portal
, “PySCF-NAO: An efficient and flexible implementation of linear response time-dependent density functional theory with numerical atomic orbitals
,” Comput. Phys. Commun.
236
, 188
(2019
).6.
S.
Iskakov
, A. A.
Rusakov
, D.
Zgid
, and E.
Gull
, “Effect of propagator renormalization on the band gap of insulating solids
,” Phys. Rev. B
100
, 085112
(2019
); arXiv:1812.07027 .7.
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:2002.12531.8.
D. G. A.
Smith
, L. A.
Burns
, A. C.
Simmonett
, R. M.
Parrish
, M. C.
Schieber
, R.
Galvelis
, P.
Kraus
, H.
Kruse
, R.
Di Remigio
, A.
Alenaizan
, A. M.
James
, S.
Lehtola
, J. P.
Misiewicz
, M.
Scheurer
, R. A.
Shaw
, J. B.
Schriber
, Y.
Xie
, Z. L.
Glick
, D. A.
Sirianni
, J. S.
O’Brien
, J. M.
Waldrop
, A.
Kumar
, E. G.
Hohenstein
, B. P.
Pritchard
, B. R.
Brooks
, H. F.
Schaefer
, A. Y.
Sokolov
, K.
Patkowski
, A. E.
DePrince
, U.
Bozkaya
, R. A.
King
, F. A.
Evangelista
, J. M.
Turney
, T. D.
Crawford
, and C. D.
Sherrill
, “PSI4 1.4: Open-source software for high-throughput quantum chemistry
,” J. Chem. Phys.
152
, 184108
(2020
).9.
M. R.
Pederson
, A.
Ruzsinszky
, and J. P.
Perdew
, “Communication: Self-interaction correction with unitary invariance in density functional theory
,” J. Chem. Phys.
140
, 121103
(2014
).10.
M. R.
Pederson
, “Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms
,” J. Chem. Phys.
142
, 064112
(2015
); arXiv:1412.3101.11.
M. R.
Pederson
and T.
Baruah
, “Self-interaction corrections within the Fermi-orbital-based formalism
,” Adv. At., Mol., Opt. Phys.
64
, 153
(2015
).12.
Z.-h.
Yang
, M. R.
Pederson
, and J. P.
Perdew
, “Full self-consistency in the Fermi-orbital self-interaction correction
,” Phys. Rev. A
95
, 052505
(2017
).13.
L.
Fiedler
, “Implementation and reassessment of the Fermi–Löwdin orbital self-interaction correction for LDA, GGA and mGGA functionals
,” M.Sc. thesis, TU Bergakademie Freiberg
, 2018
.14.
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
et al., “PySCF: The Python-based simulations of chemistry framework
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
, e1340
(2018
).15.
P.
Hohenberg
and W.
Kohn
, “Inhomogeneous electron gas
,” Phys. Rev.
136
, B864
(1964
).16.
W.
Kohn
and L. J.
Sham
, “Self-consistent equations including exchange and correlation effects
,” Phys. Rev.
140
, A1133
(1965
).17.
18.
M. R.
Pederson
and K. A.
Jackson
, “Variational mesh for quantum-mechanical simulations
,” Phys. Rev. B
41
, 7453
(1990
).19.
M. R.
Pederson
, K. A.
Jackson
, and W. E.
Pickett
, “Local-density-approximation-based simulations of hydrocarbon interactions with applications to diamond chemical vapor deposition
,” Phys. Rev. B
44
, 3891
(1991
).20.
M. R.
Pederson
and K. A.
Jackson
, “Pseudoenergies for simulations on metallic systems
,” Phys. Rev. B
43
, 7312
(1991
).21.
J. P.
Perdew
, J. A.
Chevary
, S. H.
Vosko
, K. A.
Jackson
, M. R.
Pederson
, D. J.
Singh
, and C.
Fiolhais
, “Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation
,” Phys. Rev. B
46
, 6671
(1992
).22.
D.
Porezag
and M. R.
Pederson
, “Infrared intensities and Raman-scattering activities within density-functional theory
,” Phys. Rev. B
54
, 7830
(1996
).23.
D. V.
Porezag
, “Development of ab-initio and approximate density functional methods and their application to complex fullerene systems
,” Ph.D. thesis, TU Chemnitz
, 1997
.24.
D.
Porezag
and M. R.
Pederson
, “Optimization of Gaussian basis sets for density-functional calculations
,” Phys. Rev. A
60
, 2840
(1999
).25.
J.
Kortus
and M. R.
Pederson
, “Magnetic and vibrational properties of the uniaxial Fe13O8 cluster
,” Phys. Rev. B
62
, 5755
(2000
).26.
M. R.
Pederson
, D. V.
Porezag
, J.
Kortus
, and D. C.
Patton
, “Strategies for massively parallel local-orbital-based electronic structure methods
,” Phys. Status Solidi B
217
, 197
(2000
).27.
F. W.
Aquino
and B. M.
Wong
, “Additional insights between Fermi–Löwdin orbital SIC and the localization equation constraints in SIC-DFT
,” J. Phys. Chem. Lett.
9
, 6456
(2018
).28.
F. W.
Aquino
, R.
Shinde
, and B. M.
Wong
, “Fractional occupation numbers and self-interaction correction-scaling methods with the Fermi–Löwdin orbital self-interaction correction approach
,” J. Comput. Chem.
41
, 1200
(2020
).29.
B. P.
Pritchard
, D.
Altarawy
, B. T.
Didier
, T. D.
Gibson
, and T. L.
Windus
, “A new basis set exchange: An open, up-to-date resource for the molecular sciences community
,” J. Chem. Inf. Model.
59
, 4814
(2019
).30.
S. R.
Jensen
, S.
Saha
, J. A.
Flores-Livas
, W.
Huhn
, V.
Blum
, S.
Goedecker
, and L.
Frediani
, “The elephant in the room of density functional theory calculations
,” J. Phys. Chem. Lett.
8
, 1449
(2017
); arXiv:1702.00957.31.
F.
Jensen
, “How large is the elephant in the density functional theory room?
,” J. Phys. Chem. A
121
, 6104
(2017
); arXiv:1704.08832.32.
D.
Feller
and D. A.
Dixon
, “Density functional theory and the basis set truncation problem with correlation consistent basis sets: Elephant in the room or mouse in the closet?
,” J. Phys. Chem. A
122
, 2598
(2018
).33.
S.
Lehtola
, “Polarized Gaussian basis sets from one-electron ions
,” J. Chem. Phys.
152
, 134108
(2020
); arXiv:2001.04224.34.
S.
Lehtola
, “Curing basis set overcompleteness with pivoted Cholesky decompositions
,” J. Chem. Phys.
151
, 241102
(2019
); arXiv:1911.10372.35.
S.
Lehtola
, “Accurate reproduction of strongly repulsive interatomic potentials
,” Phys. Rev. A
101
, 032504
(2020
); arXiv:1912.12624.36.
U.
Ekström
, L.
Visscher
, R.
Bast
, A. J.
Thorvaldsen
, and K.
Ruud
, “Arbitrary-order density functional response theory from automatic differentiation
,” J. Chem. Theory Comput.
6
, 1971
(2010
).37.
See https://www.tddft.org/programs/libxc/functionals/ for list of functionals in LIBXC; accessed 17 July 2020 and https://xcfun.readthedocs.io/en/latest/functionals.html for those in XCFUN; accessed 17 July 2020.
38.
S.
Lehtola
and H.
Jónsson
, “Variational, self-consistent implementation of the Perdew–Zunger self-interaction correction with complex optimal orbitals
,” J. Chem. Theory Comput.
10
, 5324
(2014
).39.
C. D.
Sherrill
, “Frontiers in electronic structure theory
,” J. Chem. Phys.
132
, 110902
(2010
).40.
K.
Burke
, “Perspective on density functional theory
,” J. Chem. Phys.
136
, 150901
(2012
); arXiv:1201.3679.41.
A. J.
Cohen
, P.
Mori-Sánchez
, and W.
Yang
, “Insights into current limitations of density functional theory
,” Science
321
, 792
(2008
).42.
J. P.
Perdew
, A.
Ruzsinszky
, L. A.
Constantin
, J.
Sun
, and G. I.
Csonka
, “Some fundamental issues in ground-state density functional theory: A guide for the perplexed
,” J. Chem. Theory Comput.
5
, 902
(2009
).43.
B. G.
Johnson
, C. A.
Gonzales
, P. M. W.
Gill
, and J. A.
Pople
, “A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction
,” Chem. Phys. Lett.
221
, 100
(1994
).44.
E.
Kraisler
and L.
Kronik
, “Piecewise linearity of approximate density functionals revisited: Implications for Frontier orbital energies
,” Phys. Rev. Lett.
110
, 126403
(2013
); arXiv:1211.5950.45.
J. P.
Perdew
and A.
Zunger
, “Self-interaction correction to density-functional approximations for many-electron systems
,” Phys. Rev. B
23
, 5048
(1981
).46.
M. R.
Pederson
and C. C.
Lin
, “Localized and canonical atomic orbitals in self-interaction corrected local density functional approximation
,” J. Chem. Phys.
88
, 1807
(1988
).47.
O. A.
Vydrov
and G. E.
Scuseria
, “Ionization potentials and electron affinities in the Perdew–Zunger self-interaction corrected density-functional theory
,” J. Chem. Phys.
122
, 184107
(2005
).48.
S.
Klüpfel
, P.
Klüpfel
, and H.
Jónsson
, “Importance of complex orbitals in calculating the self-interaction-corrected ground state of atoms
,” Phys. Rev. A
84
, 050501
(2011
); arXiv:1308.6063.49.
H.
Gudmundsdóttir
, Y.
Zhang
, P. M.
Weber
, and H.
Jónsson
, “Self-interaction corrected density functional calculations of molecular Rydberg states
,” J. Chem. Phys.
139
, 194102
(2013
).50.
G.
Borghi
, A.
Ferretti
, N. L.
Nguyen
, I.
Dabo
, and N.
Marzari
, “Koopmans-compliant functionals and their performance against reference molecular data
,” Phys. Rev. B
90
, 075135
(2014
); arXiv:1405.4635.51.
H.
Gudmundsdóttir
, Y.
Zhang
, P. M.
Weber
, and H.
Jónsson
, “Self-interaction corrected density functional calculations of Rydberg states of molecular clusters: N,N-dimethylisopropylamine
,” J. Chem. Phys.
141
, 234308
(2014
).52.
J. P.
Perdew
, A.
Ruzsinszky
, J.
Sun
, and M. R.
Pederson
, “Paradox of self-interaction correction: How can anything so right be so wrong?
,” Adv. At., Mol., Opt. Phys.
64
, 1
(2015
).53.
X.
Cheng
, Y.
Zhang
, E.
Jónsson
, H.
Jónsson
, and P. M.
Weber
, “Charge localization in a diamine cation provides a test of energy functionals and self-interaction correction
,” Nat. Commun.
7
, 11013
(2016
).54.
Y.
Zhang
, P. M.
Weber
, and H.
Jónsson
, “Self-interaction corrected functional calculations of a dipole-bound molecular anion
,” J. Phys. Chem. Lett.
7
, 2068
(2016
).55.
S.
Schwalbe
, T.
Hahn
, S.
Liebing
, K.
Trepte
, and J.
Kortus
, “Fermi–Löwdin orbital self-interaction corrected density functional theory: Ionization potentials and enthalpies of formation
,” J. Comput. Chem.
39
, 2463
(2018
).56.
G.
Borghi
, C.-H.
Park
, N. L.
Nguyen
, A.
Ferretti
, and N.
Marzari
, “Variational minimization of orbital-density-dependent functionals
,” Phys. Rev. B
91
, 155112
(2015
).57.
J.
Garza
, J. A.
Nichols
, and D. A.
Dixon
, “The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules
,” J. Chem. Phys.
112
, 7880
(2000
).58.
J.
Garza
, R.
Vargas
, J. A.
Nichols
, and D. A.
Dixon
, “Orbital energy analysis with respect to LDA and self-interaction corrected exchange-only potentials
,” J. Chem. Phys.
114
, 639
(2001
).59.
S.
Patchkovskii
, J.
Autschbach
, and T.
Ziegler
, “Curing difficult cases in magnetic properties prediction with self-interaction corrected density functional theory
,” J. Chem. Phys.
115
, 26
(2001
).60.
S.
Patchkovskii
and T.
Ziegler
, “Improving “difficult” reaction barriers with self-interaction corrected density functional theory
,” J. Chem. Phys.
116
, 7806
(2002
).61.
S.
Patchkovskii
and T.
Ziegler
, “Phosphorus NMR chemical shifts with self-interaction free, gradient-corrected DFT
,” J. Phys. Chem. A
106
, 1088
(2002
).62.
O. A.
Vydrov
and G. E.
Scuseria
, “Effect of the Perdew–Zunger self-interaction correction on the thermochemical performance of approximate density functionals
,” J. Chem. Phys.
121
, 8187
(2004
).63.
O. A.
Vydrov
, G. E.
Scuseria
, J. P.
Perdew
, A.
Ruzsinszky
, and G. I.
Csonka
, “Scaling down the Perdew–Zunger self-interaction correction in many-electron regions
,” J. Chem. Phys.
124
, 094108
(2006
).64.
C. D.
Pemmaraju
, T.
Archer
, D.
Sánchez-Portal
, and S.
Sanvito
, “Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids
,” Phys. Rev. B
75
, 045101
(2007
).65.
S.
Klüpfel
, P.
Klüpfel
, and H.
Jónsson
, “The effect of the Perdew–Zunger self-interaction correction to density functionals on the energetics of small molecules
,” J. Chem. Phys.
137
, 124102
(2012
).66.
Á.
Valdés
, J.
Brillet
, M.
Grätzel
, H.
Gudmundsdóttir
, H. A.
Hansen
, H.
Jónsson
, P.
Klüpfel
, G.-J.
Kroes
, F.
Le Formal
, I. C.
Man
, R. S.
Martins
, J. K.
Nørskov
, J.
Rossmeisl
, K.
Sivula
, A.
Vojvodic
, and M.
Zäch
, “Solar hydrogen production with semiconductor metal oxides: New directions in experiment and theory
,” Phys. Chem. Chem. Phys.
14
, 49
(2012
).67.
H.
Gudmundsdóttir
, E. Ö.
Jónsson
, and H.
Jónsson
, “Calculations of Al dopant in α-quartz using a variational implementation of the Perdew–Zunger self-interaction correction
,” New J. Phys.
17
, 083006
(2015
).68.
S.
Lehtola
, M.
Head-Gordon
, and H.
Jónsson
, “Complex orbitals, multiple local minima, and symmetry breaking in Perdew–Zunger self-interaction corrected density functional theory calculations
,” J. Chem. Theory Comput.
12
, 3195
(2016
).69.
J.
Lehtola
, M.
Hakala
, A.
Sakko
, and K.
Hämäläinen
, “ERKALE—A flexible program package for X-ray properties of atoms and molecules
,” J. Comput. Chem.
33
, 1572
(2012
).70.
71.
T.
Hahn
, S.
Liebing
, J.
Kortus
, and M. R.
Pederson
, “Fermi orbital self-interaction corrected electronic structure of molecules beyond local density approximation
,” J. Chem. Phys.
143
, 224104
(2015
); arXiv:1508.00745.72.
M. R.
Pederson
, T.
Baruah
, D.-y.
Kao
, and L.
Basurto
, “Self-interaction corrections applied to Mg-porphyrin, C60, and pentacene molecules
,” J. Chem. Phys.
144
, 164117
(2016
).73.
T.
Hahn
, S.
Schwalbe
, J.
Kortus
, and M. R.
Pederson
, “Symmetry breaking within Fermi–Löwdin orbital self-interaction corrected density functional theory
,” J. Chem. Theory Comput.
13
, 5823
(2017
).74.
D.-y.
Kao
, K.
Withanage
, T.
Hahn
, J.
Batool
, J.
Kortus
, and K.
Jackson
, “Self-consistent self-interaction corrected density functional theory calculations for atoms using Fermi–Löwdin orbitals: Optimized Fermi-orbital descriptors for Li–Kr
,” J. Chem. Phys.
147
, 164107
(2017
).75.
K.
Sharkas
, L.
Li
, K.
Trepte
, K. P. K.
Withanage
, R. P.
Joshi
, R. R.
Zope
, T.
Baruah
, J. K.
Johnson
, K. A.
Jackson
, and J. E.
Peralta
, “Shrinking self-interaction errors with the Fermi–Löwdin orbital self-interaction-corrected density functional approximation
,” J. Phys. Chem. A
122
, 9307
(2018
).76.
R. P.
Joshi
, K.
Trepte
, K. P. K.
Withanage
, K.
Sharkas
, Y.
Yamamoto
, L.
Basurto
, R. R.
Zope
, T.
Baruah
, K. A.
Jackson
, and J. E.
Peralta
, “Fermi–Löwdin orbital self-interaction correction to magnetic exchange couplings
,” J. Chem. Phys.
149
, 164101
(2018
).77.
K. P. K.
Withanage
, K.
Trepte
, J. E.
Peralta
, T.
Baruah
, R.
Zope
, and K. A.
Jackson
, “On the question of the total energy in the Fermi–Löwdin Orbital self-interaction correction method
,” J. Chem. Theory Comput.
14
, 4122
(2018
).78.
A. I.
Johnson
, K. P. K.
Withanage
, K.
Sharkas
, Y.
Yamamoto
, T.
Baruah
, R. R.
Zope
, J. E.
Peralta
, and K. A.
Jackson
, “The effect of self-interaction error on electrostatic dipoles calculated using density functional theory
,” J. Chem. Phys.
151
, 174106
(2019
).79.
K. A.
Jackson
, J. E.
Peralta
, R. P.
Joshi
, K. P.
Withanage
, K.
Trepte
, K.
Sharkas
, and A. I.
Johnson
, “Towards efficient density functional theory calculations without self-interaction: The Fermi–Löwdin orbital self-interaction correction
,” J. Phys.: Conf. Ser.
1290
, 012002
(2019
).80.
R. R.
Zope
, Y.
Yamamoto
, C. M.
Diaz
, T.
Baruah
, J. E.
Peralta
, K. A.
Jackson
, B.
Santra
, and J. P.
Perdew
, “A step in the direction of resolving the paradox of Perdew–Zunger self-interaction correction
,” J. Chem. Phys.
151
, 214108
(2019
); arXiv:1911.08659.81.
K. P. K.
Withanage
, S.
Akter
, C.
Shahi
, R. P.
Joshi
, C.
Diaz
, Y.
Yamamoto
, R.
Zope
, T.
Baruah
, J. P.
Perdew
, J. E.
Peralta
, and K. A.
Jackson
, “Self-interaction-free electric dipole polarizabilities for atoms and their ions using the Fermi–Löwdin self-interaction correction
,” Phys. Rev. A
100
, 012505
(2019
).82.
B.
Santra
and J. P.
Perdew
, “Perdew–Zunger self-interaction correction: How wrong for uniform densities and large-Z atoms?
,” J. Chem. Phys.
150
, 174106
(2019
); arXiv:1902.00117.83.
K.
Trepte
, S.
Schwalbe
, T.
Hahn
, J.
Kortus
, D.-y.
Kao
, Y.
Yamamoto
, T.
Baruah
, R. R.
Zope
, K. P. K.
Withanage
, J. E.
Peralta
, and K. A.
Jackson
, “Analytic atomic gradients in the Fermi–Löwdin orbital self-interaction correction
,” J. Comput. Chem.
40
, 820
(2019
).84.
S.
Schwalbe
, K.
Trepte
, L.
Fiedler
, A. I.
Johnson
, J.
Kraus
, T.
Hahn
, J. E.
Peralta
, K. A.
Jackson
, and J.
Kortus
, “Interpretation and automatic generation of Fermi-orbital descriptors
,” J. Comput. Chem.
40
, 2843
(2019
).85.
Y.
Yamamoto
, C. M.
Diaz
, L.
Basurto
, K. A.
Jackson
, T.
Baruah
, and R. R.
Zope
, “Fermi–Löwdin orbital self-interaction correction using the strongly constrained and appropriately normed meta-GGA functional
,” J. Chem. Phys.
151
, 154105
(2019
).86.
J.
Vargas
, P.
Ufondu
, T.
Baruah
, Y.
Yamamoto
, K. A.
Jackson
, and R. R.
Zope
, “Importance of self-interaction-error removal in density functional calculations on water cluster anions
,” Phys. Chem. Chem. Phys.
22
, 3789
(2020
).87.
S.
Lehtola
, E. Ö.
Jónsson
, and H.
Jónsson
, “Effect of complex-valued optimal orbitals on atomization energies with the Perdew–Zunger self-interaction correction to density functional theory
,” J. Chem. Theory Comput.
12
, 4296
(2016
).88.
U.
Lundin
and O.
Eriksson
, “Novel method of self-interaction corrections in density functional calculations
,” Int. J. Quantum Chem.
81
, 247
(2001
).89.
S.
Lehtola
, F.
Blockhuys
, and C.
Van Alsenoy
, “An overview of self-consistent field calculations within finite basis sets
,” Molecules
25
, 1218
(2020
); arXiv:1912.12029 .90.
J. G.
Harrison
, R. A.
Heaton
, and C. C.
Lin
, “Self-interaction correction to the local density Hartree–Fock atomic calculations of excited and ground states
,” J. Phys. B: At., Mol. Phys.
16
, 2079
(1983
).91.
M. R.
Pederson
, R. A.
Heaton
, and C. C.
Lin
, “Local-density Hartree–Fock theory of electronic states of molecules with self-interaction correction
,” J. Chem. Phys.
80
, 1972
(1984
).92.
S.
Lehtola
and H.
Jónsson
, “Unitary optimization of localized molecular orbitals
,” J. Chem. Theory Comput.
9
, 5365
(2013
).93.
S. F.
Boys
, “Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another
,” Rev. Mod. Phys.
32
, 296
(1960
).94.
C.
Edmiston
and K.
Ruedenberg
, “Localized atomic and molecular orbitals
,” Rev. Mod. Phys.
35
, 457
(1963
).95.
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
(1989
).96.
S.
Lehtola
and H.
Jónsson
, “Pipek–Mezey orbital localization using various partial charge estimates
,” J. Chem. Theory Comput.
10
, 642
(2014
).97.
W. L.
Luken
and J. C.
Culberson
, “Mobility of the Fermi hole in a single-determinant wavefunction
,” Int. J. Quantum Chem.
22
, 265
(1982
).98.
W. L.
Luken
and D. N.
Beratan
, “Localized orbitals and the Fermi hole
,” Theor. Chim. Acta
61
, 265
(1982
).99.
W. L.
Luken
, “Properties of the Fermi hole in molecules
,” Croat. Chem. Acta
57
(6
), 1283
–1294
(1984
, available at https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=286249&lang=en.100.
W. L.
Luken
and J. C.
Culberson
, “Localized orbitals based on the Fermi hole
,” Theor. Chim. Acta
66
, 279
(1984
).101.
P. O.
Löwdin
, “On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals
,” J. Chem. Phys.
18
, 365
(1950
).102.
G. N.
Lewis
, “The atom and the molecule
,” J. Am. Chem. Soc.
38
, 762
(1916
).103.
J. W.
Linnett
, “Valence-bond structures: A new proposal
,” Nature
187
, 859
(1960
).104.
J. W.
Linnett
, “A modification of the Lewis–Langmuir octet rule
,” J. Am. Chem. Soc.
83
, 2643
(1961
).105.
106.
W. F.
Luder
, “Electronic structure of molecules (Linnett, JW)
,” J. Chem. Educ.
43
, 55
(1966
).107.
J.
Kraus
, “FLOSIC-DFT analysis of chemical bonding: Application to diatomic molecules
,” B.Sc. thesis, TU Bergakademie Freiberg
, 2017
.108.
A. H.
Larsen
, J. J.
Mortensen
, J.
Blomqvist
, I. E.
Castelli
, R.
Christensen
, M.
Dułak
, J.
Friis
, M. N.
Groves
, B.
Hammer
, C.
Hargus
et al., “The atomic simulation environment—A Python library for working with atoms
,” J. Phys.: Condens. Matter
29
, 273002
(2017
).109.
C. G.
Broyden
, “The convergence of a class of double-rank minimization algorithms 1. General considerations
,” IMA J. Appl. Math.
6
, 76
(1970
).110.
R.
Fletcher
, “A new approach to variable metric algorithms
,” Comput. J.
13
, 317
(1970
).111.
D.
Goldfarb
, “A family of variable-metric methods derived by variational means
,” Math. Comput.
24
, 23
(1970
).112.
D. F.
Shanno
, “Conditioning of quasi-Newton methods for function minimization
,” Math. Comput.
24
, 647
(1970
).113.
J.
Nocedal
, “Updating quasi-Newton matrices with limited storage
,” Math. Comput.
35
, 773
(1980
).114.
D. C.
Liu
and J.
Nocedal
, “On the limited memory BFGS method for large scale optimization
,” Math. Program.
45
, 503
(1989
).115.
R. H.
Byrd
, P.
Lu
, J.
Nocedal
, and C.
Zhu
, “A limited memory algorithm for bound constrained optimization
,” SIAM J. Sci. Comput.
16
, 1190
(1995
).116.
C.
Zhu
, R. H.
Byrd
, P.
Lu
, and J.
Nocedal
, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
,” ACM Trans. Math. Software
23
, 550
(1997
).117.
E.
Bitzek
, P.
Koskinen
, F.
Gähler
, M.
Moseler
, and P.
Gumbsch
, “Structural relaxation made simple
,” Phys. Rev. Lett.
97
, 170201
(2006
).118.
R. A.
Heaton
, J. G.
Harrison
, and C. C.
Lin
, “Self-interaction correction for energy band calculations: Application to LiCl
,” Solid State Commun.
41
, 827
(1982
).119.
S.
Kim
, J.
Chen
, T.
Cheng
, A.
Gindulyte
, J.
He
, S.
He
, Q.
Li
, B. A.
Shoemaker
, P. A.
Thiessen
, B.
Yu
et al., “PubChem 2019 update: Improved access to chemical data
,” Nucleic Acids Res.
47
, D1102
(2019
).120.
J. P.
Perdew
, A.
Ruzsinszky
, G. I.
Csonka
, O. A.
Vydrov
, G. E.
Scuseria
, L. A.
Constantin
, X.
Zhou
, and K.
Burke
, “Restoring the density-gradient expansion for exchange in solids and surfaces
,” Phys. Rev. Lett.
100
, 136406
(2008
); arXiv:0711.0156.121.
F.
Jensen
, “Polarization consistent basis sets: Principles
,” J. Chem. Phys.
115
, 9113
(2001
).122.
F.
Jensen
, “Polarization consistent basis sets. II. Estimating the Kohn–Sham basis set limit
,” J. Chem. Phys.
116
, 7372
(2002
).123.
C.
Shahi
, P.
Bhattarai
, K.
Wagle
, B.
Santra
, S.
Schwalbe
, T.
Hahn
, J.
Kortus
, K. A.
Jackson
, J. E.
Peralta
, K.
Trepte
, S.
Lehtola
, N. K.
Nepal
, H.
Myneni
, B.
Neupane
, S.
Adhikari
, A.
Ruzsinszky
, Y.
Yamamoto
, T.
Baruah
, R. R.
Zope
, and J. P.
Perdew
, “Stretched or noded orbital densities and self-interaction correction in density functional theory
,” J. Chem. Phys.
150
, 174102
(2019
).124.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, “Generalized gradient approximation made simple
,” Phys. Rev. Lett.
77
, 3865
(1996
).125.
E. Ö.
Jónsson
, S.
Lehtola
, and H.
Jónsson
, “Towards an optimal gradient-dependent energy functional of the PZ-SIC form
,” Proc. Comput. Sci.
51
, 1858
(2015
).126.
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
(1989
).127.
A.
Karton
, N.
Sylvetsky
, and J. M. L.
Martin
, “W4-17: A diverse and high-confidence dataset of atomization energies for benchmarking high-level electronic structure methods
,” J. Comput. Chem.
38
, 2063
(2017
).128.
E.
Cancès
, Y.
Maday
, and B.
Stamm
, “Domain decomposition for implicit solvation models
,” J. Chem. Phys.
139
, 054111
(2013
).129.
F.
Lipparini
, B.
Stamm
, E.
Cancès
, Y.
Maday
, and B.
Mennucci
, “Fast domain decomposition algorithm for continuum solvation models: Energy and first derivatives
,” J. Chem. Theory Comput.
9
, 3637
(2013
).130.
F.
Lipparini
, G.
Scalmani
, L.
Lagardère
, B.
Stamm
, E.
Cancès
, Y.
Maday
, J.-P.
Piquemal
, M. J.
Frisch
, and B.
Mennucci
, “Quantum, classical, and hybrid QM/MM calculations in solution: General implementation of the ddCOSMO linear scaling strategy
,” J. Chem. Phys.
141
, 184108
(2014
).131.
B.
Stamm
, E.
Cancès
, F.
Lipparini
, and Y.
Maday
, “A new discretization for the polarizable continuum model within the domain decomposition paradigm
,” J. Chem. Phys.
144
, 054101
(2016
).132.
F.
Lipparini
and B.
Mennucci
, “Perspective: Polarizable continuum models for quantum-mechanical descriptions
,” J. Chem. Phys.
144
, 160901
(2016
).133.
C.
Pisani
, R.
Dovesi
, and C.
Roetti
, in Hartree–Fock Ab Initio Treatment of Crystalline Systems
, Lecture Notes in Chemistry Vol. 48 (Springer Berlin Heidelberg
, Berlin, Heidelberg
, 1988
).134.
R. A.
Heaton
, J. G.
Harrison
, and C. C.
Lin
, “Self-interaction correction for density-functional theory of electronic energy bands of solids
,” Phys. Rev. B
28
, 5992
(1983
).135.
R. A.
Heaton
and C. C.
Lin
, “Self-interaction-correction theory for density functional calculations of electronic energy bands for the lithium chloride crystal
,” J. Phys. C: Solid State Phys.
17
, 1853
(1984
).136.
A.
Svane
and O.
Gunnarsson
, “Anti-ferromagnetic moment formation in the self-interaction-corrected density functional formalism
,” Europhys. Lett.
7
, 171
(1988
).137.
A.
Svane
and O.
Gunnarsson
, “Localization in the self-interaction-corrected density-functional formalism
,” Phys. Rev. B
37
, 9919
(1988
).138.
S. C.
Erwin
and C. C.
Lin
, “The self-interaction-corrected electronic band structure of six alkali fluoride and chloride crystals
,” J. Phys. C: Solid State Phys.
21
, 4285
(1988
).139.
Z.
Szotek
, W. M.
Temmerman
, and H.
Winter
, “On the self-interaction correction of localized bands: Application to rare gas solids
,” Solid State Commun.
74
, 1031
(1990
).140.
Z.
Szotek
, W. M.
Temmerman
, and H.
Winter
, “On the self-interaction correction of localized bands: Application to the 4p semi-core states in Y
,” Physica B
165-166
, 275
(1990
).141.
A.
Svane
and O.
Gunnarsson
, “Hydrogen solid in self-interaction-corrected local-spin-density approximation
,” Solid State Commun.
76
, 851
(1990
).142.
A.
Svane
and O.
Gunnarsson
, “Transition-metal oxides in the self-interaction-corrected density-functional formalism
,” Phys. Rev. Lett.
65
, 1148
(1990
).143.
A.
Svane
, “Electronic structure of La2CuO4 in the self-interaction-corrected density-functional formalism
,” Phys. Rev. Lett.
68
, 1900
(1992
).144.
M. M.
Rieger
and P.
Vogl
, “Self-interaction corrections in semiconductors
,” Phys. Rev. B
52
, 16567
(1995
).145.
D.
Vogel
, P.
Krüger
, and J.
Pollmann
, “Ab initio electronic-structure calculations for II-VI semiconductors using self-interaction-corrected pseudopotentials
,” Phys. Rev. B
52
, R14316
(1995
).146.
M.
Arai
and T.
Fujiwara
, “Electronic structures of transition-metal mono-oxides in the self-interaction-corrected local-spin-density approximation
,” Phys. Rev. B
51
, 1477
(1995
).147.
D.
Vogel
, P.
Krüger
, and J.
Pollmann
, “Self-interaction and relaxation-corrected pseudopotentials for II–VI semiconductors
,” Phys. Rev. B
54
, 5495
(1996
).148.
A.
Svane
, “Electronic structure of cerium in the self-interaction-corrected local-spin-density approximation
,” Phys. Rev. B
53
, 4275
(1996
).149.
A.
Svane
, W. M.
Temmerman
, Z.
Szotek
, J.
Laegsgaard
, and H.
Winter
, “Self-interaction-corrected local-spin-density calculations for rare earth materials
,” Int. J. Quantum Chem.
77
, 799
(2000
).150.
A.
Filippetti
and N. A.
Spaldin
, “Self-interaction-corrected pseudopotential scheme for magnetic and strongly-correlated systems
,” Phys. Rev. B
67
, 125109
(2003
); arXiv:cond-mat/0303042.151.
E.
Bylaska
, K.
Tsemekhman
, and H.
Jónsson
, “Self-consistent self-interaction corrected DFT: The method and applications to extended and confined systems
,” in APS Meeting Abstracts
, 2004
.152.
M.
Lüders
, A.
Ernst
, M.
Däne
, Z.
Szotek
, A.
Svane
, D.
Ködderitzsch
, W.
Hergert
, B. L.
Györffy
, and W. M.
Temmerman
, “Self-interaction correction in multiple scattering theory
,” Phys. Rev. B
71
, 205109
(2005
).153.
E. J.
Bylaska
, K.
Tsemekhman
, and F.
Gao
, “New development of self-interaction corrected DFT for extended systems applied to the calculation of native defects in 3C–SiC
,” Phys. Scr.
T124
, 86
(2006
).154.
B.
Hourahine
, S.
Sanna
, B.
Aradi
, C.
Köhler
, T.
Niehaus
, and T.
Frauenheim
, “Self-interaction and strong correlation in DFTB
,” J. Phys. Chem. A
111
, 5671
(2007
).155.
M.
Stengel
and N. A.
Spaldin
, “Self-interaction correction with Wannier functions
,” Phys. Rev. B
77
, 155106
(2008
).156.
M.
Däne
, M.
Lüders
, A.
Ernst
, D.
Ködderitzsch
, W. M.
Temmerman
, Z.
Szotek
, and W.
Hergert
, “Self-interaction correction in multiple scattering theory: Application to transition metal oxides
,” J. Phys.: Condens. Matter
21
, 045604
(2009
).157.
N. L.
Nguyen
, N.
Colonna
, A.
Ferretti
, and N.
Marzari
, “Koopmans-compliant spectral functionals for extended systems
,” Phys. Rev. X
8
, 021051
(2018
); arXiv:1708.08518.158.
N.
Marzari
and D.
Vanderbilt
, “Maximally localized generalized Wannier functions for composite energy bands
,” Phys. Rev. B
56
, 12847
(1997
); arXiv:cond-mat/9707145.159.
E. Ö.
Jónsson
, S.
Lehtola
, M.
Puska
, and H.
Jónsson
, “Theory and applications of generalized Pipek–Mezey Wannier functions
,” J. Chem. Theory Comput.
13
, 460
(2017
); arXiv:1608.06396.160.
J. T.
Su
and W. A.
Goddard
, “Excited electron dynamics modeling of warm dense matter
,” Phys. Rev. Lett.
99
, 185003
(2007
).161.
K.
Trepte
, S.
Schwalbe
, and G.
Seifert
, “Electronic and magnetic properties of DUT-8 (Ni)
,” Phys. Chem. Chem. Phys.
17
, 17122
(2015
).162.
S.
Schwalbe
, K.
Trepte
, G.
Seifert
, and J.
Kortus
, “Screening for high-spin metal organic frameworks (MOFs): Density functional theory study on DUT-8(M1, M2) (with Mi = V, …, Cu)
,” Phys. Chem. Chem. Phys.
18
, 8075
(2016
).163.
K.
Trepte
, J.
Schaber
, S.
Schwalbe
, F.
Drache
, I.
Senkovska
, S.
Kaskel
, J.
Kortus
, E.
Brunner
, and G.
Seifert
, “The origin of the measured chemical shift of 129Xe in UiO-66 and UiO-67 revealed by DFT investigations
,” Phys. Chem. Chem. Phys.
19
, 10020
(2017
).164.
K.
Trepte
, S.
Schwalbe
, J.
Schaber
, S.
Krause
, I.
Senkovska
, S.
Kaskel
, E.
Brunner
, J.
Kortus
, and G.
Seifert
, “Theoretical and experimental investigations of 129Xe NMR chemical shift isotherms in metal-organic frameworks
,” Phys. Chem. Chem. Phys.
20
, 25039
(2018
).165.
K.
Trepte
and S.
Schwalbe
, “Systematic analysis of porosities in metal-organic frameworks
,” ChemRxiv: 10060331 (2020
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
