The correlation consistent basis sets (cc-pVnZ with n = D, T, Q, 5) for the Ga–Br elements have been redesigned, tuning the sets for use for density functional approximations. Steps to redesign these basis sets for an improved correlation energy recovery and efficiency include truncation of higher angular momentum functions, recontraction of basis set coefficients, and reoptimization of basis set exponents. These redesigned basis sets are compared with conventional cc-pVnZ basis sets and other basis sets, which are, in principle, designed to achieve systematic improvement with respect to increasing basis set size. The convergence of atomic energies, bond lengths, bond dissociation energies, and enthalpies of formation to the Kohn–Sham limit is improved relative to other basis sets where convergence to the Kohn–Sham limit is typically not observed.
REFERENCES
1.
Basis Sets in Computational Chemistry
, 1st ed., edited by E.
Perit
(Springer International Publishing
, Cham
, 2021
).2.
T.
Helgaker
, W.
Klopper
, and D. P.
Tew
, “Quantitative quantum chemistry
,” Mol. Phys.
106
(16–18
), 2107
–2143
(2008
).3.
I. Y.
Zhang
and A.
Grüneis
, “Coupled cluster theory in materials science
,” Front. Mater.
6
, 123
(2019
).4.
M.
Mörchen
, L.
Freitag
, and M.
Reiher
, “Tailored coupled cluster theory in varying correlation regimes
,” J. Chem. Phys.
153
(24
), 244113
(2020
).5.
H. S.
Yu
, S. L.
Li
, and D. G.
Truhlar
, “Perspective: Kohn-Sham density functional theory descending a staircase
,” J. Chem. Phys.
145
, 130901
(2016
).6.
W.
Kohn
and L. J.
Sham
, “Self-consistent equations including exchange and correlation effects
,” Phys. Rev.
140
(4A
), A1133
–A1138
(1965
).7.
R.
Peverati
and D. G.
Truhlar
, “Quest for a universal density functional: The accuracy of density functionals across a broad spectrum of databases in chemistry and physics
,” Philos. Trans. R. Soc., A
372
(2011
), 20120476
(2014
).8.
A. D.
Becke
, “Perspective: Fifty years of density-functional theory in chemical physics
,” J. Chem. Phys.
140
(18
), 18A301
(2014
).9.
A.
Pribram-Jones
, D. A.
Gross
, and K.
Burke
, “DFT: A theory full of holes?
,” Annu. Rev. Phys. Chem.
66
, 283
–304
(2015
).10.
J. J.
Determan
, K.
Poole
, G.
Scalmani
, M. J.
Frisch
, B. G.
Janesko
, and A. K.
Wilson
, “Comparative study of nonhybrid density functional approximations for the prediction of 3d transition metal thermochemistry
,” J. Chem. Theory Comput.
13
(10
), 4907
–4913
(2017
).11.
B. G.
Janesko
, “Replacing hybrid density functional theory: Motivation and recent advances
,” Chem. Soc. Rev.
50
(15
), 8470
–8495
(2021
).12.
P.
Morgante
and R.
Peverati
, “The devil in the details: A tutorial review on some undervalued aspects of density functional theory calculations
,” Int. J. Quantum Chem.
120
(18
), e26332
(2020
).13.
T. H.
Dunning
, “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
,” J. Chem. Phys.
90
(2
), 1007
–1023
(1989
).14.
J. M. L.
Martin
, “A simple ‘range extender’ for basis set extrapolation methods for MP2 and coupled cluster correlation energies
,” AIP Conf. Proc.
2040
(1
), 020008
(2018
).15.
N. X.
Wang
and A. K.
Wilson
, “The behavior of density functionals with respect to basis set. I. The correlation consistent basis sets
,” J. Chem. Phys.
121
(16
), 7632
–7646
(2004
).16.
N. X.
Wang
and A. K.
Wilson
, “Density functional theory and the correlation consistent basis sets: The tight d effect on HSO and HOS
,” J. Phys. Chem. A
109
(32
), 7187
–7196
(2005
).17.
N. X.
Wang
and A. K.
Wilson
, “Effects of basis set choice upon the atomization energy of the second-row compounds SO2, CCl, and ClO2 for B3LYP and B3PW91
,” J. Phys. Chem. A
107
(34
), 6720
–6724
(2003
).18.
N. X.
Wang
and A. K.
Wilson
, “Behaviour of density functionals with respect to basis set: II. Polarization consistent basis sets
,” Mol. Phys.
103
(2–3
), 345
–358
(2005
).19.
N. X.
Wang
, K.
Venkatesh
, and A. K.
Wilson
, “Behavior of density functionals with respect to basis set. 3. Basis set superposition error
,” J. Phys. Chem. A
110
(2
), 779
–784
(2006
).20.
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
(9
), 2598
–2603
(2018
).21.
A.
Mahler
, J. J.
Determan
, and A. K.
Wilson
, “Correlation consistent basis sets designed for density functional theory: Second-row (Al-Ar)
,” J. Chem. Phys.
151
(6
), 064110
(2019
).22.
J. S.
Gibson
, “From development of semi-empirical atomistic potentials to applications of correlation consistent basis sets
,” Ph.D. dissertation (University of North Texas
, Denton, TX
, 2014
).23.
B. P.
Prascher
and A. K.
Wilson
, “The behaviour of density functionals with respect to basis set. V. Recontraction of correlation consistent basis sets
,” Mol. Phys.
105
(19–22
), 2899
–2917
(2007
).24.
B. P.
Prascher
, B. R.
Wilson
, and A. K.
Wilson
, “Behavior of density functionals with respect to basis set. VI. Truncation of the correlation consistent basis sets
,” J. Chem. Phys.
127
(12
), 124110
(2007
).25.
G. S.
Heverly-Coulson
and R. J.
Boyd
, “Systematic study of the performance of density functional theory methods for prediction of energies and geometries of organoselenium compounds
,” J. Phys. Chem. A
115
(18
), 4827
–4831
(2011
).26.
J. J.
Determan
and A. K.
Wilson
, “Bonding properties of selenium-carbon complexes: Computational modeling of H3CSeH, H2CSe, HOCSeH, H2CSeO, SeC and HCSeOH
,” Comput. Theor. Chem.
1017
, 41
–47
(2013
).27.
N.
Iqbal
, M.
Yaqoob
, M.
Javed
, M.
Abbasi
, J.
Iqbal
, and M. A.
Iqbal
, “Synthesis in combination with biological and computational evaluations of selenium-N-heterocyclic carbene compounds
,” Comput. Theor. Chem.
1197
, 113135
(2021
).28.
D. K.
Lewis
, A.
Ramasubramaniam
, and S.
Sharifzadeh
, “Tuned and screened range-separated hybrid density functional theory for describing electronic and optical properties of defective gallium nitride
,” Phys. Rev. Mater.
4
(6
), 063803
(2020
).29.
D. K.
Lewis
, M.
Matsubara
, E.
Bellotti
, and S.
Sharifzadeh
, “Quasiparticle and hybrid density functional methods in defect studies: An application to the nitrogen vacancy in GaN
,” Phys. Rev. B
96
(23
), 235203
(2017
).30.
X.
Ye
, L.
Yang
, Y.
Li
, J.
Huang
, L.
Zhou
, Q.
Lei
, W.
Fang
, and H.
Xie
, “Reaction mechanisms of a tungsten–germylyne complex with one or two molecules of alcohols and arylaldehydes: A DFT study
,” Eur. J. Inorg. Chem.
2014
(9), 1502
–1511
.31.
H.
Hashimoto
, T.
Fukuda
, H.
Tobita
, M.
Ray
, and S.
Sakaki
, “Formation of a germylyne complex: Dehydrogenation of a hydrido(hydrogermylene)tungsten complex with mesityl isocyanate
,” Angew. Chem., Int. Ed.
51
(12
), 2930
–2933
(2012
).32.
J. S.
Ritch
and B. J.
Charette
, “An experimental and computational comparison of phosphorus- and selenium-based ligands for catalysis
,” Can. J. Chem.
94
(4
), 386
–391
(2016
).33.
H.
Imoto
and K.
Naka
, “The dawn of functional organoarsenic chemistry
,” Chem. - Eur. J.
25
(8
), 1883
–1894
(2019
).34.
Z.
Chen
, “Recent development of biomimetic halogenation inspired by vanadium dependent haloperoxidase
,” Coord. Chem. Rev.
457
, 214404
(2022
).35.
S.
Nardis
, F.
Mandoj
, M.
Stefanelli
, and R.
Paolesse
, “Metal complexes of corrole
,” Coord. Chem. Rev.
388
, 360
–405
(2019
).36.
G.
Zichittella
, V.
Paunović
, and J.
Pérez-Ramírez
, Chimia (Aarau)
(Swiss Chemical Society
, 2019
), pp. 288
–293
.37.
J.
Witte
, J. B.
Neaton
, and M.
Head-Gordon
, “Push it to the limit: Characterizing the convergence of common sequences of basis sets for intermolecular interactions as described by density functional theory
,” J. Chem. Phys.
144
(19
), 194306
(2016
).38.
G. G.
Camiletti
, S. F.
Machado
, and F. E.
Jorge
, “Gaussian basis set of double zeta quality for atoms K through Kr: Application in DFT calculations of molecular properties
,” J. Comput. Chem.
29
(14
), 2434
–2444
(2008
).39.
G. A.
Ceolin
, R. C.
de Berrêdo
, and F. E.
Jorge
, “Gaussian basis sets of quadruple zeta quality for potassium through xenon: Application in CCSD(T) atomic and molecular property calculations
,” Theor. Chem. Acc.
132
(3
), 1339
(2013
).40.
S. F.
MacHado
, G. G.
Camiletti
, A. C.
Neto
, F. E.
Jorge
, and R. S.
Jorge
, “Gaussian basis set of triple zeta valence quality for the atoms from K to Kr: Application in DFT and CCSD(T) calculations of molecular properties
,” Mol. Phys.
107
(16
), 1713
–1727
(2009
).41.
F.
Weigend
and R.
Ahlrichs
, “Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
,” Phys. Chem. Chem. Phys.
7
(18
), 3297
–3305
(2005
).42.
F.
Jensen
, “Polarization consistent basis sets. VII. The elements K, Ca, Ga, Ge, As, Se, Br, and Kr
,” J. Chem. Phys.
136
(11
), 114107
(2012
).43.
M.
Sekiya
, T.
Noro
, Y.
Osanai
, and T.
Koga
, “Contracted polarization functions for the atoms Ca, Ga-Kr, Sr, and In-Xe
,” Theor. Chem. Acc.
106
(4
), 297
–300
(2001
).44.
M.
Müller
, A.
Hansen
, and S.
Grimme
, “ωB97X-3c: A composite range-separated hybrid DFT method with a molecule-optimized polarized valence double-ζ basis set
,” J. Chem. Phys.
158
(1
), 014103
(2023
).45.
J. G.
Brandenburg
, C.
Bannwarth
, A.
Hansen
, and S.
Grimme
, “B97-3c: A revised low-cost variant of the B97-D density functional method
,” J. Chem. Phys.
148
(6
), 064104
(2018
).46.
S.
Grimme
, J. G.
Brandenburg
, C.
Bannwarth
, and A.
Hansen
, “Consistent structures and interactions by density functional theory with small atomic orbital basis sets
,” J. Chem. Phys.
143
(5
), 054107
(2015
).47.
S.
Grimme
, A.
Hansen
, S.
Ehlert
, and J. M.
Mewes
, “r2SCAN-3c: A ‘Swiss army knife’ composite electronic-structure method
,” J. Chem. Phys.
154
(6
), 064103
(2021
).48.
S. M.
Tekarli
, M. L.
Drummond
, T. G.
Williams
, T. R.
Cundari
, and A. K.
Wilson
, “Performance of density functional theory for 3d transition metal-containing complexes: Utilization of the correlation consistent basis sets
,” J. Phys. Chem. A
113
(30
), 8607
–8614
(2009
).49.
W.
Jiang
, M. L.
Laury
, M.
Powell
, and A. K.
Wilson
, “Comparative study of single and double hybrid density functionals for the prediction of 3d transition metal thermochemistry
,” J. Chem. Theory Comput.
8
(11
), 4102
–4111
(2012
).50.
J. J.
Determan
, S.
Moncho
, E. N.
Brothers
, and B. G.
Janesko
, “Simulating gold’s structure-dependent reactivity: Nonlocal density functional theory studies of hydrogen activation by gold clusters, nanowires, and surfaces
,” J. Phys. Chem. C
118
(29
), 15693
–15704
(2014
).51.
A. K.
Wilson
, D. E.
Woon
, K. A.
Peterson
, and T. H.
Dunning
, “Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton
,” J. Chem. Phys.
110
(16
), 7667
–7676
(1999
).52.
A. D.
Becke
, “Density-functional exchange-energy approximation with correct asymptotic behavior
,” Phys. Rev. A
38
(6
), 3098
–3100
(1988
).53.
C.
Lee
, W.
Yang
, and R. G.
Parr
, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
,” Phys. Rev. B
37
(2
), 785
–789
(1988
).54.
A.
Becke
, “Density-functional thermochemistry. III. The role of exact exchange
,” J. Chem. Phys.
98
(7
), 5648
–5652
(1993
).55.
J.
Perdew
, K.
Burke
, and M.
Ernzerhof
, “Generalized gradient approximation made simple
,” Phys. Rev. Lett.
77
(18
), 3865
–3868
(1996
).56.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, “Errata: Generalized gradient approximation made simple [Phys. Rev. Lett. 77, 3865 (1996)]
,” Phys. Rev. Lett.
78
, 1396
(1997
).57.
C.
Adamo
and V.
Barone
, “Toward reliable density functional methods without adjustable parameters: The PBE0 model
,” J. Chem. Phys.
110
(13
), 6158
–6170
(1999
).58.
J.
Tao
, J. P.
Perdew
, V. N.
Staroverov
, and G. E.
Scuseria
, “Climbing the density functional ladder: Nonempirical meta-generalized gradient approximation designed for molecules and solids
,” Phys. Rev. Lett.
91
, 146401
(2003
).59.
V. N.
Staroverov
, G. E.
Scuseria
, J.
Tao
, and J. P.
Perdew
, “Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes
,” J. Chem. Phys.
119
(23
), 12129
(2003
).60.
H. J.
Werner
, P. J.
Knowles
, F. R.
Manby
, J. A.
Black
, K.
Doll
, A.
Heßelmann
, D.
Kats
, A.
Köhn
, T.
Korona
, D. A.
Kreplin
, Q.
Ma
, T. F.
Miller
, A.
Mitrushchenkov
, K. A.
Peterson
, I.
Polyak
, G.
Rauhut
, and M.
Sibaev
, “The Molpro quantum chemistry package
,” J. Chem. Phys.
152
(14
), 144107
(2020
).61.
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
, and H. P.
Hratchian
, Gaussian 16, Revision C.01
, Gaussian, Inc.
, Wallingford, CT
, 2016
.62.
R. C.
Raffenetti
, “General contraction of Gaussian atomic orbitals: Core, valence, polarization, and diffuse basis sets; Molecular integral evaluation
,” J. Chem. Phys.
58
(10
), 4452
(1973
).63.
A.
Halkier
, T.
Helgaker
, P.
Jørgensen
, W.
Klopper
, H.
Koch
, J.
Olsen
, and A. K.
Wilson
, “Basis-set convergence in correlated calculations on Ne, N2, and H2O
,” Chem. Phys. Lett.
286
, 243
–252
(1998
).64.
A.
Karton
and J. M. L.
Martin
, “Comment on: ‘Estimating the Hartree-Fock limit from finite basis set calculations’ [Jensen F (2005) Theor Chem Acc 113:267]
,” Theor. Chem. Acc.
115
(4
), 330
–333
(2006
).65.
S. F.
Boys
and F.
Bernardi
, “The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors
,” Mol. Phys.
19
(4
), 553
–566
(1970
).66.
L. A.
Curtiss
, P. C.
Redfern
, and K.
Raghavachari
, “Assessment of Gaussian-3 and density-functional theories on the G3/05 test set of experimental energies
,” J. Chem. Phys.
123
(12
), 124107
(2005
).67.
P.
Krauss
, “Extrapolating DFT toward the complete basis set limit: Lessons from the PBE family of functionals
,” J. Chem. Theory Comput.
17
(9
), 5651
–5660
(2021
).68.
NIST Standard Simultation Website
, NIST Standard Database
, edited by V. K.
Shen
, D. W.
Siderius
, W. P.
Krekelberg
, and H. W.
Hatch
(National Institute of Standards and Technology
, Gaithersburg, MD
, 2017
).69.
R.
Weber
, B.
Hovda
, G.
Schoendorff
, and A. K.
Wilson
, “Behavior of the Sapporo-nZP-2012 basis set family
,” Chem. Phys. Lett.
637
, 120
–126
(2015
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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