Quantum chemical calculations using density functional theory are reported for the diatomic molecules LiF, BeO, and BN. The nature of the interatomic interactions is analyzed with the Energy Decomposition Analysis–Natural Orbitals of Chemical Valence (EDA-NOCV) method, and the results are critically discussed and compared with data from Quantum Theory of Atoms in Molecules, Natural Bond Orbital, and Mayer approaches. Polar bonds, like nonpolar bonds, are caused by the interference of wave functions, which lead to an accumulation of electronic charge in the bonding region. Polar bonds generally have a larger percentage of electrostatic bonding to the total attraction, but nonpolar bonds may also possess large contributions from Coulombic interaction. The term “ionic contribution” refers to valence bond structures and is misleading because it refers to separate fragments with negligible overlap that occur only in the solid state and in solution, not in a molecule. The EDA-NOCV method gives detailed information about the individual orbital contributions, which can be identified by visual inspection of the associated deformation densities. It is very important, particularly for polar bonds to distinguish between the interatomic interactions of the final dissociation products after bond rupture and the interactions between the fragments in the eventually formed bond. The bond formation in LiF is dominated by orbital interactions (90%) between Li and F yielding a single bond, but the eventually formed bond comes mainly from the electrostatic attraction between Li+ and F−, where the minor orbital interactions (10%) have equally strong σ and π components. The symmetry allowed bond formation of BeO between Be in the 1S ground state and O in the excited 1D state is dominated (90%) by a strong dative Be → O σ bond with negligible π interactions. The final bond situation in BeO is best described by the interaction between Be+ and O−, where the Coulombic forces provide 60% of the attraction and the orbital interactions give equally strong σ and π bonds. The chemical bond in BN is analyzed in the X3Π ground state and the a1Σ+ excited state. Both states have triple bonds with strong π bonds, which are in the a1Σ+ state even stronger than the σ bond.
REFERENCES
1.
W.
Heitler
and F.
London
, Z. Phys.
44
, 455
(1927
).2.
G. N.
Lewis
, J. Am. Chem. Soc.
38
, 762
(1916
).3.
W.
Heisenberg
, Z. Phys.
33
, 879
(1925
).4.
E.
Schrödinger
, Ann. Phys.
384
, 361
(1926
).5.
(a)
L.
Zhao
, W. H. E.
Schwarz
, and G.
Frenking
, Nat. Rev. Chem.
3
, 35
(2019
);(b)
L.
Zhao
, S.
Pan
, N.
Holzmann
, P.
Schwerdtfeger
, and G.
Frenking
, Chem. Rev.
119
, 8781
(2019
).
[PubMed]
6.
(a)
K.
Ruedenberg
, Rev. Mod. Phys.
34
, 326
(1962
);(d)
T.
Bitter
, S. G.
Wang
, K.
Ruedenberg
, and W. H. E.
Schwarz
, Theor. Chem. Acc.
127
, 237
(2010
);(f)
M. W.
Schmidt
, J.
Ivanic
, and K.
Ruedenberg
, in The Chemical Bond. 1. Fundamental Aspects of Chemical Bonding
, edited by G.
Frenking
andS.
Shaik
(Wiley-VCH
, Weinheim
, 2014
), pp. 1
–67
;7.
H.
Hellmann
, Einführung in die Quantenchemie (Introduction to Quantum Chemistry)
(Deuticke
, Leipzig and Wien
, 1937
).8.
See the discussion in:
W.
Kutzelnigg
, Angew. Chem., Int. Ed.
12
, 546
(1973
).9.
(a)
A. E.
Reed
, L. A.
Curtiss
, and F.
Weinhold
, Chem. Rev.
88
, 899
(1988
);(b)
C. R.
Landis
and F.
Weinhold
, “The NBO view of chemical bonding
,” in The Chemical Bond: Fundamental Aspects of Chemical Bonding
, edited by G.
Frenking
andS.
Shaik
(Wiley-VCH
, Weinheim
, 2014
), pp. 91
–120
;(c)
F.
Weinhold
and C. R.
Landis
, Discovering Chemistry With Natural Bond Orbitals
(Wiley
, NJ
, 2012
);(d)
C. R.
Landis
and F.
Weinhold
, Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective
(Cambridge University Press
, Cambridge
, 2005
).10.
R. F. W.
Bader
, Atoms in Molecules: A Quantum Theory
(Oxford University Press
, Oxford
, 1990
).11.
(b)
A.
Martín Pendás
,E.
Francisco
, andM. A.
Blanco
, J. Chem. Theory Comput.
1
, 1096
(2005
);
[PubMed]
(d)
M.
Menéndez
, R.
Álvarez Boto
, E.
Francisco
, and Á.
Martín Pendás
, J. Comput. Chem.
36
, 833
(2015
).
[PubMed]
12.
A. D.
Becke
and K. E.
Edgecombe
, J. Chem. Phys.
92
, 5397
(1990
).13.
R. G.
Parr
, R. A.
Donnelly
, M.
Levy
, and W. E.
Palke
, J. Chem. Phys.
68
, 3801
(1978
).14.
For example, the NBO method has been modified several times since its introduction in the 1980s, and results can change significantly when different versions are used. This is because various parameters have been changed over time.
15.
(a)
K.
Fukui
, Acc. Chem. Res.
4
, 57
(1971
);(b)
K.
Fukui
Theory of Orientation and Stereoselection
(Springer Verlag
, Berlin
, 1975
).16.
R. B.
Woodward
and R.
Hoffmann
, The Conservation of Orbital Symmetry
(Verlag Chemie
, Weinheim
, 1970
).17.
K.
Kitaura
and K.
Morokuma
, Int. J. Quantum Chem.
10
, 325
(1976
).18.
T.
Ziegler
and A.
Rauk
, Theor. Chim. Acta
46
, 1
(1977
).19.
(a)
D. S.
Levine
, P. R.
Horn
, Y.
Mao
, and M.
Head-Gordon
, J. Chem. Theory Comput.
12
, 4812
(2016
);
[PubMed]
20.
(b)
Z.
Tang
, Y.
Song
, S.
Zhang
, W.
Wang
, Y.
Xu
, D.
Wu
, W.
Wu
, and P.
Su
, J. Comput. Chem.
42
, 2341
(2021
).
[PubMed]
21.
J.
Andrés
, P. W.
Ayers
, R. A.
Boto
, R.
Carbó‐Dorca
, H.
Chermette
, J.
Cioslowski
, J.
Contreras‐García
, D. L.
Cooper
, G.
Frenking
, C.
Gatti
, F.
Heidar‐Zadeh
, L.
Joubert
, Á.
Martín Pendás
, E.
Matito
, I.
Mayer
, A. J.
Misquitta
, Y.
Mo
, J.
Pilmé
, P. L. A.
Popelier
, M.
Rahm
, E.
Ramos‐Cordoba
, P.
Salvador
, W. H. E.
Schwarz
, S.
Shahbazian
, B.
Silvi
, M.
Solà
, K.
Szalewicz
, V.
Tognetti
, F.
Weinhold
, and É.-L.
Zins
, J. Comput. Chem.
40
, 2248
(2019
).22.
P.
Jerabek
, P.
Schwerdtfeger
, and G.
Frenking
, J. Comput. Chem.
40
, 247
(2019
).23.
(a)
Q.
Zhang
, W.-L.
Li
, C.-Q.
Xu
, M.
Chen
, M.
Zhou
, J.
Li
, D. M.
Andrada
, and G.
Frenking
, Angew. Chem., Int. Ed.
54
, 11078
(2015
);(b)
D. M.
Andrada
and G.
Frenking
, Angew. Chem., Int. Ed.
54
, 12319
(2015
);(c)
D. S.
Weinberger
, N. A.
Sk
, K. C.
Mondal
, M.
Melaimi
, G.
Bertrand
, A. C.
Stückl
, H. W.
Roesky
, B.
Dittrich
, S.
Demeshko
, B.
Schwederski
, W.
Kaim
, P.
Jerabek
, and G.
Frenking
, J. Am. Chem. Soc.
136
, 6235
(2014
);
[PubMed]
(d)
L. T.
Scharf
, M.
Andrada
, G.
Frenking
, and V. H.
Gessner
, Chem. - Eur. J.
23
, 442
(2017
);(e)
M.
Hermann
and G.
Frenking
, Chem. - Eur. J.
23
, 3347
(2017
);(f)
D. C.
Georgiou
, L.
Zhao
, D. J. D.
Wilson
, G.
Frenking
, and J. L.
Dutton
, Chem. - Eur. J.
23
, 2926
(2017
);(g)
D. M.
Andrada
, J. L.
Casals-Sainz
, Á.
Martín Pendás
, and G.
Frenking
, Chem. - Eur. J.
24
, 9083
(2018
);(h)
R.
Saha
, S.
Pan
, G.
Merino
, and P. K.
Chattaraj
, Angew. Chem., Int. Ed.
58
, 8372
(2019
);(k)
Z.
Li
, X.
Chen
, D. M.
Andrada
, G.
Frenking
, Z.
Benkö
, Y.
Li
, J. R.
Harmer
, C.-Y.
Su
, and H.
Grützmacher
, Angew. Chem., Int. Ed.
56
, 5744
(2017
);(l)
Z.
Wu
, J.
Xu
, L.
Sokolenko
, Y. L.
Yagupolskii
, R.
Feng
, Q.
Liu
, Y.
Lu
, L.
Zhao
, I.
Fernández
, G.
Frenking
, T.
Trabelsi
, J. S.
Francisco
, and X.
Zeng
, Chem. - Eur. J.
23
, 16566
(2017
);24.
(a)
F. M.
Bickelhaupt
, M.
Solà
, and C.
Fonseca Guerra
, J. Chem. Theory Comput.
2
, 965
(2006
);
[PubMed]
25.
(a)
M.
Mitoraj
and A.
Michalak
, Organometallics
26
, 6576
(2007
);26.
27.
(a)
I.
Cukrowski
, Wiley Interdiscip. Rev.: Comput. Mol. Sci.
12
, e1579
(2022
);(b)
F.
Fantuzzi
, D. W. O.
de Sousa
, and M. A. C.
Nascimento
, ChemistrySelect
2
, 604
(2017
).28.
(a)
A. D.
Becke
, Phys. Rev. A
38
, 3098
(1988
);(b)
J. P.
Perdew
, Phys. Rev. B
33
, 8822
(1986
).29.
S.
Grimme
, J.
Antony
, S.
Ehrlich
, and H.
Krieg
, J. Chem. Phys.
132
, 154104
(2010
).30.
F.
Weigend
and R.
Ahlrichs
, Phys. Chem. Chem. Phys.
7
, 3297
(2005
).31.
Gaussian 16, Revision A.03,
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.
Montgomery
, Jr., 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, Inc.
, Wallingford, CT
, 2016
.32.
T.
Lu
and F.
Chen
, J. Comput. Chem.
33
, 580
(2012
).33.
E.
van Lenthe
and E. J.
Baerends
, J. Comput. Chem.
24
, 1142
(2003
).34.
(a)ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, http://www.scm.com;
(b)
G.
te Velde
, F. M.
Bickelhaupt
, E. J.
Baerends
, C.
Fonseca Guerra
, S. J. A.
Van Gisbergen
, J. G.
Snijders
, and T.
Ziegler
, J. Comput. Chem.
22
, 931
(2001
).35.
The name quasiclassical has been suggested by Ruedenberg, Ref. 6a.
36.
F. M.
Bickelhaupt
, N. M. M.
Nibbering
, E. M.
Van Wezenbeek
, and E. J.
Baerends
, J. Phys. Chem.
96
, 4864
(1992
).37.
J. P.
Wagner
and P. R.
Schreiner
, Angew. Chem., Int. Ed.
54
, 12274
(2015
).38.
For a discussion of bond strength see:
L.
Zhao
, M.
Zhi
, and G.
Frenking
, Int. J. Quantum Chem.
122
, e26773
(2022
).39.
L.
Pecher
and R.
Tonner
, Wiley Interdiscip. Rev.: Comput. Mol. Sci.
9
, e1401
(2019
).40.
(a)
L.
Zhao
, M.
Hermann
, W. H. E.
Schwarz
, and G.
Frenking
, Nat. Rev. Chem.
3
, 48
(2019
);(b)
L.
Zhao
, M.
von Hopffgarten
, D. M.
Andrade
, and G.
Frenking
, Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
, e1345
(2018
);(c)
G.
Frenking
and F.
Matthias Bickelhaupt
, in The Chemical Bond: Fundamental Aspects of Chemical Bonding
, edited by G.
Frenking
andS.
Shaik
(Wiley-VCH
, Weinheim
, 2014
), pp. 121
–158
;(d)
G.
Frenking
, R.
Tonner
, S.
Klein
, N.
Takagi
, T.
Shimizu
, A.
Krapp
, K. K.
Pandey
, and P.
Parameswaran
, Chem. Soc. Rev.
43
, 5106
(2014
);
[PubMed]
(e)
G.
Frenking
, M.
Hermann
, D. M.
Andrada
, and N.
Holzmann
, Chem. Soc. Rev.
45
, 1129
(2016
).
[PubMed]
41.
K. P.
Huber
and G.
Herzberg
, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules
(Van Nostrand-Reinhold
, New York
, 1979
).42.
A. F.
Wells
, Structural Inorganic Chemistry
, 5th ed. (Oxford Science Publications
, 1984
).43.
G.
Frenking
, C.
Loschen
, A.
Krapp
, S.
Fau
, and S. H.
Strauss
, J. Comput. Chem.
28
, 117
(2007
).44.
(a)
S.
Shaik
, D.
Danovich
, W.
Wu
, P.
Su
, H. S.
Rzepa
, and P. C.
Hiberty
, Nat. Chem.
4
, 195
(2012
);
[PubMed]
(b)
D.
Danovich
, P. C.
Hiberty
, W.
Wu
, H. S.
Rzepa
, and S.
Shaik
, Chem. - Eur. J.
20
, 6220
(2014
);(c)
S.
Shaik
, D.
Danovich
, B.
Braida
, and P. C.
Hiberty
, Chem. - Eur. J.
22
, 4116
(2016
);(d)
P. B.
Karadakov
and J.
Kirsopp
, Chem. - Eur. J.
23
, 12949
(2017
), and further references therein;(e)For an opposing view see:
M.
Hermann
and G.
Frenking
, “The chemical bond in C2
,” Chem. - Eur. J.
22
, 4100
(2016
);(f)
M.
Piris
, X.
Lopez
, and J. M.
Ugalde
, Chem. - Eur. J.
22
, 4109
(2016
);(g)
D. L.
Cooper
, R.
Ponec
, and M.
Kohout
, Mol. Phys.
114
, 1270
(2016
);(h)
W.
Zou
and D.
Cremer
, Chem. - Eur. J.
22
, 4087
(2016
);45.
M.
Lorenz
, J.
Agreiter
, A. M.
Smith
, and V. E.
Bondybey
, J. Chem. Phys.
104
, 3143
(1996
).46.
(a)
J. M. L.
Martin
, T. J.
Lee
, G. E.
Scuseria
, and P. R.
Taylor
, J. Chem. Phys.
97
, 6549
(1992
);(b)
K. A.
Peterson
, J. Chem. Phys.
102
, 262
(1995
).47.
H.
Bredohl
, I.
Dubois
, Y.
Houbrechts
, and P.
Nzohabonayo
, J. Mol. Spectrosc.
112
, 430
(1985
).48.
C.
Mohapatra
, S.
Kundu
, A. N.
Paesch
, R.
Herbst-Irmer
, D.
Stalke
, D. M.
Andrada
, G.
Frenking
, and H. W.
Roesky
, J. Am. Chem. Soc.
138
, 10429
(2016
).49.
A.
Krapp
, F. M.
Bickelhaupt
, and G.
Frenking
, Chem. - Eur. J.
12
, 9196
(2006
).50.
(a)
I.
Mayer
, Int. J. Quantum Chem.
26
, 151
(1984
);(b)
I.
Mayer
Chem. Phys. Lett.
97
, 270
(1983
).51.
(a)
O.
Mó
, M.
Yáñez
, A.
Martín Pendás
, J. E.
Del Bene
, I.
Alkorta
, and J.
Elguero
, Phys. Chem. Chem. Phys.
9
, 3970
(2007
);
[PubMed]
(b)
A.
Martín Pendás
, M. A.
Blanco
, and E.
Francisco
, Chem. Phys. Lett.
417
, 16
(2006
);(c)
J.
Poater
, M.
Solà
, and F. M.
Bickelhaupt
, Chem. - Eur. J.
12
, 2902
(2006
);(d)
A.
Kovács
, C.
Esterhuysen
, and G.
Frenking
, Chem. - Eur. J.
11
, 1813
(2005
);(f)
A.
Haaland
, D. J.
Shorokhov
, and N. V.
Tverdova
, Chem. - Eur. J.
10
, 4416
(2004
);(g)
S.-G.
Wang
, Y.-X.
Qiu
, and W. H. E.
Schwarz
, Chem. - Eur. J.
16
, 9107
(2010
).52.
For a lucid discussion on the topic of electron density characteristics at bond critical points see:
B.
Bankiewicz
, P.
Matczak
, and M.
Palusiak
, J. Phys. Chem. A
116
, 452
(2012
).53.
D.
Cremer
and E.
Kraka
, Angew. Chem., Int. Ed.
23
, 627
(1984
).54.
K. B.
Wiberg
, Tetrahedron
24
, 1083
(1968
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
