In this study, we perform accurate calculations via multireference configuration interaction and coupled cluster methodologies on the dimolybdenum molecule in conjunction with complete series of correlation and weighted core correlation consistent basis sets up to quintuple size. The bonding, the dissociation energies, and the spectroscopic parameters of the seven states that correlate with the ground state products are calculated. The ground state has a sextuple chemical bond, and each of the calculated excited states has one less bond than the previous state. The calculated values for the ground X1Σg+ state of Mo2 have been extrapolated to the complete basis set limits. Our final values, re = 1.9324 Å and De (D0) = 4.502 ± 0.007(4.471 ± 0.009) eV, are in excellent agreement with the experimental values of re = 1.929, 1.938(9) Å and D0 = 4.476(10) eV. Mo2 in the Σg+13 state is a weakly bound dimer, forming 5s⋯5pz bonds, with De = 0.120 eV at re = 3.53 Å. All calculated excited states (except Σg+13) have a highly multireference character (C0 = 0.25–0.55). The ordering of the molecular bonding orbitals changes as the spin is increased from quintet to septet state resulting in a change in energy separation ΔS,S−1 of the calculated states. The quite low bond dissociation energy of the ground state is due to the splitting of the molecular bonding orbitals in two groups differing in energy by ∼3 eV. Finally, the bond breaking of Mo2, as the multiplicity of spin is increased, is analyzed in parallel with the Mo–Mo bond breaking in a series of Mo2Clx complexes when x is increased. Physical insight into the nature of the sextuple bond and its low dissociation energy is provided.

1.
G. N.
Lewis
,
J. Am. Chem. Soc.
38
,
762
(
1916
).
2.
C. A.
Coulson
,
Rev. Mod. Phys.
32
,
170
177
(
1960
).
3.
L.
Pauling
,
The Nature of the Chemical Bond
, 3rd ed. (
Cornell University Press
,
Ithaca, NY
,
1960
), Chap. 1.
4.
G.
Frenking
and
N.
Fröhlich
,
Chem. Rev.
100
,
717
774
(
2000
).
5.
L.
Zhao
,
S.
Pan
,
N.
Holzmann
,
P.
Schwerdtfeger
, and
G.
Frenking
,
Chem. Rev.
119
,
8781
8845
(
2019
).
6.
M. W.
Schmidt
,
J.
Ivanic
, and
K.
Ruedenberg
, “
The physical origin of covalent bonding
,” in
The Chemical Bond: Fundamental Aspects of Chemical Bonding
, edited by
G.
Frenking
and
S.
Shaik
(
Wiley-VCH Verlag GmbH & Co. KGaA
,
2014
), Chap. 1, pp.
1
67
.
7.
A. C.
West
,
M. W.
Schmidt
,
M. S.
Gordon
, and
K.
Ruedenberg
,
J. Phys. Chem. A
119
,
10376
10389
(
2015
).
8.
M. W.
Schmidt
,
J.
Ivanic
, and
K.
Ruedenberg
,
J. Chem. Phys.
140
,
204104
(
2014
).
9.
K.
Ruedenberg
,
Rev. Mod. Phys.
34
,
326
(
1962
).
10.
C.
Edmiston
and
K.
Ruedenberg
,
J. Phys. Chem.
68
,
1628
(
1964
).
11.
R. R.
Rue
and
K.
Ruedenberg
,
J. Phys. Chem.
68
,
1676
(
1964
).
12.
M. J.
Feinberg
,
K.
Ruedenberg
, and
E. L.
Mehler
,
Adv. Quantum Chem.
5
,
27
(
1970
).
13.
M. J.
Feinberg
and
K.
Ruedenberg
,
J. Chem. Phys.
54
, 1495 (
1971
);
M. J.
Feinberg
and
K.
Ruedenberg
J. Chem. Phys.
55
, 5804 (
1971
).
14.
W. H. E.
Schwarz
,
P.
Valtazanos
, and
K.
Ruedenberg
,
Theor. Chim. Acta
68
,
471
506
(
1985
).
15.
W. H. E.
Schwarz
,
K.
Ruedenberg
,
L.
Mensching
,
L. L.
Miller
,
P.
Valtazanos
, and
W.
von Niessen
,
Angew. Chem., Int. Ed.
28
,
597
600
(
1989
).
16.
K.
Ruedenberg
and
M. W.
Schmidt
,
J. Comput. Chem.
28
,
391
410
(
2006
).
17.
T.
Bitter
,
K.
Ruedenberg
, and
W. H. E.
Schwarz
,
J. Comput. Chem.
28
,
411
422
(
2006
).
18.
K.
Ruedenberg
and
M. W.
Schmidt
,
J. Phys. Chem. A
113
,
1954
1968
(
2009
).
19.
T.
Bitter
,
S. G.
Wang
,
K.
Ruedenberg
, and
W. H. E.
Schwarz
,
Theor. Chem. Acc.
127
,
237
257
(
2010
).
20.
G. B.
Bacskay
,
S.
Nordholm
, and
K.
Ruedenberg
,
J. Phys. Chem. A
122
,
7880
7893
(
2018
).
21.
G.
Schoendorff
,
M. W.
Schmidt
,
K.
Ruedenberg
, and
M. S.
Gordon
,
J. Phys. Chem. A
123
,
5249
5256
(
2019
).
22.
G.
Schoendorff
,
K.
Ruedenberg
, and
M. S.
Gordon
,
J. Phys. Chem. A
125
,
4836
4846
(
2021
).
23.
H. M.
Leicester
, “
Alexander Mikhaĭlovich Butlerov
,”
J. Chem. Educ.
17
,
203
209
(
1940
).
24.
F. A.
Cotton
and
C. B.
Harris
,
Inorg. Chem.
4
,
330
(
1965
);
L.
Gagliardi
and
B. O.
Roos
,
Inorg. Chem.
42
,
1599
1603
(
2003
).
[PubMed]
25.
S.
Shaik
,
D.
Danovich
,
W.
Wu
,
P.
Su
,
H. S.
Rzepa
, and
P. C.
Hiberty
,
Nat. Chem.
4
,
195
200
(
2012
).
26.
J.
Grunenberg
,
Nat. Chem.
4
,
154
155
(
2012
).
27.
S.
Shaik
,
H. S.
Rzepa
, and
R.
Hoffmann
,
Angew. Chem., Int. Ed.
52
,
3020
3033
(
2013
).
28.
D.
Danovich
,
P. C.
Hiberty
,
W.
Wu
,
H. S.
Rzepa
, and
S.
Shaik
,
Chem. Eur. J.
20
,
6220
6232
(
2014
).
29.
L. T.
Xu
and
T. H.
Dunning
,
J. Chem. Theory Comput.
10
,
195
201
(
2014
).
30.
M.
Hermann
and
G.
Frenking
,
Chem. Eur. J.
22
,
4100
4108
(
2016
).
31.
S.
Shaik
,
D.
Danovich
,
B.
Braida
, and
P. C.
Hiberty
,
Chem. Eur. J.
22
,
4116
4128
(
2016
).
32.
D. W. O.
de Sousa
and
M. A. C.
Nascimento
,
J. Chem. Theory Comput.
12
,
2234
2241
(
2016
).
33.
L. F.
Cheung
,
T.-T.
Chen
,
G. S.
Kocheril
,
W.-J.
Chen
,
J.
Czekner
, and
L.-S.
Wang
,
J. Phys. Chem. Lett.
11
,
659
663
(
2020
).
34.
D.
Tzeli
and
I.
Karapetsas
,
J. Phys. Chem. A
124
,
6667
(
2020
).
35.
D.
Tzeli
,
J. Comput. Chem.
42
,
1126
1137
(
2021
).
36.
T.
Nguyen
,
A. D.
Sutton
,
M.
Brynda
,
J. C.
Fettinger
,
G. J.
Long
, and
P. P.
Power
,
Science
310
,
844
847
(
2005
).
37.
B. O.
Roos
,
A. C.
Borin
, and
L.
Gagliardi
,
Angew. Chem., Int. Ed.
46
,
1469
1472
(
2007
).
38.
D. J.
Matthew
,
S. H.
Oh
,
A.
Sevy
, and
M. D.
Morse
,
J. Chem. Phys.
144
,
214306
(
2016
).
39.
G. A.
Ozin
and
W.
Klotzbücher
,
J. Mol. Catal.
3
,
195
206
(
1977
).
40.
W.
Klotzbücher
,
G. A.
Ozin
,
J. G.
Norman
, Jr.
, and
H. J.
Kolari
,
Inorg. Chem.
16
,
2871
(
1977
).
41.
S. K.
Gupta
,
R. M.
Atkins
, and
K. A.
Gingerich
,
Inorg. Chem.
17
,
3211
(
1978
).
42.
Y. M.
Efremov
,
A. N.
Samoilova
,
V. B.
Kozhukhovsky
, and
L. V.
Gurvich
,
J. Mol. Spectrosc.
73
,
430
440
(
1978
).
43.
M. J.
Pellin
,
T.
Foosnaes
, and
D. M.
Gruen
,
J. Chem. Phys.
74
,
5547
(
1981
).
44.
J. B.
Hopkins
,
P. R. R.
Langridge‐Smith
,
M. D.
Morse
, and
R. E.
Smalley
,
J. Chem. Phys.
78
,
1627
(
1983
).
45.
B.
Simard
,
M.-A.
Lebeault-Dorget
,
A.
Marijnissen
, and
J. J.
ter Meulen
,
J. Chem. Phys.
108
,
9668
(
1998
).
46.
D.
Kraus
,
M.
Lorenz
, and
V. E.
Bondybey
,
PhysChemComm
4
,
4
48
(
2001
).
47.
L. A.
Heimbrook
,
M.
Rasanen
, and
V. E.
Bondybey
,
J. Phys. Chem.
91
,
2468
2474
(
1987
).
48.
C.
Wood
,
M.
Doran
,
I. H.
Hillier
, and
M. F.
Guest
,
Faraday Symp. Chem. Soc.
14
,
159
169
(
1980
).
49.
J. G.
Norman
and
P. B.
Ryan
,
J. Comput. Chem.
1
,
59
63
(
1980
).
50.
B. E.
Burstean
and
F. A.
Cotton
,
Faraday Symp. Chem. Soc.
14
,
180
193
(
1980
).
51.
M. M.
Goodgame
and
W. A.
Goddard
 III
,
Phys. Rev. Lett.
48
,
135
(
1982
).
52.
P. M.
Atha
,
I. H.
Hillier
, and
M. F.
Guest
,
Chem. Phys. Lett.
75
,
84
86
(
1980
).
53.
P. M.
Atha
and
I. H.
Hillier
,
Mol. Phys.
45
,
285
293
(
1982
).
54.
M.
Castro
,
J.
Keller
, and
P.
Mareca
,
Int. J. Quantum Chem.
20
,
429
435
(
1981
).
55.
W.
von Niessen
,
J. Chem. Phys.
85
,
337
(
1986
).
56.
E. A.
Boudreaux
and
E.
Baxter
,
Int. J. Quantum Chem.
102
,
866
868
(
2005
).
57.
S.
Lee
,
D. M.
Bylander
, and
L.
Kleinman
,
Phys. Rev. B
37
,
10035
(
1988
).
58.
L.
Xue-Ling
,
Chin. Phys. B
19
,
107103
(
2010
).
59.
Y.-L.
Wang
,
H.-S.
Hu
,
W.-L.
Li
,
F.
Wei
, and
J.
Li
,
J. Am. Chem. Soc.
138
,
1126
1129
(
2016
).
60.
W.
Zhang
,
X.
Ran
,
H.
Zhao
, and
L.
Wang
,
J. Chem. Phys.
121
,
7717
(
2004
).
61.
J.
Joy
and
E. D.
Jemmis
,
Chem. Commun.
53
,
8168
(
2017
).
62.
Y.
Chen
,
J.-y.
Hasegawa
,
K.
Yamaguchi
, and
S.
Sakaki
,
Phys. Chem. Chem. Phys.
19
,
14947
(
2017
).
63.
R.
Pis Diez
and
J. A.
Alonso
,
J. Chem. Phys.
123
,
134313
(
2005
).
64.
F.
Ruipérez
,
M.
Piris
,
J. M.
Ugalde
, and
J. M.
Matxain
,
Phys. Chem. Chem. Phys.
15
,
2055
(
2013
).
65.
C.
Angeli
,
A.
Cavallini
, and
R.
Cimiraglia
,
J. Chem. Phys.
127
,
074306
(
2007
).
66.
A. H.
Kulahlioglu
and
L.
Mitas
,
Comput. Theor. Chem.
1170
,
112642
(
2019
).
67.
R. A.
Kok
and
M. B.
Hall
,
Inorg. Chem.
22
,
728
(
1983
).
68.
F. A.
Cotton
,
J. Mol. Spectrosc.
59
,
97
108
(
1980
).
69.
S.-C.
Liu
,
W.-L.
Ke
,
J.-S. K.
Yu
,
T.-S.
Kuo
, and
Y.-C.
Tsai
,
Angew. Chem., Int. Ed.
51
,
6394
(
2012
).
70.
T.
Chen
and
T. A.
Manz
,
RSC Adv.
9
,
17072
17092
(
2019
).
71.
R.
Haque
,
M.
Pelino
, and
K. A.
Gingerich
,
J. Chem. Phys.
71
,
2929
2933
(
1979
).
72.
K. A.
Peterson
,
D.
Figgen
,
M.
Dolg
, and
H.
Stoll
,
J. Chem. Phys.
126
,
124101
(
2007
).
73.
M.
Douglas
and
N. M.
Kroll
,
Ann. Phys.
82
,
89
(
1974
);
B. A.
Hess
,
Phys. Rev. A
32
,
756
(
1985
);
B. A.
Hess
Phys. Rev. A
33
, 3742 (
1986
);
G.
Jansen
and
B. A.
Hess
,
Phys. Rev. A
39
,
6016
(
1989
).
74.
H. J.
Werner
and
P. J.
Knowles
,
J. Chem. Phys.
89
,
5803
5814
(
1988
).
75.
S. R.
Langhoff
and
E. R.
Davidson
,
Int. J. Quantum Chem.
8
,
61
72
(
1974
).
76.
P. J.
Knowles
,
C.
Hampel
, and
H. J.
Werner
,
J. Chem. Phys.
99
,
5219
5227
(
1993
).
77.
D.
Tzeli
,
I.
Karapetsas
,
D. M.
Merriles
,
J. C.
Ewigleben
, and
M. D.
Morse
,
J. Phys. Chem. A
126
,
1168
1181
(
2022
).
78.
S. N.
Khan
and
E.
Miliordos
,
J. Phys. Chem. A
123
,
5590
5599
(
2019
).
79.
J.
Tao
,
J. P.
Perdew
,
V. N.
Staroverov
, and
G. E.
Scuseria
,
Phys. Rev. Lett.
91
,
146401
(
2003
).
80.
P. J.
Knowles
,
G.
Knizia
,
F. R.
Manby
,
M.
Schütz
,
P.
Celani
,
W.
Györffy
,
D.
Kats
,
T.
Korona
,
R.
Lindh
 et al, molpro 2015.1 is a package of ab initio programs written by H.-J. Werner.
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.
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 16, Revision C.01,
Gaussian, Inc.
,
Wallingford, CT
,
2016
.
82.
K. A.
Peterson
,
D. E.
Woon
, and
T. H.
Dunning
,
J. Chem. Phys.
100
,
7410
7415
(
1994
).
83.
D.
Tzeli
,
A.
Mavridis
, and
S. S.
Xantheas
,
J. Chem. Phys.
112
,
6178
6189
(
2000
).
84.
D.
Feller
,
J. Chem. Phys.
138
,
074103
(
2013
).
85.
I. R.
Ariyarathna
and
E.
Miliordos
,
J. Phys. Chem. A
124
,
9783
9792
(
2020
).
86.
D.
Tzeli
,
U.
Miranda
,
I. G.
Kaplan
, and
A.
Mavridis
,
J. Chem. Phys.
129
,
154310
(
2008
).
87.
J.
Beck
and
F.
Wolf
,
Acta Crystallogr., Sect. B
53
,
895
903
(
1997
).
88.
A.
Bino
and
F. A.
Cotton
,
Inorg. Chem.
18
,
1381
(
1979
).

Supplementary Material

You do not currently have access to this content.