We present a detailed analysis of the addition-elimination reaction pathways for the gas-phase conversion of molecular hydrogen and methane on FeO+ to water and methanol, respectively, using first-principles calculations. These two reactions represent paradigmatic, challenging test cases for electronic structure approaches to transition-metal catalysis. We compare here density-functional approaches against state-of-the-art coupled-cluster and multireference quantum chemistry approaches. The quantum chemical approaches are found to be in close agreement between themselves as well as with the available experimental evidence. For the density-functional calculations, we employ a recently introduced ab initio, self-consistent Hubbard-like correction, coupled here with a generalized-gradient approximation (GGA) for the exchange-correlation functional. We find that our formulation provides a remarkable improvement in the description of the electronic structure, hybridization, and multiplet splittings for all calculated stationary points along these reaction pathways. The Hubbard term, which is not a fitting parameter and, in principle, can augment any exchange-correlation functional, brings the density-functional theory results in close agreement with the reference calculations. In particular, thermochemical errors as large as 1.4 eV in the exit channels with the GGA functional are reduced by an order of magnitude, to less than 0.1 eV on average; additionally, close agreement with the correlated-electron reference calculations and experiments are achieved for intermediate spin splittings and structures, reaction exothermicity, and spin crossovers. The role that the Hubbard U term plays in improving both quantitative and qualitative descriptions of transition-metal chemistry is examined, and its strengths as well as possible weaknesses are discussed in detail.

1.
D.
Schroder
,
H.
Schwarz
,
D. E.
Clemmer
,
Y. M.
Chen
,
P. B.
Armentrout
,
V. I.
Baranov
, and
D. K.
Bohme
,
Int. J. Mass Spectrom. Ion Process.
161
,
175
(
1997
).
2.
D.
Schroder
,
A.
Fiedler
,
M. F.
Ryan
, and
H.
Schwarz
,
J. Phys. Chem.
98
,
68
(
1994
).
3.
D. E.
Clemmer
,
Y. M.
Chen
,
F. A.
Khan
, and
P. B.
Armentrout
,
J. Phys. Chem.
98
,
6522
(
1994
).
4.
J. M.
Mercero
,
J. M.
Matxain
,
X.
Lopez
,
D. M.
York
,
A.
Largo
,
L. A.
Eriksson
, and
J. M.
Ugalde
,
Int. J. Mass. Spectrom.
240
,
37
(
2005
).
5.
D.
Danovich
and
S.
Shaik
,
J. Am. Chem. Soc.
119
,
1773
(
1997
).
6.
M.
Filatov
and
S.
Shaik
,
J. Phys. Chem. A
102
,
3835
(
1998
).
7.
E.
Derat
,
S.
Shaik
,
C.
Rovira
,
P.
Vidossich
, and
M.
Alfonso-Prito
,
J. Am. Chem. Soc.
129
,
6346
(
2007
).
8.
H.
Hirao
,
D.
Kumar
,
L.
Que
, and
S.
Shaik
,
J. Am. Chem. Soc.
128
,
8590
(
2006
).
9.
K.
Andersson
,
P. A.
Malmqvist
,
B. O.
Roos
,
A. J.
Sadlej
, and
K.
Wolinski
,
J. Phys. Chem.
94
,
5483
(
1990
).
10.
A.
Fiedler
,
D.
Schroder
,
S.
Shaik
, and
H.
Schwarz
,
J. Am. Chem. Soc.
116
,
10734
(
1994
).
11.
S.
Chiodo
,
O.
Kondakova
,
M. D.
Michelini
,
N.
Russo
,
E.
Sicilia
,
A.
Irigoras
, and
J. M.
Ugalde
,
J. Phys. Chem. A
108
,
1069
(
2004
).
12.
A.
Irigoras
,
J. E.
Fowler
, and
J. M.
Ugalde
,
J. Am. Chem. Soc.
121
,
8549
(
1999
).
13.
M.
Rosi
and
C. W.
Bauschlicher
,
J. Chem. Phys.
90
,
7264
(
1989
).
14.
F.
Aguirre
,
J.
Husband
,
C. J.
Thompson
,
K. L.
Stringer
, and
R. B.
Metz
,
J. Chem. Phys.
119
,
10194
(
2003
).
15.
M.
Bronstrup
,
D.
Schroder
, and
H.
Schwarz
,
Chem.-Eur. J.
5
,
1176
(
1999
).
16.
K.
Yoshizawa
,
Y.
Shiota
, and
T.
Yamabe
,
Organometallics
17
,
2825
(
1998
).
17.
Y.
Shiota
and
K.
Yoshizawa
,
J. Am. Chem. Soc.
122
,
12317
(
2000
).
18.
K.
Yoshizawa
,
Y.
Shiota
, and
T.
Yamabe
,
J. Chem. Phys.
111
,
538
(
1999
).
19.
20.
H. J.
Kulik
,
M.
Cococcioni
,
D. A.
Scherlis
, and
N.
Marzari
,
Phys. Rev. Lett.
97
,
103001
(
2006
).
21.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
22.
A. I.
Liechtenstein
,
V. I.
Anisimov
, and
J.
Zaanen
,
Phys. Rev. B
52
,
R5467
(
1995
).
23.
F.
Zhou
,
M.
Cococcioni
,
C. A.
Marianetti
,
D.
Morgan
, and
G.
Ceder
,
Phys. Rev. B
70
,
235121
(
2004
).
24.
M.
Cococcioni
and
S.
de Gironcoli
,
Phys. Rev. B
71
,
035105
(
2005
).
25.
H.
Jacobsen
and
L.
Cavallo
,
Organometallics
25
,
177
(
2006
).
26.
K. E.
Riley
and
K. M.
Merz
,
J. Phys. Chem. A
111
,
6044
(
2007
).
27.
K.
Leung
,
S. B.
Rempe
,
P. A.
Schultz
,
E. M.
Sproviero
,
V. S.
Batista
,
M. E.
Chandross
, and
C. J.
Medforth
,
J. Am. Chem. Soc.
128
,
3659
(
2006
).
28.
Y.
Zhao
and
D. G.
Truhlar
,
J. Chem. Phys.
124
,
224105
(
2006
).
29.
F.
Furche
and
J. P.
Perdew
,
J. Chem. Phys.
124
,
044103
(
2006
).
30.
A.
Sorkin
,
M. A.
Iron
, and
D. G.
Truhlar
,
J. Chem. Theory Comput.
4
,
307
(
2008
).
31.
J. P.
Perdew
,
R. G.
Parr
,
M.
Levy
, and
J. L.
Balduz
,
Phys. Rev. Lett.
49
,
1691
(
1982
).
32.
P. H.-L.
Sit
,
M.
Cococcioni
, and
N.
Marzari
,
Phys. Rev. Lett.
97
,
028303
(
2006
).
33.
Q.
Wu
,
C. L.
Cheng
, and
T.
Van Voorhis
,
J. Chem. Phys.
127
,
164119
(
2007
).
34.
S.
Fabris
,
S.
de Gironcoli
,
S.
Baroni
,
G.
Vicario
, and
G.
Balducci
,
Phys. Rev. B
71
,
041102
(
2005
).
35.
QUANTUM-ESPRESSO is a community project for high-quality quantum-simulation software, based on DFT, and coordinated by Paolo Giannozzi. See http://www.quantum-espresso.org and http://www.pwscf.org.
36.
State symmetry assignments were made based upon the absolute total angular momentum, |Λ|, of the density and the overall symmetry of the component densities, λ, which remain as “good” quantum numbers in our density-functional formalism. Additionally, the preserved spin quantum number of our systems is Ŝz.
37.
G.
Henkelman
and
H.
Jonsson
,
J. Chem. Phys.
113
,
9978
(
2000
).
38.
G.
Henkelman
,
B. P.
Uberuaga
, and
H.
Jonsson
,
J. Chem. Phys.
113
,
9901
(
2000
).
39.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
 et al, GAUSSIAN 03, Revision B.05, Gaussian, Inc., Wallingford, CT,
2004
.
40.
MOLPRO, a package of ab initio programs designed by
H. J.
Werner
,
P. J.
Knowles
,
R.
Lindh
 et al, Version 2006.1, see http://www.molpro.net, Cardiff UK,
2006
.
41.
See EPAPS Document No. E-JCPSA6-129-009837 for multireference and single-reference quantum chemistry details including method comparisons regarding multireference character, as well as Hubbard U-dependent geometries of intermediates and TSs at integer values of U. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
42.
We note that energetic differences at the CCSD(T) level of the different TS geometries were small and did not noticeably affect barrier height estimates.
43.
J. M.
Matxain
,
J. M.
Mercero
,
A.
Irigoras
, and
J. M.
Ugalde
,
Mol. Phys.
102
,
2635
(
2004
).
44.
I.
Dabo
,
A.
Wieckowski
, and
N.
Marzari
,
J. Am. Chem. Soc.
129
,
11045
(
2007
).
45.
The reaction coordinates of different methods have been aligned at the I6nt1. The curves associated with GGA and GGA+U reaction coordinates are splines of points from the minimum energy path as determined by NEB calculations.

Supplementary Material

You do not currently have access to this content.