Realistic energy surfaces for real-world systems: An IMOMO CCSD(T):DFT scheme for rhodium-catalyzed hydroformylation with the 6-dppon ligand

Article abstract of DOI:10.1002/chem.201302132

The hydroformylation of terminal alkenes is one of the most important homogeneously catalyzed processes in industry, and the atomistic understanding of this reaction has attracted enormous interest in the past. Herein, the whole catalytic cycle for rhodium-catalyzed hydroformylation with the 6-diphenylphosphinopyridine-(2H)-1-one (6-DPPon) ligand 1 was studied. This catalytic transformation is challenging to describe computationally, since two requirements must be met: 1) changes in the hydrogen-bond network must be modeled accurately and 2) bond-formation/bond-breaking processes in the coordination sphere of the rhodium center must be calculated accurately. Depending on the functionals used (BP86, B3LYP), the results were found to differ strongly. Therefore, the complete cycle was calculated by using highly accurate CCSD(T) computations for a PH₃ model ligand. By applying an integrated molecular orbital plus molecular orbital (IMOMO) method consisting of CCSD(T) as high level and DFT as low-level method, excellent agreement between the two functionals was achieved. To further test the reliability of the calculations, the energetic-span model was used to compare experimentally derived and computed activation barriers. The accuracy of the new IMOMO method apparently makes it possible to predict the catalytic potential of real-world systems. Copyright

Full text of DOI:10.1002/chem.201302132

DOI: 10.1002/chem.201302132
Realistic Energy Surfaces for Real-World Systems: An IMOMO
CCSD(T):DFT Scheme for Rhodium-Catalyzed Hydroformylation with the
6-DPPon Ligand**
[
a]
[b]
[c]
[a]
Urs Gellrich,* Daniel Himmel, Markus Meuwly, and Bernhard Breit*
Abstract: The hydroformylation of ter-
minal alkenes is one of the most impor-
tant homogeneously catalyzed process-
es in industry, and the atomistic under-
standing of this reaction has attracted
enormous interest in the past. Herein,
the whole catalytic cycle for rhodium-
catalyzed hydroformylation with the 6-
diphenylphosphinopyridine-(2H)-1-one
tion/bond-breaking processes in the co-
ordination sphere of the rhodium
center must be calculated accurately.
Depending on the functionals used
(BP86, B3LYP), the results were found
to differ strongly. Therefore, the com-
plete cycle was calculated by using
highly accurate CCSD(T) computations
integrated molecular orbital plus mo-
lecular orbital (IMOMO) method con-
sisting of CCSD(T) as high level and
DFT as low-level method, excellent
agreement between the two functionals
was achieved. To further test the relia-
bility of the calculations, the energetic-
span model was used to compare ex-
perimentally derived and computed ac-
tivation barriers. The accuracy of the
new IMOMO method apparently
makes it possible to predict the catalyt-
ic potential of real-world systems.
for a PH model ligand. By applying an
3
(
6-DPPon) ligand 1 was studied. This
catalytic transformation is challenging
to describe computationally, since two
requirements must be met: 1) changes
in the hydrogen-bond network must be
modeled accurately and 2) bond-forma-
Keywords: ab initio calculations ·
density functional calculations · ho-
mogeneous catalysis · hydroformy-
lation · self-assembling ligands
Introduction
the ligands more expensive than the noble-metal source. As
an alternative approach for efficient crafting of the microen-
[4]
[5]
The hydroformylation of terminal alkenes is one of the most
important industrial processes which relies on homogeneous
vironment around the metal center, we and others re-
cently introduced the concept of monodentate-to-bidentate
ligand self-assembly. For this we studied the rather simple 6-
diphenylphosphino-(2H)-1-one system, which has hydrogen-
bonding capabilities between the pyridone and hydroxypyri-
dine forms in the coordination sphere of a transition metal
(Scheme 1).
[
1]
6
catalysis. More than 9ꢀ10 t of oxo products are produced
[
2]
annually. The best regioselectivity for the frequently more
desirable linear aldehyde can be obtained with rhodium cat-
alysts modified with chelating diphosphine and diphosphite
ligands. Despite their unique selectivities, the synthesis of
these classic bidentate ligands can be difficult and may in-
clude many synthetic steps, and in some cases this makes
[
3]
[
a] U. Gellrich, Prof. Dr. B. Breit
Institut fꢁr Organische Chemie
Albert-Ludwigs-Universitꢂt Freiburg
Albertstrasse 21, 79104 Freiburg i. Brsg. (Germany)
Fax : (+49) 761-203-8715
E-mail: ursgellrich@gmx.de
Scheme 1. Self-organization of 1 in the coordination sphere of a late tran-
bernhard.breit@chemie.uni-freiburg.de
sition metal.
[
b] Dr. D. Himmel
Institut fꢁr Anorganische Chemie
Albert-Ludwigs-Universitꢂt Freiburg
Albertstrasse 21, 79104 Freiburg i. Brsg. (Germany)
In previous studies we were able to show that the expect-
ed ligand–ligand interaction indeed occurs in a [Cl Pt(1) ]
2
2
[
c] Prof. Dr. M. Meuwly
Department of Chemistry, University of Basel
Klingelbergstrasse 80, 4056 Basel (Switzerland)
[6]
complex. The hydrogen bonds in the [Cl Pt(1) ] complex
2
2
were intensively studied, and the enthalpic stabilization
through hydrogen bonding was determined to be 14–15 kcal
[
**] 6-DPPon: 6-diphenylphosphinopyridine-(2H)-1-one; IMOMO: inte-
ꢀ
1 [6a]
mol .
Furthermore, we were able to demonstrate that
grated molecular orbital plus molecular orbital.
this ligand system shows selectivity towards the linear alde-
hyde in rhodium-catalyzed hydroformylation similar to
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/chem.201302132.
16272
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Chem. Eur. J. 2013, 19, 16272 – 16281

FULL PAPER
intrinsic drawbacks. We first
validate the approach by con-
sidering a model system for
which rigorous calculations at
the CCSD(T) level are possi-
ble. Rhodium-catalyzed hydro-
formylation with the 6-diphe-
nylphosphinopyridine-(2H)-1-
one (6-DPPon) ligand 1 was
chosen as a case study. First,
the accuracy of the functionals
for describing hydrogen-bond
energies is assessed by compar-
ison to experimental results.
Next, the results for the ele-
mentary steps of the catalytic
transformation are discussed in
Scheme 2. Results of the rhodium-catalyzed hydroformylation of 1-octene with PPh
DPPon (1) ligands. Conditions: Rh:L:substrate=1:20(10):7500, 808C, 10 bar, toluene.
3
(2), Xantphos (3) and 6-
those obtained with bidentate ligands such as Xantphos (3).
The turnover frequencies (TOF) are even higher than those
determined for the monodentate triphenylphosphine (2)
under identical conditions (Scheme 2). Furthermore, we
were able to detect hydrogen bonds in a competent inter-
mediate of the catalytic transformation, namely, the rhodi-
the light of experimental results. Finally, the two-layer inte-
grated molecular orbital plus molecular orbital (IMOMO)
method is introduced and validated.
Results and Discussion
[7]
um acyl complex [(COR)Rh(1) (CO) ] (R=C H ).
2
2
8
17
These results imply that for a realistic energy surface of
the catalytic cycle the hydrogen-bond properties and the re-
action energies for the elementary steps of the catalytic
transformation must be predicted accurately. Density func-
tional calculations are routinely applied to gain insight into
the mechanisms of transition metal catalyzed transforma-
tions. In the last few years a growing number of DFT func-
tionals was developed (for ex-
Performance of the DFT functionals for the hydrogen-bond
properties: In a previous work we presented the X-ray struc-
[6a]
ture of symmetric pyridine dimer 1A·1A (Figure 1). This
solid-state structure was used to evaluate the performance
of the DFT functionals applied herein for predicting the ge-
ometries of the hydrogen bonds in the 1A·1A dimer
(Table 1). Both functionals describe the structural features
[8]
ample
meta-hybrid
and
[9]
double-hybrid functionals ) to
overcome the known shortcom-
ings (reaction barriers, disper-
sion) of DFT calculations.
However, the results of DFT
calculations strongly depend on
the chosen functional, and how
appropriate a functional is to
determine enthalpies is always
questionable, since the perfor-
mance of functionals normally
depends on their parameteriza-
[10]
tion. Furthermore, no system-
atic improvement of the accura-
cy of DFT calculations by ap-
plying larger basis sets is possi-
[
11]
ble. We herein present an ap-
proach which is based on high-
level ab initio computations for
a small model system. The ac-
curate ab initio calculations
allow standard DFT calcula-
tions of larger real-world sys-
Figure 1. Overlay of the solid-state structure of the symmetric 6-DPPon dimer (1A·1A). and the DFT comput-
tems to be corrected for their ed structures (blue: BP86/SDD-6-31G**, full color: B3LYP/SDD-6-31G**, black: X-ray.
Chem. Eur. J. 2013, 19, 16272 – 16281
ꢃ 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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16273

U. Gellrich, B. Breit et al.
of the hydrogen-bond system
in satisfactory agreement with
the X-ray structure. BP86
slightly underestimates the dis-
tance between the two ligands
by 0.05 ꢄ. Furthermore, we
were able to determine the
free dimerization enthalpy of
1
A by NMR titration experi-
[6a]
ments. The results of the cal-
culations using the BP86 and
Scheme 3. Synthesis of [HRh(1)
3
(CO)] (4). The box marks the monomeric unit used for assessment of the
DFT functionals.
Table 1. N···O distance and NꢀH···O angle in the symmetric 1A·1A
dimer.
X-ray
BP86/6-31G**
B3LYP/6-31G**
[
[
a]
a]
[a]
NH···O [ꢄ]
NꢀH···O [8]
2.777(1)
177.3(2)
2.729
179.1
2.772
179.7
[a]
[
a] Values taken from ref. [6a].
the B3LYP functional are in good agreement with the ex-
periment (Table 2). This finding is consistent with previous
studies by Perdew et al, who predicted the dissociation
energy of ten hydrogen-bonded complexes with mean abso-
ꢀ
1
lute errors (MAE) of 0.76 and 0.43 kcalmol for the BP86
[
12]
and the B3LYP functional, respectively. For the study pre-
sented herein, this is important, since it suggests that
changes in the hydrogen bond system during the catalytic
transformation can also be expected to be described accu-
rately.
Figure 2. Overlay of the solid-state structure of 4 and the DFT computed
structures (blue: BP86/SDD-6-31G**, full color: B3LYP/SDD-6-31G**,
black: X-ray).
3
Table 3. Equilibrium structure of [HRh(1) (CO)] measured by X ray and
calculated by DFT.
Table 2. Free dimerization enthalpy of 1A determined by NMR titration
X-ray
BP86/SDD-6-31G** B3LYP/SDD-6-31G**
experiments and computed at the BP86 and B3LYP level of theory.
RhꢀP1 [ꢄ]
RhꢀP2 [ꢄ]
2.3023(7) 2.341
2.3027(6) 2.359
P1-Rh-P2 [8] 115.23(3) 113.98
2.366
2.389
115.08
1.913
3.035
165
NMR
BP86/6-31G**
B3LYP/6-31G**
ꢀ
1
[a]
[a]
DG [kcalmol
]
ꢀ5.95ꢁ0.075
ꢀ5.18
ꢀ6.05
RhꢀCO [ꢄ]
1.908(3)
2.892(3)
169(3)
1.902
2.949
167
[
a] Values taken from ref. [6a].
NH···N [ꢄ]
NꢀH···N [8]
OH···O [ꢄ]
OꢀH···O [8]
2.657(4)
170(4)
2.553
169
2.602
168
Performance of the DFT functionals for rhodium complexes
bearing 6-DPPon (1) ligands: We previously reported the
[
7]
synthesis of [HRh(1) (CO)] (4). This complex, which is
ment to the X-ray structure. Furthermore, both functionals
show good agreement for the P-Rh-P angle in comparison
to the X-ray structure. The P-Rh-P angle was identified pre-
viously as an important parameter for the catalytic perfor-
mance of bidentate phosphine ligands in rhodium-catalyzed
3
present as a dimer in solution and in the solid state, was
characterized by X-ray analysis. To save CPU time we calcu-
lated only one monomeric unit and compared the structure
obtained to that derived from X-ray analysis (Scheme 3).
An overlay of the DFT calculated structures and the X-ray
structure is shown in Figure 2. Clearly, both functionals pre-
dict the relative orientation of the heteroaromatic rings
forming the hydrogen-bond network in close agreement
with the solid-state structure (Figure 2).
Comparing the X-ray and DFT structures (Table 3) re-
veals that BP86 shows good agreement for the bond lengths
at the rhodium center. For example, the rhodium–phospho-
rous bond lengths differ by only 0.04 ꢄ. B3LYP overesti-
mates the rhodium–phosphorus bond lengths by 0.08 ꢄ, but
the predicted rhodium–carbon bond length is in close agree-
[13]
hydroformylation.
[14]
The catalytic cycle: The generally accepted mechanism
for rhodium catalyzed hydroformylation summarized in
Scheme 4 consists of CO dissociation (step I), alkene coordi-
nation (step II), hydrometalation followed by CO coordina-
tion (steps III and IV) and migratory insertion (step V)
leading to a rhodium acyl complex, which can undergo oxi-
dative addition in the presence of H (step VI). A final re-
2
ductive elimination leads to a 16 valence electron (VE) spe-
cies and concomitant formation of aldehyde (step VII).
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Realistic Energy Surfaces for Real-World Systems
FULL PAPER
have good performance by pre-
dicting
the
hydrogen-bond
strength compared to the ex-
periment (Table 2), one would
expect that the free-energy
change of CO dissociation is in
good agreement between the
two functionals. However, the
opposite is the case (Table 5).
The E+zpv and DG values pre-
dicted by the BP86 and the
B3LYP functional differ by
ꢀ
1
more than 8 kcalmol . Howev-
er, since kinetic studies re-
vealed an inverse first-order de-
pendence of the TOF on the
CO partial pressure, an accu-
rate description of the energet-
ics of this elementary step is de-
sirable.
Furthermore,
Scheme 4. Generally accepted mechanism for the rhodium-catalyzed hydroformylation of terminal alkenes.
We now focus on the individual elementary steps and in-
troduce the IMOMO protocol used in the following, which
will be validated for CO dissociation from the 18-VE com-
plex [HRh(1) (CO) ] (5) to furnish the 16-VE complex 6.
Table 4. Changes in the N···N and O···O distance by going from eqeq-5
to trans-6.
BP86/SDD-6-31G**
B3LYP/SDD-6-31G**
eqeq-5
trans-6
eqeq-5
trans-6
2
2
NH···N [ꢄ]
OH···O [ꢄ]
2.90
2.57
3.40
2.59
2.96
2.63
3.51
2.63
CO dissociation: Both DFT functionals employed herein
predict trans-[HRh(1) (CO)] (trans-6) to be more stable
2
[15]
than cis-[HRh(1) (CO)] (cis-6).
Both functionals predict
Table 5. E+zpv and DG values for the conversion of eqeq-5 to trans-6.
2
nearly identical structural changes on going from eqeq-5 to
trans-6 (Figure 3). Regarding the changes in the hydrogen-
bond network, both functionals predict elongation of the
NH···N bond by 0.5 ꢄ, whereas the OH···O bond length re-
mains unchanged at both levels of theory (Table 4).
ꢀ1
ꢀ1
E+zpv [kcalmol
]
DG [kcalmol ]
BP86/SDD-6-31G**
B3LYP/SDD-6-31G**
29.91
21.71
18.89
10.49
Since both functionals predict similar (or identical)
changes in the hydrogen-bond network and were proven to
[HRh(1) (CO) ] was identified as resting state of the catalyt-
2 2
ic transformation by in situ IR spectroscopy (Figure 4).
These results clearly indicate
that CO dissociation may
strongly contribute to the over-
all barrier of rhodium-catalyzed
hydroformylation with the 6-
DPPon (1) ligand.
The importance of this ele-
mentary step is also highlighted
by the fact that, in a thorough
investigation on the rate-deter-
mining step for hydroformyla-
tion with xanthene-based li-
gands, CO dissociation from the
trigonal-bipyramidal
[HRh-
_
AHCTUNGERTG(NNUN PP)(CO) ] complex was dis-
2
cussed to be rate-determin-
[16]
ing. We therefore performed
high-level ab initio single-point
calculations for
a simplified
Figure 3. Formation of trans-6 by CO dissociation from eqeq-5. The 3D figure shows an overlay of the BP86
(
blue) and the B3LYP (full color) optimized structure.
model system in which the li-
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16275

U. Gellrich, B. Breit et al.
B3LYP functional, we performed additional single-point cal-
culations for the model system with the parameter-free
hybrid PBE0 functional, the meta-GCA functional M06L,
the global meta-hybrid M06 functional, and the long-range
and dispersion-corrected wB97X-D functional. The aug-cc-
pVTZ-PP (AVTZ) basis set was used for these calculations.
Indeed, comparison of the CCSD(T) and the DFT results
shows that BP86 tends to overestimate the energy required
for CO dissociation, whereas B3LYP in conjunction with the
double-zeta basis set is in excellent agreement with the
CCSD(T) calculations. Employing larger basis sets is of lim-
ited use (Table 6, entries 3 and 5). In combination with the
AVTZ basis set, the B3LYP-D3, M06L and w-B97X-D func-
tionals show the smallest deviation from the energy calculat-
ed at the CCSD(T)-MP2 level of theory.
Figure 4. Changes in the IR spectrum after addition of 1-octene to pre-
formed [HRh(1) (CO) ] at room temperature in toluene.
2
2
Alkene coordination: We next investigated alkene coordina-
tion leading to alkene complex eqeq-7 (Figure 5). Ethene
gands are replaced by PH (Scheme 5). To obtain reliable
3
geometries BP86 was used in conjunction with the small-
core ECP28MDF and the corresponding Dunning aug-cc-
pVTZ basis set (in the following denoted AVTZ), which
was also used for all other atoms.
Table 6. Comparison of the results for the model reaction Model-5!
Model-6 calculated by CCSD(T)-MP2 and DFT.
ꢀ
1
ꢀ1 [c]
DE [kcalmol
]
DDE [kcalmol ]
[
a]
CCSD(T)-MP2/AwCVQZ
CCSD(T)/AVTZ
BP86/SDD-6-31G**
BP86/AVTZ
20.99
21.73
28.86
26.08
28.86
20.95
17.65
20.10
23.99
22.62
22.68
16.34
16.60
19.38
-
ꢀ0.74
ꢀ7.86
ꢀ5.08
ꢀ7.86
ꢀ0.05
3.35
BP86-D3/AVTZ
B3LYP/SDD-6-31G**
[
a]
B3LYP/AVTZ
[
a]
B3LYP-D3/AVTZ
0.89
Scheme 5. Model reaction used for the ab initio calculations.
[a]
PBE0/AVTZ
ꢀ2.99
ꢀ1.62
ꢀ1.68
4.65
4.39
1.62
[
[
a]
b]
M06-L/AVTZ
M06-L/AVTZ
Since for the small system containing the PH3 ligand
CCSD(T) calculations above the triple-z level are also not
suitable, additional MP2 calculations were used to extrapo-
late the CCSD(T) computations to the quadruple-z level
[
a]
M06/AVTZ
M06/AVTZ
[b]
[a]
w-B97X-D/AVTZ
[
[
a] Single-point energy calculations on BP86/AVTZ optimized structures.
b] Single-point energy calculations on M06 L/AVTZ optimized struc-
(
i.e., aug-cc-pwCVQZ). This level of theory is in the follow-
ing denoted as CCSD(T)-MP2/AwCVQZ, the basis set re-
ferring to the largest basis used
tures. [c] DDE=DECCSD(T)ꢀDEDFT.
in the MP2 calculations. To de-
termine whether the difference
in predicting the reaction en-
thalpy of eqeq-5 to trans-6 may
originate from an insufficient
description of the RhꢀCO bond
strength, the model reaction
was recalculated by using BP86/
SDD-6-31G** and B3LYP/
SDD-6-31G**.
Furthermore,
the DFT functionals were used
in combination with the AVTZ
basis set to investigate their
basis-set dependence and to-
gether with the D3 correction
of Grimme et al. to evaluate
the importance of dispersion
[17]
correction. To exclude short-
Figure 5. Alkene coordination leading to eqeq-7. The 3D figure shows an overlay of the BP86 (blue) and the
comings of the BP86 and the B3LYP (full color) optimized structures.
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Realistic Energy Surfaces for Real-World Systems
FULL PAPER
was used as model substrate to decrease the number of pos-
of DFT functionals against only one elementary step of
a catalytic transformation can be misleading. This can also
be seen from the fact that, in combination with the AVTZ
basis set, the PBE0 functional displays the smallest devia-
tion of the energetics of the alkene coordination from the
CCSD(T)-MP2/AwCVQZ compound calculation (Table 8).
The M06L and w-B97X-D functionals, which were found to
predict the CO dissociation rather accurately with respect to
the CCSD(T)-MP2/AwCVQZ calculations (Table 6), show
deviations of about 4 kcalmol for alkene coordination.
However, by comparing the performance of the BP86 and
B3LYP functionals with the D3-corrected variants, it is obvi-
ous that the dispersion correction can indeed partially solve
the problem of predicting the rhodium–ethene binding. The
sible conformers. On comparing the E+zpv values predict-
ꢀ
1
ed at the DFT level, again a difference of 8 kcalmol was
found between BP86 and B3LYP. Moreover, BP86 predicts
the reaction to be exergonic, whereas B3LYP predicts an en-
dergonic reaction (Table 7).
Table 7. E+zpv and DG values for the conversion of trans-6 to eqeq-7.
ꢀ
1
ꢀ1
E+zpv [kcalmol
]
DG [kcalmol ]
ꢀ
1
BP86/SDD-6-31G**
B3LYP/SDD-6-31G**
ꢀ15.51
ꢀ8.12
ꢀ1.78
5.45
ꢀ
1
To establish a realistic mechanistic picture of the rhodi-
um-catalyzed hydroformylation with ligand 1, obtaining a re-
alistic enthalpy for alkene coordination by means of compu-
tational chemistry is important, since kinetic experiments re-
vealed a first-order dependence of the TOF on the concen-
popular M06 functional shows deviations of 4.7 kcalmol
ꢀ
1
for CO dissociation and 8.0 kcalmol for alkene coordina-
tion from the CCSD(T)-MP2/AwCVQZ calculations. In
summary, we were not able to identify a DFT functional
which leads to reliable results for both CO dissociation and
alkene coordination.
[6a]
tration of 1-octene. Furthermore, many important homo-
genously catalyzed reactions start with coordination of an
alkene to a late transition metal (e.g., rhodium-catalyzed hy-
The CCSD(T):DFT IMOMO scheme: Following earlier
work of Morokuma et al., we decided that quantitative in-
formation about the intrinsic error of the DFT calculations
for a specific elementary step of the catalytic cycle can be
[18]
[19]
drogenation and the Tsuji–Trost reaction). Establishing
a methodology which would enable reliable prediction of
the energetics of the addition of an unsaturated CꢀC bond
[20]
to a transition metal seems therefore indispensable. Again,
a model reaction in which the 6-DPPon ligand was replaced
used to design a two-layer IMOMO scheme. The idea of
an IMOMO calculation is to split the investigated system
into two layers which are treated by different methods and
by PH was investigated by means of ab initio calculations.
3
[21]
Interestingly, by comparison between the CCSD(T) calcula-
tions and the DFT calculations, BP86/SDD-6-31G** is
found to be in good agreement with the ab initio calcula-
tions (Table 8), whereas B3LYP underestimates the energy
basis sets. The model complex serves as high layer and is
treated with a high-level ab initio method [here CCSD(T)],
whereas the real-world system, treated at the DFT level, can
be regarded as the low layer (Scheme 6). The IMOMO
ꢀ
1
gained by alkene coordination by 8 kcalmol .
Table 8. Comparison of the results for the model reaction Model-6!
Model-7 calculated by CCSD(T) and DFT.
ꢀ
1
ꢀ1 [c]
DE [kcalmol
]
DDE [kcalmol ]
[
a]
CCSD(T)-MP2/AwCVQZ
CCSD(T)/AVTZ
BP86/SDD-6-31G**
BP86/AVTZ
ꢀ17.62
ꢀ18.14
ꢀ17.30
ꢀ14.20
ꢀ19.33
ꢀ9.90
–
0.53
ꢀ0.32
ꢀ3.42
1.71
ꢀ7.72
ꢀ11.35
ꢀ6.87
ꢀ2.23
ꢀ4.02
ꢀ4.07
ꢀ7.97
ꢀ7.94
ꢀ4.49
BP86-D3/AVTZ
Scheme 6. Schematic representation of the two-layer IMOMO extrapola-
tion scheme used herein.
B3LYP/SDD-6-31G**
[
a]
B3LYP/AVTZ
B3LYP-D3/AVTZ
ꢀ6.27
[
a]
ꢀ10.75
ꢀ15.38
ꢀ13.56
ꢀ13.61
ꢀ9.65
[
a]
PBE0/AVTZ
[
[
a]
M06-L/AVTZ
M06-L/AVTZ
energy is then obtained by three independent methods
b]
[
Eq. (1)].
[
a]
M06/AVTZ
M06/AVTZ
[
b]
ꢀ9.68
[
a]
w-B97X-D/AVTZ
ꢀ13.13
DE
¼ DEreal world ðDFTÞ
IMOMOðCCSDðTÞ:DFTÞ
ð1Þ
[
[
a] Single-point energy calculations on BP86/AVTZ optimized structures.
b] Single-point energy calculations on M06 L/AVTZ optimized struc-
þ ðDEModel ðCCSDðTÞÞ ꢀ DEModel ðDFTÞ
Þ
tures. [c] DDE=DECCSD(T)ꢀDEDFT.
Since the BP86 and B3LYP functionals in combination
with a double-z basis set were shown to have a good perfor-
mance for the hydrogen-bond properties and the structural
Since the B3LYP functional was shown to be in excellent
agreement with the CCSD(T)-MP2/AwCVQZ calculations
for the first elementary step (CO dissociation) the results
presented herein show that benchmarking the performance
features of a the [HRh(1) (CO)] complex, we used these ef-
3
ficient combinations of functionals and basis sets for the de-
Chem. Eur. J. 2013, 19, 16272 – 16281
ꢃ 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
16277

U. Gellrich, B. Breit et al.
scription of the real-world system. The IMOMO scheme
which uses CCSD(T) single-point calculations extrapolated
with MP2 to the aug-cc-pwCVQZ basis set on BP86/aug-cc-
pVTZ optimized structures on the model system in combi-
nation with DFT calculations using SDD-6-31G** on the
real-world system is in the following designated CCSD(T)-
MP2:DFT. By applying this IMOMO method to the “real-
world” CO dissociation step (Scheme 3), excellent agree-
ment between BP86 and B3LYP was achieved.
Table 11. Reaction enthalpies and activation energies of the individual
steps of the catalytic transformation as displayed in Scheme 4. All values
are Gibbs free energies [kcalmol ].
ꢀ
1
[a]
Reaction
BP86
18.89
10.34
ꢀ1.78
11.83
B3LYP CCSD(T):BP86 CCSD(T):B3LYP
eqeq-5!trans-6
trans-6!TS-1
trans-6!eqeq-7
eqeq-7!TS-2
10.49
11.00
5.45
11.03
7.21
ꢀ2.10
12.15
0.99
10.54
6.85
ꢀ2.27
12.20
2.37
13.02
eqeq-7!cis-8
1.99 ꢀ1.33
cis-8!eqeq-9
ꢀ11.59 ꢀ4.67
ꢀ4.89
13.29
2.10
ꢀ5.67
12.91
3.39
eqeq-9!TS-3
eqeq-9!trans-10
trans-10!TS-4
trans-10!eqeq-11
eqeq-11!TS-5
8.07
9.81
Applying the IMOMO scheme reduces the difference in
the predicted energy and enthalpy changes for CO dissocia-
tion from eqeq-5 between the two functionals is from more
ꢀ0.77 ꢀ3.34
9.57
1.48
13.01
3.43
9.54
5.65
7.93
3.55
ꢀ
1
ꢀ1
than 8 kcalmol to less than 1 kcalmol (Table 9). By ap-
10.04
11.25
8.10
7.96
[
b]
eqeq-11!trans-6
ꢀ21.01 ꢀ28.52 ꢀ23.13
ꢀ23.55
Table 9. E+zpv and DG values for the conversion of eqeq-5 to trans-6
obtained with DFT and IMOMO methods.
[
a] The given energies and enthalpies are referred to the sum of the ener-
gies and enthalpies of eqeq-5 and the substrates. [a] With concomitant
formation of the product, in this case propanal.
ꢀ
1
ꢀ1
E+zpv [kcalmol
]
DG [kcalmol ]
BP86/SDD-6-31G**
B3LYP/SDD-6-31G**
CCSD(T)-MP2:BP86
CCSD(T)-MP2:B3LYP
29.91
21.71
22.06
21.28
18.89
10.49
11.03
10.37
problems in accounting for p-backdonation effects. Further-
more, the BP86 functional predicts ethene coordination to
be rate-determining. However, with the IMOMO method,
independent of the DFT functional, hydrometalation is pre-
dicted to be rate-determining.
plying the CCSD(T)-MP2:DFT IMOMO scheme to the
real-world reaction for alkene coordination, a difference of
less than 0.3 kcalmol for the E+zpv and DG values is pre-
dicted with CCSD(T)-MP2:BP86 and CCSD(T)-
MP2:B3LYP (Table 10, entries 3 and 4). Furthermore, both
functionals now predict that alkene coordination is exother-
mic and exergonic.
ꢀ
1
Comparison to the experimentally determined barrier: the
energetic-span model: The kinetics discussed herein makes
it seem difficult to identify a single step of the rhodium-cata-
lyzed hydroformylation as rate-determining step. However,
the experimentally found inverse first-order dependence on
the alkene concentration and first-order dependence on the
Table 10. E+zpv and DG values for the conversion of trans-6 to eqeq-7
obtained with DFT and IMOMO methods.
1
-octene concentration can be rationalized in terms of the
[23]
ꢀ
1
ꢀ1
energetic-span concept introduced by Shaik et al.
The
E+zpv [kcalmol
]
DG [kcalmol ]
[
HRh(1) (CO) ] complex, which was identified as resting
2 2
BP86/SDD-6-31G**
B3LYP/SDD-6-31G**
CCSD(T)-MP2:BP86
CCSD(T)-MP2:B3LYP
ꢀ15.51
ꢀ8.12
ꢀ1.78
5.45
state of the catalytic transformation by means of in situ IR
spectroscopy, can then be regarded as the TOF-determining
intermediate (TDI) and the transition state of the hydrome-
talation would represent the TOF-determining transition
state (TDTS). On going from the [HRh(1) (CO) ] complex
ꢀ15.83
ꢀ15.84
ꢀ2.10
ꢀ2.27
2
2
The IMOMO energy surface: The individual reaction en-
thalpies and activation energies of the elementary steps of
the catalytic cycle calculated at the BP86/SDD-6-31G**,
to the transition state for hydrometalation, one molecule of
CO leaves the cycle, whereas one molecule 1-octene enters
the cycle, and this explains the experimentally found de-
pendence on the substrate concentrations. Both DFT func-
B3LYP/SDD-6-31G**,
CCSD(T)-MP2:B3LYP levels are summarized in Table 11.
CCSD(T)-MP2:BP86,
and
[
22]
°
tionals (BP86 and B3LYP) predict a DG value of 28.9 kcal
ꢀ
1
On applying the IMOMO method presented herein, the
average difference in the predicted reaction enthalpies be-
tween CCSD(T)-MP2:BP86 and CCSD(T)-MP2:B3LYP is
mol for ethene as substrate. In contrast, calculations based
on the IMOMO method lead to a barrier of 20–21 kcal
ꢀ
1
ꢀ1
mol
(21.07 kcalmol
at the CCSD(T)-MP2:BP86 and
ꢀ
1
ꢀ1
ꢀ1
0
.9 kcalmol , as opposed to 5.4 kcalmol when the pure
20.47 kcalmol at the CCSD(T)-MP2:B3LYP level). For
a direct comparison with the experimentally determined en-
ergetics, the energetic-span model was used to translate the
DFT functionals are applied. More importantly, the maxi-
ꢀ1
mum difference is reduced from 8.4 to 2.1 kcalmol . The
free-energy surfaces derived from the IMOMO and DFT
calculations are depicted in Figure 6.
[25]
measured TOFs into free activation energies [Eq. (2)],
Interestingly, the largest differences between the pure
GGA and the hybrid DFT functional were observed in the
early steps of the catalytic transformation (e.g., CO dissocia-
tion, alkene coordination, CO coordination to 8), in which
the type of p-accepting ligands change. These findings clear-
ly indicate that the DFT functionals studied herein have
DGTS=RT
ꢀ
TOF ¼ ðk T=hÞe
½octeneꢂ=½COꢂ
ð2Þ
B
where kB denotes the Boltzmann constant and h Planckꢅs
TS
constant. Herein, DG represents the energetic span of the
catalytic transformation.
16278
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Chem. Eur. J. 2013, 19, 16272 – 16281

Realistic Energy Surfaces for Real-World Systems
FULL PAPER
Figure 6. Gibbs free-energy surface calculated at the BP86/SDD-6-31G**, B3LYP/SDD-6-31G**, CCSD(T)-MP2:BP86, and CCSD(T)-MP2:B3LYP
levels of theory.
To account for the difference between ethene and 1-
octene, the TDTS was reoptimized with propene as smallest
model substrate for a monosubstituted alkene. The results at
different temperatures are listed in Table 12. Indeed, both
functionals overestimate the experimentally found barrier
IMOMO method makes it seem possible to predict the cata-
lytic potential of given transition metal/ligand combinations.
To prove this, we compared the 6-DPPon (1) ligand with the
Xantphos ligand (3). Since experimental and computational
data suggest that the same rate-determining states account
for the TOF in the case of Xantphos-catalyzed hydroformy-
ꢀ
1
by 8–9 kcalmol . The uncorrected PES displayed in
Figure 6 clearly shows that BP86 overestimates the energetic
span because the energy required for CO dissociation is
overestimated. In case of the B3LYP functional, alkene co-
ordination is predicted to be endergonic, and this results in
overestimation of the overall barrier. In stark contrast, the
IMOMO methods show the desired chemical accuracy with
[13,21c]
lation,
the TDI and TDTS were reoptimized with this
ligand (Scheme 7).
As expected from the results presented in Table 12, the
pure GGA functional BP86 and hybrid functional B3LYP
deliver completely unrealistic TOFs (0.03 and 0.01, and 0.01
and 0.001, respectively, as opposed to the experimentally ob-
served TOFs of 3359 for the 6-DPPon (1) catalyst and 726
for the Xantphos (3) catalyst, see Table 13.
ꢀ1
deviations of 1 kcalmol from the experimentally deter-
[24]
mined values.
Conversely, by applying the CCSD(T)-MP2:DFT method,
realistic TOFs were calculated for both catalyst systems
(Table 13). Taking into account the exponential dependence
Comparison to the experimentally determined TOF of the
-DPPon (1) and Xantphos (3) ligands: The accuracy of the
6
TS
of the TOF on the DG values, the observed deviation be-
Table 12. Experimental free activation barriers derived from the energet-
ic-span model and the barriers computed by the pure DFT functionals
and the IMOMO method. Propene was used as model substrate for the
experimentally used 1-octene.
tween experiment and theory is surprisingly small. There-
fore, the CCSD(T):DFT IMOMO method presented herein
is a promising step towards in silico catalyst design.
TS
ꢀ1
T
TOF
DG [kcalmol ]
ꢀ
1
[
8C]
A[ h
C
H
T
U
N
G
T
R
E
N
N
U
N
G
]
Exptl
BP86 B3LYP CCSD(T)- CCSD(T)-
MP2:BP86 MP2:B3LYP
Conclusion
60
70
80
1527ꢁ39 23.91ꢁ0.02 32.90 33.57
2375ꢁ319 24.36ꢁ0.09 32.97 33.65
3359ꢁ240 24.84ꢁ0.05 33.04 33.72
25.03
25.10
25.18
25.09
25.16
25.24
We have provided a comprehensive computational investi-
gation of the catalytic cycle of rhodium-catalyzed hydrofor-
Chem. Eur. J. 2013, 19, 16272 – 16281
ꢃ 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
16279

U. Gellrich, B. Breit et al.
Table 13. Experimental free activation barriers and TOFs of the 6-DPPon (1) and Xantphos (3) ligands in comparison to the values computed with the
pure DFT functional and the IMOMO method. Propene was used as model substrate for the experimentally used 1-octene.
ꢀ
1
TS
ꢀ1
Ligand
TOF [h
B3LYP
]
DG [kcalmol ]
[
a]
[a]
Exptl
BP86
CCSD(T)-
MP2:BP86
CCSD(T)-
MP2:B3LYP
Exptl
BP86
B3LYP
CCSD(T)-
MP2:BP86
CCSD(T)-
MP2:B3LYP
6
-DPPon (1)
3359ꢁ240
726ꢁ40
0.03
0.002
0.01
0.001
2028
140
1913
218
24.84ꢁ0.05
25.91ꢁ0.04
33.04
34.94
33.72
35.25
25.18
27.17
25.24
26.77
Xantphos (3)
[
a] Conditions: Rh:L:substrate=1:20(10):7500, 808C, 10 bar, toluene.
imaginary frequency. All discussed re-
action energetics were calculated
under standard conditions (1 bar ideal
gas for all species and 298.15 K).
Model system: To obtain reliable ener-
gies for
ligand 1 was replaced by PH
a
model system in which
, we per-
3
formed coupled cluster calculations in-
cluding double excitation and approxi-
mate triple excitations [CCSD(T)].
However, these calculations require
large basis sets to display the desired
accuracy. For the model system,
CCSD(T) calculations at the quadru-
ple-z level are also not feasible. There-
fore, the following scheme based on
the nearly identical convergence be-
havior of CCSD(T) and MP2 towards
Scheme 7. The rate-determining states for hydroformylation with the 6-DPPon (1) and Xantphos (3) ligands.
mylation with the 6-DPPon (1) ligand using an CCSD(T)-
MP2:DFT IMOMO method. The calculations were support-
ed by analysis of previously determined turnover frequen-
cies within the framework of the energetic-span model. Cal-
culations based on the IMOMO scheme yield excellent
agreement with the experimental results for two popular
DFT functionals (BP86 and B3LYP). This may be related to
the observation that DFT calculations on the geometries
and hydrogen-bond strengths in the ligand backbone lead to
favorable agreement with experimental results. Further-
more, by applying the IMOMO methodology, the predicted
activation barrier is now found to be in excellent agreement
with the experimentally determined activation barrier for
the 6-DPPon (1) and Xantphos (3) ligands. In summary, we
have documented that IMOMO schemes can be used to
reach the chemical accuracy of high-level ab initio methods
for real-world systems, which suggests that this methodology
may be useful for computer-aided catalyst design. Further-
more, the IMOMO scheme is rather modular and can be
easily modified for specific cases. For example, if dispersion
interactions in the real world system are important, DFT
can be replaced by DFT-D3 as low-layer method.
the basis set limit was applied: 1) Geometry optimizations were per-
formed by using the BP86 functional together with the Stuttgart–Kçln
[
33]
full relativistic ECP28MDF core potential and the corresponding aug-
33
cc-pVTZ-PP basis set for Rh. The standard aug-cc-pVTZ basis set was
[34]
used for all other atoms.
2) An MP2 single-point energy calculation
1
8
with the cc-pwCVDZ basis set (cc-pwCVDZ-PP for Rh) including core
valence functions was performed. 3) An additional MP2 single-point
energy calculation with the aug-cc-pwCVQZ basis set (aug-cc-pwCVQZ-
PP for Rh) including diffuse and core valence functions was performed.
4
) To account for correlation effects beyond second-order perturbation
theory a coupled-cluster calculation with single and double substitutions
and with inclusion of perturbative triple excitations [CCSD(T)] together
with cc-pwCVDZ basis set was performed. 5) The final single-point
energy was obtained by the equation CCSD(T)/cc-pwCVDZ+MP2/aug-
cc-pwCVQZꢀMP2/cc-pwCVDZ. Using additional MP2 calculations to
extrapolate CCSD(T) to the quadruple-z limit is an established proce-
[
36]
dure. To check for a possible multiconfigurational character in case of
the CCSD(T) calculations, the largest T2 amplitudes were investigated
[
37]
and found to be less than 0.1. Additional single-point calculations for
the model system were performed with the parameter-free hybrid
[37]
[8]
[8]
PBE0 functional, the meta-GCA M06L and meta-hybrid M06 func-
[
39]
tionals, and long-range and dispersion-corrected wB97X-D functional.
The aug-cc-pVTZ-PP basis set was used for these calculations. The D3
[
40]
calculations were performed with the ORCA program package, and all
[
41]
other calculations by using the Gaussian 09 suite of programs.
Acknowledgements
Experimental Section
Funding of both groups via the IRTG 1038 “Catalysts and Catalytic Re-
action for Organic Synthesis” from DFG and the Swiss National Science
Foundation is acknowledged. The work in Freiburg was further supported
by the Fonds of the Chemical Industry (PhD fellowship to U.G.) and the
Alfred-Krupp Award (to B.B.). The Freiburg group is indebted to the
companies BASF and Umicore for gifts of precious-metal salts. The work
in Basel is supported by the Swiss National Science Foundation under
Grant No. 200021-117810 (to M.M.). We thank Dr. Ansgar Schꢂfer for
helpful discussions.
Real-world system: All intermediates and transition states containing
ligand 1 of the catalytic cycle were fully optimized with the BP86
and B3LYP functionals. The Stuttgart–Dresden relativistic core poten-
in conjunction with the D95 double-zeta basis set
used for rhodium. The full-electron 6-31G** basis set was used for all
other atoms. Thermodynamic corrections were calculated at the same
level of theory from a harmonic vibrational analysis. Transition states and
minimum structures were identified by the presence or absence of one
[
26,27]
[
28]
[
29]
[30]
tial
(SDD) was
[
31]
[
32]
16280
www.chemeurj.org
ꢃ 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2013, 19, 16272 – 16281

Realistic Energy Surfaces for Real-World Systems
FULL PAPER
2
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the CO dissociation being rate-determining.
[
3] See for example: T. J. Devon, G. W. Philips, T. A. Puckette, J. L. Sta-
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ꢀ
1
[
4] a) B. Breit, W. Seiche, J. Am. Chem. Soc. 2003, 125, 6608; b) W.
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1
488; c) F. Chevallier, B. Breit, Angew. Chem. Int. 2006, 118, 1629;
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ꢀ1
by using a Henry constant of 11.61 MPam kmol , which was deter-
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can refer to the conclusions drawn herein.
[
[
1
16, 14406.
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[
1
[
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35] This level of theory was chosen since it reproduces the experimen-
tally gas-phase determined rhodium–phosphorous and rhodium–
carbon distances of two rhodium complexes with a mean unsigned
error of only 0.01 ꢄ. Nevertheless, DFT optimizations of transition-
state structures may remain an error source.
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between eqeq-5 and axeq-5 as well as between trans-6 and cis-6.
These results are reported in the Supporting information.
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Supporting Information.
[
[
[
[
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[
[
40] ORCA program, Version 2.6, revision 35. Developed by F. Neese
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Published online: October 14, 2013
Chem. Eur. J. 2013, 19, 16272 – 16281
ꢃ 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
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