Rh2(II,III) Catalysts with Chelating Carboxylate and Carboxamidate Supports: Electronic Structure and Nitrene Transfer Reactivity

Article abstract of DOI:10.1021/jacs.5b12790

Dirhodium-catalyzed C-H amination is hypothesized to proceed via Rh₂-nitrene intermediates in either the Rh₂(II,II) or Rh₂(II,III) redox state. Herein, we report joint theoretical and experimental studies of the ground electronic state (GES), redox potentials, and C-H amination of [Rh₂^II,III(O₂CCH₃)₄(L)_n]⁺ (1-L) (L = none, Cl^-, and H₂O), [Rh₂(esp)₂]⁺ (2), and Rh₂(espn)₂Cl (3) (esp = α,α,α′,α′-tetramethyl-1,3-benzenedipropanoate and espn = α,α,α′,α′-tetramethyl-1,3-benzenedipropanamidate). CASSCF calculations on 1-L yield a wave function with two closely weighted configurations, (δ?)²(π₁?)²(π₂?)¹ and (δ?)²(π₁?)¹(π₂?)², consistent with reported EPR g values [ Chem. Phys. Lett. 1986, 130, 20-23 ]. In contrast, EPR spectra of 2 show g values consistent with the DFT-computed (π?)⁴(δ?)¹ GES. EPR spectra and Cl K-edge XAS for 3 are consistent with a (π?)⁴(δ?)¹ GES, as supported by DFT. Nitrene intermediates 2N-L and 3N-L are also examined by DFT (the nitrene is an NSO₃R species). DFT calculations suggest a doublet GES for 2N-L and a quartet GES for 3N-L. CASSCF calculations describe the GES of 2N as Rh₂(II,II) with a coordinated nitrene radical cation, (π?)⁴(δ?)²(π_nitrene,1)¹(π_nitrene,2)⁰. Conversely, the GES of 3N is Rh₂(II,III) with a coordinated triplet nitrene, (π?)⁴(δ?)¹(π_nitrene,1)¹(π_nitrene,2)¹. Quartet transition states (⁴TSs) are found to react via a stepwise radical mechanism, whereas ²TSs are found to react via a concerted mechanism that is lower in energy compared to ⁴TSs for both 2N-L and 3N-L. The experimental (determined by intramolecular competition) and ²TS-calculated kinetic isotopic effect (KIE) shows a KIE ～ 3 for both 2N and 3N, which is consistent with a concerted mechanism.

Full text of DOI:10.1021/jacs.5b12790

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Article
Rh2(II,III) Catalysts with Chelating Carboxylate and Carboxamidate
Supports: Electronic Structure and Nitrene Transfer Reactivity
Adrián Varela-Álvarez, Tzuhsiung Yang, Heather Jennings, Katherine P. Kornecki, Samantha N. MacMillan,
Kyle M. Lancaster, James Booker Christianson Mack, J. Du Bois, John F. Berry, and Djamaladdin G Musaev
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.5b12790 • Publication Date (Web): 28 Jan 2016
Downloaded from http://pubs.acs.org on January 28, 2016
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Rh2(II,III) Catalysts with Chelating Carboxylate and Carboxamidate
Supports: Electronic Structure and Nitrene Transfer Reactivity
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Adrián Varela-Álvarez,a,† Tzuhsiung Yang,b,† Heather Jennings,b Katherine P.
Kornecki,b Samantha N. Macmillan,c Kyle M. Lancaster,c J. B. C. Mack,d J.
Du Bois,d John F. Berry,b,* and Djamaladdin G. Musaeva,*
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a) The Cherry L. Emerson Center for Scientific Computation, 1515 Dickey Dr., Emory
University, Atlanta, GA 30322
b) Department of Chemistry, University of Wisconsin – Madison, 1101 University Ave. Madison,
WI 53706
c) Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853
d) Department of Chemistry, Stanford University, Stanford, CA 94305
Email: berry@chem.wisc.edu, dmusaev@emory.edu
†These authors have contributed equally to this work
Abstract
Dirhodium-catalyzed C–H amination is hypothesized to proceed via Rh2-nitrene intermediates in
either the Rh2(II,II) or Rh2(II,III) redox state. Herein, we report joint theoretical and
experimental studies of the ground electronic state (GES), redox potentials, and C–H amination
of [Rh2II,III(O2CCH3)4(L)n]+ (1_L) (L = none, Cl–, and H2O), [Rh2(esp)2]+ (2), and Rh2(espn)2Cl
(3) (esp = α,α,α’,α’-tetramethyl-1,3-benzenedipropanoate and espn = α,α,α’,α’-tetramethyl-1,3-
benzenedipropanamidate). CASSCF calculations on 1_L yield a wavefunction with two closely
weighted configurations (δ*)2(π1*)2(π2*)1 and (δ*)2(π1*)1(π2*)2, consistent with reported EPR g
values [Chem. Phys. Lett. 1986, 130, 20-23]. In contrast, EPR spectra of 2 show g values
consistent with the DFT-computed (π*)4(δ*)1 GES. EPR spectra and Cl K-edge XAS for 3 are
consistent with a (π*)4(δ*)1 GES, as supported by DFT. Nitrene intermediates 2N_L and 3N_L
are also examined by DFT (the nitrene is an NSO3R species). DFT calculations suggest a doublet
GES for 2N_L and a quartet GES for 3N_L. CASSCF calculations describe the GES of 2N as
Rh2(II,II) with a coordinated nitrene radical cation, (π*)4(δ*)2(πnitrene,1)1(πnitrene,2)0. Conversely,
the GES of 3N is Rh2(II,III) with a coordinated triplet nitrene, (π*)4(δ*)1(πnitrene,1)1(πnitrene,2)1.
Quartet transition states (4TSs) are found to react via a stepwise radical mechanism, whereas
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2TSs are found to react via a concerted mechanism that is lower in energy as compared to TSs
for both 2N_L and 3N_L. The experimental (determined by intramolecular competition) and
2TS-calculated kinetic isotopic effect (KIE) shows a KIE ~ 3 for both 2N and 3N, which is
consistent with a concerted mechanism.
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1. Introduction
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C–H amination via nitrene transfer catalysis (NTC) has the potential to be a
transformative method in synthetic organic chemistry.1-5 Some of the leading catalysts for intra-
and intermolecular C–H amination via NTC are coordination complexes with a Rh(II)‒Rh(II)
bond (Scheme 1), such as the Rh2-tetracarboxylates and the Rh2(esp)2 (esp = α, α, α’, α’-
tetramethyl-1,3-benzenedipropanoate) catalyst bearing chelating dicarboxylate ligands, which
operate best with sulfamate-derived nitrene species
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(NSO3R).6 Other catalysts such as silver,7-11 iron,12-17
manganese,13, 18-20 ruthenium,18, 21-23 copper,24-30 and
cobalt31-34 complexes have been shown to perform C–
H amination as well. The Rh2(II,II) complexes were
initially presumed to perform C–H amination via a
nitrene interception/insertion mechanism, as shown in
Scheme 1,6, 35 in analogy to related carbene transfer
reactions.36 However, subsequently, Du Bois and
Berry have independently shown the formation of
mixed-valent Rh2(II,III) species (including
a
Rh2(II,III)-nitrene species proposed by Du Bois and
Zare) under the highly oxidative NTC conditions,
which are also believed to be active in NTC
reactivity.37-39
Recently, the Berry group reported a new
amidate-ligated Rh2(II,III) catalyst, Rh2(espn)2Cl
Scheme 1. NTC cycle for Rh2(esp)2 and
Rh2(espn)2Cl.
(espn
=
α,
α,
α’,
α’-tetramethyl-1,3-
benzenedipropanamidate), which is not only capable of performing intramolecular C–H
amination, but it also has a long lifetime under NTC conditions, achieving turnover numbers
higher than those of Rh2(esp)2 by a factor of three in head-to-head intramolecular competition
experiments.40 The longer lifetime of Rh2(espn)2Cl during NTC as compared to Rh2(esp)2 may
be attributed to the greater thermodynamic stability of the former complex. As has been well
documented, amidate ligands not only bind more strongly to the Rh2 core than do carboxylate
ligands, but they also lower the potential required for oxidation of Rh2(II,II) to the Rh2(II,III)
level.41
As compared to Rh2(II,II) compounds, there are far fewer investigations of Rh2(II,III)
species. The most extensive electronic structure study of Rh2(II,III) species, done by Norman and
coworkers in 1979,42 was very thorough but utilized methods that are now out of date and known
to lead to inaccurate conclusions. The electronic structure of Rh2(II,III) species is complex
because of the existence of multiple low-lying electronic
configurations, which could contribute to their total
ground state wavefunction. Rh2(II,II) complexes have a
single Rh–Rh bond by virtue of the (σ)2(π)4(δ)2(δ*)2(π*)4
electron configuration where all Rh–Rh bonding and
antibonding orbitals are filled with the exception of the σ*
antibonding orbital.43 The π* and δ* orbitals located
below the σ* orbital are very close in energy,44 and thus,
Chart 1. Possible ground states of
Rh2(II,III) compounds
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upon oxidation of Rh2(II,II) to Rh2(II,III), it is a priori unclear whether a π* or δ* electron would
be removed leading, in rigorous D4h symmetry, to a Eu or B1u ground electronic state (GES),
respectively (Chart 1).
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In principle, the Eu and 2B1u states may be distinguished by EPR spectroscopy since the
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first-order spin-orbit coupling of the former state leads to the appearance of unusual EPR signals
with g values widely different from the free electron value.45 In this way, Kawamura and
coworkers have shown that a range of Rh2(II,III) carboxylate (O,O-donor) complexes have the
2Eu ground state whereas Rh2(II,III) compounds with N,N-donor ligands (e.g., formamidinates)
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have the B1u ground state.46-49 An interesting question arises in considering Rh2(II,III)
complexes with amidate (N,O-donor) ligands: will these compounds have a 2Eu ground state like
the corresponding carboxylate compounds, or is the π-donation of the equatorial ligand field now
strong enough that the δ* orbital is raised above the π* leading to a 2B1u ground state, like in the
corresponding formamidinate compounds? An acetamidate-supported Rh2(II,III) complex has
been characterized by EPR spectroscopy in acetonitrile and DMSO solution, and was found to
have g values, 푔⊥ ~ 2.1 and 푔∥ ~ 1.9, consistent with a single Kramer’s doublet and therefore
indicative of a 2B1u-type (δ*)1 ground state.50
Here we address the Rh2(II,III) GES of [Rh2(OAc)4(L)n]m+, 1_(L)n, [Rh2(esp)2(L)n]m+,
2_(L)n, and [Rh2(espn)2(L)n]m+, 3_(L)n, [where L = none with m=1; L = H2O, n=1 or 2 with
m=1; L = Cl–, n=1 with m =0; and L = Cl–, n=2, with m = –1] species by EPR spectroscopy and,
where applicable, Cl K-edge XAS, as well as by computational approaches including density
functional theory (DFT) and ab initio state-averaged complete active space self-consistent field
methods (SA-CASSCF), where necessary. Dynamic electronic correlation effects were included
by utilizing multireference difference-dedicated configuration interaction theory with two
degrees of freedom (MR-DDCI2). We also elucidate the impact of the nature of the GES of these
Rh2(II,III) complexes to the stability and reactivity of their proposed nitrene intermediates by
investigating the intramolecular C–H amination catalyzed by 2_L and 3_L species. Although it
is instructive to compare the GES of 2_L and 3_L with that of the simplified 1_L species, the
latter species are not included in the reactivity studies because NTC by 1_L has not been
established to utilize the Rh2(II,III) oxidation state.
2. Results and Discussion.
2.A. Analysis of the Rh2(II,III) Compounds.
2.A.1. Electronic Structure of Rh2(II,III) Complexes. At first, we elucidate the GES of the
Rh2(II,III) complexes using the BP86 density functional method in conjunction with TZVP basis
sets51 for optimization of geometries. Reported DFT energies were derived from single-point
B3LYP calculations on the BP86-optimized structures.52-55 Redox potential calculations were
performed using an established methodology.56 MR-DDCI2:SA-CASSCF calculations were
performed using various active spaces (see the Computational Methodology section for more
details).
[Rh2(OAc)4(L)n]m+, 1_(L)n, species. We start our discussion with Rh2(II,III) tetra-
acetate complexes [Rh2(OAc)4]+, 1, [Rh2(OAc)4(H2O)2]+, 1_(H2O)2, [Rh2(OAc)4Cl], 1_Cl, and
[Rh2(OAc)4(Cl)2]-, 1_Cl2. Herein, we mostly focus on 1_(H2O)2 and 1_Cl2 for which
experimental data are available, but we also compare those to 1 to gauge the effect of axial
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ligand coordination to the Rh2(II,III) core. EPR spectra of [Rh2(OAc)4(L)n]m+ have been reported
with L = H2O, EtOH, and THF with n = 2 and m = 1, and Cl with n =2 and m = –1. The spectra
are axial with 푔∥ = 3.38 – 4.00 and 푔⊥ = 0.6 – 1.5.48 These unusual g values are described by
Kawamura and coworkers as the result of a first-order spin-orbit interaction derived from the
nearly-degenerate π* orbitals of the 2Eu state, but computational support for these
phenomenological assignments is lacking.46-49
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To validate DFT methods against these experimental data, the GES and EPR parameters
for the compounds 1, 1_(H2O)2, 1_Cl and 1_(Cl)2, were calculated. These DFT calculations
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converged to the expected Eu GES for all four complexes.57 However, despite predicting the
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anticipated Eu ground state, the DFT-calculated EPR g values are incompatible with the
available experimental data: DFT predicts a markedly rhombic g tensor with abnormal values
giving g1, g2, and g3 of 7.36, 2.61, and 2.04 for 1, 3.41, 2.32, and 2.07, for 1_(H2O)2, 27.4, 2.43,
and 2.13 for 1_Cl, and 18.5, 2.77, and 2.14 for 1_Cl2, respectively, whereas the experimental
spectra are axial with 푔∥ ~ 4.00 and 푔⊥ << 2.00 (see Table 1).
The aforementioned discrepancy between the experimental and DFT findings can be
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explained by the multi-determinant nature of the Eu electronic state, where the energetic
degeneracy of the * orbitals presents an inherent problem for all single-determinant based
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methods, including DFT.58 Indeed, a “proper” wavefunction of the Eu electronic state should
include, at least, the following two simplified determinants
1
∗ 2
∗ 1
∗ 1
∗ 2
Ψ(2퐸푢) = √
eq. 1
[|( ) ( ) | |( ) ( ) |]
휋1 휋2 + 휋1 휋2
2
because the unpaired electron has an equal probability of being housed in either the 휋1∗ or the 휋2∗
orbital. In order to properly describe such a multi-determinant system allowing for an accurate
prediction of g tensors of the complexes, the CASSCF approach is utilized.
The leading determinants of the SA-CASSCF wavefunctions with their weights are given
in Table 2. For all 1_L compounds, there are two leading determinants that contribute equally, or
nearly equally, to their total wavefunctions. In all cases, these two leading determinants are those
that differ in their π*1 and π*2 occupation, as anticipated from the above discussion. Thus, the
CASSCF results are fully consistent with 2Eu-derived ground states for these compounds.
The MR-DDCI2 method was used on the converged SA-CASSCF wavefunction to
predict the g values of [Rh2(OAc)4]+: an axial signal with g|| = 4.00 and g = 0.05 is predicted.
As seen in Table 1, where we provide all calculated and experimental g values for [Rh2(OAc)4]+,
[Rh2(OAc)4(H2O)2]+, Rh2(OAc)4Cl
and [Rh2(OAc)4Cl2]–, the MR-DDCI2:SA-CASSCF-
calculated EPR g values are in close agreement with the experimental values. These findings
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additionally support that all these species have a Eu ground state containing a (π*)3 valence
electron configuration.
Thus, due to existence of the orbital degeneracy in 1_L+, the DFT approach is not the
best method to calculate the lowest energy electronic states and related properties of these
compounds.
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[Rh2(esp)2L]+. To date, only one set of crystallographic data is available for a metastable
Rh2(II,III) complex bearing esp ligands, [Rh2(esp)2Cl2]–.39 In this paper, we report optimized
geometries of the species [Rh2(esp)2]+, 2, [Rh2(esp)2(H2O)]+, 2_H2O, and Rh2(esp)2Cl, 2_Cl. In
Table 3, we compare the optimized parameters of these species with the available
crystallographic values. As seen from this table, the DFT approach describes the Rh–Rh and Rh–
Oav distances well.
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DFT calculations on 2 surprisingly predict a B1u-derived GES with a (δ*)1 electron
configuration. Analysis shows that in this compound, like in the case of the [Rh2(OAc)4]+
complexes, the δ* orbital has significant anti-bonding contributions from the O–C–O π*
carboxylate (bridging) orbitals. However, unlike the case of [Rh2(OAc)4]+ complexes, the δ*
orbital of 2 also has a contribution from the m-phenylene moieties of the esp ligands, an apparent
through-space interaction at 4.3 Å. This interaction slightly destabilizes the δ* orbital, and,
consequently, makes the B1u-type (δ*)1 electronic state more favorable for [Rh2(esp)2]+
2
compared to the [Rh2(OAc)4]+ complexes.
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To experimentally substantiate the computationally predicted B1u-derived ground state
with a (δ*)1 orbital configuration of 2, we turned our attention to spectroscopic studies. As
shown previously, Rh2(esp)2 is not stable in the Rh2(II,III) redox state, but in CH2Cl2 solution it
can be oxidized coulometrically to the corresponding Rh2(II,III) species 2.39 The coulometric
oxidation was monitored by UV-vis spectroscopy, which showed near-isosbestic behavior
indicative of oxidation to an isostructural
product with the possibility of a partial
transformation of the oxidized product via a
chemical
reaction.
A
sample
of
electrochemically generated 2 was frozen
upon generation and analyzed by EPR
spectroscopy. The EPR spectrum given in
Figure 1 is surprising in two ways. First, the
spectrum cannot be simulated by a single S =
½ species and therefore indicates that 2
actually contains two Rh2(II,III) species that
are similar in structure as evidenced by the
similarity of their axially symmetric EPR
signals. Second, the best-simulated EPR g
values, 푔⊥ = 2.124 and 푔∥ = 1.928 for the
first species, and 푔⊥ = 2.255 and 푔∥ = 1.893
for the second species, are indicative of a
relatively simple S = ½ species with a single
Kramers’ doublet excluding the possibility
of having a ground state with the (π*)3
orbital configuration for 2. The observed g
values instead fit well in the range of those
observed for compounds with a ground state
containing a (δ*)1 orbital.50 As for the reason
that two EPR-active species are produced
Figure 1. X-Band EPR spectrum measured at 10
K of an electrochemically oxidized solution of
Rh2(esp)2. The spectrum is modeled with two
axially symmetric subspecies present in a 1:1
ratio. Species 1: g⊥ = 2.124, g|| = 1.928, A⊥ = 95
MHz. Species 2: g⊥ = 2.255, g|| = 1.893, A⊥ = 93
MHz, A|| = 150 MHz. Instrument parameters: mw
frequency = 9.3814 GHz, power = 0.6325 dB,
attenuation = 25 dB, modulation frequency = 100
kHz, modulation amplitude = 4 G, receiver gain
= 70 dB, time constant = 163.84 ms, conversion
time = 10 ms.
during coulometric oxidation of [Rh2(esp)2], this is likely due to partial coordination of a solvent
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or electrolyte species in the axial site of the Rh2 molecule to generate Rh2 species such as
Rh2(esp)2Cl, which has been observed in a high-resolution mass spectrum,35 and is consistent
with the imperfect isosbestic behavior of the oxidation. Notably, the EPR parameters predicted
by DFT for 2, g1 = 2.24, g2 = 2.11, g3 = 2.06, differ in symmetry but are close to the
experimental values.
Comparison of the DFT calculated electronic state and aforementioned EPR data clearly
show that the utilized DFT approach provides an adequate description of the ground state
wavefunction of 2 and its derivatives. Thus DFT can be used to further explore the chemistry of
these species.
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[Rh2(espn)2L]+, 3_L. Recently, Berry and coworkers have reported a new amidate-
ligated catalyst, Rh2(espn)2Cl, 3_Cl, which can form
as any one of four possible isomers: the (cis-2,2)-,
(4,0)-, (trans-2,2)-, and (3,1)-isomers. However, the
synthesis of 3_Cl results in two structural isomers
(cis-2,2)-(3_Cl) and (4,0)-(3_Cl), with the cis-2,2
isomer favored in
a
4:1 ratio.40 At low
concentrations, 3_Cl dissociates Cl– in CH2Cl2 to
form [Rh2(espn)2]+, 3, and it was possible to assign
electrochemical features to both the Cl-bound and
unbound species.40
We report here experimental EPR and XAS
measurements aimed at elucidating the nature of the
ground state of 3. EPR data on the [Rh2(espn)2L]+
complexes in solution are consistent with an S = 1/2
ground state for these species. Indeed, the spectra of
these compounds can be straightforwardly simulated
by near-axial S = 1/2 signals showing 103Rh
hyperfine splitting of the 푔∥ signal. The best
simulations of these spectra yield the following
parameters: 푔⊥ = 2.11, 푔∥ = 1.927, 퐴∥ = 90 MHz for
(cis-2,2)-(3_Cl) and 푔⊥ = 2.105, 푔∥ = 1.905, 퐴∥ =
Figure 2. X-Band EPR spectrum measured
at 10 K of 4,0-Rh2(espn)2Cl. The spectrum
is modeled with g⊥ = 2.105, g|| = 1.905, and
A|| = 135 MHz. Instrument parameters: mw
frequency = 9.3792 GHz, power = 0.6385
mW, attenuation = 25.0 dB, modulation
frequency
=
100 kHz, modulation
amplitude = 4 G, receiver gain = 30 dB,
time constant = 327.68 ms, conversion time
= 10.0 ms.
135 MHz for (4,0)-(3_Cl) (see Figure 2). Our results compare favorably with those reported by
Kadish, Bear, and coworkers on Rh2(II,III) acetamidate analogs, which have 푔⊥ = 2.11-2.13, 푔∥
= 1.89-1.92, and 퐴∥ = 79-90 MHz.50 These data support the assignment of the GES with a (δ*)1
configuration for 3.
Another spectroscopic method that has not yet been used with metal-metal bonded
compounds but in principle can distinguish between the (π*)3 and (δ*)1 states in [Rh2(II,III)]-Cl
complexes is Cl K-edge X-ray absorption spectroscopy (XAS). Cl K pre-edge transitions may be
formally assigned as Cl 1s  “φ” where φ represents a molecular orbital of the form [(Rh 4d) +
√1 − 훼2 (Cl 3p)]. Here, the presence of Cl 3p character in partially unoccupied valence orbitals
is required for non-zero Cl K pre-edge intensity. From symmetry considerations, Cl character
can be mixed into σ- or π-type orbitals in a linear Rh–Rh–Cl structure, but cannot be mixed into
δ-symmetry orbitals. Thus, a (π*)3 compound should display a pre-edge feature below the main
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σ* transition corresponding to the partially filled
Rh2 π* level, and a (δ*)1 compound should not.
Thus, in the case of the anticipated (δ*)1 ground
state of 3_Cl we expect to observe a Cl 1s  σ*
pre-edge transition, whereas with a (π*)3 ground
state there would be an additional, resolvable
lower energy transition: Cl 1s  π*. The Cl pre-
edge region for 3_Cl is shown along with its
corresponding second-derivative plot and least-
squares fit in Figure 3. The pre-edge region
comprises a single peak at 2822.1 eV. The
presence of a single peak is consistent with a GES
having a Rh–Rh * SOMO.
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Figure 3. Pre-edge region and second
derivative plot of (cis-2,2)-Rh2(espn)2Cl Cl
K-edge XAS. Pseudo-Voigt peaks are shown
in gray.
To support these experimental results, we
have computationally investigated the (cis-2,2) and
(4,0)
isomers
of
[Rh2(espn)2]+,
3,
[Rh2(espn)2(H2O)]+, 3_H2O, and Rh2(espn)2Cl,
3_Cl species. Their calculated and experimental
geometries at the ground doublet electronic states (with the unpaired electron in the Rh–Rh δ*
orbital) are given in Table 4. One should mention that the (4,0)-(3_L) species could have two
isomers, which differ by coordination of the L ligand to the Rh2-center surrounded by either four
N-centers or four O-centers. Below, we call these isomers as (4,0)N and (4,0)O, respectively. In
general, the (4,0)N isomer is found to be energetically a few kJ/mol more favorable than the
(4,0)O isomer for both doublet and quartet state species. The energy difference between these
isomers is slightly larger for L = Cl than H2O. For simplicity, below we discuss only the
energetically more stable (4,0)N isomers of 3_H2O and 3_Cl species, but we include all energy
and geometry results for the less stable (4,0)O isomers of 3_H2O and 3_Cl in the supporting
material.
As seen from Table 4, in general, the calculated geometries of the doublet S = 1/2 GESs
of 3, 3_H2O and 3_Cl with the unpaired electron in the Rh–Rh δ* orbital match closely their
experimental values. One major disagreement between the calculated and experimental
structures occurs for (cis-2,2)-(3_Cl): the experimental structure of this species is polymeric,
with Cl– ions bridging an infinite chain of Rh2 species. In contrast, its calculated structure is
molecular with a monodentate Cl– ligand. As a result, the Rh–Cl bond distance is severely
underestimated in the calculation, which, in turn, leads to an overestimation of the Rh–Rh bond
distance. Since the Cl-bridged structure is a feature only of the solid-state packing of this
compound and is likely absent in homogeneous solution, the calculated structure is presumably a
more accurate model for the compound in solution during catalysis.
After elucidating the electronic and geometric structures of the aforementioned Rh2(II,III)
species, we are well positioned to discuss their redox potentials, which are vital for
understanding the stability and reactivity of these species. Based on the above-presented
comparison of DFT, and experimental data, one may confidently use DFT methods to calculate
redox potentials and provide insight into the proclivity for axial ligand binding of the Rh2(II,III)
species 2_L and 3_L. We excluded 1_L species from reactivity studies due to the facts that: (a)
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NTC by 1_L has not been established to utilize the Rh2(II,III) oxidation state, and (b) the GES of
1 is multi-configurational and, therefore, may not be accurately described by the DFT approach.
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2.A.2. Energy Landscape: Redox Potentials and Axial Ligand Effects. For [Rh2(esp)2]+,
2, experiments showed that the 20/+ redox potential is at 0.80 V vs Fc/Fc+.39, 59 DFT predicts a
value of 0.78 V, which in excellent agreement with the experimental value (see Scheme 2). The
calculated [2_Cl]0/- redox potential is –0.72 V vs Fc/Fc+. Since previous experiments showed
that 2 strongly binds Cl– ions,35 we also calculated the impact of a second Cl– ligand binding to
[Rh2(esp)2]+, 2. It was found that the binding of two Cl– ligands to 2 greatly lowers the
Rh2(II,II)/Rh2(II,III) (in short Rh24+/5+) redox potential by 2.27 V. These findings show that
increasing the concentration of chloride (or any other anionic potential axial ligand for that
matter) in reaction mixture, could strongly favor catalysis in the Rh2(II,III) regime, though if the
concentrations are too high catalysis could be hindered by blocking of both axial sites.
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Scheme 2. Energy landscape of compounds 2, 2_Cl and 2_Cl2. DFT-calculated and
experimental redox potentials are given without and with parentheses, respectively.
As mentioned above, experiments showed that complex 3_Cl could have several isomers
among which the (cis-2,2) and (4,0) isomers are experimentally observed, with the cis-2,2 isomer
favored in a 4:1 ratio.40 Consistent with this finding, DFT calculations predict the (cis-
2,2)_(3_Cl) isomer to be lower in energy than the (4,0) isomer by 12.1 kJ/mol (see Scheme 3).
Dissociation of the axial chloride ligand leads to the active cationic catalyst, [Rh2(espn)2]+, the
(cis-2,2)-3 isomer of which is higher in energy by 15.5 kJ/mol than its (4,0)-3 isomer. The four
nitrogen atoms bound to the high oxidation state RhIII center in the (4,0) isomer, therefore,
appear to provide greater stabilization to the Rh atom than two nitrogen and two oxygen atoms as
in the (2,2) isomer.
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-Cl-
+Cl-
[(cis-2,2)-Rh2(espn)2]2+
[(cis-2,2)-Rh2(espn)2Cl]+
[(4,0)-Rh2(espn)2]2+
[(4,0)-Rh2(espn)2Cl]+
17.3 kJ/mol
+Cl-
-Cl-
-8.4 kJ/mol
+e-
-e-
-e- +e-
-e-
+e-
-e-
0.56 V
(0.60 V)
+e-
0.48 V
1.11 V
1.57 V
(1.01 V)
-Cl-
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+Cl-
-Cl-
[(cis-2,2)-Rh2(espn)2]+
[(cis-2,2)-Rh2(espn)2Cl]
[(4,0)-Rh2(espn)2]+
[(4,0)-Rh2(espn)2Cl]
-12.1 kJ/mol
15.5 kJ/mol
+Cl-
+e-
-e-
-e-
+e-
+e-
-e-
-e- +e-
-0.44 V
(-0.33 V)
-1.41 V
-0.43 V
-1.47 V
+Cl-
-Cl-
-Cl-
[(cis-2,2)-Rh2(espn)2Cl]-
[(4,0)-Rh2(espn)2Cl]-
[(cis-2,2)-Rh2(espn)2]
[(4,0)-Rh2(espn)2]
+Cl-
-9.5 kJ/mol
15.8 kJ/mol
(cis-2,2) isomer
(4,0) isomer
Scheme 3. Energy landscape of compounds (cis-2,2)-3 and (cis-2,2)-(3_Cl), as well as (4,0)-3
and (4,0)-(3_Cl). DFT-calculated and experimental redox potentials (listed relative to the Fc/Fc+
couple) are given without and with parentheses, respectively. Presented relative energies (in
kJ/mol) are listed relative to the corresponding (4,0)-isomers.
Cyclic voltammetry experiments were performed for (cis-2,2)-3 which showed two
reversible waves corresponding to [Rh2(espn)2]0/+ at –0.33 V and [Rh2(espn)2]+/2+ at 1.01 V. A
third quasi-reversible peak was observed at 0.60 V which was assigned to the chloride bound
[Rh2(espn)2Cl]0/+ redox couple.40 For (cis-2,2)-3, DFT calculations predicted the [Rh2(espn)2]0/+
couple at –0.44 V and the [Rh2(espn)2]+/2+ couple at 1.57 V. The [Rh2(espn)2Cl]0/+ couple is
predicted at 0.56 V. Here the agreement between calculated and experimentally measured redox
potentials is superb, providing excellent support for the assignments of these waves as well as
validation for the DFT methods used (see Computational procedure for more details). The one
exception is the redox couple involving the dicationic species [(cis-2,2)-Rh2(espn)2]2+, where the
discrepancy is likely the result of stronger solvation effects on the energy of the dication. For the
(4,0) isomer of 3, the [Rh2(espn)2]0/+ couple was predicted at –0.43 V and the [Rh2(espn)2]+/2+
couple at 1.11 V. The [Rh2(espn)2Cl]0/+ couple was predicted at 0.48 V. All of the calculated and
measured redox potentials are summarized in Scheme 3.
This analysis of Rh2 electronic states and redox potentials now positions us to investigate
catalytically relevant intermediates of the mixed-valent Rh2(II,III) complexes 2_L and 3_L, and
study intimate mechanistic details of C–H amination catalyzed by these systems, where L =
none, H2O and Cl.
2.B. Rh2(II,III) Nitrene Complexes and Mechanism of the intramolecular C–H amination.
2.B.1. Electronic Structure of the Rh2(II,III)-Nitrene Intermediates. As mentioned above (see
Scheme 1), one of the most important intermediates of both intra- and intermolecular C–H
amination by the mixed-valent Rh2(II,III) species under oxidative NTC conditions is the transient
Rh2(II,III)-nitrene complex. Since isolation and characterization of these transient complexes
has, to date, not been possible, DFT and CASSCF computations, validated above, appear to be
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the most valuable tool to study the electronic and geometric structures, as well as reactivity of
these species.
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DFT calculations were used to optimize structures of the 2N_L and 3N_L nitrene
complexes of the species 2_L and 3_L, respectively, as described in more detail in the
Computational Methodology section. The results are given in Tables 5 and 6. In all structures,
the Rh–Rh distances of 2.39 – 2.48 Å are not much changed from those of 2_L and 3_L.
Importantly, the addition of an L ligand has little effect on the Rh–Rh distances but elongates the
Rh–Nax bond distance, more notably in the doublet state for 2N_L, but the effect is seen in both
spin states of 3N_L compounds. Interestingly, in doublet 2N, the C1–H1 bond of the nitrene
fragment interacts with the N-center and, already, is partly activated with C1–H1, N–H1, and Rh–
N distances of 1.15, 1.65, and 1.92 Å, respectively (see also Figure 8).
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In all 2N_L and 3N_L complexes, the doublet and quartet states are predicted by DFT to
be quite close in energy. For the 2N_L series, the doublet states are predicted to be lowest in
energy by 9.6 and 13.8 kJ/mol with L = none and Cl–, respectively. The aquo complex is
predicted to have the quartet state lower in energy by a (practically negligible) 4.6 kJ/mol. For
the 3N_L compounds, the quartet states are all lower in energy, presumably due to the higher
destabilization of the δ* orbital by the more electron-donating equatorial N-donors. The energy
differences to the doublet states range from 9 – 15 kJ/mol for the cis-(2,2) isomers, and from 8 –
11 kJ/mol for the (4,0) isomers.
In general, the sulfamate-derived
nitrene can utilize its σ and two π orbitals to
form bonds with the σ- and π-symmetry
orbitals of the Rh2(II,III) core, similar to those
previously described for Rh2-carbene and Ru2-
nitride compounds.60-68 The important frontier
orbitals of the nitrene complexes are the Rh2-
centered δ* orbital, two three-center Rh–Rh–N
π* orbitals, and the three-center Rh–Rh–N σ*
orbital (see Chart 2). The δ* and π* orbitals are
expected to be close in energy, as is well-
known in other Rh2 and Ru2 systems with a
similar electron count.5, 63-67, 69 However, the π*
orbitals are expected to differ in energy since
one of these two orbitals, denoted π*, is also
Chart 2. Molecular orbital ordering of [Rh–Rh]–
NSO3R compounds, with the highlighted electron
configurations of the doublet and quartet states.
Only the major electron configuration is shown
in each case. Two π* orbitals are shown as
degenerate only for simplicity.
involved in the N–S bond of the bent nitrene unit. Thus, the similar energies of the doublet or
quartet states for the nitrene complexes are derived from configurations with differing population
of the δ* and π* levels. The configuration of the quartet state is (δ*)1(π*)1(π*″)1, but there are
several possible doublet configurations to consider. Importantly, the major acceptor orbitals for
electrophilic reactivity are the Rh–Rh–N π* orbitals, which are heavily polarized towards the N
atoms.
Due to the several possible electron configurations for the doublet state, we may expect
the doublet states of 2N and 3N to be multi-configurational, with three valence electrons in the
near-degenerate δ*, π*, and π*″ orbitals. To gauge the importance of this effect, and to extract a
useful description of the bonding in these compounds, both DFT and CASSCF calculations on
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2N and 3N complexes were performed with the simplifying truncation of CH3 for the organic
substituent on the nitrene group (labeled 2N and 3N). Two distinct DFT models for doublet-
state 2N were considered containing either a singlet or triplet nitrene coordinated to the Rh2 unit.
As shown in Table S1, these two configurations are nearly isoenergetic but have drastically
different spin distributions. For reference, the DFT frontier orbitals of the singlet nitrene
configuration are shown in Figure S1. A similar situation arises when the doublet state of 3N is
examined by DFT methods (Table S1). Two drastically differing doublet states are found to be
different by only ~ 8 kJ/mol. Due to the ambiguity in the DFT-calculated electronic structure,
further analysis of the bonding in these intermediates was made at the CASSCF level.
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The CASSCF electronic configurations of 2N and 3N and their corresponding weights
are given in Tables 7 and 8. The natural orbitals of the multiconfigurational wavefunction are
shown in Figures 4 and 5. Both quartet states are quite similar, with the anticipated
(δ*)1(π*)1(π*″)1 configurations and spin delocalized throughout the Rh–Rh–N unit. The doublet
states of 2N and 3N are electronically distinct. As seen in Figure 4, there is significant mixing
of the orbitals of δ* and π*″ symmetry in 2N leading to some fluidity in its electronic structure.
We may describe the electronic structure as a resonance hybrid between a (δ*)2(π*)1(π*″)0
configuration and an antiferromagnetic (δ*)d(π*)u(π*″)u configuration (here d and u denote spin-
down and spin-up, respectively). The former configuration may be described in valence bond
terms as having a Rh2(II,II) unit with a coordinated nitrene radical cation, while the latter
configuration indicates a Rh2(II,III) species that is antiferromagnetically coupled to a triplet
nitrene group. The view that both of these configurations contribute to the ground state is
supported by the Mulliken spin populations showing very little (but negative) spin on the Rh
centers and 1.05 spin on the nitrene N atom. It is remarkable that the calculations support partial
+
oxidation of the nitrene moiety, itself a strong oxidant, by the Rh2(esp)2 core. This result is,
0/+
however, in agreement with the high Rh2(esp)2 redox potential, but since we have shown the
redox potentials to drop considerably upon chloride binding, it is likely that the electronic
structure will change significantly as a function of the axial ligands.
σ* [0.112562]
π''*-δ* [0.807063]
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π'* [1.028932]
π''*+δ* [1.227204]
Figure 4. Frontier orbitals of the natural orbitals of doublet 2N' from CASSCF. Occupation
numbers are shown in bracket.
As expected from the greater stabilization of higher oxidation states by espn, the major
configuration of 3N, (δ*)1(π*)2(π″*)0, is best described as consisting of an Rh2(II,III) unit
coordinated by a singlet nitrene species (see the orbitals and occupation numbers given in Figure
5. Here, the spin population is clearly localized on the Rh2 unit. In each case, there are other
minor configurations contributing up to 26% of the wavefunction that are due to double- and
single-exitations from the main configuration.
σ* [0.160539]
π''* [0.411299]
δ* [1.031735]
π'* [1.997225]
Figure 5. Frontier orbitals of the natural orbitals of doublet 3N' from CASSCF. Occupation
numbers are shown in brackets.
It is instructive at this juncture to compare the electronic structure of 2N and 3N to Co
porphyrin complexes, which have been shown to undergo metal-centered oxidation upon the
binding of alkyl sulfamate nitrenes to give Co(III)(Por)(NSO3R•−) species.70 As shown in Figure
6, the electronic structures of both 2N and 3N are quite different from that of the Co species.
One reason for this difference can be understood from the redox potentials of the respective
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catalysts. 2 exhibits a Rh24+/5+ couple at 0.78 V vs Cp2Fe and 3 exhibits a Rh25+/6+ couple at 1.57
V vs Cp2Fe in CH2Cl2 (vide supra). In contrast, Co(TPP) (TPP = tetraphenylporphyrin) has been
shown to exhibit three oxidation waves at 0.24, 0.45, and 0.61 V vs Cp2Fe in CH2Cl2,
corresponding to one metal-centered and two ring-centered oxidations, respectively.71 Thus,
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+
Co(II) is able to reduce the nitrene group to a radical anion while neither the Rh2(esp)2 core nor
+
+
the Rh2(espn)2 core are reducing. In fact, Rh2(esp)2 is highly oxidizing and there is a
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contribution to the GES of 2N from a Rh2(II,II) species bearing a nitrene radical cation. In
+
contrast, the Rh2(espn)2 core is content in the Rh2(II,III) oxidation state and supports a bound
singlet nitrene. In addition to the difference in the redox potentials, there is also a difference in
the mechanism of C–H amination between the Co(Por) system, which has been proposed to
proceed via stepwise mechanism,72 whereas we propose here that both Rh2 systems operate via a
concerted mechanism (vide infra).
Figure 6. Comparison of the electronic structure of Co-porphyrin-nitrene(radical) species (left)
with 2N (center) and 3N (right). Here, the two π-symmetry orbitals are shown separately and
localized on N, and in the Rh2 cases the δ* electrons are also shown.
We further investigated, at the DFT level, both doublet and quartet potential energy
surfaces for C–H amination via the nitrene complexes {Rh2(esp)2(L)[NSO3(CH2)3Ph]}n+, 2N_L,
and {Rh2(espn)2(L)[NSO3(CH2)3Ph]}n+, 3N_L keeping in mind the caveat that the doublet states
are multi-configurational and that the DFT description of their electronic structure does not
explicitly take this complexity into account. A full analysis of the potential energy surfaces at the
CASSCF level cannot be performed because it is prohibitively expensive.
2.B.2. Mechanistic details of intramolecular C–H amination via 2N_L and 3N_L
nitrene complexes. There are two limiting mechanisms for nitrenoid C–H amination that should
be considered: concerted (C) and stepwise (S) insertion of the nitrene into a substrate C–H bond
(Scheme 4). In the C mechanism, there is a single transition state leading to C1–N bond
formation, C1–H1 bond cleavage, and N–H1 bond formation. The S mechanism starts by
hydrogen atom (H1) transfer (HAT) to produce a protonated nitrene radical anion and a benzylic
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radical followed by radical recombination to yield the products. Unpaired spin density on the
nitrene N atom is often naively suggested to support HAT in an S mechanism, but there are
strong
kinetic
and
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thermodynamic
arguments
against such generalizations.73
Below,
we
develop
an
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electronic
structure-based
approach to understand the
differences between a C and S
mechanism.
If we consider the
orbital requirements for a C
mechanism,
the
three-
membered N–C1–H1 ring of the Scheme 4. Schematic presentation of the concerted (C) and
stepwise (S) mechanisms of intramolecular nitrene insertion
into a substrate C–H bond in the 2N_L and 3N_L nitrene
complexes.
transition state will require one
orbital from each of the nuclei
involved: a N p-orbital (or spx
hybrid), a C1 p- or spx-hybrid orbital, and a H1 1s-orbital. The stabilization of a three-membered
ring with three orbitals requires the presence of two electrons, to form a 3c/2e bond. These two
electrons obviously originate from the C1–H1 bond of the substrate. Thus, this mechanism
requires an empty (but energetically accessible) N-centered orbital that can accept two electrons
from the C–H bond.
The electronic requirements of the S mechanism are different. This mechanism relies on
an HAT step, and requires the N atom to accept a single electron. Therefore, this mechanism
requires either an empty or half-filled N-centered orbital capable to accept the incoming H1
atom with one unpaired electron.
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Figure 7. Schematic representation of the calculated reactants, intermediates, transition states
and products, alone with their relative energies (relative to the corresponding reactants, in
kJ/mol), of the intramolecular C–H amination in the 2N_L and 3N_L nitrene complexes.
Based on the aforementioned discussion, it can be expected that intramolecular C–H
amination in the doublet state nitrene complexes with an empty and easily accessible Rh–Rh–N
π* orbital, will proceed via a C mechanism. On the other hand, the same process in the quartet
state nitrene complexes, having two half-filled Rh–Rh–N π* orbitals, is expected to proceed via
the S mechanism. Thus, the spin state of the nitrene intermediate is expected to play a significant
role in determining the mechanism of C–H amination. This is not a consequence of differing spin
population, but orbital populations. Considering the electronic structure in Figure 6, one can
easily see why the Co porphyrins use an S mechanism.
Armed with the aforementioned electronic structure-based prediction of the reactivity of
the 2N_L and 3N_L nitrene species, we set out to investigate the mechanisms (energy and
geometries of all transition states, intermediates and products) and controlling factors of
intramolecular benzylic C–H bond amination in NSO3(CH2)3Ph. Since the calculated energy
difference between the doublet and quartet states of both starting 2N_L and 3N_L nitrene
species is relatively small and is strongly dependent on the chemical compositions of these
complexes, one may not clearly suggest which electronic state (doublet or quartet) of the 2N_L
and 3N_L species is responsible in the amination reaction in experiments. In principle,
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depending on the concentrations of exogenous L ligands in solution, any of these electronic
states of both 2N_L and 3N_L nitrene species could be a catalytically important one. Therefore,
we studied the mechanisms of the intramolecular benzylic C–H bond amination with the
NSO3(CH2)3Ph ligand for all these species at their lowest energy doublet and quartet states. The
calculated important intermediates, transition states and products of these reactions with their
relative free energies are given in Figure 7. Representative transition state structures are given in
Figure 8. More details of all these structures are given in the Supporting Materials.
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C1
C1
H1
H1
Rh1
N
N
Rh1
Rh2
L
Rh2
L
(cis-2,2)-(3N_L)
(cis-2,2)-(3N_L_TS12)
C1
H1
C1
N
N
H1
Rh1
Rh1
Rh2
Rh2
L
L
(cis-2,2)-(3N_L_TS1)
(cis-2,2)-(3N_L_TS2)
Figure 8. Calculated structures of the nitrene complex, and transition states TS1, TS2 and TS12.
The structures of L = Cl- are shown here as an example. See Supporting Materials for similar
structures for other species.
Intramolecular C–H Amination. The exact mechanism of C–H amination is expected to
depend strongly on the spin state of the nitrene reactant. As seen in Figure 7, all doublet nitrene
species uniformly undergo nearly barrierless (0.4 – 9.6 kJ/mol, at the transition state TS12),
concerted insertion of the nitrene into the C1–H1 bond. On the other hand, the quartet nitrene
species undergo stepwise C1–H1 functionalization via a mechanism involving: (1) H1-atom
abstraction with energy barriers of 3.8 – 42.3 kJ/mol, TS1, followed by (2) radical
recombination, TS2. The recombination step is essentially barrierless for the 2N species, but for
3N is uphill from the intermediate PROD-1 by 5.8 – 53.5 kJ/mol, due to the different
occupancies of the π* orbitals, depending strongly on the identity of L.
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While it is tempting to assign the concerted
pathway as the lowest-energy pathway and therefore
the preferred pathway for catalysis, we must also
keep in mind that in 3N_L the quartet states are
lower in energy, and spin crossover to the doublet
surface would be necessary in order to access the
fastest rates of the doublet potential energy surface
(see Scheme 5).74-75 However, we should also
consider that formation of 3N is most likely to take
place on a doublet surface (2Rh2(II,III) + 1PhINSO3R
→ 23N + PhI). The main assumption underlying the
proposed two-state reactivity for 3N is that spin state
crossover is fast compared to the other barriers
involved in nitrene formation and C–H amination.
Under this assumption, the energy barriers are
necessarily steeper for the 3N_L compounds than
their 2N_L analogs since the former must undergo a
spin state change.
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Scheme
5.
Simplified
reaction
coordinate diagram for C–H amination
by Rh2(II,III) complexes.
Kinetic Isotope Effects. One way to assess
the computed reaction pathways is comparison of the predicted and measured kinetic isotope
effect (KIE) of the reactions. We have experimentally determined the KIE under identical
conditions for compounds 2 and 3 (see Chart 3), which are 2.9 and 2.6, respectively. These are
remarkably similar, especially considering that catalyst 2 is proposed to utilize both a Rh2(II,III)
and an Rh2(II,II) mechanism. In comparison, the KIE for 1, 1.9,76-77 is somewhat smaller and
may suggest that a Rh2(II,III) pathway is not viable for 1. Undoubtedly, the KIE must be a
product of all of the potential mechanisms, and can even change over the course of a reaction if
the nature of the active catalyst is changing, as is likely the case here. Given that KIEs of ~ 2 are
established for concerted nitrene transfer reactions, whereas values of ~6 are associated with
HAT steps, the experimental KIE values are more suggestive of a concerted intramolecular
nitrene insertion mechanism.78
In agreement with this assessment, the
calculated KIE values are 3.1, 2.3 and 2.8 for
doublet state 2_N_L with L = none, H2O and Cl–
, respectively, while the corresponding values for
the quartet surface are 6.3, 6.1 and 5.9. For the
3_N_L catalysts (L =none, H2O and Cl–), the
doublet KIE’s are calculated to be 2.5, 1.8 and
2.1 and the quartet values are 5.9, 6.3 and 5.4.
Chart 3. Reaction and conditions for
experimental KIE measurement
Thus, the calculated KIEs are significantly larger for the quartet state pathways than they are on
the doublet state analogs. Moreover, the quartet values are too large compared to the
experimental values. Thus, the doublet transition state appears to be the most important one for
defining the C–H amination pathway despite the fact that the 3N_L nitrene intermediates favor a
quartet ground state. It is worth mentioning that since the exact identities of catalytic
intermediates and active oxidant remain obscure at this time, we cannot hope to achieve better
agreement between the experimental and computed KIE’s.
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3. Conclusions
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From the above presented joint computational and experimental studies we may draw the
following conclusions:
(a) Rh2(II,III) tetracarboxylate complexes, [Rh2II,III(O2CCH3)4(L)n]+ (1_L) (L = none, Cl–,
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and H2O), have a Eu-derived ground electronic state with degenerate π*-orbitals and a
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(π*)3 valence electronic configuration; therefore, the electronic structure of these
compounds cannot be adequately modeled at the DFT level. CASSCF calculations of the
EPR g values are in good agreement with their experimental values.
(b) Unlike typical Rh2(II,III) tetracarboxylates, [Rh2(esp)2(L)n]m+, 2_(L)n, and
[Rh2(espn)2(L)n]m+, 3_(L)n, [where L = none with m=1, L = H2O, n=1 or 2, with m=1, L
2
= Cl–, n=1, with m =0, and L = Cl–, n=2, with m = –1] species have a B1u-derived
ground electronic state with a (δ*)1 valence electronic configuration, as evidenced by
EPR spectroscopy and Cl K-edge XAS. Importantly, this state is not a multi-reference
state and, therefore, can be modeled well using DFT methods.
(c) Nitrene complexes 2N_L and 3N_L of [Rh2(esp)2(L)n]m+, 2_(L)n, and
[Rh2(espn)2(L)n]m+, 3_(L)n, respectively, are proposed to be reactive intermediates in C–
H amination. For 2N, a complex multideterminental doublet state is predicted to be
lowest in energy, whereas 3N favors a high-spin quartet ground electronic state with a
(δ*)1(π*)2 valence electronic configuration. Binding π-donor axial ligands destabilizes
the quartet state.
(d) The calculated energy barriers for stepwise C–H amination in the quartet state are found
to be uniformly higher than for concerted C–H amination in the doublet state. While 2N
is able to access the doublet surface directly, 3N must undergo a change in spin state first,
which leads in effect to higher barriers to C–H amination by the latter species. Thus, the
gain in catalyst robustness in changing from carboxylate to amidate equatorial ligands is
counterbalanced by a loss in catalyst efficiency.
(e) Experimental KIE measurements yield values that are too low to be in agreement with a
stepwise, C–H abstraction/radical recombination pathway and show better agreement
with the mechanism outlined in Scheme 5.
4. Experimental Section
General Reagents and Methods. Catalysts 1 and 2 were prepared by published
methods.6, 40 All solvents were used as received without further purification unless otherwise
noted. Electrochemical oxidation of 1 was performed according to a published protocol.39
Electron Paramagnetic Resonance. EPR data were acquired using a Varian Line X-
band spectrometer equipped with a Varian E102 microwave bridge interfaced with a Linux
system. An Oxford Instruments ESR-900 continuous-flow helium flow cryostat and an Oxford
Instruments 3120 temperature controller were used to set and maintain the sample temperature.
A Hewlett-Packard 432A power meter was used for microwave power calibration. Simulations
were performed using EasySpin software.79 The hyperfine fittings are based on line shape
analysis.
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X-Ray Absorption Spectroscopy. Cl K-edge XAS spectra were measured at SSRL
beamline 4-3 under ring conditions of 3 GeV and 500 mA. Samples were ground to a fine
powder and were spread to a vanishing thickness onto 38 µm low-S Mylar tape. All samples
were measured in a He atmosphere at room temperature in fluorescence mode using a Lytle
detector. The incident beam energy was calibrated by setting the energy of the first inflection
point in the Cl K-edge spectrum of KCl to 2824.8 eV. Intensity was normalized with respect to
the incident beam using a He-filled ion chamber upstream of the sample. Data represent an
average of 6 scans measured from 2720 to 3150 eV. Data were processed with SIXPACK.
Spectra were normalized by fitting a polynomial flattened to energies below 2840 eV to the data
and normalizing the region above this energy to unity.
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General Procedure for KIE experiments. 3-phenylpropyl-3-d sulfamate (105 mg, 0.48
mmol, 1.0 equiv) was combined with MgO (45mg, 1.11 mmol, 2.3 equiv), dirhodium catalyst
(12 mmol, 0.025 equiv) and 3.0 mL of CH2Cl2. The resulting suspension was stirred for 5 min,
after which time PhI(OAc)2 (172 mg, 0.534 mmol, 1.1 equiv) was added in a single portion. The
reaction flask was sealed and the mixture was stirred for 12 h. At the conclusion of this period,
the suspension was filtered through a short pad of Celite, and the flask and filter cake were
rinsed with 5–10 mL of CH2Cl2. The filtrate was concentrated under reduced pressure to a
purple oil. Purification of this material by chromatography on silica gel (20% EtOAc in
hexanes) afforded the desired product mixture as a white solid. The kinetic isotope effect value
was determined by 13C NMR analysis using the method of Wang and Adams.80
Computational Methods. Calculations of g-tensors, redox potentials, and
multiconfigurational electronic structures were performed using the ORCA software package.81
Potential energy surface calculations were performed by the Gaussian_09 suite of programs.82
Orbitals were visualized using the MOLEKEL software program83 or UCSF chimera software
program.84
Calculation of EPR g-tensors of 1_L and 2L. EPR g-tensors of 1_L and [trans-
Rh2(esp)2]+ was calculated on top of DFT optimized geometry according to the method described
above. For 1_Cl2, the geometry was obtained from the reported crystal structure of
((NH2)3C)2[Rh2(OAc)4Cl2] without further optimization. To calculate the g-tensors for all the
complexes studied, B3LYP functional with scalar relativistically recontracted basis set of TZVP
(SARC-TZVP)85-86 was used. Scalar relativistic effects were accounted for in the Hamiltonian by
the zeroth order regular approximation (ZORA) using the model potential of van Wullen.87
Ab initio multireference configuration interaction (MRCI) calculations of the molecular
g-tensors for dirhodium tetraacetate complexes were performed on top of DFT optimized
geometries, except for [Rh2(OAc)4Cl2]– (vide infra). The DFT geometries were optimized using
the BP8688-89 functional with the SARC-def2-TZVPP basis set on Rh and the SARC-def2-SVP
basis set on the rest of the atoms. Scalar relativistic effects were accounted for by ZORA. The
evaluation of the Coulomb integrals were approximated by the resolution of identity (RI)
approach.90 Dispersion effects were treated with the D391 correction. The MRCI calculations
were performed at the state-averaged complete active space self-consistent field (SA-CASSCF)92
wavefunctions. Here, the MRCI approach was modeled by the multireference diference-
dedicated configuration interaction theory with two degrees of freedom (MR-DDCI2).93-94 To
calculate the molecular g-tensors, first order perturbation on the converged MRDDCI2:CASSCF
wavefunction using the electronic Zeeman Hamiltonian was performed. The effect of spin-orbit
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coupling was introduced using the quasi-degenerate perturbation theory (QDPT)95-96 with the
spin-orbit mean field Hamiltonian (SOMF). In the SA-CASSCF calculations we used different
active spaces to incorporate the effects of axial ligands. An active space of thirteen electrons in
eight orbitals (13,8) was used for the axially-free [Rh2(OAc)4]+ complex to include all metal d-
orbitals except the two dx2-y2 orbitals which are highly antibonding with respect to the equatorial
ligands. An active space of (17,10), which includes all spin-orbitals in (13,8) and four electrons
in two σ orbitals from both H2O ligands, was used for the bis(aquo) complex. An active space of
(19,11), which includes all spin-orbitals in (13,8) and six electrons in three orbitals from the 3p
orbitals of Cl-, was used for the chloro complex. An active space of twenty-five electrons in
fourteen orbitals (25,14), which includes all spin-orbitals in (13,8) and twelve electrons in six
orbitals from the 3p orbitals of both Cl-, was used for the dichloro complex.
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CASSCF calculations on the nitrene complexes, 2N and 3N, were performed on
truncated models, denoting 2N and 3N, with the organic substituent on the nitrene replaced by a
methyl group. A (19,12) active space was used. This active space includes (13,8) from both
rhodium atoms and (7,4) from the nitrene, which are N 2s orbital and nitrene one σ and two π
orbitals. The inclusion of N 2s orbital helps stabilize the convergence of the CASSCF
calculations.
Calculation of the redox potentials of 2_L and 3_L. DFT prediction of redox potentials
was performed using a slightly modified procedure following an established method.56
Geometries were optimized in gas phase followed by single point energy calculations in CH2Cl2.
Solvation were modeled by conductor-like screening model (COSMO). The Gibbs free energies
of the redox half reaction in CH2Cl2 were calculated as follow:
푎푏푠,푟푒푑표푥
푠표푙푣
표
Δ퐺
= ΔG푔abs,redox + Δ퐺푠 푅푒푑
( )
and the calculated Gibbs free energies were converted to absolute electron redox potential
according to Nernst equation:
abs,redox
solv
푎푏푠
ΔG
= −퐹퐸
푐푎푙푐
where F is the Faraday constant, 96,500 C mol-1. The calculated absolute redox potentials of the
half reaction were converted to standard potentials:
푎푏푠
퐸푐표푎푙푐 = 퐸
+ 퐸푎푏푠(퐻2/퐻+)
푐푎푙푐
97
푎푏푠
where 퐸 (퐻2/퐻+) is a literature value of –4.44 V. The calculated standard potentials were
푐푎푙푐
converted to referenced potentials (vs Fc/Fc+):
퐹푐
퐸
= 퐸푐표푎푙푐 − 퐸표(퐹푐/퐹푐+)
푐푎푙푐
where 퐸표(퐹푐/퐹푐+) is 0.46 V.98
Calculation of the C-H amination by 2N_L and 3N_L. Studies of potential energy
surfaces of the C–H amination in 2N_L and 3N_L complexes, used the M06L density
functional99 in conjunction with the 6-31G** basis sets for C, H, N, O and S atoms100 and
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LANL08(f) basis sets (with their corresponding ECPs) for Rh atoms (referred to below as basis
sets BS1).101-103 All reported structures were fully optimized without any geometry constraints.
Previously, it was reported that this computational method describes the energies and geometries
of organometallic compounds well.64-67 Frequency calculations were carried out to verify the
nature of the located stationary points. Graphical analysis of the imaginary vibrational normal
modes as well as the performed IRC calculations confirmed the nature of the located transition-
states. Energetics of the reported structures were improved by performing single-point energy
calculations at the M06L level of theory in conjunction with the 6-311+G(df,p) basis sets for C,
H, O, N, S atoms100 and LANL08(f) for the Rh-centers (referred to below as basis sets BS2). In
these calculations we used the M06L/BS1 optimized geometries, respectively. The reported
thermodynamic data were computed at the 298.15K temperature and 1atm pressure. Solvent
effects in dichloromethane were included by means of the PCM method.104 In these calculations
the free energy of solvation was computed as:
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Gsolv = Gsolv,PCM - Eel
where the final free energy in solution is obtained as:
Gsolv = Ggas + Gsolv
Acknowledgments. We thank the Center for Selective C-H Functionalization supported by
National Science Foundation (CHE-1205646). J.F.B. additionally thanks the DOE (DE-FG02-
10ER16204). K.M.L. acknowledges NSF CHE-1454455 for support. The authors gratefully
acknowledge NSF MRI-R2 grant (CHE-0958205) and the use of the resources of the Cherry
Emerson Center for Scientific Computation. The computational and EPR facilities at UW–
Madison are supported by grants from the National Science Foundation (CHE-0840494 and
CHE-0741901, respectively). The UCSF Chimera package is developed by the Resource for
Biocomputing, Visualization, and Informatics at the University of California, San Francisco
(supported by NIGMS P41-GM103311).
Supporting Information Available. Figures S1 and S2, and Tables S1 – S3. This information is
available free of charge on the Internet via the ACS Publications website.
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13
We note that this KIE increases to 2.6 when one uses a longer delay time on the C
NMR acquisition, as described in Ref. 64. Thus, we cannot completely rule out a Rh2(II,III)
pathway for Rh2(OAc)4.
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Table 1. Calculated and experimentally measured EPR parameters of the [Rh2(OAc)4(L)n]m+,
1_L, species (where L = none, H2O and Cl-).
8
9
Species
g1
g2
g3
Methods
RI-B3LYP
MR-DDCI2:SA-CASSCF(13e/8o)
Experiment48
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59
60
[Rh2(OAc)4]+
7.36 2.61 2.04
4.00 0.05 0.05
[Rh2(OAc)4(H2O)2]+
3.61 1.50 1.50
3.41 2.32 2.07
3.83 0.87 0.87
RI-B3LYP
MR-DDCI2:SA-CASSCF(17e/10o)
Rh2(OAc)4Cl
27.4 2.43 2.13
3.99 0.18 0.18
RI-B3LYP
MR-DDCI2:SA-CASSCF(19e/11o)
[Rh2(OAc)4(Cl)2]– a)
4.00 0.60 0.60
18.5 2.77 2.14
4.01 0.01 0.01
Experiment48
RI-B3LYP
MR-DDCI2:SA-CASSCF(25e/14o)
[Rh2(esp)2]–
2.14 2.14 1.93
2.25 2.25 1.89
2.24 2.11 2.06
Experiment (this work)
Experiment (this work)
RI-B3LYP
a) No crystal structure of [Rh2(OAc)4(Cl)2]– was available, so the geometry was optimized using
coordinates from the structure of [Rh2(OAc)4Cl2]2–.105
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Table 2. Leading configurations in the SA-CASSCF wavefunctions of [Rh2(OAc)4(L)n]m+, 1_L,
3
4
5
species (where L = none, H2O and Cl-). a
6
7
8
Compound
Active Space
CSFsb
Weight (in %)
9
2
2
[Rh2(OAc)4]+
(13,8)
δ2δ*2π1 π2 σ2π* 2π* 1σ*0
43.3
43.3
1
2
10
11
12
13
14
15
16
17
18
19
20
21
22
23
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58
59
60
2
2
δ2δ*2π1 π2 σ2π* 1π* 2σ*0
1
2
2
2
[Rh2(OAc)4(H2O)2]+ (17,10)
π* 2σ* 2δ2δ*2π1 π2 σ2π* 2π* 1σ* 0
43.5
43.5
4.6
2,+
+
1
2,-
-
2
2
π* 2σ* 2δ2δ*2π1 π2 σ2π* 1π* 2σ* 0
2,+
+
1
2,-
-
u
2
π* 2σ* 2δ2δ*2π1 π2 σdπ* 2π* 2σ* u
2,+
+
1
2,-
-
2
u
π* 2σ* 2δ2δ*2π1 π2 σdπ* 2π* 2σ* u
4.6
2,+
+
1
2,-
-
2
2
2
2
Rh2(OAc)4Cl
(19,11)
(25,14)
δ2δ*2π1 π2 π1,nb π2,nb2σ2σnb π* 2π* 1σ*0 41.9
1 2
δ2δ*2π1 π2 π1,nb π2,nb2σ2σnb π* 1π* 2σ*0 41.9
2
2
2
2
1
2
δ2δ*2π1 π2 π1,nb π2,nb2σ2σnb π* 2π* 1σ*2 4.2
2
2
2
0
1
2
δ2δ*2π1 π2 π1,nb π2,nb2σ2σnb π* 1π* 2σ*2 4.2
2
2
2
0
1
2
[Rh2(OAc)4Cl2]-c
π1,+ π2,+2π*1,+2π* 2σ+ δ δ*2σ* 2π1,-
2
2 2
2,+ +
43.2
42.8
5.0
2π2,- σ-2π*1,- π*2,- σ*-0
2
2
1
π1,+ π2,+2π*1,+2π* 2σ+ δ δ*2σ* 2π1,-
2
2 2
2,+
+
2π2,- σ-2π*1,- π*2,- σ*-0
2
1
2
π1,+ π2,+2π*1,+2π* 2σ+ δ δ*2σ* 2π1,-
2
2 2
2,+
+
uπ2,- σ-dπ*1,- π*2,- σ*-u
2
2
1
π1,+ π2,+2π*1,+2π* 2σ+ δ δ*2σ* 2π1,-
2
2 2
2,+
+
5.0
0π2,- σ-dπ*1,- π*2,- σ*-u
u
2
1
aconfigurations with weight > 3% are reported. bCSFs = configuration state functions. All orbital
symbols have their normal meaning; nb = non-bonding, + and – refer to in-phase and out-of-
c
phase contributions of the equatorial ligands. geometry for the single point calculation was
obtained without further optimization from the crystal structure of [(NH2)3C]2[Rh2(OAc)4Cl2].105
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Table 3. Calculated and experimentally available important geometry parameters (distances in
Å, and angles in deg.) of the [Rh2(esp)2L]+, 2_L, species (where L = none, H2O and Cl–).
6
7
8
Species
Rh-Rh
Rh-L
Rh-Oav Rh-Rh-L
9
Calculated: This work
10
11
12
13
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[Rh2(esp)2]+
2.362
2.378
2.394
---
2.041
2.043
2.065
---
[Rh2(esp)2(H2O)]+
2.253
178.9
180.0
Rh2(esp)2Cl
2.361
Experiment39
[Rh2(esp)2(Cl)2]–
2.360(1) 2.475(1) 2.023(1) 174.4(1)
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