Observation of inductive effects that cause a change in the rate-determining step for the conversion of rhenium azides to imido complexes

Article abstract of DOI:10.1021/ic2017853

The cationic oxorhenium(V) complex [Re(O)(hoz)₂(CH ₃CN)][B(C₆F₅)₄] [1; Hhoz = 2-(2′-hydroxyphenyl)-2-oxazoline] reacts with aryl azides (N ₃Ar) to give cationic cis-rhenium(VII) oxoimido complexes of the general formula [Re(O)(NAr)(hoz)₂][B(C₆F₅) ₄] [2a-2f; Ar = 4-methoxyphenyl, 4-methylphenyl, phenyl, 3-methoxyphenyl, 4-chlorophenyl, and 4-(trifluoromethyl)phenyl]. The kinetics of formation of 2 in CH₃CN are first-order in both azide (N ₃Ar) and oxorhenium(V) complex 1, with second-order rate constants ranging from 3.5 × 10^-2 to 1.7 × 10^-1 M ^-1 s^-1. A strong inductive effect is observed for electron-withdrawing substituents, leading to a negative Hammett reaction constant ρ = -1.3. However, electron-donating substituents on phenyl azide deviate significantly from this trend. Enthalpic barriers (ΔH ^?) determined by the Eyring-Polanyi equation are in the range 14-19 kcal mol^-1 for all aryl azides studied. However, electron-donating 4-methoxyphenyl azide exhibits a large negative entropy of activation, ΔS^? = -21 cal mol^-1 K ^-1, which is in sharp contrast to the near zero ΔS ^? observed for phenyl azide and 4-(trifluoromethyl)phenyl azide. The Hammett linear free-energy relationship and the activation parameters support a change in the mechanism between electron-withdrawing and electron-donating aryl azides. Density functional theory predicts that the aryl azides coordinate via N_α and extrude N₂ directly. For the electron-withdrawing substituents, N₂ extrusion is rate-determining, while for the electron-donating substituents, the rate-determining step becomes the initial attack of the azide. The barriers for these two steps are inverted in their order with respect to the Hammett σ values; thus, the Hammett plot appears with a break in its slope.

Full text of DOI:10.1021/ic2017853

ARTICLE
pubs.acs.org/IC
Observation of Inductive Effects That Cause a Change in the
Rate-Determining Step for the Conversion of Rhenium Azides
to Imido Complexes
Nicholas E. Travia,†,‡ Zhenggang Xu,§ Jason M. Keith,§,^ Elon A. Ison,†,z Phillip E. Fanwick,†
Michael B. Hall,*,§ and Mahdi M. Abu-Omar*,†
†Brown Laboratory, Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907, United States
§Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States
S Supporting Information
b
ABSTRACT: The cationic oxorhenium(V) complex [Re(O)(hoz)2(CH3CN)]-
[B(C6F5)4] [1; Hhoz = 2-(20-hydroxyphenyl)-2-oxazoline] reacts with aryl
azides (N3Ar) to give cationic cis-rhenium(VII) oxoimido complexes of the
general formula [Re(O)(NAr)(hoz)2][B(C6F5)4] [2aꢀ2f; Ar = 4-methoxy-
phenyl, 4-methylphenyl, phenyl, 3-methoxyphenyl, 4-chlorophenyl, and
4-(trifluoromethyl)phenyl]. The kinetics of formation of 2 in CH3CN are
first-order in both azide (N3Ar) and oxorhenium(V) complex 1, with second-
order rate constants ranging from 3.5 ꢁ 10ꢀ2 to 1.7 ꢁ 10ꢀ1 Mꢀ1 sꢀ1. A strong
inductive effect is observed for electron-withdrawing substituents, leading to a
negative Hammett reaction constant F = ꢀ1.3. However, electron-donating
substituents on phenyl azide deviate significantly from this trend. Enthalpic
barriers (ΔHq) determined by the EyringꢀPolanyi equation are in the range
14ꢀ19 kcal molꢀ1 for all aryl azides studied. However, electron-donating
4-methoxyphenyl azide exhibits a large negative entropy of activation, ΔSq = ꢀ21 cal molꢀ1 Kꢀ1, which is in sharp contrast to
the near zero ΔSq observed for phenyl azide and 4-(trifluoromethyl)phenyl azide. The Hammett linear free-energy relationship and
the activation parameters support a change in the mechanism between electron-withdrawing and electron-donating aryl azides.
Density functional theory predicts that the aryl azides coordinate via Nα and extrude N2 directly. For the electron-withdrawing
substituents, N2 extrusion is rate-determining, while for the electron-donating substituents, the rate-determining step becomes the
initial attack of the azide. The barriers for these two steps are inverted in their order with respect to the Hammett σ values; thus, the
Hammett plot appears with a break in its slope.
’ INTRODUCTION
approximately 1.5 and 2.5, respectively (bond lengths of 1.24 and
1.13 Å for HN3).18 The internal Nα is more basic19 and is, there-
fore, the most likely location for coordination to an electron-poor
metal center.
Organic azides, RN3, have found extensive use in synthetic
reactions.1 Their propensity toward the release of N2 has enabled
their utility as a source of reactive nitrene [RN] species. There-
fore, their study has been largely focused on various ways to trap
and/or transfer nitrene intermediates for transformations such as
amination2ꢀ5 and aziridination.6ꢀ13 More recently, organic
azides have gained widespread attention for their metal-catalyzed
1,3-dipolar [3 + 2] cycloaddition to alkynes to give 1,2,3-
triazoles,14ꢀ16 a methodology known as “click” chemistry.17
Many reactions have been realized, thus far, in which [RN]
transfer is catalyzed by transition-metal complexes, and in most
cases, it is assumed that azide coordinates to the metal center
prior to activation. Metal imido [MdNR] intermediates have
been invoked in nitrene-transfer reactions. The reactive site of
organic azides is the linear NNN moiety, which possesses
zwitterionic character. Two resonance forms delocalizing a
negative charge between Nα and Nγ can be envisaged
(Scheme 1). The bond orders for NαꢀNβ and NβꢀNγ are
Several examples of isolable organoazide complexes are known.20ꢀ26
They display a variety of resonance forms and binding modes
(Scheme 2). Several pathways have been proposed for the
formation of metal imido from the reaction of organic azides
with transition-metal complexes. In 1967, Kwart and Kahn
observed N2 evolution from benzylsulfonyl azide stirred over
copper powder and tentatively proposed a metallocycle inter-
mediate in which copper is coordinated to both Nα and Nγ of the
azide.27 Later, the Lewis acid catalyzed (AlCl3) rearrangement of
1-azidoadamantane was proposed to proceed by aluminum
coordination to Nα only.28 Osborne and Trogler provided mech-
anistic insight by preparing exclusively (Cp*)2V15NPh from a
Received: August 16, 2011
Published: September 09, 2011
r
2011 American Chemical Society
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|

Inorganic Chemistry
ARTICLE
Scheme 2. Coordination Modes of Organic Azides: (a)
Scheme 1. Resonance Forms of Phenyl Azide
Terminal Azide Nitrogen (Nγ) Complexation; (b) Coordi-
nation through Nα; (c) η2-Adduct Analogue of Olefin Com-
plexation; (d) Diazenimido and (e) Bridging μ-Imido
Ligation
labeled phenyl azide (Ph15NNN). They proposed a short-lived
intermediate whereby PhN3 coordinates to vanadium through
the labeled Nα to give an η1-diazoamine complex (Scheme 2b).29ꢀ31
Density functional theory (DFT) computations strongly sug-
gested that copper- and ruthenium-catalyzed 1,3-dipolar cycload-
dition to alkynes proceeds through a similar η1-diazoamine
coordination to the metal alkynyl.32,33 Alternatively, Cp2TaMe-
(N3Ar) and Cp2Zr(μ-NtBu)(μ-N3Ph)IrCp* have been sug-
gested to decompose through anti/syn isomerization of the ini-
tial diazenimido (Scheme 2d), followed by attack of Nα onto the
metal to form a four-membered tetraazametallocyclobutene
intermediate.34 Computational studies demonstrated that both
types of intermediates (azametallocycle and diazoamine) are avai-
lable for the imide formation from (dtbpe)Ni(η2-N3R), but a
highly negative entropy of activation was more consistent with
the four-membered ring azametallocycle pathway.35
Trityl tetrakis(hexafluorophenyl)borate and trityl hexafluorophosphate
were purchased from Strem and used as received. The cationic rhenium
oxo complex [Re(O)(hoz)2(CH3CN)][B(C6F5)4] (1) was synthesized
according to published procedures.40,41 NMR spectra were recorded on
Varian Inova 300 instruments. Mass spectrometry was performed by
the Purdue University Campus Wide Mass Spectrometry Center.
UVꢀvis spectra were recorded on a Shimadzu UV-2501 spectrophot-
ometer. Stopped-flow kinetics was collected on an Applied Photophysics
SX.18MV stopped-flow reaction analyzer. Data fitting was done using
KaleidaGraph 3.0 software.
Computational Details. All of the geometry optimization and
frequency determinations were performed with the Gaussian09 package
of programs42 at the B3LYP level.43 Transition states were located with
use of the synchronous transit-guided, quasi-Newton method.44 The
basis set used for rhenium is the effective-core-potential, extended val-
ence double-ζ LANL2DZ45 basis, in which the 6p functions were
replaced by the reoptimized functions of Couty and Hall,46 and a set
of diffuse f functions (exponent = 0.869) were added.47 The 6-31G**
basis sets were used for all hydrogen, carbon, nitrogen, oxygen, chlorine,
and fluorine atoms.48 Solvation energies were obtained from single-
point calculations on gas-phase geometries by applying the SMD solva-
tion model49 for acetonitrile with default radii and nonelectrostatic
terms. The three-dimensional molecular structures were drawn by the
JIMP2 program.50
Pseudo-First-Order Kinetics. Equal volumes of solutions of 1 in
acetonitrile (5.56 mM) and ArN3 (Ar = 4-methoxyphenyl, 4-methyl-
phenyl, phenyl, 3-methoxyphenyl, 4-chlorophenyl) were mixed in a
stopped-flow analyzer at 298.0 ( 0.2 K to give reaction solutions
with half of the loaded concentrations (2.78 mM in rhenium and
0.015ꢀ0.30 M in aryl azide). For 4-(trifluoromethyl)phenyl azide, the
reaction was slow enough to follow by conventional UVꢀvis spectro-
photometry. 1 in acetonitrile (2.78 mM) and 4-(trifluoromethyl)phenyl
azide (0.030ꢀ0.30 M) were mixed in a 1.00-cm-path-length quartz
UVꢀvis cell regulated to 298.0 ( 0.2 K. The increase in the absorbance
of the rhenium(VII) oxo imido product was monitored at 560 nm.
Observed first-order rate constants, kψ, were obtained by the nonlinear
fitting of A560 versus time to the equation Abst = Abs∞ + (Abs0 ꢀ Abs∞)
exp(ꢀkψt). Plots of kψ versus [aryl azide] were linear, consistent with a
first-order dependence on aryl azides (Figure 1). Fits of the data to the
rate law d[2]/dt = k[1][ArN3] yielded a second-order rate constant (k)
for each aryl azide (Table 1).
Temperature-Dependent Studies. Equal volumes of solutions
of 1 in acetonitrile (5.56 mM) and ArN3 (0.222 M for 4-methoxyphenyl
azide and 0.0522 M for phenyl azide) were mixed in the stopped-flow
analyzer at temperatures over the range (280.0ꢀ313.0) ( 0.2 K to give
reaction solutions with half of the loaded concentrations (2.78 mM in 1,
and 0.111 and 0.0261 M in aryl azide). 1 in acetonitrile (2.78 mM) and
4-(trifluoromethyl)phenyl azide (0.049 M) were mixed in a 1-cm-path-
length quartz cell regulated to temperatures over the range (285.0ꢀ318.0) (
0.2 K. The increase in the absorbance due to the formation of 2a, 2c, or
Cationic rhenium(VII) oxoimido complexes of salen, saldach,
and bis(oxazoline) ligand architectures can be prepared by the
reaction of aryl azides with mononuclear cationic oxorhenium-
(V) complexes.36 The reaction proceeds cleanly at room tem-
perature and features reproducible kinetics with first-order
dependence in both rhenium and azide. Drawing from other d2
examples, we tentatively assigned a mechanism whereby the aryl
azide coordinates via the terminal Nγ before proceeding through
an azametallocycle analogous to the mechanism described by
Bergman for Cp2TaMe(N3Ar).34 Recently, Hall and co-workers
offered an alternative mechanism based on DFT computations.
The organic azide binds rhenium through the internal Nα to give
a η1-diazoamine intermediate, which extrudes N2 directly.37
These computations showed that while a tetraazametallocyclo-
butene intermediate was accessible for the tantalum complex of
Bergman, a prohibitive activation barrier (>50 kcal molꢀ1) was
required for the cationic oxorhenium(V) salen complex. In
comparison, the activation energy for direct N2 extrusion is only
13 kcal molꢀ1
.
In this contribution, we clarify the mechanism of azide
reaction with [Re(O)(hoz)2(CH3CN)][B(C6F5)3] [1; Hhoz =
2-(20-hydroxyphenyl)-2-oxazolinine; Scheme 3]. Detailed ki-
netic analysis revealed that the reaction is indeed first-order in
rhenium and azide for a variety of electronically substituted aryl
azides over a wide range of concentrations. Hammett F/σ ana-
lysis revealed a drastic change in the electronic effect between
electron-donating and -withdrawing aryl substitutions. DFT cal-
culations described herein predict a multistep mechanism invol-
ving (1) isomerization of 1, (2) attack of the azide, (3) N2 extru-
sion, and (4) rearrangement of the product, with steps 2 and 3
being rate-determining for electron-donating and -withdrawing
substituents, respectively.
’ EXPERIMENTAL AND COMPUTATIONAL DETAILS
Materials and Methods. Acetonitrile was degassed and purified
with a solvent purification system (Anhydrous Engineering Inc.) prior
to use. Aniline derivatives and sodium azide were purchased from
Aldrich and used as received. Aryl azides were synthesized based on
published procedures38,39 (details in the Supporting Information).
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ARTICLE
Scheme 3. Formation of Rhenium(VII) Oxoimido Complexes
Figure 1. Plots of (a) the pseudo-first-order rate constant, kψ, versus [aryl azide] and (b) Hammett relationship for aryl azides with substituents, with
the fit showing a linear relationship for electron-withdrawing substituents. Key: 9, p-MeO; b, p-Me; 2, H; 0, m-MeO; O, p-Cl; Δ, p-CF3. Data collected
in CH3CN at 560 nm and 25.0 ( 0.2 ꢀC.
Table 1. Second-Order Rate Constants and Selected Activation Parameters for the Formation of 2aꢀ2fa
a Pseudo-first-order conditions, 2.78 mM 1, 0.030ꢀ0.30 M aryl azide, ArN3, in CH3CN at 25.0 ( 0.2 ꢀC. Data were collected at 560 nm using a
stopped-flow analyzer. b Conventional UVꢀvis spectrometry at 560 nm.
2f was monitored at 560 nm under pseudo-first-order conditions. The
kψ values were obtained by the nonlinear fitting of A560 versus time
to the equation Abst = Abs∞ + (Abs0 ꢀ Abs∞) exp(ꢀkψt). Plots of
ln(kψ/T) versus 1/T were linear (Figure 2). Fits to the Eyring equation
ln(kψ/T) = ꢀ(ΔHq/R)(1/T) + (ΔSq/R) + ln(kB/h) gave values for the
activation parameters ΔHq and ΔSq.
’ RESULTS
Kinetics of the Reaction of Cationic Oxorhenium(V) 1 with
Aryl Azides, ArN3. The reaction of 1 with excess ArN3 in
CH3CN or CH2Cl2 gave a change in color from green to intense
red, corresponding to a change in the oxidation state from ReV to
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Inorganic Chemistry
ReVII 36
ARTICLE
.
After isolation, 2aꢀ2f were recovered in high yields,
the origin (Figure 1a). The slopes from Figure 1a provided
second-order rate constants, k, tabulated in Table 1. Saturation
kinetics was not observed for any of the azide substrates over a
wide concentration range. At very high azide concentrations
(>0.50 M), the kinetic profiles deviated from strict first-order
kinetics (data not included in the fit), although the values of
kψ remained consistent with the fitted data in Figure 1a.
Linear Free-Energy Relationship and Activation Param-
eters. The Hammett F/σ analysis was used to measure the
inductive effect of electronic substitutions on the rate of reac-
tion.51 A plot of log(k/kH) versus substituent constant σ for para-
and meta-substituted aryl azides showed a linear correlation
for electron-withdrawing substituents p-CF3, p-Cl, and m-MeO
passing through the value for PhN3 with a slope, with reaction
constant F = ꢀ1.3 ( 0.1 suggesting a strong inductive effect as
the reaction is accelerated by electron donation on the arene.
Surprisingly, for aryl azides with electron-donating substituents,
p-Me and p-MeO, the values of k remained nearly unchanged
from that of PhN3 (Figure 1b).
characterized to be the oxoimido complexes by electrospray
ionization mass spectrometry (ESI-MS), and confirmed to be
1
pure by H NMR. The pseudo-first-order kinetics of ReVII
formation by >10-fold excess azide in CH3CN was monitored
by stopped-flow or conventional UVꢀvis spectrometry at
560 nm and 25.0 ( 0.2 ꢀC for a series of electron-donating
and -withdrawing aryl azides. In all cases, product formation
showed first-order dependence on the limiting reagent 1, and
plots of kψ versus [ArN3] were linear with fits passing through
The kinetics remained clean and first-order for all tempera-
tures up to ca. 50 ꢀC before azide thermal decomposition began
to compete with the reaction under investigation. Thermody-
namic activation constants for the formation of 2a (p-OMePhN3),
2c (PhN3), and 2f (p-CF3PhN3) were determined by the Eyring
method over a 35 ꢀC range to give nearly identical valueꢀs1for 2c
(ΔHq = 19 ( 1 kcal molꢀ1; ΔSq = ꢀ6 ( 4 cal molꢀ1 K ) and
2f (ΔHq = 18.8 ( 0.6 kcal molꢀ1; ΔSq = ꢀ9 ( 2 cal molꢀ1 Kꢀ1);
however, 2a exhibited less enthalpic and more pronounced
entropic barriers (ΔHq = 14.8 ( 0.8 kcal molꢀ1; ΔSq = ꢀ21 (
3 cal molꢀ1 Kꢀ1; Figure 2 and Table 1).
Figure 2. Temperature dependence for the formation of (9) 2a, (2)
2c, and (4) 2f.
Characterization of Complexes 2aꢀ2f. After isolation,
2aꢀ2f were recovered in high yields and characterized by ESI-
MS to be the oxoimido complexes. 1H NMR spectroscopy sup-
ported a cis-oxoimido orientation for all complexes with broken
symmetry in the hoz ligand aromatic region. Spectra of these com-
pounds showed distinguishing features different from structurally
similar cis-ReO2(hoz)2 and cis-Re(O)(hoz)2Cl complexes36,52
+
highlighted by two aromatic doublets (one proton each) shifted
significantly upfield (δ 6.31ꢀ6.18) and a qualitatively different
splitting pattern for the oxazoline methylene protons. Aromatic
and substituent protons on the imido moiety were shifted
downfield relative to the free azide ArN3.
Multiple attempts to crystallize [2aꢀ2f][B(C6F5)4] failed to
yield single crystals suitable for X-ray diffraction. Hence, [1]-
[PF6] was prepared from the metathesis reaction of Re(O)-
(hoz)2Cl and trityl hexafluorophosphate. The reaction of [1]-
[PF6] with a slight excess of p-MeOPhN3 in acetonitrile yielded a
deep-red solution. Suitable crystals of the product were obtained
Figure 3. ORTEP molecular structure representation of [2a][PF6].
Thermal ellipsoids are shown at 40% probability. Hydrogen atoms and
the anion have been omitted for clarity.
Table 2. Comparison between the Crystal and Computed Structures for Selected Bond Lengths (Å) and Angles (deg) for 2a
exp
calc
exp
calc
exp
calc
ReꢀO33
ReꢀN3
ReꢀO122
ReꢀN111
ReꢀN211
1.716
1.763
2.016
2.081
2.103
1.699
1.772
2.015
2.075
2.124
C31ꢀN3ꢀRe
168.2
101.7
89.5
160.9
101.8
91.0
N3ꢀReꢀN111
90.2
84.9
91.1
86.7
99.2
84.3
80.9
167.4
91.2
84.2
92.3
86.3
97.1
86.0
80.3
168.6
O33ꢀReꢀN3
O122ꢀReꢀN111
O222ꢀReꢀN111
O33ꢀReꢀN211
N3ꢀReꢀN211
O33ꢀReꢀO122
N3ꢀReꢀO122
O33ꢀReꢀO222
N3ꢀReꢀO222
O122ꢀReꢀO222
O33ꢀReꢀN111
C31ꢀN3ꢀRe-O33
168.4
164.9
88.8
167.0
164.2
88.3
O122ꢀReꢀN211
O222ꢀReꢀN211
N111ꢀReꢀN211
80.8
79.8
99.7
99.6
152.4
173.1
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ARTICLE
by the vapor diffusion of diethyl ether into a concentrated aceto-
nitrile solution at room temperature. Complex 2a adopts a dis-
torted octahedral geometry, with the angles around rhenium
ranging from 80ꢀ to 168ꢀ (Figure 3 and Table 2). The rhenium
imido bond is linear ReꢀN3ꢀC31 [168.2(6)ꢀ], ReꢀN30 =
1.751(4) Å, and ReꢀO = 1.714(3) Å, which are within the
normal range for Re(heteroatom) multiple bonds.53ꢀ57 The
ReꢀO bond length is identical with that of the analogous
[Re(O)(NMes)(saldach)][B(C6F5)4] complex36 and longer
than that of the cationic oxorhenium(V) complexes [cis-Re(O)-
(saldach)(H2O)][B(C6F5)4] [1.664(3) Å]41 and aqua [1][OTf]
[1.679(7) Å].52 ReꢀO bonds trans to multiply bonded ligands
are lengthened, ReꢀO122 = 2.016(5) Å trans to imido and Reꢀ
O222 = 2.024(5) Å trans to oxo, per the trans influence expected
for multiply bonded ligands.
differences to packing effects within the crystal as our structures
are optimized in the gas phase.
Although the structures of the reactant and other products
have not been determined, all possible isomers for reactant 1 and
the simplest product 2c were optimized. The reactant 1 has two
isomers, for which the two equatorial oxazoline nitrogen atoms
occupy trans and cis positions, 1_trans and 1_cis (Figure 4).
Because of the repulsion between the hydrogen atoms on the two
Scheme 5. Different Isomers of Product 2aꢀ2f
DFT Results. The rhenium(V) reactant 1 can bind an azide in
two possible modes to form intermediates 3_αand 3_γ(Scheme4).
3_γ is lower in energy than 3_α, in part because of steric
crowding in 3_α. As described in a previous work,37 the four-
membered ring intermediate proposed in Bergman’s mech-
anism,20,34 where the Nα in 3_γ bends over and also binds to
the metal before losing N2, is highly unfavorable in energy
(ΔGsqol > 50 kcal molꢀ1) because the seven-coordinate species
is both sterically crowded and a 20 eꢀ species if it maintains the
RetO bond. Thus, Bergman’s mechanism is very unlikely for
this system but is viable with coordinatively and electronically
unsaturated early metals. Here, the α-bonding intermediate,
which extrudes N2 directly via the previously proposed mech-
anism,37 dominates the reaction.
As a first step, the structure of the experimentally determined
product, [Re(O)(p-MeOPhN)(hoz)2] (2a), was optimized as
described above, and some selected bond lengths and angles are
compared to those of the crystal structure in Table 2. The
agreement is fairly good, with the largest error in the bond
lengths being 0.02 Å, while the largest angular errors occur for
C31ꢀN3ꢀRe and the C31ꢀN3ꢀReꢀO33 dihedral angle.
Optimizing the structure of this product with other functionals
yielded similar values for these two angles (see Table S1 in the
Supporting Information). One might attribute these angular
Table 3. Reaction Energies for Different Isomers of 2c
Relative to 1_trans + PhN3 (kcal molꢀ1
)
2c_iso1 2c_iso2 2c_iso3 2c_iso4 2c_iso5 2c_iso6
a1
ΔEelec
ΔHa2
ꢀ18.86 ꢀ44.73 ꢀ47.42 ꢀ19.22 ꢀ39.76 ꢀ46.76
ꢀ19.65 ꢀ45.49 ꢀ48.06 ꢀ20.07 ꢀ40.54 ꢀ47.43
ꢀ17.62 ꢀ45.65 ꢀ46.42 ꢀ18.82 ꢀ39.52 ꢀ46.61
ꢀ13.20 ꢀ39.97 ꢀ40.83 ꢀ14.00 ꢀ37.85 ꢀ41.20
a3
ΔGgas
a4
ΔGsol
ΔGqsol
b
Scheme 4. α and γ Intermediates of Rhenium
42.15
29.59
32.63
46.13
33.27
24.30
a Electronic energies (1), enthalpies (2), gas-phase free energies (3), and
solvated free energies (4) for different isomers of the product. All
energies are relative to the initial reactants 1 and PhN3. b The free-energy
barriers for elimination of N2 in different pathways to form the various
product isomers 2c_iso1ꢀ6 relative to the initial reactants 1 and PhN3.
Figure 4. Structures and some selected bonds lengths of 1_trans (left) and 1_cis (right). The ligands lying in the equatorial plane are relatively flat in
1_trans and fairly twisted in 1_cis.
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Table 4. Comparisons of Energy between iso3 and iso6 for
2aꢀ2f (kcal molꢀ1
)
iso6ꢀiso3
2a
2b
2c
2d
2e
2f
ΔEelec
ΔH
0.48
0.46
0.61
0.54
0.66
0.63
0.70
0.64
0.68
0.61
0.77
0.70
0.39
0.15
ΔGgas
ΔGsol
ꢀ0.13
ꢀ0.11
ꢀ0.27
ꢀ0.37
ꢀ0.19
ꢀ0.37
ꢀ0.09
ꢀ0.21
ꢀ0.26
ꢀ0.40
nitrogen atoms in 1_cis, the ligands in the equatorial plane adopt
a twisted conformation that contributes to making 1_cis higher in
free energy than 1_trans by 8.5 kcal molꢀ1. The imido product 2
from the reaction between 1 and an azide could exist in six
possible isomers (2_iso1ꢀ6; see Scheme 5). The reaction
energies for the formation of 2c_iso1ꢀ6 (see Table 3) can be
rationalized to some extent by the trans influence. The OtRe
triple bond uses the dz2, dxz, and dyz orbitals of rhenium, so it is
particularly difficult for the imido nitrogentobond trans tooxo, so
2c_iso1 and 2c_iso4 are significantly higher in energy than the
other isomers. Because the alkoxide OꢀRe bond has more ionic
character than imine coordination to a Re bond, among the other
four isomers, the ones with O trans to oxo (2c_iso3 and 2c_iso6)
are more stable than those with N trans to oxo (2c_iso2 and
2c_iso5). However, the energies of these four isomers, and
particularly the two most stable ones, are quite close. Because
the differences are sosmall, the preferred arrangementof ligands in
these isomers may be influenced by aspects other than the trans
influence.
Figure 5. Rearrangement between 2_iso6 and 2_iso3.
directly bind an azide to form 3_α_iso1ꢀ3, while in paths 4ꢀ6,
1_trans isomerizes to 1_cis before coordinating an azide mole-
cule. The results in Table 3 show that the lowest free-energy
barrier, ΔGqsol, between 1 + azide and 2c exists in path 6,
indicating that path 6 is the most probable. Although the next
highest barrier (path 2) is only ∼5 kcal molꢀ1 higher, DFT
energy differences for the barriers of these two very similar steps,
extruding N2, should be accurate enough to eliminate all paths
but path 6 from further consideration because the experimental
The similarity in the relative energies for the two most stable
isomers, 2_iso3 and 2_iso6, seen above for 2c is true for all of the
products 2aꢀ2f (see Table 4). The 2_iso3 isomers are lower in
electronic energy than the 2_iso6 isomers for all six substituents.
The crystal structure obtained for 2a corresponds to the com-
puted structure 2a_iso3, an observation that suggests that the
final products prefer the iso3 structure. On the other hand, the
computational results predict that 2_iso6 isomers have lower
solvated free energies than 2_iso3 isomers for all species except
2f. Because of the increased number of approximations involved
in the calculation of H and Gsol, such as the harmonic approx-
imation for vibrational frequencies and implicit solvation model,
the electronic energy differences may more accurately reflect the
preferred solid-state structure (different functionals also produce
similar results; see Table S3 in the Supporting Information).
Thus, we will assume that 2_iso3 isomers represent the final
products in accordance with experiment. The energy barriers for
rearrangement between isomers 2_iso6 and 2_iso3 are computed
to be ∼24 kcal molꢀ1 (see Figure 5). Thus, their rearrangement
couldoccuratroom temperature; furthermore, thealternativefinal
product does not influence the rate of the reaction for the
mechanism described below because this rearrangement would
occur after formation of the very stable products.
ΔGq values span a range of only 2 kcal molꢀ1
.
A detailed free-energy profile for the reaction between 1 and all
six substituted azides through path 6 is shown in Figure 6. The
profile shows three barriers with similar free energies between the
reactants 1_trans + azide and the initial product 2_iso6a-f. These
transition states correspond to TS-1, the 1_trans to 1_cis
isomerization, which is necessary to access the lowest energy
path for the remainder of the reaction (path 6), TS-2, the attack
of the azide on 1_cis, which distorts to accommodate the
incoming azide, and TS-3, the extrusion of N2 to form the
product. Because the two intermediates, 1_cis + azide and
3_α_iso6, are similarly less stable than the reactant 1_trans +
azide and because the product is much more stable, the rate-
determining step should correspond to the highest point on the
free-energy profile. Close examination of Figure 6 shows that TS-
1 is always lower in energy than the rate-determining step, which
varies between TS-2 and TS-3 depending on the azide. Thus,
isomerization of the reactant never serves as a rate-determining
step in the reactions, a conclusion in agreement with the
experimental result that all of the reactions are first-order in
both azide and the rhenium complex. The observed second-
order rate constant corresponds to the transition-state theory
expression for the highest remaining barrier, TS-2 or TS-3.
The first of the two key free-energy barriers, TS-2, corre-
sponds to attack of the azide in the forward direction or loss
of azide from the six-coordinate intermediate, 3_α_iso6, in the
backdirection. On the electronic energy surface, 3_α_iso6 is
more stable than 1_cis + azide, while the entropy loss in forming
3_α_iso6 from 1_cis + azide results in a higher free energy for
3_α_iso6, as shown in Figure 6. A scan of the electronic energy
for removal of the bound azide from 3_α_iso6 results in a
In the reaction examined here, the reactant 1 first binds an
azide molecule to form intermediate 3_α, which then extrudes
N2 directly to yield the desired product 2. Because several
different isomers of the intermediates and products need to be
considered, we will refer to the paths for each of the various
isomeric products by using the isomer label of the product. For
example, path 6 is the reaction path from 1 + azide to the product
2_iso6. We begin by noting that, in paths 1ꢀ3, 1_trans can
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Figure 6. Solvated ΔG (kcal molꢀ1) diagram for the reaction of the rhenium oxo complex with ArN3 (solvent: CH3CN).
coordinate toward products and, hence, has the lowest barrier
to N2 loss. Thus, the order of the free-energy barriers for TS-3
corresponds directly to the order of the stability for the inter-
mediate, 3_α_iso6.
The source of the “break” in the slope of the Hammett plot lies
in the inverted order of the similar magnitude barriers for TS-2
_
and TS-3 for the different azides, 2a 2f. So, for TS-2, the order
from highest to lowest barrier is 2a to 2f, while for TS-3, the order
is 2f to 2a. This inverted order is easily explained by the stability
of the intermediate 3_α_iso6. Because this species is the bound
azide adduct, the least strongly bound azide, 2f, will be both
the easiest to remove and the most difficult to react to product.
Thus, for reactions between 1_cis and (2f) p-CF3PhN3, (2e)
p-ClPhN3, (2d) m-MeOPhN3, and (2c) PhN3, the rate-deter-
mining step is the extrusion of N2 (TS-3). However, for the other
two azides, (2a) p-MeOPhN3 and (2b) p-MePhN3, the rate-
determining step switches to the adduct formation (TS-2). It is
this change of the rate-determining step that results in these two
points having a different slope in the computed Hammett plot
(Figure 7). One can also observe corresponding trends in the
bond distances that reinforce these conclusions. For example,
the least stable 3_α_iso6 intermediate, (f) p-CF3ArN3, has a
ReN bond length of 2.246 Å, while the most stable one, (a)
p-MeOArN3, has a ReN distance of 2.208 Å. Thus, the most
stable 3_α_iso6 intermediate (a) has the shortest (and
strongest) ReN bond, which means it will have the most difficult
azide to remove (TS-2) and it is also the furthest along the
forward reaction coordinate and will have the lowest barrier for
imido formation (TS-3).
Figure 7. Computed Hammett plot showing fairly good agreement
with the experimental plot. Key: 9, p-OMe; b, p-Me; 2, H; 0, m-OMe;
O, p-Cl; 4, p-CF3. The log(k/kH) is computed from ΔGqsol in Figure 6
using the standard TS theory.
smooth increase in the energy as the system returns to 1_cis +
azide (see Figure S3 in the Supporting Information). Thus, the
free-energy barrier for the loss of azide from 3_α_iso6 is
dominated by the enthalpy difference between 3_α_iso6 and
1_cis + azide, so TS-2 is located on the free-energy profile at this
energy.58 Because of this relationship, the order of TS-2’s free-
energy barriers corresponds inversely to the order of the stability
for the intermediate, 3_α_iso6, so the most stable intermediate,
3_α_iso6, has the highest barrier for the loss of azide. The
second key free-energy barrier, TS-3, corresponds to the extru-
sion of N2 from the intermediate 3_α_iso6. Here, the most
stable intermediate, 3_α_iso6, is further along the reaction
Although the energy differences between the various azides for
both TS-2 and TS-3 are small and less than the absolute accuracy
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Scheme 6. Proposed Kinetic Mechanism for the Reaction of
ArN3 with 1
determined second-order rate constants would correspond to Kk2.
DFT calculations are consistent with the proposed kinetic mechan-
ism, and they provide new insight on the fast initial trans to cis ligand
isomerization in 1 and on the preferred mode of coordination,
namely, via Nα of the azide.
d½ReVII
dt
ꢂ
k1k2½ReðOÞꢂ½ArN3ꢂ
¼
¼
ð1Þ
ð2Þ
k2 þ k
ꢀ1
of DFT calculations, DFT typically reproduces such trends much
more accurately, as is observed here. Alternative choices for the
functional reproduce the trends for the order of the azides 2aꢀ2f
for each of the TSs and reproduce the inverse of the order of the
free energies within the two transition states discussed above.
Furthermore, the range of the experimental rates for the forma-
tion of 2a-f_iso6 is consistent with the computed barriers whose
range is within 2 kcal molꢀ1. Because the inductive effect of the
substitution should affect the barriers of all paths similarly, the
lowest overall barriers for reactions between different substituted
azide species and 1 should always be found in path 6, which is
more than 5 kcal molꢀ1 lower than the next lowest path. The
d½ReVII
dt
ꢂ
Kk2½ReꢂT½ArN3ꢂ
= Kk2½ReꢂT½ArN3ꢂ
1 þ K½ArN3ꢂ
Analysis of the Inductive Effect. Even though the kinetic
behavior is consistent for all of the aryl azides employed in this
study, the abrupt change observed in the Hammett correlation is
very informative. Deviations in the linear free-energy relation-
ships often indicate changes in the mechanism.59 A negative
reaction constant F is observed for electron-withdrawing sub-
stituents on the aryl azide, demonstrating a positive charge
buildup in the transition state. We presume that azide coordina-
tion to the electron-deficient Re center is accelerated by electron-
donating azides. Two coordination modes are considered for the
oxorhenium(V) system, (1) diazenylimido through Nγ and (2) a
η1-azide adduct through Nα. The first has been observed by
Bergman and Cummins in their respective Ta and V d2 sys-
tems.20,21 The second has been shown by Wu and Hall by DFT to
be the relevant intermediate along the reaction pathway for
oxorhenium(V) saldach reaction with phenyl azide37 and herein
for this system and aryl azides with different substituents. In the
Bergman mechanism, the reaction is presumed to proceed via an
anti/syn rotation about the TaNꢀNNAr bond followed by rapid
generation of a tetraazametallocycle intermediate that extrudes
N2. Electron-withdrawing substituents on phenyl azide strongly
accelerated the reaction and F = +0.66 was observed. A rate-
determining step involving anti/syn isomerization was proposed,
and it was argued that the disruption of extended conjugation
produced a negative charge buildup on the [ArNꢀ] fragment.
This was supported by the observed activation entropy,
computed absolute overall barriers are around 25 kcal molꢀ1
,
slightly higher than 21 kcal molꢀ1 obtained experimentally, but
this systematic error of DFT does not mar the relative trends of
concern here. However, one must be cautious about the relative
energy of TS-2 with respect to that of TS-3 because these two
TSs are different in their electronic structure so an alternative
functional may shift all of the TS-2 free energies with respect to
those of TS-3. Apparently, the B3LYP functional with the basis
set and solvation corrections used here places the two transition
states at the correct relative energy such that the “break” in the
predicted Hammett plot (Figure 7) occurs in the same region as
the experimental one (Figure 1). Although other functionals may
not produce such accurate results, they would produce the same
trends and would result in the same explanation of the experi-
mental results. Thus, it is the judicious combination of experi-
ment and theory that leads to the insight about this mechanism.
’ DISCUSSION
ΔSq = ꢀ0.7 cal molꢀ1
K
ꢀ1. If our system here follows a
Analysis of the Kinetic Mechanism. The rate expression for
the reaction of aryl azides with 1 implicates a transition state
composed of one molecule each of aryl azide and the oxorhe-
nium(V) complex [1][B(C6F5)4]. We have previously reported
that, upon treatment with 1 equiv of p-CF3PhN3 at ꢀ80 ꢀC, the
analogous oxorhenium(V) saldach complex reacted to give an
observable intermediate that yielded the corresponding rhenium-
(VII) oxoimido product upon warming.36 We presume a mech-
anism by which a ReꢀN3Ar adduct is formed prior to product
formation (Scheme 6), although on the basis of kinetics alone,
adduct formation is not mandatory. The rate expression for the
mechanism in Scheme 6 assuming steady state for [ReꢀN3Ar] is
given in eq 1. Both steps are rate-determining, and the experi-
mental second-order rate constants in Table 2 are a composite of
mechanism similar to Bergman’s, a reasonable explanation of
the Hammett analysis would be that, for electron-withdrawing
aryl azides, coordination is rate-determining and all subsequent
steps are fast. This explanation can be refuted because a near-
zero entropy of activation for PhN3 and p-CF3PhN3 would make
little sense if coordination is rate-determining. In contrast, the
mechanism calculated herein by DFT would proceed via N2
extrusion from an η1-diazoamine intermediate and would be
decelerated by electron-withdrawing aryl substituents. Indeed,
the computed reaction profiles for electron-withdrawing aryl
azides show that the N2 extrusion step from the Nα azide adduct
is rate-determining (Figure 6). Furthermore, the computed
activation barriers are consistent with the observed experimental
trend for PhN3, m-MeOPhN3, p-ClPhN3, and p-CF3PhN3.
In order for a mechanism comprised of more than one elec-
tronically sensitive elementary step to show a near-zero Hammett
reaction constant, two or more electronically influenced steps
must be offsetting each other. A possible explanation is a change
in the rate-determining step rather than a change in the overall
pathway. For the substrates with electron-donating substituents
p-MeOPhN3 and p-MePhN3, the rate-determining step becomes
Nα azide adduct formation (Figure 6). The large and negative
k1k2/(k + k2). Another kinetically indistinguishable mechan-
ꢀ1
ism is the formation of the rhenium azide adduct, [ReꢀN3Ar],
in an a priori equilibrium followed by extrusion of N2 in the
rate-determining step. The rate law for this scenario is given in
eq 2. Because kinetic saturation in [N3Ar] is not observed, it is
reasonable to assume that k . k1[N3Ar] and, hence, the
ꢀ1
rhenium azide intermediate does not accumulate to appreciable
concentrations to allow detection. In this instant, the experimentally
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ARTICLE
entropy of activation measured for p-MeOPhN3 (ΔSq = ꢀ21 cal
Energy (Grant DE-FG02-06ER15794) and by the Chemistry Divi-
sion of the National Science Foundation (Grant CHE-0910552) and
The Welch Foundation (Grant A-0648).
molꢀ1
K
ꢀ1) is consistent with adduct formation being rate-
determining. It should be noted that, even though there is a
strong inductive effect from aryl substitutions, the change in the
rate-determining step is allowed to occur because the overall
barriers are close in energy within 4 kcal molꢀ1. Had their
energies deviated more, the break in the Hammett plot might not
have been observed. Thus, the unusual switch in rate-determin-
ing steps between TS_2 and TS_3, as revealed by computation
(Figure 6), is the result of both (1) the close relative barriers of
the two steps and (2) the inverted order in the reaction barriers
from 2aꢀ2f between coordination and N2 extrusion.
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‡Los Alamos National Laboratory, Mail Stop J-514, Los Alamos,
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^Theoretical Division, MS B268, Los Alamos National Labora-
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zDepartment of Chemistry and Biochemistry, North Carolina
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Support of this work was provided by the Chemical Sciences
Division, Office of Basic Energy Sciences, U.S. Department of
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