Distinct water-exchange mechanisms for trinuclear transition-metal clusters

Article abstract of DOI:10.1021/ic0609608

Mechanisms for water exchange from the bioxo-capped M-M-bonded trinuclear clusters, [M₃(μ₃-O)₂(μ-O ₂CCH₃)₆-(OH₂)₃] ²⁺ [M = Mo(IV) and W(IV)], were investigated using high-pressure ¹⁷O NMR and compared to our previous work on a similar Rh(III) trimer. Reaction rates decrease by more than a factor of 2 when pressure is increased from 6 to 250 MPa for the Mo(IV) trimer, while exchange rates increase by less than a factor of 1.2 (10-229 MPa) for the W(IV) trimer. From the pressure dependence of the reaction rate, activation volumes (ΔV ^?) were calculated to be ΔC^? = +8.0 (±0.4) cm³ mol^-1 and ΔC^? = -1.9 (±0.2) cm³ mol^-1 for the Mo(IV) cluster and W(IV) cluster, respectively, which is the largest difference (～10 cm ³ mol^-1) in activation volumes for any pair of 4d-5d (and 3d-4d) transition metal species located within the same group of the periodic table. If we interpret these activation volumes in terms of Swaddle's semiempirical model, which he established for simple octahedral monomers (Associative (A) = ΔV^? ≈ -13; Interchange (I) = ΔV^? ≈ 0; or Dissociative (D) = ΔV ^? ≈ +13), our results suggest that water exchange follows a dissociative-interchange (I_d) mechanism for the Mo(IV) cluster and an associative-interchange (I_a) activation mode for the W(IV) trimer. These volumes exhibit a unique changeover in the water-exchange mechanism despite considerable similarities in molecular structure and reactivity. This changeover could provide a standard for computational simulations of ligand-exchange pathways in molecules that are more complicated than monomers.

Full text of DOI:10.1021/ic0609608

Inorg. Chem. 2006, 45, 7962−7967
Distinct Water-Exchange Mechanisms for Trinuclear Transition-Metal
Clusters
Jacqueline R. Houston,† David T. Richens,‡ and William H. Casey*,†,§
Departments of Chemistry and Geology, UniVersity of California, DaVis, California 95616, and
Chemistry Department, UniVersity of St. Andrews, North Haugh, St. Andrews, KY16 9ST, Scotland,
United Kingdom
Received May 31, 2006
Mechanisms for water exchange from the bioxo-capped M
−
M-bonded trinuclear clusters, [M3(
µ
3-O)2(
µ
-O2CCH3)6-
+
(OH2)3]2 [M
)
Mo(IV) and W(IV)], were investigated using high-pressure 17O NMR and compared to our previous
work on a similar Rh(III) trimer. Reaction rates decrease by more than a factor of 2 when pressure is increased
from 6 to 250 MPa for the Mo(IV) trimer, while exchange rates increase by less than a factor of 1.2 (10 229 MPa)
Vq) were calculated
0.2) cm3 mol- for the Mo(IV) cluster and W(IV) cluster,
10 cm3 mol-1) in activation volumes for any pair of 4d
5d (and
4d) transition metal species located within the same group of the periodic table. If we interpret these activation
−
for the W(IV) trimer. From the pressure dependence of the reaction rate, activation volumes (
∆
1
1
to be
∆
Vq ) +8.0 (
±
0.4) cm3 mol- and
∆
Vq ) −1.9 (
±
respectively, which is the largest difference (
∼
−
3d
−
volumes in terms of Swaddle’s semiempirical model, which he established for simple octahedral monomers
(Associative (A) ) ∆Vq ≈ −13; Interchange (I) ) ∆Vq
≈
0; or Dissociative (D) ) ∆Vq ≈ +13), our results
suggest that water exchange follows a dissociative−interchange (Id) mechanism for the Mo(IV) cluster and an
associative−interchange (Ia) activation mode for the W(IV) trimer. These volumes exhibit a unique changeover in
the water-exchange mechanism despite considerable similarities in molecular structure and reactivity. This changeover
could provide a standard for computational simulations of ligand-exchange pathways in molecules that are more
complicated than monomers.
Introduction
demonstrated that activation pathways for water-exchange
mechanisms become increasingly associative (A) for aqueous
metal ions as one moves down the same group of the periodic
table [e.g., [Fe(OH2)6]2+ (+3.8 cm3 mol-1), [Ru(OH2)6]2+
(-0.4 cm3 mol-1); [Fe(OH2)6]3+ (-5.4 cm3 mol-1), [Ru-
(OH2)6]3+ (-8.3 cm3 mol-1); [Rh(OH2)6]3+ (-4.2 cm3
mol-1), [Ir(OH2)6]3+ (-5.7 cm3 mol-1)].2-6 This increasingly
associative character is explained as resulting from a gradual
increase in ionic radii, which allows for more association
with the incoming ligand.14,15 These trends led us to wonder
if they persist for larger multinuclear clusters. The ideal
Activation volumes calculated from high-pressure NMR
measurements have been used for nearly three decades to
assign mechanisms for ligand-exchange reactions.1 Merbach
et al.2-8 and Swaddle4,9-13 were pioneers in this field and
* To whom correspondence should be addressed. E-mail: whcasey@
ucdavis.edu.
† Department of Chemistry, University of California, Davis.
§ Department of Geology, University of California, Davis.
‡ University of St. Andrews.
(1) Merbach, A. E.; Vanni, H. HelV. Chim. Acta 1977, 60, 1124-7.
(2) Ducommun, Y.; Newman, K. E.; Merbach, A. E. Inorg. Chem. 1980,
19, 3696-703.
(3) Rapaport, I.; Helm, L.; Merbach, A. E.; Bernhard, P.; Ludi, A. Inorg.
Chem. 1988, 27, 873-9.
(9) Sisley, M. J.; Yano, Y.; Swaddle, T. W. Inorg. Chem. 1982, 21, 1141-
5.
(10) Swaddle, T. W. Inorg. Chem. 1980, 19, 3203-5.
(11) Tong, S. B.; Krouse, H. R.; Swaddle, T. W. Inorg. Chem. 1976, 15,
2643-4.
(12) Weekes, M. C.; Swaddle, T. W. Can. J. Chem. 1975, 53, 3697-701.
(13) Guastalla, G.; Swaddle, T. W. Can. J. Chem. 1973, 51, 821-7.
(14) Merbach, A.E; Akitt, J. W. High-resolution Variable pressure NMR
for chemical kinetics, NMR Basic Principles and Progress; Springer-
Verlag: Berlin; Heidelberg, 1990; Vol. 24, p 201.
(4) Swaddle, T. W.; Merbach, A. E. Inorg. Chem. 1981, 20, 4212-16.
(5) Laurenczy, G.; Rapaport, I.; Zbinden, D.; Merbach, A. E. Magn. Reson.
Chem. 1991, 29 (Special Issue), S45-S51.
(6) Cusanelli, A.; Frey, U.; Richens, D. T.; Merbach, A. E. J. Am. Chem.
Soc. 1996, 118, 5265-5271.
(7) Pittet, P.-A.; Elbaze, G.; Helm, L.; Merbach, A. E. Inorg. Chem. 1990,
29, 1936-42.
(8) Bleuzen, A.; Pittet, P.-A.; Helm, L.; Merbach, A. E. Magn. Reson.
Chem. 1997, 35, 765-773.
(15) Helm, L.; Merbach, A. E. Chem. ReV. 2005, 105, 1923-1959.
7962 Inorganic Chemistry, Vol. 45, No. 19, 2006
10.1021/ic0609608 CCC: $33.50
© 2006 American Chemical Society
Published on Web 08/25/2006

Water-Exchange Mechanisms for Transition-Metal Clusters
experimental test would involve molecules containing iso-
electronic metal ions located within the same group.
Only recently have researchers begun to conduct high-
pressure 17O NMR experiments on aqueous multinuclear
clusters and hydrolytic oligomers.16-18 To our knowledge,
there are only three such high-pressure 17O NMR studies on
clusters (see also Murmann and Giese, 197819). The high-
pressure 17O NMR study on the polyoxocation GaO4Al12-
7+
(OH)24(H2O)12 (GaAl12) was the first of its kind because
not only was an activation volume for water exchange
reported (∆Vq ) +3 cm3 mol-1) but also for exchange of
one of the hydroxyl-bridge sites (∆Vq ) +7 cm3 mol-1).16
Houston et al. (2005) recently reported the pressure depen-
dence of water exchange from the acetate-bridged oxo-
centered rhodium(III) trimer, [Rh3(µ3-O)(µ-O2CCH3)6(OH2)3]+
Materials and Methods
+
Solutions. Perchlorate salts of the metal complexes were prepared
(abbreviated as Rh3 ) and found that the activation pathway
using the method of Powell et al.21 Characterization of the powder
followed an dissociative-interchange mechanism (∆Vq )
+5.3 cm3 mol-1).17 This positive activation volume contrasts
with the negative value (-4.2 cm3 mol-1)5 for water
exchange on octahedral monomeric [Rh(OH2)6]3+ and is
attributed to labilization from the planar µ3-oxo, facilitating
a more dissociative water-exchange mechanism for this
trinuclear cluster. Activation volumes for exchange of the
cis and trans water molecules from the hydroxo-bridged
rhodium(III) dimer (abbreviated as Rh24+) also indicate
highly dissociative activation pathways [∆Vq ) +8.5 cm3
mol-1 (trans); +10.1 cm3 mol-1 (cis)],18 which contrasts with
the behavior of monomeric [Rh(OH2)6]3+. One should bear
in mind, however, that the extent to which Swaddle’s
interpretations of activation volumes, which were established
for octahedral monomeric ions of the 3d series (Associative
(A) ) ∆Vq ≈ -13; Interchange (I) ) ∆Vq ≈ 0; or
Dissociative (D) ) ∆Vq ≈ +13),20 can be extended to large
clusters is yet to be fully established.
was performed using UV-vis (Mo32+, λmax ) 509 nm, λ ) 430
2+
nm; W3
λ
) 444 nm, λ ) 358 nm)21 and 1H NMR (δ Mo32+(µ-
max
O2CCH3) ) 2.31 ppm; δ W32+(µ-O2CCH3) ) 2.39 ppm; CD3OD,
T ) 298 K) to ensure the purity of the compounds prior to
performing the exchange experiments.
For the 17O NMR kinetic experiments, the appropriate amount
of the Mo3 perchlorate salt was dissolved in 2.4 mL of 17OH2
2+
(40%) to give a cluster concentration of 10 mM. To observe the
bound water (η-OH2) signal at +94 ppm, the large bulk water signal
was broadened beyond detection by the addition of [Mn(OH2)6]-
(ClO4)2 to give a [Mn2+] ) 0.1 M.22 All solutions were acidified
with HClO4 ([H+] ) 0.6 M) to ensure that the complexes were in
their fully protonated forms21 and augmented with NaClO4 to give
I ) 1.0 M. Perchlorate was chosen because it provides a signal
downfield (301 ppm; T ) 298 K) that can be used as a constant-
intensity internal standard. After the solutions were mixed, the
samples were subsequently filtered through a 0.22 µm filter to
remove any suspended particulates. To prevent oxidation at the
experimental temperature (T ) 310.3 K), samples were flushed with
argon for 10-15 min. After the kinetic experiments were complete,
UV-vis spectra were collected on all samples in order to ensure
that no degradation or polymerization had occurred during the
measurements.
Because W32+ is prone to oxidation in high perchlorate concen-
trations, samples were prepared using CF3SO3H/CF3SO3Na ac-
cording to the method of Powell et al.21 Other than this difference
in background electrolyte, the sample preparation and reagent
concentrations were nearly identical to those used for Mo32+; [W3
) 10 mM, [H+] ) 0.6 M. To see the η-OH2 signal at +83 ppm,
[Mn(OH2)6](CF3SO3)2 was added to give a [Mn2+] ) 0.1 M. Since
there was insufficient perchlorate to provide an internal standard
To extend the field, we have chosen to examine water
exchange from the bioxo-capped M-M-bonded trinuclear
clusters, [M3(µ3-O)2(µ-O2CCH3)6(OH2)3]2+ (M ) Mo(IV) and
W(IV)) [abbreviated in subsequent text as Mo32+ and W32+].
These clusters are particularly good candidates for study
because previous water-exchange experiments exhibited
markedly different activation parameters (Mo32+: ∆Hq )
126 kJ mol-1, ∆Sq ) 77 J mol-1 K-1; W32+: ∆Hq ) 58 kJ
mol-1, ∆Sq ) -164 J mol-1 K-1),21 indicating a unique
changeover in the exchange mechanism even though these
two clusters possess very similar, almost identical, structures.
Thus, these two clusters afford the rare opportunity to
investigate how the tetravalent transition metal ion alone
influences the water-exchange mechanism.
2+
]
3+
for the rate measurements, 50 µL of Al(OH2)6 (prepared from
the perchlorate salt, [Al3+] ) 250 mM) was added to the solution.
This signal (+28 ppm) provided a stable and constant reference
throughout the experiment because the η-OH2 on the Al3+ ion are
in isotopic-exchange equilibrium with the bulk water at the
experimental temperature (T ) 333.3 K). Because the temperature
was relatively high and the solution extremely acidic ([H+] ) 0.6
M), no hydrolysis products from Al3+ were detected on the 17O
NMR spectrum.
(16) Loring, J. S.; Yu, P.; Phillips, B. L.; Casey, W. H. Geochim.
Cosmochim. Acta 2003, 68, 2791-2798.
(17) Houston, J. R.; Yu, P.; Casey, W. H. Inorg. Chem. 2005, 44, 5176-
5182.
Variable-Pressure 17O NMR Spectroscopy. 17O NMR spectra
were acquired in unlocked mode on a Bruker AQS500 NMR
(18) Drljaca, A.; Zahl, A.; Van Eldik, R. Inorg. Chem. 1998, 37, 3948-
3953.
(19) Murmann, R. K.; Giese, K. C. Inorg. Chem. 1978, 17, 1160-1166.
(20) Swaddle, T. W. Inorg. Chem. 1983, 22, 2663-5.
(21) Powell, G.; Richens, D. T. Inorg. Chem. 1993, 32, 4021-9.
(22) Swift, T. J.; Connick, R. E. J. Chem. Phys. 1962, 37, 307-320.
Inorganic Chemistry, Vol. 45, No. 19, 2006 7963

Houston et al.
spectrometer equipped with a wide-bore (89 mm) 11.7 T magnet
located at the University of California, Davis, Keck Nuclear
Magnetic Resonance Facility. Spectral data was collected at ν0 )
67.8 MHz with single-pulse excitation using a pulse length of 30
µs (π/2 ) 60 µs), a sweep width of 95 kHz, and a recycle delay of
2+
15 ms. Averaging of 55 000 scans for Mo32+ and 120 000 for W3
was used to achieve adequate signal-to-noise. To ensure the B0 field
was homogeneous, the magnet was shimmed on a 0.1 M Al3+
solution in an identical high-pressure tube at all experimental
pressures and temperatures (27Al line-width 5-7 Hz; 17O line-width
100-150 Hz, depending on temperature). To remove baseline roll
due to acoustic ringing, the first 12 data points were recalculated
from the remainder of the free-induction decay using a backward
linear-prediction algorithm. All chemical shifts are referenced to
an external source of tap water (0 ppm; coaxial insert; T ) 298
K); however, all samples contained paramagnetic Mn2+, and so
17O signals may be slightly shifted relative to previously published
data.21
All 17O NMR measurements were made using a high-pressure
NMR probe assembly (titanium alloy vessel: 61.5 mm o.d., 20
mm i.d.; pressurizing fluid: n-hexanes), which has been described
in detail elsewhere.16,17,23 To transmit pressure to the sample, the
solution was placed inside a quartz NMR tube (two 8 mm o.d.
tubes connected via a capillary) and sealed with a movable PTFE
piston seated with two O-rings.23 The movable piston allows
pressure from the n-hexanes to be transferred to the sample from
the pressure-generating system (a large-volume manual syringe
pump; High-Pressure Research, Inc.).
Data were acquired at P ) 6, 52, 102, 150, 202, and 250 MPa
(T ) 310.3 K) for Mo32+ and P ) 10, 60, 110, 176, and 229 MPa
(T ) 333.3 K) for W32+. By circulating water through the probe
jacket, the sample temperature was controlled to within (0.2 K.
Temperature was continuously monitored with a copper-constantan
thermocouple symmetrically disposed from the sample inside the
pressure chamber. Experimental pressures were also measured
continuously with an electronic gauge (High-Pressure Research,
Inc.) and controlled to within (4 MPa or better. Before data
acquisition commenced, the solutions were allowed to thermally
equilibrate for 60 min at the experimental temperatures and
pressures.
Kinetic Analysis. Rates of water exchange were determined by
monitoring the height of the 17O NMR signal from the η-OH2 as a
function of time. To account for any instrumental fluctuations during
the kinetic run, peak heights were normalized to an internal standard,
which was the ClO4- signal for Mo32+ and η-OH2 on the Al3+ ion
for W32+. All 17O NMR signals were fit to Lorentzian curves. To
calculate a pseudo-first-order rate coefficient, the normalized peak
heights were fit to a standard three-parameter exponential growth
equation (eq 1).17
2+
Figure 1. 17O NMR spectrum for Mo3 at T ) 310.3 K and P ) 250
MPa; [Mo32+] ) 10 mM, [Mn2+] ) 0.1 M, [H+] ) 0.6 M, I ) 1.0
M(NaClO4). Signals at +94 and ∼263 ppm are from η-OH2 and µ-O2-
CCH3, respectively. This spectrum was collected following equilibration
of η-OH2 sites using 55 000 scans at ν0 ) 67.8 MHz with single-pulse
excitation of 30 µs, 15 ms pulse delay, and a sweep width of 95 kHz.
The variation of reaction rate with pressure can be related to the
activation volume (∆Vq) by eq 2.24
∆V‡
RT
∂ ln(kex)
) -
(2)
(
)
∂P
T
The terms P and T are the experimental pressure and temperature,
respectively. Assuming that the compressibility of the molecules
is negligible over the pressure range studied here (6-250 MPa),
eq 3 applies and allows the direct calculation of ∆Vq.24-26
P∆V‡
RT
ln(kex,P) ) ln(kex,P)0) -
(3)
The terms kex,P and kex,P)0, refer to the rate constant at the
experimental pressure and at zero pressure, respectively. For water-
exchange reactions in which there is no creation or destruction of
charge, electrostriction effects can safely be ignored. Therefore,
∆Vq can be directly diagnostic of geometrical changes, such as
bond-breaking and making during the formation of the activated
complex.24-26
Results
17O NMR Spectra. A typical 17O NMR spectrum for
2+
Mo3 is shown in Figure 1. This spectrum, as well as the
2+
17O NMR spectrum for the W3 trimer [δ(η-OH2) ) +83
ppm; ∼1 kHz; not shown], shows a broad signal for the
+
η-OH2 (+94 ppm), ∼1 kHz wide. When compared to Rh3 ,
ext
It ) I0 + a(1 - e-k
)
(1)
these line widths are greater by nearly 800 Hz [δ(η-OH2) )
-57 ppm; ∼285 Hz at T ) 298K].17 Because magnetic-
The term kex refers to the rate coefficient for water exchange, a is
an adjustable parameter, and t is the elapsed time after mixing.
The term I0 is the normalized height of the bound water resonance
at t ) 0, which was chosen as an adjustable parameter because it
took nearly an hour for the sample to equilibrate to temperature.
The term It refers to the normalized peak height during the course
of the experiment.
2+
susceptibility measurements for Mo3 indicate that this
trinuclear structure is diamagnetic,27 lower symmetry at the
M-OH2 sites is most likely responsible for the significant
line-broadening effect via rapid quadrupolar relaxation. Also
(25) Richens, D. T. The Chemistry of Aqua Ions; John-Wiley: Chichester;
New York, 1997.
(26) Wilkins, R. G. Kinetics and Mechanism of Reactions of Transition
Metal Complexes, 2nd ed.; VCH: Weinheim, Germany, 1991.
(27) Bino, A.; Cotton, F. A.; Dori Z. J. Am. Chem. Soc. 1981, 103, 243-
244.
(23) Jonas, J.; Koziol, P.; Peng, X.; Reiner, C.; Campbell, D. J. Magn.
Reson. B 1993, 102, 299.
(24) Merbach, A. E. Pure Appl. Chem. 1982, 54, 1479.
7964 Inorganic Chemistry, Vol. 45, No. 19, 2006

Water-Exchange Mechanisms for Transition-Metal Clusters
Table 1. Kinetic Data for Water Exchange from
[M3(µ3-O)2(µ-O2CCH3)6(OH2)3]2+ (M ) Mo(IV) and W(IV))
complex
Mo(IV)
temp (K)
310.3
pressure (MPa)
105 kex (s-1
)
6 ((3)
3.13 ((0.26)
2.61 ((0.11)
2.37 ((0.22)
2.01 ((0.12)
1.65 ((0.28)
1.47 ((0.08)
0.583 ((0.020)
0.601 ((0.020)
0.618 ((0.017)
0.655 ((0.024)
0.681 ((0.017)
52 ((3)
102 ((3)
150 ((4)
202 ((3)
250 ((4)
10 ((1)
60 ((2)
110 ((2)
176 ((2)
229 ((3)
W(IV)
333.3
2+
shown on the Mo3 spectrum is a broad signal at ∼263
ppm [W32+; δ(µ-O2CCH3) ) ∼247 ppm] assigned to spin-
labeled 17O in the acetate bridges (µ-O2CCH3), which was
+
observed for Rh3 (δ(µ-O2CCH3) ) 131 ppm) as well.17
Kinetic data for more than one half-life could not be obtained
within a reasonable period of time due to the slow exchange
rates at the experimental temperatures. Isotopic substitution
into the capping oxos (µ3-O) was not observed.
Variable-Pressure Kinetics. Over the course of the
exchange experiment, the peak height of the isotopically
tagged η-OH2 grew exponentially as a function of time. Peak
heights were normalized to a constant-intensity internal
standard (see Materials and Methods) and plotted versus time
to extract pseudo-first-order rate coefficients using eq 1. For
Mo32+, this experiment was repeated at six pressures (P )
6, 52, 102, 150, 202, and 250 MPa; T ) 310.3 K), and for
W32+, the exchange experiment was repeated at five pressures
(P ) 10, 60, 110, 176, and 229 MPa; T ) 333.3 K) (Table
1). Water-exchange data indicate that, with increasing
pressure, the rate constants decrease by a factor of 2 for
Mo32+ (P ) 6-250 MPa) and increase by a factor of 1.2 (P
Figure 2. Variation of the normalized intensity of the η-OH2 signal as a
2+
function of time. Lines are weighted least-squares fits to eq 1. For Mo3
,
water-exchange rates decrease with increasing pressure (6, 150, 250 MPa)
(a) and for W32+, reaction rates increase with increasing pressure (10 and
229 MPa) (b).
) 10-229 MPa) for W32+. Selected kinetic data for both
Mo32+ and W32+experiments are shown in Figure 2 (Mo3
,
2+
first 33 h; W32+, first 97 h) to illustrate the pressure
dependence of the reaction rates. To calculate a reliable rate
constant, exchange experiments for the Mo32+ were typically
2+
monitored for 2.5 days and for the more inert W3
experiments were monitored for 5-6 days.
,
A plot of ln[kex (s-1)] vs pressure (atm) allows for the
calculation of ∆Vq from a weighted least-squares fit of the
line (eq 3). Volumes of activation were calculated as ∆Vq
) +8.0 ((0.4) cm3 mol-1 for Mo32+ and ∆Vq ) -1.9 ((0.2)
cm3 mol-1 for W32+. Shown in Figure 3 are the pressure-
dependent kinetic data for the Mo32+ and W32+ experiments,
+
in addition to the previously published data for Rh3 [∆Vq
) +5.3 ((0.4) cm3 mol-1].17
Figure 3. Pressure dependence of the pseudo-first-order rate coefficient
2+
+
for water exchange from Mo32+ (gray circle), W3 (empty circle), and Rh
Discussion
3
(black circle) clusters. The lines correspond to a weighted least-squares fit
to eq 3, which yields ∆Vq ) +8.0 ((0.4) cm3 mol-1 for Mo32+ and ∆Vq )
-1.9 ((0.2) cm3 mol-1 for W32+. The data for Rh3+ are from ref 17 (∆Vq
) +5.3 ((0.4) cm3 mol-1).
Although these two molecules are nearly isostructural (M-
OH2 ) 2.129, 2.128 Å; M-M ) 2.759, 2.747 Å; M-µ3-O
) 1.994-2.000 Å; M ) Mo(IV),W(IV), CF3SO3 salts)28,29
and have similar exchange rates (kex298(Mo32+) ) 5.6 × 10-6
s-1 and kex298(W32+) ) 1.0 × 10-6 s-1),21 the activation
volumes are strikingly different (Mo32+: +8.0 cm3 mol-1;
W32+: -1.9 cm3 mol-1). Although Swaddle’s model for
assigning mechanisms from activation volumes10 is not yet
(28) Cotton, F. A.; Dori, Z.; Marler, D. O.; Schwotzer, W. Inorg. Chem.
1983, 22, 3104-3106.
(29) Bino, A.; Cotton, F. A.; Dori, Z.; Koch, S.; Kuppers H.; Millar, M.;
Sekutowski, J. C. Inorg. Chem. 1978, 17, 3245-3253.
Inorganic Chemistry, Vol. 45, No. 19, 2006 7965

Houston et al.
verified for multinuclear molecules such as these, the new
experimental data clearly indicate a change in mechanism.
Using his semiempirical model [Associative (A) ) ∆Vq ≈
-13; Interchange (I) ) ∆Vq ≈ 0; or Dissociative (D) ) ∆Vq
≈ +13], the water exchange mechanism changes from D or
Id (Mo32+) to Ia (W32+), which is consistent with other
distinctly different activation parameters, [Mo32+: ∆Hq )
126 kJ mol-1, ∆Sq ) 77 J mol-1 K-1; and for W32+: ∆Hq )
58 kJ mol-1, ∆Sq ) -164 J mol-1 K-1].21 These volumes
represent the largest difference in ∆Vq values (∼10 cm3
mol-1) for any two isostructural 4d-5d and 3d-4d metal
species located within the same group, and based on their
different magnitudes, demonstrate a unique mechanistic
changeover.30 These data may become as useful as the
changeover in mechanism for octahedral first row transition
metal ions that has served as a reliable test case for computer
simulations.31,32
Figure 4. Volumes of activation and entropies for water exchange from
multinuclear metal complexes. The data presented above are from this work
and refs 16-18. Two points are plotted for the Rh24+ cluster corresponding
to separate rates for the bound waters that are cis and trans to the µ2-OH
bridge.
For isoelectronic metal ions with the same coordination
geometry, as is the case for Mo32+ and W32+, the size of the
metal ion dictates the activation pathway. Large ions typically
have more room for association with the entering molecule.15
Unfortunately, however, Mo(IV) and W(IV) ionic radii for
nonacoordination, as in these trimeric molecules, are not
available to compare. We anticipate that ionic radii for the
nine-coordinate Mo(IV) and W(IV) would be similar to one
another because of the lanthanide contraction. For example,
these metals in hexacoordination have ionic radii of 65 and
66 pm, respectively, for Mo(IV) and W(IV).33 The local
structures around each of the metal ions are also similar and
do not immediately suggest a reason that one pathway would
be considerably more dissociative than the other. For
example, the angle between µ-O2CCH3 and the η-OH2 [e.g.,
(CH3CO)O-M-O(OH2)] for both molecules is roughly
75°,28,34 as estimated from crystal data. Although crowding
around the metal center would inhibit attack by the incoming
ligand and lead to a more dissociative activation state, we
the coordinated ligands have greater negative NBO charge
in W32+ versus Mo32+ [Mo32+: H3CCOO ) -0.672/-0.640,
H2O ) -0.871; W32+: H3CCOO ) -0.677/-0.713, H2O
) -0.899). These data indicate a larger degree of charge
separation in the W32+ cluster and thus greater bond polarity.
We speculate that this greater charge separation stabilizes
the incoming water molecule during the formation of the
transition-state complex, resulting in a more associatively
activated pathway for W32+. A comprehensive and detailed
computational study aimed to simulate the activation barrier
for both molecules is currently underway.
The reactivity trends that we observe here for the trinuclear
clusters are qualitatively consistent with trends evident in
the 4d-5d group monomeric aqua ions. Exchange mecha-
nisms for monomeric ions become increasingly associative
deeper in the 4d-5d group.15 For example, water exchange
3+
2+
becomes more associative for the larger Ir(OH2)6 vs the
only see evidence for a dissociative pathway for the Mo3
cluster, yet crowding is similar in the W3 molecule.
3+
2+
slightly smaller Rh(OH2)6 ion (Rh(III) ) 0.665 Å, Ir(III)
) 0.680 Å)33 based on the reported activation volumes (∆Vq
) -4.2 and -5.7 cm3 mol-1, respectively).5,6 As another
example, albeit not for octahedral ions, the activation volume
for [Pt(OH2)4]2+ (∆Vq ) -4.6 cm3 mol-1) is more negative
than that of [Pd(OH2)4]2+ (∆Vq ) -2.2 cm3 mol-1),37,38 even
though the ionic radius of Pt(II) is smaller (Pd(II) ) 0.64
Å, Pt(II) ) 0.60 Å).33 These examples demonstrate an
increase in associative character as one goes deeper into the
group, but not a drastic change in mechanism, such as we
find here for the trinuclear clusters.
The profound difference in mechanism for these otherwise
similar molecules suggests that they might be well suited
for simulation,31,32,35 which we have underway. Preliminary
data from DFT calculations (B3LYP/LANL2DZ)36 indicate
a difference in bonding character from the metal centers to
the ligands for the Mo32+ and W32+ clusters in their ground
states. The NBO charges at the tetravalent metal are
significantly different for the two clusters; the NBO charge
on W(IV) is slightly greater than Mo(IV) [Mo(IV) ) +1.424;
W(IV) ) +1.698]. Correspondingly, the oxygen atoms in
Most importantly, there are now enough high-pressure 17
O
NMR data to establish mechanistic trends for several
multinuclear aqueous complexes. The data compiled in
Figure 4 show that activation volumes for water exchange
correlate linearly with the corresponding activation entropies.
Similar trends have been previously found for water ex-
(30) Helm, L.; Merbach, A. E. J. Chem. Soc., Dalton Trans. 2002, 5, 633-
641.
(31) Rotzinger, F. P. HelV. Chim. Acta 2000, 83, 3006-3020.
(32) Rotzinger, F.P. J. Am. Chem. Soc. 1997, 119, 5230-5238.
(33) Shannon, R. D. Acta Crystallogr., Sect. A 1976, 32, 751-767.
(34) Bino, A.; Hesse, K. F.; Kueppers, H. Acta Crystallogr., Sect. B 1980,
B36, 723-725.
(35) (a) Stack, A. G.; Rustad, J. R.; Casey, W.H J. Phys. Chem. B 2005,
109, 23771-23775. (b) Rotzinger, F. P. Chem. ReV. 2005, 105, 2003-
2037.
(37) Helm, L.; Elding L. I.; Merbach, A. E. HelV. Chim. Acta 1984, 67,
1453-60.
(36) Glendening, E. D.; Weinhold, F. J. Comp. Chem. 1998, 19, 610-
(38) Helm, L.; Elding L. I.; Merbach A. E. Inorg. Chem. 1985, 24, 1719-
627.
21.
7966 Inorganic Chemistry, Vol. 45, No. 19, 2006

Water-Exchange Mechanisms for Transition-Metal Clusters
change and racemization at monomeric metal ions (see Twigg
(1977) and Wilkins (1991)),26,39 but not for molecular clusters
such as those we present here. This correlation includes
reactions with profoundly different mechanisms (D to Ia) and
for a variety of aqueous clusters with vastly different
molecular structures (e.g., GaAl12 vs Mo32+). One extreme
is provided by the recent study of solvent exchange on the
Rh24+ ion by Drljaca et al.,18 who report ∆Vq for the cis and
trans waters of the rhodium(III) dimer to be +8.5 ((0.8)
and +10.1 ((0.8) cm3 mol-1, both of which correspond to
a D mechanism. These are the largest values yet measured
for clusters and serve as the upper limit in Figure 4, although
the ∆Vq values are smaller than the +13 cm3 mol-1 originally
suggested by Swaddle for simple octahedral metal ions.
Recently though, ∆Vq values of ∼+9 cm3 mol-1 have been
assigned to the limiting D pathway.40,41 The rationale for this
reassignment is that the effective radius of a water molecule
is reduced in a close-packed structure. Expulsion of a bound
water from this close-packed structure to the bulk would
result in a volume change of ∼18-9 ) ∼+9 cm3 mol-1.
for predicting mechanisms of ligand exchange for a variety
of molecular clusters on the basis of the activation entropies
alone. We do recognize, however, that activation entropies
can carry large experimental uncertainties due to extrapola-
tion to infinite temperature. In addition, factors that remain
to be evaluated include the compressibility of the molecules,
which might differ considerably from monomeric species,
and the extent to which the transmission coefficients vary
with pressure. Both of these uncertainties, however, can be
assessed by computation. Even without the simulations,
however, the high-pressure 17O NMR data allow us to
establish key reactivity trends and show that the values of
∆Vq are not vastly different than what is expected from the
many studies of aqueous monomer complexes.15
Conclusions
Mechanisms for water exchange from the bioxo-capped
M-M-bonded trinuclear clusters, [M3(µ3-O)2(µ-O2CCH3)6-
(OH2)3]2+ (M ) Mo(IV) and W(IV)) are profoundly differ-
ent, although the clusters are virtually isostructural. The
difference in activation volume is the largest (∼10 cm3
mol-1) yet reported for any 4d-5d (and 3d-4d) isostructural
transition metal ions located in the same group of the periodic
table. These volumes, when combined with high-pressure
17O NMR data from other aqueous metal clusters, allow us
to establish a strong correlation between the activation
volumes and entropies. This correlation can be used to assign
mechanisms for water-exchange reactions for a variety of
different aqueous metal clusters.
2+
The datum that we report here for the W3 molecule
provides the other limiting extreme in the experimental
measurements. The extent to which this molecule exchanges
water via a purely A or Ia pathway is not yet established,
although we suspect that it is clearly more associative than
the activation volume indicates.
Predictions fall directly from the correlation in Figure 4.
For example, rate parameters for the mono-oxo-capped
mixed-valence W(III,III,IV) trimer are also consistent with
a similar associative activation pathway for water exchange
(∆Hq ) 53 kJ mol-1, ∆Sq ) -131 Jmol-1K-1).21 Using the
correlation in Figure 4, we predict that the ∆Vq value should
fall near the W32+ ion of slightly less than 0 cm3 mol-1, for
which we await experimental verification. This type of
correlation could turn out to be an extremely powerful tool
Acknowledgment. The authors gratefully acknowledge
Prof. James Rustad for helpful discussions on the simulation
results. We also thank three anonymous referees for their
comments and suggestions. Support for this research was
from ACS (PRF Grant No. 40412-AC2). We acknowledge
the Keck Foundation for support of the solid-state NMR
center at UC Davis.
(39) Twigg, M. V. Inorg. Chim. Acta 1977, 24, L84-L86.
(40) Richens, D. T. Chem. ReV. 2005, 105, 1961-2002.
(41) Richens, D. T. Comm. Inorg. Chem. 2005, 26, 217-232.
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