Transition state characterization for the reversible binding of dihydrogen to bis(2,2′-bipyridine)rhodium(I) from temperature- and pressure-dependent experimental and theoretical studies

Article abstract of DOI:10.1021/ic0515498

Thermodynamic and kinetic parameters for the oxidative addition of H ₂ to [Rh^I(bpy)₂]⁺ (bpy = 2,2′-bipyridine) to form [Rh^III(H)₂(bpy) ₂]⁺ were determined from either the UV-vis spectrum of equilibrium mixtures of [Rh^I(bpy)₂]⁺ and [Rh^III(H)₂(bpy)₂]⁺ or from the observed rates of dihydride formation following visible-light irradiation of solutions containing [Rh^III(H)₂(bpy)₂] ⁺ as a function of H₂ concentration, temperature, and pressure in acetone and methanol. The activation enthalpy and entropy in methanol are 10.0 kcal mol^-1 and -18 cal mol^-1 K-1, respectively. The reaction enthalpy and entropy are -10.3 kcal mol^-1 and -19 cal mol^-1 K^-1, respectively. Similar values were obtained in acetone. Surprisingly, the volumes of activation for dihydride formation (-15 and -16 cm³ mol^-1 in methanol and acetone, respectively) are very close to the overall reaction volumes (-15 cm³ mol^-1 in both solvents). Thus, the volumes of activation for the reverse reaction, elimination of dihydrogen from the dihydrido complex, are approximately zero. B3LYP hybrid DFT calculations of the transition-state complex in methanol and similar MP2 calculations in the gas phase suggest that the dihydrogen has a short H-H bond (0.823 and 0.810 A, respectively) and forms only a weak Rh-H bond (1.866 and 1.915 A, respectively). Equal partial molar volumes of the dihydrogenrhodium(I) transition state and dihydridorhodium(III) can account for the experimental volume profile found for the overall process.

Full text of DOI:10.1021/ic0515498

Inorg. Chem. 2006, 45, 1595−1603
Transition State Characterization for the Reversible Binding of
Dihydrogen to Bis(2,2’-bipyridine)rhodium(I) from Temperature- and
Pressure-Dependent Experimental and Theoretical Studies
Etsuko Fujita,*,† Bruce S. Brunschwig,†,‡ Carol Creutz,† James T. Muckerman,† Norman Sutin,†
David Szalda,§ and Rudi van Eldik£
Chemistry Department, BrookhaVen National Laboratory, Upton, New York 11973-5000, and
Institute for Inorganic Chemistry, UniVersity of Erlangen-Nu¨rnberg, Egerlandstrasse 1,
91058 Erlangen, Germany
Received September 9, 2005
Thermodynamic and kinetic parameters for the oxidative addition of H2 to [RhI(bpy)2]+ (bpy
) 2,2′-bipyridine) to
form [RhIII(H)2(bpy)2]+ were determined from either the UV vis spectrum of equilibrium mixtures of [RhI(bpy)2]+ and
−
[RhIII(H)2(bpy)2]+ or from the observed rates of dihydride formation following visible-light irradiation of solutions
containing [RhIII(H)2(bpy)2]+ as a function of H2 concentration, temperature, and pressure in acetone and methanol.
1
1
The activation enthalpy and entropy in methanol are 10.0 kcal mol- and
−
18 cal mol- K-1, respectively. The
1
1
reaction enthalpy and entropy are
−
10.3 kcal mol- and
−
19 cal mol- K-1, respectively. Similar values were
1
obtained in acetone. Surprisingly, the volumes of activation for dihydride formation (
−15 and
−
16 cm3 mol- in
methanol and acetone, respectively) are very close to the overall reaction volumes (
−
15 cm3 mol-1 in both solvents).
Thus, the volumes of activation for the reverse reaction, elimination of dihydrogen from the dihydrido complex, are
approximately zero. B3LYP hybrid DFT calculations of the transition-state complex in methanol and similar MP2
calculations in the gas phase suggest that the dihydrogen has a short H−H bond (0.823 and 0.810 Å, respectively)
and forms only a weak Rh H bond (1.866 and 1.915 Å, respectively). Equal partial molar volumes of the
−
dihydrogenrhodium(I) transition state and dihydridorhodium(III) can account for the experimental volume profile
found for the overall process.
+
Introduction
tigated the oxidative addition of H2 to RhI(bpy)2 (bpy )
2,2′-bipyridine) to form the corresponding cis-dihydride-
rhodium(III) complex (eq 1).9
Efforts to clarify the nature of the interaction of dihydrogen
with low-valent metal centers and the formation of molecular
dihydrogen complexes or high-valent dihydride complexes
has attracted much attention.1-8 We have previously inves-
kf
RhI(bpy)2+ + H2 y
\
z cis-RhIII(H)2(bpy)2
(1)
+
kr
* To whom correspondence should be addressed. E-mail: fujita@bnl.gov.
† Brookhaven National Laboratory.
Irradiation (λ > 300 nm) of this reaction mixture results in
‡ Permanent address: Molecular Material Research Center, Beckman
Institute, MC 139-74, California Institute of Technology, Pasadena, CA
91125.
the dissociation of the dihydrido complex and the formation
+
of H2 and RhI(bpy)2 , which is followed by the thermal
relaxation of the perturbed system to re-form cis-RhIII(H)2-
(bpy)2+ when the light is extinguished. It was found that the
observed pseudo-first-order rate constant for the relaxation
process is given by eq 2, with kf ) 24.4 M-1 s-1 and kr )
1.70 × 10-2 s-1 in acetone at 25 °C.9
§ Permanent address: Department of Natural Sciences, Baruch College,
New York, NY 10010.
£ University of Erlangen-Nu¨rnberg.
(1) Kubas, G. Acc. Chem. Res. 1988, 21, 120-128.
(2) Crabtree, R. H. Acc. Chem. Res. 1990, 23, 95-101.
(3) Jessep, G.; Morris, R. H. Coord. Chem. ReV. 1992, 121, 155-284.
(4) Heinekey, D. M.; Oldham, W. J., Jr. Chem. ReV. 1993, 93, 913-926.
(5) Kubas, G. J. Metal Dihydrogen and σ-Bond Complexes: Structure,
Theory, and ReactiVity; Kluwer Academic/Plenum Publishers: New
York, 2001.
(8) Heinekey, D. M.; Lledos, A.; Lluch, J. M. Chem. Soc. ReV. 2004, 33,
175-182.
(9) Yan, S. G.; Brunschwig, B. S.; Creutz, C.; Fujita, E.; Sutin, N. J. Am.
Chem. Soc. 1998, 120, 10553-10554.
(6) McGrady, G. S.; Guilera, G. Chem. Soc. ReV. 2003, 32, 383-392.
(7) Andrews, L. Chem. Soc. ReV. 2004, 33, 123-132.
10.1021/ic0515498 CCC: $33.50
Published on Web 01/05/2006
© 2006 American Chemical Society
Inorganic Chemistry, Vol. 45, No. 4, 2006 1595

Fujita et al.
NMR spectroscopy. (Warning: The perchlorate salts used in this
study may be explosiVe and are potentially hazardous.)
kobs ) kf[H2] + kr
(2)
The ratio of the rate constants, kf/kr ) 1.43 × 103 M-1, is in
close agreement with the value of the equilibrium constant,
KH ) 1.45 × 103 M-1, obtained from equilibrium measure-
Thermodynamic Measurements. For the equilibrium and
kinetic studies at 25 °C, 0.01-1.0 mM solutions of RhI(bpy)2 in
+
acetone or methanol were prepared either by photochemical
reduction of [RhIII(C2O4)(bpy)2](ClO4) or by dissolution of [RhI(bpy)2]-
PF6. Measurements were made using glass reaction vessels (total
volume of 120 mL) directly attached to both 1 and 10 mm path
length optical cells. Only the optical cell chamber containing an
∼3 mL aliquot was thermostatically controlled. After a spectrum
ments.9 Kinetic isotope effects for reductive elimination (kr(H)
/
k
r(D)) and for oxidative addition (kf(H)/kf(D)) were reported to
be 2.3 and 1.0, respectively.9
In the present work, we have extended our studies of this
system as a function of temperature, pressure, and solvent
in an effort to gain further insight into the nature of the
transition state associated with the formation of the dihydrido
complex. While the activation enthalpies (∆H‡) and entropies
(∆S‡) and the reaction enthalpies (∆H0) and entropies (∆S0)
for oxidative addition (or coordination) of hydrogen have
been extensively investigated for a number of organometallic
complexes,5 there are few data for their activation (∆V‡) or
reaction (∆V0) volumes. To our knowledge, no reaction
volume data exist for oxidative addition reactions of H2 to
metal complexes. Only activation volumes at 10 °C for
Vaska’s complex, IrCl(CO)(PPh3)2, at 10 °C are known.10
We have also restudied this reaction for comparison purposes.
Activation and reaction volume data can be used to construct
the volume changes that occur along the reaction coordinate
+
of RhI(bpy)2 (1 mm optical cell) was recorded, an equilibrium
mixture of RhI(bpy)2 and RhIII(H)2(bpy)2 was prepared by the
addition of the desired amount of H2 (with Ar added for a total
pressure of 760 Torr). Spectra of the equilibrium mixture of RhI-
+
+
+
+
(bpy)2 and RhIII(H)2(bpy)2 (10 mm cell) were measured before
and after all kinetic measurements to check for decomposition. For
the kinetic measurements, the solutions were irradiated for 10 s
using a 150 W xenon lamp equipped with a 300 nm long-path filter
to liberate H2 from the dihydrido complex. The disappearance of
the photogenerated RhI(bpy)2 was monitored with a HP 8452 A
+
spectrophotometer (eq 1). Plots of the observed rate constants for
the formation of RhIII(H)2(bpy)2+ as a function of the H2 concentra-
tion were straight lines with slope and intercept of kf and kr,
respectively.9 The equilibrium constant (KH) can also be obtained
+
from the equilibrium concentrations of RhI(bpy)2 and RhIII(H)2-
+
(bpy)2
.
+
for a particular reaction.11 The poised RhI(bpy)2 /RhIII(H)2-
+
[RhIII(H2)(bpy)2
]
(bpy)2+ system is ideal for investigating both activation and
equilibrium thermodynamic parameters experimentally. Here
we report that the volume of activation for reaction 1 is
approximately equal to the overall reaction volume, with the
result that the back reaction exhibits almost no activation
volume. B3LYP (i.e., Becke’s three-parameter hybrid func-
tional using the Becke exchange and the Lee-Yang-Parr
correlation functionals) density functional theory (DFT)
KH )
(3)
[Rh1(bpy)2+][H2]
For the pressure- and temperature-dependent experiments, the
+
solution containing RhIII(C2O4)(bpy)2 and H2 was transferred by
syringe to a gastight pillbox optical cell16 that had been flushed
with H2. The pillbox was placed in a thermostated, four-window,
high-pressure vessel16 mounted in a HP 8452 A spectrophotometer.
+
The photolysis of RhIII(C2O4)(bpy)2 to form a mixture of RhI-
+
calculations including solvent effects on RhI(bpy)2 , RhIII-
+
+
+
(bpy)2 and RhIII(H)2(bpy)2 was performed in the pillbox cell
within the high-pressure vessel while the solution was stirred with
a glass-coated magnetic stirring bar. During syringe transfer of the
solution to the pillbox cell, a small amount of dissolved H2 escapes.
Therefore, actual hydrogen concentrations were estimated from the
observed rates at 25 °C using the kobs vs [H2] data shown in Figure
S1 (Supporting Information).
(H)2(bpy)2 , and the transition-state (TS) complex were also
carried out. These were supplemented with ab initio MP2
(Møller-Plesset second-order perturbation theory) calcula-
tions of all three species in the gas phase. The thermodynamic
and mechanistic implications are discussed in detail.
Experimental Section
Toluene solutions of Ir(H)2Cl(CO)(PPh3)2 were prepared by
dissolving IrCl(CO)(PPh3)2 under a known concentration of H2. The
reaction rates for hydride formation were obtained with the same
method used for RhIII(H)2(bpy)2+, except for a temperature of 35
°C.
Materials. [RhIII(C2O4)(bpy)2]ClO4 and [RhI(bpy)2]ClO4 were
prepared as previously described.12-14 [RhI(bpy)2]PF6 was obtained
by reducing the Rh(III) complex with NaBH4.15 IrCl(CO)(PPh3)2
was purchased from Strem Chemicals, Inc. and used without
purification. All complexes were characterized by UV-vis, IR, and
Electronic Structure Calculations. B3LYP hybrid DFT and ab
+
+
initio MP2 calculations on RhI(bpy)2 and RhIII(H)2(bpy)2 in the
gas phase were carried out using D95V(d,p) (H,C,N,O)17 and
LANL2DZ (n + 1) ECP (Rh)18,19 basis sets with the Gaussian 03
program.20 To evaluate the solvation effect, we carried out B3LYP
DFT calculations using the LACVP** basis set, consisting of
6-31G(d,p) (H,C,N,O)21 and LANL2DZ (n + 1) ECP (Rh), with
(10) Schmidt, R.; Geis, M.; Kelm, H. Z. Phys. Chem. 1974, 92, 223.
(11) (a) van Eldik, R.; Du¨cker-Benfer, C.; Thaler, F. AdV. Inorg. Chem.
2000, 49, 1. (b) van Eldik, R.; Hubbard, C. D. In High-Pressure
Chemistry: Synthetic, Mechanistic and Supercritical Applications; van
Eldik, R., Kla¨rner, F.-G., Eds.; VCH-Wiley, Weinheim, Germany,
2002, p 3-40. (c) van Eldik, R.; Hubbard, C. D. In Chemistry at
Extreme Conditions; Riad Manaa, M., Ed.; Elsevier: Amsterdam,
2005; Chapter 4. (d) Franke, A.; Stochel, G.; Jung, C.; van Eldik, R.
J. Am. Chem. Soc. 2004, 126, 4181.
(16) (a) le Noble, W. J.; Schlott, R. ReV. Sci. Instrum. 1976, 47, 770-771.
(b) Spitzer, M.; Ga¨rtig, F.; van Eldik, R. ReV. Sci. Instrum. 1988, 59,
2092.
(17) Dunning, T. H. J.; Hay, P. J. Modern Theoretical Chemistry;
Plenum: New York, 1976; Vol. 3.
(18) (a) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270-283. (b)
Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299-310.
(19) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985, 82, 284-298.
(12) Gillard, R. D.; De Jesus, J. P.; Sheridan, P. S. Inorg. Synth. 1980, 20,
58-60.
(13) Shinozaki, K.; Takahashi, N. Inorg. Chem. 1996, 35, 3917-3924.
(14) Chan, S. F.; Chou, M.; Creutz, C.; Matsubara, T.; Sutin, N. J. Am.
Chem. Soc. 1981, 103, 369-379.
(15) Martin, B.; McWhinnie, W. R.; Waind, G. M. J. Inorg. Nucl. Chem.
1961, 23, 207-233.
1596 Inorganic Chemistry, Vol. 45, No. 4, 2006

Binding of Dihydrogen to Bis(2,2′-bipyridine)rhodium(I)
+
+
Table 1. Spectroscopic, Thermodynamic, and Kinetic Parameters for the Reaction of RhI(bpy)2 with H2 to Form RhIII(H)2(bpy)2
DFT (B3LYP) calcd
MP2 calcd
gas phase
solvent
methanol
acetone
methanol
UV-vis spectrum of
RhI(bpy)2+: λmax (ꢀ)
(nm (mM-1 cm-1))
246(24.5), 298(32.1),
362(6.8), 518sh(8.5),
552(13.1), 656sh(2.5),
750sh(0.5)
514sh(5.1), 552(12.5),
648(2.5), 750sh(0.5)
kf at 25 °C (M-1 s-1
kr at 25 °C (s-1
kf/kr at 25 °C (M-1
)
37 ( 2
28 ( 2
)
(1.5 ( 0.2) × 10-2
(1.9 ( 0.3) × 10-2
(1.5 ( 0.2) × 103
(3.4a ( 0.2) × 103
(2.0 ( 0.2) × 103
)
(2.5 ( 0.2) × 103
KH at 25 °C (M-1
∆E° (kcal mol-1
∆H° (kcal mol-1
∆S0 (cal mol-1 K-1
∆V0 (cm3 mol-1
∆Ef‡ (kcal mol-1
∆Hf‡ (kcal mol-1
∆Sf‡ (cal mol-1 K-1
∆Vf‡ (cm3 mol-1
∆Hr‡ (kcal mol-1
∆Sr‡ (cal mol-1 K-1
)
(2.7 ( 0.2) × 103
b
)
-6.3
-14.6
)
-10.3 ( 0.4
-19 ( 2
-15 ( 1
-9.7 ( 0.5
-18 ( 2
-15 ( 1
-4.4 (-5.0)c
-25 (-16)c
-12.0 (-12.6)c
-25 (-16)c
)
)
)
)
12.1
12.1
10.0 ( 0.7
-18 ( 2
-16 ( 1
20.0 ( 0.7
0 ( 2
8.5 ( 0.7
11.7 (11.1)c
-26 (-17)c
12.2 (11.6)c
-26 (-17)c
)
)
-23 ( 2
)
)
-15 ( 1, -14a( 1
18.1 ( 0.6
-6 ( 2
16.1 (16.1)c
24.2 (24.2)c
-1 (-1)c
-1 (-1)c
a With D2 instead of H2. b From spectroscopic equilibrium measurement, KH ) [RhIII(H)2(bpy)2+]/[RhI(bpy)2+][H2]. c The experimental thermodynamic
values are obtained relative to a 1 M concentration standard state. The theoretical values (i.e., 1 atm pressure standard state) are converted to a concentration
standard state and shown in parentheses.
the Jaguar 5.5 program.22 The effect of solvation was calculated
using the self-consistent reaction field (SCRF) method as imple-
mented in the Jaguar program. The Cartesian coordinates for RhI-
(bpy)2+, RhIII(H)2(bpy)2+, and the transition-state complex in
MeOH, optimized at the B3LYP-DFT level of theory, are presented
in Tables S1-S3 (Supporting Information). Time-dependent DFT
(TDDFT) B3LYP calculations for RhI(bpy)2+ were carried out with
the Gaussian 03 program to understand the electronic transition
energies and excitations, as well as oscillator strengths.
a limited data set and the quality of the crystal, the structure could
only be refined to an R value of 15.7. The crystal also exhibited
diffuse scattering.
Results
+
Reactivity of RhI(bpy)2 . RhI(bpy)2+ is stable in degassed
acetone or methanol, showing an intense MLCT band at 552
nm. The spectrum shows additional shoulders between 450
and 750 nm, as summarized in Table 1. It is known23 that
Data Collection, Determination, and Refinement of the
Crystal Structure. A black rod crystal (0.25 mm × 0.10 mm ×
+
aqueous solutions of RhI(bpy)2 contain several species,
including [RhI(bpy)2]22+, Rh(H)(bpy)2(H2O)2+, and [Rh-
(bpy)2]2H3+, depending on the total Rh concentration and
+
0.02 mm) of RhI(bpy)2 obtained from CH3CN was coated with
perfluoropolyether and sealed inside a glass capillary. A wavelength
of 0.956 Å was used, and the data were collected using image plates
at the beam line X7B at the National Synchrotron Light Source
(NSLS) at Brookhaven National Laboratory. The crystal exhibited
monoclinic symmetry and systematic absences 0k0, k ) 2n + 1
and h0l, h ) 2n + 1 consistent with the space group P21/a, a
nonstandard setting of space group P21/c. Unit cell dimensions and
other crystallographic information are reported in Table S4 (Sup-
porting Information).
+
pH of the solution. The spectra of the monomer, RhI(bpy)2 ,
and the dimer, [RhI(bpy)2]22+, have a λmax of 505 and ∼530
nm, respectively, with very similar molar absorptivities (∼104
M-1 cm-1, per Rh(I) center) at their respective maxima.23
In acetone or methanol, no shift in the absorption maximum
of the RhI(bpy)2+ is observed when the Rh(I) concentration
is increased from 0.01 to 2 mM (the solubility limit). This
indicates the existence of only the monomer in these solvents.
Further, no spectral changes were observed with temperature
between 10 and 40 °C. Two shoulders at 750 and 650 nm
were observed in both methanol and acetone that were not
previously reported for water or alcohol solutions.23 Our
TDDFT calculations predict that the transition at 750 nm
corresponds to the HOMO-to-LUMO transition (see Theo-
retical Investigation).
The structure was solved by standard heavy-atom Patterson
methods. The asymmetric unit contains two formula units. Due to
(20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin,
K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone,
V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G.
A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.;
Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai,
H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.;
Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R.
E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J.
W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.;
Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari,
K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.;
Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.;
Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.;
Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.;
Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A.
Gaussian 03, revision B.04; Gaussian, Inc.: Wallingford, CT, 2004.
(21) (a) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213.
(b) Francl, M. M.; Petro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon,
M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654.
(22) Jaguar 5.0; Schro¨dinger, LLC: Portland, OR.
Effects of H2 Concentration and Temperature on the
+
Formation of RhIII(H)2(bpy)2 . The UV-vis spectra of
+
equilibrium mixtures of RhI(bpy)2+ and cis-RhIII(H)2(bpy)2
were recorded as a function of [H2] at 25.0 °C. The solubility
of H2 in methanol and acetone under 1 atm pressure is 3.95
and 4.0 mM at 25 °C, respectively.24,25 Assuming that only
+
RhI(bpy)2 absorbs at 552 nm (ꢀ ) 13.1 and 12.5 mM-1
(23) Chou, M.; Creutz, C.; Mahajan, D.; Sutin, N.; Zipp, A. P. Inorg. Chem.
1982, 21, 3989-3997.
(24) Fogg, P. G. T.; Gerrard, W. Solubility of Gases in Liquids; Wiley:
Chichester, 1991.
Inorganic Chemistry, Vol. 45, No. 4, 2006 1597

Fujita et al.
+
nm increases due to a shift in equilibrium toward RhI(bpy)2 ,
thus indicating that reaction 1 is exothermic. From the slope
and the intercept of a plot of ln(KH) versus 1/T (Figure 1,
bottom) and eq 4, where R is the gas constant, we obtained
∆H0 ) -10.3 ( 0.4 kcal mol-1 and ∆S0 ) -19 ( 2 cal
mol-1 deg-1.
∆H0
T
R ln(KH) ) -
+ ∆S0
(4)
The temperature dependence of the rate of oxidative
addition of H2 to photogenerated RhI(bpy)2+ was studied by
UV-vis spectroscopy by monitoring the decay of the RhI-
+
(bpy)2 absorption under a known pressure of H2 in the
temperature range 10-35 °C using a gastight pillbox cell.
The activation parameters (∆Hf‡, ∆Sf‡, ∆Hr‡, and ∆Sr‡) in
methanol and acetone were obtained from the slope (∆Hf‡
and ∆Hr‡) and the intercept (∆Sf‡ and ∆Sr‡) of the plots
(shown in Figure S2a and b, Supporting Information) using
eqs 5 and 6, where h is Planck’s constant and kB is
Boltzmann’s constant. The results are summarized in Table
1.
hkobsKH
∆Hf‡
R ln
R ln
) -
) -
+ ∆Sf‡
+ ∆Sr‡
(5)
(6)
(
(
)
)
T
kBT(KH[H2] + 1)
hkobs
∆Hr‡
Figure 1. (Top) Temperature-dependent spectra of the equilibrium mixture
+
+
of RhI(bpy)2 and RhIII(H)2(bpy)2 in methanol at 9.9, 15.0, 19.9, 25.2,
29.7, and 34.4 °C. The higher the temperature, the more RhI(bpy)2+ exists.
(Bottom) Plot of ln(KH) versus 1/T from which ∆H0 ) -10.3 ( 0.4 kcal
mol-1 and ∆S0 ) -19 ( 2 cal mol-1 K-1 were obtained.
T
kBT(KH[H2] + 1)
The activation enthalpy and entropy for the forward reaction
are 10 kcal mol-1 and ≈ -20 cal mol-1 K-1, respectively.
To make the comparison of experimental enthalpies and
theoretical activation and reaction parameters, it is necessary
to recognize that the standard state for H2 employed in the
theory is 1 atm pressure while that in the current experiment
is 1 M. The correction for this change in the standard states
is given in the Supporting Information.
cm-1 in methanol and acetone, respectively), the equilibrium
constant can be calculated from KH ) (A0 - A)/[H2]A where
A0 and A are the absorbances prior to and after addition of
H2 (see eqs 1 and 3). Values for KH of (2.7 ( 0.2) × 103
and (2.0 ( 0.2) × 103 M-1 in methanol and acetone,
respectively, were obtained. The value obtained in acetone
is slightly larger than that previously reported9 of 1.45 ×
103 M-1 at 25 °C.
Effects of Pressure on the Formation of [RhIII(H)2-
(bpy)2]+. UV-vis spectra of an equilibrium mixture of
+
+
RhI(bpy)2 and cis-RhIII(H)2(bpy)2 were recorded as a
function of pressure at 25 °C. With an increase in pressure,
the reaction shifts to the right and the absorbance at 552 nm
The forward and reverse rate constants for reaction 1 in
methanol and acetone were determined as a function of H2
concentration. Figure S1 (Supporting Information) shows the
+
(RhI(bpy)2 ) decreases, as shown in Figure 2a for methanol.
+
observed rate constants for the formation of RhIII(H)2(bpy)2
Thus, increasing pressure favors product formation, RhIII-
in methanol. The slope and the intercept of the plot yield kf
) 37 ( 1.5 M-1 s-1 and kr ) (1.5 ( 0.2) × 10-2 s-1. Similar
experiments in acetone yield kf ) 28 ( 2 M-1 s-1 and kr )
(1.9 ( 0.3) × 10-2 s-1, close to the values reported
previously (kf ) 24.4 M-1 s-1 and kr ) 1.70 × 10-2 s-1).9
The equilibrium constants calculated from kf/kr in methanol
and acetone are (2.5 ( 0.2) ×103 and (1.5 ( 0.2) × 103
M-1, respectively, and are consistent with the values obtained
from the spectroscopic measurements.
+
(H)2(bpy)2 , while increasing temperature favors the reac-
+
tants, H2 and RhI(bpy)2 . The spectral changes observed on
changing the pressure were reversible and were used to
calculate the value of KH as function of pressure. A plot of
ln(KH) versus pressure is significantly curved, Figure 2b, i.e.,
the reaction volume, ∆V0 calculated from the slope
() -∆V0/RT) of the line decreases with increasing pressure.
This effect is due to the compressibility of the solvent. To
determine the reaction volume at ambient conditions, the data
were fit with a parabolic function (eq 7),11c
The UV-vis spectra of equilibrium mixtures of RhI(bpy)2+
+
and cis-RhIII(H)2(bpy)2 were recorded as a function of
temperature in methanol (Figure 1) and in acetone. When
the temperature is increased, the intensity of the peak at 552
ln(KH) ) a + bP + cP2
(7)
and the initial slope was used to calculate the reaction volume
from eq 8,
(25) Young, C. L. Hydrogen and Deuterium; Pergamon Press: Oxford,
1982; Vol. 5/6.
1598 Inorganic Chemistry, Vol. 45, No. 4, 2006

Binding of Dihydrogen to Bis(2,2′-bipyridine)rhodium(I)
Figure 3. Pressure dependence of the rate constant for formation of RhIII-
+
(H)2(bpy)2 in methanol according to reaction 1.
numbering (Figure S5a), crystal data and structure refinement
(Table S4), and CIF files are given as Supporting Informa-
tion.
In each complex in the asymmetric unit, the rhodium atom
is coordinated by the nitrogen atoms of two bidentate
bipyridine ligands. The formula unit also contains a per-
chlorate anion and two acetonitrile molecules of crystalliza-
tion. The average Rh-N bond distance is 2.01 Å. The
coordination sphere about the rhodium has a tetrahedrally
distorted square-planar geometry. The nitrogen atoms of the
two bipyridine ligands are 0.32 and 0.23 Å out of the least-
squares plane formed by the four nitrogen atoms and the
rhodium atom. The least-squares planes between the two
bipyridine ligands within a complex form angles of 40.1°
and 39.8° with one another. Within the bipyridine ligand,
the two pyridine rings are folded forming angles of 13.8°,
15.9° and 14.1°, 12.3°. Thus, to relieve the steric crowding
of the two bipyridine rings, the coordination sphere has a
tetrahedral distortion and the bipyridine rings are bent (see
Figure S5a and b, Supporting Information). The rhodium
complexes are stacked in infinite chains along the crystal-
lographic 2-fold screw axis with a Rh-Rh distance of 3.64
Å with eclipsing bipyridines rings, as shown in Figure S5b.
The two crystallographically independent chains are almost
identical.
Figure 2. Pressure dependence of the equilibrium constant for reaction 1
in methanol; top: the spectral change observed on changing the pressure
50, 500, 1000, 1500, and 2000 atm (solid lines), then 1500, 1000, 500, and
50 atm (dashed lines). The intensity of the band at 552 nm decreases with
increasing pressure; bottom: a plot of ln(KH) vs pressure.
∆V0
RT
b ) -
(8)
This yields ∆V0 ) -15 ( 1 cm3 mol-1 in both methanol
(shown in Figure 2b) and acetone.
The forward rate constants for reaction 1 in methanol and
acetone were determined under various pressures at 25 °C.
Since under our conditions kf[H2] . kr, the limiting form
kobs ≈ kf[H2] can be used. The effect of pressure on the
relaxation process was found to be reproducible for a
complete pressure cycle, i.e., increasing the pressure stepwise
from ambient to 2000 atm and then decreasing the pressure
stepwise back to ambient conditions. A plot of ln(kobs) versus
pressure in methanol is shown in Figure 3. The activation
volume (viz. -16 cm3 mol-1) was estimated from the initial
slope of the plot (b ) - ∆V‡/RT). The results are summarized
in Table 1 and Figure 4.
Theoretical Investigation. Quantum mechanical calcula-
+
tions were used to predict the structure of RhIII(H)2(bpy)2 ,
+
RhI(bpy)2 , and the transition state for the oxidative addition
+
of H2. Initial gas-phase DFT calculations26-28 on RhI(bpy)2
and RhIII(H)2(bpy)2+ were carried out using the Gaussian 03
program.20 Preliminary geometry optimizations were per-
formed for both rhodium complexes without symmetry
constraints. From these results, it became clear that
RhI(bpy)2+ adopts a structure of D2 symmetry while RhI(bpy)2-
(H)2+ and the RhI(bpy)2(H2) TS complex (see below) adopt
a structure of C2 symmetry. The structures were then re-
optimized with the appropriate symmetry constraints. Also,
gas-phase MP2 and solvent-phase DFT calculations were
Effects of Pressure on the Formation of Ir(H)2Cl(CO)-
(PPh3)2. Reaction rates for oxidative addition of H2 to IrCl-
(CO)(PPh3)2 in toluene were obtained using the same method
+
as used for RhIII(H)2(bpy)2 . Because oxidative addition of
H2 to IrCl(CO)(PPh3)2 is much slower than for that of
+
RhI(bpy)2 , the former reaction was studied at 35 °C. Figure
S3 shows the spectral changes of IrCl(CO)(PPh3)2 to form
Ir(H)2Cl(CO)(PPh3)2 at 2 min intervals under 1 atm H2 at
35 °C. From a plot of ln(kobs) versus pressure in toluene
(Figure S4), the activation volume of -20 ( 1 cm3 mol-1
was obtained for reaction with both H2 and D2.
Structure of [RhI(bpy)2](ClO4). Selected bond lengths
and angles (Table 2), an ORTEP drawing showing the atom
(26) Becke, A. D. Phys. ReV. A 1988, 38, 3098.
(27) Lee, C.; W., Y.; Parr, R. G. Phys. ReV. B 1988, 37, 785.
(28) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989,
157, 200.
Inorganic Chemistry, Vol. 45, No. 4, 2006 1599

Fujita et al.
+
Figure 4. Experimental energy, entropy, and volume profiles for the oxidative addition of H2 to RhI(bpy)2 in methanol (red) and acetone (blue): (a)
enthalpy, (b) entropy, and (c) partial molar volume.
Table 2. Experimental and Theoretical Bond Lengths [Å] and Angles
distance in the MP2 structure is 0.1 Å shorter than that in
the DFT structures. The geometry around Rh is approxi-
+
[deg] for RhI(bpy)2
DFT (B3LYP) DFT (B3LYP)
mately octahedral with a H-Rh-H angle of ≈83 ( 2°. The
X-ray
calcd
calcd
MP2 calcd
gas phase
B3LYP Rh-N bond distances perpendicular to the plane
made by H-Rh-H in the gas phase and methanol are 2.064
and 2.081 Å, respectively, and the others are 2.235 and 2.226
Å, respectively. The long bond distances observed in all
structures are due to the trans effect of the Rh-H bond. The
tendency of MP2 calculation to yield shorter bond distances
than those obtained from DFT calculations is as expected.29
The B3LYP gas-phase geometry of the TS complex was
calculated by the same method used for the stable complexes.
The optimized geometries (C2 symmetry) of the TS complex
in the gas phase (B3LYP and MP2) and in methanol
(B3LYP) are similar, as shown in Table 3. As can be seen
from Figures 5 and S6a, the geometry around the Rh is not
octahedral, but rather it is closer to a five-coordinate side-
on H2 complex with a H-Rh-H angle of ≈25°. The H2
axis is not aligned with one N-Rh-N plane but is rotated
slightly (Figure S6b). The Rh-N distance perpendicular to
the H-Rh-H plane is 2.068 Å, and the other Rh-N distance
is 2.196 Å in methanol. The Rh-H distance in general is
structurea
gas phase
methanol
Rh-N
2.01
1.38
1.38
1.38
1.41
1.40
1.35
1.49
2.069
1.365
1.401
1.396
1.400
1.395
1.350
1.473
2.093
1.366
1.398
1.393
1.395
1.391
1.350
1.472
2.014
1.373
1.404
1.398
1.405
1.397
1.361
1.466
N-C2
C2-C3
C3-C4
C4-C5
C5-C6
C6-N
C2-C2′
N-Rh-Nb
N-Rh-Nc
N-Rh-Nd
Rh-N-C2
N-C2-C3
C2-C3-C4
C3-C4-C5
C4-C5-C6
C5-C6-N
C6-N-C2
C6-N-Rh
N-C2-C2′
C2′-C2-C3
78.6
103.4
164.6
118
124
121
118
116
127
113
78.6
104.1
162.8
115.7
121.7
119.7
118.5
118.8
123.2
118.1
125.0
114.6
123.7
78.0
104.5
163.2
115.6
121.4
119.6
118.8
118.8
122.9
118.4
124.8
114.9
123.6
79.5
103.4
161.8
116.2
121.9
119.7
118.4
119.2
122.9
117.8
124.5
113.6
124.4
127
112
124
a Averaged bond length. b Both N atoms in one bpy. c N atoms in the
different bpy ligands. d N atoms located in the trans position.
+
long at 1.88 Å (compared to 1.55 Å for RhIII(H)2(bpy)2 ),
and the H-H distance is very short at 0.82 Å (close to 0.74
Å for free dihydrogen). The TS complex can be characterized
as a dihydrogen-like complex. The dihedral angles between
two least-squares planes of the bpy ligands are ≈42°, 86°,
performed. Table 2 lists the principal geometric properties
+
of the optimized RhI(bpy)2 complex in the gas phase and
in methanol, together with X-ray crystal data. Table 3 shows
+
the geometric properties of the optimized RhIII(H)2(bpy)2
+
+
and 58° for RhI(bpy)2 , RhIII(H)2(bpy)2 , and the TS
complex, respectively. The MP2 structure is similar to the
B3LYP structures except that the Rh-N distances are slightly
shorter. While the MP2 calculations were useful in cor-
roborating the geometrical properties of the various Rh
complexes studied here, the primary reason for carrying them
out was to obtain a better theoretical estimate of the
energetics of activation and reaction.
and the transition-state complex. Figure 5 shows the opti-
+
+
mized structures of RhI(bpy)2 , RhIII(H)2(bpy)2 , and the TS
complex in the gas phase at the B3LYP level of theory.
The geometry-optimized DFT (B3LYP) structure of
+
RhI(bpy)2 is very similar to that of the single-crystal
structure, Table 2. While the observed Rh-N distances are
slightly longer for the DFT-calculated (0.06 and 0.08 Å
longer for the gas phase and methanol, respectively), they
are very close for the MP2 calculation. The coordination
sphere around Rh has a tetrahedrally distorted square-planar
geometry, as observed. The planes between the two bipyri-
dine ligands form angles of 42° with one another.
Thermodynamic parameters (1 atm pressure standard state)
obtained from the B3LYP and MP2 calculations are shown
together with those relative to a 1 M concentration standard
state in parentheses in Table 1 (see the correction in the
Supporting Information). Previous calculations on rhenium
bipyridine complexes29 indicated that the B3LYP relative
energetics were not accurate to better than 4-6 kcal mol-1,
The DFT (B3LYP) coordination geometries in RhIII(H)2-
+
(bpy)2 in the gas phase and in methanol and the MP2
coordination geometry are all similar, as shown in Table 3.
The distances within the bpy ligand are all similar. The H-H
(29) Fujita, E.; Muckerman, J. T. Inorg. Chem. 2004, 43, 7636-7647.
1600 Inorganic Chemistry, Vol. 45, No. 4, 2006

Binding of Dihydrogen to Bis(2,2′-bipyridine)rhodium(I)
Table 3. Selected Calculated Bond Lengths [Å] and Angles [deg] for RhIII(H)2(bpy)2 and the TS Complex
+
RhIII(H)2(bpy)2
RhIII(H)2(bpy)2
TS complex
DFT (B3LYP)
calcd gas phase
TS complex
DFT (B3LYP)
calcd methanol
+
+
+
DFT (B3LYP)
calcd gas phase
DFT (B3LYP)
calcd methanol
RhIII(H)2(bpy)2
TS complex
MP2 gas phase
(MP2) gas phase
Rh-H
H-H
Rh-N
H-Rh-H
1.550
2.034
2.064, 2.235
82.1
1.553
2.109
2.081, 2.226
85.5
1.537
1.992
2.028, 2.179
80.8
1.887
0.817
2.053, 2.172
25.0
1.866
0.823
2.068, 2.196
25.5
1.915
0.810
2.009, 2.072
24.4
2
the transition at 441 nm, where the dz -to-dxy character cannot
be totally ignored. The predicted and observed transitions
and relative intensities are in excellent agreement, except
for the shoulder observed at ≈520 nm.
The orbital interactions between molecular hydrogen and
RhI(bpy)2+ are reflected in the orbitals of the transition state
for the oxidative addition of H2. The HOMO of the transition
2
state is essentially the antibonding combination of the dz
HOMO of RhI(bpy)2+ with the σ-bonding orbital of H2. The
bonding combination of the metal dz and H2 σ-bonding
2
orbital is of much lower energy and contributes two partial
metal-hydrogen bonds. The HOMO-1 of the transition state
corresponds to the bonding combination of the dxz HOMO-1
of RhI(bpy)2+ and the σ* antibonding orbital of H2 (resulting
in two additional partial metal-hydrogen bonds). The net
result is two partial metal-hydrogen bonds and a weakened
H-H bond in the transition state.
Figure 5. Calculated gas-phase structures of RhI(bpy)2 (top two
structures), the TS complex (bottom left), and RhIII(H)2(bpy)2+ (bottom right)
at the DFT (B3LYP) gas-phase level of theory.
+
Discussion
+
The spectroscopic behavior of RhI(bpy)2 in alcohol and
while MP2 calculations could account for the observed
conformer of the dimer skewed-cis-[Re(bpy)(CO)3]2. Indeed,
in the present work, the calculated B3LYP energetics (in
the concentration standard) in methanol are in some dis-
agreement with the observed reaction exothermicity (-5.0
vs -10.3 kcal mol-1 in methanol, see Table 1) but are in
good agreement with the activation enthalpy (11.1 vs 10.0
kcal mol-1 in methanol). The gas-phase MP2 results, using
the calculated B3LYP vibrational frequencies to compute
zero-point energy and thermal effects, are in reasonably good
agreement with both reaction (-12.6 kcal mol-1) and
activation (11.6 kcal mol-1) enthalpies. The difference in
solvation energies for reaction (-1.7 kcal mol-1) and
activation (1.1 kcal mol-1) in the B3LYP calculations in
methanol, if added to the gas-phase MP2 results, would make
the discrepancies larger. The discrepancies are likely due to
the fact that many of the vibrational frequencies are too low
to be treated in the harmonic approximation.
water has been extensively studied.23 In water at high pH,
the tetrahedrally distorted square-planar RhI(bpy)2+ complex
(λmax ) 505 nm) and the dimer with a weak Rh-Rh
interaction (λmax ) 530 nm) are present at low and high total
Rh(I) concentrations, respectively.23 Rh-Rh bond formation
between d8 complexes is well-known, and in the crystal, the
+
RhI(bpy)2 complexes are stacked in infinite chains along
the crystallographic 2-fold screw axis with a Rh-Rh distance
of 3.64 Å with eclipsing bipyridine rings (Figure S5b). We
have observed weak absorption bands (i.e., shoulders) around
650 and 750 nm in acetone and methanol that were not
previously observed in water or alcohol.23 The time-depend-
ent B3LYP calculations on RhI(bpy)2+ predict that the lowest-
energy transition is the HOMO-to-LUMO excitation at 777
nm (Table 4). We therefore assign the observed 750 nm
absorption (rather than the 505 nm transition as previously
assigned in water)23 to the lowest-energy MLCT transition.
In general, the predicted transitions and relative intensities
are in good agreement with the experimental UV-vis
spectrum (Table 4); however, the assignment of a shoulder
around 520 nm near the strongest absorption at 550 nm is
not clear. The three weak absorptions predicted around 440
nm are unlikely to account for the 520 nm shoulder.
Alternatively, solvent bonding to form a five-coordinate (or
six-coordinate) species could shift the 550 nm band to higher
energy. Supporting this suggestion, we observe that the
shoulder around 520 nm is more pronounced in methanol
than in acetone.
In both RhI(bpy)2+ and RhIII(H)2(bpy)2 , the HOMOs are
+
metal-based orbitals and the LUMOs are bpy-based orbitals.
+
The frontier orbitals of RhI(bpy)2 are shown in Figure 6.
Table 4 summarizes the observed and calculated (TDDFT)
transitions for RhI(bpy)2+ in methanol. The TDDFT calcula-
+
tions predict that the lowest-energy transition of RhI(bpy)2
is the HOMO-to-LUMO excitation at 777 nm with an
oscillator strength of 0.0016 while the strongest is the
HOMO-2-to-LUMO at 533 nm with an oscillator strength
of 0.1867. The HOMO, HOMO-1, and HOMO-2 are all
predominately metal centered, while the LUMO, LUMO+1,
and LUMO+2 are mainly bpy π* in character. Thus, we
may characterize all of these as MLCT transitions except
Figure 4 indicates thermodynamic profiles (i.e., enthalpy,
entropy, and partial molar volume change) for the oxidative
Inorganic Chemistry, Vol. 45, No. 4, 2006 1601

Fujita et al.
Figure 6. Frontier orbitals for RhI(bpy)2+: viewed parallel to the average plane made by Rh and four nitrogen atoms (top) and perpendicular to the average
plane (bottom) from gas-phase B3LYP calculations.
+
Table 4. Observed and Calculated Visible Transitions for RhI(bpy)2 in Methanol and the Gas Phase, Respectively
observed transitions
calculated transitions
λ
max (ꢀ)
orbital
assignment
transition
character
λmax
nm
oscillator
strength
nm (mM-1 cm-1
)
2
750sh (0.5)
656sh (2.5)
552 (13.1)
518sh (8.5)
HOMO to LUMO
HOMO-1 to LUMO
HOMO-2 to LUMO
dz to bpy π*
777
634
533
0.0016
0.0063
0.1867
d
yz to bpy π*
xz to bpy π*
d
2
HOMO to LUMO+2
HOMO to LUMO+6
HOMO to LUMO+5
HOMO-1 to LUMO+2
dz to bpy π*
447
441
423
397
0.0013
0.0013
0.0024
0.0062
2
dz to (dxy and bpy π*)
2
dz to bpy π*
362 (6.8)
dyz to bpy π*
+
addition of H2 to RhI(bpy)2 (eq 1) in methanol (red line)
and acetone (blue line). The differences in the values obtained
in methanol and acetone are small (Table 1). The heats of
formation and activation energies calculated with the B3LYP
and MP2 methods for formation of RhIII(H)2(bpy)2+ are also
given in Table 1. The MP2 calculated values for ∆H0 and
∆Hf‡ are in reasonable agreement with the experimental
values.
complexes are formed,30,31 significant volume effects are to
be expected for both the forward and back reactions in eq 1.
The partial molar volumes of H2 are 26.7, 38, and 35 cm3
mol-1 in water, acetone, and methanol, respectively.32-34
There are few data on the activation volumes for oxidative
addition of H2 to metal complexes. The activation volume
for oxidative addition of dihydrogen to trans-[Ir(CO)Cl-
(PPh3)2] has been reported to be -19 ( 1 cm3 mol-1 in DMF,
chlorobenzene, or toluene at 10 °C measured by a conven-
tional mixing method.10 As shown in Figure S4, we obtained
-20 ( 1 cm3 mol-1 in toluene at 35 °C for the oxidative
addition of either H2 or D2 to IrCl(CO)(PPh3)2 using the same
The negative values of the experimental reaction and
activation entropies are consistent with an associative reac-
tion. However, it is surprising that the activation volumes
in methanol and acetone are very similar to the overall
reaction volumes (within 1 cm3 mol-1, Table 1), indicating
that the activation volume for the reverse reaction, elimina-
tion of dihydrogen from the dihydrido complex, is practically
zero. In general, oxidative addition reactions are expected
to be accompanied by significant volume changes. Such
reactions involve not only significant bond formation in
reaching the transition state but also a change in the oxidation
state and coordination number of the metal complex. These
effects are expected to cause significant reaction volume
contraction (over -20 cm3 mol-1), such that these reactions
should exhibit a rather large pressure sensitivity. On the basis
of activation volumes reported in the literature for typical
oxidative addition and reductive elimination reactions10,11 and
reaction volumes reported for the interaction of Co(I)
complexes with CO2 and weak acids during which Co(III)
method used for RhI(bpy)2 . The observed volume of
+
activation for the binding of dihydrogen to IrCl(CO)(PPh3)2
is ≈30% more negative than those found for the binding to
[RhI(bpy)2]+ of ≈ -15 cm3 mol-1 in methanol or acetone.
Unfortunately, the overall reaction volume, ∆V0, for the
oxidative addition of H2 to IrCl(CO)(PPh3)2 could not be
determined, owing to the large equilibrium constant of that
reaction.
(30) Fujita, E.; van Eldik, R. Inorg. Chem. 1998, 37, 360-362.
(31) Fujita, E.; Wishart, J. F.; van Eldik, R. Inorg. Chem. 2002, 41, 1779-
1583.
(32) Hildebrand, J. H.; Scott, R. L. Solutions of Non-Electolytes; Reinhold
Publishing Corporation: New York, 1950.
(33) Pierotti, R. A. J. Phys. Chem. 1965, 69, 281-288.
(34) Moore, J. C.; Battino, R.; Rettich, T. R.; Handa, Y. P.; Wilhelm, E.
J. Chem. Eng. data 1982, 27, 22-24.
1602 Inorganic Chemistry, Vol. 45, No. 4, 2006

Binding of Dihydrogen to Bis(2,2′-bipyridine)rhodium(I)
Volumes of reaction and activation can be estimated using
the structures of the reactants, transition state, and products.
We have used both DFT and ab initio quantum calculations
The stability of the dihydrido complex is not significantly
dependent on the polarity of the solvent. In the case of the
Ir and Rh systems, the volume of activation was found to
be insensitive to solvent (DMF, chlorobenzene, and toluene
for the Ir system and acetone and methanol for the Rh
system). This suggests that the polarity of the transition state
is similar to that of the reactant.
The above discussion also allows us to understand the
enthalpy and entropy profiles. The TS complex has a partially
broken H-H bond and only a very weak partially formed
Rh-H bond. Thus, the transition state does not energetically
resemble either the reactants or products and is at higher
energy than either of them. However, in entropic terms, the
situation is much different. The H2 has entered into the inner
coordination sphere of the Rh complex and is shielded from
the solvent by the large, slightly distorted bipyridine ligands,
so the TS complex is entropically quite similar to the
products, indicating a late transition state. As a consequence,
the reaction and activation entropy for the forward reactions
are very similar, as observed.
+
+
to obtain the structures of RhI(bpy)2 , RhIII(H)2(bpy)2 , and
+
the TS species. The structures obtained for the Rh(bpy)2
are in good agreement with the observed crystal structure
(Table 2). When a H2 molecule approaches a tetrahedrally
+
distorted square-planar RhI(bpy)2 complex, the two bpy
ligands twist to form a five-coordinate geometry with the
incoming H2 (see Figure S6). The TS complex has C2
symmetry and can be characterized as a dihydrogen-like
complex. The dihydrido product exhibits a pseudo-octahedral
geometry with the hydride ligands being nearly trans to the
N-Rh bonds (Figure 5, bottom right).
A possible reason for the smaller activation volume
associated with oxidative addition of H2 in the Rh system
than that in the case of IrCl(CO)(PPh3)2 may be the influence
of the bulky bipyridine ligands that dominate the partial
molar volumes of the Rh complexes, while dihydrogen and
dihydride are comparatively small ligands. Thus, the transi-
tion state that includes the dihydrogen within the inner
coordination sphere of the Rh complex (i.e., within the arms
of the bpy ligands) would have a volume that is insensitive
to the actual Rh-H or H-H distances. As a consequence,
the volume of the TS and the product would be similar and
account for the near equality in the reaction and activation
volumes for the forward reaction and the practically zero
activation volume observed for the reverse reductive elimina-
tion process.
Acknowledgment. We thank Percefoni Doufou, Hideo
Konno, and Mohamed S. A. Hamza for obtaining preliminary
data. R.v.E. and M.S.A.H. gratefully acknowledge financial
support from the Deutsche Forschungsgemeinschaft and the
Alexander von Humboldt Foundation. X-ray data collection
was performed with help of Dr. Jonathan Hanson at Beam
Line X7B of the National Synchrotron Light Source at
Brookhaven National Laboratory. This work was performed
at BNL, funded under contract DE-AC02-98CH10886 with
the U.S. Department of Energy and supported by its Division
of Chemical Sciences, Office of Basic Energy Sciences.
We can calculate the displacement volumes assuming that
the molecules are tumbling in solution and that they occupy
a spherical cavity defined by their longest axis. Using the
longest H-to-H distances of RhI(bpy)2+ (11.57 Å), RhIII(H)2-
Note Added after ASAP Publication. This article was
released ASAP on January 5, 2006, with an incorrectly
placed bracket in the numerator of eq 3 and an incorrect
sign in the seventh line of the Electronic Structure Calcula-
tions section. The correct version was posted on January 11,
2006.
+
(bpy)2 (11.88 Å), and the transition-state complex (11.87
Å) and adding 2.4 Å for the van der Waals radii of two H
atoms,35 the displacement volumes are calculated as 1430,
1525, and 1521 Å3, respectively. The displacement volumes
of the transition-state dihydrogen complex and the dihydrido
product RhIII(H)2(bpy)2+ are indeed very similar, as suggested
above. Thus, the activation and reaction volumes should be
very similar, as is observed. We do not estimate the reaction
volume since the displacement volume for dihydrogen, for
which a single solvation shell would greatly affect the
effective volume, would not be a reliable estimate of its
contribution to ∆V0. Furthermore, the possible existence of
a solvent-bound five- (or six-)coordinate Rh reactant com-
plicates estimates of the reaction volume.
Supporting Information Available: Crystal data and structure
refinement, and other X-ray crystallographic data in CIF format;
conversion of standard states; DFT-optimized Cartesian coordinates
for RhI(bpy)2+, RhIII(H)2(bpy)2+, and the transition-state complex;
+
complete bond distances and angles for RhIII(H)2(bpy)2 and the
transition-state complex; plot of rate constants for formation of
+
RhIII(H)2(bpy)2 as a function of [H2]; plots for the determination
of activation parameters; an ORTEP drawing and a packing diagram
of RhI(bpy)2+; and two views of the transition-state complex. This
materialisavailablefreeofchargeviatheInternetathttp://pubs.acs.org.
(35) CRC Handbook of Chemistry and Physics, 70th ed.; CRC Press: Boca
Raton, FL, 1989.
IC0515498
Inorganic Chemistry, Vol. 45, No. 4, 2006 1603