Equilibrium Thermodynamic Studies in Water: Reactions of Dihydrogen with Rhodium(III) Porphyrins Relevant to Rh-Rh, Rh-H, and Rh-OH Bond Energetics

Article abstract of DOI:10.1021/ja039218m

Aqueous solutions of rhodium(III) tetra p-sulfonatophenyl porphyrin ((TSPP)Rh(III)) complexes react with dihydrogen to produce equilibrium distributions between six rhodium species including rhodium hydride, rhodium(I), and rhodium(II) dimer complexes. Equilibrium thermodynamic studies (298 K) for this system establish the quantitative relationships that define the distribution of species in aqueous solution as a function of the dihydrogen and hydrogen ion concentrations through direct measurement of five equilibrium constants along with dissociation energies of D₂O and dihydrogen in water. The hydride complex ([(TSPP)Rh-D(D₂O)]^-4) is a weak acid (K_a(298 K) = (8.0 ± 0.5) x 10^-8). Equilibrium constants and free energy changes for a series of reactions that could not be directly determined including homolysis reactions of the Rh ^II-Rh^II dimer with water (D₂O) and dihydrogen (D₂) are derived from the directly measured equilibria. The rhodium hydride (Rh-D)_aq and rhodium hydroxide (Rh-OD)_aq bond dissociation free energies for [(TSPP)Rh-D(D₂O)]^-4 and [(TSPP)Rh-OD(D₂O)]^-4 in water are nearly equal (Rh-D = 60 ± 3 kcal mol^-1, Rh-OD = 62 ± 3 kcal mol^-1). Free energy changes in aqueous media are reported for reactions that substitute hydroxide (OD^-) (-11.9 ± 0.1 kcal mol^-1), hydride (D^-) (-54.9 kcal mol^-1), and (TSPP)Rh^I: (-7.3 ± 0.1 kcal mol^-1) for a water in [(TSPP)Rh ^III(D₂O)₂]^-3 and for the rhodium hydride [(TSPP)Rh-D(D₂O)]^-4 to dissociate to produce a proton (9.7 ± 0.1 kcal mol^-1), a hydrogen atom (～60 ± 3 kcal mol^-1), and a hydride (D^-) (54.9 kcal mol^-1) in water.

Full text of DOI:10.1021/ja039218m

Published on Web 02/04/2004
Equilibrium Thermodynamic Studies in Water: Reactions of
Dihydrogen with Rhodium(III) Porphyrins Relevant to Rh-Rh,
Rh-H, and Rh-OH Bond Energetics
Xuefeng Fu and Bradford B. Wayland*
Contribution from the Department of Chemistry, UniVersity of PennsylVania,
Philadelphia, PennsylVania 19104-6323
Received October 24, 2003; E-mail: wayland@sas.upenn.edu
Abstract: Aqueous solutions of rhodium(III) tetra p-sulfonatophenyl porphyrin ((TSPP)Rh(III)) complexes
react with dihydrogen to produce equilibrium distributions between six rhodium species including rhodium
hydride, rhodium(I), and rhodium(II) dimer complexes. Equilibrium thermodynamic studies (298 K) for this
system establish the quantitative relationships that define the distribution of species in aqueous solution
as a function of the dihydrogen and hydrogen ion concentrations through direct measurement of five
equilibrium constants along with dissociation energies of D2O and dihydrogen in water. The hydride complex
([(TSPP)Rh-D(D2O)]-4) is a weak acid (Ka(298 K) ) (8.0 ( 0.5) × 10-8). Equilibrium constants and free
energy changes for a series of reactions that could not be directly determined including homolysis reactions
of the RhII-RhII dimer with water (D2O) and dihydrogen (D2) are derived from the directly measured equilibria.
The rhodium hydride (Rh-D)aq and rhodium hydroxide (Rh-OD)aq bond dissociation free energies for
[(TSPP)Rh-D(D2O)]-4 and [(TSPP)Rh-OD(D2O)]-4 in water are nearly equal (Rh-D ) 60 ( 3 kcal mol-1
,
Rh-OD ) 62 ( 3 kcal mol-1). Free energy changes in aqueous media are reported for reactions that
substitute hydroxide (OD-) (-11.9 ( 0.1 kcal mol-1), hydride (D-) (-54.9 kcal mol-1), and (TSPP)RhI:
(-7.3 ( 0.1 kcal mol-1) for a water in [(TSPP)RhIII(D2O)2]-3 and for the rhodium hydride [(TSPP)Rh-
D(D2O)]-4 to dissociate to produce a proton (9.7 ( 0.1 kcal mol-1), a hydrogen atom (∼60 ( 3 kcal mol-1),
and a hydride (D-) (54.9 kcal mol-1) in water.
Introduction
evaluating the scope of organometallic reactions and thermo-
dynamic parameters for rhodium porphyrin species in water.6
Rhodium porphyrins accomplish a remarkable array of
organometallic substrate reactions in both organic1-5 and
aqueous media.6 Reactions of substrates such as H2, CH4, CO,
and aldehydes with rhodium porphyrins that achieve observable
equilibria in benzene provide one of the more reliable and
extensive sets of organo-transition metal bond dissociation
enthalpies (BDE) in organic media.7,8 Current interest in
converting organometallic processes from organic to aqueous
media9-11 has stimulated us to direct our attention toward
Interpretation of thermodynamic measurements in water is
complicated by solvation energies,12,13 but aqueous media have
the advantageous property that the equilibrium distribution of
species can often be tuned by changing the hydrogen ion
concentration which provides a strategy for evaluating equilib-
rium constants that are either too large or too small for direct
measurement. This Article describes a set of simultaneous
equilibria that result from reactions of dihydrogen (H2/D2) with
rhodium(III) porphyrin aquo and hydroxo complexes in water
that form rhodium hydride, rhodium(I), and rhodium(II) com-
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Reibenspies, J. H.; Joo, F.; Darensbourg, D. J. Organometallics 2000, 19,
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9
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J. AM. CHEM. SOC. 2004, 126, 2623-2631
2623

A R T I C L E S
Fu and Wayland
Table 1. Characteristic 1H NMR Shifts (ppm) for (TSPP)Rh Species at 298 K in D2Oa
a The [(TSPP)Rh-D(D2O)]-4 (5) phenyl 1H NMR spectrum is an AB pattern (8.27 ppm, 8.20 ppm) at 360 K, but it is a single exchange broadened peak
centered at 8.25 ppm at 298 K in D2O.
plexes. Each of these types of rhodium porphyrin species (Rh-
(I), Rh(II), Rh(III), Rh-H, and Rh-OH) functions as a
precursor for a group of organometallic substrate reactions.6,14
The detailed equilibrium studies presented in this Article
establish a foundation for equilibrium thermodynamic studies
in aqueous media for substrate reactions associated with these
organometallic precursor species and also report on the direct
evaluation of the acid dissociation constant for the Rh-H along
with estimates of the rhodium-hydride and rhodium-hydroxide
bond dissociation free energies in water.
Results
Aqueous solutions of rhodium(III) tetra p-sulfonatophenyl
porphyrin ((TSPP)Rh(III)) complexes react with dihydrogen to
produce equilibrium distributions between six rhodium species
including rhodium hydride, rhodium(I), rhodium(II) dimer, and
three rhodium(III) aquo and hydroxo complexes. Each of these
Figure 1. Data points are the observed limiting fast exchange mole fraction
averaged pyrrole 1H NMR chemical shifts for compounds 2, 3, and 4 in
D2O as a function of -log10[D+]. The solid line is the nonlinear least-
squares best fit line giving K1(298 K) ) (1.40 ( 0.2) × 10-8, K2(298 K)
1
(TSPP)Rh species can be readily distinguished by H NMR
) (2.8 ( 0.3) × 10-12, and δ3(pyr) ) 9.04 ppm; 2 is [(TSPP)RhIII(D2O)2]-3
,
δ2(pyr) ) 9.15 ppm; 4 is [(TSPP)RhIII(OD)2]-5, δ4(pyr) ) 8.94 ppm; 3 is
spectroscopy in D2O (Table 1). The porphyrin pyrrole and
phenyl 1H NMR shifts that are used in identifying the (TSPP)-
Rh species in D2O are listed in Table 1. In aqueous solution,
water molecules are assigned to axial rhodium coordination sites
so as to produce an electronically saturated (18-electron) metal
[(TSPP)RhIII(D2O)(OD)]-4
.
resonances for the equilibrium distribution of 2, 3, and 4 (Figure
1, Table 1). The mole fraction averaged pyrrole proton resonance
for equilibrium distributions of 2, 3, and 4 as a function of the
concentration of D+ was used in determining the acid dissocia-
tion constants (298 K) for 2 (K1 ) (1.4 ( 0.2) × 10-8) and 3
(K2 ) (2.8 ( 0.3) × 10-12)6 by nonlinear least-squares curve
fitting to the equation: δ2,3,4(obs)(pyr) ) (K1K2δ4(pyr) + K1-
[D+]δ3(pyr) + [D+]2δ2(pyr))/(K1K2 + K1[D+] + [D+]2). The
1
center. H NMR shift and intensity measurements were used
effectively in quantifying the distribution of species in solution.
Aquo and Hydroxo Complexes of (TSPP)Rh(III). A
convenient entry point into the chemistry of water-soluble
rhodium porphyrin species is through the hydrated rhodium-
(III) derivative of rhodium tetra p-sulfonatophenyl porphyrin
(Na3[(TSPP)Rh(D2O)2]‚18D2O (1)). Dissolution of 1 in D2O
results in solutions of the bisaquo complex [(TSPP)RhIII(D2O)2]-3
(2) in an equilibrium distribution with the mono and bishydroxo
complexes, [(TSPP)RhIII(D2O)(OD)]-4 (3), [(TSPP)RhIII(OD)2]-5
(4) (eqs 1, 2).
lower acidity for the D2O complex 2 (K1(D2O) ) 1.4 × 10-8
)
as compared to that of the previously studied H2O derivative
(K1(H2O) ) 9.67 × 10-8 15
)
parallels the smaller ion product
constant for D2O (Kw(D2O) ) 1.35 × 10-15) and ion dissociation
constant (K3(D2O) ) 2.44 × 10-17) as compared to those of
H2O (Kw(H2O) ) 1.0 × 10-14 and K3(H2O) ) 1.8 × 10-16) at
298 K (Table 2, eq 3).
[(TSPP)RhIII(D2O)2]-3
h
Reactions of H2/D2 with Solutions of 1 in D2O. The bis
aquo complex [(TSPP)RhIII(D2O)2]-3 (2) reacts slowly with H2/
[(TSPP)RhIII(D2O)(OD)]-4 + D+ (1)
D2 (P ≈ 0.5-0.8 atm) in acidic D2O media ([D+] > 10-5) to
[(TSPP)RhIII(D2O)(OD)]-4
h
H2
form complex 5 which is assigned as the hydride complex
[(TSPP)Rh-D(D2O)]-4 (eq 4).
[(TSPP)RhIII(OD)2]-5 + D+ (2)
[(TSPP)RhIII(D2O)2]-3 + D2 h
Rapid interchange of hydrogens from coordinated water and
hydroxide with the bulk solvent water (T ) 275-300 K) results
1
[(TSPP)Rh-D(D2O)]-4 + D+ + D2O (4)
in a single set of mole fraction averaged porphyrin H NMR
(14) Subsequent papers in this series will focus on organometallic reactions of
(TSPP)Rh-H and (TSPP)Rh-OH with CO, olefins, aldehydes, and ketones.
(15) Ashley K. R.; Shyu, S. B.; Leipoldt, J. G. Inorg. Chem. 1980, 19, 1613.
9
2624 J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004

Equilibrium Thermodynamic Studies in Water
A R T I C L E S
Table 2. The Measured Equilibrium Constants of (TSPP)Rh Reactions in D2O (T ) 298 K)a
equilibrium constants
∆G°(298 K)
kcal mol-1
(TSPP)Rh reactions
K (298 K)
n
(1) [RhIII(D2O)2]-3 h [RhIII(OD)(D2O)]-4 + D+
(2) [RhIII(OD)(D2O)]-4 h [RhIII(OD)2]-5 + D+
(3) D2O h OD- + D+
K1 ) (1.4 ( 0.2) × 10-8
K2 ) (2.8 ( 0.3) × 10-12
K3 ) 2.44 × 10-17
K5 ) (8.0 ( 0.5) × 10-8
K6 ) (2.3 ( 0.5) × 105
K7 ) 5.2 × 1037
+10.7 ( 0.1
+15.8 ( 0.1
+22.6b
-1.7 ( 0.1
+9.7 ( 0.1
-7.3 ( 0.1
-53.2c
(4) [RhIII(D2O)2]-3 + D2 h [Rh-D(D2O)]-4 + D+ + D2O
(5) [Rh-D(D2O)]-4 h [RhI(D2O)]-5 + D+
(6) [RhIII(D2O)2]-3 + [RhI(D2O)]-5 h [RhII(D2O)]2-8 + D2O
(7) D+ + D- h D2
K4 ) 18.2 ( 0.5
a The reported K values correspond to equilibrium constant expressions that contain all of the constituents given in the chemical equation including water.
b The ion product of D2O (14.869) and the D2O density (1.1044) were used to determine that K3 ) 2.44 × 10-17 at 298 K. c E°(2H+ + 2e h H2) ) 0.00
V and E°(2H- h H2 + 2e) ) +2.23 V were used to evaluate ∆G°(H+ + H- h H2) ) -51.4 kcal mol-1 and ∆G°(D+ + D- h D2) ) -53.2 kcal mol-1
CRC Handbook of Chemistry and Physics, 71st ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1990-1991; pp 8-38, 6-11, and 8-17.
.
(275-350 K) is consistent with the porphyrin macrocycle being
an effective plane of symmetry as expected for a rhodium(I)
complex (Figure 2B). Reactions of (TSPP)Rh(III) complexes
(2, 3, 4) in D2O with an excess of NaBD4 produce a species in
1
solution with a H NMR spectrum identical to that of 6 and
thus is assigned as the rhodium(I) complex, [(TSPP)RhI(D2O)]-5.
Solutions of 6 in D2O react rapidly with CH3I exclusively to
form a rhodium methyl derivative [(TSPP)Rh-CH3(D2O)]-4
which is a signature reaction of the nucleophilic rhodium(I)
center in 6. The Rh-CH3 complex is recognized easily in D2O
1
by the characteristic high field HNMR methyl resonance (δ6-
(CH3) ) -6.59 ppm). The Rh-CH3 unit results in an inequiva-
lence of the porphyrin faces which is manifested by an ABCD
1H NMR porphyrin phenyl resonance pattern like that observed
for the hydride 5 in DMF. Spectroscopic and reactivity
studies clearly identify 6 as the rhodium(I) derivative,
[(TSPP)RhI(D2O)]-5. The reactivity of the Rh(I) complex (6)
is not strongly influenced by the solvent donor properties
because the 16-electron fragment species [(TSPP)RhI]-5 resists
addition of more than one donor molecule.
Figure 2. 1H NMR (360 MHz) spectra in D2O. (A) [(TSPP)RhI(D2O)]-5
(6) in D2O, [D+] < 10-10 M, T ) 298 K; (B) [(TSPP)Rh-D(D2O)]-4 (5),
[D+] < 10-4 M, T ) 360 K. a, pyrrole hydogens; b, phenyl hydrogens.
Reaction 4 achieves a conveniently measurable equilibrium
distribution of species. The equilibrium constant for reaction 4
Acid Dissociation Constant of [(TSPP)Rh-D(D2O)]-4
.
1
(K4(298 K) ) 18.2 ( 0.5) was evaluated from the H NMR
Protonation of [(TSPP)RhI(D2O)]-5 (6) produces the rhodium
hydride complex 5 by the reverse of eq 5.
studies in combination with D+ concentration measurements and
the solubility of D2 in water.16 Formation of the hydride complex
5 from reaction of H2 in H2O with 2 followed by removal of
water and dissolution in DMF-d6 results in the observation of
a characteristic hydride 1H NMR resonance (δRh-H ) -38 ppm;
JRh-H ) 31 Hz) and an ABCD porphyrin phenyl resonance
pattern associated with a static Rh-H unit that produces
inequivalence of the porphyrin faces. This behavior contrasts
with that of solutions of 5 in water and methanol where the
hydride hydrogen rapidly exchanges as a proton with solvent
hydroxylic hydrogens.
[(TSPP)Rh-D(D2O)]-4 h [(TSPP)RhI(D2O)]-5 + D+ (5)
Aqueous solutions that contain both 5 and 6 manifest a single
1
mole fraction averaged H NMR spectrum that is a result of
rapid proton interchange. A plot of δ5,6(obs)(pyr) for the equi-
librium distribution of 5 and 6 in D2O at a series of hydrogen
ion (D+) concentrations is illustrated in Figure 3. The mole
fraction averaged pyrrole proton resonances (δ5,6(obs)(pyr)), as
a function of the molar concentration of D+, were used to
determine the acid dissociation constant for the hydride 5 at
298 K (K5 ) (8.0 ( 0.5) × 10-8) by nonlinear least-squares
curve fitting to the relationship: δ5,6(obs)(pyr) ) (K5δ6(pyr) +
[D+]δ5(pyr))/(K5 + [D+]).
Solutions of 1 in basic media ([D+] ≈ 10-8-10-11 M), where
the (TSPP)Rh(III) mono and bis hydroxo complexes 3 and 4
predominate, give a much faster reaction with H2/D2 than was
observed for 2 and result in the formation of a rhodium(I)
complex, [(TSPP)RhI(D2O)]-5 (6). The relatively high field 1H
NMR positions for the porphyrin pyrrole (δ6(pyr) ) 8.32 ppm)
and phenyl hydrogens (δï,o′ ) 8.20 ppm, δm,m′ ) 8.11 ppm)
observed for 6 are characteristic of the electron-rich metal site
in rhodium(I) tetraphenyl porphyrin derivatives (Figure 2A,
Table 1).17 The AA′BB′ phenyl proton pattern which is observed
for 5 throughout the convenient temperature range for water
Formation of a RhII-RhII Bonded Species in D2O. Mixing
D2O solutions of [(TSPP)RhIII(D2O)2]-3 (2) with solutions
containing the [(TSPP)RhI(D2O)]-5 complex (6) results in an
equilibrium distribution with a RhII-RhII bonded dimer,
[(TSPP)RhII(D2O)]2 (7) (eq 6, Figure 4).
-8
[(TSPP)RhIII(D2O)2]-3 + [(TSPP)RhI(D2O)]-5
h
[(TSPP)RhII(D2O)]2-8 + D2O (6)
(16) Fog, P. G. T.; Gerrard, W. Solubility of Gases In Liquids: A Critical
EValuation of Gas/Liquid Systems in Theory and Practice; Wiley: Chich-
ester, NY, 1991.
(17) Wayland, B. B.; Van Voorhees, S. L.; Wilker, C. Inorg. Chem. 1986, 25,
4039.
The equilibrium constant at 298 K for the formation of
[(TSPP)RhII(D2O)]2-8 from the bisaquo complex 2 and rhodium-
9
J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004 2625

A R T I C L E S
Fu and Wayland
CH3(D2O)]-4 gives the Rh(I) complex 6 exclusively, and in
acidic solution ([D+] > 10-4), only the bisaquo Rh(III) species
2 is observed. The initial photo process probably results in Rh-
CH3 bond homolysis to produce a (TSPP)RhII species that di-
merizes to 7. The RhII-RhII bonded complex 7 disproportionates
by the reverse of reaction 6 into an equilibrium distribution of
7 with rhodium(III) and rhodium(I) species in D2O.
The qualitative relationships between the (TSPP)Rh species
(Rh(III), Rh(II), Rh(I), Rh-D) in D2O are summarized by the
pentagon shown in Scheme 1. Experimentally measured quan-
titative relationships between the solution species 2-7 depicted
by eqs 1-7 are summarized in Table 2.
Discussion
Reactions of (TSPP)Rh(III) aquo and hydroxo species with
dihydrogen in water produce a series of equilibria where the
equilibrium constants have been directly evaluated (Table 2).
In aqueous solution, the equilibrium distributions for all of the
(TSPP)Rh reaction precursor species, RhIII, RhI, Rh-D, and
RhII, are either directly or indirectly dependent on the hydrogen
ion concentration ([D+]). Variation of the hydrogen ion con-
centration provides an effective method for controlling the
equilibrium distribution of (TSPP)Rh species in water that is
not available in organic solvent media. The hydrogen ion
concentration determines the distribution of the bisaquo complex
(2) with the mono and bis hydroxo species (3, 4), which in turn
influences the distribution of product species at equilibrium.
Reactions of (TSPP)RhIII species (2, 3, 4) with H2/D2 in D2O
are prime examples where both the fraction of conversion for
Rh(III) species (eqs 4, 8, 9) and the distribution of Rh-D and
RhI products (eq 5) are dependent on the concentration of D+.
Figure 3. Data points are the fast exchange mole fraction averaged 1H
NMR chemical shifts for [(TSPP)Rh-D(D2O)]-4 (5) and [(TSPP)RhI(D2O)]-5
(6) in D2O as a function of -log10[D+]. The solid line is the nonlinear
least-squares best fit line giving K5(298 K) ) (8.0 ( 0.5) × 10-8, δ5(pyr)
) 8.78 ppm, δ6(pyr) ) 8.32 ppm.
(I) complex 6 depicted by reaction 6 (K6 ) [7][D2O]/([2][6])
) (2.3 ( 0.5) × 105) was determined from the 1H NMR
chemical shifts and intensities in combination with equilibrium
constants determined for the equilibria involving 2 with 3 (eq
1) and 5 with 6 (eq 5). The RhII-RhII bonded dimer 7 is
observed as a prominent species only when the solution is close
to neutrality ([D+] ≈ 10-8-10-7), and 7 is not observed in the
1H NMR spectra in acidic ([D+] > 10-5) or basic ([D+] < 10-10
)
solutions.
The RhII-RhII bonded dimer (7) is readily identified in
1
solution by comparison of the distinctive porphyrin H NMR
spectrum of 7 (Figure 4) with previously reported NMR spectra
for [(por)RhII]2 complexes17 and other metal-metal bonded face-
to-face dimers.18 1H NMR shifts of the four sets of phenyl
hydrogens in monoporphyrin (TSPP)Rh complexes occur within
a small range (δ ) 8.3 ( 0.2 ppm), but in the diporphyrin
complex 7 they occur over a range of 2.5 ppm (δ ) 9.5-7.0
ppm) (Figure 4). The magnetic field from the combined ring
currents of adjacent porphyrin rings produces an exceptionally
large downfield shift for the ortho phenyl hydrogens (δ7(ortho)
) 9.5 ppm) that are situated between the porphyrin rings and
an unusually high field position for the exterior ortho phenyl
hydrogens (δ7(ortho) ) 7.0 ppm). The exceptionally low field
peak positions for the ortho phenyl hydrogens that occur
between the porphyrin rings are uniquely characteristic of
metal-metal bonded dimers of tetraphenyl porphyrin deriva-
tives. The ortho phenyl hydrogens that are directed between
the two porphyrin planes experience the combined deshielding
ring current effects associated with the periphery of the aromatic
rings, and the resulting unique low field position for these
hydrogens in the 1H NMR spectrum is an unmistakable signature
for a face-to-face diporphyrin structure (Figure 4). The relatively
high field position for the pyrrole hydrogens of 7 (δ7(pyr) )
[(TSPP)RhIII(OD)(D2O)]-4 + D2 h
[(TSPP)Rh-D(D2O)]-4 + D2O (8)
[(TSPP)RhIII(OD)2]-5 + D2 h
[(TSPP)RhI(D2O)]-5 + D2O (9)
The extent of conversion of the Rh(III) species depends on the
distribution of aquo and hydroxo species that is described by
eqs 1 and 2, while the distribution of the hydride (5) and Rh(I)
complex (6) is determined by the acid dissociation constant of
(8.0 ( 0.5) × 10-8 for [(TSPP)Rh-D(D2O)]-4 (eq 5). In basic
solution ([D+] < 10-8), high conversion to [(TSPP)RhI(D2O)]-5
(6) occurs, while in acidic media, the hydride [(TSPP)Rh-
D(D2O)]-4 is the dominant species, but the extent of conversion
for Rh(III) is lower (eq 4).
Equilibrium constants for a series of reactions including
reactions 8 and 9 that are derived from measured K values for
reactions 1-7 are given in Table 3 (K8 ) K1-1K4 ) 1.3 × 109;
∆G8° ) -12.4 kcal mol-1; K9 ) K1-1K2-1K4K5 ) 3.6 × 1013;
∆G9° ) -18.5 kcal mol-1). The large negative values for ∆G8°
and ∆G9° illustrate that the reactions of H2/D2 with (TSPP)-
RhIII species are much more thermodynamically favorable for
the hydroxo species 3 and 4 as compared to the bisaquo complex
2. The acidic condition needed to give high conversion of the
RhI complex 6 to the hydride complex 5 (eq 5) is also associated
with the presence of [(TSPP)RhIII(D2O)2]-3 by the reverse of
reaction 4. Stable equilibrium concentrations of the hydride (5)
require the presence of H2/D2 to achieve equilibrium with the
1
8.46 ppm) is another characteristic feature of the H NMR
spectrum of 7 that is shared with [(TPP)RhII]2.17
The RhII-RhII bonded dimer (7) is also observed along with
Rh(III) and Rh(I) species in the photolysis (λ > 350 nm) of
[(TSPP)Rh-CH3(D2O)]-4 in neutral D2O solution. When the
[D+] is less than 10-8 ([D+] < 10-8), photolysis of [(TSPP)Rh-
(18) Collman, J. P.; Barnes, C. E.; Collins, T. J.; Brothers, P. J. J. Am. Chem.
Soc. 1981, 103, 7030.
9
2626 J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004

Equilibrium Thermodynamic Studies in Water
A R T I C L E S
-8
Figure 4. 1H NMR (360 MHz) spectrum of [(TSPP)RhII(D2O)]2 (7) in equilibrium with [(TSPP)RhI]-5 (6) and (TSPP)Rh(III) species 2 and 3 in D2O
([D+] ) 10-8 M), where a and b designated the pyrrole and phenyl hydrogens, respectively, in species 3, 6, and 7.
Scheme 1. The (TSPP)Rh Species in Simultaneous Multiple
Equilibria in Water
Thermodynamics for Displacement of a Water Molecule
from [(TSPP)RhIII(D2O)2]-3 by [(TSPP)RhI(D2O)]-5, Hy-
droxide (OD-), and Hydride (D-). Equilibrium constants and
standard free energy changes for displacement of water (D2O)
from the rhodium(III) center in 2 ([(TSPP)RhIII(D2O)2]-3) by
the rhodium(I) complex (6) (eq 6), hydroxide (OD-) (eq 12),
and hydride (D-) (eq 13) are either directly measured (eq 6,
Table 2) or derived from measured thermodynamic values for
reactions 1-7 (eqs 12, 13; Table 3).
[(TSPP)RhIII(D2O)2]-3 + OD- h
[(TSPP)Rh-OD(D2O)]-4 + D2O (12)
[(TSPP)RhIII(D2O)2]-3 + D h
Rh(III) complexes (2, 3, 4) (eq 4) and maintain the simultaneous
multiple equilibria with the Rh-D and Rh(I) species (5, 6).
[(TSPP)Rh-D(D2O)]-4 + D2O (13)
When Rh(III) and Rh(I) species are simultaneously present
The rhodium(I) complex ([(TSPP)RhI(D2O)]-5) functions as
a metal-centered nucleophile through use of the pair of electrons
in dz2 (RhI:). Substitution of [(TSPP)RhI(D2O)]-5 for D2O in 2
produces an equilibrium with the RhII-RhII bonded dimer
([(TSPP)RhII(D2O)]2-8) 7 that has been directly evaluated (eq
6, K6(298 K) ) (2.3 ( 0.5) × 105, ∆G6°(298 K) ) -7.3 kcal
mol-1). Substitution of hydroxide (OD-) and hydride (D-) for
water is derived from reactions 1 and 3 (∆G12° ) ∆G1° - ∆G3°
) -11.9 kcal mol-1) and reactions 4 and 7 (∆G13° ) ∆G4° +
∆G7° ) -54.9 kcal mol-1), respectively. The free energy
changes for reactions 6, 12, and 13 (∆G6°, ∆G12°, ∆G13°)
correspond to differences in the heterolytic BDFE value for
RhIII-X (X ) OD-, D-, RhI) in complexes 3, 5, 7, and the
RhIII(D2O) BDFE in 2. Each of these water displacement
reactions is highly favorable, but hydride stands out as an
exceptionally strong donor (∆G13° ) -54.9 kcal mol-1).
The Bond Dissociation Free Energy (BDFE) Difference
between Rh-OD and Rh-D. The difference in Rh-OD and
Rh-D bond dissociation free energies can be obtained by using
reaction 8 ([(TSPP)RhIII-OD(D2O)]-4 + D2 h [(TSPP)Rh-
D(D2O)]-4 + D2O). Reaction 8 is an example process that
effectively occurs to completion at the attainable range of
experimental conditions and thus could not be directly deter-
mined. Combining reaction 4 with the reverse of reaction 1
results in reaction 8, and the derived equilibrium constant K8 is
given by K4/K1 (K8 ) K4/K1 ) 1.3 × 109; ∆G8° ) -12.4 kcal
mol-1). The difference in the (Rh-OD)aq and (Rh-D)aq bond
dissociation free energies (BDFE) can be derived by expressing
∆G8° in terms of a BDFE for each bond formed or broken in
in aqueous solution, then a RhII-RhII bonded dimer(II) also
occurs in accord with reaction 6 (K6(298 K) ) (2.3 ( 0.5) ×
105). Compound 7 can be viewed as resulting from the
nucleophilic Rh(I) center sharing the pair of dz2 electrons with
the empty dz2 on the Rh(III) species (RhI: f RhIII). The RhII-
RhII bonded dimer [(TSPP)RhII(D2O)]2-8 (7) achieves 1H NMR
observable concentrations at near neutral conditions where the
rhodium(III) bisaquo complex (2) and the rhodium(I) complex
-8
(6) occur together. Although production of [(TSPP)RhII(D2O)]2
by reaction 6 is not directly dependent on the [D+], the fraction
of (TSPP)Rh species in solution that are in equilibrium with 7
are highly sensitive to the [D+]. The quantity of RhII-RhII
bonded dimer (7) that occurs at equilibrium becomes small at
both high and low [D+] because the conversion of the rhodium-
(I) complex (6) to the hydride (5) occurs at high [D+] and
conversion of the Rh(III) bisaquo complex (2) to the mono and
bis hydroxo complexes (3, 4) occurs at low [D+] (eqs 10, 11).
[(TSPP)RhII(D2O)]2-8 + D+ + D2O h
[(TSPP)Rh-D(D2O)]-4 + [(TSPP)RhIII(D2O)2]-3 (10)
[(TSPP)RhII(D2O)]2-8 + OD- h
[(TSPP)RhI(D2O)]-5 + [(TSPP)Rh-OD(D2O)]-4 (11)
Equilibrium constants (298 K) for reaction 10 derived from
-1
measured K values for reactions 1, 3, 5, and 6 (K10 ) K5-1K6
) 54) and 11 (K11 ) K6-1K1K3 ) 2.4 × 103) show that
-1
reactions of 7 with both D+ and OD- in D2O are thermody-
namically favorable.
reaction 8 (∆G8° ) -12.4 kcal mol-1 ) (Rh-OD)aq
+
9
J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004 2627

A R T I C L E S
Fu and Wayland
Table 3. Equilibrium Constants (298 K) for (TSPP)Rh Reactions Derived from Reactions in Table 2a
equilibrium constants
∆G°(298 K)
kcal mol-1
derived (TSPP)Rh reactions
K (298 K)
n
(8) [RhIII(OD)(D2O)]-4 + D2 h [Rh-D(D2O)]-4 + D2O
(9) [RhIII(OD)2]-5 + D2 h [RhI(D2O)]-5 + D2O
K8 ) K1-1K4 ) 1.3 × 109
-12.4 ( 0.1
-18.5
K9 ) K1-1K2-1K4K5 ) 3.6 × 1013
(10) [RhII(D2O)]2-8 + D+ + D2O h [Rh-D(D2O)]-4 + [RhIII(D2O)2]-3
(11) [RhII(D2O)]2-8 + OD- h [RhI(D2O)]-5 + [RhIII(OD)(D2O)]-4
(12) [RhIII(D2O)2]-3 + OD- h [Rh-OD(D2O)]-4 + D2O
(13) [RhIII(D2O)2]-3 + D- h [Rh-D(D2O)]-4 + D2O
(14) [RhII(D2O)]2-8 + D2 h 2[Rh-D(D2O)]-4
K10 ) K5-1K6-1 ) 54
-2.4 ( 0.1
-4.6 ( 0.1
-11.9 ( 0.1
-54.9
K11 ) K6-1K1K3-1 ) 2.4 × 103
K12 ) K1K3-1 ) 5.7 × 108
K13 ) K4K7 ) 2.0 × 1041
K14 ) K4K5-1K6-1 ) 9.8 × 102
-4.1 ( 0.1
+8.4 ( 0.1
(15) [RhIII(D2O)]2-8 + D2O h [Rh-D(D2O)]-4 + [Rh-OD(D2O)]-4
K15 ) K1K5-1K6-1 ) 7.5 × 10-7
a The reported K values correspond to equilibrium constant expressions that contain all of the constituents given in the chemical equation including water.
K5K6 ) 9.8 × 102, ∆G14° ) -4.1 kcal mol-1; K15 ) K1/K5K6
Table 4. Summary of ∆H° and ∆G°(298 K) for Bond Homolysis of
H-H, D-D, H-OH, and D-ODa
) 7.5 × 10-7; ∆G15° ) +8.4 kcal mol-1).
BDFE
kcal mol-1
BDE
kcal mol-1
•
•
[(TSPP)RhII(D2O)]2-8 + D2 h 2[(TSPP)Rh-D(D2O)]-4
(14)
X−Y f X + Y
H-Hg
97.1
101.8
98.7
103.4
112.0
116.1
113.5
117.6
104.2
103.2
105.9
104.5
118.8
123.5
120.3
124.8
H-Haq
D-Dg
[(TSPP)RhII(D2O)]2-8 + D2O h [(TSPP)Rh-D(D2O)]-4
+
D-Daq
H-OHg
H-OHaq
D-ODg
D-ODaq
[(TSPP)RhIII-OD(D2O)]-4 (15)
Expressing ∆G14° as a series of BDFE terms (∆G14° ) -4.1
kcal mol-1 ) (Rh-Rh)aq + (D-D)aq - 2(Rh-D)aq) shows that
evaluation of the absolute rhodium-hydride ((Rh-D)aq) BDFE
and rhodium hydroxide ((Rh-OD)aq) in water requires deter-
mining the (Rh-Rh)aq BDFE ((Rh-D)aq BDFE ) 53.8 kcal
a See the Experimental Section for the analysis of ∆H° and ∆G°(298
K) for bond homolysis of H-H, D-D, H-OH, and D-OD in water.
(D-D)aq - (Rh-D)aq - (D-OD)aq; ((Rh-OD)aq - (Rh-D)aq)
) -12.4 - (D-D)aq + (D-OD)aq ) -12.4 - 103.4 + 117.6
) 1.8 kcal mol-1). The difference of ∼1.8 kcal mol-1 between
the (Rh-OD)aq and (Rh-D)aq BDFE should be highly reliable
because it is based on equilibrium measurements that give ∆G°
values that are accurate within 0.1 kcal mol-1 (Tables 2, 3) and
well-established thermodynamic values for D2 and D2O in the
gas phase and in aqueous solution (Table 4).
Equilibrium studies relevant to transition metal-hydride
homolytic dissociation are quite rare. The studies most closely
analogous to those reported here are displacement equilibria in
THF for Cp*(PMe3)2Ru-OH with H2 to form Cp*(PMe3)2-
Ru-H and H2O which were used to generate a scale of relative
homolytic bond dissociation energies including both Ru-OH
and Ru-H.19 The difference of the Ru-OH and Ru-H BDFE
mol-1
+
1/2(Rh-Rh)aq BDFE). Reaction 15 describes the
homolysis of water by the RhII-RhII species which is thermo-
dynamically unfavorable (∆G15° ) +8.4 kcal mol-1) because
of the RhII-RhII BDFE.
RhII-RhII Heterolysis and Estimated Homolysis Energet-
ics. Heterolytic bond cleavage of the RhII-RhII bonded dimer
[(TSPP)RhII(D2O)]2-8 (7) to form [(TSPP)RhIII(D2O)2]-3 (2) and
[(TSPP)RhI(D2O)]-5 (6) was directly measured by the
reverse of reaction 6 ([(TSPP)RhII(D2O)]2
+ D2O h
-8
[(TSPP)RhIII(D2O)2]-3 + [(TSPP)RhI(D2O)]-5; K6-1 ) (2.4 (
0.3) × 10-4; ∆G6°-1(298 K) ) +7.3 ( 0.1 kcal mol-1). Efforts
to observe homolytic dissociation of the RhII-RhII dimer into
monomeric Rh(II) species were precluded because the lower
energy heterolytic dissociation into ions is virtually complete
before achieving a temperature where the 1H NMR line
broadening as chemical shifts from the higher activation energy
bond homolysis process would be observed. The inability to
measure a RhII-RhII bond homolysis free energy and enthalpy
for 7 prohibits an entirely experimental evaluation of the Rh-D
BDFE in 5 and the Rh-OD BDFE in 3.
was found to be ∼9 kcal mol-1 19
,
which is much larger than
the observed difference for the (TSPP)Rh hydroxo and hydride
complexes in water ((Rh-OD) - (Rh-D) ≈ 1.8 kcal mol-1
;
(Rh-OH) - (Rh-H) ≈ 2.8 kcal mol-1). The smaller difference
in M-OH and M-H BDFE in water may reflect differences
in the solvation energies of H• and •OH in water that result from
water being a more highly structured medium than THF. The
1H NMR line broadening for the rhodium(II) dimers of octa-
ethylporphyrin and tetraphenyl porphyrin in benzene was pre-
viously used in deriving RhII-RhII bond homolysis activation
enthalpies and estimation of the homolysis enthalpy in the range
•
difference between the free energy for hydration of OH and
H• is ∼7 kcal mol-1 (∆G°hyd(H•)(298 K) ) +4.5 kcal mol-1
;
∆G°hyd(•OH)(298 K) ) -2.4 kcal mol-1),25a,b which could be
responsible for most of the difference in the ((Rh-OH) -
(Rh-H)) BDFE observed in water as compared to that in THF.
Substrate reactions of [(TSPP)RhII]2-8 with hydrogen (eq 14)
and water (eq 15) that describe Rh-D and Rh-OD homolysis
processes are derived from reactions 1 and 4-6 (K14 ) K4/
of 16-18 kcal mol-1 20
. Aquation of these weak acceptor species
should not differ greatly, and thus the RhII-RhII bond homolysis
energy is expected to be comparable to those in benzene (∆H° ≈
(22) (a) Ellis, W. W.; Miedaner, A.; Curtis, C. J.; Gibson, D. H.; DuBois, D. L.
J. Am. Chem. Soc. 2002, 124, 1926. (b) Curtis, C. J.; Miedaner, A.; Ellis,
W. W.; DuBois, D. L. J. Am. Chem. Soc. 2002, 124, 1918.
(23) Values obtained from: J. Phys. Chem. Ref. Data 1982, 11, supplement 2.
Standard state used: 298.15 K, 0.1 MPa.
(24) Blanksby, S. J.; Ellison, G. B. Acc. Chem. Res. 2003, 36, 255.
(25) (a) Han, P.; Bartels, D. M. J. Phys. Chem. 1990, 94, 7294. (b) Schwarz,
H.; Dodson, R. W. J. Phys. Chem. 1984, 88, 3643. (c) Hamad, S.; Lago,
S.; Mejias, J. A. J. Phys. Chem. A 2002, 106, 9104.
(19) Bryndza, H. E.; Fong, L. K.; Paciello, R. A.; Tam, W.; Bercaw, J. E. J.
Am. Chem. Soc. 1987, 109, 1444.
(20) Wayland, B. B.; Coffin, V. L.; Farnos, M. D. Inorg. Chem. 1988, 27, 2745.
(21) Kristjansdottir, S. S.; Norton, J. R. In Transition Metal Hydrides; Dedieu,
A., Ed.; VCH: New York, 1992; Chapter 9, pp 316-323.
9
2628 J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004

Equilibrium Thermodynamic Studies in Water
A R T I C L E S
18 kcal mol-1; ∆G° ≈ 10-14 kcal mol-1). The preliminary
estimate of 60 ( 3 kcal mol-1 for the (Rh-D)aq BDFE is made
from an estimation of 12 ( 3 kcal mol-1 for the RhII-RhII
BDFE in water.
are performed on an Orion model 410 plus pH meter and Orion 9802
electrode precalibrated by Thermo Orion buffer solutions of pH ) 4.01,
7.00, and 10.01.
Na3[(TSPP)RhIII(D2O)2]. Na3[(TSPP)RhIII(D2O)2] was synthesized
by literature methods of Ashley.15 1H NMR (D2O, 360 MHz) δ(ppm):
9.15 (s, 8H, pyrrole), 8.44 (d, 8H, o-phenyl, J1H-1H ) 8 Hz), 8.25 (d,
8H, m-phenyl, J1H-1H ) 8 Hz).
Concentration of Complexes and Ionic Strength of Aqueous
Solutions. Thermodynamic studies of (TSPP)Rh complexes in water
were carried out at concentrations less than 2 × 10-3 M to minimize
molecular and ionic association. Most equilibrium constant measure-
ments were performed at a low ionic strength (µ ≈ 10-3) where the
ion activity coefficients approach unity. Variation of the ionic strength
in the low range where the Debye-Hu¨ckel equation pertains (5 ×
10-4-2 × 10-2) did not perturb the spectroscopic parameters for the
(TSPP)Rh species in D2O or alter the measured acid dissociation
constants beyond the reported error limits. High ionic strength (µ >
0.1) obtained by addition of NaClO4 produces significant changes in
the 1H NMR spectra for the (TSPP)Rh solution species which may be
associated with both ion pairing and ionic competing with water for
coordination of the rhodium center.
Proton, Hydrogen Atom, and Hydride Donor Energetics
for (TSPP)Rh-D in Water. The acid dissociation constant for
the hydride [(TSPP)Rh-D(D2O)]-4 was directly evaluated as
(8.0 ( 0.5) × 10-8 in water (K5(298 K) ) (8.0 ( 0.5) × 10-8
;
∆G5°(298 K) ) 9.7 ( 0.1 kcal mol-1). The hydride 5 is
somewhat more acidic than most metal hydrides,21 and the pKa
falls between the values for the rhodium hydride derivatives of
tetraphenyl porphyrin (pKa ) 11) and the perfluorinated
derivative (pKa) 2.1) measured in DMSO.4 Displacement of
hydride (D-) from 5 by D2O occurs with a ∆G° of 54.9 kcal
mol-1, and this free energy change is called the hydricity22 of
5. The Rh-D BDFE to produce a hydrogen atom (60 kcal
mol-1) and the heterolysis process to produce a hydride (54.9
kcal mol-1) are both very high energy processes as compared
to proton donation (∆G°(298 K) ) 9.7 ( 0.1 kcal mol-1). Acid
dissociation of the rhodium hydride complex provides a facile
source of rhodium(I) species with an accessible site for substrate
reactions at the nucleophilic rhodium(I) center.
[(TSPP)Rh-D]-4 (5)/[(TSPP)RhI]-5 (6). First, 0.3 mL of
[(TSPP)RhIII(D2O)2]-3 D2O stock solutions ((1.2-1.8) × 10-3 M, [D+]
> 10-5 M) was added into a vacuum adapted NMR tube. H2/D2 (300-
500 Torr) was pressurized into the NMR tube after three freeze-pump-
thaw cycles, and the tube was flame-sealed. The reaction of 2 with
H2/D2 producing 5 in acidic solution achieves equilibrium distributions
of (TSPP)RhIII and [(TSPP)Rh-D]-4 species within 2 months at 298
K. The equilibrium constant was evaluated from the intensity integra-
Summary
Reactions of (TSPP)Rh(III) aquo and hydroxo complexes with
H2/D2 in D2O result in simultaneous multiple equilibria involv-
ing Rh-D, Rh(I), Rh(II), and Rh(III) species. Equilibrium
thermodynamic relationships between the (TSPP)Rh species in
D2O are described by a set of experimentally determined
equilibrium constants (298 K) (Table 2). The hydrogen ion
([D+]) dependence of the reactions in D2O was used to establish
distributions of species appropriate to measure solution equilibria
1
tions of the H NMR spectrum of each species in combination with
the D+ concentration measurement and the solubility of H2/D2 in
water.16 Following the same procedure, (TSPP)RhIII complexes com-
pletely converted to 6 in basic D2O solution ([D+] < 10-10 M) in 7
1
days at 298 K. H NMR (5) (D2O, 360 MHz) δ (ppm): 8.78 (s, 8H,
1
pyrrole), δ ) 8.25 (s, 16H, phenyl). H NMR (6) (D2O, 360 MHz) δ
1
(ppm): 8.32 (s, 8H, pyrrole), 8.20 (d, 8H, o-phenyl, J1H-1H ) 8.2 Hz),
8.11 (d, 8H, m-phenyl, J1H-1H ) 8.2 Hz).
using H NMR spectroscopy and to identify conditions where
specific species are dominant. The hydride complex (Rh-D) 5
functions as a weak acid in water (D2O) (Ka ) 8.0 × 10-8) and
is thus a facile source of the rhodium(I) complex 6. Thermo-
dynamic parameters for the directly observed reactions were
used in the derivation of thermodynamic values for a series of
reactions where the equilibrium constants were either too small
or too large to be directly evaluated. The difference between
the (Rh-D)aq BDFE in 5 and the (Rh-OD)aq BDFE in 3 is
determined to be small (∼ +1.8 kcal mol-1), and the (Rh-D)
BDFE is estimated to be ∼60 ( 3 kcal mol-1. Each of the
(TSPP)Rh species reported in this Article has a substantial scope
of substrate organometallic reactivity, and the equilibrium
studies reported in this Article establish a foundation for
thermodynamic measurements for a wide array of substrate
reactions in aqueous media.
[(TSPP)Rh-Rh(TSPP)]-8 (7). Equal molar quantities of 6 and 2
in D2O solution (∼10-3 M) were mixed in a NMR tube in an inert
atmosphere box, and the reaction reaches equilibrium in 24 h. 1H NMR
spectroscopy was used to determine the equilibrium distribution of RhIII
species including complex 2 and 3, rhodium hydride 5, rhodium(I) 6,
and rhodium(II) dimer 7. The equilibrium constant of reaction 6 is
evaluated from the intensity integration of each rhodium species in
combination with equilibrium constants of eq 1 and 5 which determine
the equilibrium distribution of rhodium complex 2 with 3 and 5 with
6, respectively. 1H NMR (7) (D2O, 360 MHz) δ (ppm): 8.46 (s, pyrrole,
16H), 9.51 (d, 4H, o-phenyl, J1H-1H ) 8 Hz), 8.47 (d, 4H, m-phenyl,
J1H-1H ) 8 Hz), 7.80 (d, 4H, m-phenyl, J1H-1H ) 8 Hz), 6.95 (d, 4H,
o-phenyl, J1H-1H ) 8 Hz).
[(TSPP)Rh-CH3]-4. [(TSPP)Rh-CH3]-4 was formed immediately
after vacuum transfer of CH3I into vacuum adapted NMR tubes
containing D2O solutions of 6. 1H NMR (6) (D2O, 360 MHz) δ (ppm):
8.81 (s, 8H, pyrrole), 8.39 (d, 4H, o-phenyl, J1H-1H ) 7.2 Hz), 8.30 (d,
4H, o-phenyl, J1H-1H ) 7.2 Hz), 8.23 (d, 4H, m-phenyl, J1H-1H ) 7.2
Hz), 8.19 (d, 4H, m-phenyl, J1H-1H ) 7.2 Hz), -6.59 (d, 3H).
Experimental Section
General Considerations. D2O was purchased from Cambridge Iso-
tope Laboratory Inc. and degassed by three freeze-pump-thaw cycles
before use. Tetra p-sulfonatophenyl porphyrin sodium salt was pur-
chaced from Mid-Centurary Chemicals. Research grade hydrogen was
purchased from Matheson Gas Products and used without further
purification.
Acid Dissociation Constant Measurements for [(TSPP)RhIII
-
(D2O)2]-3 (2). Samples of [(TSPP)RhIII(OD)2]-5 (4) were prepared by
mixing a standardized solution of NaOH D2O with the stock solutions
of complex 1 ((1.0-5.0) × 10-3M) in NMR tubes. A series of HCl
and NaOH deuterium oxide solutions were used to tune the pH values,
1
Proton NMR spectra were obtained on a Bruker AC-360 interfaced
to an Aspect 300 computer at ambient temperature. Chemical shifts
were referenced to 3-trimethylsilyl-1 propanesulfonic acid sodium salt.
Proton NMR spectra was used to identify solution species and to
determine the distribution of species at equilibrium. pH measurements
and the (TSPP)RhIII pyrrole hydrogen H NMR chemical shifts were
1
recorded. A plot of the pyrrole hydrogen H NMR chemical shifts to
pD value (pD ) pH + 0.45) is illustrated in Figure 1. Nonlinear least-
squares curve fitting to the equation δ2,3,4(obs)(pyr) ) (K1K2δ4(pyr) +
K1[D+]δ3(pyr) + [D+]2δ2(pyr))/(K1K2 + K1[D+] + [D+]2) gives K1 )
9
J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004 2629

A R T I C L E S
Fu and Wayland
(1.4 ( 0.2) × 10-8, K2 ) (2.8 ( 0.3) × 10-12, corresponding to eqs 1,
2. The equation is derived from the following analysis:
N2, N3, and N4 are the mole fractions of rhodium complexes 2, 3,
and 4, respectively. δ2(pyr), δ3(pyr), and δ4(pyr) are the chemical shifts
for each of these species.
Replace the expressions N2, N3, and N4 in the equation δ2,3,4obs(pyr)
) N2 × δ2(pyr) + N3 × δ3(pyr) + N4 × δ4, and the equation
δ
2,3,4(obs)(pyr) )
K1 × K2 × δ4(pyr) + K1 × [D+] × δ3(pyr) + [D+]2 × δ2(pyr)
N3
N2
N4
N3
K1 × K2 + K1 × [D+] + [D+]2
N2 + N3 + N4 ) 1, K1 )
N2 × K1
× [D+], K2 )
× [D+]
is derived.
Acid Dissociation Constant Measurement for [(TSPP)Rh-D]-4
N2 × K1
N3 )
, N4 ) 1 - N2 - N3 ) 1 - N2 -
(5). HCl and [(TSPP)RhI]-5 (6) (2.2 × 10-3 M) deuterium oxide
solutions are degassed by three freeze-pump-thaw cycles and then
carried into a glovebox. Samples with different pH values were obtained
by mixing HCl and [(TSPP)RhI]-5 (6) deuterium oxide stock solutions
in NMR tubes. The total concentration of the rhodium species is within
the range of (1.2-1.8) × 10-3 M. The tubes were taken out of the
glovebox after being capped with a septum and sealed with Teflon
[D+]
[D+]
Replace N3 and N4 with
N2 × K1
N3 )
[D+]
1
tape. H NMR spectra were recorded, and pH values were measured
and
to determine the equilibrium distribution of rhodium(I) and rhodium
1
N2 × K1
hydride. A plot of the pyrrole hydrogen H NMR chemical shifts to
N4 ) 1 - N2 -
pD value (pD ) pH + 0.45) is illustrated in Figure 3. Nonlinear least-
squares curve fitting to the equation δ5,6(obs)(pyr) ) (K5δ6(pyr) + [D+]δ5-
(pyr))/(K5 + [D+]) gives K5 ) (8.0 ( 0.5) × 10-8, corresponding to
eq 5. The curve fitting equation is derived from the following analysis:
N5 and N6 are the mole fractions of rhodium complexes 5 and 6,
respectively, and δ5(pyr) and δ6(pyr) are the pyrrole chemical shifts
for each of these species.
[D+]
to the equation
N4
K2 )
× [D+]
N3
then
N6 × [D+]
N5 + N6 ) 1, K5 )
N2 × K1
N5
1 - N2 -
× [D+]2
[D+]
(
)
K2 )
N2 )
So
N2 × K1
K5
N6 )
So
K5 + [D+]
[D+]2
and
K1 × K2 + K1 × [D+] + [D+]2
K5
N5 ) 1 - N6 ) 1 -
K5 + [D+]
is derived. Replace
[D+]2
N2 )
Replace the expressions of
K1 × K2 + K1 × [D+] + [D+]2
K5
N5 ) 1 -
with the equation
K5 + [D+]
N2 × K1
N3 )
and
[D+]
K5
N6 )
and
K5 + [D+]
N2 × K1
N4 ) 1 - N2 -
[D+]
in the equation of δ5,6obs(pyr) ) N5 × δ5(pyr) + N6 × δ6(pyr), and
then
[D+]2
K1
K5
K5
N3 )
×
K1 × K2 + K1 × [D+] + [D+]2 [D+]
δ
5,6(obs)(pyr) )
δ6(pyr) + 1 -
δ5(pyr)
K5 + [D+]
K5 + [D ]
+
(
)
and
K5 × δ6(pyr) + [D+] × δ5(pyr)
K5 + [D+]
δ
5,6(obs)(pyr) )
[D+]2
N4 ) 1 -
-
K1 × K2 + K1 × [D+] + [D+]2
is obtained.
[D+]2
K1
Analysis of ∆H° and ∆G°(298 K) for Bond Homolysis of H-H,
D-D, H-OH, and D-OD in Water. (a) The bond dissociation free
energies (BDFE) and bond dissociation enthalpies (BDE) of the (H-
H)g and (H-OH)g are derived from the formation free energies and
×
K1 × K2 + K1 × [D+] + [D+]2 [D+]
are obtained.
2630 J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004
9

Equilibrium Thermodynamic Studies in Water
A R T I C L E S
the formation enthalpies of H•, H2, •OH, and H2O, respectively (∆fGg°-
(H•) ) 203.24 kJ mol-1, ∆fHg°(H•) ) 217.94 kJ mol-1, ∆fGg°(H2) )
and BDE of (D-D)aq and (D-OD)aq are estimated on the basis of the
corresponding H-H and H-OH values and the zero-point energy
difference of (H-H) with (D-D) (∼1.7 kcal mol-1) and (H-OH) with
(D-OD) (∼1.5 kcal mol-1) resulting from the streching frequency
difference (BDFE(D-D)aq ) 103.4 kcal mol-1, BDE(D-D)aq ) 104.5 kcal
mol-1, BDFE(D-OD)aq ) 117.6 kcal mol-1, and BDE(D-OD)aq ) 124.8
kcal mol-1).
0 kJ mol-1, ∆fHg°(H2) ) 0 kJ mol-1, ∆fGg°(•OH) ) 37.4 kJ mol-1
,
and ∆fGg°(H2O) ) -228.6 kJ mol-1 at 298 K),23 (BDFE(H-H)g ) 97.1
kcal mol-1, BDE(H-H)g ) 104.2 kcal mol-1, BDFE(H-OH)g ) 112 kcal
mol-1, and BDE(H-OH)g ) 118.8 kcal mol-1 24). (b) The hydration
energies of •H, •OH, and H2O (∆Ghdy°(•H) ) ∆Ghdy°(H2) ∼ +4.5 kcal
mol-1, ∆Ghdy°(•OH) ≈ -2.4 kcal mol-1, ∆Ghdy°(H2O) ≈ -2.1 kcal
mol-1, ∆Hhdy°(•H) ≈ -1 kcal mol-1, ∆Hhdy°(•OH) ≈ -4.8 kcal mol-1
,
Acknowledgment. The authors acknowledge support of this
research from the Department of Energy, Division of Chemical
Sciences, Office of Science through grant DE-FG02-86ER-13615.
and ∆Hhdy°(H2O) ≈ -10.5 kcal mol-1
)
25 are used in combination with
the BDFE and BDE of (H-H)g and (H-OH)g to evaluate BDFE(H-H)aq
) 101.8 kcal mol-1, BDE(H-H)aq ) 103.2 kcal mol-1, BDFE(H-OH)aq
116.1 kcal mol-1, and BDE(H-OH)aq ) 123.5 kcal mol-1. (c) The BDFE
)
JA039218M
9
J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004 2631