Why does D2 bind better than H2? A theoretical and experimental study of the equilibrium isotope effect on H2 binding in a M(η2-H2) complex. Normal coordinate analysis of W(CO)3(PCy3)2(η2-H2)

Article abstract of DOI:10.1021/ja971009c

Vibrational data (IR, Raman and inelastic neutron scattering) and a supporting normal coordinate analysis for the complex trans-W(CO)₃(PCy₃)2(η²-H₂) (1) and its HD and D₂ isotopomers are reported. The vibrational data and force constants support the well-established η²-bonding mode for the H₂ ligand and provide unambiguous assignments for all metal-hydrogen stretching and bending frequencies. The force constant for the HH stretch, 1.3 mdyn/A?, is less than one-fourth the value in free H₂ and is similar to that for the WH stretch, indicating that weakening of the H-H bond and formation of W-H bonds are well along the reaction coordinate to oxidative addition. The equilibrium isotope effect (EIE) for the reversible binding of dihydrogen (H₂) and dideuterium (D₂) to 1 and 1-d₂ has been calculated from measured vibrational frequencies for 1 and 1-d₂. The calculated EIE is 'inverse' (1-d₂ binds D₂ better than 1 binds H₂ With K(H)/K(D) = 0.78 at 300 K. The EIE calculated from vibrational frequencies may be resolved into a large normal mass and moment of inertia factor (MMI = 5.77), an inverse vibrational excitation factor (EXC = 0.67), and an inverse zero-point energy factor (ZPE = 0.20), where EIE = MMI x EXC x ZPE. An analysis of the zero-point energy components of the EIE shows that the large decrease in the HH stretching frequency (force constant) predicts a large normal EIE but that zero-point energies from five new vibrational modes (which originate from translational and rotational degrees of freedom from hydrogen) offset the change in zero-point energy from the H₂(D₂) stretch. The calculated EIE is compared to experimental data obtained for the binding of H₂ or D₂ to Cr(CO)₃(PCy₃)₂ over the temperature range 12-36 °C in THF solution. For the binding of H₂ ΔH = -6.8 ± 0.5 kcal mol^-1 and ΔS = -24.7 ± 2.0 cal mol^-1 deg^-1; for (D)2 ΔH = -8.6 ± 0.5 kcal/mol and ΔS = -30.0 ± 2.0 cal/(mol deg). The EIE at 22 °C has a value of K(H)/K(D) = 0.65 ± 0.15. Comparison of the equilibrium constants for displacement of N₂ by H₂ or D₂ in the complex W(CO)₃(PCy₃)₂(N₂) in THF yielded a value of K(H)/K(D) = 0.70 ± 0.15 at 22 °C.

Full text of DOI:10.1021/ja971009c

J. Am. Chem. Soc. 1997, 119, 9179-9190
9179
Why Does D2 Bind Better Than H2? A Theoretical and
Experimental Study of the Equilibrium Isotope Effect on H2
Binding in a M(η2-H2) Complex. Normal Coordinate Analysis
of W(CO)3(PCy3)2(η2-H2)
Bruce R. Bender,*,† Gregory J. Kubas,*,‡ Llewellyn H. Jones,‡ Basil I. Swanson,‡
Juergen Eckert,‡ Kenneth B. Capps,§ and Carl D. Hoff*,§
Contribution from Catalytica Inc., 430 Ferguson DriVe, Mountain View, California 94043,
Los Alamos National Laboratory, MS-J514, Los Alamos, New Mexico 87545, and
the Department of Chemistry, UniVersity of Miami, Coral Gables, Florida 33124
ReceiVed March 31, 1997X
Abstract: Vibrational data (IR, Raman and inelastic neutron scattering) and a supporting normal coordinate analysis
for the complex trans-W(CO)3(PCy3)2(η2-H2) (1) and its HD and D2 isotopomers are reported. The vibrational data
and force constants support the well-established η2-bonding mode for the H2 ligand and provide unambiguous
assignments for all metal-hydrogen stretching and bending frequencies. The force constant for the HH stretch, 1.3
mdyn/Å, is less than one-fourth the value in free H2 and is similar to that for the WH stretch, indicating that weakening
of the H-H bond and formation of W-H bonds are well along the reaction coordinate to oxidative addition. The
equilibrium isotope effect (EIE) for the reversible binding of dihydrogen (H2) and dideuterium (D2) to 1 and 1-d2
has been calculated from measured vibrational frequencies for 1 and 1-d2. The calculated EIE is “inverse” (1-d2
binds D2 better than 1 binds H2), with KH/KD ) 0.78 at 300 K. The EIE calculated from vibrational frequencies may
be resolved into a large normal mass and moment of inertia factor (MMI ) 5.77), an inverse vibrational excitation
factor (EXC) 0.67), and an inverse zero-point energy factor (ZPE ) 0.20), where EIE ) MMI × EXC × ZPE. An
analysis of the zero-point energy components of the EIE shows that the large decrease in the HH stretching frequency
(force constant) predicts a large normal EIE but that zero-point energies from five new vibrational modes (which
originate from translational and rotational degrees of freedom from hydrogen) offset the change in zero-point energy
from the H2(D2) stretch. The calculated EIE is compared to experimental data obtained for the binding of H2 or D2
to Cr(CO)3(PCy3)2 over the temperature range 12-36 °C in THF solution. For the binding of H2 ∆H ) -6.8 ( 0.5
kcal mol-1 and ∆S ) -24.7 ( 2.0 cal mol-1 deg-1; for D2 ∆H ) -8.6 ( 0.5 kcal/mol and ∆S ) -30.0 ( 2.0
cal/(mol deg). The EIE at 22 °C has a value of KH/KD ) 0.65 ( 0.15. Comparison of the equilibrium constants for
displacement of N2 by H2 or D2 in the complex W(CO)3(PCy3)2(N2) in THF yielded a value of KH/KD ) 0.70 ( 0.15
at 22 °C.
Introduction
hydrides/deuterides2g,h and, more recently, to various transition-
metal complexes in solution to form either metal dihydride/di-
deuteride complexes2a-c (eqs 1 and 2) or dihydrogen/dideuterium
complexes (eq 3, left half).2d-f Observed EIE’s for H2 versus
D2 addition are usually “inverse” (KH < KD), showing that metal
complexes counterintuitively bind D2 better than they do H2.
Isotope effects can be extremely informative in mechanistic
studies in organometallic chemistry, especially for M-H
systems.1 Yet they often are poorly understood or even
perplexing. Unlike the situation in organic chemistry, the ability
of metal centers (enzymes included) to reversibly coordinate
substrates prior to rate determining steps complicates isotope
effect “rules” that were formulated (correctly) by organic
chemists. Several reports2 have appeared concerning deuterium
equilibrium isotope effects (EIE’s) for the reversible addition
of H2 and D2 to transition metal centers to form interstitial
KH
H
(1)
H2 + "MLn"
D2 + "MLn"
MLn
MLn
H
KD
D
D
(2)
* Authors to whom correspondence should be addressed.
† Catalytica Inc.
The discovery3 of molecular hydrogen complexes4 altered our
understanding of H2 oxidative addition to transition-metal
complexes by showing that H2 may act as a two-electron ligand
without undergoing complete oxidative addition and that such
dihydrogen σ complexes are intermediates along the pathway
of H2 oxidative addition (eq 3).
‡ Los Alamos National Laboratory.
§ University of Miami.
X Abstract published in AdVance ACS Abstracts, September 1, 1997.
(1) Bullock, R. M. In Transition Metal Hydrides; Dedieu, A., Ed.; VCH
Publishers, Inc.: New York, 1992; p 263.
(2) (a) Hostetler, M. J.; Bergman, R. G. J. Am. Chem. Soc. 1992, 114,
7629. (b) Rabinovich, D.; Parkin, G. J. Am. Chem. Soc. 1993, 115, 353.
(c) Abu-Hasanayn, F.; Krogh-Jespersen, K.; Goldman, A. S. J. Am. Chem.
Soc. 1993, 115, 8019. (d) Gusev, D. G.; Bakhmutov, V. I.; Grushin, V. V.;
Vol’pin, M. E. Inorg. Chim. Acta 1990, 177, 115. (e) Hauger, B. E.; Gusev,
D. G.; Caulton, K. G. J. Am. Chem. Soc. 1994, 116, 208. (f) Bakhmutov,
V. I.; Bertran, J.; Esteruelas, M. A.; Lledos, A.; Maseras, F.; Modrego, J.;
Oro, L. A.; Sola, E. Chem. Eur. J. 1996, 2, 815. (g) Wiswall, R. H., Jr.;
Reilly, J. J. Inorg. Chem. 1972, 11, 1691. (h) Luo, W.; Clewley, J. D.;
Flanagan, T. B. J. Phys. Chem. 1990, 93, 6710.
H
H
H
H
H2 + "MLn"
(3)
MLn
MLn
Depending on M and L, the H-H separation has been found
to vary in a near continuum from 0.82 to 1.6 Å, the point at
S0002-7863(97)01009-3 CCC: $14.00 © 1997 American Chemical Society

9180 J. Am. Chem. Soc., Vol. 119, No. 39, 1997
Bender et al.
which the bond generally is considered to be broken to give a
classical dihydride (right side of eq 3).4,5 This indicates that
oxidative addition can be arrested anywhere along the reaction
coordinate. A tautomeric equilibrium can even exist in solution
between the dihydrogen and dihydride forms in eq 3 in certain
cases, including W(CO)3(PCy3)2(η2-H2), 1,3b the complex that
is the subject of this paper.
tance of zero-point energies from new vibrational modes and
rotational energy contributions to EIE’s when H2 coordinates.
KH
H
(4)
(5)
H2 + "MLn"
D2 + "MLn"
MLn
MLn
H
D
KD
We wondered what the deuterium EIE would be for the
formation of a dihydrogen complex from H2 and a metal
complex like 1 (left side of eq 3 and eqs 4 and 5 below). This
could lead to increased understanding of σ-bond coordination
and improved methods for hydrogen isotope separations wherein
molecular binding is necessary (metal-hydride formation would
give isotopic exchange). EIE’s have been reported2d-f for the
binding of H2 versus D2 in complexes of the type MHx(H2)Ln,
although these also contained hydride/deuteride ligands, intro-
ducing a secondary isotope effect. The data showed that such
EIE’s were inverse, with typical values of KH/KD ) 0.36-0.50
over a large temperature range. These values are somewhat
more “inverse” than those (ca. 0.5) measured and calculated
for the binding of H2/D2 in dihydride complexes.2a-c
The prototype dihydrogen complexes, W(CO)3(PR3)2(η2-H2),
including 1 (R ) Cy), have been extensively characterized by
diffraction (X-ray and neutron) and vibrational spectroscopic
methods (IR, Raman, and inelastic neutron scattering, INS), as
well as by NMR (1J(HD) NMR coupling constant and T1
relaxation times). All data concur that ν(HH) and ν(DD)
frequencies (hence bond order) are lowered when H2/D2 binds
to a metal center; this should result in a “normal” equilibrium
isotope effect if changes in the HH(DD) force constant were
the major contributor to the EIE. However, we also anticipated
(as elucidated by Krogh-Jespersen and Goldman2c) the impor-
D
Here we have used vibrational modes measured and assigned
for 1 and its D2 analogue, W(CO)3(PCy3)2(η2-D2), 1-d2, to
calculate the EIE (KH/KD) for eq 4 and eq 5 using the formalism
of Bigeleisen and Goeppert-Mayer.6 We have experimentally
verified the same EIE for the binding of H2/D2 to 1 and 1-d2 in
THF solution. In addition, we have determined the EIE for
the binding of H2 and D2 to Cr(CO)3(PCy3)2 in THF solution
and have determined the temperature dependence of that
equilibrium. We also include here the details of a normal
coordinate vibrational analysis of 1 and 1-d2 plus the related
HD complex (1-d1), which we carried out to support vibrational
mode assignments and determine force constants and interaction
constants for metal-dihydrogen coordination. These data give
valuable information relating to the degree of activation of the
H-H bond and help explain inconsistencies in the correlation
of ν(HH) with electronics at the metal and other properties of
H2 complexes.
Experimental Section
The complexes 1, 1-d1, and 1-d2 were prepared as previously
described.3b,c Infrared spectra were measured for Nujol mulls between
CsBr windows and recorded on a Perkin-Elmer 521.3b Raman spectra
were taken on samples sealed inside glass capillary (melting point)
tubes, using the 6471 Å line of a Spectra Physics krypton laser and a
SPEX double monochromator. Despite the use of low power (ca. 1
mW) and cooling of the sample to 77 K, partial decomposition slowly
took place when the sample was illuminated by the laser beam during
the course of the experiments. Surprisingly, the rate of decomposition
was higher at 77 K than at 298 K (possibly due to a sample phase
change), so spectra were recorded at room temperature.
Inelastic neutron scattering (INS) vibrational data for W(CO)3(PCy3)2-
(η2-H2) were obtained on the Filter Difference Spectrometer at the
Manuel Lujan Jr. Neutron Scattering Center of Los Alamos National
Laboratory by procedures similar to those published for the P-i-Pr3
analogue.4e
Infrared measurements for the experimental determination of equi-
libria were made on a Perkin Elmer 2000 FTIR spectrometer in a special
cell obtained from Harrick Scientific. The stainless steel cell is fitted
with germanium windows and attached to a thermostated high-pressure
Hoke bomb of 40-mL capacity. Temperature and pressure measure-
ments were made by calibrated thermistor and quartz pressure transducer
elements obtained from Omega Scientific and in direct contact with
the cell contents. The complexes W(CO)3(PCy3)2(N2)7 and Cr(CO)3-
(PCy3)28 were prepared as previously described. Deuterium, hydrogen,
and nitrogen were obtained from Matheson Gas or Liquid Carbonic
and were of 99.9995% purity. THF solvent was freshly distilled from
Na/benzophenone.
Equilibrium Measurements for the Binding of H2 and D2 to Cr-
(CO)3(PCy3)2. A 40-mL Schlenk tube was loaded in a glovebox with
0.2 g of Cr(CO)3(PCy3)2 and 30 mL of THF. The solution (25 mL)
was loaded under a slight argon pressure into a high-pressure FTIR
cell/reaction vessel. After allowing 10-15 min for pressure and
temperature equilibration and running of an initial IR spectrum, the
cell was filled with D2 to a total pressure of 6.1 atm. The pressure of
D2 at each temperature was calculated by subtracting out the vapor
(3) (a) Kubas, G. J.; Ryan, R. R.; Swanson, B. I.; Vergamini, P. J.;
Wasserman, H. J. J. Am. Chem. Soc. 1984, 106, 451. (b) Kubas, G. J.;
Unkefer, C. J.; Swanson, B. I.; Fukushima, E. J. Am. Chem. Soc. 1986,
108, 7000. (c) Kubas, G. J. Inorg. Synth. 1990, 27, 1.
(4) Reviews: (a) Heinekey, D. M.; Oldham, W. J., Jr. Chem. ReV. 1993,
93, 913. (b) Jessop, P. G.; Morris, R. H. Coord. Chem. ReV. 1992, 121,
155. (c) Crabtree, R. H. Acc. Chem. Res. 1990, 23, 95. (d) Kubas, G. J.
Acc. Chem. Res. 1988, 21, 129. (e) Eckert, J. Spectrochim. Acta A 1992,
48A, 363. Other relevant work: (f) Kubas, G. J.; Nelson, J. E.; Bryan, J.
C.; Eckert, J.; Wisniewski, L.; Zilm, K. Inorg. Chem. 1994, 33, 2954. (g)
Andrea, R. R.; Vuurman, M. A.; Stufkens, D. J.; Oskam, A. Recl. TraV.
Chim. Pays-Bas 1986, 105, 372. (h) Upmacis, R. K.; Poliakoff, M.; Turner,
J. J. J. Am. Chem. Soc. 1986, 108, 3645. (i) Zilm, K. W.; Millar, J. M.
AdV. Magn. Opt. Reson. 1990, 15, 163. (j) Kubas, G. J.; Burns, C. J.; Eckert,
J.; Johnson, S.; Larson, A. C.; Vergamini, P. J.; Unkefer, C. J.; Khalsa, G.
R. K.; Jackson, S. A.; Eisenstein, O. J. Am. Chem. Soc. 1993, 115, 569. (k)
Khalsa, G. R. K.; Kubas, G. J.; Unkefer, C. J.; Van Der Sluys, L. S.; Kubat-
Martin, K. A. J. Am. Chem. Soc. 1990, 112, 3855. (l) Gadd, G. E.; Upmacis,
R. K.; Poliakoff, M.; Turner, J. J. J. Am. Chem. Soc. 1986, 108, 2547. (m)
Van Der Sluys, L. S.; Eckert, J.; Eisenstein, O.; Hall, J. H.; Huffman, J.
C.; Jackson, S. A.; Koetzle, T. F.; Kubas, G. J.; Vergamini, P. J.; Caulton
K. G. J. Am. Chem. Soc. 1990, 112, 4831. (n) Harman, W. D.; Taube, H.
J. Am. Chem. Soc. 1990, 112, 2261. (o) Kohlmann, W.; Werner, H. Z.
Naturforsch. B 1993, 48b, 1499. (p) Eckert, J.; Albinati, A.; Bucher, U. E.;
Venanzi, L. M. Inorg. Chem. 1996, 35, 1292. (q) Martensson, A.-S.; Nyberg,
C.; Andersson, S. Phys. ReV. Lett. 1986, 57, 2045. (r) Ozin, G. A.; Garcia-
Prieto, J. J. Am. Chem. Soc. 1986, 108, 3099. (s) George, M. W.; Haward,
M. T.; Hamley, P. A.; Hughes, C.; Johnson, F. P. A.; Popov, V. K.;
Poliakoff, M. J. Am. Chem. Soc. 1993, 115, 2286. (t) Hodges, P. M.;
Jackson, S. A.; Jacke, J.; Poliakoff, M.; Turner, J. J.; Grevels, F.-W. J. Am.
Chem. Soc. 1990, 112, 1234. (u) Klooster, W. T.; Koetzle, T. F.; Jia, G.;
Fong, T. P.; Morris, R. H.; Albinati, A. J. Am. Chem. Soc. 1994, 116, 7677.
(v) Hasegawa, T.; Li, Z.; Parkin, S.; Hope, H.; McMullan, R. K.; Koetzle,
T. F.; Taube, H. J. Am. Chem. Soc. 1994, 116, 4352. (w) King, W. A.;
Luo, X-L.; Scott, B. L.; Kubas, G. J.; Zilm, K. W. J. Am. Chem. Soc. 1996,
118, 6782. (x) Moreno, B.; Sabo-Etienne, S.; Chaudret, B.; Rodriguez, A.;
Jalon, F.; Trofimenko, S. J. Am. Chem. Soc. 1995, 117, 7441. (y) Sweany,
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(5) H-H distances less than 1.6 Å have been measured in over forty
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state NMR methods (longer distances exist in classical hydrides).

Normal Coordinate Analysis of W(CO)3(PCy3)2(η2-H2)
J. Am. Chem. Soc., Vol. 119, No. 39, 1997 9181
Figure 2. Infrared spectra of Nujol mulls of 1 (upper) and 1-d2 (lower).
The ν(HH) region was recorded for the perdeuteriophosphine species.
Figure 1. Vibrational modes for the dihydrogen ligand in addition to
ν(HH).
pressure of THF and that of argon from the measured pressure. The
equilibrium constant was measured at various temperatures in the range
13-36 °C by analysis of the peaks at 1838 cm-1 due to Cr(CO)3(PCy3)2-
(D2) and at 1822 cm-1 due to Cr(CO)3(PCy3)2.
Equilibrium Measurements for the Displacement of N2 from
W(CO)3(PCy3)2(N2) by H2 and D2. A 6 mM solution of W(CO)3-
(PCy3)2(N2) in dry O2-free THF was prepared under an atmosphere of
N2. This solution was transferred to the high-pressure cell/reactor and
allowed to equilibrate at room temperature at a total pressure of 2.25
atm. Following equilibration, saturation of solvent with gas, and
running of an initial FTIR spectrum, an additional 2.25 atm of H2 or
D2 was added. The ratio of binding was determined from the decrease
in the peak at 2117 cm-1 attributed to coordinated N2 in W(CO)3(PCy3)2-
(N2) when exposed to either H2 or D2. At 22 °C a clear preference for
binding of D2 versus H2 was seen in all experiments, and a value of
KH/KD ) 0.70 ( 0.15 was measured for the net binding of H2 or D2 to
W(CO)3(PCy3)2 relative to N2 at 22 °C.
Figure 3. Infrared spectrum of Nujol mull of 1-d1. The broad ν(HH)
signal at 2360 cm-1 is superimposed over sharper atmospheric CO2
bands. The shoulder at 360 cm-1 is ascribed to δ(WHD) in-plane.
analysis (a not uncommon situation). However, because of the
large isotopic shifts resulting upon deuteration of the H2 ligand,
we are confident of the assignment of the modes associated with
the η2-H2. Importantly in this regard, the HD complex shows
W-η2-HD bands intermediate in frequency to those of the HH
and DD complexes rather than as superimpositions of M(H)2
and M(D)2 bands as found for classical hydride-deuteride
complexes M(H)(D).
Results
Vibrational Frequency Assignments and Force Field for
W(CO)3(PCy3)2(H2) (1). When diatomic H2 combines with a
metal-ligand fragment to form a molecular hydrogen complex
like 1 (eq 4), five “new” vibrational modes are created (in
addition to ν(HH)) which are related to the “lost” translational
and rotational degrees of freedom for H2 (Figure 1). Six
fundamental vibrational modes for 1 are expected to be formally
isotope sensitive, as observed. As described earlier,3b the
infrared spectra of solid W(CO)3(PCy3)2(η2-H2) (1), W(CO)3-
(PCy3)2(η2-HD) (1-d1), and W(CO)3(PCy3)2(η2-D2) (1-d2) dis-
play many overlapping vibrational frequencies, but a substantial
number of them show isotopic shifts (Figures 2 and 3). On the
basis of isotope shifts and force field calculations, the observed
frequencies have been assigned to vibrational modes as shown
in Table 1. These do not include frequencies that are associated
with the phosphine ligands nor W-P modes which would be
expected to occur at low frequencies (<300 cm-1) and could
not be located with any certainty.
The single vibrational mode for H2, ν(HH), remains intact,
but is shifted to much lower frequency, 2690 cm-1, compared
to free H2.3 It is not formally forbidden in the IR of H2
complexes, but is polarized along the direction of the M-H2
bond in highly symmetric complexes. Therefore, intensity arises
only from coupling of ν(HH) with other modes of the same
symmetry such as νs(MH2) or ν(CO) if CO is present. Thus
ν(HH) is almost always very weak, and in 1 could only be
clearly observed in the IR by using thick Nujol mulls of the
complex containing perdeuteriophosphine ligands to remove
interference from the CH bands of the cyclohexyl groups (Figure
2). The large breadth of the absorption is ascribed to rapid
hindered rotation of the H2 ligand about the W-H2 axis4e or
some other motion/behavior that dephases ν(HH), “hot” band
contributions, and a flat rotational potential.9
There is significant mixing between the modes associated with
the H2 and CO ligands, and there is less available frequency
data than that needed for a fully determined normal coordinate

9182 J. Am. Chem. Soc., Vol. 119, No. 39, 1997
Bender et al.
Table 1. Observeda and Calculated Vibrational Frequencies (cm-1) and Mode Assignments for 1, 1-d2, and 1-d1
1
1-d2
1-d1
method/
intensity
symmetry
C2V/Cs
obsd
2690
1962
1857c
953
558
465
452
1575
623
calcd
obsd
calcd
obsd
calcd
assignment
IR, w
2692.1
1965.3
1854.3
949.0
546.7
464.1
452.2
1574.7
626.8
523.4
456.2
400.0
640.0
∼1900b
1962
1847c
703
1909.9
1965.4
1849.4
703.1
544.5
443.4
455.6
1136.1
612.2
523.0
326.0
413.0
442.0
2360
1962
2357.8
1965.3
1853.6
799.8
545.8
459.9
451.0
1357.9
617.1
523.2
368.7
A1/A′
A1/A′
A1/A′
A1/A′
A1/A′
A1/A′
A1/A′
B1/A′
B1/A′
B1/A′
B1/A′
B2/A′′
B2/A′′
A2/A′′
ν(HH)
IR, R, s
IR, R, vs
IR, R, m
IR, R, w
R, s
R, s
IR, w
IR, s
R, w
IR, w
ν(CO)eq
ν(CO)ax
νs(WH2)
δ(WCO)eq
1853c
791
551
450
456
553
ν(WC)ax + νs(WH2) + ν(HH)
ν(WC)eq
∼1144
∼1360
614
-
νas(WH2)
δ(WCO)ax
612
527
522
319
413
δ(WCO)eq
δ(WH2)in-plane
e
462d
400
360
R, w
νas(WC) + δ(WH2)out-of-plane + δ(WCO)
δ(WH2)out-of-plane
INS,f IR, w
INS, m
640g
442h
385 (325)i
τ(WH2)
a Resolution: 2 cm-1 b Raman; very weak and broad. c Raman frequencies. d Also observed in INS. e This mode shows a greater observed isotope
.
shift than calculated. We believe it arises from the δ (WH2) in-plane rocking coordinate coupled strongly with other coordinates. f INS ) Inelastic
neutron scattering. g Observed in INS only. h Observed in IR only. i Split mode (see ref 4e).
Figure 4. Raman spectra of 1 and 1-d2 and difference spectrum.
ν(HD) was observed in the IR as a weak broad band at ca.
2360 cm-1 (Figure 3) in 1-d1, but ν(DD) was obscured by ν-
Figure 5. Inelastic neutron scattering (INS) spectra of 1 at 15 K
obtained as difference spectra by subtracting the spectrum of 1-d2 from
(CO) in 1-d2. However, Raman spectra of 1-d2 showed a very
1 (scattering from deuterium is negligible; only bands due to the H2
broad, barely visible feature centered near 1900 cm-1 that
ligand appear). The lower spectrum with higher resolution shows
apparently mixes with ν(CO)ax. This results in a shift of 10
cm-1 to lower energy for the latter on going from the H2
complex to the D2 complex (Figure 4). The asymmetry in the
ν(CO)ax peak for 1-d2 also suggests the presence of ν(DD) as
an underlying feature, the intensity of which is enhanced by
the mixing (ν(HH) was not observed in Raman spectra,
apparently because it is not so enhanced and is thus too weak
to be seen in these experiments). The W-H2 stretches were
observed clearly in the IR at 1575 (νas(WH2)) and 953 cm-1
(νs(WH2)), but in the Raman only νs(WH2) was seen. νas(WD2)
and νas(WHD) were partially obscured, and their frequencies
could only be estimated. 1-d1 contained some 1 and 1-d2
because slow isotopic scrambling occurs, even in the solid state.
This is obvious in Figure 3 in the νs(WH2) and δ (WH2) in-
plane regions which show peaks due to all three isotopomers.
splitting in the torsional mode (385/325 cm-1).
excited librational states (J ) 1, 2).4e The two WH2 deforma-
tional modes at 640 and 462 cm-1 were also seen in the INS,
as broad features. The deformation around 640 cm-1 was
obscured in the IR but was seen to be shifted to 442 cm-1
in the IR for the D2 isotopomer. Several other metal-ligand
modes also show small shifts to higher or lower wavenumber
upon deuterium substitution due to vibrational coupling be-
tween modes which belong to the same symmetry block and
which are close in energy. This is especially obvious in the
IR spectra3b of 1 and 1-d2 near 625 cm-1 and Raman spectra
in the region below 650 cm-1 (Figure 4). For example, a
band at 400 cm-1 due mainly to νas(WC) shifts 13 cm-1 to
higher frequency for the D2 complex, presumably because of
mixing with δ(WD2)out-of-plane. Such shifts have also been
observed in other complexes containing both H2 and CO
ligands.4h,z
The torsional mode, τ(WH2), was located in the inelastic
neutron scattering (INS) difference spectrum (Figure 5) as a
split mode at 385 and 325 cm-1 due to transitions to two split
Normal Coordinate Analysis of 1, 1-d2, 1-d1, and Simpli-
fied Model Complexes. It is clear that the Cy (cyclohexyl)
(9) Turner, J. J.; Poliakoff, M.; Howdle, S. M.; Jackson, S. A.;
McLaughlin, J. G. Faraday Discuss. 1988, 86, 271.

Normal Coordinate Analysis of W(CO)3(PCy3)2(η2-H2)
J. Am. Chem. Soc., Vol. 119, No. 39, 1997 9183
Table 3. Force Constants and Interaction Constants for
CO-Related Modes (mdy/Å for stretching coordinates; mdyn‚Å/rad2
for bending coordinates)
Scheme 1
coordinate
coordinate
COeq + CO, CO′
COax
WCeq + WC, WC′
WCax
15.07
13.38
3.54
4.00
1.18
0.7
0.8
0.12
0.25
WH2(s), WCax
WH2(s), WCO (s)
COeq, COax
COeq, WCeq
COax, WCax
WC(s), WCax
WH2(as), WCOeq(s)
WH2(as), WCOax
0.70
0.1
0.28
0.6
0.75
0.1
0.05
0.48
WCOax
WCOeq(as)
WCOeq(s)
torsion (τ)
WH2(s), COax
Table 2. Force Constants (mdyn/Å) for Hydrogen-Related Modes
in W(CO)3P2(H2) and Triatomic Model Complex
W(CO)3P2(H2)
W(H2)
1.46
the HH stretch has considerable WH stretch character so it
cannot be treated as an isolated HH mode. The low value of
FHH would suggest a longer HH distance, ca. 0.94 Å,12 than
either the value of 0.82 Å observed by neutron diffraction3b in
W(CO)3(P-i-Pr3)2(H2) or 0.89 Å determined by solid state
NMR4i for both the R ) i-Pr and Cy species. Thus ν(HH) is
not a reliable predictor of HH bond length for molecular
hydrogen complexes.13
FHH
1.32
1.46
1.42
1.44
0.02
0.67
FWH(s)
FWH(as)
FWH
FWH,WH′
FHH,WH
1.43
-0.05
0.62
groups should not show formal HH, HD, DD isotope shifts,
nor should they be significantly coupled to vibrations other than
Cy and P-Cy modes; therefore for force field calculations we
treated only the “W(H2)(CO)3P2” fragment. The symmetry of
that fragment is C2V, with two H atoms, two P atoms, the axial
CO group, and W defining one (xz) plane; the three CO groups
and W define the other (yz) plane as in Scheme 1. However,
to include the HD species, the symmetry is reduced to Cs.
We have assigned the observed IR and Raman frequencies
to the A′ block of Cs; 11 modes of this symmetry were observed
(WP modes were not located). This includes 7 modes of A1
symmetry and 4 B1 modes of C2V symmetry for the HH and
DD species. To carry out the force constant calculations it was
necessary to include input force constants for all modes,
including those unobserved such as those for W-P (a force
constant of 2-3 was assumed and all interaction coordinates,
F(WP,x) were set to zero). There are 10 A1 modes, 7 B1 modes,
3 A2 modes, and 7 B2 modes; the number of force constants
required for each symmetry block is n(n + 1)/2, where n is the
number of frequencies in that block. This means there are 55
general quadratic force constants to fit 7 observed A1 modes,
28 to fit 4 B1 modes, etc. Obviously a large number of force
constants had to be fixed for the calculations. For these
constants we assumed values that seemed reasonable based on
experience with other systems such as W(CO)6.10 Several
calculations were performed, and the values of some of the
“fixed” constants were varied to improve the fit. The solution
arrived at is given in Table 1. The agreement of observed and
calculated frequencies is off by several wavenumbers in some
cases, which is not surprising considering the necessary ap-
proximations. Overall, the analysis suffices to assign the
observed vibrational modes for 1 and its isotopomers as well
as provide meaningful force constants for the dihydrogen-related
modes.
The WH stretching constant is surprisingly as large as that
for the HH stretch, and the WH, WH′ interaction is negligible.
The HH, HW interaction is very large (0.67 mdyn/Å), indicating
that stretching the HH bond leads to strengthening of the HW
bonds, and vice versa.
The WC stretching force constants (Table 3) are quite large
relative to those for W(CO)6. Thus for the equatorial WC
bonds, FWC + FWC,WC′ ) 3.54 mdyn/Å compared to 2.92
mdyn/Å for W(CO)6.10 This is reasonable as the respective
distances are 2.0114 and 2.06 Å.15 The axial (trans to H2) WC
stretching constant is even greater (4.0 mdyn/Å), in accord
with its shorter distance (1.99 Å). This stretching mode is
noticeably weakened in the D2 isotopomer (465 cm-1 for 1
versus 450 cm-1 for 1-d2). This might reflect a greater trans
influence for D2 versus H2 (an “electronic” isotope effect);
however, we might then expect a corresponding increase in νCO
for 1-d2 (a weakening of WC should be accompanied by a
decrease in WfCO π-back-bonding). The observed decrease
in the axial WC stretching frequency for 1-d2 no doubt arises
because it is coupled with the symmetric W-D stretch and the
D-D stretch.
The equatorial C-O stretching constant is about 15 mdyn/Å
compared to ca. 16 for W(CO)6. The value for the axial CO
stretch is 13.4 mdyn/Å. The increase in MC bond strength and
decrease in CO bond strength is consistent with stronger MfCO
π-back-bonding when there are fewer π-acceptor groups avail-
able, particularly opposite the CO. Also in accord with this
notion, the M-C-O bending constants are greater than for
W(CO)6. They are 0.8 mdyn‚Å/rad2 for the equatorial and 1.3
for the axial MCO, compared to <0.6 for W(CO)6.
There is a weak Raman band at 400 cm-1 which shifts
upward to 413 cm-1 for 1-d2 (Table 1). Our calculations
(12) An empirical correlation between bond length and force constant,
known as Badger’s rule, ke ) b/(re - a)3, would predict an HH bond length
of ca. 0.94 Å: Badger, R. M. J. Chem. Phys. 1934, 2, 128.
(13) See ref 4e and the Discussion section. A similar situation arises for
metal-ethylene complexes: ν(CC) is not a reliable parameter of CC bond
length because of normal mode coupling to same-symmetry C2H4 wagging
and scissoring modes: Anson, C. E.; Sheppard, N.; Powell, D. B.; Bender,
B. R.; Norton, J. R. J. Chem. Soc., Faraday Trans. 1994, 90, 1449 and
references therein.
(14) Kubas, G. J.; Ryan, R. R.; Wasserman, H. J. Unpublished data. The
H2 ligand was obscured by a CO ligand, which is disordered across the
center of symmetry located at the tungsten center. However, the overall
geometry of the complex was similar to that for the i-Pr analogue wherein
the H2 was located.
The force constants given in Table 2 that pertain to the H2
ligand are extremely valuable in gaining understanding of the
W-H2 bonding interactions. The first and most important mode
to consider is the HH stretch. The value of 1.3 mdyn/Å is much
smaller than the value for free H2 (5.7 mdyn/Å).11 The ratio of
the square of frequencies for bound and free H2, (2690/4395)2
) 0.37, would lower 5.7 to 2.1 mdyn/Å. However, we see that
(10) Jones, L. H.; McDowell, R. S.; Goldblatt, M. Inorg. Chem. 1969,
8, 2349.
(11) Levine, I. N. Molecular Spectroscopy; Wiley: New York, 1975; p
160
(15) Arnesen, S. P.; Seip, H. M. Acta Chem. Scand. 1966, 20, 2711.

9184 J. Am. Chem. Soc., Vol. 119, No. 39, 1997
Bender et al.
QA*QAro*t QtBrQrBot
Table 4. Frequency Fit for the Triatomic W(H2) Model Complex
tr
(cm-1
)
MMI )
EXC )
(8)
A
A
B* B*
(
)(
)
QtrQrot Qtr Qrot
HH
DD
HD
obsd
calcd
obsd
calcd
obsd
calcd
3N-6
1 - exp(-µi)
2690.0
1575.0
953.0
2691.2
1576.9
964.6
∼1900
∼1140
1905.8
1115.7
685.2
2360.0
1350.0
791.0
2358.1
1347.5
791.5
∏
1 - exp(-µ*i)
1 - exp(-µj)
1 - exp(-µ*j)
i
703.0
(9)
3N-6
∏
indicate that this mode arises from the antisymmetric WC stretch
strongly coupled with the WD2 out-of-plane deformation
(wagging) coordinate, which leads to the upward shift for 1-d2.
Coupling to the two out-of-plane WCO bending coordinates is
also present. For the (A2-symmetry) torsion mode, we calculate
a constant of 0.12 mdyn‚Å/rad2 with the torsion described by
changes in CWH angles.
We have also calculated stretching force constants for an
isolated WH2 group using the frequencies observed for the HH
and WH stretches. The results are shown in Table 2 for
comparison with the more complete treatment. Surprisingly the
agreement is quite good, suggesting that one can do rather well
with the simplified treatment, though it does not tell us about
the rest of the molecule. The frequency agreement for the
simplified triatomic treatment is shown in Table 4. It is seen
to be rather poor by comparison, particularly for the symmetric
WH2 stretch. One can obtain better agreement by including
rather large anharmonicity corrections for the WH stretches;
however, the more complete treatment without anharmonicity
is perhaps more appropriate as the many isotope shifts of a few
wavenumbers indicate significant coupling of H coordinates with
non-H coordinates.
j
3N-6
exp(µi/2)
exp(µ*i/2)
exp(µj/2)
exp(µ*j/2)
∏
i
ZPE )
(10)
3N-6
∏
j
As a first approximation, we assumed that changes in mass
and moments of inertia between 1 and 1-d2 are negligible (i.e.,
that both the translational and rotational partition function ratios
for 1 and 1-d2 are equal to 1) and calculated the MMI factor
from the appropriate mass and moment of inertia ratios of H2
and D2 alone.17 The classical description of the translational,
(2πMkBT)3/2/h3, and rotational, 8π2IkBT/σh2 (linear molecule),
energies18,19 gives ratios of 2.83 and 2.00, respectively, leading
to an MMI term of 5.66.2c
We may independently calculate the MMI term for the EIE
in eq 6 from measured vibrational frequencies for 1, 1-d2, H2,
and D2, using the Teller-Redlich product rule20 (shown in its
most concise form in eq 11). This important theorem allows
the ratios of molecular masses and moments of inertia of
isotopically related species to be expressed as a product of
atomic masses and vibrational frequencies.
Calculated Deuterium Equilibrium Isotope Effect (EIE).
Division of eq 4 by eq 5 (with MLn ) W(CO)3L2) leads to eq
6, and KH/KD is a direct measure of the deuterium equilibrium
isotope effect (EIE).
D
D
H
H
K
H /KD
3/2
1/2
3/2
N
3N-6
IA*IB*IC*
IAIBIC
m*j
ν*i
H2 +
D2 +
M*
W(CO)3L2
1-d2
W(CO)3L2
(6)
×
)
×
(11)
∏
∏
(
)
(
)
(
)
M
mj
νi
j
i
1
In eq 11, IA, IB, and IC are the principal molecular moments
KH/KD in eq 6 may be calculated from vibrational data if all
isotopically sensitive frequencies for the four species are known
or can be reliably estimated. The electronic potentials on both
sides of eq 6 are identical (with the Born-Oppenheimer and
harmonic oscillator assumptions), and the only sources of an
EIE deviation from unity are mass-related, i.e., translational,
rotational, and vibrational. Thus the EIE in eq 6 may be
calculated from molecular translational, rotational, and vibra-
tional partition function ratios as described in the general
treatment of equilibrium isotope effects by Bigeleisen and
Goeppert-Mayer.6
of inertia, M and M* are molecular masses, and mj and m*j are
atomic masses (asterisks denote the heavier isotope). For the
linear molecules H2 and D2, the vibrational product contains
only one frequency, and the ratio of moments of inertia contains
one less moment of inertia.
Division of eq 11 for isotopic dihydrogens by the corre-
sponding eq 12 for 1 and 1-d2 yields eq 12 (the products of
atomic masses on both sides of eq 6 are the same and therefore
are eliminated), therefore the MMI factor (eq 8) may be replaced
with the vibrational product (VP) factor (eq 12), which accounts
for the mass and moment of inertia ratios needed to calculate
the EIE.
EIE ) MMI × EXC × ZPE
(7)
(17) We have assumed that the solution translational and rotational
partition function ratios for H2 and D2 resemble those in the gas phase; the
rotation of H2 appears to be only slightly hindered in aqueous solution:
Taylor, D. G., III; Strauss, H. L. J. Chem. Phys. 1989, 90, 768. (b) Hunter,
J. E., III; Taylor, D. G., III; Strauss, H. L. J. Chem. Phys. 1992, 97, 50.
(18) In eqs 9 and 10, µi,j ) hcνij/kT, where νi,j are vibrational frequencies
(in cm-1); c is the speed of light, c ) 2.997924 × 1010 cm/s; h is Planck’s
constant, h ) 6.626176 × 10-34 J s; k is Boltzmann’s constant, and k )
1.380662 × 10-23 J/K. All values of physical constants were taken from:
Handbook of Chemistry and Physics, 62nd ed.; Weast., R. C., Ed.; CRC
Press: Boca Raton, FL, 1981-82; Table F-203.
The calculated EIE is the product of three factors16 (the usual
symmetry factor cancels for this case). They are a rotational
and translational factor containing the reduced (classical)
rotational and translational partition function ratios of isotopic
species (abbreviated MMI, eq 8), a factor accounting for
contributions from excitations of vibrational energy levels
(abbreviated EXC, eq 9), and a factor comprising zero-point
energy contributions (abbreviated ZPE, eq 10).
(19) Moelwyn-Hughes, E. A. Physical Chemistry; Pergamon Press: New
York, 1961; pp 427-1007.
(16) We have used the equations presented by: McLennan, D. J. Isotopes
in Organic Chemistry; Buncel, E., Lee, E., Eds.; Elsevier: New York, 1987;
Vol. 7, Chapter 6, pp 393-480.
(20) Melander, L.; Saunders, W. H. Reaction Rates of Isotopic Molecules;
Wiley: New York, 1980; p 20.

Normal Coordinate Analysis of W(CO)3(PCy3)2(η2-H2)
J. Am. Chem. Soc., Vol. 119, No. 39, 1997 9185
and D2 were determined in a similar fashion to that described
in an earlier report.21 For the chromium complex, Cr(CO)3-
(PCy3)2, the equilibrium shown in eq 13 is rapidly established
under moderate pressures of H2 (1-10 atm) in THF solution:
νD
2
D2
D
1-H2 1-H2
2
νH
Qtr Qrot
QHtr2QHro2t
Q
Qrot
2
tr
VP )
)
×
) MMI
(12)
1-d2
1-D2 1-D2
3N-6
νi
Q
Qrot
tr
Cr(CO)3(PCy3)2(soln) + H2 h Cr(CO)3(PCy3)2(H2)(soln)
∏
νi1
(13)
i
Cr(CO)3(PCy3)2(soln) + D2 h Cr(CO)3(PCy3)2(D2)(soln)
The vibrational product in the denominator on the left side
of eq 12 is a product over all vibrational modes for isotopomers
of both molecules; however, several modes common to 1 and
1-d2 will exactly cancel in eqs 11 and 12 if they are not
isotopically sensitiVe and may thus be omitted from further
consideration. We have used this to advantage by omitting the
cyclohexyl mode frequencies for 1 and 1-d2 that are not isotope
sensitive.
(14)
Because oxidative addition does not occur for the chrom-
ium complex, equilibrium data for eqs 13 and 14 do not
incorporate the dihydrogen/dihydride equilibrium shown in eq
3. Experimental data for the equilibrium constant (in atm-1
)
are shown in Figure 6. These data also incorporate earlier data
for the dihydrogen case. Thermochemical parameters for
binding of H2 (eq 13) are ∆H ) -6.8 ( 0.5 kcal mol-1 and
∆S ) -24.7 ( 2.0 cal mol-1 deg-1. For the binding of D2 (eq
14) ∆H ) -8.6 ( 0.5 kcal mol-1 and ∆S ) -30.0 ( 2.0 cal
mol-1 deg-1. The data for the H2 case differ slightly from those
reported earlier:21 ∆H ) -7.3 kcal mol-1 and ∆S ) -25.6 cal
mol-1 deg-1 for H2. The principal reason for this is that the
earlier data were measured by taking the pressure readings
directly from the pressure gauge without correcting for solvent
and atmospheric pressure. The current data in Figure 6
incorporate both the new data and earlier data corrected for
pressure.
The EIE value for the tungsten complex could not be
measured directly because there is near quantitative uptake of
H2 or D2 gas at pressures near 1 atm, presumably due to stronger
W(H2) bonding. The highly air sensitive nature of the agostic
complex W(CO)3(PCy3)2 also limits the accuracy of data at low
partial pressures of H2. The equilibrium shown in eq 15
provides a means of determining accurate EIE values:
For the VP factor in eq 12 we have used 14 normal vibrational
modes measured and assigned for 1 and 1-d2 (Table 1). We
used an average value of 355 cm-1 for the split torsion mode
and have calculated the torsional mode frequency (251 cm-1
)
for 1-d2 from reduced mass considerations. The calculated VP
factor is 5.77 and agrees well with the value (5.66) calculated
from the mass and moment of inertia ratios of H2 and D2 alone.
This agreement is also an independent check of the accuracy
of the vibrational frequencies (but not assignments) of 1 and
1-d2. The calculated VP factor (which represents translational
and rotational contributions to eq 6 (MMI) is large and “normal”
(5.77); this factor is a direct consequence of the significant mass
and moment of inertia ratios of D2 and H2 (eq 11).
The calculated EIE value (KH/KD ) 0.78) for eq 6 is modestly
inverse at 300 K. The individual EXC and ZPE factors for the
single H2(D2) mode and six W(H2) modes were calculated and
the results are gathered in Table 5. For convenience of
discussion, we have separated the six normal modes of the “W-
(H2)” fragment from the other modes which show slight but
significant isotope shifts (Table 6).
It should be pointed out that the overall calculated EIE is
independent of individual mode assignments for 1 and 1-d2.
Because the factors comprising the product terms in eqs 9-12
commute for a given species, the calculated EIE is independent
of assignments. Mode assignments, however, are useful for
interpreting the “origin” of the EIE in terms of changes in
particular vibrational frequencies, thus each assignment is shown
with its individual contributions to the EXC and ZPE factors.
These results give insight into the origin of the calculated EIE
for the complexation of dihydrogen isotopes to W(CO)3L2.
The change in zero-point energy for the HH(DD) stretching
mode contributes a large “normal” factor to the total EIE as
expected; the calculated ZPE contribution would predict an EIE
of ca. 3.2 for eq 6 if changes in the HH(DD) stretching force
constant were the only contributor to the EIE. The five “new”
vibrational normal modes of 1 and 1-d2 all contribute modest
inverse EXC and ZPE factors to the calculated EIE for eq 6
(last two columns in Table 5). When multiplied together, these
modest inverse EXC and ZPE contributions from the five “new”
vibrational modes collectively overcome the strong “normal”
ZPE component from the νHH stretch (and the “normal” MMI
factor), and predict an overall “inverse” EIE of 0.78 at 300 K.
Two modes contribute significant inverse EXC factors to the
overall EIE. They are the low-frequency a2-symmetry torsional
and the b1-symmetry in-plane deformation (wag) modes (il-
lustrated in Scheme 1); these low-frequency modes are signifi-
cantly more populated at 300 K (Boltzmann excitation) for 1-d2
than for 1.
W(CO)3(PCy3)2(N2)(soln) + H2(gas) h
W(CO)3(PCy3)2(H2)(soln) + N2(gas) (15)
Spectroscopic measurements with calibrated H2/N2 and
D2/N2 gas mixtures allowed determination that KH/KD
)
0.70 ( 0.15 in THF solvent at 22 °C. This value refers to
the “net” binding of H2 (vs D2) and does not distinguish be-
tween the tautomeric forms (eq 3). Because the equilibrium in
eq 3 displays temperature dependence (and this could be
different for H2 and D2, vide infra), no attempt was made to
measure the temperature dependence of the tungsten equilibrium
constant.
Discussion
Vibrational Analysis of Dihydrogen Complexes. The
complete set of six vibrational modes has been identified only
in the first and most intensely-studied H2 complex, W(CO)3-
(PR3)2(H2) (R ) Cy, i-Pr).22 The main reason for this is that
all but νs(MH2) are weak in the IR and Raman and most of the
bands tend to be obscured by other ligand modes. Also, τ(H2),
and δ(MH2)out-of-plane have been observed only by inelastic
neutron scattering (INS) methods. The frequency of most
interest ν(HH) varies tremendously, but is often near the CH
stretch region, the worst possible position because most ancillary
ligands contain CH bonds. Nevertheless, it has been observed
in about 20 complexes in the range 2080-3200 cm-1, which is
(21) Gonzalez, A. A.; Hoff, C. D. Inorg. Chem. 1989, 28, 4295.
(22) For general discussion of the vibrational spectra of M(H)2 and M(H2)
species see: Sweany, R. L. Transition Metal Hydrides; Dedieu, A., Ed.;
VCH Publishers: New York, 1991; pp 65-101.
Experimental Determination of the EIE for M(CO)3-
(PCy3)2, M ) Cr and W. Equilibria for the binding of H2

9186 J. Am. Chem. Soc., Vol. 119, No. 39, 1997
Bender et al.
Table 5. Equilibrium Isotope Effect Contributions from Individual Modes for H2(D2) Complexation at T ) 300 K
mode (sym)
H2(D2) (cm-1
)
1(1-d2) (cm-1
)
EXC
ZPE
ν(H2) (A1)
4395 (3118)
2690 (1900)
953 (703)
1575 (1144)
640 (442)
462 (319)
355 (251)
1.000
0.976
0.996
0.923
0.879
0.856
3.215
0.549
0.356
0.622
0.710
0.780
ν(WH2) (A1)
ν(WH2) (B1)
δ(WH2) (B2)
δ(WH2) (B1)
τ(WH2) (A2)
∏ EXC ) 0.675
∏ ZPE ) 0.216
Table 6. Equilibrium Isotope Effect Contributions From
Additional Modes (300 K)
vibrations and deformations (dppm ) Ph2PCH2PPh2). The
reported assignments (as listed in Table 7) are questionable
however, because the H-H bond is weak (d(HH) ) 1.10 Å),
which implies strong Ru-H bonds, yet the RuH2 frequencies
are among the lowest ever reported.
As expected there is generally a large dependence of the
modes on both metal and ligand. However, vibrational analysis
of a metal-η2-H2 system is complicated by the three-center,
two-electron bonding. The bonding is essentially of the Dewar-
Chatt-Duncanson type present in metal-olefin complexes,
where there is a strong MfH2 σ* back-donation component,
EBD, to the bonding in addition to electron donation, ED, to the
empty metal d-orbital from the H2 electron pair.
mode
1(1-d2) (cm-1
)
EXC
ZPE
ν(COeq)
ν(COax)
δ(WCO)
W-Cax
ν(WCeq)
δ(MCOax)
δ(MCOeq)
νas(WC)
1962 (1963)
1857 (1847)
558 (551)
465 (450)
452 (456)
623 (612)
527 (522)
400 (413)
1.000
1.000
0.997
0.991
1.002
0.997
0.998
1.010
1.000
0.976
0.983
0.965
1.010
0.974
0.988
1.032
∏ EXC ) 0.995
∏ ZPE ) 0.929
Theoretical calculations by Ziegler on 1 have shown that the
EBD component is energetically as strong as ED, and up to twice
as strong in other H2 complexes with more phosphine donor
ligands.24 Back-bonding is much weaker in complexes with
mostly π-acceptors, although the calculations24a show that EBD
in Mo(CO)5(H2) still has about one-half the energy of ED (ν-
(CO) values also indicate H2 is still a good π-acceptor here4g).
One might anticipate a correlation of ν(HH) with the back-
bonding ability (electron richness) of the metal center, as found
for ν(NN) and ν(CO) in similar π-acceptor N2 and CO ligands.
The decrease in ν(HH) on going from Mo(CO)5(H2) to Mo-
(CO)3(PCy3)2(H2) to Mo(CO)(dppe)2(H2) at first glance does
seem to reflect increased H-H bond weakening by the more
electron-rich metal centers. However, ν(HH) decreases in the
order Mo > Cr > W for M(CO)5(H2), whereas Cr should be
the worst back-bonder and give the highest ν(HH). The value
of ν(HH) in W(CO)5(H2) (2711 cm-1) is far out of line with
the much higher values in the Cr and Mo congeners (3030 and
3080 cm-1) and also differs little (20 cm-1) from that in vastly
more electron rich W(CO)3(PCy3)2(H2). The pentacarbonyl is
unstable at room temperature and is presumed to have a shorter
HH distance and a stronger H-H bond (although as discussed
below such electrophilic metal centers may offset lower EBD
by higher ED). In any event it is quite clear from the data in
Table 7 that ν(HH) does not correlate well with H-H distance.
Although the two complexes with the longest H-H separations
(<1.1 Å) show the lowest ν(HH), these values are not that much
lower than those for complexes considered to be “true” H2
complexes with H-H distances less than 0.9 Å. This is mainly
a result of the “give and take” bonding synergism here (ED and
EBD), which represents concomitant formation of M-H bonds
and cleavage of the H-H bond. Thus the HH stretch cannot
be viewed as an isolated mode in H2 complexes. The normal
coordinate analysis of W(CO)3(PCy3)2(H2) indeed treats the
Figure 6. Plot of ln Keq vs 1/T for the binding of H2 and D2 to Cr-
(CO)3(PCy3)2 in THF solution.
considerably lowered from that for unbound H2 gas (4300 cm-1).
Table 7 lists all known vibrational data for H2 complexes as
well as H-H distances. The M-H2 stretching and deforma-
tional modes have been less often reported, partly because of
interference from coligands or in difficulty in assignment,
especially if hydride ligands are also present. This was the case
for Tp*RuH(H2)2 (Tp* ) hydridotris(3,5-dimethylpyrazolybo-
rate)), which showed four unassignable bands at 458-834
cm-1 4x
Recently near-IR laser Raman data were reported for
.
23
[CpRu(dppm)(H2)]BF4 which included the lowest reported
value for ν(HH), 2082 cm-1, and also low-frequency RuH2
(23) Chopra, M.; Wong, K. F.; Jia, G.; Yu, N.-T. J. Mol. Struct. 1996,
379, 93.
(24) (a) Li, J.; Ziegler, T. Organometallics 1996, 15, 11482. (b) Li, J.;
Dickson, R. M.; Ziegler, T. J. Am. Chem. Soc. 1995, 117, 11482.

Normal Coordinate Analysis of W(CO)3(PCy3)2(η2-H2)
Table 7. IR Frequencies for ν(HH) and MH2 Modes in Stable and Unstable Dihydrogen Complexesa
J. Am. Chem. Soc., Vol. 119, No. 39, 1997 9187
complex
ν(HH)
2642
νas(MH2)
νs(MH2)
δ(MH2)
d(HH)b
ref
4s
CpV(CO)3(H2)
CpNb(CO)3(H2)
Cr(CO)5(H2)
2600
3030
4s
4h,4y
4f
4h
3b
3b
4j
4h
4t
3b
3b
4k
3b
4z
4z
4l
1380
1540
869, 878
950
Cr(CO)3(PCy3)2(H2)
Mo(CO)5(H2)
Mo(CO)3(PCy3)2(H2)
Mo(CO)3(PCy2-i-Pr)2(H2)
Mo(CO)(dppe)2(H2)
W(CO)5(H2)
W(CO)4(C2H4)(H2)
W(CO)3(P-i-Pr3)2(H2)
W(CO)3(PCy3)2(H2)
W(CO)3(PCyp3)2(H2)
W(CO)3(PCy2-i-Pr)2(H2)
MnCl(CO)4(H2)
563c
471
∼465
0.85
0.87
0.88
3080
∼2950d
∼1420d
885
∼870
875
2650
2711
2717
2695
2690
919
1567
1575
1565
1570
{1357, 1322}
{1392, 1369}
1374
953
953
938
937
764
465
462
0.89
0.89
456
MnBr(CO)4(H2)
789
Fe(CO)(NO)2(H2)
Co(CO)2(NO)(H2)
FeH2(H2)(PEtPh2)3
RuH2(H2)(PMe3)3
[CpRu(dppm)(H2)]+
Tp*RuH(H2)2
Tp*RuH(H2)(THT)
[Os(NH3)5(H2)]2+
Tp*RhH2(H2)
2973
{3100, 2976}e
2380
2360
2082
2361
2250
2231
2238
∼870
1345
868
4l
850
500, 405f
486
0.82 g
4m
4o
23
4x
4x
4n
4p
4r
1358
679
1.10h
0.90i
0.89i
1.34j
0.94k
Pd(H2)
960
670
Ni(510)-(H2)l
3205
1185
4q
a Frequencies in cm-1; complexes in italics are unstable at room temperature. Samples in mineral oil mulls for stable complexes and in liquid
Xe or matrices for unstable species. Abbreviations: Cyp ) cyclopentyl; Tp* ) hydridotris(3,5-dimethylpyrazoylborate; dppm ) Ph2PCH2PPh2;
THT ) tetrahydrothiophene. b H-H distance in Å (solid state NMR distance from ref 4i except where noted). c Assignment unclear; could be
δ(MH2)out-of-plane.
d Estimated from observed D2 isotopomer bands. e Split possibly by Fermi resonance. f Assignment unclear (data from INS).
g Neutron diffraction distance. Actual distance is undoubtedly longer when corrected for H2 libration as in the case of the Mo-dppe complex (ref
4j). h For the Cp* analogue (ref 4u). i Calculated from T1 data from solution NMR measurements. j For [Os(ethylenediamine)2(H2)(acetate)]+ (ref
4v). k Calculated from inelastic neutron scattering data. l Data from EELS spectroscopy. H2 believed to be bound in η2 fashion on stepped edges
of the Ni surface.
W-H2 interaction as a triangulo system, i.e. where direct back-
bonding electronic interactions exist between W and H atoms
(below, left) rather than as the strictly 3-center bonding
representation (below right).
frequencies for all of which are intermediate in value to those
for the H2 and D2 isotopomers) must eventually transform into
two widely-separated M-H and M-D stretches. The question
is how and at what point might this happen, given the continuum
nature of the system.
H
H
H
H
Importantly, the force constant analysis appears to indicate
that the H2 ligand in 1 is further activated than may have been
previously thought. It has always been a paradox that the H-H
distances in 1 or any of the Group 6 complexes in Table 7
(0.85-0.89 Å, solid state NMR) are not as “stretched” as some
of those found in later transition element complexes (1.0-1.5
Å),4a-c yet the H-H bond in 1 undergoes equilibrium cleavage
in solution (eq 3). Thus the H-H distance may not always
reflect the degree of “readiness to break”, i.e. a very late
transition state may exist. At the other end of the spectrum,
for W(CO)5(H2) and other highly electrophilic complexes, the
T-shaped entity pictured above with one internal coordinate,
the H-H stretch, may be a more appropriate model for
vibrational analysis, as mentioned in a footnote in Poliakoff’s
paper.4h However, it is difficult to draw the line on which
analysis should be applied because some degree of back-bonding
and incipient M-H bond formation will always be present.
Furthermore, the T-shaped bonding that represents the purely
three-center interaction (ED) in σ complexes can be reasonably
strong by itself in the absence of much back-bonding. The
Lewis-base type interaction of H2 with a highly electrophilic
metal center (Lewis acid) has a much stronger ED than with a
more electron-rich metal center, and this can completely offset
the lower EBD. For example, the cationic H2 complex [Mn-
(CO)(dppe)2(H2)]+ has remarkably similar properties, e.g. H-H
distance and JHD, to its isoelectronic neutral analogue, Mo(CO)-
(dppe)2(H2).4w In the case of electrophilic cationic complexes,
M
M
This is confirmed by the fact that the WH stretching force
constant is as large as that for the HH stretch and that the HH,
WH interaction is very large, indicating that stretching the HH
bond leads to strengthening of WH, and vice versa. This
extensive mixing along with the reduction of the ν(HH) force
constant to one-fourth the value in free H2 indicates that
weakening of the H-H bond and formation of W-H bonds is
already well along the reaction coordinate to oxidative addition
in 1. Furthermore, as the H-H bond becomes more activated
(stretched) on a metal fragment, the observed ν(HH) mode will
have increasing M-H character relative to H-H character.
Upon H-H cleavage, this mode will then be assimilated into
the M-H stretching mode, which generally occurs in the 1700-
2300 cm-1 range. Thus the 2231-cm-1 frequency in Table 7
for the cationic Os complex with a very long H-H separation
(<1.3 Å) probably should be thought more of as ν(OsH) than
ν(HH). The frequency of this highly mixed mode could possibly
go down then back up again on a given metal fragment as the
H-H bond is activated and then broken by changing the ligand
environment. This is overall an unprecedented situation in
chemistry and vibrational spectroscopy. It would be most
interesting to study the gradual activation of a series of M-η2-
HD complexes since ν(HD) and the two ν(M-HD) modes (the

9188 J. Am. Chem. Soc., Vol. 119, No. 39, 1997
Bender et al.
the H-H bond can be considerably weakened (although cannot
be broken) by the ED bonding component alone without much
back-bonding from the metal.
The lack of reliable correlation of vibrational versus other
properties brought about by the bonding complexities extends
to the M-H2 modes. These also show metal/ligand dependence,
though to a lesser degree than ν(HH) (Table 7). νs(MH2) is
∼70 cm-1 lower in Mo(CO)3(PCy3)2(H2) than in the W
congener (1), which combined with the higher ν(HH) for the
Mo species suggests weaker coordination of H2 to Mo than W.
This correlates well with the known thermal stabilities. The
νs(MH2) and νas(MH2) values for the unstable W, Fe, Co
carbonyl and Pd(H2) species are also lower than those for stable
1. However, one would have anticipated νs(MH2) to be
appreciably higher for 1 than for its Cr analogue because of
the higher M-H2 binding energy measured for 1 and the far
greater stability of 1 to H2 dissociation in solution.4f The
frequencies were nearly identical, however, and a minor ligand
change from PCy3 to tricyclopentylphosphine affected νs(MH2)
more than changing the metal. Also νs(MH2) values are nearly
identical for Mo(CO)3(PCy3)2(H2) and Mo(CO)(dppe)2(H2)
though ν(HH) is 300 cm-1 lower for the latter. As is the case
for ν(HH), the metal-hydrogen stretching frequencies represent
an inseparable combination of MH and HH interactions.
Experimentally Determined Equilibrium Isotope Effects
(EIE’s). Measurements of the EIE values for the Cr and W
complexes (made after the calculations had been performed)
agree within experimental error with the calculated value of
0.78 for eq 6. It should be noted that the measured equilibrium
constants are Kp values expressed in terms of the pressure of
H2(D2) above the solution. Care was taken to make sure that
the solvent was saturated with H2 or D2. What limited data are
available indicate that D2 is about 3% more soluble than H2 in
water and common organic solvents.25 Accurate values for the
solubility of D2 in THF were not found, so the activity of the
gas is used in all equilibrium expressions.
Figure 7. Plot of ln(KH/KD) vs 1/T for the EIE calculated from
vibrational data.
responsible for the preferred binding of D2 (and the inverse EIE
in eq 16). The fact that, for the chromium complex at least,
the analogue of reaction 6 is actually endothermic by this amount
implies that zero-point (and excited state) vibrational energies
for the dihydrogen species determine the EIE.
Enthalpic Origin of the Deuterium EIE for Binding of
Dihydrogen to a Molecular Hydrogen Complex. Relative
enthalpic and entropic contributions to the calculated equilibrium
in eq 6 were obtained from a plot of calculated ln(KH/KD) values
vs 1/T, Figure 7. We obtained ∆H and ∆S for the equilibrium
in eq 6 from the slope and intercept of this line. These results
gave a small positive ∆H of 0.64 kcal mol-1 and a ∆S term of
1.7 cal mol-1 deg-1 for eq 6. These calculated thermodynamic
parameters for the tungsten system may be judiciously compared
to the corresponding measured parameters for the Cr analog:
∆∆H ) 1.8 kcal mol-1; ∆∆S ) 5.3 cal mol-1 deg-1. The
calculated tungsten values differ slightly in magnitude from
those measured for the Cr case; however, in both cases, an
unfavorable enthalpy term overcomes a favorable entropy term.
Thus D2 binds better for enthalpic reasons, eVen though the
complexation of D2 is disfaVored entropically.
The equilibrium isotope effect for both dissociative and
nondissociative addition of H2 to metal complexes in solution
has been studied by several groups,2 and the results of a few
recent studies are summarized in Table 8. For more meaningful
comparison, we have used the authors’ Arrhenius parameters
to calculate EIE’s at the common temperature of 300 K.
All of the entries in Table 8 show inverse EIE’s for the
binding of H2 vs D2, and their corresponding measured
Arrhenius parameters reveal that in each case D2 binding is
enthalpically favored over H2 binding, while D2 binding is
disfavored entropically. It should be pointed out that two entries
in Table 8 contain contributions from R and â secondary
deuterium effects. The first entry, Bergman’s heterobimetallic
Ta-Ir complex, contains bridging CH2(CD2) ligands which
contribute a â-secondary effect to the observed EIE. Caulton’s
Ir(III) complex, entry 3, is the measured EIE for the binding of
H2 vs D2 to the corresponding hydride and deuteride complexes.
Thus the measured EIE contains an R secondary effect.
Goldman and Krogh-Jespersen have estimated the magnitudes
of such R and â secondary effects for the addition of H2/D2 to
MX and M(CX3) (X ) H, D) model complexes. These studies
give normalized R and â secondary effects of 0.88 and 0.84 (at
300 K). Correcting Bergman’s and Caulton’s EIE would
decrease the apparent EIE’s (make them slightly less inverse)
KH/D
Cr(CO)3(PCy3)2(D2) + H2 y z Cr(CO)3(PCy3)2(H2) + D2
(16)
Division of eq 13 by eq 14 gives eq 16, the EIE for the
binding of H2 vs D2 to Cr(CO)3(P(Cy)3)2 in solution. The
experimental EIE was determined from the equilibrium data for
the binding of H2 and D2 to the chromium complex Cr(CO)3-
(PCy3)2 (eqs 13 and 14). The inverse EIE (KH/D ) 0.65 ( 0.15
at 22 °C for eq 16) arises from an unfavorable enthalpy term,
∆∆H ) 1.8 ( 1.0 kcal mol-1, overcoming a favorable entropy
term, ∆∆S ) 5.3 ( 4.0 cal mol-1 deg-1 26
of D2 gas (34.6 cal mol-1 deg-1 27 is 3.4 cal mol-1 deg-1 more
.
The standard entropy
)
positive than that of H2 gas (31.2 cal mol-1 deg-1); the more
negative entropy of binding of D2 gas is due to the greater loss
of rotational and translational entropy for the heavier D2.
In light of the fact that the free D-D bond is 1.8 kcal mol-1
stronger than the H-H bond, a naive view would be to expect
H2 to bind preferentially. Thus if the W(D2) and W(H2) bonds
were of equal strength, eq 6 would be predicted to be exothermic
by -1.8 kcal mol-1 based on the fact that the D-D bond is
that much stronger. The more negative enthalpy of binding D2
more than overcomes the unfavorable entropic barrier and is
(25) Cook, M. W.; Hanson, D. N.; Alder, B. J. J. Chem. Phys. 1957, 26,
748.
(26) The ∆∆H for eq 16 is ∆H(eq 13) - ∆H(eq 14) ) -6.8 -(-8.6)
kcal mol-1. The ∆∆S for eq 16 is ∆S(eq 13) - ∆S(eq 14) ) -24.7 -
(-30.0) cal mol-1 deg-1
.
(27) Handbook of Chemistry and Physics, 62nd ed.; Weast., R. C., Ed.;
CRC Press: Boca Raton, FL, 1981-82; Table F-203.

Normal Coordinate Analysis of W(CO)3(PCy3)2(η2-H2)
J. Am. Chem. Soc., Vol. 119, No. 39, 1997 9189
Table 8. Comparison of Thermodynamic Parameters for the Binding of H2 and D2 to Various Metal Complexes
∆H
(kcal/mol)
∆S
Keq
(cal/(mol deg))
EIE
ref
[Cp2Ta(µ-CH2)2Ir(CO)2(H)2]/{[H2][Cp2Ta(µ-CH2)2Ir(CO)2]}
[Cp2Ta(µ-CD2)2Ir(CO)2(D)2]/{[D2] [Cp2Ta(µ-CD2)2Ir(CO)2]}
[W(H)2L4I2]/{[H2] [WL4I2]}
-12.0 (0.2)
-13.0 (0.4)
-19.7 (0.6)
-21.6 (0.7)
-6.8 (0.2)
-7.7 (0.5)
-6.8 (0.5)
-8.6 (0.5)
-23.7 (0.6)
-25.9 (1.2)
-45 (2)
0.56a
2a
2e
0.85a
0.47a
0.70a
[W(D)2L4I2]/{[D2] [WL4I2]}
-51 (3)
[Ir(H)2Cl(L)2(H2)]/{[H2] [Ir(H)2Cl(L)2]}
[Ir(D)2Cl(L)2(D2)]/{[D2][Ir(D)2Cl(L)2]}
[Cr(H2)L2(CO)3]/{[H2] [CrL2(CO)3]}
-19.2 (0.7)
-20.7 (1.8)
-25 (2)
this work
[Cr(D2)L2(CO)3]/{[D2] [CrL2(CO)3]}
-30 (2)
a EIE calculated from Arrhenius parameters at 300 K.
Table 9. Comparison of Calculated Thermodynamic Parameters
for Deuterium EIE’s
and bring them closer to the measured and calculated values
for our Cr/W dihydrogen case.
∆∆H°
∆∆S° (cal
Goldman and Krogh-Jespersen clarified the vibrational origin
of “inverse” EIE’s for both solution dihydride cases cited in
Table 8. As part of a more general examination of primary
and secondary isotope effects for dihydrogen and alkane addition
to metal complexes,2c they measured and calculated the EIE
for the addition of H2 and D2 to a Vaska’s type complex, trans-
Ir(CO)L2Cl (eq 17 and 18). Dividing eq 17 by eq 18 gives eq
19, an expression for the EIE.
KH/KD
MMI EXC ZPE EIE (kcal mol-1
)
deg-1 mol-1
)
{[D2] [3]}/
5.66a 0.84a 0.10a 0.46a
1.15
0.64
2.28
1.7
{[H2][3-d2]}
{[D2] [1]}/
{[H2][1-d2]}
5.77b 0.67b 0.20b 0.78b
a Data from ref 2c; EIE data calculated at 300 K. b This work; EIE
data calculated at 300 K.
(the EIE’s were calculated over the same temperature range:
280 to 320 K).
KH
(L)2Ir(CO)Cl + H2 y\z (L)2Ir(H)2(CO)Cl
(17)
(18)
(19)
Finally, we note that the calculated and measured EIE for
binding of H2 vs D2 to the tungsten dihydrogen complex 1 is a
factor of 1.7 less “inverse” than the corresponding EIE
calculated and measured by Krogh-Jespersen and Goldman for
the binding of H2/D2 to Vaska’s complexsthis difference has
important implications for the predicted and measured EIE for
tautomerization equilibria like those in eqs 3 and 20.
KD
(L)2Ir(CO)Cl + D2 y
\
z (L)2Ir(D)2(CO)Cl
(L) Ir(H) (CO)Cl
z D2 +
KH/KD
y
(L) Ir(D) (CO)Cl
H2 +
2
2
2
2
3
3-d2
The measured EIE2c for eq 19 (L ) PPh3) was inverse: KH/
KD ) 0.55(6) at ambient temperature; a similar EIE was
calculated from computed vibrational frequencies (L ) PH3,
KH/KD ) 0.46 at 300 K). Thus both theory and experiment
concur that D2 binds better than H2 to Vaska’s complex. The
calculated values, ∆∆H° ) 1.14 kcal mol-1 and ∆∆So ) 2.28
cal mol-1 deg-1, for eq 23 are in good agreement with those
measured experimentally by Werneke and Vaska:28 ∆∆H° )
0.8 kcal mol-1 and ∆∆So ) 2.0 eu (no errors given).
When H2 (or D2) forms a dihydride complex, the combined
inverse ZPE and EXC contributions from new isotope sensitive
vibrational modes overcome the normal ZPE contribution from
the HH (DD) stretch and rotational effects which oppose the
observed inverse EIE.2c This conclusion provided the first
theoretical explanation of Bergman’s2a and Parkin’s2b observed
inverse effects, and is the important precedent for our analysis
of the EIE for the binding of H2/D2 in a molecular hydrogen
complex. More recently, the importance of new isotope-sensi-
tive vibrational modes in the complexation of alkenes29 and
alkanes30 to transition-metal complexes has been reported and
discussed.
D
EIET
H
H
H
D
D
+
+
MLn
(20)
MLn
MLn
MLn
H
D
If we assume that the EIE for eq 6 is typical for the nonclassical
M(H2) case and that the EIE of eq 19 is typical for a classical
M(H)2 case, we may estimate the EIE for the tautomerization
in eq 20: EIET ) EIE(eq 6)/EIE(eq 19). Using the calculated
EIE’s for eq 6 (0.78) and that for eq 19 (0.45), we predict that
the EIE in eq 20 is “normal”si.e., that deuterium favors the
classical site at 300 K.
Because the MMI factors are (and should be) similar for eqs
6 and 19 (∆S for eq 20 is negligible), the predicted preference
for deuterium in the classical tautomer may be traced to the
more “inverse” ZPE factor for eq 19 (0.10) versus the corre-
sponding ZPE factor for eq 6 (0.20, see Table 9). Because
∆ZPE changes for the dihydride and molecular hydrogen cases
are both referenced to free H2(D2), we conclude that changes
in MH2 force constants between tautomers (not the conversion
of molecular translations and rotations into vibrations) lead to
the predicted preference of deuterium in the dihydride tautomer.
This reasoning is also consistent with an increase in the
corresponding force constants for low-frequency modes when
the “loose” M(H2) fully adds (despite the weakening of the
bound HH(DD) force constant). Indeed the predicted preference
of deuterium in the dihydride tautomer merely parallels (but
for different reasons) the preference of deuterium in a complex
versus as a free, unbound molecule.
In Table 9 we have compared our calculated enthalpy and
entropy terms from the EIE temperature dependence for the
formation of a dihydrogen complex to those calculated by
Krogh-Jespersen and Goldman2c for the formation of a dihydride
(28) Werneke, M. F. Ph.D. Thesis, Clarkson College of Technology,
1971. Results quoted from ref 2c.
(29) Bender, B. R. J. Am. Chem. Soc. 1995, 117, 11239.
(30) (a) Bengali, A. A.; Arndtsen, B. A.; Burger, P. M.; Schultz, R. H.;
Weiller, Kyle, K. R.; Moore, C. B.; Bergman, R. G. Pure Appl. Chem.
1995, 67, 281. (b) Schultz, R. H.; Bengali, A. A.; Tauber, M. J.; Weiller,
B. H.; Wasserman, E. P.; Kyle, K. R.; Moore, C. B.; Bergman, R. G. J.
Am. Chem. Soc. 1994, 116, 7369. (c) Bengali, A. A.; Schultz, R. H.; Moore,
C. B.; Tauber, M. J.; Weiller, B. H.; Wasserman, E. P.; Kyle, K. R.;
Bergman, R. G. J. Am. Chem. Soc. 1994, 116, 9585.
Because we do not have vibrational frequencies for the
“classical” dihydride tautomer of 1 and 1-d2, we cannot test
our predicted EIE for the W(CO)3L2(H)2/W(CO)3L2(H2) tau-
tomeric equilibrium in eq 20. The predicted “normal” EIE for
eq 20 is supported by the corresponding “normal” KIE for
conversion of classical to nonclassical tautomers measured

9190 J. Am. Chem. Soc., Vol. 119, No. 39, 1997
Bender et al.
earlier by some of us.31 EIE’s for equilibria like that of eq 20
have been reported, but the conclusions diverge: Luo and
Crabtree reported32 that deuterium favors the nonclassical site
in [ReH2(H2)(CO)L3]+; Poliakoff and co-workers also found33
that deuterium favors the nonclassical site in CpNb(CO)3(H2)
versus CpNb(CO)3H2. On the other hand, Heinekey and
Oldham found34 that deuterium favors the classical site in
[Cp*IrL(H)(H2)]+ and Henderson and Oglieve reported35 that
deuterium favors the classical tautomer in the complex [Cp2-
WH2]+. In light of the fact that these studies ranged over very
different temperatures, we think it unwise to state a general rule
concerning whether deuterium favors a classical versus a
nonclassical site.
contributions36 from new low-frequency modes oppose and
overcome a large mass and moment (MMI) factor and a large
zero-point energy (ZPE) factor change for the HH stretch, much
like the case for the addition of H2 to metal complexes to form
dihydrides. We also have calculated the enthalpy and entropy
parameters associated with the temperature dependence of the
EIE.
We have experimentally confirmed the calculated “inverse”
equilibrium isotope effect for the binding of H2 and D2 to
W(CO)3(PCy3)2 and Cr(CO)3(PCy3)2 in solution. The preferred
binding of D2 versus H2 is enthalpic in nature in accord with
our analysis of the same EIE from measured vibrational
frequencies of 1 and 1-d2. Conceptually it should thus be
possible to separate hydrogen isotopes, including tritium, at room
temperature on metal complexes that reversibly bind H2
molecularly (hydrides will give exchange), using for example
cationic complexes supported on alumina. The separation
factors calculated for H2/D2 and eight other37 mixed H-D-T
isotopomeric combinations on W(CO)3(PCy3)2 at 25 °C are
generally better than those at the cryogenic temperatures (ca.
-150 °C) currently used for such separations on alumina-type
supports.
Conclusions
A normal coordinate analysis has been performed on W(CO)3-
(PCy3)2(H2) (1) and its isotopomers with HD (1-d1) and D2 (1-
d2). The major revelation was the high extent of mixing between
the HH stretch and the WH2 modes, where in fact the WH
stretching force constant is as large as that for the HH stretch.
The frequency of the HH stretch in H2 complexes would thus
not be expected to be a reliable predictor of HH bond length,
bond strength, or any related parameter. The force constant
for the HH stretch, 1.3 mdyn/Å, is less than one-fourth the value
in free H2. This indicates that weakening of the H-H bond
and formation of W-H bonds are quite far along the reaction
coordinate to oxidative addition even in “true” H2 complexes
that possess the shortest measured H-H distances (0.85-0.89
Å, solid state NMR). The two-dimensional nature of the
reaction coordinate which involves coupling of H-H and M-H
modes is an intriguing problem for future study.
Acknowledgment. We dedicate this work to Jacob Big-
eleisen and to the memory of Maria Goeppert-Mayer on the
50th anniversary of the publication of their general treatment
of equilibrium isotope effects (ref 6). The authors thank Jacob
Bigeleisen and Alan Goldman for helpful discussions. B.R.B.
thanks Rick Finke for indirect financial support of this research.
G.J.K. acknowledges funding support by the Department of
Energy, Office of Basic Energy Sciences, Division of Chemical
Sciences. This work has also benefitted from the use of facilities
at the Manuel Lujan Jr. Neutron Scattering Center, a National
User Facility funded as such by the Department of Energy,
Office of Basic Energy Sciences.
Using the vibrational modes established for 1 and 1-d2, we
have calculated the deuterium equilibrium isotope effect for the
binding of H2 and D2 to 1 and 1-d2. The calculated EIE is
inverse (D2 is bound better than H2), and a detailed consideration
of component factors shows that zero-point energy contributions
from five new vibrational modes and Boltzmann excitation
JA971009C
(36) Another point evident from our comparison is that the EXC term
for the molecular hydrogen case is less than that for the dihydride case
(0.68 vs 0.84). The greater deviation from unity for the molecular hydrogen
case arises from the presence of more low-frequency isotope sensitive modes
(hence more excited states) in the molecular hydrogen case than in the
dihydride case. Bergman has called attention to the presence of such low-
frequency modes in alkane σ-complexes and their contributions to observed
“inverse” EIE’s for alkane complex equilibria at low temperatures (see ref
30c).
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(37) King, W. A.; Kubas, G. J. Unpublished results.