Evaluation of the Thermodynamic Properties of H
2
Binding in
Solid State Dihydrogen Complexes [M(
η
2
-H
2
)(CO)dppe
2
][BArF
24
]
(M = Mn, Tc, Re): an Experimental and First Principles Study
David G. Abrecht
*
and
Brent Fultz
W. M. Keck Laboratory, California Institute of Technology, 1200 E California Blvd., MC 138-78,
Pasadena, CA, 91125 USA
Abstract
The solid state complex [Mn(CO)dppe
2
][BArF
24
] was synthesized and the thermodynamic
behavior and properties of the hydrogen absorption reaction to form the dihydrogen complex
[Mn(
η
2
-H
2
)dppe
2
][BArF
24
] were measured over the temperature range 313K-373K and pressure
range 0–600 torr using the Sieverts method. The absorption behavior was accurately described by
Langmuir isotherms, and enthalpy and entropy values of
Δ
H
∘
=−52.2 kJ/mol and
Δ
S
∘
=−99.6 J/
mol-K for the absorption reaction were obtained from the Langmuir equilibrium constant. The
observed binding strength was similar to metal hydrides and other organometallic complexes,
despite rapid kinetics suggesting a site-binding mechanism similar to physisorption materials.
Electronic structure calculations using the LANL2DZ-ECP basis set were performed for hydrogen
absorption over the organometallic fragments [M(CO)dppe
2
]
+
(M= Mn, Tc, Re). Langmuir
isotherms derived from calculation for absorption onto the manganese fragment successfully
simulated both the pressure-composition behavior and thermodynamic properties obtained from
experiment. Results from calculations for the substitution of the metal center reproduced
qualitative binding strength trends of 5d > 3d > 4d previously reported for the group 6 metals.
Introduction
The Kubas binding interaction, in which a hydrogen molecule binds chemically without
dissociation to a coordinatively-unsaturated metal center, has received the focus of
numerous research groups for its potential to improve the energetics of physisorptive
hydrogen storage materials. This interaction, characterized by
σ
donation of electron density
from the H-H bond to the metal center and
π
donation from the d-orbitals of the transition
metal back to the
σ
* orbital of the hydrogen molecule, produces a stable metal-dihydrogen
bond with a higher binding enthalpy than typical physisorption materials, leading to
improvements in room temperature storage capacity. Early work on the use of unsaturated
metal centers in metal-organic frameworks
1, 2, 3
(MOFs) and Prussian blue analogs
4
showed
enhancement in the isosteric heat of adsorption by approximately 2 kJ/mol H
2
over similar
materials if unsaturated metal centers were included in the framework. Later investigations
aimed at exploiting Kubas binding by incorporating unsaturated metal centers into several
classes of materials to improve physisorption energetics. Computational studies have
dominated the efforts, with some examples being the examination of H
2
interactions in
transition metal-modified fullerenes,
5, 6
decorated polymers,
7
and more traditional
organometallics.
8
These studies have obtained binding energies between −20 and −60 kJ/
mol. Recently, experimental attempts to design hydrogels containing Kubas sites
9
have
shown experimental isosteric heats as low as −40 kJ/mol. These increases in the binding
To whom correspondence should be addressed, dabrecht@caltech.edu.
NIH Public Access
Author Manuscript
J Phys Chem C Nanomater Interfaces
. Author manuscript; available in PMC 2013 October 25.
Published in final edited form as:
J Phys Chem C Nanomater Interfaces
. 2012 October 25; 116(42): 22245–22252. doi:10.1021/jp308176f.
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energy over more typical physisorption values of 5–10 kJ/mol represent significant
improvements in materials properties for hydrogen storage applications. However, recent
experimental studies
10
have also demonstrated unusual behaviors arising from the
incorporation of metal centers, such as activation energies and plateaus within the isotherms,
that are not typically associated with physisorption processes, prompting the need for further
investigation into the mechanism of these interactions to enable rational materials design.
Evaluation of the behavior of Kubas sites in materials designed for hydrogen storage is
complicated by the presence of other physisorptive binding sites that contribute to the
observable sorption properties, and studies of materials exhibiting only the Kubas
interaction would considerably aid analytical efforts. Such materials are represented by the
class of original dihydrogen complexes first reported by Kubas et al.
11
in 1984.
Unfortunately, the available thermodynamic data on direct hydrogenations to form
dihydrogen complexes remains scarce. Calorimetric studies have reported solution-state
binding enthalpies of
Δ
H
∘
= −41.8 and −46.9 kJ/mol for the complexes W(CO)
3
(PCy
3
)
2
and
W(CO)
3
(P-i-Pr
3
)
2
in toluene, respectively.
12, 13
A similiar study in THF, attempting to
develop relationships between the group 6 metals in the complexes M(CO)(PCy
3
)
2
(M=Cr,
Mo, W), found
Δ
H
∘
between −27.2 kJ/mol and −41.8 kJ/mol, and entropy values
Δ
S
∘
between −100 and −110 J/mol-K..
14
Solid-state measurements are limited and show
deviations from solution behavior, with one study giving
Δ
H
∘
= −13.22 kJ/mol and
Δ
S
∘
=
−9.62 J/mol-K for hydrogen absorption over the complex
15
[Ir(cod)(PPh
3
)
2
]SbF
6
,
representing a significant reduction in binding strength and an unexpected increase in the
entropy of the bound state. While most of the data are consistent with values obtained from
hydrogen storage materials, the current measurements represent a wide range of metals and
ligands providing different chemical properties that, apart from the systematic study
performed by Gonzalez, et al. for the group 6 complexes, do not provide chemical trends to
aid in the design of new materials.
Difficulties in obtaining systematic thermodynamic data for dihydrogen complexes arise
from their inherent stability, with the equilibrium pressures of most known materials falling
outside of acceptable ranges for traditional chemistry techniques. To help resolve these
difficulties and enable the generation of systematic thermodynamic data, we used the
Sieverts method to obtain experimental isotherm measurements on the interaction of
hydrogen gas with the dihydrogen complex [Mn(CO)dppe
2
][BArF
24
] (dppe = 1,2-
bis(diphenylphosphino)ethane, BArF
24
= tetrakis-(3,5-trifluoromethyl)phenylborate). In
addition, we report electronic structure calculations on the hydrogenation of the fragments
[M(CO)dppe
2
]
+
(M=Mn,Tc,Re) to examine trends in the binding energy within the group 7
metals. We interpret our results in terms of the solid-state binding mechanism for hydrogen
in these materials, and show a relatively rapid and facile means to quantitatively evaluate
thermodynamic properties and establish chemical trends that are useful for materials design.
Experimental
Unless otherwise stated, all reactions were performed under a dinitrogen atmosphere using
either a controlled atmosphere glovebox or Schlenck line techniques. Manganese
pentacarbonyl bromide, magnesium metal and sodium tetrafluoroborate were purchased
from Alfa-Aesar and used without further purification. 1,2-bis(diphenylphosphino)ethane
was purchased from Strem Chemicals and used without further purification. 3,5-
bis(trifluoromethyl)bromobenzene was purchased from Sigma-Aldrich and was degassed
using three freeze-pump-thaw cycles and dried over activated alumina before use. Research-
grade gases were purchased from Matheson and used directly. All solvents were dried and
deoxygenated by purging with dry dinitrogen gas for 15 minutes before passing through
packed columns of activated alumina and activated copper. Mass spectroscopy of off-
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gassing products was performed using a Stanford Research Systems RGA-200 residual gas
analyzer with observable pressure ranges from 10
−8
to 10
−5
torr. After synthesis, materials
were stored under dry argon in an atmosphere-controlled glovebox until used for sorption
measurements.
Solution-state NMR spectra were recorded on a Varian 300MHz instrument with
1
H shifts
reported relative to the residual solvent peak, and
31
P peaks reported relative to 85% H
3
PO
4
.
Deuterated NMR solvents were purchased from Cambridge Isotopes Laboratories.
Deuterated dichloromethane was vacuum distilled from a sodium/benzophenone solution
before use. Deuterated acetone was vacuum distilled twice from CaSO
4
and stored over 4A
molecular sieves before use.
Preparation of Na[BArF
24
]
This procedure was a modification of one in the literature.
17
3,5-
bis(trifluoromethyl)bromobenzene (5 mL, 8.55 grams, 2.918 mmol) was added to a
suspension of anhydrous NaBF
4
(0.8173 grams, 7.446 mmol) and magnesium metal (5.028
grams, 206.87 mmol, excess) in 150 mL of diethyl ether under a nitrogen atmosphere,
causing the solution to turn olive-green. The suspension was stirred for 24 hours, producing
an orange solution with white precipitate. The solution was exposed to air and quenched
with 20 mL of saturated aqueous sodium carbonate solution, followed by filtration over a
coarse frit to remove precipitated salt. The ether layer was removed, and the aqueous layer
was washed with 50 mL of fresh ether. The ether layers were combined, dried over sodium
sulfate and filtered. The solvent was removed
in vacuo
and the resulting residue was
dissolved in benzene and distilled in a Dean-Stark apparatus under nitrogen for three hours
to remove residual water. The benzene was then removed
in vacuo
, and the residue was
washed with dichloromethane and filtered to produce the product as an off-white
powder.
1
H NMR (300MHz) in d
6
-acetone:
δ
7.67 (s, 4H); 7.79 (t, 8H).
Preparation of
fac
-MnBr(CO)
3
dppe
This procedure was a modification of one in the literature.
18
A solution of the phosphine
ligand 1,2-bis(diphenylphosphino)ethane (dppe, 3.5326 grams, 8.866 mmol) in 100 mL
benzene was added to crystalline Mn(CO)
5
Br (1.2180 grams, 4.430 mmol) in a 250 mL
quartz roundbottom and allowed to stir for one hour, causing Mn(CO)
5
Br to slowly dissolve
and release CO gas to produce a yellow solution containing both the remaining free ligand
and the product. The compound was observed by NMR in CD
2
Cl
2
but not isolated.
1
H NMR
(300MHz) in CD
2
Cl
2
:
δ
2.80 (m, 4H); 3.16 (m, 4H); 7.41(m, 20H).
31
P NMR (300MHz) in
CD
2
Cl
2
:
δ
69.6 (s).
Preparation of
trans
-MnBr(CO)dppe
2
This procedure was a modification of one in the literature.
18
The solution of
fac
-
MnBr(CO)
3
dppe and free ligand in benzene from the previous synthesis was irradiated with
UV light for 2 hours under an evacuated headspace and strong stirring in a 250 mL fused
quartz roundbottom, causing the precipitation of 0.8 grams of red-orange solid that adhered
to the roundbottom walls and blocked further irradiation. The solvent was removed
in vacuo
,
and the resulting residue was washed with fresh benzene and filtered to obtain the product as
an orange powder. The filtrate was collected and the procedure was repeated until no
additional precipitate was formed. Total yield 3.365 grams (3.506 mmol, 79.1%) on
manganese.
1
H NMR (300MHz) in CD
2
Cl
2
:
δ
2.52 (m, 4H); 2.80 (m, 4H); 7.04 (t, 16H);
7.10 (m, 8H); 7.22 (quart., 8H), 7.32 (m, 8H).
31
P NMR (300MHz) in CD
2
Cl
2
:
δ
72.1.
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Preparation of [Mn(CO)dppe
2
][BArF
24
]
This procedure was a modification of one in the literature.
19
Solid Na[BArF
24
] (3.059
grams, 3.452 mmol) was mixed with solid trans-MnBr(CO)dppe
2
(3.266 grams, 3.403
mmol) in a 100 mL roundbottom flask and 50 mL of dichloromethane was added to the solid
mixture, immediately forming an emerald green solution that was stirred for one hour. After
one hour the solution was filtered over celite to remove excess insoluble Na[BArF
24
] and
bromide salts. The filtrate was collected and the solvent removed
in vacuo
, causing a color
change from emerald green to aquamarine blue. The residue was redissolved in toluene,
producing a green solution, and filtered to remove any remaining bromide salts. The filtrate
was collected and the solvent removed
in vacuo
, producing a blue-green powder containing
mixed adducts and toluene within the structure, as described by King et. al.
19
Removal of
adducts and toluene was performed under high vacuum conditions at 373K until no
additional toluene was observable by residual gas mass spectroscopy, producing the five-
coordinate product in 90% purity.
1
H NMR (300MHz) in CD
2
Cl
2
under argon atmosphere:
δ
2.78 (s, 8H); 6.20 (s, broad, 8H); 6.95-7.40 (m, 32H); 7.56 (s, 4H); 7.73 (s, 8H).
31
P NMR
(300MHz) in CD
2
Cl
2
under argon atmosphere:
δ
82.47 (s, broad).
Reaction of [Mn(CO)dppe
2
][BArF
24
] with H
2
for NMR spectroscopy
Confirmation of the dihydrogen absorption ability of [Mn(CO)dppe
2
][BArF
24
] was
performed by solution NMR. CD
2
Cl
2
was vacuum transferred into a J. Young tube
containing solid [Mn(CO)dppe
2
][BArF
24
], forming a deep blue solution. One atmosphere of
hydrogen gas was introduced into the tube, and upon shaking the solution rapidly turned
yellow.
1
H NMR (300MHz) in CD
2
Cl
2
:
δ
−7.22 (s, broad, 1.5H); 2.24 (s, 4H); 2.52 (s, 4H);
6.88-7.44 (m, broad, 40H); 7.56 (s, 4H); 7.73 (s, 8H).
31
P NMR (300MHz) in CD
2
Cl
2
:
δ
85.2 (s, broad).
H
2
absorption measurements
Iterative isotherm and kinetic rate measurements were performed on 2.9 grams of degassed
[Mn(CO)dppe
2
] [BArF
24
] using a custom-built Sieverts apparatus, described in detail
previously.
20
Samples were loaded into a 14 mL stainless steel reactor under an argon
atmosphere and sealed before transfer to the instrument. Swagelok VCR copper filter
gaskets with 2 μm stainless steel filters were used to confine the powdered sample to the
reactor during measurements. After transferring the reactor to the assembly, samples were
allowed to pump down overnight to 3.1×10
−7
torr at the pump inlet before measurements
were performed. Pressure on the reactor and manifold during isotherm measurements was
measured using an MKS model 120AA-25000RBJ capacitance transducer with a resolution
of 0.25 torr in the range of interest. Higher pressures during kinetic measurements were
recorded using an MKS model 870B33PCD2GC1 capacitance transducer with a 0–3000 psi
range. The time resolution of the instrument was 1500 ms during kinetic measurements.
Manifold and reactor volumes were calibrated prior to absorption measurements through
iterative expansion from a calibrated volume with argon gas. Isotherms and kinetic rate
measurements were recorded by expanding an equilibrated amount of hydrogen gas from the
manifold into the reactor, and the quantity of hydrogen absorbed was determined by ideal
gas mole balance between the two volumes after equilibration. This procedure was repeated
until no additional hydrogen uptake was observed. After completion of the measurement, the
reactor and manifold were evacuated to 10
−7
torr before heating to the next temperature.
Computations
Electronic structure calculations were performed for the singlet state of the cationic
fragments [M(
η
2
-H
2
)(CO)dppe
2
]
+
and [M(CO)dppe
2
]
+
(M = Mn, Tc, Re), and the hydrogen
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molecule using the GAMESS-US software package.
21
Geometry optimizations for the
organometallic fragments were performed using fully spin-restricted (RHF) density
functional theory calculations, with the B3LYP exchange-correlation functional
22, 23
and the
LANL2DZ basis set.
24, 25, 26, 27
An additional
p
polarization shell for light atoms and
d
polarization shell for heavier atoms was added to augment the basis set. Effective core
potentials
25, 26, 27
representing the core 10 electrons for manganese and phosphorous atoms,
the core 28 electrons for technetium and the core 60 electrons for rhenium were used. SCF
convergence was set to 5.0 × 10
−6
for all calculations. Geometry optimizations were
performed to a tolerance of 10
−4
au.
The initial structure for [M(
η
2
-H
2
)(CO)dppe
2
]
+
was taken from structural data reported
previously for the manganese compounds by King, et al.
28
Two structures representing both
an “open” geometry, in which the hydrogen molecule was removed from the H
2
adduct
geometry, and the rearranged “agostic” geometry reported by King et al., in which ortho
hydrogens from phenyl groups on the ligands form long-range bonds with the open
coordination site, were used for [M(CO)dppe
2
]
+
. Differences between the relaxed structures
obtained from calculations and the reported experimental geometries for the manganese
complexes were unremarkable, beyond a contraction of all bond lengths within the structure
attributable to thermal effects. The H-H bond in each dihydrogen complex was found to
align parallel to the phosphorus-metal-phosphorus axis, as shown by the relaxed structure
for [Mn(CO)(
η
2
-H
2
)dppe
2
]
+
appearing in Figure 1.
Ab-initio ground state electronic energies were calculated using the spin-component scaled
Møller-Plesset second order perturbation
29
(SCS-MP2) scheme with the LANL2DZ-ECP
basis set from the optimized geometries found from DFT calculations, which has been
shown by Tomàs et al. to lead to accurate calculations for dihydrogen complexes.
30, 31
To
obtain thermal corrections to the energy and normal mode frequencies, the Hessian matrix
for each fragment was calculated at the B3LYP/LANL2DZ-ECP level of theory using
seminumerical methods, with contributions from positive and negative displacements of
0.01 bohr. Vibrational analysis in the rigid rotor approximation was performed to obtain
partition functions and normal modes of the fragments,
q
tot
, at 1 atm pressure. A scaling
factor of 0.96 was used for the vibrational analysis to correct known errors in the LANL2DZ
basis set, consistent with common practice.
32
The chemical potential of hydrogen gas was calculated from the partition function for the
hydrogen molecule obtained from GAMESS, through the relationship:
(1)
where
k
is Boltzmann’s constant,
T
is the temperature in Kelvin,
P
is the pressure of the
system, and
P
∘
is the standard pressure of the system, taken to be 1 atm. Rotational
degeneracy for the hydrogen molecule is included in the calculated partition function from
the GAMESS software.
The corrected energy,
E
, for each fragment was obtained as the sum of the ground-state
energy,
ε
0
, and the thermal correction to the energy obtained from vibrational analysis,
ε
corr
(
T
), which contains contributions from translational, vibrational, and rotational motions
of the molecule. The binding energy of the hydrogen molecule to the organometallic site
was calculated from the corrected energies as:
(2)
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where the subscripts M-H
2
, H
2
, and M represent the organometallic adduct fragment,
hydrogen gas, and the bare organometallic fragment, respectively.
Results and Discussion
Experimental Results
Absorption isotherms were measured for H
2
onto [Mn(CO)dppe
2
][BArF
24
] at temperatures
of 313K, 333K, 343K, 353K, 363K, and 373K, and are shown in Figure 2. Reversible
absorption capacity for all temperatures was approximately 0.35 H
2
molecules per
manganese center. No irreversible absorption was observed. This capacity value was
consistent throughout measurements at all temperatures, and was stable after multiple
absorption/desorption cycles performed during the course of isotherm and kinetic
measurements. These properties are consistent with previous reports for solid state
dihydrogen materials.
15
Initial rate kinetics measurements were performed at 298K and 318K to determine the
dependence of the absorption rate on pressure and quantity absorbed. The results for 318K
appear in Figure 3. The rate of change of the pressure was determined to be linearly
dependent on the pressure and the remaining capacity, such that:
where
θ
is the fraction of the reversible absorption capacity absorbed, and
k
is the rate
constant. Rate constants for 298K and 318K were 0.3090 s
−1
and 0.3116 s
−1
, respectively.
The Arrhenius activation energy obtained from these values is
E
a
= 330 J/mol, indicating a
very low activation barrier to absorption.
The isotherms presented in Figure 2 do not demonstrate a maximum like with physisorptive
materials, but rather achieve a stable plateau at 0.35 H
2
molecules per manganese. This
behavior is particularly evident in the isotherm at 313K. The existence of the stable plateau
in the experimental isotherms is consistent with total absorption
33
and indicates that
hydrogen absorbs into the bulk material instead of adsorbing onto the surface. However, the
absorption rate is comparable to physisorption materials, despite no additional processing
used to increase the surface area of the solid or the exposure of manganese centers to the
gas. This rapid absorption is likely due to the loose packing of the bulky organic ligands in
the solid, which allows the small hydrogen molecule to diffuse rapidly through the
structure.
28
The rapid kinetics and high reversibility observed in the absorption process suggest a site-
binding mechanism for the binding interaction of H
2
with solid [Mn(CO)dppe
2
][BArF
24
]
that is similar to physisorptive materials. In organometallic dihydrogen complexes, the
binding orientation of the ligands is considered fixed by the atomic orbitals of the metal
center, producing distinct binding sites for each ligand at the metal center. The isolation of
the metal centers by the organic constituents ensures both non-interacting sites and chemical
uniformity, suggesting the binding interaction at each site is isoenergetic. With this
interpretation of the coordination site, we investigated the binding behavior by fitting the
experimental isotherms to the Langmuir model. The Langmuir isotherm model assumes an
established equilibrium between a mobile phase of guest molecules and fixed sites capable
of binding a single molecule, with homogeneous, non-interacting, and isoenergetic
interactions, representing an appropriate description of the organometallic coordination site
if the behavior is similar to other site-binding mechanisms.
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For the assumed ideal gas reaction:
(3)
in which a single hydrogen molecule binds to the open coordination site on the metal,
represented by
M
, the Langmuir isotherm is given by:
(4)
where
n
is the number of bound hydrogen molecules,
N
is the total number of active binding
sites,
P
is the pressure of the gas in atmospheres,
R
is the universal gas constant,
T
is the
system temperature in Kelvin, and K
eq
is the equilibrium constant for Equation 3.
Langmuir fits to the experimental data are shown as the solid lines in Figure 2. The fit for
313K was obtained by varying both the total number of active binding sites,
N
, and
α
as
fitting parameters. A value of 0.344 H
2
per manganese center was found for
N
at 313K, and
was held constant for the fits at all other temperatures. The values for
K
eq
derived from the
fitted values for
α
and the R
2
values of the fits appear in Table 1. As can be seen from the
figure and the R
2
values, the Langmuir model very accurately describes hydrogen absorption
by the manganese complex, indicating that the open coordination sites within
[Mn(CO)dppe
2
][BArF
24
] interact with hydrogen gas through a site-binding mechanism.
The standard enthalpy and entropy of the absorption interaction are readily obtained from
the values of the equilibrium constant in Equation 4 through the van’t Hoff equation:
(5)
where
Δ
S
∘
and
Δ
H
∘
are the entropy and enthalpy of the absorption reaction, as defined by
Equation 3, at standard conditions of one atmosphere pressure and 298K. A van’t Hoff plot
of the equilibrium constants from the Langmuir fits appears in Figure 4. Linear regression
gives values of
Δ
H
∘
= −52.2 kJ/mol and
Δ
S
∘
= −99.6 J/mol-K for hydrogen absorption over
[Mn(CO)dppe
2
][BArF
24
]. This enthalpy is similar to experimental values found by
Gonzalez and Hoff
14
for hydrogen binding to the group 6 complexes M(CO)
3
(PCy
3
)
2
(M =
Cr, Mo, W) by solution calorimetry, and represents an interaction of comparable strength to
chemisorption seen in the formation of metal hydrides. In addition, a significant increase in
the absorption entropy from the standard
34
−131 J/mol-K typical for hydrogen storage
materials is observed. The higher enthalpy and entropy values allow [Mn(CO)dppe
2
]
[BArF
24
] to bind hydrogen effectively near room temperature while exhibiting the rapid
absorption kinetics and long cycle life characteristic of physisorption materials, a
combination of properties that are highly favorable for hydrogen storage applications.
The kinetic absorption behavior is consistent with observations made by Gonzalez, et al.
12
that the kinetics of absorption and dissociation of H
2
with W(CO)
3
(PCy
3
)
2
in solution were
several times faster than oxidative (dissociative) addition, which also supports the site-
binding model. The solution results also imply that the site-binding mechanism is not
limited to the solid state. Qualitative assessments of affinities based on competitive ligand
binding would thus require control of the local hydrogen concentration, particularly in
solution state measurements where the concentration of dissolved hydrogen depends on the
solvent used. This additional aspect needs to be considered before using such assessments to
disqualify materials as potential candidates.
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Computational Results
The physics of the Langmuir model are well defined at the molecular scale and calculation
of the isotherms from simulated binding energies is straightforward, allowing for direct
comparison between experimental and computational results to establish the accuracy of
computational methods. From statistical mechanics, the fractional coverage of absorbed
molecules at the binding sites in the Langmuir model is:
(6)
where
β
= (
kT
)
−1
,
W
is the grand potential of the bound system,
〈
n
〉
represents the ensemble
average number of absorbed molecules, and
q
s
e
β
(
μ
gas
−
Δ
E
)
is the partition function of the
molecular species at the binding site. The pressure dependence of the fractional occupancy
is expressed through the chemical potential of the gas, as shown in Equation 1. The values
of
ε
corr
(
T
) obtained from GAMESS contain the contributions to the partition function from
the normal modes of hydrogen at the binding site. However, because symmetry is calculated
based on the entire organometallic fragment, the output from GAMESS does not treat
rotational symmetry of the hydrogen molecule appropriately, and the variable
q
s
in Equation
6 is used as a correction term to account for degeneracy in the rotational mode.
Carbonyl stretch frequencies obtained from the vibrational analysis were found to be
1824.32, 1820.56, and 1849.69 cm
−1
for the open configuration of [Mn(CO)dppe
2
]
+
, the
agostic configuration, and [Mn(CO)(
η
2
-H
2
)dppe
2
]
+
, respectively, in good agreement with
the literature values.
19, 28
The standard Gibbs free energy for the transformation from the
open configuration to the agnostic configuration was also calculated from the vibrational
analysis, and was found to be
Δ
G
∘
= −39.6 kJ/mol, similar to values found for other agostic
interactions.
12
Six primary normal modes for dihydrogen motion at the binding site were defined as the
modes having the largest magnitude eigenvectors on the dihydrogen molecule as obtained
from the output of vibrational analysis on each adduct fragment. For the manganese
complex, these modes correlated well with literature values obtained from inelastic neutron
scattering.
28
In all three cases only the rotational mode, with frequencies of 196.79 cm
−1
,
269.2 cm
−1
, and 556.7 cm
−1
for Mn, Tc, and Re, respectively, was found to be significantly
populated at the temperatures of interest. The symmetry of the rotational mode was
determined from analysis of the components of the eigenvector associated with the atoms of
the hydrogen molecule, and the mode was defined as symmetric if the x,y, and z
components were opposite in sign and had differences in their magnitude of less than 0.1
millidyne/angstrom. Within this definition, dihydrogen rotational modes in the manganese
and technetium adducts were found to be symmetric, while rotation in the rhenium adduct
was asymmetric with respect to the center of mass of the hydrogen molecule. To correct for
the degeneracy of the symmetric modes in the manganese and technetium adducts,
q
s
was
defined such that:
(7)
where
Θ
v
=
h
ν
/
k
is the characteristic mode temperature obtained from the rotational mode
frequency,
ν
. This correction removes half of the mode contribution from the total partition
function, accounting for the reduction in states due to symmetric rotation. For rhenium, a
value of
q
s
=1 was used, since no degeneracy exists in the asymmetric rotation mode.
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Simulated equilibrium constants and standard binding energies for absorption onto both the
open and agostic configurations appear in Table 1 and Table 2, and simulated isotherms for
the manganese fragment in the open geometry appear as solid lines against the experimental
data in Figure 5. Simulated isotherms for the open geometry are nearly identical to fits for
the experimental data, indicating that the open geometry sites are the active sites for the
absorption reaction. The simulated enthalpy and entropy values, calculated from Equations
4, 5, and 6 are
Δ
H
∘
= −53.5 kJ/mol and
Δ
S
∘
= −103.8 J/mol-K, demonstrating that both
pressure-composition behavior and thermodynamic properties can be accurately simulated
through electronic structure calculations using the B3LYP/LANL2DZ level of theory for
geometry optimization and vibrational analysis, and the MP2/LANL2DZ level of theory for
the electronic energy used to obtain the binding energy.
Calculations for absorption onto the agostic geometry validate the observation by King et
al.
28
that direct hydrogenation of the agostic manganese complex in the solid state fails
under one atmosphere of hydrogen pressure. Evaluation of Equation 6 for the agostic
complex at one atmosphere hydrogen pressure and 313K gives a fractional coverage of
1.443 × 10
−5
, indicating that molecules in the agostic configuration do not contribute to
hydrogen binding in the experimental results. The experimental result of 0.344 for the
fraction of active manganese centers evidently represents the fraction of the total manganese
centers in the open configuration. This number was maintained throughout all temperatures
studied, indicating that no exchange between the agostic and open configurations occurs in
the solid, despite the favorable value of the free energy for the agostic complex found from
calculation. Solution NMR results reported by King, et al. for the same compound
19
in
CH
2
Cl
2
found a similar 37% of the manganese centers were active for N
2
absorption at
room temperature. It is likely that the precipitation of the N
2
adduct and subsequent release
of the N
2
molecule produce the open configuration in the solid state necessary for H
2
absorption. Once precipitated, the thermal stability of the active site fraction suggests that
kinetic stabilization in the solid state prevents exchange between the two configurations.
This stabilization would prevent hydrogen absorption over agostic complexes in the solid
state even if favorable thermodynamics were predicted, due to the inability of the ligand to
leave the binding site.
With the accuracy of the calculation method established, standard energies, enthalpies, and
entropies were obtained from calculation for hydrogen absorption over [Tc(CO)dppe
2
]
+
and
[Re(CO)dppe
2
]
+
. These values appear in Table 2. The resulting binding enthalpies for the
open configuration are similar in strength to findings for other dihydrogen complexes. The
trends in the binding enthalpies and entropies in the group 7 metals from these simulations
are in good agreement with the solution calorimetry results for group 6 metals reported by
Gonzalez and Hoff,
14
with the enthalpy increasing as 5d > 3d > 4d. Quantitatively, the
energetic difference between 3d and 4d metals matches with the value found for the group 6
metals, despite the differences in group, molecular charge, and chemical environment. A
slightly lower energetic difference of 4 kJ/mol between manganese and rhenium complexes
was found relative to the reported 11 kJ/mol difference between chromium and molybdenum
complexes. The good quantitative agreement implies a consistent trend in the
thermodynamic values within the transition metals. Unfortunately, no direct cause for this
relationship was evident from the calculations. The relationships are expected to rely upon
the relative
σ
- and
π
- donation ability at the metal center, a complex property dependent
upon the metal-ligand interactions and geometry.
16
Although several studies have examined
the governing principles behind these properties, their exact nature remains
uncertain.
35, 36, 37, 38
The individual contribution of excited rotational modes to the site entropy can be calculated
from Equation 7 through the expression:
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(8)
Values for the rotational entropy of the bound state at 298K and 373K for each of the
complexes appear in Table 2. Since only the bound state is considered, the value is
equivalent for both the open and agostic configurations. The softer rotational mode in the
manganese adduct leads to increased entropic contributions at all temperatures, and an
increased dependence on temperature relative to the other two complexes. The near
equivalence of the standard entropies of technetium and manganese, despite a much lower
contribution from rotation of the hydrogen molecule in technetium, is due to increased
contributions from other modes within the organometallic complex. The asymmetry of the
rotation in the rhenium complex leads to higher contributions to the entropy than in the
technetium adduct, despite the high stiffness in the mode. The much stiffer, asymmetric
rotational mode in the rhenium complex, along with the higher binding enthalpy, suggest
that the H
2
molecule may have undergone oxidative addition and dissociated to form the
dihydride complex. However, because both hydrogen atoms remain bound to the same metal
center, the assumptions of the Langmuir isotherm are not violated. Effects from this
transition are modeled in the Langmuir isotherm as a contribution to the site binding energy.
This allows the absorption enthalpy to be modeled accurately by the Langmuir isotherm in
cases of oxidative addition, but does not allow determination of whether the compound is a
dihydrogen complex or a dihydride.
Conclusions
We report experimental and computational results on the properties of dihydrogen
complexes, and interpretations with the Langmuir isotherm model. Langmuir fits for the
absorption of hydrogen onto [Mn(CO)dppe
2
][BArF
24
] to form the dihydrogen complex
[Mn(
η
2
-H
2
)(CO)dppe
2
][BArF
24
] were found to accurately describe the experimental
pressure-composition behavior, giving an enthalpy and entropy for the binding interaction of
Δ
H
∘
= −52.2 kJ/mol and
Δ
S
∘
= −99.6 J/mol-K, in general agreement with previous
observations of model Kubas complexes. While the complexes within this study do not meet
gravimetric or volumetric capacity expectations for vehicular hydrogen storage, they exhibit
a unique binding motif capable of storing hydrogen at desirable temperatures and pressures
with kinetics rivaling physisorption materials. The combination of these properties holds
strong promise for the development of lower weight organometallic storage materials for
applications.
Computationally derived isotherms using a mixed calculation scheme of B3LYP/
LANL2DZ-ECP for geometry optimization and vibrational analysis and MP2/LANL2DZ-
ECP for total energy were also found to accurately describe the experimental behavior of the
manganese complex and have provided additional insight into the configuration of the active
binding site and the individual contributions from configurational and rotational entropy to
the binding properties. Calculations for substitution of the metal center with other group 7
metals found similar trends in the thermodynamic properties to experimental reports for
group 6 metals, with increasing binding enthalpy such that 5d > 3d > 4d, suggesting an
overall trend in properties for transition metals moving down the periodic table.
Acknowledgments
The authors wish to thank David Vandervelde of Caltech for his assistance with NMR experiments, and Joseph
Reiter and Jason Zan at the Jet Propulsion Laboratory in Pasadena, CA for their assistance in planning
thermodynamic measurements. Sieverts instrument work was performed at the Jet Propulsion Laboratory, which is
operated by the California Institute of Technology under contract with NASA. The Caltech NMR facility is
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partially supported by the National Institutes of Health through grant number NIH RR027690. We are grateful to
the Resnick Sustainability Institute for financial support.
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Figure 1.
Relaxed structure of the [Mn(
η
2
-H
2
)(CO)dppe
2
]
+
cation, showing the hydrogen molecule
aligned along the P-Mn-P axis. Alkyl and aryl hydrogens have been removed for clarity.
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Figure 2.
Absorption isotherms for hydrogen gas onto [Mn(CO)dppe
2
][BArF
24
]. Solid lines are
Langmuir isotherm fits to the data.
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