Reactions of diborane with ammonia and ammonia borane: catalytic effects for multiple pathways for hydrogen release.
ABSTRACT High-level electronic structure calculations have been used to construct portions of the potential energy surfaces related to the reaction of diborane with ammonia and ammonia borane (B2H6 + NH3 and B2H6 + BH3NH3)to probe the molecular mechanism of H2 release. Geometries of stationary points were optimized at the MP2/aug-cc-pVTZ level. Total energies were computed at the coupled-cluster CCSD(T) theory level with the correlation-consistent basis sets. The results show a wide range of reaction pathways for H2 elimination. The initial interaction of B2H6 + NH3 leads to a weak preassociation complex, from which a B-H-B bridge bond is broken giving rise to a more stable H3BHBH2NH3 adduct. This intermediate, which is also formed from BH3NH3 + BH3, is connected with at least six transition states for H2 release with energies 18-93 kal/mol above the separated reactants. The lowest-lying transition state is a six-member cycle, in which BH3exerts a bifunctional catalytic effect accelerating H2 generation within a B-H-H-N framework. Diborane also induces a catalytic effect for H2 elimination from BH3NH3 via a three-step pathway with cyclic transition states. Following conformational changes, the rate-determining transition state for H2 release is approximately 27 kcal/mol above the B2H6 + BH3NH3 reactants, as compared with an energy barrier of approximately 37 kcal/mol for H2 release from BH3NH3. The behavior of two separated BH3 molecules is more complex and involves multiple reaction pathways. Channels from diborane or borane initially converge to a complex comprising the H3BHBH2NH3adduct plus BH3. The interaction of free BH3 with the BH3 moiety of BH3NH3 via a six-member transition state with diborane type of bonding leads to a lower-energy transition state. The corresponding energy barrier is approximately 8 kcal/mol, relative to the reference point H3BHBH2NH3 adduct + BH3. These transition states are 27-36 kcal/mol above BH3NH3 + B2H6, but 1-9 kcal/mol below the separated reactants BH3NH3 + 2 BH3. Upon chemical activation of B2H6 by forming 2 BH3, there should be sufficient internal energy to undergo spontaneous H2 release. Proceeding in the opposite direction, the H2 regeneration of the products of the B2H6 + BH3NH3reaction should be a feasible process under mild thermal conditions.
- SourceAvailable from: Minh Tho Nguyen[Show abstract] [Hide abstract]
ABSTRACT: The reactivity of hydrazine in the presence of diborane has been investigated using ab initio quantum chemical computations (MP2 and CCSD(T) methods with the aug-cc-pVTZ basis set). Portions of the relevant potential energy surface were constructed to probe the formation mechanism of the hydrazine diborane (BH(3)BH(3)NH(2)NH(2)) and hydrazine bisborane (BH(3)NH(2)NH(2)BH(3)). The differences between both adducts are established. The release of hydrogen molecules from hydrazine bisborane adducts has also been characterized. Our results suggest that the BH(3)NH(2)NH(2)BH(3) adduct, which has been prepared experimentally, is formed from the starting reactants hydrazine + diborane. The observed adduct is produced by a transfer of a BH(3) group from BH(3)BH(3)NH(2)NH(2) rather than by the direct attachment of a separate BH(3) group, generated by predissociation of diborane, to BH(3)NH(2)NH(2).Physical Chemistry Chemical Physics 03/2011; 13(14):6649-56. · 4.20 Impact Factor
Reactions of Diborane with Ammonia and Ammonia Borane: Catalytic Effects for Multiple
Pathways for Hydrogen Release
Vinh Son Nguyen,‡Myrna H. Matus,†Minh Tho Nguyen,*,†,‡and David A. Dixon*,†
Department of Chemistry, The UniVersity of Alabama, Shelby Hall, Tuscaloosa, Alabama 35487-0336, and
Department of Chemistry, UniVersity of LeuVen, B-3001 LeuVen, Belgium
ReceiVed: May 28, 2008; ReVised Manuscript ReceiVed: July 16, 2008
High-level electronic structure calculations have been used to construct portions of the potential energy surfaces
related to the reaction of diborane with ammonia and ammonia borane (B2H6+ NH3and B2H6+ BH3NH3)
to probe the molecular mechanism of H2release. Geometries of stationary points were optimized at the MP2/
aug-cc-pVTZ level. Total energies were computed at the coupled-cluster CCSD(T) theory level with the
correlation-consistent basis sets. The results show a wide range of reaction pathways for H2elimination. The
initial interaction of B2H6+ NH3leads to a weak preassociation complex, from which a B-H-B bridge
bond is broken giving rise to a more stable H3BHBH2NH3adduct. This intermediate, which is also formed
from BH3NH3 + BH3, is connected with at least six transition states for H2 release with energies 18-93
kcal/mol above the separated reactants. The lowest-lying transition state is a six-member cycle, in which BH3
exerts a bifunctional catalytic effect accelerating H2generation within a B-H-H-N framework. Diborane
also induces a catalytic effect for H2elimination from BH3NH3via a three-step pathway with cyclic transition
states. Following conformational changes, the rate-determining transition state for H2release is ∼27 kcal/
mol above the B2H6+ BH3NH3reactants, as compared with an energy barrier of ∼37 kcal/mol for H2release
from BH3NH3. The behavior of two separated BH3molecules is more complex and involves multiple reaction
pathways. Channels from diborane or borane initially converge to a complex comprising the H3BHBH2NH3
adduct plus BH3. The interaction of free BH3with the BH3moiety of BH3NH3via a six-member transition
state with diborane type of bonding leads to a lower-energy transition state. The corresponding energy barrier
is ∼8 kcal/mol, relative to the reference point H3BHBH2NH3adduct + BH3. These transition states are 27-36
kcal/mol above BH3NH3+ B2H6, but 1-9 kcal/mol below the separated reactants BH3NH3+ 2 BH3. Upon
chemical activation of B2H6by forming 2 BH3, there should be sufficient internal energy to undergo spontaneous
H2release. Proceeding in the opposite direction, the H2regeneration of the products of the B2H6+ BH3NH3
reaction should be a feasible process under mild thermal conditions.
Diborane (B2H6, db) dissociates slowly at room temperature
in the absence of moisture or lubricants.1It can be conveniently
prepared in pure form and is used as a reagent for a variety of
syntheses. The presence of the bridge B-H-B bond in db
constituted the basis for a novel rationalization and theory for
the molecular structure of the boranes and carboranes.2Stock
and Kuss3reported in 1923 the reaction of db with ammonia,
in which db was shown to take up two molecules of ammonia
to form a salt. On heating the resulting “diammoniate of
diborane” salt (dadb) in a closed tube up to 200 °C, a
considerable amount of B3N3H6was produced.4The latter was
confirmed to have a six-member ring structure by electron
diffraction5(this cyclic compound analogous to benzene was
first named “triborine triamine”6and later named “borazine”).
The salt was initially proposed to be [B2H42-][NH4+]2, whose
solution was found to have a low electric conductivity.1,7
Subsequently, Schlesinger and co-workers8interpreted the
reaction as an initial addition of borane (BH3, B, formed from
bond cleavage of db) to ammonia (A), followed by other
reactions leading to a final product ion pair product
[H3BNH2BH3-][NH4+]. The other ion pair alternative [H3NBH2-
NH3+][BH4-] was not considered in these early reports. During
the course of the db + A reaction, small quantities of a new
volatile compound having the molecular formula (B2H7N) were
identified,8and the latter compound was subsequently obtained
in high yield by passing an excess of db over the salt.9The
(B2H7N) compound formally corresponds to the product of an
elimination of H2from the db + A reactants. The diborane plus
ammonia reaction remains one of the ways of preparing borazine
and is a precursor for the epitaxial growth of boron nitride thin
films on a silicon substrate by chemical vapor deposition
(CVD).10-12When a mixture of db and A was passed through
a heated quartz tube in a gas-phase pyrolysis process, aminobo-
rane H2BNH2is formed and has been characterized by Sugie
et al.13using microwave spectroscopy (T ) 500 °C) and by
Carpenter and Ault14using matrix isolation infrared spectroscopy
(T ) 360 °C).
McKee15probed the molecular mechanism of this gas-phase
process by exploring a portion of the relevant potential energy
surface (PES) at the MP4/6-31+G(2d,p)//MP2(6-31G(d) + ZPE
level of ab initio molecular orbital theory (his energy profiles
are shown in Figure S1 of the Supporting Information). He found
the following: (i) the initial addition of ammonia to db yielding
a B2H6NH3 adduct is prohibited by a non-negligible energy
barrier; (ii) the adduct having a B-H-B bridged bond is the
common adduct of the barrier-free condensation of ammonia
* Corresponding authors. E-mail: firstname.lastname@example.org (D.A.D.).
‡University of Leuven.
†The University of Alabama.
J. Phys. Chem. A 2008, 112, 9946–9954
10.1021/jp804714r CCC: $40.75
2008 American Chemical Society
Published on Web 09/04/2008
borane (BH3NH3, ab) to BH3; (iii) the structure of the transition
state (TS) for H2 release from B2H6NH3 is that for the
unimolecular release of H2from BH3NH3(via 1,2-H2elimina-
tion) plus a destabilizing interaction with the second BH3
molecule; and (iv) there is an overall increase of 6.4 kcal/mol
for the energy barrier for H2 formation, relative to that in
BH3NH3. The rate-determining TS was calculated to be 42.4
kcal/mol above the separated db + A reactants.15This value is
above the calculated 0 K enthalpy for dissociation of B2H6into
two BH3molecules of 38.1 kcal/mol.16In subsequent studies,
Sakai17,18proposed a different mechanism for BH2NH2forma-
tion in the reaction db + A, which basically involves the same
initial adduct but instead undergoes H2 loss through a six-
member cyclic TS (Supporting Information Figure S2, ESI).
At the MP4/6-31G(d,p)//MP2/6-31G(d,p) + ZPE level, this
cyclic TS is ∼17 kcal/mol above the separated reactants. The
favorable HOMO-LUMO interaction was identified as a
stabilizing factor of the cyclic TS.17
We19,20have extensively investigated H2release starting from
the ab + B reactants, with coupled-cluster CCSD(T) theory
using the aug-cc-pVnZ (n ) D, T, Q) basis sets extrapolated to
the complete basis set limit. We confirmed the initial formation
of the monobridged B-H-B complex which is the same
complex formed from db + A. From this common complex
we found three different channels for H2 elimination, which
included the paths found earlier by McKee15and Sakai.17,18Our
high-accuracy results agreed with Sakai demonstrating the low-
energy pathway via the six-member cyclic TS, and we pointed
out the role of the second borane molecule, which acts as a
Lewis acid bifunctional catalyst for H2release from ab, and its
potential use in the perspective of chemical hydrogen storage
for transportation sector.21-26Ammonia was also found to
provide a catalytic effect on H2elimination from ab through a
cyclic six-member TS containing a N-H-H-B framework,19
but the overall reduction of the energy barrier by ammonia is
smaller, and the Lewis base NH3is a less effective catalyst than
the Lewis acid BH3. A substituted diborane intermediate has
been proposed to react with imidazole-borane in the formation
of the condensation polymer of imidazole-borane with loss of
When constructing the PES of the ab + B reaction,19we did
are somewhat incomplete, and a global view of the processes
in this important region of the PES is still missing. We have
further explored the regions of the PES for both the B2H6+
NH3and BH3NH3+ BH3channels using a uniform high level
of theory. Because borane can act as a Lewis acid catalyst for
H2formation, two questions are (i) can diborane act as such a
catalyst, and (ii) do two separated borane molecules reinforce
the catalytic effect? To address these questions, we have studied
the PES describing the reaction of ammonia borane with
diborane BH3NH3 + B2H6, and ammonia borane with two
borane molecules BH3NH3+ 2BH3.
The calculations were performed by using the Gaussian-0328
and MOLPRO29suites of programs. The geometry parameters
were initially optimized using second-order perturbation theory
(MP2)30in conjunction with the correlation-consistent aug-cc-
pVDZ basis set.31The character of each stationary point was
determined to be an equilibrium structure or a first-order saddle
point, by calculations of harmonic vibrational frequencies at
the same level. To ascertain the identity of each TS, intrinsic
reaction coordinate (IRC)32calculations were systematically
carried out at the MP2/aVDZ level. Geometry parameters of
relevant structures were then reoptimized using the MP2 method
with the larger aug-cc-pVTZ basis set (denoted hereafter as
aVnZ, with n ) D and T). The latter optimized geometries were
subsequently utilized for single-point electronic energies using
coupled-cluster CCSD(T) theory with the same basis set.33In
all of the MP2 and CCSD(T) calculations, the core orbitals were
kept frozen. The zero-point energies (ZPEs) were calculated by
using MP2/aVDZ harmonic vibrational frequencies scaled by
a factor of 0.9787 for boron hydrides (BnHm) and 0.9876 for
ammonia borane derivatives. The scaling factors were derived
from previous evaluations of the ZPEs for B2H616,34and
BH3NH3.25Due to the large number of structures considered,
the PESs considered were constructed using CCSD(T)/aVTZ
electronic energies with the appropriate ZPE corrections. In our
previous studies,19,20,35we have shown that the relative energies
obtained at this level of theory deviate by about (1.0 kcal/mol
with respect to the values obtained by CCSD(T)/CBS + ZPE
calculations, in which the coupled-cluster energies were ex-
trapolated to the complete basis set limit for these types of
reactions. A slightly larger deviation of 1.6 kcal/mol is found
for the dimerization energy of 2BH3f B2H6. Unless otherwise
noted, the relative energies quoted hereafter refer to the
CCSD(T)/aVTZ + ZPE results.
Results and Discussion
Table S1 of the Supporting Information lists the total and
ZPEs of all the stationary points considered and imaginary
frequencies of the TSs. Supporting Information Table S2 lists
the relative energies for the stationary points related to the B2H6
+ NH3 reaction for Figure 3, Table S3 of the Supporting
Information lists those for the BH3NH3 + B2H6 reaction for
Figure 6, and Table S4 of the Supporting Information lists those
for the BH3NH3+ B2H6reaction for Figure 7, all calculated at
the MP2/aVDZ, CCSD(T)/aVDZ, and CCSD(T)/aVTZ + ZPE
levels. Supporting Information Table S5 describes the Cartesian
coordinates of MP2/aVTZ optimized geometries, and Figures
S3 and S4 of the Supporting Information display the shape and
selected geometrical parameters of the structures not shown in
Reaction Pathways for H2Release from B2H6+ NH3(db
+ A). The structures of the most relevant stationary points, along
with selected MP2/aVTZ geometrical parameters, are given in
Figure 1. Selected MP2/aVTZ geometry parameters of db, dba-com,
ba-com, and transition state structure (TS), dba-ts. Bond distances in
are angstroms, and bond angles are in degrees.
Diborane Reactions with Ammonia and Ammonia Borane
J. Phys. Chem. A, Vol. 112, No. 40, 2008 9947
Figures 1 and 2. A few stationary points have already been given
in our previous study of the ab + B reaction,19so to facilitate
comparison, we keep, where possible, the same labeling as for
the structures already reported. These are the adduct ba-com
and some TSs connecting it to different products. Profiles for
relative energies along the reaction pathways are illustrated in
Starting from the reactants db + A, we find a weak interaction
between the N lone pair and the bridged B-H bond, which
leads to formation of the complex, dba-com. This first step is
barrier-free with a small complexation energy. There are small
changes in dba-com with respect to the geometry of db (Figure
1). The two B-H-B bridged bonds are slightly distorted, 0.006
Å, from db to dba-com. The B-B distance in dba-com shortens
relative with respect to that in db, by 0.012 Å. In comparison
with previous work,15,17,18dba-com represents a new complex
for the reaction of diborane with ammonia.
dba-com rearranges to ba-com via TS dba-ts, only 6.4 kcal/
mol above the reactants. dba-ts is the same as the TS reported
earlier by Sakai,17and his energy barrier computed at a lower
level differs by +3.0 kcal/mol from our value. The geometry
parameters (Figure 1) show that dba-ts is formed by a nearly
perpendicular approach of the NH3-nitrogen to a B atom of
diborane. The NH3group moves out of the plane containing
the bridged B-B/B-H bonds. The attack of N to one B-H
bridge bond breaks another bond from the opposite side and
opens the diborane framework forming a BH3-type fragment
(cf., Figure 1). IRC calculations in both the forward and reverse
directions from dba-ts confirm its connection to both complexes.
ba-com can be reached by free rotation of BH3around the B-H
axis. ba-com has been shown to be the common adduct of ab
and B.19We note that this complex contains only one bridge
B-H-B bond and the B-H distance differs by 0.4 Å from
that in diborane. ba-com is lower in energy than dba-com.
Starting from ba-com, H2elimination can occur through at
least six TSs associated with a range of energy barriers from
18 to 93 kcal/mol with respect to the reactants db + A. In our
previous work,19only three TSs were reported. On the basis of
the role of BH3group, we can divide the six TSs into three
different types. In the first type, BH3plays an active role in H2
formation by donating and receiving H atoms. These include
tsba-BN and tsba-BB discussed previously.19In Figure 3, the
Figure 2. Selected MP2/aVTZ geometry parameters of transition state
structures (TS) for H2elimination from ba-com. Bond distances are in
angstroms, and bond angles are in degrees.
Figure 3. Schematic energy profiles illustrating different reaction
pathways for H2release from diborane + ammonia db + A. Relative
energies are in kcal/mol from CCSD(T)/aVTZ + ZPE calculations.
The red profiles are the lowest-energy pathways.
Figure 4. Selected MP2/aVTZ geometry parameters of two complexes
dbab-c1 (perpendicular) and dbab-c2 (planar) between diborane and
ammonia borane db + ab. Bond distances are in angstroms, and bond
angles are in degrees.
J. Phys. Chem. A, Vol. 112, No. 40, 2008
Nguyen et al.
lowest-energy pathway, tsba-BN, is drawn in a bold red line.
The most important difference between the pathways through
tsba-BN and tsba-BB is the way in which the departing H2is
formed. In the former, the H2is lost from the N and the attacking
BH3, and in the latter, it is lost from B and the attacking BH3.
The energy barrier through tsba-BN is 41.7 kcal/mol smaller
than that via tsba-BB. Such a difference, larger than the
dissociation energy of diborane to separated BH3 molecules
(38.1 kcal/mol at 0 K),16exhibits itself in substantial differences
in the character of both TSs. In tsba-BN, the B-H-B bridged
bond remains and the H2 is formed within a B-H-H-N
framework. In contrast, the B-H-H-B bonds in tsba-BB are
disfavored by the repulsive charge distributions on the two
reacting negative B-H bonds. As shown by the IRC analysis,
both TSs connect to the same products BH2NH2+ BH3+ H2,
4.6 kcal/mol above the reactants.
We found four TSs in which the BH3group has the role of
a classical Lewis acid. The letter tsba-lew is used to designate
this type of TS, with lew standing for a Lewis type of interaction.
Dependent on the position (B or N in BH3NH3) where the B
atom of BH3is attached to, the labels tsba-lewBB and tsba-
lewBN are used. Attachment of B to N results in tsba-lewBN,
which is the only TS found for this type and has been described
previously (dashed line in Figure 3).19This TS is calculated to
be at 22.1 kcal/mol above tsba-BN and gives rise to the most
stable cyclic product pro-lewBN.
Attachment of B to B leads to the third type of TS and
includes three TSs named tsba-lewBB-1, tsba-lewBB-2, and
tsa-lewBB-N (Figure 3). The numbers 1 and 2 indicate two
different positions of the departing H2 with regard to the
attaching BH3group. The H2release from the back-side tsba-
lewBB-1 occurs with a dihedral angle BBNH of 112°. tsba-
lewBB-2 is formed by a bridged B-H-B bond at the lateral-
side position of BH3NH3, with a dihedral angle BBNH of only
3°. Both TSs describe the same kind of H2release from BH3NH3
with H-transfer from NH3 to a B atom accompanied by an
elongation of a B-H bond giving H2.19Both TSs have a similar
energy content, with a difference of only 0.5 kcal/mol in favor
of tsba-lewBB-1. As seen in Figure 3, all three TSs lead to the
same product pro-lewBB, as confirmed by their IRC pathways.
This product BH3NH2BH2(aminodiborane) + H2is more stable
than db + A.
The letter N in tsba-lewBB-N stands for H2departure from
two H atoms of NH3. This TS is given only for the sake of
completeness, because due to the breaking of two NH bonds, it
is located at the highest-energy position above db + A and is
The results summarized in Figure 3 show that, at an early
stage, both db + A and ab + B channels converge to the common
The calculated energy barriers range from 18.1 to 93.2 kcal/mol
relative to db + A. With respect to the results reported in our
previous study,19the three additional TSs remain substantially
higher in energy than tsba-BN. Therefore, they do not affect the
conclusions already drawn concerning the reaction ab + B,
where we note again the important role of the borane molecule
as a Lewis acid catalyst for H2 release. The current results
complete the PES for H2release and directly link the two starting
systems, BH3NH3+ BH3and B2H6+ NH3.
Figure 5. Selected MP2/aVTZ geometry parameters of six TSs related to the reaction of diborane + ammonia borane db + ab and an intermediate
complex. Bond distances are in angstroms, and bond angles are in degrees.
Diborane Reactions with Ammonia and Ammonia Borane
J. Phys. Chem. A, Vol. 112, No. 40, 2008 9949
For the diborane plus ammonia reaction, our current results
that tsba-BN is only 18.1 kcal/mol above the reactants db + A
are in agreement with experimental studies12-14showing
production of gaseous aminoborane (BH2NH2) upon thermal
decomposition of BH3NH3under mild conditions. This provides
us with further support for H2 release from BH3NH3 in the
presence of the catalyst BH3passing through the six-member
cyclic TS tsba-BN. Proceeding in an opposite direction with a
reaction beginning from BH2NH2+ H2+ BH3, or from the
adduct ba-com, if available, leads to formation of diborane.
Reaction Pathways from B2H6+ BH3NH3(db + ab). In
our search for lower energy H2 release processes, we have
investigated the reaction between diborane and ammonia borane
db + ab to determine if diborane can act as a catalyst for H2
release from ammonia borane. The initial interaction between
db and ab gives rise to two relatively weak complexes having
the same type of long B-H-H-B and B-H-H-N bonds,
but with different orientations. The complexes are referred to
as dbab-c1 and dbab-c2, in which the letter c denotes a complex
and the number their relative stability. Figure 4 shows selected
geometry parameters in both front and side views of their
equilibrium structures. The complexation energies of dbab-c1
and dbab-c2 are <0.5 kcal/mol with respect to the reactants,
respectively, and may or may not exist at higher levels of theory.
The pair of complexes is connected by almost free rotation of
NH3around the BHHB skeleton. dbab-c1 results from a nearly
perpendicular approach between the two monomers. This
complex has two weak B-H-H-B and B-H-H-N interac-
tions. dbab-c2 is characterized by an arrangement with all B
and N atoms of both monomers in the same plane. The H-H
distances within the B-H-H-N dihydrogen bond are longer
than those of dbab-c1 by 0.04-0.16 Å.
The geometry parameters for the relevant TSs and product
are shown in Figure 5, and the schematic potential energy
profiles for H2release are illustrated in Figure 6. We located
four TSs for direct H2elimination, which can be divided into
two types. The first type of TS starts from dbab-c1 and dbab-
c2 and includes dbab-c1-tslew, dbab-c2-tslew1, and dbab-c2-
tslew2 (Figure 5). dbab-c1-tslew is a TS for H2elimination
from the BH3NH3 group within dbab-c1. It is built from
interactions between B2H6 with the TS for loss of H2 from
BH3NH3 via weak dihydrogen-bridged B-H-H-B and
B-H-H-N bonds. The position of B2H6is still perpendicular
to the BH3NH3group as in dbab-c1. The B-H, N-H, B-N,
and H-H distances in the ab group are similar to those of the
BH3NH3monomer, which was analyzed in detail previously.19
In comparison with the corresponding values in dbab-c1, the
H-H distances in dbab-c1-tslew are elongated by 0.18-0.44
Å, whereas the B-H and N-H distances are slightly com-
pressed. The energy of dbab-c1-tslew is 37.8, 38.1, and 12.5
kcal/mol above the reactants db + ab, dbab-c1, and db + A
+ B, respectively.
Similarly, dbab-c2-tslew1 is formed by two B-H-H-B and
B-H-H-N interactions between B2H6 and the BH3NH3
monomer TS. All of the heavy atoms are again in a plane. The
changes in the B-H, N-H, and H-H distances within the
dihydrogen bridges B-H-H-B and B-H-H-N are not large
(∼0.04 Å) as compared to dbab-c2. dbab-c2-tslew1 is only
0.1 kcal/mol below dbab-c1-tslew and dbab-c2-tslew2 is only
0.5 kcal/mol higher in energy than dbab-c2-tslew1. In contrast
to dbab-c2-tslew1, formation of dbab-c2-tslew2 has only one
B-H-H-B and one B-H-H-N dihydrogen bond with the
BH3NH3monomer TS. The H-H distances in dbab-c2-tslew2
are shorter by 0.1-0.4 Å than those of dbab-c2-tslew1.
Molecular H2is generated in a plane nearly perpendicular to
that containing the heavy atoms (<BBNB ) 2.3°). IRC
calculations confirm that the products from these three different
TSs are the B2H6+ BH2NH2+ H2fragments.
Figure 6. Schematic energy profiles of pathways for rearrangement and H2release from two complexes between diborane plus ammonia borane
db + ab. Relative energies are in kcal/mol from CCSD(T)/aVTZ + ZPE calculations. The red profiles are the lowest-energy pathways.
J. Phys. Chem. A, Vol. 112, No. 40, 2008
Nguyen et al.
The second type of TS, which originates from dbab-c1, is
dbab-c1-tsBB (Figures 5 and 6). As above, the letter BB stands
for a H2loss from two B atoms. Formation of H2is characterized
by a combination of one H atom from the bridge B-H-B bond
in B2H6and another H atom from a B-H bond of BH3NH3.
The B-H bond in BH3NH3from which an H atom is lost is
longer than the other by ∼0.2 Å. The N-H bonds, which
interact with B2H6, are elongated by ∼0.13 Å. Breaking a
B-H-B bond and shortening of B-H bonds in B-H-H-N
interactions make it more difficult to form dbab-c1-tsBB. dbab-
c1-tsBB is ∼8 kcal/mol higher in energy than the two previous
TSs. The products from this TS are B2H6+ BH2NH2+ H2.
This TS can be compared with TS tsba-BB (Figure 2). Relative
to tsba-BB, the energy barrier via dbab-c1-tsBB is reduced
from 65.7 to 45.8 kcal/mol with respect to the relevant
H2 elimination from dbab-c1 can proceed via two-step
pathways. The first step is formation of the intermediate comB1-
s3 through TS dbab-c1-tscom. The second step is H2elimina-
tion from comB1-s3, via two different TSs: comB1-s3-tsBN1
and comB1-s3-tsBN2. Intermediate comB1-s3 is calculated to
be 8.9 kcal/mol above the reactants db + ab; the diborane
moiety is partially disrupted with only one B-H-B1 bridge,
and a new B1-H-B2 bridge forms connecting ab and db. In
TS dbab-c1-tscom, the B-H distances indicate bond cleavage.
The attack of B(db) on H of BH3(ab) induces four weak
B-H-H-B and B-H-H-N bonds (cf., Figure 5). These
numerous interactions tend to stabilize dbab-c1-tscom, so it is
only 10.9 kcal/mol above the reactants db + ab. IRC calcula-
tions along the forward direction result in comB1-s3 (Figure
Although TS dbab-c1-tscom is of low-energy, TS comB1-
s3-tsBN1 and TS comB1-s3-tsBN2, involving H2 formation
from B-H-H-N, are much higher in energy. comB1-s3-tsBN1
is an eight-member ring forming H2 from a B-H bond of
terminal borane. comB1-s3-tsBN2 is a six-member ring in which
H2is formed from an internal borane B-H bond (of diborane).
It appears that the two-step H2release is ∼5 kcal/mol favored
over the one-step pathway. In addition, the intermediate comB1-
s3 links to another region of the PES as described in the
The results summarized in Figure 6 show how diborane
affects the H2release reaction. db can behave as a conventional
Lewis acid interacting with the TS for H2release from ammonia
borane. This interaction does not happen via BB or BN bonds
but rather via dihydrogen-bridged bonds which can stabilize the
TS. In comparison to the previous results18,19on the energy
barriers for H2 elimination, this type of approach is not
significant: 36.8 kcal/mol for ab, 5.5 kcal/mol for ab + B
(Figure 3), and for ab + db, 37.7 kcal/mol via the one-step
pathway, and 32.7 kcal/mol via the two-step pathway (energies
for the same type of effect relative to separated reactants).
Starting from the weak preassociation complexes does not
change the energetics. In this pathway, even though the bridge
Figure 7. Schematic energy profiles illustrating pathways for H2release from ammonia borane plus two boranes ab + 2B. Relative energies are
in kcal/mol obtained from CCSD(T)/aVTZ + ZPE calculations. The red profiles are the lowest-energy pathways. ∆E(B2H6+ BH2NH2+ H2) )
-6.6, ∆E(B2H5NH2BH3 + H2) ) 10.1, ∆E(ring-B3H8NH2 + H2) ) 9.9, ∆E(BH3HB2H4NH2 + H2) ) 9.4, ∆E(B2H6NH2BH2 + H2) ) 10.5,
∆E(B2H4HBH3NH2+ H2) ) -4.6, and ∆E(B2H4HBH3NH2+ H2) ) -4.9 kcal/mol.
Diborane Reactions with Ammonia and Ammonia Borane
J. Phys. Chem. A, Vol. 112, No. 40, 2008 9951
B-H-B bonds are not broken, the energy of the TS is still
high. We conclude that diborane, when reacting as a stable and
compact entity, exerts a small catalytic effect for H2release of
ammonia borane, in reducing the energy barrier by ∼4 kcal/
mol from the BH3NH3 monomer to the B2H6 + BH3NH3
reaction involving a two-step pathway via TS comB1-s3-tsBN1.
Thus, B2H6is not a catalyst as effective as BH3.
H2Release from Reactions of Ammonia Borane with Two
Borane Molecules (ab + 2B). As discussed above, the adduct
ba-com (BH3HBH2NH3) is formed either from a direct com-
bination ab + B or via the reaction db + A. We briefly consider
the pathways for ab + 2B starting from ba-com + B, and the
schematic potential energy profiles are shown in Figure 7. There
are a large number of molecular complexes resulting from direct
interactions between ba-com and B in all possible orientations.
We selected 10 low-energy complexes within ∼10 kcal/mol
which act as preassociation structures for H2release, including
the complex comB1-s3 discussed above. They basically involve
the bridged B-H-B bonds between B of free B with H’s
belonging to both BH3 moieties of ba-com. The shape and
selected geometrical parameters of these complexes are sum-
marized in Figure S3 of the Supporting Information. Table S3
of the Supporting Information lists the relative energies of the
stationary points considered for this system at three levels of
The complexes can be classified on the basis of the attachment
position of the free boranes, their orientation, and their relative
energy. The most important factor is the attachment position in
such a way that both complexes comB1 and comB2 can be
distinguished from each other. B1 denotes an attachment of the
B atom of free B to the BH bonds surrounding the terminal B1
atom of ba-com, and B2 denotes an attachment to the central
B2 atom. The letters s and o indicate the orientation of B in the
resulting complex; s corresponds to the disposition of both
terminal BH3and NH3groups at the same side (cis configura-
tion) with respect to the central B1-B2 groups, o corresponds
to a disposition at the opposite side (trans configuration), and
the numbers 1, 2, 3 refer to the relative energy ordering.
The class of complexes comB1-s is formed by attachment
of B (in free B) to H atoms on the same side as NH3. This
class includes four complexes, comB1-s1, comB1-s2, comB1-
s3, and comB1-s4, calculated from 8.2 to 9.2 kcal/mol above
the reference point db + ab. As expected, the difference in
their energies is small corresponding to small variations in the
position of the added B moiety. This is illustrated by a difference
of 45-70° in the BBNB dihedral angles between comB1-s1
(31.5°), comB1-s2 (-13.5°), comB1-s3 (32.6°), and comB1-
s4 (-37.7°). The variations of H-bridged bond distances and
angles in these complexes are small, with a maximal change of
0.007 Å in bond distances and 1.1° in bond angles. With respect
to ba-com + B, comB1-s1 is the most stable complex. The
four complexes comB1-on, n ) 1, 2, 3, and 4, having a trans
configuration, are consistently less stable, with energies ranging
from 13.4 to 14.9 kcal/mol above the reference. This result
points out the substantial stabilizing interactions between the
terminal H(BH3) and H(NH3) atoms in the cis complexes
The second class of complexes is characterized by the
H-bridged bond between B(B) with H(B2). Only two complexes
comB2-s and comB2-o were located, 10.9 and 11.2 kcal/mol
above the reference state, but 8.6 and 8.3 kcal/mol below ba-
com + B, respectively. Formation of two opposite B-H-B
bridged bonds makes the molecular system more symmetric.
Despite the fact that some BH/HN interactions are present in
com-B2, they are ∼2 kcal/mol higher in energy than com-B1.
Figure 7 shows that there is a spectrum of prereaction
complexes formed from the interaction of ba-com with B with
a range of complexation energies from ∼5 to ∼11 kcal/mol.
Their interconversion is likely to be a facile process resulting
from rotation of B around ba-com in such a way that each
moiety can undergo H2 release through the lowest-lying TS.
From these complexes, we located a number of TSs for H2
release. Their shape, main geometrical parameters, and the
relative energies are shown in Figure S4 of the Supporting
Different TSs denoted as tslew and tsBN have been located
connecting to the class of complexes com-B1. Each complex
is connected with one of these TSs. As above, a tslew
characterizes a TS in which both the H(B) and H(N) atoms
of the original BH3NH3component contribute to the departing
H2. In such a TS, the remaining component BH2HBH3plays
the role of a classical Lewis acid, and the interaction takes place
via bridged B-H-B bonds. Again, a TS tsBN has the same
feature as tsba-BN discussed above, but in this case either one
or two BH3group(s) can actively take part in the H2formation
by giving and receiving H atoms.
The TSs derived from com-B1-s1 are comB1-s1-tslew1 and
comB1-s1-tslew2 and have the same framework for H2release
but differ from each other only by the position of the B1-B
group. Their relative energy positions are high. These pathways
are much less favored than many of those discussed above.
comB1-s1-tsBN1 is characterized by an eight-member cyclic
B-H-B-H-B-H-H-N structure with participation of a
BH2HBH3group in the H-transfer. Thus, one H is donated from
B while another H is transferred to B1. In contrast, comB1-
s1-tsBN2 contains only a six-member ring as in tsba-BN. The
second BH3molecule interacts from outside and does not take
part in the H2generation. Both TSs connect to the same products
BH2NH2+ H2+ B2H6with much lower relative energies than
the energies of the two TSs labeled tslew. Similar features can
be found for the TSs connecting the complexes comB1-s2,
comB1-s3, comB1-s4, comB1-o1, comB1-o2, comB1-o3, and
comB1-o4. In most cases, the tslew’s are in the range of 58-61
kcal/mol, whereas the tsBNs are about 32-40 kcal/mol above
the reactant reference db + ab (Figure 7).
A tslew and a tsBN have been found for each of the s or o
conformers of the comB2 complexes. In both comB2-s-tslew
and comB2-o-tslew, the H2departs from the central BH3NH3
moiety, from which two BH3 molecules interact with two
remaining BH bonds. The relative energies for tslew’s derived
from comB2 are slightly higher than those connecting comB1.
With reference to the separated ab + 2B system (36.5 kcal/
mol above the reference point db + ab) the TSs tslew are
∼21-22 kcal/mol higher in energy. These values can be
compared with the energy barrier for H2loss of 36.8 kcal/mol
in the monomer ab19or that of 26.8 kcal/mol in ab + B via
tsba-lewBB (Figure 3). The second borane molecule induces a
small additional effect in this type of TS, in comparison to the
effect produced by the first borane, i.e., the beneficial interaction
with the ab monomer is mostly contributed by the first borane.
comB2-s-tsBN and comB2-o-tsBN also belong to the TS
class tsBN, but their main characteristic is that, besides having
a six-member cycle as in tsba-BN, the second borane is attached
to the BH3 of BH3NH3 in such a way that the B2-B group
now has two bridge B-H-B bonds. Due to this extra diborane-
type stabilization, these TSs become much lower in energy,
27-28 kcal/mol relative to db + ab, 16-17 kcal/mol above
J. Phys. Chem. A, Vol. 112, No. 40, 2008
Nguyen et al.
the complex comB2, and only 7-8 kcal/mol above the point
ba-com + B. The TSs are actually 9-10 kcal/mol below the
reactant asymptote with two separated borane molecules ab +
2B. The TSs of the comB1-s-tsBN family are also found to be
located at ∼1-3 kcal/mol below the separated asymptote ab +
As discussed above, complex comB1-s3 is also the interme-
diate connecting dbab-c1 with the products B2H6+ BH2NH2
+ H2(Figure 6). Thus, owing to the diversity of conformations
and orientations, the complexes comB1 and comB2 are a point
of convergence of three different entrance channels on the PES
before the supersystem undergoes H2elimination.
tsba-BN is 23.9 kcal/mol above ba-com (Figure 3), and
comB2-s-tsBN is 16.1 kcal/mol above comB2-s so that the
interaction of the second borane leads to a reduction of 7.8 kcal/
mol on the barrier height. The participation of a second borane
molecule reduces the energy barrier for H2 release from
ammonia borane by more than that if just one borane is present.
Taken together, the calculated results shown in Figure 7 suggest
that the starting ab + 2B system can lead to spontaneous H2
release via the TSs comB2-tsBN and comB1-tsBN.
The product B2H5NH2BH3+ H2formed from TS comB2-
s-tsBN and its different conformers is calculated to be ∼9-10
kcal/mol above the reactants db + ab and has nearly the same
energy content as the complexes comB2 (Figure 7). The product
B2H5NH2BH3is an isomer of ammonia triborane (B3H7NH3)
and is 15.6 kcal/mol above the most stable form of B3H7NH3.20
The addition of H2 to B2H5NH2BH3 is characterized by an
energy barrier of 17.1 kcal/mol through TS comB2-s-tsBN.
Electronic structure calculations at the CCSD(T)/aug-cc-
pVTZ level have been used to study the PESs related to
hydrogen release in the reactions of diborane with ammonia
(B2H6+ NH3) and ammonia borane (B2H6+ BH3NH3). Starting
from B2H6 + NH3, the initial steps lead to a stable
H3BHBH2NH3 adduct ba-com, which is also formed from
condensation of ammonia borane with borane (BH3NH3+ BH3).
From this common intermediate, six TSs for H2loss have been
located with energy barriers ranging from 18 to 93 kcal/mol
relative to the reactants. The lowest-lying TS tsba-BN is
characterized as a six-member cycle in which BH3 exerts a
bifunctional catalytic effect favoring the H2generation within
a B-H-H-N framework. In the processes starting from B2H6
+ BH3NH3, the diborane molecule induces a slight reduction
in the energy barrier. An effective catalytic effect takes place
through a comparable six-member cyclic TS with B-H-H-N
transfer. The corresponding TS is ∼36 kcal/mol above the
separated reactants. The behavior of two separated borane
molecules is more complex involving multiple preassociation
complexes and TSs. Some of the pathways are beneficial with
a substantial decrease of barrier heights. Different channels from
either diborane or borane appear to converge to complexes
comprised of the adduct ba-com interacting with borane at
different positions and orientations. The complexation energies
range from 5 to 11 kcal/mol. Classical Lewis-type interactions
of boranes with the TS of the monomer BH3NH3 are not
important. Participation of both borane molecules in a six-
member cyclic TS reduces the energy barrier to 8 kcal/mol
(relative to ba-com + B), which is more efficient than
interaction of borane with the BH3of ammonia borane in tsba-
BN leading to a diborane type of bonding. The corresponding
energy barrier is now ∼8 kcal/mol relative to the same
asymptote ba-com + B. These TSs are from 1 to 9 kcal/mol
below the separated reactant BH3NH3 + 2BH3 (ab + 2B)
asymptote, suggesting that, under thermal conditions, if am-
monia borane interacts with two free borane molecules spon-
taneous H2release could occur. The present results confirm the
efficient action of both borane and diborane molecules as
bifunctional catalysts for H2 release. H2 regeneration of the
B2H5NH2BH3product is possible due to the near thermoneu-
trality of the B2H6+ BH3NH3reaction and an energy barrier
for H2addition of ∼17 kcal/mol.
Acknowledgment. Funding was provided in part by the
Department of Energy, Office of Energy Efficiency and Renew-
able Energy under the Hydrogen Storage Grand Challenge,
Solicitation No. DE-PS36-03GO93013. This work was done as
part of the Chemical Hydrogen Storage Center. D.A.D. is
indebted to the Robert Ramsay Endowment of the University
of Alabama. V.S.N. thanks the Belgian Technical Cooperation
Agency (BTC) for a doctoral scholarship. M.T.N. is indebted
to the FWO-Vlaanderen for supporting his sabbatical leave at
the University of Alabama.
Supporting Information Available: Tables of total energies
and zero-point energies of equilibrium structures, transition
states, and products, and imaginary frequencies of the transition
structures, for the pathways of H2release from B2H6+ NH3
(db + A), B2H6+ BH3NH3(db + ab), and BH3NH3+ 2BH3
(ab + 2B) and geometries of the structures of the stationary
points optimized at the MP2/aug-cc-pVTZ level in Cartesian
coordinates (Å); relative energies in kcal/mol of the stationary
points for the H2release from B2H6+ NH3(db + A) and from
B2H6+ BH3NH3(db + ab) for Figures 3, 6, and 7 at the MP2/
aVDZ, CCSD(T)/aVDZ, and CCSD(T)/aVTZ levels of calcula-
tion; figures of the energy profiles reported by McKee calculated
at the MP4/6-31+G(2d,p)//MP2(6-31G(d) + ZPE level; the six-
member cyclic TS optimized by Sakai at the MP2/6-31G(d,p)
level; selected MP2/aVTZ geometrical parameters of different
complexes comB1-s1, comB1-s2, comB1-s3, comB1-s4, comB1-
o1, comB1-o2, comB1-o3, comB1-o4, comB2-s, and comB2-
o; and selected MP2/aVTZ geometrical parameters of transition
state structures for H2 elimination from different complexes
comB1-sn and comB1-on (n ) 1-4) and comB2-s, comB2-o.
This material is available free of charge via the Internet at http://
References and Notes
(1) Stock, A. Hydrides of Boron and Silicon; Cornell University Press:
Ithaca, NY, 1933; pp 51-59.
(2) Lipscomb, W. N. Boron Hydrides; W. A. Benjamin Inc.: New York,
(3) Stock, A.; Kuss, E. Chem. Ber. 1923, 56B, 789.
(4) Stock, A.; Pohland, E. Chem. Ber. 1926, 59B, 2215.
(5) Stock, A.; Wierl, R. Z. Anorg. Allg. Chem. 1931, 203, 228.
(6) Schlesinger, H. I.; Burg, A. B. J. Am. Chem. Soc. 1936, 58, 409.
(7) Wiberg, E. Z. Anorg. Allg. Chem. 1926, 173, 210.
(8) (a) Schlesinger, H. I.; Burg, A. B. J. Am. Chem. Soc. 1938, 60,
290. (b) Schlesinger, H. I.; Ritter, D. M.; Burg, A. B. J. Am. Chem. Soc.
1938, 60, 1296.
(9) Schlesinger, H. I.; Ritter, D. M.; Burg, A. B. J. Am. Chem. Soc.
1938, 60, 2297.
(10) (a) Adams, A. C.; Capio, C. C. J. Electrochem. Soc. 1980, 127,
339. (b) Dworschak, W.; Jung, K.; Erhardt, H. Thin Solid Films 1995, 254,
65. (c) Andujar, J. L.; Bertran, E.; Polo, M. C. J. Vac. Sci. Technol., A
1998, 16, 578.
(11) (a) Go ´mez-Aleixandre, C.; Dı ´az, D.; Orgaz, F.; Albella, J. M. J.
Phys. Chem. 1993, 97, 11043. (b) Go ´mez-Aleixandre, C.; Essafti, A.;
Fernandez, M.; Fierro, J. L. G.; Albella, J. M. J. Phys. Chem. 1996, 100,
(12) Franz, D.; Hollenstein, M.; Hollenstein, Ch. Thin Solid Films 2000,
Diborane Reactions with Ammonia and Ammonia Borane
J. Phys. Chem. A, Vol. 112, No. 40, 2008 9953
(13) (a) Sugie, M.; Takeo, H.; Matsumura, C. Chem. Phys. Lett. 1979,
64, 573. (b) Sugie, M.; Takeo, H.; Matsumura, C. J. Mol. Spectrosc. 1987,
(14) Carpenter, J. D.; Ault, B. S. J. Phys. Chem. 1991, 95, 3502.
(15) McKee, M. L. J. Phys. Chem. 1992, 96, 5380.
(16) Feller, D.; Dixon, D. A.; Peterson, K. A. J. Phys. Chem. A 1998,
(17) Sakai, S. Chem. Phys. Lett. 1994, 217, 288.
(18) Sakai, S. J. Phys. Chem. 1995, 99, 9080.
(19) Nguyen, M. T.; Nguyen, V. S.; Matus, M. H.; Gopakumar, G.;
Dixon, D. A. J. Phys. Chem. A 2007, 111, 679.
(20) Nguyen, V. S.; Matus, M. H.; Nguyen, M. T.; Dixon, D. A. J.
Phys. Chem. C 2007, 111, 9603.
(21) Parry, R. W.; Schultz, D. R.; Girardot, P. R. J. Am. Chem. Soc.
1958, 80, 1.
(22) Sorokin, V. P.; Vesnina, B. I.; Klimova, N. S. Russ. J. Inorg. Chem.
1963, 8, 32.
(23) (a) Geanangel, R. A.; Wendlandt, W. W. Thermochim. Acta 1985,
86, 375. (b) Sit, V.; Geanangel, R. A.; Wendlandt, W. W. Thermochim.
Acta 1987, 113, 379. (c) Wang, J. S.; Geanangel, R. A. Inorg. Chim. Acta
1988, 148, 185.
(24) (a) Wolf, G.; van Miltenburg, R. A.; Wolf, U. Thermochim. Acta
1998, 317, 111. (b) Wolf, G.; Baumann, J.; Baitalow, F.; Hoffmann, F. P.
Thermochim. Acta 2000, 343, 19. (c) Baitalow, F.; Baumann, J.; Wolf, G.;
Jaenicke-Rlobler, K.; Leitner, G. Thermochim. Acta 2002, 391, 159.
(25) (a) Dixon, D. A.; Gutowski, M. J. Phys. Chem. A 2005, 109, 5129.
(b) Grant, D. J.; Dixon, D. A. J. Phys. Chem. A 2005, 109, 10138. (c)
Matus, M. H.; Anderson, K. D.; Camaioni, D. M.; Autrey, S. T.; Dixon,
D. A. J. Phys. Chem. A 2007, 111, 4411. (d) Stephans, F. H.; Baker, R. T.;
Matus, M. H.; Grant, D. J.; Dixon, D. A. Angew. Chem., Int. Ed. 2007, 46,
746. (e) Nguyen, M. T.; Matus, M. H.; Dixon, D. A. Inorg. Chem. 2007,
(26) (a) Stephens, F. H.; Pons, V.; Baker, R. T. Dalton Trans. 2007,
2613. (b) Marder, T. B. Angew. Chem., Int. Ed. 2007, 46, 8116.
(27) Keller, P. C.; Knapp, K. K.; Rund, J. V. Inorg. Chem. 1985, 24,
(28) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.;
Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;
Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li,
X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.;
Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;
Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.;
Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich,
S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;
Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.;
Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,
P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.;
Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,
B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03,
revision C.01; Gaussian, Inc.: Wallingford, CT, 2004.
(29) MOLPRO, a package of ab initio programs designed by Werner,
H.-J. and Knowles, P. J., version 2002.6; Amos, R. D.; Bernhardsson, A.;
Berning, A.; Celani, P.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.;
Eckert, F.; Hampel, C.; Hetzer, G.; Knowles, P. J.; Korona, T.; Lindh, R.;
Lloyd, A. W.; McNicholas, S. J.; Manby, F. R.; Meyer, W.; Mura, M. E.;
Nicklass, A.; Palmieri, P.; Pitzer, R.; Rauhut, G.; Schu ¨tz, M.; Schumann,
U.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T.; Werner, H.-J.
(30) Pople, J. A.; Seeger, R.; Krishnan, R. Int. J. Quantum Chem.,
Quantum Chem. Symp. 1977, 11, 149.
(31) (a) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (b) Kendall,
R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796.
(32) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154.
(33) (a) Cizek, J. AdV. Chem. Phys. 1969, 14, 35. (b) Purvis, G. D.;
Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. (c) Pople, J. A.; Head-Gordon,
M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968.
(34) Shimanouchi, T. Tables of Molecular Vibrational Frequencies
Consolidated, Volume I; NSRDS-NBS 39; National Bureau of Standards;
U.S. Government Printing Office: Washington, DC, 1972.
(35) Nguyen, V. S.; Matus, M. H.; Grant, D. J.; Nguyen, M. T.; Dixon,
D. A. J. Phys. Chem. A 2007, 111, 8844.
J. Phys. Chem. A, Vol. 112, No. 40, 2008
Nguyen et al.