i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
Available online at www.sciencedirect.com
ScienceDirect
journal homepage: www.elsevier.com/locate/he
A theoretical study of the spectroscopic properties
of B2H6 and of a series of BxHz
y species (x ¼ 1¡12,
y ¼ 3¡14, z ¼ 0¡2): From BH3 to B12H2
12
Daniel Sethio, Latevi Max Lawson Daku*, Hans Hagemann
Department of Physical Chemistry, University of Geneva, 1211 Geneva, Switzerland
article info
abstract
Article history:
The characterization of boron-hydrogen compounds is an active research area which en-
Received 23 October 2015
compasses subjects as diverse as the chemistry and structures of closoboranes or the
Received in revised form
thermal decomposition mechanism of the borohydrides. Due to their high gravimetric
19 February 2016
hydrogen content, borohydrides are considered as potential hydrogen storage materials.
Accepted 20 February 2016
Their thermal decompositions are multistep processes, for which the intermediate prod-
Available online 30 March 2016
ucts are not easily identified. To help address this issue, we have extensively investigated
the vibrational and NMR properties of 21 relevant BmHz
n boron-hydrogen species (m ¼ 1
Keywords:
e12; n ¼ 1e14; z ¼ 0e2) within density functional theory. We could thus show that the
Boron-hydrogen species
B3LYP-D2 dispersion-corrected hybrid can be used in combination with the large cc-pVTZ
11
basis set for the reliable prediction of the
Vibrational frequencies
species, and also for the reliable prediction of their IR and Raman spectra while taking
Anharmonicity
into account the anharmonicity of their molecular vibrations.
Density functional theory
Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
B and 1H NMR chemical shifts
11
B and 1H NMR spectra of the boron-hydrogen
reserved.
Introduction
Boron-hydrogen compounds attract a lot of interest for a variety of reasons. On one side, the chemistry and structures of
closoboranes continues to be studied, as shown in the recent
structural studies of M2B7H7 and MB7H8 (M ¼ PPh4, PNP, and
N(n-Bu4)) [1,2]. The chemistry of B3H
8 has also been recently
discussed in detail [3e7].
Many previous theoretical studies have addressed the
structures and relative energies of different boron-hydrogen
species [8e19]. These species can also behave as complexants. In this respect, quantum chemistry was recently applied
to the design of the Li@B10H14 electride and to the study of its
electronic and vibrational nonlinear optical properties
[20e22]. Of most interest to us, metal borohydrides have been
receiving considerable attention from both physicists and
chemists because of their potential use as hydrogen storage
materials [23]. These materials have high gravimetric
hydrogen content [24,25] which is suitable for mobile applications [25e28]. Their thermal decomposition leads to various
intermediate compounds [7,29e36] which are not easily
identified. Moreover the thermal paths are complex and pass
through many steps [27].
In this study, we performed DFT [37,38] calculations on a
series of BxHz
y compounds (x ¼ 1e12; y ¼ 3e12,14; z ¼ 0e2)
from BH3 to B12H2
12 with the aim to obtain a consistent set of
calculated vibrational and NMR spectroscopic data. The
* Corresponding author.
E-mail address: [email protected] (L.M. Lawson Daku).
http://dx.doi.org/10.1016/j.ijhydene.2016.02.121
0360-3199/Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
compound B2H6 is first studied in detail to choose the best
practical theoretical method, which is capable of treating
molecules as large as B12H2
12 and which takes into account as
much as possible the anharmonicity of their molecular vibrations. This method is then applied to all other compounds.
These data are critically compared to the available experimental data and are expected to allow, by a combined
computational and experimental approach, the identification
of intermediate species formed during the decomposition of
borohydrides.
6815
approach. Subsequently, this approach is applied systematically to all other compounds and the results compared with
available literature data.
Diborane, B2H6
Diborane, B2H6 [61], is the simplest stable borohydride at
ambient condition [62]. It has a ring-type molecular structure
and has two-bridging hydrogens [63] (see Fig. 1). Begue [64]
used high-level calculations to investigate the anharmonic
vibrational properties of this compound.
Computational details
Structure of diborane
All calculations were performed using the Gaussian09 package [39]. For the benchmark study of B2H6, DFT calculations
were carried out with the B3LYP [40,41], PBE0 [42,43] and M06HF [44] functionals. The influence of dispersion correction was
assessed by using the Grimme's D2 [45], D3 [46] and D3BJ [47]
correction schemes. Ab initio calculations were also performed with the Hartree-Fock, the second-order Møller-Plesset perturbation theory (MP2) [48] and the CCSD(T) [49]
methods. Several basis sets were employed for describing the
B and H atoms: the 6-31G* [50,51] Pople basis set of split
valence polarized quality, the 6-311þþG** [52,53] Pople basis
set of triple-z polarized quality augmented with diffuse functions, the Ahlrichs def2-TZVP [54] basis set of triple-z polarized
quality, and the Dunning cc-pVTZ [55] correlation-consistent
basis set. Several other Ahlrichs and Dunning basis sets of
lesser or higher flexibility were also used to probe the influence of the basis sets. To ease the reading of the manuscript,
the corresponding results are given as Supporting Information: the results obtained with the largest of these Ahlrichs
(resp., Dunning) basis sets and with the aforementioned def2TZVP (resp., cc-pVTZ) basis set are indeed very similar. The
benchmark DFT calculations were extended to B3H
8 and the
B3LYP-D2/cc-pVTZ method was used for the study of the
remaining boron-hydrogen species.
The characterization of a species at a given theoretical
level consisted first in the optimization of its geometry using
an “ultrafine” grid of 99 radial shells and 590 angular points per
shell and “tight” convergence criteria for the forces and displacements, which help ensure well converged calculated
frequencies (see Supporting Information). Vibrational frequencies analyses are then conducted both in the harmonic
and in the anharmonic approximation using second-order
perturbation theory as implemented by Barone [56e58] in
the Gaussian09 package. Using the optimized geometry, NMR
chemical shifts are calculated with the Gauge-independent
atomic orbital (GIAO) method [59] using BF3OEt2 [60] and tetramethylsilane (TMS) as references for 11B and 1H chemical
shifts, respectively.
Diborane has one BeB, four terminal and two bridging BeH
bonds as shown in Fig. 1. It has D2h symmetry. It has a planar
ring which consists of two-bridging hydrogens and two boron
atoms.
Table 1 compares the experimental and calculated structural data for B2H6. The experimental data were obtained from
high-resolution infra-red spectroscopy (Exp. (IR)) [65] and from
gas-phase electron diffraction (Exp. (GED)) [66]. The calculated
values are in good agreement with experimental data. The
BeHb(bridge) bond is longer than the terminal Be H bond by ca.
0.1 A. The structural parameters obtained with different levels
of theory are comparable and show that the ring of diborane is
planar with a HbeBeHbeB dihedral angle of 0 deg.
NMR chemical shifts of diborane
The calculated NMR chemical shifts of diborane are shown in
Table 2. The calculated values of the 11B chemical shifts are
typically 1e2 ppm smaller than the experiment value. Using
B3LYP and PBE0 with different types of basis sets give comparable results which are better than those obtained with
MP2. The calculated NMR data will be discussed in more details below, taking into account all compounds which we have
studied.
Vibrational spectroscopy of diborane
B2H6 has D2h symmetry. Diborane has 18 vibrational modes. Its
normal modes transform as 4Ag, 2B1g, 2B2g, 1B3g, 1Au, 2B1u,
3B2u, and 3B3u. The Ag, B1g, B2g, and B3g modes are Raman active
while the B1u, B2u, B3u modes are IR active, and the Au mode is
neither IR nor Raman active. The vibrational spectra of
diborane and its isotopic analogs have been thoroughly
studied by Duncan [68]. The combination of all experimental
data allowed to estimate the harmonic frequencies for this
molecule, which are also included in Table 3.
Results and discussion
At first, the spectroscopic properties of B2H6 were calculated
with different theoretical approaches in order to determine
the best practical approach which is applicable for larger
molecules (such as B12H2
12 ) and to discuss the limits of this
Fig. 1 e The structure of B2H6.
6816
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
and bond
Table 1 e Selected calculated and experimental structural parameters for B2H6: bond distances are given in A
angles in deg.
B3LYP
6-311þþG**
cc-pVTZ
def2-TZVP
PBE0
MP2
cc-pVTZ
6-311þþG**
BeB
BeH
BeHb
HeBeH
HbeBeHb
BeHbeB
HbeBeHbeB
1.764
1.186
1.315
121.7
95.8
84.2
0.0
1.758
1.185
1.312
121.7
95.8
84.2
0.0
1.758
1.186
1.312
121.6
95.8
84.2
0.0
1.747
1.190
1.314
121.7
96.7
83.3
0.0
1.768
1.188
1.316
122.3
95.6
84.4
0.0
BeB
BeH
BeHb
HeBeH
HbeBeHb
BeHbeB
HbeBeHbeB
B3LYP-D2
cc-pVTZ
1.764
1.186
1.315
121.8
95.8
84.2
0.0
B3LYP-D3BJ
cc-pVTZ
1.757
1.185
1.312
121.7
95.9
84.1
0.0
CCSD(T)
cc-pVTZ
1.763
1.188
1.315
122.3
95.8
84.2
47.9
Exp.
(IR)a
1.743
1.184(3)
1.314(3)
121.5(5)
96.9(5)
e
e
Exp.
(GED)b
1.747(7)
1.182(11)
1.303 (11)
120.5
95.9
e
e
a
b
Ref. [65].
Ref. [66].
In Table 3, calculated PBE0/cc-pVTZ and B3LYP/cc-pVTZ
harmonic and anharmonic frequencies are compared to the
experimental values. Drawings of the corresponding modes
are given in the Supplementary Materials. Modes n9 and n10
correspond to the bending modes of the terminal BH2 groups.
Modes n11en14 are associated with motions of the bridging H
atoms; and modes n15en18 are the stretching modes of the
terminal BH2 groups. The values of the harmonic low frequencies (n1en10) and of the terminal stretching modes
correspond quite well to the experimental harmonic frequencies. However significant differences appear for the
modes n11en14. In order to improve the agreement, anharmonic calculations have been performed and are compared
with the experimental anharmonic data in Table 3.
The inclusion of anharmonicity immediately led to an
improvement of the calculated frequencies with respect to the
experimental values. In order to evaluate the influence of the
level of calculations, we have systematically varied the functionals, the basis sets and we also performed CCSD(T) calculations to obtain a benchmark reference. Different
convergence criteria were tested and showed that using
“tight” convergence criteria for the forces is necessary to
obtain well converged frequencies (see Supporting Information). The results thus obtained are summarized in Table 4,
which shows the RMS errors with respect to the experimental
frequencies.
Inspection of Table 4 shows that both PBE0 and B3LYP give
comparable results, with slightly better RMS values for PBE0
(using the same basis set). However, if one excludes the modes
n11en14 from the RMS calculations (RMS+ values in Table 4), it
appears that B3LYP gives significantly better results for all
other frequencies. Different basis sets were tested and show
that better results are obtained using Dunning's type (ccpVTZ) and Ahlrich's type (def2TZVP) basis sets. The lowest
RMS+-value is found for B3LYP (cc-pVTZ). Finally, dispersion
was considered. The use of the dispersion-corrected B3LYP-
D2, -D3 and -D3BJ functionals does not have a significant influence on the predicted geometries (Table 1). However, the
use of B3LYP-D2 led to the smallest RMS value of 27.2 cm1,
compared to the value of 22.8 cm1 obtained with the CCSD(T)
benchmark calculations. Thus, B3LYP-D2/cc-pVTZ was chosen for all other compounds.
B3H
8
B3H
8 has been reported as an intermediate during the
decomposition of Mg(BH4)2 and Y(BH4)3 [7,31,69]. Olson and
Boldyrev [70] have shown that this ion exists in different
forms which can transform into each other by hydrogen
migration. This fluxional behavior is seen experimentally by
solution NMR studies [31,71,72]. Fig. 2 shows two different
conformations of B3H
8.
The most stable one has two BeHeB bridges in C2v symmetry (Fig. 2a). Three equivalent isomers can be formed, and
they transform into each other through the transition state
of Cs symmetry shown in Fig. 2. As with B2H6, a series of
calculations with different basis sets were performed both in
the harmonic and anharmonic approach, including
Table 2 e Calculated 11B NMR and 1H chemical shifts of
diborane (in ppm) relative to BF3·OEt2 and TMS,
respectively. Available experimental data are also given.
Method
MP2/6-31G*
MP2/6-311þþG**
B3LYP/6-311þþG**
B3LYP/def2TZVP
B3LYP/cc-pVTZ
PBE0/cc-pVTZ
Exp.a
a
Ref. [67].
Calc. d
12.2
14.1
15.0
15.6
15.1
16.0
16.6
11
B
Hterminal
Hbridge
4.32
4.27
4.57
4.57
4.45
4.66
e
0.88
0.90
0.64
0.66
0.76
0.60
e
6817
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
Table 3 e Calculated harmonic and anharmonic frequencies of B2H6, and RMS errors with respect to experimental data
(frequencies are in cm¡1; the cc-pVTZ basis set was used for all calculations).
Mode
n1
n2
n3
n4
n5
n6
n7
n8
n9
n10
n11
n12
n13
n14
n15
n16
n17
n18
RMS
a
Symm
B2u
Ag
Au
B2g
B1g
B2u
B1u
B3g
B3u
Ag
B3u
B2g
B1u
Ag
B3u
Ag
B1g
B2u
Harmonic
Empirical
Exp.a
Anharmonic
PBE0
B3LYP
Harmonica
PBE0
B3LYP
B3LYP-D2
329
821
850
898
912
930
979
993
1181
1189
1722
1894
2039
2192
2604
2618
2695
2710
73.13
360
801
850
894
940
954
992
1022
1197
1205
1717
1860
1996
2180
2609
2621
2695
2710
65.18
376
798
850
877
933
968
993
1041
1196
1207
1652
1814
1984
2153
2611
2622
2690
2704
53.23
340
787
824
868
907
885
958
957
1154
1162
1553
1745
1973
2108
2509
2520
2583
2594
29.96
362
766
823
860
917
923
970
998
1169
1177
1545
1702
1835
2111
2512
2523
2580
2598
31.44
365
774
819
858
922
914
965
971
1174
1177
1541
1699
1943
2115
2516
2526
2579
2598
27.19
369
790
833
860
915
949
973
1020
1172
1183
1603
1760
1925
2088
2520
2530
2596
2609
Ref. [68].
dispersion corrections. Comparison with the experimental
vibrational frequencies showed that the smallest RMS is
obtained using B3LYP-D2/cc-pVTZ, as previously found for
B2H6. As expected, the structural parameters do not change
very much with the different levels of calculations (see
Supporting Information). These parameters agree with the
reported experimental values. Note that in contrast to B2H6,
the BeHeB bridges are not symmetrical, with BeH bond
distances of 1.49 and 1.26 A respectively. Olson and Boldyrev
[70] obtained a zero-point energy difference of 1.2 kcal/mol
(5.0 kJ/mol) between the ground state and the transition state
using B3LYP/6-311þþG**. We obtain 1.1 kcal/mol (4.6 kJ/mol).
An imaginary frequency of 151i cm1 is obtained for the firstorder transition state.
NMR chemical shifts of B3H
8
The NMR chemical shifts are summarized in Table 5. Experimentally, only one peak is seen both in the 11B and 1H NMR
spectra, confirming the fluxional behavior of this ion
[12,31,70e72]. For 11B, the experimental value is 30.8 or
30.4 ppm, which is close to the average of the calculated
static values indicated in Table 5. Similarly, the average value
for the chemical shift of 1H is close to the experimental value
of 0.2 ppm.
Vibrational spectroscopy of B3H
8
B3H
8 has 27 vibrational modes. The normal modes of B3H8
transform as 9A1, 5A2, 6B1, and 7B2. The A1, B1, and B2 modes
are both IR and Raman active, while the A2 mode is only
Raman active. The calculated and experimental frequencies
[75,76] are compared in Table 6. Note that the experimental
frequencies are somewhat scattered for different samples
(NaB3H8, CsB3H8) and experimental techniques (IR, Raman,
INS). The 8 highest frequencies correspond to B-H stretching
modes which are observed between 2080 and 2479 cm1.
Using B3LYP-D2/cc-pVTZ, the corresponding harmonic frequencies stretch from 2187 to 2518 cm1, while the anharmonic frequencies range from 2058 to 2399 cm1.
As for B2H6, the RMS decreases when anharmonicity and
dispersion correction are included in the calculations (Table
7), however the value of 43 cm1 is still quite large. Inspection of Table 6 shows that the modes n3 and n18, which correspond to the motions of the bridging hydrogens, contribute
largely to the RMS. Thus, at the B3LYP-D2/cc-pVTZ level, for
mode n3, the calculated anharmonic frequency is 392 cm1
and the observed one is 455e472 cm1; and for mode n18, the
predicted calculated anharmonic frequency is 1134 cm1
while the observed one is 1218e1255 cm1. Combining the
results for B2H6 and B3H
8 , it appears that the BeHbridge
stretching and bending frequencies are subject to the largest
discrepancies between experimental and theoretical values
and call for caution when comparing experimental and
theoretical spectra. However, the lower frequency spectral
region (below 1000 cm1) appears to be satisfactorily described
in the anharmonic approximation.
In total, we have studied the following 21 boron-hydrogen
2
species: BH3, BH
4 , B2H6, B2H7 , B3H8 , B4H10, B4H9 , B5H5 , B5H9,
2
2
2
2
B5H11, B6H2
,
B
H
,
B
H
,
B
H
,
B
H
,
B
H
,
B
H
6 10
6 12
7 7
8 8
8 12
9 9 , B10H10 ,
6
2
2
B10H14, B11H11 , B12H12 . The results for each individual species
are summarized in the supplementary material together with
corresponding literature data. In the following sections, we
summarize the general trends resulting from these
calculations.
General trends in the vibrational and in the NMR
spectroscopic data
NMR
11
B chemical shifts
Fig. 3 shows that there is a good correlation between experimental (dexp) and calculated (dcalc) values of the 11B chemical
6818
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
Table 4 e RMS errors with respect to experimental data
(in cm¡1) for the different levels of theory used to
calculate the vibrational frequencies of B2H6.
Harmonic
Anharmonic
Adding
Dispersion
Method
RMS error
RMS+ error
MP2/6-31G*
MP2/6-311þþG**
B3LYP/6-311þþG**
HF/cc-pVTZ
M06-HF/cc-pVTZ
PBE0/6-311þþG**
PBE0/cc-pVTZ
PBE0/def2TZVP
B3LYP/6-311þþG**
B3LYP/cc-pVTZ
B3LYP/def2TZVP
CCSD(T)/cc-pVTZ
B3LYP-D2/cc-pVTZ
B3LYP-D3/cc-pVTZ
B3LYP-D3BJ/cc-pVTZ
133.82
94.34
59.15
66.20
58.35
32.86
29.96
29.74
37.67
31.44
31.13
22.76
27.19
35.68
32.39
114.70
80.33
52.94
71.89
22.37
30.67
27.24
27.11
18.87
14.05
15.24
24.87
19.01
17.18
14.98
+
The RMS error of vibrational frequencies excluding the B-Hbridge
modes.
shift. The experimental values were retrieved from the literature [11,12,17,60,72,77,78] and from the on-line database of
the Cole research group [79]. Using B3LYP-D2/cc-pVTZ, the
fitting equation is: dexp ¼ 0.921 dcalc þ 4.082 ppm with
R2 ¼ 0.993. This shows that in this case, the calculated values
of the chemical shift are systematically smaller than the
experimental values and that one has systematic errors of
several ppm. Using B3LYP/6311þþG**, the fitting equation
becomes dexp ¼ 0.926 dcalc þ 1.830 ppm (see Supporting Information), which is in closer agreement with experiment.
Vibrational frequencies
Fig. 4 compares the calculated anharmonic frequencies with
the corresponding experimental data for 11 compounds in the
low frequency region (below 1500 cm1). The correlation is
very good with a slope very close to 1 (0.996). This correlation
shows that in this spectral region, the calculated values are
typically and systematically 14(±8) cm1 smaller than the
experimental values. This is illustrated in the Raman spectrum of B10H14 shown below.
In the case of B2H
7 for which the bent or linear nature of its
BeHeB bridge has long been debated, the calculations were
performed using the accepted bent model of C2 symmetry
[9,80e84]. The very good agreement observed in Fig. 4 between
experimental and calculated anharmonic frequencies support
the C2 model. However, an imaginary anharmonic frequency
is obtained for the vibrational mode of lowest harmonic frequency (see Supporting Information). For such a soft mode,
which is associated to the motion of the bridging H atom along
the C2 axis, this actually indicates a breakdown of the validity
of the anharmonic treatment that follows from the fact that
the potential energy surface (PES) is flat around the two
possible C2 minima (the PES along this mode can indeed be
viewed as a double-well potential with a small to vanishing
barrier).
Fig. 5 compares the calculated harmonic and anharmonic Raman spectra with the experimental Raman spectrum of B10H14 below 1500 cm1. This Figure clearly
highlights the improvement of the agreement achieved
using the anharmonic calculations. Below 800 cm1, the
harmonic calculation reproduces very well the experimental data. However, the bands calculated above
1050 cm1 are far away from the experimental results. With
the anharmonic calculation, one obtains a much better
agreement above 800 cm1, but in the region between 500
and 700 cm1 several weak bands do not match well with
the experimental data.
The overall agreement in the B-H stretching mode region
(above 2000 cm1) is not so good. In the graph of the experimental frequencies (nexp) vs calculated anharmonic frequencies (nanh
calc; Fig. 6), the data are somewhat scattered and
þ 175:9 with a rather
yield a fitting equation nexp ¼ 0:937 nanh
calc
poor R2 ¼ 0.898. The scatter of the data can be explained in part
by the fact that at this stage, we did not consider the strong
Fermi resonances which can occur, as we previously quantitatively did for BH
4 [85]. If one plots the calculated harmonic
frequencies (nharm
calc ) versus the anharmonic frequencies between 2000 and 2650 cm1, one obtains an excellent correla¼ nharm
119:6, i.e. the
tion (R2¼0.994) with the equation nanh
calc
calc
Fig. 2 e Two possibles structures of B3H
8 : (a) at its lowest-energy minimum with C2v symmetry, and (b) at its transition state
of Cs symmetry (B3LYP-D2/cc-pVTZ results).
6819
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
Table 5 e Calculated 11B and 1H NMR chemical shifts of B3H
8 (in ppm) relative to BF3·OEt2 and TMS, respectively.
d11B
B3LYP/6-311þþG**
B3LYP/cc-pVTZ
B3LYP-D2/cc-pVTZ
Exp.
a
b
d1H
(1B)
(2B)
Average
(2H)
(4H)
(2H)
Average
11.9
14.9
14.3
48.8
51.8
51.4
36.5
39.5
39.0
30.8a,30.4b
1.03
1.16
1.13
0.02
0.14
0.12
2.21
2.05
2.06
0.29
0.15
0.17
0.2a
Ref. [73].
Refs. [6], [74].
harmonic frequencies are systematically ca. 120 cm1 larger
than the experimental ones. Globally, it appears that the
harmonic B-H stretching frequencies are closer to the experimental values, while the anharmonic calculations somewhat
underestimate these frequencies.
Table 7 e RMS errors of calculated harmonic and
¡1
anharmonic frequencies of B3H
8 (in cm ).
B3LYP
6-311þþG**
RMS
Conclusion
B3LYP/cc-pVTZ
Without D
Har.
Anhar.
Har
Anhar.
52
66
63
57
D2
D3
D3BJ
Anhar.
43
64
59
Har.: harmonic; Anhar.: Anharmonic.
Using B3LYP-D2/cc-pVTZ, we have systematically studied 21
boron-hydrogen species. We have calculated harmonic and
Table 6 e Calculated B3LYP-D2/cc-pVTZ harmonic and
anharmonic frequencies of B3H
8 , and RMS errors with
respect to experimental IR data (in cm¡1).
Mode
n1
n2
n3
n4
n5
n6
n7
n8
n9
n10
n11
n12
n13
n14
n15
n16
n17
n18
n19
n20
n21
n22
n23
n24
n25
n26
n27
RMS
Symm
A2
B1
B2
A1
A1
B1
B2
A2
A1
B1
A2
B2
B1
A2
A1
B2
A1
B2
A1
B2
A1
B2
A1
A1
A2
B1
B1
Exp.+
Calculated
Har
Anhar
205
433
494
524
721
735
805
837
835
918
1017
1068
1093
1186
1196
1202
1218
1299
1414
2187
2229
2468
2480
2483
2493
2505
2518
79
179
408
392
488
658
706
749
794
828
870
968
1021
1046
1078
1142
1143
1168
1134
1303
2058
2131
2367
2373
2387
2376
2375
2399
43
a
IR
Ramanb
INSc
555
472
580
462
791
anharmonic vibrational frequencies as well as NMR chemical
shifts. The comparison with available experimental vibrational data shows that the inclusion of anharmonicity
significantly improves the agreement, especially below
1200 cm1. The motions of bridging hydrogen atoms being
strongly anharmonic, the agreement between experiment
and theory turns out to remain limited for these vibrations.
Fig. 5 illustrates both the advantages and limitations of the
anharmonic calculations and suggests that, within the
perturbational anharmonic framework of the calculations,
792
1013
1178
1050
1116
1185
1218
2092
2130
2338
2364
2088
2132
2330
2370
2432
2479
2455
+
Refs. [75] and [75].
The Infrared spectra of CsB3H8 in solution.
b
The Raman spectra of solid CsB3H8 [76].
c
The Neutron scattering spectra of solid CsB3H8 at 77 K [75].
a
Fig. 3 e Correlation between calculated and experimental
11
B chemical shifts (B3LYP-D2/cc-pVTZ results).
6820
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
Fig. 4 e Correlation between the calculated anharmonic
and the experimental vibrational frequencies for the low
frequency region (B3LYP-D2/cc-pVTZ results).
one should use both harmonic and anharmonic results for
comparison with experimental data. The large anharmonic
effects that could be evidenced also show that the inclusion
of anharmonicity is key for the accurate prediction of the
thermochemistry of these BxHz
y species (work in progress).
Finally, the 11B NMR spectra calculated with different approaches (in our case, B3LYP-D2/cc-pPVTZ and B3LYP/
6311þþG**) show excellent correlations with experimental
data. We believe that these calculations as well as the
methodology used will be helpful to identify intermediate
decomposition products in the study of potential hydrogen
storage materials.
In this paper, we have calculated the properties of BxHz
y
species in the gas phase. In solids, their spectroscopic properties may change somewhat due the influence of their environment in crystals. Thus, in the case of BH
4 , we have
observed [86] that the IR active B-H stretching frequency can
vary from 2210 cm1 to 2380 cm1 depending on the crystalline surroundings. The bending frequencies may additionally
be influenced by the number of coordinating cations. Another
aspect is the lowering of symmetry in the crystal, which can
lead to significant splitting and additional bands due to the
modified selection rules. Using the GF method [86], it is in
principle possible to predict the extent of these splittings.
Alternatively, one can theoretically simulate this lower symmetry, as was shown with DFT calculations on a Li2B12H12
cluster in the gas phase [87]. B3H
8 can bind in both a bidentate
or a tridentate way with its hydrogen atoms to metals [88]. In
the complex (CO)3Mn(B3H8) [89], there are 3 bridging BeHeMn
bonds, and the bridging BeHeB bonds are maintained. In this
case, one should calculate the vibrational properties of the
entire complex, as was also reported previously for complex
borohydride ions such as ScðBH4 Þ
4 [90] and for those present
in the AZn2(BH4)5 (A ¼ Li, Na) and NaZn(BH4)3 compounds [91].
In the case of the compounds with BH
4 , the librational frequencies can reach frequencies of about 500 cm1. However,
with increasing size of the BH
4 ions, these frequencies will
tend towards lower energies and thus the librational modes
interact less with internal modes of the ions. In the case of
Na2B12H12, a periodic DFT calculation has been performed [92]:
the calculated translational and librational modes range up to
175 cm1, while the lowest frequency internal mode appears
at 532 cm1. The reactivity of species with bridging hydrogen
bonds cannot be simply predicted by the results obtained in
this paper, as it can be assumed that the presence of a metal
ion next to the BxHz
y ions will significantly modify the electron densities of the borohydrides. This topic will be
addressed in the future to gain more information about
possible decomposition reactions pathways of borohydrides
for hydrogen storage.
exp. B10H14
calc. Anharmonic B10H14
calc. Harmonic B10H14
3.0
Intensity (a.u.)
2.5
2.0
1.5
1.0
0.5
0.0
200
400
600
800
-1
Raman Shift (cm )
1000
1200
Fig. 5 e Comparison of the calculated harmonic and anharmonic Raman spectra with the experimental Raman spectrum
(532 nm, room temperature) of solid B10H14 below 1500 cm¡1(B3LYP-D2/cc-pVTZ results).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
Fig. 6 e Correlation between the calculated anharmonic
and the experimental vibrational frequencies for the high
frequency region (B3LYP-D2/cc-pVTZ results).
Acknowledgment
This work was supported by the Swiss National Science
Foundation (grants nr. 200020_156681 and 200021_144361).
Appendix A. Supplementary data
Supplementary data related to this article can be found at
http://dx.doi.org/10.1016/j.ijhydene.2016.02.121.
Supporting information
The Supporting Information consists of two files. The supporting material referred to in the text is given in the first file.
The second file collects calculated and available experimental
vibrational and NMR data for all the studied species.
references
[1] Schlüter F, Bernhardt E. Syntheses and Crystal structures of
the closo-borates M2[B7H7] and M[B7H8] (M ¼ PPh4, PNP, and
N(n-Bu4)): the missing Crystal structure in the series [BnHn]2
(n¼612). Inorg Chem 2011;50(6):2580e9. http://dx.doi.org/
10.1021/ic102434t. http://dx.doi.org/10.1021/ic102434t.
[2] Kopytin AV, Zhizhin KY, Urusov YI, Mustyatsa VN,
Kokunov YV, Kuznetsov NT. Ion-selective electrodes for the
determination of closoborate anions. J Anal Chem
2011;66(7):666e9. http://dx.doi.org/10.1134/
S1061934811070070. http://link.springer.com/article/10.1134/
S1061934811070070.
6821
[3] Bykov AY, Razgonyaeva GA, Mal'tseva NN, Zhizhin KY,
Kuznetsov NT. A new method of synthesis of the B3H
8 anion.
Russ J Inorg Chem 2012;57(4):471e3. http://dx.doi.org/
10.1134/S0036023612040055. http://link.springer.com/article/
10.1134/S0036023612040055.
[4] Bykov AY, Mal'tseva NN, Generalova NB, Zhizhin KY,
Kuznetsov NT. Reactions of sodium tetrahydroborate with
alkyl and aryl halides: a new approach to the synthesis of
2
B3H
8 and b12H12 anions. Russ J Inorg Chem
2013;58(11):1321e3. http://dx.doi.org/10.1134/
S003602361311003X. http://link.springer.com/article/10.1134/
S003602361311003X.
[5] Bykov AY, Zhizhin KY, Kuznetsov NT. The chemistry of the
octahydrotriborate anion B3H
8 . Russ J Inorg Chem
2014;59(13):1539e55. http://dx.doi.org/10.1134/
S0036023614130026. http://link.springer.com/article/10.1134/
S0036023614130026.
[6] Huang Z, Lingam HK, Chen X, Porter S, Du A, Woodard PM,
et al. Synthesis, structural analysis, and thermal
decomposition studies of [(NH3)2BH2]B3H8. RSC Adv
2013;3(20):7460e5. http://dx.doi.org/10.1039/C3RA22836C.
00000, http://pubs.rsc.org/en/content/articlelanding/2013/ra/
c3ra22836c.
[7] Yan Y, Remhof A, Rentsch D, Lee Y-S, Cho YW, Züttel A. Is
Y2(B12H12)3 the main intermediate in the decomposition
process of Y(BH4)3? Chem Commun 2013;49(45):5234e6.
[8] Beaudet RA. Ch. 20. In: Advances in boron and boranes. VCH;
1988. p. 417.
yer PVR. Application and evaluation of ab initio
[9] Bühl M, Schle
chemical shift calculations for boranes and carboranes. how
reliable are “accurate” experimental structures? J.Am Chem
Soc 1992;114:477e91.
yer PVR. Decisive electron
[10] Bühl M, Gauss J, Hofmann M, Schle
correlation effects on computed boron-11 and carbon-13 nmr
chemical shifts. application of the giao-mp2 method to
boranes and carbaboranes. J.Am Chem Soc
1993;115(26):12385e90. http://dx.doi.org/10.1021/
ja00079a020.
[11] Łodziana Z, Błonski P, Yan Y, Rentsch D, Remhof A. Nmr
chemical shifts of 11B in metal borohydrides from firstprinciple calculations. J Phys Chem C 2014;118(13):6594e603.
http://dx.doi.org/10.1021/jp4120833.
[12] McKee ML, Lipscomb WN. Ab initio study of the transient
boron hydrides B3H7, B3H9, B4H8, and B4H12 and the fluxional
anion B3H
8 . Inorg Chem 1982;21(7):2846e50. http://
dx.doi.org/10.1021/ic00137a060.
[13] McKee ML, Wang Z-X, Schl’eyer P v R. Ab initio study of the
hypercloso Boron hydrides BnHn and BnH
n . Exceptional
Stability of Neutral B13 H13. J Am Chem Soc
2000;122(19):4781e93. http://dx.doi.org/10.1021/ja994490a.
00000, http://dx.doi.org/10.1021/ja994490a.
[14] Meier P, Neff M, Rauhut G. Accurate vibrational
frequencies of borane and its isotopologues. J Chem
Theory Comput 2011;7(1):148e52. http://dx.doi.org/10.1021/
ct1004752.
[15] Nguyen MT, Matus MH, Dixon DA. Heats of formation of
Boron hydride anions and dianions and their ammonium
y
salts [BnHm ][NHþ
4 ]y with y ¼ 12. Inorg Chem
2007;46(18):7561e70. http://dx.doi.org/10.1021/ic700941c.
00000, http://dx.doi.org/10.1021/ic700941c.
[16] Scott AP, Radom L. Harmonic vibrational frequencies: an
evaluation of Hartree-Fock, Møller-Plesset, quadratic
configuration interaction, density functional theory, and
semiempirical scale factors. J Phys Chem
1996;100(41):16502e13. http://dx.doi.org/10.1021/jp960976r.
[17] Todd LJ, Siedle AR. NMR studies of boranes, carboranes and
hetero-atom boranes. Prog NMR Spectroscopy
1979;13:87e176.
6822
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
[18] Tian AX. Ab initio and electron propagator theory study of
boron hydrides. J Phys Chem A 2005;109:5471e80.
[19] Wann DA, Lane PD, Robertson HE, Holub J, Hnyk D.
Structures of, and related consequences of deprotonation on,
two cs-symmetric arachno nine-vertex heteroboranes,
4,6-X2B7H9 (X ¼ CH2; S) studied by gas electron diffraction/
quantum chemical calculations and GIAO/NMR. Inorg Chem
2013;52(8):4502e8. http://dx.doi.org/10.1021/ic302776d. pMID:
23541164. http://dx.doi.org/10.1021/ic302776d.
[20] Muhammad S, Xu H, Liao Y, Kan Y, Su Z. Quantum
mechanical design and structure of the Li@B10H14 basket
with a remarkably enhanced electro-optical response. J Am
Chem Soc 2009;131(33):11833e40. http://dx.doi.org/10.1021/
ja9032023. pMID: 19642644. arXiv:http://dx.doi.org/10.1021/
ja9032023, http://dx.doi.org/10.1021/ja9032023.
[21] Muhammad S, Xu H, Su Z. Capturing a synergistic effect of a
conical push and an inward pull in fluoro derivatives of
Li@B10H14 basket: toward a higher vertical ionization
potential and nonlinear optical response. J Phys Chem A
2011;115(5):923e31. http://dx.doi.org/10.1021/jp110401f.
pMID: 21226521. arXiv:http://dx.doi.org/10.1021/jp110401f,
http://dx.doi.org/10.1021/jp110401f.
s M, Sola
M, Luis JM, Kirtman B. Electronic and
[22] Garcia-Borra
vibrational nonlinear optical properties of five representative
electrides. J Chem Theory Comput 2012;8(8):2688e97. http://
dx.doi.org/10.1021/ct300433q. arXiv:http://dx.doi.org/10.
1021/ct300433q, http://dx.doi.org/10.1021/ct300433q.
[23] Schlapbach L, Züttel A. Hydrogen-storage materials for
mobile applications. Nature 2001;414(6861):353e8. http://
dx.doi.org/10.1038/35104634. http://dx.doi.org/10.1038/
35104634.
[24] Züttel A, Borgschulte A, Orimo S-I. Tetrahydroborates as new
hydrogen storage materials. Scr Mater 2007;56(10):823e8.
http://dx.doi.org/10.1016/j.scriptamat.2007.01.010.
[25] Orimo S-I, Nakamori Y, Eliseo JR, Züttel A, Jensen CM.
Complex hydrides for hydrogen storage. Chem Rev
2007;107(10):4111e32. http://dx.doi.org/10.1021/cr0501846.
[26] Fichtner M, Chlopek K, Longhini M, Hagemann H. Vibrational
spectra of Ca(BH4)2. J Phys Chem C 2008;112(30):11575e9.
http://dx.doi.org/10.1021/jp801482b. http://dx.doi.org/10.
1021/jp801482b.
[27] Nakamori Y, Miwa K, Ninomiya A, Li H, Ohba N, Towata S-I,
et al. Correlation between thermodynamical stabilities of
metal borohydrides and cation electronegativites: firstprinciples calculations and experiments. Phys Rev B
2006;74(4):045126. http://dx.doi.org/10.1103/
PhysRevB.74.045126.
[28] Kim J-H, Shim J-H, Cho YW. On the reversibility of hydrogen
storage in Ti- and Nb-catalyzed Ca(BH4)2. J Power Sources
2008;181(1):140e3. http://dx.doi.org/10.1016/
j.jpowsour.2008.02.094.
[29] Liu Y, Giri S, Zhou J, Jena P. Intermediate phases during
decomposition of metal borohydrides, M(BH4)n
(M ¼ Na, Mg, Y). J.Phys Chem C 2014;118:28456. http://
dx.doi.org/10.1021/jp509223d.
[30] Paskevicius M, Pitt MP, Webb CJ, Sheppard DA, Filsø U,
Gray EM, Buckley CE. In-situ x-ray diffraction study of gMg(BH4)2 decomposition. J Phys Chem C
2012;116(29):15231e40. http://dx.doi.org/10.1021/jp302898k.
[31] Chong M, Karkamkar A, Autrey T, Orimo S-I, Jalisatgi S,
Jensen CM. Reversible dehydrogenation of magnesium
borohydride to magnesium triborane in the solid state under
moderate conditions. Chem Commun 2011;47(4):1330e2.
http://dx.doi.org/10.1039/C0CC03461D. 00033.
[32] Newhouse RJ, Stavila V, Hwang S-J, Klebanoff LE, Zhang JZ.
Reversibility and improved hydrogen release of magnesium
borohydride. J Phys Chem C 2010;114(11):5224e32. http://
dx.doi.org/10.1021/jp9116744.
[33] Li H-W, Miwa K, Ohba N, Fujita T, Sato T, Yan Y, et al.
Formation of an intermediate compound with a B12H12
cluster: experimental and theoretical studies on magnesium
borohydride Mg(BH4)2. Nanotechnology 2009;20(20):204013.
http://dx.doi.org/10.1088/0957-4484/20/20/204013.
[34] Hwang S-J, Bowman RC, Reiter JW, Rijssenbeek JW,
Soloveichik GL, Zhao J-C, Kabbour H, Ahn CC. NMR
confirmation for formation of [B12H12]2 complexes during
hydrogen desorption from metal borohydrides. J Phys
Chem C 2008;112(9):3164e9. http://dx.doi.org/10.1021/
jp710894t.
[35] Ohba N, Miwa K, Aoki M, Noritake T, Towata S-I, Nakamori Y,
Orimo S-I, Züttel A. First-principles study on the stability of
intermediate compounds of LiBH4. Phys Rev B
2006;74(7):075110. http://dx.doi.org/10.1103/
PhysRevB.74.075110. 00000.
[36] Sharma M, Sethio D, D'Anna V, Hagemann H. Theoretical
study of B12HnF(12n) 2 species. Int J Hydrogen Energy
2015;40(37):12721e6. http://dx.doi.org/10.1016/j.ijhydene.
2015.07.125. http://www.sciencedirect.com/science/article/
pii/S036031991501928X.
[37] Hohenberg P, Kohn W. Inhomogeneous electron gas. Phys
Rev 1964;136:B864e71.
[38] Kohn W, Sham LJ. Self-consistent equations including
exchange and correlation effects. Phys Rev
1965;140:A1133e8.
[39] Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA,
Cheeseman JR, et al. Gaussian 09 revision D.01. Wallingford
CT: gaussian Inc; 2009.
[40] Gaussian NEWS. Becke3LYP method references and general
citation guidelines. v. 5, no. 2, summer. 1994. p. 2.
[41] Becke AD. Density-functional thermochemistry. III. The role
of exact exchange. J Chem Phys 1993;98(7):5648e52. http://
dx.doi.org/10.1063/1.464913. http://jcp.aip.org/resource/1/
jcpsa6/v98/i7/p5648_s1.
[42] Perdew JP, Ernzerhof M, Burke K. Rationale for mixing exact
exchange with density functional approximations. J Chem
Phys 1996;105:9982e5.
[43] Adamo C, Barone V. Toward reliable density functional
methods without adjustable parameters: the PBE0 model. J
Chem Phys 1999;110:6158e70.
[44] Zhao Y, Truhlar DG. Density functional for spectroscopy: no
long-range self-interaction error, good performance for
Rydberg and charge-transfer states, and better performance
on average than B3LYP for ground states. J Phys Chem A
2006;110:13126e30.
[45] Grimme S. Semiempirical GGA-type density functional
constructed with a long-range dispersion correction. J
Comput Chem 2006;27:1787e99.
[46] Grimme S, Antony J, Ehrlich S, Krieg H. A consistent and
accurate ab initio parametrization of density functional
dispersion correction (DFT-D) for the 94 elements H-Pu.
J Chem Phys 2010;132:154104.
[47] Grimme S, Ehrlich S, Goerigk L. Effect of the damping
function in dispersion corrected density functional theory. J
Comput Chem 2011;21:1456e65.
[48] Møller C, Plesset MS. Note on an approximation treatment
for many-electron systems. Phys Rev 1934;46:618e22. http://
dx.doi.org/10.1103/PhysRev.46.618. http://link.aps.org/doi/10.
1103/PhysRev.46.618.
[49] Raghavachari K, Trucks GW, Pople JA, Head-Gordon M. A
fifth-order perturbation comparison of electron correlation
theories. Chem Phys Lett 1989;157:479e83.
[50] Hariharan PC, Pople JA. The influence of polarization
functions on molecular orbital hydrogenation energies.
Theor Chim Acta 1973;28:213e22.
[51] Francl MM, Petro WJ, Hehre WJ, Binkley JS, Gordon MS,
DeFrees DJ, et al. Self-consistent molecular orbital methods.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
[52]
[53]
[54]
[55]
[56]
[57]
[58]
[59]
[60]
[61]
[62]
[63]
[64]
[65]
[66]
[67]
[68]
[69]
xxiii. a polarization-type basis set for second-row elements. J
Chem Phys 1982;77:3654e65.
Raghavachari K, Binkley JS, Seeger R, Pople JA. Selfconsistent molecular orbital methods. XX. A basis set for
correlated wave functions. J Chem Phys 1980;72:650e4.
Clark T, Chandrasekhar J, Spitznagel GW, Schleyer PVR.
Efficient diffuse function-augmented basis sets for anion
calculations. iii. the 3-21þG basis set for first-row elements,
Li-F. J Comput Chem 1983;4(3):294e301. http://dx.doi.org/
10.1002/jcc.540040303. http://dx.doi.org/10.1002/jcc.
540040303.
Weigend F, Ahlrichs R. Balanced basis sets of split valence,
triple zeta valence and quadruple zeta valence quality for H
to Rn: design and assessment of accuracy. Phys Chem Chem
Phys 2005;7:3297e305.
Dunning Jr TH. Gaussian basis sets for use in correlated
molecular calculations. i. the atoms boron through neon and
hydrogen. J Chem Phys 1989;90:1007e23.
Barone V. Vibrational zero-point energies and
thermodynamic functions beyond the harmonic
approximation. J Chem Phys 2004;120(7):3059e65. http://
dx.doi.org/10.1063/1.1637580.
Barone V. Anharmonic vibrational properties by a fully
automated second-order perturbative approach. J Chem Phys
2005;122(1):014108. http://dx.doi.org/10.1063/1.1824881.
Bloino J, Barone V. A second-order perturbation theory route
to vibrational averages and transition properties of
molecules: general formulation and application to infrared
and vibrational circular dichroism spectroscopies. J Chem
Phys 2012;136(12):124108. http://dx.doi.org/10.1063/
1.3695210.
Cheeseman JR, Trucks GW, Keith TA, Frisch MJ. A
comparison of models for calculating nuclear magnetic
resonance shielding tensors. J Chem Phys
1996;104(14):5497e509. http://dx.doi.org/10.1063/1.471789.
http://scitation.aip.org/content/aip/journal/jcp/104/14/10.
1063/1.471789.
nek S. NMR as a tool for elucidation of structures and
Herma
estimation of electron distribution in boranes and their
derivatives. Inorg Chim Acta 1999;289(12):20e44. http://
dx.doi.org/10.1016/S0020-1693(99)00055-9. http://www.
sciencedirect.com/science/article/pii/S0020169399000559.
Norman AD, Jolly WD. Inorg Synth 1968;11:15.
Limpscomb WN. Boron hydrides. New York: W. A. Benjamin;
1963.
Torabi A, Song Y, Staroverov VN. Pressure-induced
polymorphic transitions in crystalline diborane deduced by
comparison of simulated and experimental vibrational
spectra. J Phys Chem C 2013;117(5):2210e5. http://dx.doi.org/
10.1021/jp3100415.
Begue D, Pouchan C, Guillemin J-C, Benidar A. Anharmonic
treatment of vibrational resonance polyads - the diborane: a
critical case for numerical methods. Theor Chem Acc
2012;131(3):1122. http://dx.doi.org/10.1007/s00214-012-11221.
Duncan J, Harper J. The structure of the diborane molecule.
Mol Phys 1984;51(2):371e80. http://dx.doi.org/10.1080/
00268978400100251. 00043.
Bartell LS, Carrol BL. J Chem Phys 1965;42(-):1135.
Onak TP, Landersman HL, Williams RE, Shapiro I. J Chem
Phys 1959:533.
Duncan JL, Harper J, Hamilton E, Nivellini GD. The empirical
harmonic potential function of diborane. J Mol Spectrosc
1983;102(2):416e40. http://dx.doi.org/10.1016/0022-2852(83)
90052-8. 00032.
Chong M, Matsuo M, Orimo S-I, Autrey T, Jensen CM.
Selective reversible hydrogenation of Mg(B3H8)2/MgH2 to
Mg(BH4)2: pathway to reversible borane-based hydrogen
[70]
[71]
[72]
[73]
[74]
[75]
[76]
[77]
[78]
[79]
[80]
[81]
[82]
[83]
6823
storage? Inorg Chem 2015;54(8):4120e5. http://dx.doi.org/
10.1021/acs.inorgchem.5b00373. http://dx.doi.org/10.1021/
acs.inorgchem.5b00373.
Olson JK, Boldyrev AI. Ab initio characterization of the
flexural anion found in the reversible dehydrogenation.
Comput Theor Chem 2011;967(1):1e4. http://dx.doi.org/
10.1016/j.comptc.2011.04.011.
Bushweller CH, Beall H, Grace M, Dewkett WJ, Bilofsky HS.
Temperature dependence of the proton nuclear magnetic
resonance spectra of copper(i) borane complexes, B3H
8 salts,
and icosahedral carboranes. quadrupole-induced spin
decoupling. fluxional behavior. J Am Chem Soc
1971;93(9):2145e9. http://dx.doi.org/10.1021/ja00738a009.
Beall H, Bushweller CH, Dewkett WJ, Grace M. Intramolecular
exchange and ”thermal” decoupling in B3H8-compounds. J
Am Chem Soc 1970;92(11):3484e6. http://dx.doi.org/10.1021/
ja00714a053.
Yan Y, Remhof A, Mauron P, Rentsch D, Łodziana Z, Lee Y-S,
Lee H-S, Cho YW, Züttel A. Controlling the dehydrogenation
reaction toward reversibility of the LiBH4-Ca(BH4)2 eutectic
system. J Phys Chem C 2013;117(17):8878e86. http://
dx.doi.org/10.1021/jp401628g.
Huang Z, Chen X, Yisgedu T, Zhao J-C, Shore SG. Highcapacity hydrogen release through hydrolysis of NaB3H8. Int J
Hydrogen Energy 2011;36(12):7038e42. http://dx.doi.org/
10.1016/j.ijhydene.2011.03.033. http://www.sciencedirect.
com/science/article/pii/S0360319911006227.
Tomkinson J, Ludman CJ, Waddington TC. The i.r., raman
and inelastic neutron scattering spectra of caesium
octahydridotriborate, CsB3H8. Spectrochim Acta Part A Mol
Spectrosc 1979;35(2):117e22. http://dx.doi.org/10.1016/05848539(79)80171-3. http://www.sciencedirect.com/science/
article/pii/0584853979801713.
Il’inchik EA, Gulyaev RV, Svintsitskii DA, Myakishev KG,
Volkov VV. The ESCA analysis of the B3H
8 anion. Russ J Gen
Chem 2010;80(8):1550e6. http://dx.doi.org/10.1134/
S1070363210080025. 00001, http://link.springer.com/article/
10.1134/S1070363210080025.
nek S. Boron-11 NMR spectra of boranes, main-group
Herma
heteroboranes, and substituted derivatives. Factors
influencing chemical shifts of skeletal atoms. Chem Rev
1992;92(2):325e62. http://dx.doi.org/10.1021/cr00010a007.
http://dx.doi.org/10.1021/cr00010a007.
Teixidor F, Vinas C, Rudolph RW. Rules for predicting the
boron-11 NMR spectra of closo-boranes and closoheteroboranes. Inorg Chem 1986;25(19):3339e45. http://
dx.doi.org/10.1021/ic00239a005. 00047, http://dx.doi.org/10.
1021/ic00239a005.
http://www.chemistry.sdsu.edu/research/BNMR [last
accessed: 10.08.15].
Matsui Y, Taylor RC. Vibrational spectra and structure of the
heptahydrodiborate ion, [B2H7] in glycol ethers.
Spectrochim Acta A 1989;45(2):299e304. http://dx.doi.org/10.
1016/0584-8539(89)80137-0. http://www.sciencedirect.com/
science/article/pii/0584853989801370.
Raghavachari K, von Rague Schleyer P, Spitznagel GW.
Theoretical structure of the B2H
7 anion. J Am Chem Soc
1983;105(18):5917e8. http://dx.doi.org/10.1021/ja00356a035.
arXiv:http://dx.doi.org/10.1021/ja00356a035.
Shore SG, Lawrence SH, Watkins MI, Bau R. Structure of the
[B2H7] anion. J Am Chem Soc 1982;104(26):7669e70. http://
dx.doi.org/10.1021/ja00390a053. arXiv:http://dx.doi.org/10.
1021/ja00390a053.
Khan SI, Chiang MY, Bau R, Koetzle TF, Shore SG,
Lawrence SH. A neutron diffraction study of
[N(PPh3)2]þ[B2H7]e$CH2Cl2 at 80 k. J Chem Soc, Dalton Trans
1986:1753e7. http://dx.doi.org/10.1039/DT9860001753. http://
dx.doi.org/10.1039/DT9860001753.
6824
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 6 8 1 4 e6 8 2 4
[84] Sapse AM, Osorio L. An ab initio study of the B2H
7 anion.
Inorg Chem 1984;23(5):627e8. http://dx.doi.org/10.1021/
ic00173a030. arXiv:http://dx.doi.org/10.1021/ic00173a030.
re P, Hagemann H. Fermi resonances of
[85] Carbonnie
borohydrides in a crystalline environment of alkali
metals. J Phys Chem A 2006;110(32):9927e33. http://
dx.doi.org/10.1021/jp062091d. http://dx.doi.org/10.1021/
jp062091d.
[86] D'Anna V, Lawson Daku LM, Hagemann H. Quantitative
spectra-structure relations for borohydrides. J Phys Chem C
2015;119:21868e74. http://dx.doi.org/10.1021/
acs.jpcc.5b06045. arXiv:http://dx.doi.org/10.1021/acs.jpcc.
5b06045, http://dx.doi.org/10.1021/acs.jpcc.5b06045.
[87] He L, Li H-W, Nakajima H, Tumanov N, Filinchuk Y,
Hwang S-J, Sharma M, Hagemann H, Akiba E. Synthesis of a
bimetallic dodecaborate LiNaB12H12 with outstanding
superionic conductivity. Chem Mater 2015;27(16):5483e6.
http://dx.doi.org/10.1021/acs.chemmater.5b01568.
[88] Serrar C, Es-sofi A, Boutalib A, Ouassas A, Jarid A. Synthesis,
structural characterization, and theoretical calculations of a
[89]
[90]
[91]
[92]
new copper(i)-octahydrotriborate complex. Inorg Chem
2000;39(10):2224e6. http://dx.doi.org/10.1021/ic990909m.
Hildebrandt SJ, Gaines DF, Calabrese JC. Low-temperature
crystal and molecular structure of tricarbonyl
[octahydrotriborato(1-)]manganese, (CO)3MnB3H8. Inorg
Chem 1978;17(4):790e4. http://dx.doi.org/10.1021/
ic50182a002.
Hagemann H, Longhini M, Kaminski JW, Wesolowski TA,
Cerný
R, Penin N, et al. LiSc(BH)44: a novel salt of Liþ and
discrete Sc(BH4)
4 complex anions. J Phys Chem A
2008;112(33):7551e5. http://dx.doi.org/10.1021/jp803201q.
Cerný
R, Kim KC, Penin N, D'Anna V, Hagemann H, Sholl DS.
AZn2(BH)45 (A ¼ Li, Na) and NaZn(BH)43: structural studies. J
Phys Chem C 2010;114(44):19127e33. http://dx.doi.org/
10.1021/jp105957r.
Caputo R, Garroni S, Olid D, Teixidor F, Surinach S,
Baro MD. Can Na2[B12H12] be a decomposition product of
NaBH4? Phys Chem Chem Phys 2010;12:15093e100. http://
dx.doi.org/10.1039/C0CP00877J. http://dx.doi.org/10.1039/
C0CP00877J.