Raman and Density Functional Theory Studies of Li2Mo4O13 Structures in Crystalline and Molten States

Article abstract of DOI:10.1021/acs.inorgchem.7b02263

The Li₂Mo₄O₁₃ melt structure and its Raman spectral characteristics are the key for establishing the composition-structure relationship of lithium molybdate melts. In this work, Raman spectroscopy, factor group analysis, and density functional theory (DFT) were applied to investigate the structural and spectral details of the H-Li₂Mo₄O₁₃ crystal and a Li₂Mo₄O₁₃ melt. Factor group analysis shows that the crystal has 171 vibrational modes (84A_g + 87A_u), including three acoustic modes (3A_u), six librational modes (2A_g + 4A_u), 21 translational modes (7A_g + 14A_u), and 141 internal modes (75A_g + 66A_u). All of the A_g modes are Raman-active and were assigned by the DFT method. The Li₂Mo₄O₁₃ melt structure was deduced from the H-Li₂Mo₄O₁₃ crystal structure and demonstrated by the DFT method. The results show that the Li₂Mo₄O₁₃ melt is made up of Li⁺ ions and Mo₄O₁₃^2- groups, each of which is formed by four corner-sharing MoO₃?/MoO₂?₂ tetrahedra (? = bridging oxygen). The melt has three acoustic modes (3A) and 54 optical modes (54A). All of the optical modes are Raman-active and were accurately assigned by the DFT method.

Full text of DOI:10.1021/acs.inorgchem.7b02263

Article
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Cite This: Inorg. Chem. XXXX, XXX, XXX-XXX
Raman and Density Functional Theory Studies of Li2Mo4O13
Structures in Crystalline and Molten States
Songming Wan,*,†,‡ Bo Zhang,† Yanan Yao,†,§ Guimei Zheng,†,§ Shujie Zhang,†,§ and Jinglin You*,‡
†Anhui Key Laboratory for Photonic Devices and Materials, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of
Sciences, Hefei 230031, China
§University of Science and Technology of China, Hefei 230026, China
‡School of Material Science and Engineering, Shanghai University, Shanghai 200072, China
S
* Supporting Information
ABSTRACT: The Li2Mo4O13 melt structure and its Raman spectral
characteristics are the key for establishing the composition−structure
relationship of lithium molybdate melts. In this work, Raman spectros-
copy, factor group analysis, and density functional theory (DFT) were
applied to investigate the structural and spectral details of the H-
Li2Mo4O13 crystal and a Li2Mo4O13 melt. Factor group analysis shows that
the crystal has 171 vibrational modes (84Ag + 87Au), including three
acoustic modes (3Au), six librational modes (2Ag + 4Au), 21 translational
modes (7Ag + 14Au), and 141 internal modes (75Ag + 66Au). All of the Ag
modes are Raman-active and were assigned by the DFT method. The
Li2Mo4O13 melt structure was deduced from the H-Li2Mo4O13 crystal
structure and demonstrated by the DFT method. The results show that
the Li2Mo4O13 melt is made up of Li+ ions and Mo4O132− groups, each of
which is formed by four corner-sharing MoO3Ø/MoO2Ø2 tetrahedra (Ø
= bridging oxygen). The melt has three acoustic modes (3A) and 54 optical modes (54A). All of the optical modes are Raman-
active and were accurately assigned by the DFT method.
2, 3, and 4) melts.11 Voronko et al. deemed that the spectral
1. INTRODUCTION
changes arose from a series of structural changes. When MoO3
Alkali molybdates are one kind of old and versatile flux used to
produce various single-crystal materials.1 The first reported
alkali molybdate flux is lithium molybdate, which was employed
to prepare emerald crystals as early as 1888.2 Intense interest in
alkali molybdate fluxes was kindled by the emergence of borate
nonlinear optical crystals in the 1980s, during which the
K2Mo3O10 flux was widely used to grow a large variety of
huntite-type crystals with the general formula RM3(BO3)4 (R =
rare-earth element; M = Al, Sc, Fe, Ga, or Cr).3 In the following
2 decades, Li2Mo3O10/Li2Mo4O13 and Cs2Mo2O7 fluxes were
frequently used to grow LiB3O5 and CsB3O5 crystals of high-
quality and large size, respectively.4−9 The widespread
application of alkali molybdates has attracted great interest in
the study of their fluxing behavior, which is believed to be
essential in understanding numerous crystal growth processes.
The structures of alkali molybdate melts are an important
aspect for a full understanding of their fluxing behavior.
Recently, Voronko and co-workers investigated the structures
of four potassium molybdate melts with the general formula
K2MonO3n+1 (n = 1, 2, 3, and 4) by high-temperature Raman
spectroscopy.10 Their results showed that the melt spectra
changed systematically with an increase in the MoO3 content
but subtly upon a further addition of MoO3 into a MoO3-rich
melt such as K2Mo3O10. Similar spectral characteristics were
also observed as we studied the spectra of Li2MonO3n+1 (n = 1,
2−
was added into a Li2MoO4 melt, monomeric MoO4 groups
connected with MoO3 molecules and stepwise-formed
2−
Mo2O72−, Mo3O102−, and Mo4O13 groups that consist of
two, three, and four corner-sharing MoO3Ø/MoO2Ø2 (Ø =
bridging oxygen) units, respectively.10 The viewpoint is very
important for establishing the composition−structure relation-
ship of alkali molybdate melts. However, extracting structural
information from a melt Raman spectrum often suffers from
limited spectral resolution because of the low-intense, broad,
and overlapping Raman bands at high temperature, which often
leads to uncertainty in the band assignments and then in
structural determination. Therefore, theoretical studies are
essential for analyzing the Raman spectra and structures of
most melts including the alkali molybdate melts.
First-principles calculation provides a means to simulate the
Raman spectrum of a melt with an established structure and is
an effective tool for aiding the experimental analyses of various
melt Raman spectra and structures.12−15 Recently, Wang and
co-workers studied the Raman spectra of the K2MonO3n+1 (n =
1, 2, and 3) melts with the restricted Hartree−Fock (RHF)
method,16 and we studied the Raman spectra of the
Received: September 3, 2017
© XXXX American Chemical Society
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Li2MonO3n+1 (n = 2 and 3) melts with the density functional
theory (DFT) method.11 However, the Raman spectra of alkali
molybdate melts rich in MoO3, such as alkali tetramolybdate
melts, still remain unexplored, although they are especially
important to unraveling the subtle spectral characteristics of
MoO3-rich melts and then to determine the composition−
structure relationship of alkali molybdate melts. In this paper,
the DFT method is used to analyze the structure of the
Li2Mo4O13 melt. Prior to this, we study the Raman spectrum of
the H-Li2Mo4O13 crystal because of its correlation with that of
the Li2Mo4O13 melt.
Li2Mo4O13 is the most stable phase at both room and high
temperatures. The XRD pattern of the synthesized Li2Mo4O13
polycrystalline powder is shown in Figure 1. It matches with the
H-Li2Mo4O13 standard pattern (JCPDS 70-1709), indicating
that the product is H-Li2Mo4O13. The Raman spectrum of H-
Li2Mo4O13 is presented in Figure 2.
2. EXPERIMENTAL SECTION
Li2Mo4O13 polycrystalline powder was prepared using a two-step solid-
state synthesis method. Analytical-grade Li2CO3, H3BO3, and MoO3,
purchased from Sinopharm Chemical Reagent Co. Ltd., were used
without further purification. In the first step, polycrystalline Li2MoO4
was synthesized by heating a mixture of Li2CO3 and MoO3 with a
molar ratio of 1:1 at 500 °C for 12 h and then sintering at 650 °C for
12 h. In the second step, the polycrystalline Li2Mo4O13 was
synthesized by heating twice a mixture of Li2MoO4 and MoO3 in a
Li2MoO4/MoO3 molar ratio of 1:3 at 550 °C for 12 h. Prior to each
heat treatment, the reactants were ground and mixed thoroughly in an
agate mortar. The formation of Li2MoO4 and Li2Mo4O13 was
confirmed by X-ray diffraction (XRD) analysis, which was performed
on a computer-controlled MXPAHF diffractometer with graphite-
monochromatized Cu Kα radiation (λ = 1.54056 Å).
Figure 1. XRD pattern of the synthesized Li2Mo4O13 polycrystalline
powder with the standard XRD pattern of H-Li2Mo4O13 (JCPDS 70-
1709).
The Li2Mo4O13 polycrystalline powder was placed in a 2 mm × 5
mm × 10 mm platinum boat and heated by a homemade
microfurnace. When the sample began to melt, the temperature was
held until a clear and homogeneous melt was obtained. Raman spectra
of the polycrystalline powder/melt were recorded on a Jobin Yvon
LABRaman HR800 spectrometer equipped with a confocal micro-
scope. The 532 nm line of a Q-switched pulsed SHG−Nd:YAG laser
was employed as the excitation source with a power of about 1.0 W.
The scattering light was collected in a back-scattering configuration
with a total integration time of 200 s for the polycrystalline sample and
100 s for the melt sample. The spectral resolution was less than 1.0
cm−1.
All of the DFT calculations were carried out using plane-wave basis
sets and the Wu−Cohen functional of the generalized gradient
approximation17 available in the Cambridge Sequential Total Energy
Package (CASTEP) code.18 Ion−valence electron interaction was
represented by norm-conserving pseudopotentials. The valence
electron configurations were 2s1 for lithium, 4s24p64d55s1 for
molybdenum, and 2s22p4 for oxygen. In these calculations, the
tolerances of the self-consistent field, force, and stress were set as 5 ×
10−7 eV/atom, 0.05 eV/Å, and 0.1 GPa, respectively. According to the
results of convergence tests for the total energies of the Li2Mo4O13
crystal and melt (see Tables S1 and S3 and Figures S1 and S2 for more
details), the Brillouin zone integrations were done over a 2 × 1 × 2
Monkhorst−Pack grid for the crystal and over a 3 × 3 × 1
Monkhorst−Pack grid for the melt; a plane-wave cutoff of 800 eV was
set for both the crystal and melt.
Figure 2. Experimental and calculated Raman bands of the H-
Li2Mo4O13 crystal and their corresponding modes (ν, stretching
vibration; δ, bending vibration; ω, wagging vibration; τ, twisting
vibration).
Much work has been done to show the spectral dependence
of structural variations.26−28 Considering that the Li2Mo4O13
melt is evolved from the H-Li2Mo4O13 polycrystalline powder,
analysis of the H-Li2Mo4O13 crystal Raman spectrum should be
helpful for determining the melt spectrum and structure. Here,
we used the factor group analysis method to classify the
vibrational modes of the H-Li2Mo4O13 crystal under the
assumption that the internal vibrations of the molybdate
groups are independent of the lattice vibrations.29,30 The H-
Li2Mo4O13 crystal structure has been reported by Gatehouse
Density functional perturbation theory (DFPT) was employed to
probe the lattice dynamics of the Li2Mo4O13 crystal and melt.19−21
Raman frequencies were obtained by diagonalization of the dynamical
matrices. Raman intensities were calculated using a hybrid DFPT−
finite displacement method and corrected by Bose−Einstein factors
corresponding to the experimental temperatures (300 K for the
Li2Mo4O13 crystal and 850 K for the Li2Mo4O13 melt) and the
wavelength of the excitation source (532 nm). The Raman lines were
broadened with a Lorentzian line-shape function using the SWizard
software.22
and Miskin.23 It crystallizes in the triclinic P1 space group with
̅
three formulas per unit cell. All of the atoms occupy the 2i sites
except for an oxygen atom, which occupies the 1b site. The
factor group of the H-Li2Mo4O13 crystal at the Brillouin zone
center is isomorphic to the Ci point group. Table 1 lists the
symmetry operations of the Ci point group, the numbers of the
atoms invariant under the operation R (NR), and the characters
of the irreducible representation under the symmetry operation
R (χR). According to factor group analysis, the H-Li2Mo4O13
crystal has 171 vibrational modes (84Ag + 87Au), including
three acoustic modes (3Au), 21 translational modes (7Ag +
3. RESULTS AND DISCUSSION
Li2Mo4O13 exists in three different crystalline modifications,
defined as H, M, and L phases.23−25 Among them, H-
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Table 1. Factor Group Analysis of H-Li2Mo4O13 Vibrational
Modes
a
N, s, and v are the numbers of total atoms, molybdate groups plus
lithium ions, and lithium ions in the H-Li2Mo4O13 unit cell,
respectively. NR(N), NR(s), and NR(s−v) are the numbers of the
total atoms whose positions remain invariant, the molybdate groups
plus the lithium ions whose centers of mass remain invariant, and the
molybdate groups whose centers of mass remain invariant under the
b
symmetry operation R, respectively. χR(N), χR(T), χR(T′), χR(R′),
Figure 3. Atomic displacements for five selected Raman modes of the
H-Li2Mo4O13 crystal.
and χR(n) are the characters of the irreducible representation under
the symmetry operation R. N, T, T′, R′, and n denote all of the
vibrational modes, the translational modes of the H-Li2Mo4O13 unit
cell as a whole, the other translational modes, the librational modes,
and the internal modes, respectively. The plus or minus sign is used
according to whether R is a pure rotation or a rotation accompanied by
a reflection.
temperature (see Figure 4b for an example). The phenomenon
can be qualitatively interpreted in terms of anharmonic forces
14Au), six librational modes (2Ag + 4Au), and 141 internal
modes (75Ag + 66Au). All of the Ag modes are Raman-active.
The calculated Raman spectrum of the H-Li2Mo4O13 crystal
is presented in Figure 2 and compared with the experimental
one. The comparison shows a satisfactory agreement between
the calculated and experimental frequencies and an overall
agreement between the intensities. It is worth noting that the
calculated intensities of some modes in the high-frequency
region are underestimated. Similar results were also found in
the calculated Raman spectra of K2MonO3n+1 (n = 1, 2, and 3)
crystals;16 we thus believe that the underestimation is due to
the inherent shortcoming of the calculated method.
Figure 4. Raman spectra of the H-Li2Mo4O13 polycrystalline powder
recorded at (a) room temperature and (b) 550 °C. Raman spectra of
the Li2Mo4O13 melt recorded at (c) 570 and (d) 585 °C.
The calculation demonstrates that the H-Li2Mo4O13 crystal
has 84Ag Raman-active modes and provides the atomic
displacements of each mode. The two lowest-frequency
Raman modes (2Ag), located at 69 and 73 cm−1 (calculated
values, which are the same below), are primarily due to the
librational vibrations of the molybdate groups. The other seven
Raman external modes (7Ag), located at 234, 369, 376, 379,
431, 452, and 460 cm−1, are assigned to the translational
vibrations of the lithium ions. The remaining Raman modes
(75Ag) are attributed to the internal modes of the molybdate
groups, and their corresponding vibrational bands can be
divided into three regions/types (see Figure 2): (1) The bands
below 460 cm−1 arise from the wagging/twisting vibrations of
the molybdate groups, the translations of the lithium ions, or
their combination. (2) The bands in the 420−746 cm−1 range
arise from the bending vibrations of the Mo−O−Mo bonds.
(3) The bands in the 845−991 cm−1 range arise from the
stretching vibrations of the MoO bonds. Atomic displace-
ments for five typical Raman bands are illustrated in Figure 3.
The Raman spectra of the Li2Mo4O13 polycrystalline powder
recorded below its melting point show an expected broadening
of bands and an expected decrease in frequency with increasing
of chemical bonds in the H-Li2Mo4O13 crystal structure.31 This
result implies that the H-Li2Mo4O13 crystal structure is stable
below its melting point.
According to the Li2MoO4−MoO3 phase diagrams reported
by Van Der Wielen et al.,32,33 Li2Mo4O13 melts incongruently,
which indicates that a melt with a composition different from
that of Li2Mo4O13 will be produced upon melting the H-
Li2Mo4O13 polycrystalline powder. In view of this, we collected
the Raman spectra of the melts when H-Li2Mo4O13 melted
partially (Figure 4c) and completely (Figure 4d). Interestingly,
the two spectra are exactly the same, indicating that the melt
composition was fixed at Li2Mo4O13 throughout the melting
process, and thus H-Li2Mo4O13 must be a congruently melting
compound. The conclusion is consistent with the experimental
results found by Gatehouse and Miskin.25 In their experiment, a
metastable L-Li2Mo4O13 crystal was directly produced by slowly
cooling a Li2Mo4O13 melt. The congruently melting behavior of
Li2Mo4O13 suggests that the Li2Mo4O13 melt and H-Li2Mo4O13
crystal, as well as the L-Li2Mo4O13 crystal, are probably made
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up of different molybdate groups with the same chemical
composition.
optimization, the unit cell parameters and atomic positions
were relaxed in order to obtain the most stable conformation.
The result is shown in Figure 6. The optimized Mo−O bond
Figure 4 shows that the Raman bands of low and middle
frequency change drastically in the crystal−melt transition.
According to the above-calculated results, the low- and middle-
frequency bands are mainly related to the wagging/twisting
vibrations of the molybdate groups or the bending vibrations of
the Mo−O−Mo bonds (see Figures 2 and 3). The spectral
change proves that the molybdate groups in the melt are
different from those in the crystal. On the other hand, the high-
frequency bands of the crystal corresponding to the stretching
vibrations of the MoO bonds (see Figure 2 and 3) persist in
the melt spectrum, suggesting that the MoO bonds still exist
in the melt.
The H-Li2Mo4O13 crystal structure is built up of Li+ ions and
Mo−O ribbons that are formed by edge-sharing Mo−O
octahedra or corner-sharing Mo−O pyramids.23 The crystal
structure includes three types of Mo−O bonds: MoO double
bonds with lengths shorter than 180 pm, Mo−O single bonds
with lengths from 180 to 210 pm, and Mo−O weak bonds with
lengths larger than 210 pm. According to the chemical bonding
theory for describing a crystal growth/melting process,34,35 we
consider that the melting of H-Li2Mo4O13 results from breakage
of the weak Mo−O bonds. Along with the melting, the
complicated Mo−O ribbons in the crystal structure are
Figure 6. Structural model of the Li2Mo4O13 melt (top) and its
experimental and calculated Raman spectra (bottom): (a) exper-
imental spectrum; calculated spectra broadened by a Lorentzian line-
shape function with (b) experimental fwhm’s and (c) a fixed fwhm of 1
cm−1.
2−
destroyed and then transform to Mo4O13 chains, each of
which comprises four corner-sharing MoO3Ø/MoO2Ø2
2−
tetrahedra, as shown in Figure 5. Therefore, the Mo4O13
lengths and O−Mo−O angles coincide well with the reported
values (see Figure S3 and Tables S4 and S5 for more details).
The optimized structure consists of two types of Mo−O bonds:
the first one is the MoO double bond, which is pertinent to
the terminal oxygen atoms, ranging from 171.2 to 175.8 pm in
length; the second one is the Mo−O single bond with a length
of about 190 pm, which is pertinent to the bridging oxygen
atoms.
The Raman spectra of the Li2Mo4O13 melt were calculated
on the basis of the optimized structural model and are
presented in Figure 6b,c along with the experimental spectrum
(Figure 6a). Considering that different Raman bands show
different degrees of broadening at high temperatures but the
degrees are difficult to predict, experimental full widths at half-
maximum (fwhm’s) were used here to broaden the calculated
Raman bands (100, 80, and 50 cm−1 are used in the frequency
ranges lower than 500 cm−1, from 500 to 900 cm−1, and larger
than 900 cm−1, respectively). The final result is shown in Figure
6b. The spectrum broadened with a fixed fwhm of 1 cm−1 is
also presented as Figure 6c in order to provide more detailed
spectral information. Both of the calculated frequencies and
peak profiles are in agreement with the experimental results,
indicating that the optimized model can be used to describe the
Li2Mo4O13 melt. The calculated intensities of high-frequency
bands are found to be lower than the experimental ones, which
is similar to the calculated spectrum of the Li2Mo4O13 crystal
and also due to the inherent shortcoming of the calculated
method.
Figure 5. (a) H-Li2Mo4O13 crystal structure viewed along the c axis. (b
2−
and c) Mo4O13 chains viewed along directions slightly deviating
away from the b axis. The Li+ ions are omitted in the structure.
chain is the probable anion motif of the Li2Mo4O13 melt. As
mentioned above, the L-Li2Mo4O13 crystal structure can be
formed by cooling a Li2Mo4O13 melt. Upon breakage of the
weak Mo−O bonds in a manner similar to that used for the H-
Li2Mo4O13 crystal, the molybdate groups in the L-Li2Mo4O13
crystal structure can also be regarded as an assembly of
25
Mo4O13 chains, which further supports the theory that the
The Li2Mo4O13 melt model comprises two Li+ ions and one
Mo4O132− chain that is formed by four corner-sharing MoO3Ø/
MoO2Ø2 tetrahedra. The model contains 19 atoms and thus
has 57 vibrational modes (57A). With the exception of three
acoustic modes (3A), the rest of the 54 modes (54A) are
optical modes. DFT calculation demonstrates that the 54
2−
2−
Mo4O13 chain is the anion motif of the Li2Mo4O13 melt.
On the basis of the above structural analyses, a Li2Mo4O13
2−
melt structural model was constructed. One Mo4O13 chain,
together with two Li+ ions, was placed in a monoclinic unit cell.
Then the geometry of the model was optimized. During
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optical modes are all Raman-active. Their frequencies and
mode assignments are shown in Figure 7 (see Table S6 for
942 and 950 cm−1 and those of the MoO3Ø tetrahedra at 888
and 898 cm−1; the MoO symmetric stretching vibrations of
the MoO2Ø2 tetrahedra are located at 980 and 981 cm−1 and
those of the MoO3Ø tetrahedra at 952 and 960 cm−1. The
result reveals that the MO bonds of the MoO2Ø2 tetrahedra
are stronger than those of the MoO3Ø tetrahedra.
4. CONCLUSIONS
Factor group analysis and the DFT method have been used to
analyze the Raman spectrum of the H-Li2Mo4O13 crystal. The
crystal has 171 vibrational modes (84Ag + 87Au), including
three acoustic modes (3Au), six librational modes (2Ag + 4Au),
21 translational modes (7Ag + 14Au), and 141 internal modes
(75Ag + 66Au). All of the 84Ag modes are Raman-active. The
Raman bands below 460 cm−1 are related to the wagging/
twisting vibrations of the molybdate groups, the translations of
the Li+ ions, or their mixture; the Raman bands in the range of
420−746 cm−1 arise from the bending vibrations of the Mo−
O−Mo bonds; the Raman bands in the range of 845−991 cm−1
are attributed to the stretching vibrations of the MoO bonds.
The Li2Mo4O13 crystal melts congruently. In the melting
process, two types of weak Mo−O bonds in the crystal break.
As a result, the Mo−O octahedra/pyramids in the Li2Mo4O13
crystal structure transform to Mo−O tetrahedra in the
Li2Mo4O13 melt structure. The anion motif in the melt was
demonstrated to be the Mo4O132− chain that is formed by four
corner-sharing MoO3Ø/MoO2Ø2 tetrahedra. The Raman
bands in the range of 160−440 cm−1 are mainly attributed to
Figure 7. Calculated Raman bands of the Li2Mo4O13 melt and their
mode assignments (ν, stretching vibration; δ, bending vibration; ω,
wagging vibration; τ, twisting vibration).
more details). The bands in the range of 160−440 cm−1 are
attributed to the wagging and twisting vibrations of the
Mo4O13 chain. The bands in the range of 460−570 cm−1
2−
mainly arise from the motions of the Li+ ions. The bands with
frequencies of 747, 869, and 876 cm−1 can be assigned to the
bending vibrations of the Mo−O−Mo bonds. The bands with
frequencies larger than 880 cm−1 are related to the stretching
vibrations of the MoO bonds. Five typical vibrational modes
are depicted in Figure 8.
2−
the wagging/twisting vibrations of the Mo4O13 chain; the
Raman bands in the range of 460−570 cm−1 mainly arise from
the motions of the Li+ ions; the Raman bands with frequencies
of 747, 869, and 876 cm−1 can be assigned to the bending
vibrations of the Mo−O−Mo bonds; the Raman bands with
frequencies larger than 880 cm−1 belong to the stretching
vibrations of the MoO bonds. The Mo−O−Mo bonds
connecting two Mo−O tetrahedra are stronger than those
connecting two Mo−O octahedra/pyramids; the MoO
bonds of the MoO2Ø2 tetrahedra are stronger than those of
the MoO3Ø tetrahedra.
The work provides a new method to study the Raman
spectra and structures of alkali molybdate melts. The results can
be used to unravel the subtle spectral characteristics of various
alkali molybdate melts rich in MoO3 and further to determine
their composition−structure relationship.
ASSOCIATED CONTENT
* Supporting Information
■
S
Figure 8. Five typical Raman modes of the Li2Mo4O13 melt and their
frequencies.
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.inorg-
chem.7b02263.
A comparison between Figures 2 and 7 shows that the
frequencies of the Mo−O−Mo bending vibrations of the
Li2Mo4O13 melt are higher than those of the Li2Mo4O13 crystal,
which implies that the Mo−O−Mo bonds connecting two
Mo−O tetrahedra are stronger than those connecting two
Mo−O octahedra/pyramids. The Mo4O132− chain includes two
types of MoO bonds: one belongs to the terminal MoO3Ø
tetrahedra and the other to the middle MoO2Ø2 tetrahedra.
Our calculated results demonstrate the deduction made by
Voronko et al. that the MoO stretching vibrations of the
MoO2Ø2 tetrahedra have higher frequencies than those of the
MoO3Ø tetrahedra.10 For example, the MoO antisymmetric
stretching vibrations of the MoO2Ø2 tetrahedra are located at
Convergence tests for the Li2Mo4O13 crystal and melt
total energies with respect to the Γ-centered k-point grids
and cutoff energies, calculated Li2Mo4O13 crystal vibra-
tional modes and their frequencies, the initial Li2Mo4O13
melt structural model and its geometrical parameters,
and calculated Li2Mo4O13 melt vibrational modes and
their frequencies (PDF)
AUTHOR INFORMATION
Corresponding Authors
*E-mail: smwan@aiofm.ac.cn (S.M.W.). Fax: 86 0551
65591054.
■
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*E-mail: jlyou@staff.shu.edu.cn (J.L.Y.). Fax: 86 021 56331482.
ORCID
Songming Wan: 0000-0002-8923-7914
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
The work is financially supported by the National Natural
Science Foundations of China (Grants 51372246 and
21773152) and Open Project of State Key Laboratory of
Advanced Special Steel, Shanghai University. The calculations
were partially performed at the Center for Computational
Science, CASHIPS.
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DOI: 10.1021/acs.inorgchem.7b02263
Inorg. Chem. XXXX, XXX, XXX−XXX