# Geometric and Electronic Properties of Li2GeO3

Vo Khuong Dien  [  Nguyen Thi Han  Thi Dieu Hien Nguyen  [  [  Thi My Duyen
Huynh  Hai Duong Pham  [<EMAIL_ADDRESS>Ming Fa-Lin
<EMAIL_ADDRESS>[  [

###### Abstract

The 3D ternary Li2GeO3 compound, which could serve as the electrolyte material
in Li+-based batteries, exhibits an unusual lattice symmetry (orthorhombic
crystal), band structure, charge density distribution and density of states.
The essential properties are fully explored through the first-principles
method. In the delicate calculations and analyses, the main features of atom-
dominated electronic energy spectrum, space-charge distribution, and
atom-/orbital-projected density of states are sufficient to identify the
critical multi-orbital hybridizations of the chemical bonds: 2s-(2px, 2py,
2pz) and (4s, 4px, 4py, 4pz)-(2s, 2px, 2py, 2pz), respectively, for Li-O and
Ge-O. This system possesses a large indirect gap of Eg$=$3.77 eV. There exist
a lot of significant covalent bonds, with an obvious non-uniformity and
anisotropy. In addition, spin-dependent magnetic configurations are completely
absent. The theoretical framework could be developed to investigate the
important features of anode and cathode materials related to lithium oxide
compounds.

National Cheng Kung University]Department of Physics, National Cheng Kung
University, Taiwan National Cheng Kung University]Department of Physics,
National Cheng Kung University, Taiwan Thai Nguyen University of
Education]Department of Chemistry, Thai Nguyen University of Education, Viet
Nam National Cheng Kung University]Department of Physics, National Cheng Kung
University, Taiwan National Cheng Kung University]Department of Physics,
National Cheng Kung University, Taiwan National Cheng Kung
University]Hierarchical Green Energy Materials, Hi- esearch Center, National
Cheng Kung University, Taiwan

##  1 INTRODUCTION

Increasing demands for storage of electricity from solar and wind energy,
mobile electronic devices, electric vehicles promote the development of cost-
effective and reliable electrical energy storage 1, 2, 3. Among a large number
of possible energy storage technologies such as nickel-cadmium batteries,
zinc-manganese batteries, nickel-hydrogen batteries, fuel cells, lead-acid
batteries, redox flow batteries, Lithium-ion batteries, etc., the rechargeable
Lithium-ion batteries (LIBs) has attracted a great deal of attention due to
their high specific energy, wide working temperature range, high operational
voltage and a long cycle life 3.

A commercial LIB is composed of a negative (cathode) and positive (anode)
electrode separated by an electrolyte 3, in which each component should have a
good physical, chemical and material properties, especially for the latter
ones to ensure the rapid lithium-ion transmission, is compatible with the
electrodes and chemically inert at the same time. Apparently, a drastic change
of geometric structures is revealed in the cathode/electrolyte/anode
materials. The structural transformations between two-metastable
configurations during the battery operation is rather complex and thus very
difficult to solve.

In general, the cathode and anode systems of Li+-based batteries belong to a
class of solid-state materials, such as the three-dimensional (3D) ternary
LiFe/Co/NiO 4, 5, 6 and Li4Ti5O12/graphite compounds 7, 8, respectively,
whereas conventional electrolytes belong to liquid states, which come with
have potential security risks concerning volatilization, flammability and
explosion. Recent experimental studies indicated that secondary batteries
using inorganic solid electrolytes would be the ultimate batteries to resolve
the safety issues 9. Moreover, the battery cell design would be simplified
with solid electrolytes 10. Some candidate systems for solid-state
electrolytes are Li3OCl 11, Li2SiO3 12, 13 and Li2GeO3 14, 15, 16, 17, 18.
Among them, the later one has attracted significant research interest due to
the following reasons: the 3D ternary Li2GeO3 is produced by relatively simple
and direct methods and possesses a reliable ionic conductivity
(1.5$\times$10-5 ($\Omega$.cm)-1) 15, which is promising as an alternative for
the conventional liquid electrolytes. The ternary Li2GeO3 compound was also
reported as a new Li+ superionic conductor exhibiting an excellent
electrochemical performance, such as cycle stability, charge capacity (725
mAhg-1) and rate capability (810 mAhg-1 after 35 cycles)18. Furthermore, other
features, such as the large pyroelectric constants (5 times larger than that
of tourmaline), high piezoelectric constant (5 times larger than that of
$\alpha$-quartz), transparency in the visible region and moderate mechanical
impedance, can be used in various pyroelectric, piezoelectric, and acousto-
optic devices 19, 20.

On the theoretical side, a number of studies using the molecular dynamics (MD)
and density functional theory (DFT) were investigated on the phase stability
21, 22, 23, defect structure 24, 25, electronic properties 23 and the Li+
transport mechanisms 22, 24, 25, 26 of the electrodes or electrolyte materials
of LIBs. The complicated atomic interactions (multi-orbital hybridizations)
are generated from the diversified physical or chemical properties and the
complex material structure. Therefore, they significantly affect the
parameters that control ion-transport in the solid-state LIBs 27. However,
systematic investigations into the interaction of the chemical bonds of
Li+-rich 3D ternary compounds as a practical electrolyte for LIBs are still
rather limited. Especially, the multi-orbital hybridization that is related to
the essential properties of the Li2GeO3 compound is absent in investigations
up to now.

The previous numerical studies based on VASP simulations are sufficient in
developing the theoretical framework for understanding the diversified
material/physical/chemical phenomena. This framework has been successfully
used to conduct systematic investigations of one-dimensional (1D) graphene
nanoribbons 28, two-dimensional (2D) graphene/silicene with chemical
modifications 29, 30 and the three-dimensional (3D) ternary Li4Ti5O12 compound
7. Through the delicate analysis, the diversified phenomena of the geometric,
electronic and magnetic properties due to different dimensionalities, planar
or buckled honeycomb lattices, layer numbers, stacking configurations, adatom
chemisorptions, guest-atom substitutions and bulk properties of 3D materials
can be fully understood. Therefore, this calculation might be very suitable
for investigating the extraordinary properties in a lot of complex oxide
compounds, eg., Li2SiO3, Li2GeO3, Li4Ti5O12, LiFe/Co/NiO, in main-stream
Li+-based batteries.

In this paper, the geometric symmetries and electronic properties of the 3D
ternary Li2GeO3 compound (the electrolyte material of Li+-based batteries) are
systematically investigated. The state-of-the-art analysis conducted on the
various chemical bonds in a large unit cell, the band structure with atomic
domination, the atom-/orbital projected density of states (DOS) and the
spatial charge density is capable of providing the critical multi-orbital
hybridizations. The spin density distribution, the spin-degenerate/spin-split
energy bands around the low-energy regions, and the net magnetic moment also
be examined in the detail as to whether the magnetism could exist in this
compound. The theoretical predictions on the relaxation structure, the valence
states, the whole energy spectrum and the band gap could be examined via
Powder X-ray Diffraction (PXRD)/Tunneling Electron Microscopy (TEM)/Scanning
Electron Microscopy (SEM)/Scanning Tunneling Microscopy (STM), Angle-Resolved
Photo Emission Spectroscopy (ARPESS), Scanning Tunneling Spectroscopy (STS)
and optical absorption spectra, respectively. In addition, whether a
combination of the phenomenological models with the numerical simulations can
be achieved in a reliable manner to clarify independent cases is very
important, since this linking is for a full exploration of various properties,
such as optical, magneto-electronic and transport properties. Therefore, the
close relationship between the tight-binding model and the first-principle
calculations is thoroughly examined. The present work provides more perceptive
insights into the understanding of the diversified chemical bonding, as well
as the electronic properties of Li2GeO3 for the future promising electrolytes
of LIBs.

##  2 2\. COMPUTATIONAL DETAILS

We used the density functional theory method via the Vienna Ab-initio
Simmulation Package (VASP)31 to perform the optimization of crystal structures
and the calculation of the electronic properties. The Perdew-Burke-Ernzerhof
(PBE) generalized gradient approximation was used for the exchange-correlation
functional32. The interaction between the valence electrons and ions core was
evaluated by the projector augmented wave (PAW) method 33. The cutoff energy
for the expansion of the plane wave basis set is 600 eV for all calculation.
The Brillouin zone was integrated with a special k-point mesh of
9$\times$9$\times$9 and 21$\times$21$\times$21 in the Monkhorst-Pack sampling
technique 34 for the geometric relaxation and electronic calculation,
respectively. The convergence condition of the ground-state is set to be 10-6
eV between two consecutive simulation steps, and all atoms were allowed to
fully relax during the geometry optimization until the Hellmann-Feynman force
acting on each atom was smaller than 0.01 eV/Å. Spin-polarized calculations
were performed for the geometry optimization and the calculation of the band
structure. In the k-point sample, the cutoff energy has been checked for
convergence of the calculations.

##  3 3\. RESULTS AND DISCUSSIONS

###  3.1 3.1 Optimized structure

Figure 1: (a) Polyhedron structure of Li2GeO3, (b) Oxygen (O) coordination
around the Lithium (Li), Germanium (Ge) atoms. The geometric structure of
Li2GeO3 along the different projections (c) (100), (d) (010) and (e) (001).

In order to clearly illustrate the complex physical, chemical and material
environments in the 3D ternary Li2GeO3 compound, one of the meta-stable
configurations is chosen. The geometric configuration of Li2GeO3, as shown in
Fig. 1, corresponds to the orthorhombic structure with the Cmc21 space group.
The conventional cell considered in this work contains 24 atoms (8 Li, 4 Ge
and 12 O), with the lattice parameters being 9.612 Å, 5.462 Å and 4.874 Å for
the $x$, $y$, and $z$ directions, respectively. The basic structural unit is
comprised of corner-sharing [GeO4] and [LiO4] tetrahedra, in which both Li and
Ge ions are coordinated by four O ions.

Based on the first-principles calculations for the optimal geometric
structure, the 3D ternary Li2GeO3 electrolyte material presents unusual
crystal lattice symmetries. Obviously, there exists a highly anisotropic and
extremely non-uniform structure. The diverse atomic arrangements are easily
observed under projections on different planes. e.g., the geometric structures
for the (100), (010) and (001) directions (Figures 1 (c) - 1 (e)), where Li,
Ge, and O atoms are represented by the green, blue and red balls,
respectively. As shown in Table 1, there exist only two kinds of chemical
bonds, the Li-O and Ge-O ones, with the total number of bonds being 32 and 16,
respectively. According to the delicate first principle calculations, the
Li2GeO3 compound displays modulated bond lengths in the ranges of $\sim$ 1.930
Å - 2.126 Å and $\sim$ 1.725 Å - 1.836 Å; the fluctuation percentages
$\Delta$b(%)$=$ $\left|bond_{max}-bond_{min}\right|$/$bond_{min}$ are over
10.1% and 6.4% for the Li-O and Ge-O bonds, respectively. The various chemical
bonds, which are generated by multi-orbital hybridizations, will directly
reflect the distribution width of the spatial charge density (discussed
later). Such complicated behaviors might induce extra theoretical barriers
(various hopping integrals) in exploring the phenomenological models. Most
importantly, the strong fluctuation of bond lengths, which generate an
extremely non-uniform environment, is expected to be very important in
achieving the outstanding charging and discharging processes 35. Due to this,
the various intermediate configurations can easily be transformed during the
battery operation.

Up until recently, PXRD was the most efficient technique in identifying the
lattice symmetries of 3D materials 36. Apparently, it is very suitable to
directly observe the 3D ternary Li2GeO3 compound. Furthermore, other
quantities, such as the particle size and morphology of the sample, can be
observed by using SEM 37. The top view of the nano-materials is observed by
using TEM 38, while the side view is usually tested by using STM 39. These
methods have been successfully utilized to examine the unique geometric
structures of graphene-related systems, such as the multi-walled cylindrical
structure of carbon nanotubes 40, folded and scrolled 41, 42, profiles of
graphene nanoribbons 43, as well as stacking configurations and interlayer
distances of multi-layer graphene 44, 45. The predicted unusual geometric
structure of Li2GeO3, which includes a non-uniform and the highly anisotropic
environment, is in good agreement with the available experimental examinations
18, 46 (Table 1).

Table 1: Structure parameter of 3D ternary Li2GeO3 compound. The experimental results are also listed. | Lattice constants |  | Atomic coordianates |  | Bond length
---|---|---|---|---|---
a (Å) | b (Å) | c (Å) | Li | Ge | O1 | O2 | Li-O | Ge-O
This work | 9.612 | 5.462 | 4.874 |  | (0.175,
---
0.342,
0.016)
| (0.0,
---
0.179,
0.507)
| (0.0,
---
0.137,
0.880)
| (0.153,
---
0.318,
0.413)
| 1.930 (8)
---
1.932 (8)
1.951 (8)
2.126 (8)
| 1.725 (8)
---
1.833 (4)
1.836 (4)
| X-ray45
---
diffraction
9.632 | 5.479 | 4.842 | - | - | - | - | - | -
| X-ray18
---
diffraction
9.602 | 5.502 | 4.849 |  | (0.176,
---
0.344,
0.015)
| (0.0,
---
0.178,
0.5)
| (0,
---
0.190,
0.879)
| (0.162,
---
0.327,
0.419)
- | -

###  3.2 3.2 Electronic properties

Figure 2: (a) Electronic energy spectrum for the Li2GeO3 compound, for the
specific (b) Lithium (enlarge four times), (c) Germanium and (d) Oxygen
dominances.

The 3D ternary Li2GeO3 compound, a Li+-based electrolyte material, exhibits
unusual geometric structures and thus diversified electronic properties. The
calculated band structure of the Li2GeO3 compound is presented in Fig. 2 (a).
The zero-energy at the middle of the valence and conduction band is regarded
as Fermi energy level. The presence of numerous valence and conduction energy
sub-bands in the calculation band structure is a consequence of the many outer
orbitals and atoms in the large unit cell. The energy dispersions, which are
shown along the high symmetry points, have strongly anisotropic behavior. For
example, there exist parabolic, oscillatory and partially flat dispersions. In
addition, sub-band anti-crossing, crossing and non-crossing behaviors come
into existence frequently, consequently creating the extremely complicated
electronic structure. That is to say, it is very difficult to
identify/distinguish/examine the various structures for the different sub-
bands, as well as to characterize the width of each energy sub-band. Not only
that, but plenty of band-edge states might come into existence in the high-
symmetry points. These critical points in the energy-wave-vector space would
induce the unique van Hove singularities 47 and thus create the strong
absorption structures in the optical properties 48.

In general, the unoccupied states are highly asymmetric to the occupied states
about the Fermi level; particularly, the latter have more energy sub-bands and
therefore, are the dominating ones. This behavior might be closely related to
the complex orbital hybridizations in the Li-O and Ge-O bonds. Most
importantly, the extrema of the conduction band and the valence band are
located at the $\Gamma$ and Z point in the first Brillouin zone, respectively,
which thus leads to a large indirect band gap of 3.77 eV. This indicates that
the Li2GeO3 compound has an excellent electrochemical stability and provides a
negligible electronic conductivity26. However, the investigations for the band
structure of the Li2GeO3 compound are rather limit up to now; therefore, the
present results may provide a helpful information for the future work. It is
also noted that, under this large band gap, the spin split/degeneracy of the
conduction and the valence band near the Fermi level can be not created.
Therefore, no magnetic moment exists in this compound, making the spin density
distribution meaningless. The mentioned characteristics will be reflected in
the density of states.

In addition to the electronic band structure, the atom-dominated band
structures for valence and conduction states are available to understand the
critical chemical bondings. In Figs. 2 (b), 2 (c) and 2 (d), the contribution
to electronic states of Li, Ge and O atoms are denoted by the green, blue and
red balls, respectively. The effective energy range related to the Li-O and
Ge-O chemical bonds lies in the range of -6.5 eV - 6.5 eV. It is very hard for
the eye to observe the Li-dominations (small radii in Fig. 2 (b)) because of
only single 2s orbital takes parks in the chemical bonding. In sharp contrast,
it is clearly shown that the Ge and O atoms make a significant contribution to
the electronic energy spectrum. Especially the latter dominates almost all the
occupied and unoccupied bands, and the largest concentration at the top of the
valence band (red balls in Fig. 2 (d)) since they are related to the entirely
of the chemical bonds, with the (2s, 2px, 2py, 2pz)-orbital energies. Although
the contributions are different, almost all atoms are present in the whole
band structure, which may elucidate the large modulation of the Li-O and Ge-O
chemical bond.

From an experimental aspect, the large band gap due to the extremely strong
covalent bonding of the 3D ternary Li2GeO3 compound is directly verified by
using optical absorption spectroscopy 49. Apparently, because our system is an
indirect gap material, the optical gap should be larger than 3.8 eV as
evidenced in previous work 50. On the other hand, the predictions on the wave-
vector-dependent band structures in the occupied states could be examined by
ARPES measurements 51, which has been utilized in many previous experiments to
successfully observe the diversified valence bands in emergent graphene-
related materials. For example, the monolayer-like and bilayer-like energy
dispersions, respectively, at the K and H symmetry points in the stacked
graphite 52. The parabolic/parabolic and linear dispersions in AB-stacked
bilayer/trilayer graphene 53, 54, the Sombrero-shaped and partly flat band in
AB-stacked trilayer graphene55. The parabolic dispersions in graphene
nanoribbons56. Up to now, similar measurement on the unusual energy bands in
the 3D ternary Li2GeO3 compound is absent. Further examinations are required
for the feature-rich and unique energy spectra, including numerous energy
subbands, various energy dispersions and the large indirect energy gap. These
are useful in understanding the multi-orbital hybridizations of the chemical
bonds.

###  3.3 3.3 Charge densities and orbital hybridizations

Figure 3: The charge density distribution for the shortest/medium/longest
(a)/(b)/(c) Li-O bonds and (d)/(e)/(f) Ge-O bonds and (g) for the isolated
(Li, Ge, O) atoms.

The variation of bond lengths can be formed by the complicated contributions
of the available orbitals in different atoms. The spatial charge
distributions, ($\rho$), as indicated in Figs. 3(a) - 3(g), linking the atom-
dominated band structure (Figs. 2(b) - 2(d)) and the atom-/orbital-projected
DOS (later discussions on Fig. 5), could provide very useful information on
the chemical bondings.

It can be seen that the carrier densities are strongly dependent on the kind
of chemical bonds and very sensitive to the modulation of bond lengths. As for
the Li-O bonds (Figs. 3(a) - 3(c)), the diluted charge density around the Li
atom is only contributed by the single 2s-orbital. Its effective distribution
range is approximately 0.5 Å, as seen by the extension of the yellow to the
green parts of the outermost orbitals. Apparently, the two 1s orbitals do not
enter into the orbital hybridizations with the O atom, because it belongs to
fully filled electronic configuration. The similar, but wider distribution,
which corresponds to the O case, in which the inner and outer region (the
heavy red and green parts) is associated with 2s and (2px, 2py, 2pz) ones.
However, the O-2s orbitals are relatively far away from the Li-atom and remain
in almost the perfect spherical shape. Thus, their contributions to the Li-O
chemical bonds are negligible. A weak, but significant overlap of distinct
orbitals between Li and O atoms is observed. With the increase of the Li-O
bond length, this overlap is obviously decreased. As a result, the diverse
hopping integrals is presented in the multi-orbital 2s-(2px, 2py, 2pz)
hybridizations of Li-O bonds.

In striking contrast, the Ge-O bonds, as clearly shown in Figs. 3 (d) - 3 (f),
present very high carrier densities between the Ge and O atoms, indicating a
rather stronger chemical bonding than the Li-O bonds and thus, explain why the
former is shorter than the latter. Furthermore, we can observe that charge
density appears around the Ge atom is larger than that of Li and O ones by
reason of the larger atomic number. Its effective region (heavy red, blue-
green regions) correspond to the 4s and (4px, 4py, 4pz) orbitals. Very
interestingly, the deformed spherical distributions of the spatial charge
density between Ge-O bonds clearly illustrate that both Ge and O atoms
contribute their all valence electrons to form chemical bonds. According to
the above-mentioned features, the Ge-O chemical bonds are predicted to exhibit
the strong overlap of (4s, 4px, 4py, 4pz)-(2s, 2px, 2py, 2pz) orbitals.
However, with the bond length increase, the modifications on them are
observable, as indicated by the decreased carrier density between the Ge and O
atoms. The highly non-uniform Li-O and Ge-O chemical bondings might generate
numerous difficulties in the phenomenological models (e.g., various hopping
integrals).

As mentioned above, the strength of the Ge-O bonds is much stronger than that
of the Li-O bonds. The Bader charge analysis of the Li2GeO3 compound has been
done to verify this conclusion. It is found that the average effective charge
of Li, Ge and O atoms, respectively, are 0.88 e, 2.13 e and -1.3 e. This
indicates that the O atom receives the electron from the Li and Ge atoms to
forms the more stable configuration. Obviously, the effective charge transfer
of Ge attached to the O is much larger than that of the Li bridging to the O
and thus, illustrated the former is stronger than the latter ones. It is very
important to note that such characteristics are very necessary for the
outstanding release and recovery of lithium ions from the electrolyte material
during the charging and discharging processes. In other words, the creation of
a Li-vacancy is supported by the strong Ge-O bondings and then drives the ion
transport.

The density of states (DOS) is characterized as the number of electronic
states within a rather small energy range of dE and directly reflects the
primary characteristics of the main features of the valence and conduction
energy spectra simultaneously. The atom- and orbital-projected DOS, as shown
in Fig. 4 and Fig. 5, can be used to fully understand the significant multi-
orbital hybridizations of Li-O and Ge-O chemical bonds. As for the Fig. 4, the
ternary 3D Li2GeO3 compound exhibits a lot of special structures (Van Hove
singularities), including shoulder structures and asymmetric/symmetric peaks.
Such features originate mainly from the saddle, local minimum, maximum and
dispersionless relation in the energy band structure. Consistently with the
electronic band structure, for a wide gap semiconductor of 3.77 eV, the DOS
per unit cell of the Li2GeO3 compound vanishes around the centered Fermi
level. This disappearance separates the high asymmetry in holes and electrons
in the spectra. As can be seen, most of the atoms dominate in the occupied
states, but not in the unoccupied ones. The spin-up and spin-down DOS of the
former and the latter are the same. In them the difference determines the
strength of the net magnetic moment, this indicates an absence of magnetism in
the system. Furthermore, the three different kinds of atoms have a
significantly different contribution in the conduction and valence bands. For
example, the most prominent curve, which belongs to the O atoms, shows a large
contribution over the entire energy range, specifically for the top of the
valence band. Markedly different, the Li atoms have an almost insignificant
contribution, but they are nonetheless very important to create a solid
structure of Li2GeO3. Such a result is mainly defined by the number and
available valence orbitals of each atom in a unit cell that takes part in the
chemical bondings.

Figure 4: The atom-density of states of Li2GeO3 compound.

Generally speaking, the various orbitals making an important contribution can
be classified into three groups: (I) Li-2s orbital (black curve in the top of
Fig. 5), (II) Ge-(4s, 4px, 4py, 4pz) orbitals (black, red, green and blue
curves in the middle of Fig. 5), and (III) O-(2s, 2px, 2py, 2pz) orbitals
(black, red, blue and green curves in the lowest of Fig. 5). The effective
energy spectrum that relates to the Li-O and Ge-O chemical bonds lie in the
range of -6.5 eV - 6.5 eV, as indicated in Fig. 5. The delicate analysis of
the enlarged orbital-projected DOS clearly provides the number, energy,
intensity and form of Li-2s Van hove singularities. Such structures merge well
with the (2px, 2py, 2pz)-projected DOS for O atoms, reflecting the importance
of the multi-orbital hybridizations, and thus illustrate the large bond length
modulation (10.1%) in the Li-O chemical bonds. However, the contribution the
O-2s orbitals into the specific energy range are negligible. Because they are
quite low in energy and thus would not combine efficiently with the Li-2s
orbitals. Beside the Li-O bonds, the Ge-O bonds also exhibit a very
complicated orbital-hybridization. Concerning the Ge atoms, there exist many
strong peaks related to the (4s, 4px, 4py, 4pz) orbitals. Such peaks play a
dominating role in the deeper valence-state region [e.g., E $<$ -3 eV] and the
opposite region. Some of them merge with the (2s, 2px, 2py, 2pz) peak of the O
atoms, clearly illustrating the significance of the Ge-O bonding in the
distorted structure. Shortly, the Li-O and Ge-O chemical bonds are deduced to
have multi-orbital hybridizations of 2s-(2px, 2py, 2pz) and (4s, 4px, 4py,
4pz)-(2s, 2px, 2py, 2pz), respectively. This unusual characteristic is
strongly consistent with the spatial charge density analysis. As far as we can
tell, the existence of the complicated multi-orbital hybridization implies
that the Li2GeO3 band structure is very difficult to simulate by the tight-
binding model.

Figure 5: The orbital-projected density of states of Li2GeO3 compound.

STS measurements 57, an extension of STM, can be efficiency used to examine
the number, form, energy and intensity of special Van-hove singularities in
DOS. This powerful method has been successfully identified the diverse
electronic properties in GNRs 58, 59, carbon nanotubes, graphene 60and few-
layer graphenes 61, 62. For example, the square-root relation peaks in 1D
carbon nanotubes and GNRs 59, a symmetric V-shape structure for monolayer
graphene 61 and finite DOS at Femi level in the AB graphite stacking 60 have
all been investigated. The main features of the electronic properties in the
3D ternary Li2GeO3 compound, including the large energy spacing between the
occupied and unoccupied bands, the plethora of asymmetric/symmetric peaks, the
highly asymmetric electron and hole energy spectra, as well as their widths,
could be further investigated with STS. The theoretical predictions of Van
Hove singularities, together with the STS measurements are worthy to be
identified for the understanding of the complicated multi-orbital
hybridizations in the Li-O and Ge-O bonds, and thus the electronic properties
of Li2GeO3 compound.

Up to now, LIBs have been quickly developed, owing to their vital importance.
Their safety issues can be eliminated by changing the liquid to a solid-state
electrolyte. The 3D ternary Li2GeO3 can be adopted to manufacture batteries
that are low-cost, durable, and suitable for high-capacity energy storage.
Based on the electronic band structure with/without atomic domination, spatial
charge distribution, and atom-/orbital-projected DOS calculations, the
critical multi-orbital hybridization of Li-O and Ge-O bonds is obtained.
Apparently, the LixGeyOz compound has a certain metastable configuration;
during battery operation the transformation of many metastable structures (eg.
Li2GeO3, Li4GeO4, Li2Ge7O15) occurs. Therefore, further systematic studies on
other metastable structures are necessary to identify the most prominent
evolution paths.

Generally speaking, there exist various chemical bonds in a large unit cell, a
complicated energy sub-band with a large band gap, Eg=3.77 eV, heterogeneous
spatial charge densities in diverse chemical bonds, and multi-orbital
hybridizations in atom-/orbital-projected DOS. The first-principles electronic
structures might be too complicated to be simulated by the phenomenological
models. To be specific, the extremely non-uniform chemical and physical
environments, which survive in the large unit cells of the 3D ternary Li2GeO3
compounds, are responsible for the featured electronic structures. Such
critical factors cover a lot of multi-orbital hybridizations in the Li-O and
Ge-O bondings. The orbital-induced various hopping integral site energies
should be included in the significant Hamiltonians simultaneously. Apparently,
many parameters will be required to get a good fit. It would be very difficult
to create a good Hamiltonian diagonalization, and thus, it is very challenging
to achieve a concise physical picture for a full understanding of the featured
electronic energy spectra.

##  4 4\. CONCLUDING REMARKS

The unusual and unique geometric, electronic properties of the 3D ternary
Li2GeO3 compound, a potential electrolyte candidate for Li+-based batteries,
are investigated by using first principle calculations. The delicate analysis
on atom-dominated energy band structure, the charge density distribution in
the modulate of the chemical bonds, the atom-/orbital-projected DOS are
successfully identified the multi-orbital hybridization in Li-O and Ge-O
bonds. This theoretical framework could be generalized for other electrolytic,
cathode and anode materials of Li+-based batteries. Furthermore, the extremely
non-uniform environment with highly isotropic characteristics in the large
unit cell poses a great challenge for the tight-binding model.

In the current work, the solid-state electrolyte material Li2GeO3, with 24
atoms in a large computational cell is an orthorhombic crystal structure.
There exist 32 Li-O and 16 Ge-O chemical bonds, in which each Li/Ge atom is
surrounded by four O atoms in the tetrahedral form. Most importantly, the
strong covalent bondings create a huge indirect energy gap of Eg=3.77 eV. The
band structure lying in range -6.5 eV - 6.5 eV is strong relative to the
critical chemical bondings. There exist many sub-bands with high anisotropy,
strong energy dispersion and frequently anti-crossing/crossing/non-crossing
phenomena, and a strong contradistinction of electron and hole states appears
near the Fermi level. The band structure with atomic domination, spatial
charge density and the atom-/orbital-projected DOS are successfully identify
the important multi-orbital 2s-(2px, 2py, 2pz) and (4s, 4px, 4py, 4pz) - (2s,
2px, 2py, 2pz) hybridizations. The theoretical predictions on the structural
relaxation are verified by PXRD, TEM and SEM, while the band gap, the occupied
electronic states and the special Van-Hove singularities could be examined by
optical spectroscopy, ARPES and STS measurements, respectively.

The calculated results clearly illustrate that the 3D ternary Li2GeO3 compound
could be used as a solid-state electrolyte. During the battery operation, the
structural transformation between the current meta-stable structure with other
meta-stable structures are expected to occur at any time. This study is able
to provide certain meaningful information about the critical mechanisms in the
ion transport. It might be helpful to solve the open issue: the most optimal
evolution paths of the Li+ migration during the discharging processes of the
all solid-states LIBs.

Acknowledgments

This work was supported by the Hierarchical GreenEnergy Materials (Hi-GEM)
Research Center, from The Featured Areas Research Center Program within the
framework of the Higher Education Sprout Project by the Ministry of Education
(MOE) and the Ministry of Science and Technology (MOST 108- 3017-F-006 -003)
in Taiwan.

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