A Stable, Magnetic and Metallic Li3O4 Compound with Potential
Application in Li–Air Battery
Guochun Yang,†,‡ Yanchao Wang*†and Yanming Ma*,†
†
State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China.
‡
Faculty of Chemistry, Northeast Normal University, Changchun 130024, China.
Index
page
1. Computational details········································································2
2. Theoretical and experimental formation energies of Li2O2 and Li2O at 300 K······5
3. The lattice constant of LiO2 in Pnnm symmetry·········································5
4. Mulliken atomic charge of Li3O4 and Li2O2··············································6
5. The phonon frequencies and their infrared and Raman activity of Li3O4·············7
6. The phonon frequencies and their infrared and Raman activity of Li2O2·············8
7. The phonon frequencies and their infrared and Raman activity of Li2O··············9
8. Phonon dispersion curves and partial phonon density of states for Li3O4···········10
9. The calculated phonon entropy and experimental entropy of Li2O··················10
10. Relative formation energy of LiO2, Li3O4, and Li2O2 with respect to solid Li2O
and oxygen gas (O2) at 0 K and 300 K······················································11
11. The simulated XRD spectra of LiO2, Li2O, Li3O4, and Li2O2·······················12
12. Comparisons XRD patterns of Li3O4 or Li2O2 and discharge product·············13
13. Simulated O K-edge spectra of Li2O2 and Li3O4 ·····································14
14. Fourier transform infrared spectroscopy (FTIR) spectra of the side products
(Li2CO3, HCO2Li, and CH3CO2Li) in Li-air cell. ········································15
15. Powder X-ray diffraction (PXRD) patterns of the composite cathode in the
discharge and charge processes and simulated XRD spectra of Li3O4. ···············16
16. References··················································································17
1
Computational details
Our structural prediction approach is based on a global minimization of free energy
surfaces merging ab initio total-energy calculations through CALYPSO (Crystal
structure AnaLYsis by Particle Swarm Optimization) methodology as implemented in
its same-name CALYPSO code.1,2 The structures of stoichiometry LixOy (x = 1-4, y =
1−4) were searched with simulation cell sizes of 1−8 formula units (f.u.), except that
Li3O4 and Li4O3 with 1-6 f.u. at 1 GPa. In the first step, random structures with certain
symmetry are constructed in which the atomic coordinates are generated by the
crystallographic symmetry operations. Local optimizations using VASP code, 3 were
done with the conjugate gradients method and were stopped when the enthalpy
changes became smaller than 1 × 10-5 eV per cell. After processing the first generation
structures, 60% of them with lower enthalpies are selected to produce the next
generation structures by PSO. 40% of the structures in the new generation are
randomly generated. A structure fingerprinting technique of bond characterization
matrix is applied to the generated structures, so that identical structures are strictly
forbidden. These procedures significantly enhance the diversity of the structures,
which is crucial for the efficiency of the global search of structures. For most of the
cases, the structure searching simulation for each calculation was stopped after we
generated 1000 ~ 1200 structures (e.g., about 20 ~ 30 generations).
To further analyze the structures with higher accuracy, we select a number of
structures with lower enthalpies and perform structural optimization using density
functional theory within the generalized gradient approximation4 as implemented in
the VASP code. The cut-off energy for the expansion of wavefunctions into plane
waves is set to 700 eV in all calculations, and the Monkhorst–Pack k-mesh with a
maximum spacing of 0.02 Å−1 was individually adjusted in reciprocal space with
respect to the size of each computational cell. This usually gives total energy well
converged within ~ 1 meV/atom. The electron-ion interaction was described by means
of projector augmented wave with s1p0 and s2p4 electrons as valence for Li and O
atoms, respectively.
With the only input of chemical compositions in our CALYPSO structure searching
2
calculations, the experimental antifluorite structure of Li2O (space group Fm3m, 4
formula unit per cell)5 and hexagonal structure of Li2O26 (space group P63/mmc, 2
formula unit per cell, Figure 2a) were successfully reproduced, validating our
structure searching methodology in application to Li-O system. Moreover, the relaxed
lattice constant for antifluorite structure of Li2O was calculated to be 4.63 Å, in good
agreement with the experimental value of 4.62 Å.5 Lattice parameters of hexagonal
P63/mmc-structured Li2O2 were optimized to be a = 3.16 Å and c = 7.68 Å, in good
agreement with the experimental values of 3.14 and 7.65 Å,6 and 3.16 and 7.69 Å
from another theoretical calculations.7 These lattice parameter calculations gave
support on the validity of pseudopotentials adopted in this work.
Since density functional theory calculation overestimates binding energy of O2
molecule,[7,8-10] the experimental binding energy, ΔEexp = 5.12 eV, was introduced
into our formation energy calculations to correct the theoretical error by taking H(T =
0 K, O2) = 2H (T = 0 K, O)−ΔEexp, where H(T = 0 K, X) is the calculated ground-state
energy of an O (X = O) atom or O2 molecule (X = O2). Entropic contributions of
gas-phase O2 or O atom were obtained from tabulated experimental data.11 After the
correction, our calculated formation energies of Li2O2 and Li2O are in excellent
agreement with experimental data (Table S1). The phonon calculations were
performed to determine the dynamical stability of Li3O4 through supercell method as
implemented in the PHONOPY code.12 Phonon frequencies derived from supercell
method were further validated by using a plane-wave pseudopotential scheme within
linear response density-functional theory through the QUANTUM-ESPRESSO
package.13 The Troullier–Martins normcon pseudopotentials were generated with
valence atomic configurations of 1s22p1 and 2s22p4 for Li and O, respectively. The
electronic wave functions and the electron density were expanded by the plane-wave
basis sets with a cut-off energy of 70 Ry. 14 × 14 × 6 Monkhorst–Pack grids in the
Brillouin zone were adopted. The choices of the above computational parameters
ensured that the convergence of the phonon frequencies were within 0.08 THz.The
Mulliken charge transfer calculations were carried out with the CASTEP code.14 O
and Li K-edge spectra were calculated by solving Bethe-Salpeter equation.15 Single
3
particle core-hole effects were considered.
DFT calculations can successfully reproduce the experimental oxidation-reduction
potentials.17-19 Below, we investigate the electrochemical behavior of Li3O4 and Li2O2
by calculating the reduction and oxidation potentials. Hydrogen electrode will be used
as a reference electrode. The reference hydrogen electrode in a half-reaction has
previously been determined to be -4.36 V.20 It is noted that the use of different
reference electrodes does not affect our conclusion, because the relative potential
differences between Li2O2 and Li3O4 are considered. The reaction process in Li-air
cell is the reduction of oxygen upon discharge and oxidation upon charge16.
For Li2O2, the reaction route is
2Li+ + 2e- + O2 
Li2O2
G
(1)
For Li3O4, it is
3Li+ + 3e- + 2O2 
Li3O 4
G
(2)
The ΔG represents the free energy of the reduction or oxidation. By using Nernst
equation V = -ΔG/nF (F is the Faraday constant)21 and the reference value -4.36 V, the
resultant reduction potentials of Li3O4 and Li2O2 are 0.38 and 0.45 V, respectively.
The overpotential of Li3O4 is 0.07 V lower than that of Li2O2. Formation reaction of
Li3O4 will therefore be slightly favored over that of Li2O2. Our results showed that the
electrochemical behavior of Li3O4 is rather similar to that of Li2O2. Since Li2O2 was
observed to be reversible during the discharge and charge processes, we expect that
Li3O4 is also reversible. Future experiment is greatly demanded to assess the
reversibility of Li3O4.
4
Table S1. Theoretical and experimental formation energies (eV) of Li2O2 and Li2O
at 300 K.
Formation
energy
this work
other theories
Experiment
ΔG (Li2O2) -6.01
-5.99a, −4.94,b −5.41,c −4.98d -5.92e
ΔG (Li2O)
-5.62a ,−5.29c
a
-5.61
-5.83e
Reference 7. bReference 22. cReference 23. dReference 24. eReference 11.
It is noted that our calculation method of formation energy adopted is the same as that
in Reference 7.
Table S2. The calculated lattice constant of LiO2 in Pnnm structure.
our work
Ref. 25
Ref. 12
Ref. 26
Ref. 27
a (Å)
3.93
3.95
3.99
3.90
4.01
b (Å)
4.93
4.94
4.88
4.64
4.80
c (Å)
2.95
2.96
2.96
2.96
3.03
note
GGA
GGA
GGA
GGA
HSE
5
Table S3. Mulliken atomic charges (e) of Li3O4 and Li2O2. O1 and O2 are atoms
within peroxide and superoxide groups in Li3O4, respectively. Intramolecular O-O
bond lengths in peroxide groups are longer than those in superoxide groups since
peroxide group is more negatively charged by attracting more exotic electrons from
Li.
Li3O4
Charge
Li2O2
Charge
Li
0.89
Li
0.99
Li
0.89
Li
0.99
Li
0.95
Li
0.77
O1
-0.88
Li
0.77
O1
-0.88
O
-0.88
O2
-0.48
O
-0.88
O2
-0.48
O
-0.88
O
-0.88
6
Table S4. The zone-center phonon modes, frequencies (cm-1), Infrared and Raman
activities of Li3O4, and the experimental value of discharge product (Ref. 28).
Mode Calculation Experiment Raman Infrared
A′′2
40.3
E′
111.5
R
I
E′
187.8
R
I
E′′
223.8
R
A′′2
262.8
I
A′′2
300.9
I
E′
331.8
R
E′′
333.1
R
A′1
348.8
R
E′′
384.7
R
A′′2
483.1
I
E′
511.4
R
A′1
738.8
R
A′1
1100.5
I
1125
I
I
R
7
Table S5. The zone-center phonon modes, frequencies (cm-1), Infrared and Raman
activities, and experimental Raman frequencies (cm-1) (Ref. 29) of Li2O2.
Mode Calculation Experiment Raman Infrared
A2u
64.9
I
E1u
99.8
I
E2g
170.7
E2u
220.9
B2g
254.4
A2u
260.9
E1g
303.3
E1u
341
E2u
369.3
B2g
469.3
E1u
492.7
E2g
492.8
B1u
493.6
A2u
509.5
B1u
734.3
A1g
772.1
R
I
256
R
I
I
R
I
788
R
8
Table S6. The zone-center phonon modes, frequencies (cm-1), Infrared and Raman
activities, and experimental Raman frequencies (cm-1) (Ref. 30) of Li2O.
Mode Calculation Experiment Raman Infrared
T1u
153
I
A2u
311.5
Eu
311.6
T1g
347.5
T2g
357.6
T2u
422
T1u
424.6
I
T1u
507.3
I
T1u
543.6
I
T2g
568.9
T2u
623
T1u
625.6
A1g
746.8
R
Eg
749.1
R
R
575
R
I
9
Figure S1. Phonon dispersion curves and partial phonon density of states (PDOS) for
Li3O4
Figure S2. The calculated phonon entropy (per formula unit in J/K mol) of Li2O to
compare with the experimental data (Ref 31).
10
Figure S3. (a) Relative formation energy with respect to solid Li2O and oxygen gas
(O2) for Li2O2 and Li3O4 at 300 K. (b) Relative formation energy with respect to solid
Li2O2 and oxygen gas (O2) for Li3O4 at 300 K. (c) Relative formation energy with
respect to solid Li2O2 and LiO2 for Li3O4 at 300 K. Figures (a)-(c) clearly indicates
that Li3O4 is energetically stable with respect to dissociation into Li2O2 + O2, Li2O +
O2, and Li2O2 + LiO2.
11
Figure S4. The simulated XRD spectra of LiO2, Li2O, Li3O4, and Li2O2.
12
Figure S5. Calculated XRD patterns of Li2O2 and Li3O4 in comparison with the
experimental data (taken from Ref. 32) of discharge product. In order to understand
the broadened experimental XRD peaks, we added up the XRD patterns of Li2O2 and
Li3O4, and then fitted the data to a broadened Lorentzian line with a full width at half
maximum of 1.2º. The simulated spectrum is in excellent agreement with experiment.
13
Figure S6. Simulated O K-edge spectra of Li2O2 and Li3O4. Li3O4-O1 corresponds to
the longer O-O bond (1.54 Å) within peroxide groups, while Li3O4-O2 corresponds to
the shorter O-O bond (1.35 Å) within superoxide groups. As shown, the superoxide
group is responsible for the strong peak at 535 eV.
14
Figure S7. Fourier transform infrared spectroscopy (FTIR) spectra of the side
products (Li2CO3, HCO2Li, and CH3CO2Li) in Li-air cell. Li2CO3, HCO2Li, and
CH3CO2Li have confirmed as the discharge products by combination of IR, situ
surface enhanced Raman spectroscopy (SERS), nuclear magnetic Rresonance (NMR),
and Powder X-ray diffraction (PXRD) (Refs 33 and 34). The vibration peaks of Li3O4
are in the frequency region from 0–1150 cm-1 mainly originate from superoxide O2(1094), peroxide O22- (790), and Li-O (500) groups (Figure S1 and Table S4), which
clearly indicates that Li3O4 is not the side products.
15
Figure S8. Powder X-ray diffraction (PXRD) patterns of the composite cathode in the
discharge and charge processes and simulated XRD spectra of Li3O4. Bruce et al
found that Li2O2 was formed after 1st cycle discharge, however Li2O2 could not be
seen after 5th cycle discharge. By combination of IR, situ surface enhanced Raman
spectroscopy (SERS), nuclear magnetic resonance (NMR), and Powder X-ray
diffraction (PXRD) techniques, Li2CO3, HCO2Li, and CH3CO2Li have confirmed as
the main discharge products after 5th cycle discharge (Refs 33 and 34). Our simulated
XRD spectra of Li3O4 is similar to those of 1st cycle discharge product, and different
from those of 5th cycle discharge product. Thus, Li3O4 is not the side products
(Li2CO3, HCO2Li, and CH3CO2Li) in Li-air cell.
16
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