Journal of The Electrochemical Society, 150 共12兲 A1628-A1636 共2003兲
A1628
0013-4651/2003/150共12兲/A1628/9/$7.00 © The Electrochemical Society, Inc.
Decomposition of LiPF6 and Stability of PF5 in Li-Ion Battery
Electrolytes
Density Functional Theory and Molecular Dynamics Studies
Ken Tasaki,a,*,z Katsuya Kanda,b Shinichiro Nakamura,b and Makoto Uec,*
a
Mitsubishi Chemical Research and Innovation Center, Goleta, California 93117, USA
Mitsubishi Chemical Corporation, Science & Technology Research Center, Computational Modeling
of Materials Laboratory, Yokohama, Kanagawa 227-8502, Japan
c
Mitsubishi Chemical Corporation, Science & Technology Research Center, Electrochemistry Laboratory
& Battery System Design Laboratory, Inashiki, Ibaraki 300-0332, Japan
b
The decomposition of LiPF6 and the stability of PF5 in organic solvents, diethyl carbonate 共DEC兲, dimethyl carbonate 共DMC兲,
␥-butyrolactone 共GBL兲, and ethylene carbonate 共EC兲, have been investigated through density functional theory 共DFT兲 calculations, in which solvent was modeled as a dielectric continuum, and also by molecular dynamics 共MD兲 simulations which treated
solvents explicitly. Both calculations showed a similar trend in which the decomposition was further promoted in more polar
solvents, yet the DFT calculations predicted an endothermic decomposition, while the MD simulations indicated exothermic. This
sharp contrast in the results suggests strong solute-solvent interactions, especially for PF5 , which were not accounted for in the
DFT calculations. The specific interaction between PF5 and solvent was further investigated by DFT calculations for adduct
models and also by the MD simulations for solutions. Both calculations suggest a stable formation of a PF5 -solvent adduct in
solution and its stability depends on the solvent. It was found that PF5 is more stabilized in polar and sterically compact solvents
such as EC and GBL than in less polar and bulky, linear carbonates such as DMC and DEC. The reactivity of PF5 with organic
solvents and the difference in the stability of LiPF6 between organic and aqueous solution are also discussed.
© 2003 The Electrochemical Society. 关DOI: 10.1149/1.1622406兴 All rights reserved.
Manuscript submitted December 23, 2002; revised manuscript received May 31, 2003. Available electronically October 17, 2003.
Lithium hexafluorophosphate (LiPF6 ) is by far the most widely
used electrolyte salt in lithium-ion batteries 共LIBs兲. Electrolyte solutions of LiPF6 dissolved in binary or ternary solvents which include cyclic carbonates such as ethylene carbonate 共EC兲 or propylene carbonate 共PC兲 and linear carbonates such as dimethyl
carbonate 共DMC兲, diethyl carbonate 共DEC兲, ethyl methyl carbonate
共EMC兲, or their mixtures show high electrolytic conductivity, electrochemical stability, and enough thermal stability, although dry,
nonsolvated LiPF6 exhibits poor chemical stability.1 However, there
are still some safety concerns associated with the improvement in
safety of the LIBs, and understanding the thermal stability of the
electrolytes is essential in the design of safe LIBs.2 The thermal
decomposition produces pentafluorophosphate (PF5 ) by LiPF6
→ LiF ⫹ PF5 , which in turn reacts with solvents to initiate polymerization of solvents3 or to give other products such as phosphine
oxides, alkyl fluorides, and ethers.4
It is well known that the reaction between LiPF6 in electrolyte
solutions and trace amounts of water 共or alcohols兲 produces HF,5,6
which causes a detrimental effect in battery performance. The initial
reaction between water and LiPF6 is described by the overall reaction: LiPF6 ⫹ H2 O → LiF ⫹ POF3 ⫹ 2HF. However, little is
known about the reaction mechanism of this hydrolysis. It was proposed that PF5 , a product of the equilibrium of LiPF6 LiF
⫹ PF5 , undergoes hydrolysis with residual water to produce HF as
PF5 ⫹ H2 O → POF3 ⫹ 2HF. 7,8 This is based on the experimental
facts that LiPF6 aqueous solutions are very stable and their HF content can be determined by aqueous NaOH titration without further
HF formation by the LiPF6 hydrolysis.6,8
Therefore, understanding the salt decomposition and its process
is foremost in controlling the stability of LiPF6 in electrolyte solutions. Yet the difficulty of probing PF5 in solution hinders the chemical analysis of the reactions involved in the LiPF6 decomposition,
although several experimental studies on the reactivity of these species have been reported.3,4,8
Computer simulation may be a useful tool for examining chemi-
* Electrochemical Society Active Member.
z
E-mail: [email protected]
cally very unstable compounds.9,10 In this study we attempt to analyze the reactivity and stability of chemical components in the salt
decomposition, specifically, LiPF6 and PF5 , in organic solvents by
density functional theory 共DFT兲 calculations and molecular dynamics 共MD兲 simulations in order to shed light on the salt decomposition and reactions that follow. The salt decomposition may depend
on a number of environmental variables: temperature, impurity, salt
concentration, solvent polarity, and others. Our interest here is in the
solvent dependence of the salt decomposition in an attempt to design
electrolytes to control the decomposition.11,12
Computational Protocols
DFT calculations.—The solvents examined here included DEC,
DMC, ␥-butyrolactone 共GBL兲, and EC to cover a wide range of
solvent polarity with the dielectric constant 共⑀兲 spanning from 2.8
共DEC兲 to 90 共EC兲. DFT calculations were performed for the following reactions in each solvent by self-consistent reaction field 共SCRF兲
methods13 at the level of B3LYP/6-31G共d,p兲14,15 in conjunction with
the Onsager model16 to include the solvent effect
LiPF6 → LiF ⫹ PF5
关1兴
PF5 ⫹ S → PF5 ⫺ S
关2兴
The product in Eq. 2 represents an adduct formation of PF5 with a
solvent 共S兲 which may lead to a cascade of reactions that follow the
decomposition. Here it was intended to examine the PF5 stability in
each solvent. Gaussian 9817 was used for all ab initio and DFT
calculations.
Table I lists the dipole moment of each solute, calculated at the
SCRF-HF/6-31G共d兲 level, and the solute cavity, obtained from a
spherical volume of each solute calculated at HF/6-31G共d兲 level,
defined as the volume inside a contour of 0.001 electrons/bohr3
density.18
MD simulations.—MD simulations were performed for a system
with the reactant or the product 共one molecule兲 as a solute in Eq. 1
in each solvent 共50 solvent molecules兲 under normal temperature
and pressure conditions at T ⫽ 300 K. Solvent molecules which had
van der Waals overlaps with the solute were removed from the system upon immersion of the solute molecule in the box of solvents.
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Journal of The Electrochemical Society, 150 共12兲 A1628-A1636 共2003兲
A1629
Table I. Calculated dipole moments „␮… and solute cavities „a… of
solutes in LiPF6 decomposition.
␮, D
a, Åb
a
a
b
LiPF6
LiF
PF5
7.08
3.55
6.17
2.61
0.00
3.38
Obtained from SCRF-HF/6-31G共d兲 calculations.
See the text.
The effective concentration of each solution was around 1 ⫻ 10⫺4
M and the density ranged from 1.09 to 1.18 g cm⫺3. The concentration was set to be very small to eliminate interactions between the
solutes. This was necessitated by calculations of thermodynamic
properties. COMPASS™19 was used for the force field. The simulations were carried out by using a Cerius2 package.20 The Ewald
summation was employed for evaluating long-range electrostatic interactions. Each system was first equilibrated long enough for the
ensemble properties 共pressure, temperature, potential energy, etc.兲 to
settle, typically for 50 ps. Production runs were then performed for
500 ps more. The potential energy used for the thermodynamic
analysis was time-averaged from the production runs.
Results and Discussion
Previously we detected a small amount of POF3 and PO2 F⫺
2 as
the decomposition products in a LiPF6 -based electrolyte solution by
19
F-NMR as shown in Fig. 1; however, no PF5 was observed.8 Even
immediately after the PF5 gas was introduced into a pure PC solvent
in a nuclear magnetic resonance 共NMR兲 sample tube, no product
other than POF3 was detected, which shows the extremely high
reactivity of PF5 with a carbonate solvent. Thus, we decided to use
computer simulation as a tool for examining the stability and the
reactivity of PF5 in various solvents.
DFT calculations.—We start with the gas-phase decomposition
which serves as a reference point in this work. Figure 2 illustrates
the structures of solutes, LiPF6 and PF5 . The optimized geometries
of all solutes and the atomic charges are listed in the first column of
Table II, obtained from HF/6-31G共d兲 calculations. In the optimized
structure of LiPF6 , the Li atom coordinates with three F atoms in
equidistance, with Li and three F’s forming a tripod in the most
stable, undisturbed state. The distance between Li and F is 1.882 Å.
In order for the decomposition to occur, Li has to move to the
extension of one of the P-F bonds with the P-F¯Li angle being
Figure 1. The 19F-NMR spectrum for an electrolyte solution, 1 M
LiPF6 /EC-EMC 共3:7 in volume ratio兲, after the salt decomposition. The
estimated concentration for PO2 F⫺
2 and POF3 were 93 and 9 ppm,
respectively.
Figure 2. The optimized geometries of LiPF6 and PF5 at the HF/6-31G共d兲
level in the gas phase. The structure of PF5 is D 3h . See Table II for the
detailed geometries.
180°, the same direction as the P-F anti-bonding orbital. This coordination allows the maximum overlap of atomic orbitals between the
Li and the F atoms, thus for a reaction of Li and F to take place,
producing LiF and PF5 . When enough thermal energy is given to
the salt, this movement can take place relatively easily. Conversely,
in a highly polar solvent, the salt tends to dissociate itself, thus
removing the Li and the F distance further away from each other,
reducing the possibility of decomposition. The optimized geometry
for PF5 has the D 3h symmetry, and the transitional state of the pseudorotation with the C 4v symmetry 共not shown兲 was also found at a
higher energy by 5.6 kcal mol⫺1.
The free energy differences for the decomposition in the gas
phase calculated at two temperatures, 300 and 400 K, are listed in
the first two columns of Table III. As is shown, the decomposition is
endothermic in the gas phase for which the level of calculations
used here is highly accurate. This result demonstrates the inherent
stability of LiPF6 and suggests that the decomposition in solid or
solution is caused by the thermal and the condensed phase effect.
Next we introduce solvents to the system. It is not known how
critically the solvent plays a role in the salt decomposition. There
are basically two models treating solvents: a model treating solvent
implicitly and one treating explicitly. The former is based on the
Onsager-type reaction field theory,21 treating solvent as a dielectric
continuum, collectively known as the SCRF methods, representing
simple, less computationally expensive methods, yet sometimes resulting in inaccurate description of solute-solvent interactions. In the
SCRF treatment, in general, a solute is placed in a cavity in a continuum of solvent with the cavity representing the volume of the
solute. In light of interpreting the results, further description of the
model may be helpful. In the simplest model, a solute occupies the
fixed spherical cavity within the solvent field. A dipole of the solute
induces the polarization of the surrounding solvent, which in turn
interacts with the solute dipole, stabilizing the solute. The stabilization energy, ⌬E, depends on the solute dipole moment, ␮, the cavity, a, and the dielectric constant of the solvent, ␧
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Journal of The Electrochemical Society, 150 共12兲 A1628-A1636 共2003兲
A1630
Table II. Optimized geometries and atomic charges for solutes in
various solvents.a
Table III. Thermodynamic properties for decomposition of
LiPF6 in various solvents „kcal molÀ1….
LiPF6
r LiP
r PF1 b
r PF4 c
r LiF1 d
␪ F1 PF2 e
␪ F1 PF4 f
␪ F4 PF5 g
␪ LiF1 Ph
q Li
qP
qF
Gas
DEC
DMC
GBL
EC
2.432
1.662
1.561
1.882
83.9
90.6
94.4
86.4
0.68
2.07
⫺0.46
2.471
1.650
1.569
1.922
84.5
90.6
93.6
87.1
0.70
2.07
⫺0.46
2.474
1.650
1.569
1.926
84.6
90.7
92.6
87.1
0.70
2.06
⫺0.46
2.522
1.639
1.576
1.978
85.4
90.8
92.7
88.1
0.72
2.04
⫺0.46
2.525
1.638
1.576
1.979
85.4
90.9
92.6
88.1
0.72
2.04
⫺0.46
Gas
DEC
DMC
GBL
EC
1.555
0.66
⫺0.66
1.583
0.68
⫺0.68
1.584
0.68
⫺0.68
1.611
0.70
⫺0.7
1.611
0.70
⫺0.7
Gas
DEC
DMC
GBL
EC
1.534
1.568
1.535
90.0
120.0
1.95
⫺0.39
1.535
1.567
1.534
90.0
120.0
1.95
⫺0.39
1.535
1.567
1.534
90.0
120.0
1.95
⫺0.39
1.535
1.567
1.534
90.0
120.0
1.95
⫺0.39
1.535
1.567
1.534
90.0
120.0
1.95
⫺0.39
␧
⌬E 1
⌬H 1
⌬S 1
⌬G 1
Gasa
Gasb
DECa
DMCa
GBLa
ECa
1
52.72
52.01
0.041
39.78c
1
52.72
44.43
0.039
28.92c
2.3
49.43
48.71
0.040
36.66d
3.1
49.21
48.48
0.040
36.45d
42
47.16
46.43
0.039
34.71d
90
47.02
46.29
0.039
34.59d
a
At 300 K.
At 400 K.
⌬G 1 ⫽ ⌬H 1 兵 ⌬E 1 关 B3LYP/6-31G共d, p) 兴
⫹ thermal correction 关HF/6-31G共d)] 其 ⫺ T⌬S 1 关 HF/6-31G共d)].
d
⌬G 1 ⫽ ⌬H 1 兵 ⌬E 1 关 SCRF-B3LYP/6-31G共d, p) 兴
⫹ thermal correction 关SCRF-HF/6-31G共d)] 其
⫺ T⌬S 1 关 SCRF-HF/6-31G共d)] with Onsager’s model.
b
c
LiF
r LiF
q Li
qF
⌬G 1 ⫽ G 1 共 LiF兲 ⫹ G 1 共 PF5 兲 ⫺ G 1 共 LiPF6 兲
PF5
r PF1
r PF2 i
r PF4 j
␪ F1 PF2 k
␪ F1 PF4 l
qP
qF
r, ␪, and q refer to the distance in angstroms, the angle in degrees,
and the atomic charge, respectively. All results were obtained from
SCRF-HF/6-31G共d兲 calculations with the Onsager model, except for
the gas phase for which HF/6-31G共d兲 calculations were used.
b
r PF1 ⫽ r PF2 ⫽ r PF3 .
c
r PF4 ⫽ r PF5 ⫽ r PF6 .
d
r LiF1 ⫽ r LiF2 ⫽ r LiF3 .
e
␪ F1 PF2 ⫽ ␪ F2 PF3 ⫽ ␪ F1 PF3 .
f
␪ F1 PF4 ⫽ ␪ F1 PF5 ⫽ ␪ F2 PF4 ⫽ ␪ F2 PF6 ⫽ ␪ F3 PF5 ⫽ ␪ F3 PF6 .
g
␪ F4 PF5 ⫽ ␪ F4 PF6 ⫽ ␪ F5 PF6 .
h
␪ LiF1 P ⫽ ␪ LiF2 P ⫽ ␪ LiF3 P .
i
r PF2 ⫽ r PF3 .
j
r PF4 ⫽ r PF5 .
k
␪ F1 PF2 ⫽ ␪ F1 PF3 ⫽ ␪ F2 PF4 ⫽ ␪ F2 PF5 ⫽ ␪ F3 PF4 ⫽ ␪ F3 PF5 .
l
␪ F1 PF4 ⫽ ␪ F1 PF5 ⫽ ␪ F4 PF5 .
a
⌬E ⫽
冉
冊
␧ ⫺ 1 ␮2
2␧ ⫹ 1 a 3
vent’s role in the reactions in question, provided that the explicit
method adequately models solute-solvent interactions.
We start with the implicit model to calculate the following free
energy difference for the decomposition
关3兴
Thus, a greater dipole moment is further stabilized by more polar
solvent. Such a treatment of solvent significantly reduces the cost of
computational time, compared to calculating solute-solvent interactions individually, but it may not be recommended in general for a
system with strong solute-solvent interactions.
Alternatively, the second model, treating solvent molecules explicitly, thus specific solute-solvent interactions being accounted for,
is yet more computationally demanding. MD simulations generally
fall in this category. Thus, which protocol is chosen is a trade-off
between cost and accuracy. Here, we have chosen both models, implicit and explicit. A benefit is that a comparison between two such
protocols inevitably discloses the consequence of the difference in
treating solvents, thus revealing a degree of significance of the sol-
关4兴
The optimized geometries and the atomic charges are summarized in
Table II, obtained from SCRF-HF/6-31G共d兲 calculations and the
CHelpG method22 using the SCRF-HF/6-31G共d兲 density, respectively, for each solute in each solvent. The changes in the geometries
and the atomic charges are what is generally expected from the
treatment used, SCRF. The deviation from the gas phase, the geometry or the atomic charge, becomes greater as the polarity of the
solvent increases. Note that the distance between Li and P of LiPF6
increases in going from DEC to EC by 2%, predicting qualitatively
the experimental trend of a larger dissociation of LiPF6 in a more
polar solvent.23,24 The exception is PF5 whose geometry and atomic
charge show little change over a wide range of solvents. This is due
to PF5 ’s nonpolarity, having no dipole moment 共see Table I兲 due to
its molecular symmetry. This invariability of both the geometry and
the atomic charge of PF5 reflects on the following thermodynamic
properties.
Table III summarizes the thermodynamic properties (⌬E 1 ,
⌬H 1 , ⌬S 1 , and ⌬G 1 ) obtained from SCRF-DFT calculations at the
B3LYP/6-31G共d,p兲 level in various solvents represented by their
dielectric constants 共⑀兲. The frequency calculations were performed
at the level of SCRF-HF/6-31G共d兲 from which the thermal corrections to the enthalpy and the entropy were obtained. Though the
entropic contributions, T⌬S, are not small, ⬃12 kcal mol⫺1, the
values stay almost the same across the solvents and are thus inconsequential to the comparison among the solvents. As is known, LiF
is insoluble in the solvents used in this study, so the numbers in
Table III cannot be directly compared to experimental data, if any.
Still, they offer helpful insight for discussion regarding the relative
stability of each solute, which is the main objective of this work.
According to the SCRF-DFT calculations, the decomposition is
largely endothermic in these solvents and shifts more toward the
products with increasing polarity of the solvent, which is expected
from the model used. The relative stability of each solute expressed
by the solvation free energy, ⌬G solv关 ⫽ ⌬G 1 (solvent)⌬G 1 (gas) 兴 ,
is illustrated in Fig. 3 as a function of the dielectric constant of the
solvent. The stability of PF5 stays virtually unchanged, whereas the
other solutes become more stable as the polarity of the solvent increases with the stability increase of LiF being the largest. This is in
general explained by Eq. 3. Though the dipole moment of LiPF6 is
higher than that of LiF, its larger cavity offsets the solvation energy
by a power of 3. This model does not treat solvent molecules individually. A nonpolar solute such as PF5 does not change its stability
over a wide range of solvents due to its very small dipole moment,
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Journal of The Electrochemical Society, 150 共12兲 A1628-A1636 共2003兲
A1631
Table IV. Free energies for PF5 -solvent adduct „kcal molÀ1….a
⌬G 2
a
Figure 3. The solvation free energy of each solute as a function of the
dielectric constant of the solvent obtained by SCRT-DFT calculations.
but experimental data seem to show otherwise. The amount of PF5
in different solvents has been reported to vary from solvent to
solvent.4 The experimental findings seem to contradict with the results from the implicit model. In order to take into account a thermal
effect, the frequency calculations were also performed at 400 K, at
which the salt decomposition was clearly observed.4 Yet, this only
reduces the free energy by around 10 kcal mol⫺1, leaving the reaction still endothermic.
Next, we improve the model by using a more explicit treatment
of the solvent. Since the previous decomposition reactions were estimated to be all endothermic, our attention was directed toward the
stability of the products which may be underestimated by the continuum model. PF5 is a strong Lewis acid and may form a solvent
adduct in solution. In this calculation, a solvent adduct of PF5 was
immersed in each solvent continuum in order to treat somewhat
explicitly the PF5 -solvent interaction. Similar calculations were reported for the PF5 -H2 O adduct in the gas phase.9 Here, the structures of the adducts were constructed from the optimized gas-phase
structure of PF5 with the P atom coordinating with the carbonyl
oxygen of the solvent, then optimized in each solvent. The adducts
with the P atom pointing at the ether oxygen of the solvent were also
examined. It was found that the former adduct formation is more
stable than the latter for all the solvent. Thus, the results for the
former are only shown here. The optimized geometry obtained from
SCRF-HF/6-31G共d兲 calculations in solution are displayed in Fig. 4.
The structure of PF5 in each adduct has no longer the D 3h symmetry
due to the interactions with the adjacent solvent.
Table IV lists the free energies (⌬G 2 ) of each PF5 -solvent adduct calculated in each solvent, obtained similarly to the calculations
in Table III, for the process defined by Eq. 2. As the negative values
of the free energies indicate, the process is voluntary for the all the
solvents, moreso in a polar solvent, suggesting a stable formation of
DEC
DMC
GBL
EC
⫺1.47
⫺1.85
⫺5.2
⫺5.3
Obtained from SCRF-B3LYP/6-31G共d,p兲 calculations with Onsager’s
model.
PF5 -solvent adduct in solution. The results are also in line with the
experimental observation that the reactivity of PF5 depends on the
solvent.4
To examine the differences in the relative stability of PF5 adducts, the atomic charges were calculated for each adduct based on
the CHelpG method using the SCRF-HF/6-31G共d兲 density, shown
for the carbonate group or the carboxyl group of each adduct by
italic in Fig. 4. The charges of the carbonate group are larger than
those of the lactone group due to the greater polarization around the
O-C(⫽O兲-O moiety than the C-C(⫽O兲-O moiety. The higher
charges of the carbonyl and the ether oxygens in general result in
unfavorable interactions with the electron-rich F atoms of PF5 ,
which make the adduct less stable. These interactions are reflected
on the geometries of each adduct, especially on the distances between the solvent and PF5 , with the longer P-共C⫽)O distances for
the linear carbonate solvents, as is seen in Fig. 4. The smaller oxygen charges give rise to a more stable adduct in GBL. In fact,
PF5 -GBL adduct has the shortest P-共C⫽)O distance. The large
charges of the carbonate group are screened by the polar solvent,
EC. Unfavorable interactions with the F atoms are thus shielded,
having a comparable geometry to that of the GBL adduct. These
results have an important implication in the reactivity of PF5 in
different solvents. The stability of these adducts affects the reaction
of PF5 with solvent that follows the LiPF6 decomposition, and these
adducts could well be some of the reaction intermediates. For example, a similar adduct PF5 -H2 O with the P atom coordinating with
the water oxygen is an intermediate for PF5 hydrolysis.25
The adduct stabilization (⌬G 2 ) energy was added to Eq. 4 to
give the following equation
⌬G ⬘ ⫽ ⌬G 1 ⫹ ⌬G 2
关5兴
Table V gives the values of resultant ⌬G ⬘ . The decomposition processes become less endothermic than they are with ⌬G 1 alone, and
yet, are still prohibited in solution. In the next model we treat solvent explicitly.
Figure
4. The
structures
of
PF5 -solvent adducts used for SCRFDFT calculations with the adduct P-O
bond drawn in the figure. The geometry was optimized by HF/6-31G共d兲
geometry optimization starting with
the P atom pointing at the carbonyl
oxygen. The optimized distances and
the atomic charges are also partially
included. The P-O-C bond angles are
132° for all the adducts. See the text
for the atomic charge calculations.
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Journal of The Electrochemical Society, 150 共12兲 A1628-A1636 共2003兲
A1632
Table V. Free energies for LiPF6 decomposition recalculated
from Table IV „kcal molÀ1….
⌬G ⬘
a
a
DEC
DMC
GBL
EC
35.19
34.59
29.51
29.29
Table VI. Enthalpies of decomposition of LiPF6 in various solvents „kcal molÀ1….
Enthalpies and their components
DEC
LiPF6
⌬G ⬘ ⫽ ⌬G 1 ⫹ ⌬G 2 .
E gas
solvent
E sol
E sol
⌬E sol
⌬H sol
MD simulations.—To treat the solvent effect more rigorously, we
performed MD simulations in which all interactions between the
solute and the solvent and among the solvent molecules are explicitly included. Using the thermodynamic cycle shown in Fig. 5, one
decomp
may estimate the decomposition enthalpy in solution (⌬H sol
PF5
LiPF6
LiF
⫽ H sol ⫹ H sol ⫺ H sol ) according to Eq. 6
PF
LiPF6
decomp
decomp
LiF
⫽ ⌬H gas
⫹ ⌬H sol
⫹ ⌬H sol5 ⫺ ⌬H sol
⌬H sol
DMC
E gasa
solvent
E sol
E sola
⌬E sol
⌬H sol
关6兴
where ⌬H sol represents the heat of solution, e.g.
PF
PF
⌬H sol5 ⫽ ⌬E sol5 ⫹ P⌬V ⫺ RT
PF
PF
PF
solvent
⌬E sol5 ⫽ E sol5 ⫺ E sol
⫺ E gas5
关7兴
关8兴
where P, V, R, and T are the pressure, volume, gas constant, and
PF
PF
absolute temperature, respectively, and E sol5 and E gas5 the internal
energies of PF5 in solvent and in the gas phase, respectively, and
solvent
E sol
the internal energy of solvent. The simulations were performed under zero pressure; thus, P⌬V disappears in Eq. 7. Each
quantity in Eq. 6-8 was obtained from an ensemble average over 500
ps of simulation for a box of solvent and one solute, LiPF6 , PF5 , or
LiF (Esol), and over 100 ps for those in the gas phase (E gas). For
such simulations, the thermodynamics properties can depend on the
initial configuration of the system. The final values were obtained by
averaging over five independent simulations to increase the statistical significance of each property.
Table VI summarizes the results from the MD simulations. For
decomp
⌬H gas
the values from the DFT calculations in the gas phase
were used. Again, these values are primarily used for comparison of
the relative stability of each solute. The number of solvent molecules in each system was 50 for the LiF solution and 49 for the
LiPF6 and the PF5 solution, respectively. The enthalpy of decomposition now is negative in all solvents, the process being more exothermic with the increasing polarity of the solvent. Figure 6 illustrates the heat of solution for each solute as a function of the
dielectric constant of the solvent. The dependence of PF5 stability
on the solvent is well demonstrated and the contrast from Fig. 3 is
apparent. The sharp contrast in the results between the DFT calculations and the MD simulations unambiguously suggests the strong
interactions of the solute with the solvent, especially for PF5 , because the difference in the results between the two protocols, the
implicit and the explicit model, is most profound.
In order to further examine the PF5 -solvent interactions, the trajectories from the MD simulations were inspected. Figure 7 depicts
the first shell solvation of each solute shown by snapshots taken
Figure 5. The thermodynamics cycle for the LiPF6 decomposition.
GBL
E gasa
solvent
E sol
E sola
⌬E sol
⌬H sol
EC
E gasa
solvent
E sol
E sola
⌬E sol
⌬H sol
a
a
a
LiF
PF5
10.51
⫺2636.69
⫺2723.14
⫺96.96
⫺97.56
⫺171.88
⫺2689.42
⫺2947.71
⫺86.41
⫺87.01
64.98
⫺2636.69
⫺2638.68
⫺66.97
⫺67.57
10.51
⫺1640.18
⫺1747.71
⫺118.04
⫺118.64
⫺171.88
⫺1672.98
⫺1953.59
⫺108.72
⫺109.32
64.98
⫺1672.98
⫺1675.63
⫺67.63
⫺68.22
10.51
⫺1343.60
⫺1470.92
⫺137.83
⫺138.43
⫺171.88
⫺1343.60
⫺1651.52
⫺136.04
⫺136.64
64.98
⫺1343.60
⫺1373.36
⫺94.74
⫺95.33
10.51
⫺3316.15
⫺3436.08
⫺130.44
⫺131.04
⫺171.88
⫺3382.47
⫺3641.50
⫺129.67
⫺130.27
64.98
⫺3316.15
⫺3346.45
⫺95.28
⫺95.88
Enthalpies of decomposition
DEC
decomp
⌬H gas
LiPF6
⌬H sol
LiF
⌬H sol
PF
⌬H sol5
decomp
⌬H sol
a
DMC
GBL
EC
52.01
52.01
52.01
52.01
⫺97.56
⫺118.64
⫺138.43
⫺131.04
⫺87.01
⫺109.32
⫺136.64
⫺130.27
⫺67.57
⫺68.22
⫺95.33
⫺95.88
⫺1.33
⫺3.21
⫺41.53
⫺43.10
The errors for the condensed phase simulations are within 10 and 0.2
kcal mol⫺1 for the gas-phase simulations.
from the trajectories. It was found that PF5 is well solvated by the
cyclic solvents, EC and GBL, closely surrounded by the solvent
molecules, whereas the linear carbonates are somewhat distant from
the solute, creating an extra cavity between the solute and the solvent. According to Eq. 3, a larger cavity gives rise to a poor solvation energy in general.
Pair distribution functions were calculated from the trajectories
to evaluate the number of solvent molecules near PF5 . Table VII
summarizes the solvation of PF5 by each solvent. The numbers of
the carbonyl oxygen, the ether oxygen, and the methyl carbon
共DMC and DEC兲 or the methylene carbon 共EC and GBL兲 are calculated by integrating the relevant pair distribution function up to 5
Å. In the case of EC, the number of the ether oxygen can include
those in the same molecule or those in different molecules due to the
symmetry of the molecules. The results in the tables demonstrate the
stronger affinity to PF5 by EC and GBL, compared to the linear
carbonates. The number of the carbonyl oxygen within 5 Å from the
P atom of PF5 in EC or GBL is almost eightfold higher than that in
DEC. Further, the total number of oxygens tends to be higher for the
polar solvents than the nonpolar solvents. These observations can be
rationalized in that in addition to the polarization effect by the solvents, the sterically compact solvents such as EC or GBL have a
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Journal of The Electrochemical Society, 150 共12兲 A1628-A1636 共2003兲
A1633
Table VII. The solvation structure around PF5 in various
solvents.
a
r P¯共C-兲O⫽ , Å
r P¯共C-兲O- , b Å
n (C-兲O⫽c
n (C-兲O- d
n CH3 /CH2 e
DEC
DMC
GBL
EC
5.21
4.71
0.37
1.98
1.07
3.63
4.21
1.68
1.63
1.08
3.63
3.77
3.09
3.01
2.07
2.95
4.85
2.92
1.54
1.68
a
Figure 6. The heat of solvation for each solute in various solvents as a
function of the dielectric constant of the solvent obtained from MD simulations.
better access to PF5 , while the bulky, flexible molecules such as
DEC create a large cavity between PF5 and the solvent. As to the
solvation site, the polar solvents tend to solvate the P atom of PF5
with the carbonyl oxygen, while the less polar solvents are likely to
solvate with the ether oxygen. The solvation by GBL and DMC falls
somewhere in between EC and DEC. In particular, in the case of
GBL, a larger negative atomic charge was assigned for the ether
oxygen than for the carbonyl charge in the force field used for simulations. What plays in the preference in the solvation site is not clear
at this point.
Table VIII lists the values for the Li-P distance of LiPF6 averaged over 500 ps of simulations in various solvents, compared to
those obtained from the SCRF-HF optimizations listed in Table II. It
is clear that the SCRF-HF calculations largely underestimate the
dissociation of the salt pair, the Li-P distance, moreso in the polar
solvents. Our previous study showed that the trend in the dissociation of LiPF6 in various organic solutions can be reasonably reproduced by MD simulations.12
Comparison of two protocols.—Though the results from MD
simulations are consistent with the SCRF-DFT calculations in that
the decomposition is further promoted in more polar solvent, it is
The averaged shortest distance between the P atom and the carbonyl
oxygen of solvent.
b
The averaged shortest distance between the P atom and the ether
oxygen of solvent.
c
The number of the carbonyl oxygen of solvent within 5 Å from the P
atom of PF5 .
d
The number of the ether oxygen of solvent within 5 Å from the P
atom of PF5 .
e
The number of the methyl 共DEC or DMC兲 or the methylene 共GBL or
EC兲 carbon of solvent within 5 Å from the P atom of PF5 .
unambiguously found from the MD simulations that the stability of
PF5 strongly depends on the solvent and apart from the polarization
effect by the solvent, the steric effect of the solvent on solvation also
seems to be at work, which is absent in the SCRF-DFT calculations.
The difference in the results between the SCRF-DFT calculations,
including the PF5 adduct model, and the MD simulations primarily
stems from the insufficient treatment of solvation. In particular, the
PF5 adduct model included only one solvent molecule in the SCRFDFT calculations. MD simulations revealed more than one solvent
molecule are involved in solvation of PF5 .
Remember that the two protocols, SCRF-DFT calculations and
MD simulations, are based on different theoretical foundations: the
DFT calculations on quantum mechanics and the MD simulations on
classical mechanics, i.e., the Newtonian mechanics, using a semiempirically derived force field for energy evaluation. The higher
level of accuracy for the former over the latter in general is undisputable in principle. Yet it is the way solvent molecules are treated
that sharply differentiated the results between the two protocols. The
MD simulations predicted the strong solvent dependence of PF5
stability, as experimentally suggested, while the SCRF calculations
basically do not distinguish its stability over a wide variety of solvents. It is shown in this study that the explicit solute-solvent interactions described by the classical MD simulations still seem to provide more accurate results, compared to otherwise more accurate
DFT calculations using an implicit solvent model. The difference
also demonstrates that long-range interactions are important in solvation of species involved in the LiPF6 decomposition. It is of interest to compare the two protocols in the energetics. For example,
the energy for the formation for the PF5 -EC adduct in Eq. 2 estimated from the force field calculations was ⫺4.02 kcal mol⫺1, very
close to ⫺3.90 kcal mol⫺1 obtained from the gas-phase B3LYP/631G共d,p兲 calculations, for example. Hence, it seems that the solutesolvent interactions are described by the MD simulations reasonably
well.
Table VIII. The averaged distance between the Li and the P
atom in LiPF6 .
r LiP , a Å
r LiP , b Å
DEC
DMC
GBL
EC
2.71
2.47
2.78
2.47
2.93
2.52
3.14
2.53
a
Figure 7. Snapshots for the PF5 solvation in various solvents. Only the first
solvation shell is shown, taken from dynamics trajectory.
The average distance between Li and the P atom of PF6 obtained
from MD simulations.
b
The optimized distance between PF6 obtained from SCRT-HF calculations 共see Table II兲.
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A1634
Journal of The Electrochemical Society, 150 共12兲 A1628-A1636 共2003兲
Figure 8. HOMO/LUMO energy level diagram for PF5 , BF3 , and various
solvents, obtained from HF/6-31G共d兲 calculations.
The entropic effect in the decomposition is not included in the
previous discussion based on the MD simulations. In the previous
section, the SCRF-DFT calculations showed the entropic contribution to the decomposition thermodynamics to be almost identical for
all the solvents, and thus it made little difference among the solutes
in the entropic effect on the relative stability in the different solvents. For example, the entropic change of LiPF6 in going from EC
to DEC is comparable to that of PF5 in the same solvent change.
This entropic contribution arises primarily from the change in the
molecular vibrations and translations of the solute in different solvents. Other entropic contribution stems from the solvent molecular
rearrangement upon solvation of the solute, which is not accounted
for in the SCRF calculations. This contribution should be roughly
cancelled out in the discussion of the relative stability of the solutes
in structurally similar solvents such as DMC and DEC or EC and
GBL. As to the solvation entropy difference between unlike solvents
such as EC and DEC, it is not expected to overturn the overall
outcome of the calculations. Considering the similarity in molecular
shape, the solvation of PF5 by EC, both roughly sphere, may be
entropically more favorable than the PF5 solvation by DEC, a linear
solvent.
In this study, LiF was treated as a solute, though it precipitates as
it is produced. Still, the difference in the results from the two protocols is caused largely by the increased stability of PF5 in solvent
by MD simulations which treat solute-solvent interactions more explicitly. Thus, a treatment of LiF as a solute in this study made little
difference on the overall conclusion.
Reactivity of PF5.—For a thorough investigation of the reactivity
of PF5 with solvents, the reaction pathways involving PF5 and solvents need to be clearly defined. Though some of the products such
as POF3 and PO2 F⫺
2 have been found by our experiments, the reaction mechanism is yet to be clearly understood. Thus, here we examine the reactivity of PF5 in terms of the highest occupied and
lowest unoccupied molecular orbital 共HOMO-LUMO兲 interactions
between PF5 and the solvents.
Figure 8 illustrates a diagram for the HOMO and LUMO energy
levels for PF5 and the solvents used, including those for CH3 F and
BF3 for comparison. BF3 is a product of the decomposition of another well-known Li salt, LiBF4 . The strong acidity of PF5 as a
Lewis acid is well demonstrated by the very low LUMO energy
level, 0.15 eV. The HOMO orbitals of the solvents reside mainly on
their carbonyl oxygens. According to the molecular orbital theory,
the smaller the energy gap between orbital levels belonging to different molecules, the stronger the interaction between the orbitals
becomes and thus, the higher the reactivity between the molecules in
Figure 9. The hydrolysis of LiPF6 and Et3 MeNPF6 in water and in PC with
0.5 wt % of water monitored by ion chromatography. The vertical axis is the
decomposition percentage based on F atoms, while the horizontal line is time
in days.
general. It follows that with such a low LUMO energy level PF5
easily attacks the Lewis base’s carbonyl oxygen for electrophilic
reaction. As a comparison, a weaker Lewis basis CH3 F has a lower
HOMO energy than the carbonate solvents, and thus is less likely
for the reaction with PF5 . In fact, PF5 has been identified in a CH3 F
solution by NMR spectroscopy.26 The LUMO energy level for BF3
is comparable to those for the carbonate solvents and thus, the reactions between BF3 and the solvents are less likely, which is supported by experimental observations, a reason for the stability of
LiBF4 in carbonate solvents.
Hydrolysis of LiPF6.—Previously, we have investigated the hydrolysis of LiPF6 by ion chromatography.8 Figure 9 shows the progression of hydrolysis over time for LiPF6 and Et3 MeNPF6 in water
and also in PC including 0.5 wt % water, monitored by ion chromatography. The figure demonstrates an intriguing behavior of LiPF6
being stable in aqueous solutions, while extremely prone to hydrolysis in organic solutions. We have also found that the high ion dissociation by using a quaternary ammonium cation such as Et3 MeN⫹
suppresses the hydrolysis of PF⫺
6 , because larger cations tend to
prevent the formation of the contact ion pairs.27-29
In order to understand the sharp contrast in the behavior of LiPF6
hydrolysis between aqueous and organic solutions, we also performed MD simulations of LiPF6 in a box of 50 water molecules.
The simulation protocol was similar to that used for LiPF6 decompositions. Figure 10 illustrates a snapshot from the MD trajectory,
depicting the hydration of LiPF6 with a water molecule intersecting
between the Li⫹ and the PF⫺
6 ions. Table IX lists the hydration
structure of LiPF6 in water obtained from integrating the pair distribution functions up to 5 Å. The most profound difference from the
solvation in organic solvents is the large Li-P distance, a 40% increase from that in EC 共see Table VIII兲, demonstrating a much stronger dissociating power of water for the LiPF6 ion pair. This long
distance, thus more space, between the Li and the P atom allows
water molecules to intervene the two ions, as shown in Fig. 10. At
this loose association, the shortest Li-F distance is 3.75 Å, averaged
over 500 ps, far enough for a reaction between the Li and the F atom
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Journal of The Electrochemical Society, 150 共12兲 A1628-A1636 共2003兲
Figure 10. A snapshot taken from the dynamics trajectory for LiPF6 in
water. Only water molecules in the vicinity of LiPF6 are shown.
not to occur. In EC the averaged Li-F distance is as short as 1.87 Å.
Though water has a smaller dielectric constant than EC, the size of
water molecule, smaller than EC, allows easier access to the space
between the cation and the anion, promoting the salt dissociation.
Conclusion
SCRF-DFT calculations, using an implicit solvent model,
showed the LiPF6 decomposition to be further promoted in more
polar solvent, but predicted a virtually identical stability for the
decomposition product PF5 over a wide range of solvents, predicting
an endothermic reaction in solution. The overall thermodynamics
did not change, even at a higher temperature at which the salt decomposition tends to be promoted. Inclusion of a PF5 -solvent adduct, in order to account for the stability of PF5 by solvent more
explicitly, did not significantly alter the overall outcome. MD simulations, treating solvent molecules explicitly, on the contrary, demonstrated not only a significant stabilization of PF5 , but also its
considerable stability variation over various solvents, predicting the
decomposition exothermic in all the solvents. The sharp contrast of
the results between the two calculations using distinctively different
solvent models suggests the strong solute-solvent interactions in the
salt decomposition.
In general, the continuum model fails when the solvation cannot
be described by the dielectric constant of the solvent and the size
and shape of the solute cavity. Those systems with specific interactions, such as weak bond formations between the solvent and the
solute including hydrogen bonds, may fall into this category.
Though the continuum model has been successfully applied to a
series of systems for efficiently estimating solvation energies in
general,30 it has been pointed out that the model may not be suffi-
Table IX. The hydration structure around LiPF6 in water.a
r LiP , b Å
4.41
a
r LiO , c Å
r LiF , d Å
r PO , e Å
r FH , f Å
n OLi , g Å
n OP , h Å
2.53
3.75
3.17
1.73
8.87
12.63
Averaged over 200 ps.
The averaged shortest distance between Li and the P atom of the PF⫺
6
anion.
c
The averaged shortest distance between Li and the water oxygen.
d
The averaged shortest distance between Li and the F atom of the PF⫺
6
anion.
e
⫺
The averaged shortest distance between the P atom of the PF6 anion
and the water oxygen.
f
The averaged shortest distance between the F atom of the PF⫺
6 anion
and the water hydrogen.
g
The number of water oxygens within 5 Å from Li.
h
The number of water oxygens within 5 Å from P.
b
A1635
cient for systems with a polar solute in a polar solvent.31 Yet, for a
system with a non-polar solute, PF5 , in organic solvent, it is not
clear how strong the specific solvation of PF5 may be and there are
few experimental studies reporting detailed interactions between
PF5 and the organic solvents. Our modeling study may shed light
into the solvation of PF5 .
Based on the inspection of the trajectories from MD simulations,
along with the results form SCRF-DFT calculations, it is concluded
that PF5 is more stabilized in polar and compact solvents such as EC
and GBL than in bulky, linear carbonates such as DMC and DEC.
Thus, it is expected that the decomposition of LiPF6 is promoted in
a solvent which has a large dielectric constant and is small in volumetric size. Yet it should not be forgotten that these polar solvents
are also effective in dissociating the salt which prevents the decomposition in the first place. Still, at a relatively high concentration
used in LIB electrolytes, ⬃1 M, a large degree of ion pairs is believed to remain intact, even in a polar solvent like EC. Then the
stability of PF5 by the solvent becomes an important issue. A dilemma is that a polar solvent not only helps dissociate a LiPF6 ion
pair but also stabilizes the decomposition product, PF5 . A guideline
for a better electrolyte is a design that promotes an ion pair dissociation while effectively destabilizing PF5 . Two factors which are
found to play a role in stabilizing PF5 from this study, the dielectric
constant and the volumetric size, may be used to optimize the electrolyte characteristics. Our MD simulations of LiPF6 in water provide a good example as to how these two effects contribute to the
decomposition of the salt. The calculations on the LiPF6 hydrolysis
support the model that the hydrolysis occurs via a pathway involving PF5 produced by the decomposition of LiPF6 and also demonstrate that the LiPF6 salt is more dissociated in water than in carbonate solvents, which may explain the difference in the hydrolysis
behavior between the two solutions.
Acknowledgment
The authors are grateful to Accelrys’s assistance in providing
software tools. We also thank M. Takehara, N. Sato, and Y. Sakata
for their experimental work, and N. Mine and T. Aoshima for valuable discussions at Mitsubushi Chemical Corporation.
Mitsubishi Chemical Corporation assisted in meeting the publication
costs of this article.
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