Insights into lithium manganese oxide-water interfaces using machine learning potentials
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Insights into lithium manganese oxide-water interfaces using machine
learning potentials
Marco Eckhoff1, a) and Jörg Behler1, 2, b)
1)
Universität Göttingen, Institut für Physikalische Chemie, Theoretische Chemie, Tammannstraße 6,
37077 Göttingen, Germany.
2)
Universität Göttingen, International Center for Advanced Studies of Energy Conversion (ICASEC),
Tammannstraße 6, 37077 Göttingen, Germany.
(Dated: 25 January 2022)
Unraveling the atomistic and the electronic structure of solid-liquid interfaces is the key to the design of
new materials for many important applications, from heterogeneous catalysis to battery technology. Density
arXiv:2109.14068v2 [cond-mat.mtrl-sci] 21 Jan 2022
functional theory (DFT) calculations can in principle provide a reliable description of such interfaces, but
the high computational costs severely restrict the accessible time and length scales. Here, we report machine
learning-driven simulations of various interfaces between water and lithium manganese oxide (Lix Mn2 O4 ), an
important electrode material in lithium ion batteries and a catalyst for the oxygen evolution reaction. We
employ a high-dimensional neural network potential (HDNNP) to compute the energies and forces several
orders of magnitude faster than DFT without loss in accuracy. In addition, a high-dimensional neural network
for spin prediction (HDNNS) is utilized to analyze the electronic structure of the manganese ions. Combining
these methods, a series of interfaces is investigated by large-scale molecular dynamics. The simulations
allow us to gain insights into a variety of properties like the dissociation of water molecules, proton transfer
processes, and hydrogen bonds, as well as the geometric and electronic structure of the solid surfaces including
the manganese oxidation state distribution, Jahn-Teller distortions, and electron hopping.
Keywords: Machine Learning Potentials, High-Dimensional Neural Networks, Molecular Dynamics Simula-
tions, PBE0r Local Hybrid Density Functional, Lithium Manganese Oxide-Water Interface, Oxidation States,
Electron Hopping, Interfacial Water, Water Dissociation, Hydroxide Layer, Proton Transfer
I. INTRODUCTION neutrality8,17 and allowing to control the electronic struc-
ture of the bulk material. This control is particularly
The understanding of solid-liquid interfaces is of ma- important for the OER, as the Mn oxidation states are
jor importance for a sustainable energy future.1,2 In considered to be central for this process.18 Apart from the
particular, electrode-electrolyte interfaces are central for overall composition of the material, the OER activity is
many processes, from the electrocatalytic water splitting also determined by the details of the solid-electrolyte in-
for the production of green hydrogen to energy storage terface whose geometric and electronic structure as well
in lithium ion batteries supplying, e.g., portable elec- as the atomic composition can be substantially different
tronic devices and electric vehicles.3–7 For this purpose, a from the bulk.19,20
prominent material is the lithium manganese oxide spinel The active sites of electrocatalytic reactions are often
Lix Mn2 O4 , with 0 ≤ x ≤ 2, which is a frequently used embedded in a complex environment consisting of the –
positive electrode material in lithium ion batteries but possibly reconstructed – solid surface and the electrical
can also be employed as electrocatalyst for the oxygen double layer. Small particles and porous materials have
evolution reaction (OER) representing the limiting step large surface-to-volume ratios, which are beneficial for a
of water splitting.8–11 Beyond conventional lithium ion high activity, but the exposed surfaces can exhibit very
batteries containing organic electrolytes, the Lix Mn2 O4 - different reactivities. The identification of active sites is
water interface has recently received increasing attention therefore essential in a bottom-up approach for the design
regarding the development of environment-friendly aque- of improved catalysts.21–25
ous rechargeable lithium ion batteries offering improved A practical challenge when using Lix Mn2 O4 as bat-
safety combined with higher ionic conductivity and lower- tery material is capacity fading, which is related to the
cost production.12,13 disproportionation of MnIII ions at the interface and the
Stoichiometric LiMn2 O4 contains a one-to-one ratio of dissolution of the resulting MnII ions.26–28 Consequently,
MnIII and MnIV ions.14–16 The electrochemical incorpo- the identification of tactics for controlling the Mn oxida-
ration or removal of Li ions during battery discharging tion states at the interface is important for the construc-
and charging changes this ratio by the reduction or ox- tion of batteries with improved charge/discharge cycles
idation of Mn ions, respectively, ensuring overall charge and enhanced lifetime. Hence, to unravel the relationship
between composition and reactivity, a comprehensive un-
derstanding of the geometric and electronic structure as
well as of the dynamics and reactions at the interface is
a) Electronic mail: marco.eckhoff@chemie.uni-goettingen.de required.29–31
b) Electronic mail: joerg.behler@uni-goettingen.de These insights can be gained in principle in com-
2
puter simulations, but complex interface systems still tion and spin states of the Mn ions. This method is
pose a significant challenge as they require a first based on local geometric changes associated to the details
principles-quality description.32–36 The electronic struc- of the electronic structure. Thus, in combination with
ture of Lix Mn2 O4 with coexisting MnIV and Jahn-Teller an HDNNP providing the energies and forces, nowadays
distorted high-spin MnIII ions in the bulk as well as high- nanosecond time scale investigations of the geometric and
spin MnII ions at the interface is, however, difficult to electronic structure are possible for systems containing
describe by established methods like density functional about 104 -105 atoms.
theory (DFT). For a correct representation at least the In this work we investigate the Lix Mn2 O4 -water in-
level of the generalized gradient approximation including terface employing an HDNNP in combination with an
an additional Hubbard-like term for on-site Coulomb in- HDNNS. Several {100} and {110} surfaces with different
teractions (GGA+U ) or a hybrid functional containing a terminations in contact with water are investigated to un-
fraction of exact Hartree-Fock exchange is needed.37–41 ravel the spatial distribution of Mn oxidation states and
A recent hybrid DFT benchmark of lithium manganese oxygen species, such as oxide ions O2− , hydroxide ions
oxides showed that on-site Hartree-Fock exchange terms OH− , neutral water molecules H2 O, and hydronium ions
yield a correct description of partially filled shells of H3 O+ . Starting from atomically smooth solid surfaces in
localized d electrons.41 However, up to now ab initio contact with a liquid water phase, the formation of hy-
molecular dynamics simulations using GGA+U or hy- droxide and strongly bound water layers at the interface
brid DFT functionals could only be performed for rather is studied to understand the fundamental properties of
small Lix Mn2 O4 -water model systems containing a few the interface structure. A detailed analysis of Jahn-Teller
hundred atoms on picosecond time scales due to the large distortions and the hydrogen bond network is provided
computational effort.42–46 To consider the interplay of a in the Supplementary Material. The analysis of electron
variety of different structural motifs with a liquid solvent, hopping rates between Mn ions, various PT reactions,
picosecond time scales are not sufficient. For instance, for and water species residence lifetimes under equilibrium
the equilibration of Lix Mn2 O4 -water interfaces including conditions yields a detailed understanding of the kinetics
the formation of hydroxide layers, electrical double lay- and dynamics. Finally, we compare the activity of the
ers, and/or strongly bound water at the interface as well different surfaces and sites and show that initial steps of
as to obtain reliable statistics for elementary steps of pro- the OER occur already spontaneously under equilibrium
ton transfer (PT) reactions and hydrogen bond networks conditions.
significantly larger length and time scales are required.
Machine learning potentials (MLP) combine the ef-
ficiency of simple empirical potentials with the accu- II. METHODS
racy of quantum mechanics allowing to meet these
requirements.47–50 Consequently, various MLPs have In HDNNPs59,63 , which we use to compute the energies
been developed, e.g., for water51–54 and different solid- and forces driving the molecular dynamics (MD) simu-
liquid interface systems.55–58 In previous works we could lations, the potential energy is constructed as a sum of
further show that a high-dimensional neural network po- atomic energy contributions Enα ,
tential (HDNNP),59–63 a frequently used type of MLPs, is
α
applicable to bulk materials containing transition metal elem NX
NX atoms
ions in different oxidation states64–66 and in different E({R}) = Enα . (1)
magnetic orders.66 The ability to represent different ox- α=1 n=1
idation states is mandatory for studying the Lix Mn2 O4
system. As the HDNNP’s underlying functional form Here, {R} are the nuclear coordinates for a system con-
α
is unbiased with respect to different interaction types, taining Nelem elements with Natoms for element α. The
an equally reliable description for the interactions in individual atomic energy contributions are represented
the bulk and at the interface is obtained as has been by atomic feed-forward neural networks of the form
demonstrated, e.g., for the Cu-water67,68 and ZnO-water n3
( n2
"
interfaces.69–71 Moreover, like most MLPs, HDNNPs are 4
En = b1 +
X
34 3
al1 · tanh bl +
X
akl · tanh b2k
23
reactive, i.e., they are able to describe the formation and
l=1 k=1
cleavage of bonds making them applicable to PT reac- n1 nG
!#) (2)
tions omnipresent in electrochemical systems. +
X
a12 · tanh b1j +
X
a01 · Gn,i .
jk ij
Apart from the simulation of the atomistic struc- j=1 i=1
ture, machine learning algorithms can also be applied
to obtain information about the electronic structure, The architecture nG -n1 -n2 -n3 -1 of the atomic neural
for example, atomic charges,72–76 electrostatic multipole networks contains an input layer with nG neurons pro-
moments,77,78 polarizabilities,79 and even quantum me- viding a description of the atomic environment. More-
chanical wavefunctions.80 Moreover, our recently devel- over, in this work three hidden layers with n1 , n2 , and
oped high-dimensional neural network spin (HDNNS) n3 neurons, respectively, and an output layer with one
prediction method65 can be used to identify the oxida- neuron, which yields the atomic energy contribution, are
3
used. The activation functions are hyperbolic tangents Using both, an HDNNP and an HDNNS, in MD sim-
except for the output layer, for which a linear function ulations enables a simultaneous first principles-quality
is employed. The weight parameters {aρσ σ
µν } and {bν } representation of the geometric and the qualitative elec-
of the atomic neural networks are optimized to accu- tronic structure dynamics on nanosecond time scales for
rately reproduce a training data set consisting of ener- systems containing thousands of atoms.64–66
gies E ref and atomic force components F ref of reference
structures obtained, for example, in DFT calculations.
For each element an individual atomic neural network III. COMPUTATIONAL DETAILS
is constructed making the neural network parameters
element-specific. For clarity, the index α representing For the generation of the reference data the local hy-
this element-dependence has been omitted in the quan- brid exchange-correlation functional PBE0r41,82 includ-
tities in Equation 2. ing D3 dispersion corrections83,84 was used in collinar
The atomic neural networks are able to describe the spin-polarized DFT calculations. PBE0r considers only
complex relation between the atomic energies and the on-site Hartree-Fock exchange terms yielding an accu-
local chemical environments of the atoms. These envi- rate description of the partially filled Mn d shell with
ronments are described by vectors of many-body atom- a computational effort comparable to generalized gradi-
centered symmetry functions (ACSF)81 Gα n serving as ent approximation functionals. The Car-Parrinello Pro-
structural fingerprints of the local geometry inside a cut- jector Augmented-Wave (CP-PAW) code (version from
off sphere of radius Rc . ACSFs represent a general September 28, 2016)85,86 and the DFT-D3 code (version
transformation from the Cartesian coordinates {R} to from June 14, 2016)83,84 were employed using the same
a translationally, rotationally, and permutationally in- setup as in our previous studies.41,64,65
variant structural description based on interatomic dis- The HDNNP and HDNNS were constructed using the
tances and angles. Moreover, for all atoms of a given RuNNer code (versions from October 19, 2020 and De-
element, the ACSF vectors have the same dimensionality cember 4, 2018, respectively).61,62,87 The architecture of
to ensure the applicability of the trained atomic neural the atomic neural networks is 180-25-20-15-1 for all ele-
networks to large-scale simulations of systems containing ments in the HDNNP and 180-20-15-10-1 for Mn in the
different numbers of atoms. As the ACSFs depend only HDNNS, which is the only spin-polarized atom in the
on the elements and positions of the atoms, HDNNPs system. The parameters of the 180 radial and angular
are able to describe the making and breaking of bonds. ACSFs per element with the cutoff radius Rc = 10.5 a0
The parameters defining the spatial shapes of the radial are compiled in the Supplementary Material along with
and angular ACSFs can be adjusted to optimize the per- the description of a generally applicable scheme to ad-
formance as described in the Supplementary Material. just the parameter η of the ACSFs to the element-specific
More detailed information about HDNNPs, ACSFs, their nearest-neighbor distances. a0 is the Bohr radius.
properties, and their construction are provided in several Instead of total energies, the DFT formation energies
reviews.60–63 were used for training, which were obtained from the to-
The HDNNS method65 is closely related to HDNNPs tal energies minus the sum of the atomic energies cal-
and employs the same atomic neural network topology. culated for the elements in their reference states, i.e.,
However, instead of atomic energy contributions Enα , the gaseous H2 , body centered cubic Li, gaseous O2 , and α-
atomic neural networks (Equation 2) yield the atomic Mn. In addition to the formation energies also the DFT
spins Snα , i.e., they provide the Snα ({R}) relation. A Cartesian atomic force components were used for train-
HDNNS exploits the observation that different oxidation ing the HDNNP. Of all available energies and force com-
states as well as high- and low-spin states of transition ponents 90% were used in the training set to determine
metal ions typically lead to structurally different local the neural network parameters, while the remaining 10%
environments. Thus, like for the energies and forces in were employed to test the predictive power and reliability
HDNNPs, the method is based on the assumption that for structures not included in the training process.
the atomic spins and oxidation states are uniquely de- The DFT reference atomic spins used to train the
fined by the structure. Consequently, consistent refer- HDNNS are the absolute values of projections of the
ence data corresponding to the ground state electronic spin density onto the one-center expansions of the par-
structure are mandatory for a successful construction of tial waves using atom-centered spheres with a radius of
the HDNNS. The absolute values of atomic reference 1.2 times the atomic covalent radius. The atomic spin is
spins obtained from DFT are used for training to cir- therefore equal to the absolute difference in the number
cumvent the issue that the electronic ground state is of spin-up and spin-down electrons at an atom in units
twofold degenerate with respect to the absolute sign of all of the electron spin 21 h̄. The setup of the HDNNP and
spins. Since the present work is restricted to the magnetic HDNNS construction is described in detail in the Sup-
ground state, we do not explicitly include the degrees of plementary Material.
freedom related to the relative orientations of the atomic HDNNP-driven MD simulations were performed for
spins, but we note that magnetic HDNNPs taking these Lix Mn2 O4 -water interface systems in the isothermal-
degrees of freedom into account have been proposed.66 isobaric (N pT ) ensemble at a temperature of T = 298 K
4
(a)
(b)
(c)
(d)
3
FIG. 1. Side views (zy plane) of equilibrated Lix Mn2 O4 -water interface simulation cells with a volume of about 25 · 25 · 100 Å
including the interfaces (a) {100}Li , (b) {100}Mn2 O4 , (c) {110}LiMnO2 , and (d) {110}MnO2 are shown on the left. Top views
(xy plane) of non-equilibrated vacuum solid surfaces are provided on the right. The scale bar applies to all panels. The atoms
are shown as balls whereby Li is colored green, Mn violet, and H white. The color/size of the oxygen atoms has been chosen
according to the H connectivity: O2− is red/large, OH− turquoise/small, H2 O blue/small, and H3 O+ orange/small. The O-H
bonds are shown as sticks. The surrounding black line corresponds to the boundaries of the periodic simulation cell. A side
view on the zx plane is provided in the Supplementary Material Figures S1 (a) to (d). This figure was created with OVITO
Pro (version 3.5.0).88
and a pressure of p = 1 bar. The simulation cells in- subsurface layer ({100}Li ), the {100} Mn2 O4 -terminated
clude about N ≈ 6 · 103 atoms in a volume of about surface with Li in the first subsurface layer ({100}Mn2 O4 ),
3
25 · 25 · 100 Å . The volume ratio of Lix Mn2 O4 and water the {110} LiMnO2 -terminated surface ({110}LiMnO2 ),
is approximately 1:1 with the phase boundaries parallel and the {110} MnO2 -terminated surface ({110}MnO2 ).
to the xy plane. Four different cuts of bulk Lix Mn2 O4 Top views of the clean surfaces as well as side views of
in contact with water have been investigated, which are the employed interface slab models are shown in Fig-
the {100} Li-terminated surface with Mn2 O4 in the first ures 1 (a) to (d), respectively. Both surfaces of each
5
slab are structurally identical. Therefore, the solid slab uid water that is typically very well represented by ma-
is built from bulk stoichiometric LiMn2 O4 with non- chine learning potentials.51,54 We note that in spite of
stoichiometric Lix Mn2 O4 surfaces. For each system, the increased complexity of the potential energy sur-
three simulations starting from different H2 O configu- face of the interface system, in particular the bulk
rations, which initially did not include OH− and H3 O+ Lix Mn2 O4 test set RMSE is very similar to the RMSE
ions, on top of the atomically flat solid surfaces were per- of 2.2 meV atom−1 of a previous HDNNP fitted to bulk
formed for an equilibration time of 1 ns and a subsequent Lix Mn2 O4 data only.64 The maximum energy error of all
acquisition time of 5 ns. In the same way, three bulk data in the training/test set is 13.2/15.6 meV atom−1 .
water simulations with different initial structures were Only 2.3/5.5% of the energy predictions in the train-
carried out using approximately cubic cells containing ing/test set have errors larger than 5 meV atom−1 (Fig-
around 1.5 · 104 atoms and fluctuating lattice parameters ures 2 (a) and (b)).
between about 50 and 60 Å in the N pT ensemble. To The PBE0r-D3 reference data contains force compo-
identify the oxygen and water species, each H atom has nents up to |F DFT | ≤ 5.06 eV a−10 . The force components
been assigned to its closest O atom. RMSE of all data is 0.127 eV a−1 0 for both, training and
The HDNNP-driven simulations were performed us- test set. Again, the RMSE of bulk water (0.059 eV a−1 0 ) is
ing the Large-scale Atomic/Molecular Massively Paral- lower than the RMSEs of bulk Lix Mn2 O4 (0.114 eV a−1 0 )
lel Simulator (LAMMPS)89,90 and the neural network and the interface structures (0.143 eV a−1 0 ). The force
potential package (n2p2).91,92 They were run with a components RMSE of bulk Lix Mn2 O4 is similar to the
timestep of 0.5 fs applying the Nosé-Hoover thermostat value of 0.107 eV a−1 0 of the aforementioned bulk only
and barostat93,94 with coupling constants of 0.05 ps and Lix Mn2 O4 HDNNP.64 As highlighted by the heatmaps
0.5 ps, respectively, allowing for anisotropic changes of in Figures 2 (c) and (d) most of the force components
the simulation cell. The trajectory was stored in inter- have an error smaller than 0.5 eV a−1 0 (99.33/99.32%).
vals of 0.1 ps. The maximum errors are 3.13 and 3.12 eV a−1 0 for the
training and test set.
The atomic spins of Mn are in the range 1.45 h̄ ≤
IV. RESULTS AND DISCUSSION S DFT ≤ 2.55 h̄ (Figures 2 (e) and (f)). The RMSE of the
HDNNS is 0.04 h̄ for both training and test set. Only
A. High-dimensional neural networks 0.75% of the training data and 0.76% of the test data
show errors larger than 0.2 h̄ possibly resulting in the as-
signment of a different spin and oxidation state, while the
The HDNNP and HDNNS are based on a ref-
maximum errors are 0.57 and 0.54 h̄, respectively. Con-
erence data set consisting of 15228 Lix Mn2 O4 bulk
sequently, the vast majority of the Mn oxidation states
structures,64,65 5143 water bulk structures, and 17597
is accurately predicted. The assignment to the oxidation
Lix Mn2 O4 -water interface structures and their PBE0r-
states MnIV (d electron configuration t32g e0g ), high-spin
D3 DFT energies, atomic force components, and atomic
spins. The structures include 32 to 255 atoms, with MnIII (t32g e1g ), and high-spin MnII (t32g e2g ) has been set to
the interface structures containing between 122 and 194 the intervals 1.4 h̄ ≤ S < 1.8 h̄, 1.8 h̄ ≤ S < 2.2 h̄, and
atoms. A detailed description of the reference data set 2.2 h̄ ≤ S < 2.6 h̄, respectively, based on the distribution
construction and composition is provided in the Supple- of spins shown in Figures 2 (e) and (f).
mentary Material.
The PBE0r-D3 DFT formation energies range from
−2.15 eV atom−1 to −0.83 eV atom−1 therefore spanning B. Manganese oxidation state distribution
a fitting interval of 1.32 eV atom−1 . In Figures 2 (a)
and (b) the three structure types can be identified by Using the obtained HDNNP and HDNNS, we investi-
their formation energies between about −2.2 and −1.6, gate four solid-liquid interface systems with different ge-
−1.6 and −1.3, as well as −1.0 and −0.8 eV atom−1 cor- ometric and electronic structure. In this section we first
responding to bulk Lix Mn2 O4 , interface structures, and investigate the interface from the perspective of the solid
bulk water, respectively. phase, while we focus on the liquid phase in the next sec-
The HDNNP reproduces the energies of the train- tion and finally discuss the reactivity of interfacial water
ing set with a root mean squared error (RMSE) of species in the last section.
1.9 meV atom−1 , while it is able to predict the ener- In general, HDNNP-driven MD simulations allow to
gies of the test set with an RMSE of 2.4 meV atom−1 . gain insights into the atomic structure and dynamics of
The RMSE of only the bulk water training structures the Lix Mn2 O4 -water interface in equilibrium. Further,
is about 1.0 meV atom−1 (test set 1.1 meV atom−1 ) and using the HDNNS we can in addition investigate the Mn
thus about half of the values of the RMSEs of the oxidation state distribution in the trajectories. This dis-
Lix Mn2 O4 and interface training structures, which are tribution is of major importance for understanding ca-
2.0 and 2.1 meV atom−1 , respectively (test sets 2.3 and pacity fading of Lix Mn2 O4 during battery usage because
2.8 meV atom−1 ). We ascribe this difference to the less previous studies propose the origin to be disproportion-
complex geometric and electronic structure of bulk liq- ation of MnIII ions at the interface and subsequent dis-
6
(a) (b)
(c) (d)
(e) (f)
FIG. 2. Energy errors ∆E = E HDNNP − E DFT as a function of the reference formation energy E DFT of the (a) training set
and (b) test set, force component errors ∆F = F HDNNP − F DFT as a function of the reference force components F DFT of the
(c) training set and (d) test set, and errors of the atomic spins ∆S = S HDNNP − S DFT as a function of the reference atomic
spins S DFT of the (e) training set and (f) test set. The color in the heatmaps represents the density of data points based on
discretizing the plotting areas into grids of 200 × 125 points.
solution of the emerging MnII ions. MnII is the most overall slab is neutral because of the charge compensation
stable oxidation state in aqueous solution while MnIV by the subsequent Mn2 O4 layer containing formally a
is not soluble.95 Structural features exposing only small one-to-one ratio of MnIII and MnIV ions. We note that
amounts of MnII and MnIII ions at the interface could due to the structurally identical surfaces at both sides of
thus support the development of more durable electrode the slab, the system in total contains 23 Li layers and
materials. only 22 Mn2 O4 layers resulting in a slight overall excess
of MnIII compared to MnIV ions in the system. Such
We start with the {100}Li surface (Figure 1 (a)), which
a situation is not unphysical but typical for Lix Mn2 O4 ,
is positively polarized due to Li termination, while the
7
1.0 0.5 1.0 0.5
nMnIV nMnIII nMnII νCT nMnIV nMnIII nMnII νCT
0.8 0.4 0.8 0.4
νCT / ps−1 (Mn site)−1
νCT / ps−1 (Mn site)−1
n / (Mn site)−1
n / (Mn site)−1
0.6 0.3 0.6 0.3
0.4 0.2 0.4 0.2
0.2 0.1 0.2 0.1
0.0 −20 −10 0 10 20 0.0 0.0 −20 −10 0 10 20 0.0
z / Å z / Å
(a) (b)
1.0 0.5 1.0 0.5
nMnIV nMnIII nMnII νCT nMnIV nMnIII nMnII νCT
0.8 0.4 0.8 0.4
νCT / ps−1 (Mn site)−1
νCT / ps−1 (Mn site)−1
n / (Mn site)−1
n / (Mn site)−1
0.6 0.3 0.6 0.3
0.4 0.2 0.4 0.2
0.2 0.1 0.2 0.1
0.0 −20 −10 0 10 20 0.0 0.0 −20 −10 0 10 20 0.0
z / Å z / Å
(c) (d)
FIG.3.3:Time
FIG. Timeaveraged
averagedMnMn oxidation
oxidation state
state distributions
distributions and and equilibrium
equilibrium chargecharge transfer
transfer rates νrates
CT in νthe in the different
CT different layers of
the (a) {100}
layers (b){100}
of theLi ,(a) {100}LiMn O4 , {100}
, 2(b) (c) {110} O4 , (c)
Mn2LiMnO {110}
2 , and (d) {110}
LiMnO 2
, and
MnO 2 (d)
Lix {110}
Mn 2 O 4 -water
MnO 2
Li Mn
interface
x 2 O -water
systems.
4 interface
The systems.
oxidation state
distribution
The oxidationis represented by the number
state distribution of each species
is represented by theper Mn site
number ofneach
in a species
layer. The perlines
Mn are
siteonly
n inshown to guide
a layer. the eyes.
The lines are
The zeroonly
pointshown
of z has
to been
guidesetthe to eyes.
the center
The of thepoint
zero Lix Mnof2 Oz4has
slabs.
been set to the center of the Lix Mn2 O4 slabs.
e.g., to
due forthe
different loads ofidentical
structurally Li ions compensated
surfaces at both by different
sides of terminated by Mn
ers. MnII ions are2 Overy
4 resulting in total in
rarely observed 22 Li
and, if layers
+ found,
oxidation states of Mn.
the slab, the system in total contains 23 Li layers and and 23 Mn O
2 4
they only emerge layers. The reduced amount of Li
in the topmost layer with about 10−6 ions in
In 22ourMn simulations the {100}
II system compared to the {100} system
2 O4 layers we observeinthat in the outermost Mn ions Mn
only resulting a slight overall excess 2 OMn
per 4 site. Li
MnMn
of 2 O4 IIIlayer on each sideIValmost only MnIII ions are
compared to Mn ions in the system. Such leads to a slight excess of MnIV ions instead of MnIII
In contrast to the {100}Li system, both sides of the slab
apresent
situation (Figureis not 3 (a)). The reason
unphysical for theforpreference
but typical Lix Mn2 Oof ions. In the topmost layer the fraction is about three
4, representing the {100}Mn2 O4 interface (Figure 1 (b)) are
MnIIIforions
e.g., in theloads
different topmost of Lilayer is the undercoordination
ions compensated by different MnIII to two MnIV ions (Figure 3 (b)). The increased
terminated by Mn2 O4 resulting in total in 22 Li layers
of the Mnstates
oxidation ions at interface sites by only five O2− ions
of Mn. stability of MnIV ions in the topmost layer compared to
and 23 Mn2 O4 layers. The reduced amount of Li+ ions in
compared to the octahedral coordination the {100}Li system can be explained by the coordination
In our simulations we observe that ininthe theoutermost
bulk ma- the {100}Mn2 O4 system compared to the {100}−Li system
terial. We have not observed any long-living IIIOH− ions by OH− ions. For this system we find that OH ions are
Mn2 O4 layer on each side almost only Mn ions are leads to a slight excess of MnIV ions instead of MnIII
formed by dissociation adsorbed on top of about 43% of the interface Mn ions.
present (Figure 3 (a)). ofThewater molecules,
reason for the Consequently,
preference of ions. In the topmost layer the fraction is about three
significant
III protonation of interfacial O 2−
ions and ad- TheIIImajority of the corresponding protons formed in the
Mn ions in the topmost layer is the undercoordination Mn to two MnIV ions (Figure 3 (b)). The increased
sorption of ions
hydroxide ions atsites the by
undercoordinated Mn dissociation of IV water molecules is attached to interface
of the Mn at interface only five O2− ions stability of Mn ions in the topmost layer compared to
ions does not takeoctahedral
place. Duecoordination
to this lack of negative ions, O2− ions, which are covered to about 21% forming OH− .
compared to the in the bulk ma- the {100}Li system can be explained by the coordination
the formation of Mn III
ions is favored at the interface and This value is about half of the Mn coverage by OH−
terial. We have not observe any long-living OH− ions by OH− ions. For this system we find that OH− ions are
Mn IV
ions are predominantly found in the second Mn 2 O4
ions because there are twice as many interface O2− ions
formed by dissociation of water molecules, Consequently, adsorbed on top of about 43% of the interface Mn ions.
layer (Figure 3 (a)). Deeper layers contain 2− a decreasingly as Mn ions per layer. The OH− ions of the first liquid
significant protonation of interfacial O ions and ad- The majority of the corresponding protons formed in the
pronounced alternatingions excess of either MnIII or Mn IV layer are preferably but not exclusively located at MnIV
sorption of hydroxide at the undercoordinated Mn dissociation ofIIIwater molecules is attached to interface
ions,does
respectively, which Due becomes small sites while Mn sites are typically coordinated by H O
ions not take place. to this lackafter severalions,
of negative lay- O2− ions, which are covered to about 21% forming OH2− .
ers. Mn II
ions are very rarely observed and, if found, molecules (Figure 4). The proposed intermediate state of
III
the formation of Mn ions is favored at the interface and This value is about half of the Mn coverage by OH−
theyIVonly −6 the OER, in which two OH− ions are found on top of an
Mn ions emerge in the topmost
are predominantly foundlayer
in thewith about
second Mn102 O4 ions because
IV there
6+ are 10 twice as many interface O2− ions
Mn II
ions per Mn site. [MnIII
2 Mn2 O4 ] unit, is therefore
− a rare configuration
layer (Figure 3 (a)). Deeper layers contain a decreasingly as Mn ions per layer. The OH ions of the first liquid
in our simulations explaining the low OER activity of the
pronounced to the {100}excess
In contrastalternating Li system, MnIIIofor
both sides
of either theMn IV
slab layer are preferably but not exclusively located at MnIV
stoichiometric III
LiMn2 O4 spinel.
representing
ions, respectively, the {100}
which Mnbecomes
2 O4
interface
small(Figure 1 (b)) lay-
after several are sites while Mn sites are typically coordinated by H2 O
8
bution vanishes already after about four layers. Regular
oscillations of the alternating excess of either MnIII or
MnIV , respectively, can be observed in the bulk (Figure 3
(c) and (d)). As the amplitude of these oscillations varies
for the {110}LiMnO2 and {110}MnO2 systems different ar-
rangements of MnIII and MnIV ions can lead to local min-
imum configurations. Further, due to electron hopping
processes, the MnIII and MnIV arrangements are dynami-
cal at 298 K and different local motifs are observed during
the simulations even for the same interface systems. We
note that the Mn oxidation state distribution is averaged
over (001) planes in Figures 3 (a) and (b) and over (110)
planes in Figures 3 (c) and (d) yielding different slices of
the structure.
To compensate for the undercoordination of Mn ions
by O2− , about 94% of the {110}LiMnO2 interface Mn ions
are in addition coordinated by approximately two OH−
FIG. 4. Equilibrated example structure of the {100}Mn2 O4 ions. These OH− ions are placed on bridge sites thus re-
Lix Mn2 O4 -water interface including the solid surface and the sembling the octahedral coordination in bulk Lix Mn2 O4
first layer of the liquid projected on the xy plane. The colors and are shared by two Mn ions (see Section IV C). About
are according to the definition in Figure 1 except that MnIII 46% of the interface O2− ions contain adsorbed H+ ions
ions are highlighted in pink, while MnIV ions are shown in forming OH− . For the {110}MnO2 interface this value fur-
violet. ther increases slightly to about 48%, while there is about
one adsorbed OH− ion per interfacial Mn atom. In this
case, the OH− ions originating from the liquid phase are
The second layer on each side adapts to the MnIV ex- not placed at Mn bridge sites but adopt empty octahe-
cess in the system (Figure 3 (b)). The alternating excess dral coordination sites (see section IV C). To compare the
of either MnIII or MnIV ions decays after a few layers OH− coverage between the {100}Mn2 O4 interface and the
converging to equal fractions of MnIII and MnIV ions in {110}LiMnO2 and {110}MnO2 interfaces, the number of
deeper layers. In contrast to the {100}Li system in which Mn ions per interface area has to be taken into account.
basically no MnII ions form, in the {100}Mn2 O4 system we This number is about 1.5 times higher at the {100}Mn2 O4
find about 5 · 10−4 MnII ions per Mn site in the topmost interface compared to the other two interfaces. Still,
Mn2 O4 layer with some statistical fluctuations depend- the OH− coverage is higher at the {110}LiMnO2 and
ing on the surface and simulation. Substantially longer {110}MnO2 interfaces. Hence, the dissociation degree of
simulations are expected to be required to obtain fully H2 O molecules is higher at these two interfaces, which
converged values for such small fractions. As both sides provide more empty octahedral coordination sites of the
of the Lix Mn2 O4 slab in every simulation are equal, con- interfacial Mn ions than the {100}Mn2 O4 interface.
verged results in Figure 3 are symmetric with respect to In addition to the Mn oxidation state distribution,
z = 0. Deviations from this behavior, which are small we estimated the charge transfer rates related to elec-
for most of our results, can consequently be employed to tron hopping between the MnII , MnIII , and MnIV ions.
estimate the uncertainty caused by the finite simulation These rates were determined from the number of oxi-
time. dation state changes per time. Because two oxidation
The {110}LiMnO2 (Figure 1 (c)) and {110}MnO2 (Figure states are changed by one electron hop, this number is
1 (d)) interface systems show similar amounts of about divided by two. The trajectory data was collected every
3·10−4 and 4·10−4 MnII ions per Mn sites in the topmost 0.1 ps. The data in Figures 3 (a) to (d) show that even
surface layers. While the {110}LiMnO2 system contains a the fastest processes are more than an order of magni-
slight excess of MnIII over MnIV ions, the opposite is tude slower than this sampling interval. This time scale
the case for the {110}MnO2 system. The topmost layer difference ensures that the major fraction of processes is
is still dominated by MnIII ions in both systems with a counted. To exclude counting of unsuccessful attempts
ratio of nine MnIII to one MnIV at the {110}LiMnO2 in- to change the oxidation state, a transition is only consid-
terface (Figure 3 (c)) and almost only MnIII ions at the ered in case the spin value of a MnIV ion increases above
{110}MnO2 interface (Figure 3 (d)). The reason for this 1.9 h̄, the spin value of a MnIII ion increases above 2.3 h̄
preference of MnIII ions is the low coordination of the or decreases below 1.7 h̄, or the spin value of a MnII ion
topmost Mn ions by only four O2− ions. As a conse- decreases below 2.1 h̄.
quence, the second layer in the {110}LiMnO2 system and For all systems, the charge transfer rates are found to
even the second and third layers in the {110}MnO2 in- be largest close to the interface, with a maximum typi-
terface are predominantly occupied by MnIV ions. The cally in the second to fourth Mn containing layer (Figures
influence of the interface on the oxidation state distri- 3 (a) to (d)). In the center of the solid slab the corre-
9
sponding values are between about 0.02 to 0.03 charge of MnIII over MnIV ions is predicted correctly (401:391).
transfers per ps and Mn site and hence much smaller than For the {110}MnO2 system, for which 386 MnIII and 406
at the interface. These values are close to the value of MnIV ions are predicted by the HDNNS, an even better
0.02 charge transfers per ps and Mn site obtained in our agreement with a deviation of only 0.4% is reached, as
previous study of bulk LiMn2 O4 .65 The rates in the top- this slab contains 384 Li+ ions. In conclusion, the Mn
most layer of the {110}LiMnO2 interface are higher than oxidation states of all systems identified by the HDNNS
those in the topmost layers of the other interfaces, and are very accurately described via the geometric atomic
in general lower charge transfer rates are found in layers environments of the Mn ions determined by the HDNNP
with predominant single Mn oxidation states. For the energy surface.
{110}LiMnO2 interface the rates are smaller in the sec- The MnII ions in all systems have an above-average dis-
ond layer, which corresponds to the topmost layer at the tance from the solid and are slightly displaced towards
{110}MnO2 interface. Therefore, the charge transfer rates the liquid, which can be reasoned by the larger size of
in the LiMnO2 layers seem to be higher than those in the MnII ions. The MnII ions are preferably coordinated by
MnO2 layers. H2 O instead of OH− of the water contact layer and the
The electrons are not explicitly included in the Mn-O distances are on average larger than for MnIII and
HDNNP and the HDNNS identifies different oxidation MnIV ions. Dissolution of MnII ions was not observed
states based on the local structural environment like, for in the 5 ns MD simulations at 298 K and 1 bar employ-
example, the presence or absence of Jahn-Teller distor- ing atomically flat solid surfaces without defects and in
tions. Consequently, the inhomogeneous distribution of the absence of external electric fields. Therefore, disso-
MnIII and MnIV ions in the systems as well as the elec- lution seems to be rare in equilibrium under standard
tron hopping processes raise the question if the overall conditions. Especially, the inclusion of steps and defects
numbers of these ions are conserved during the simula- at the solid surface is expected to increase the dissolu-
tions. In principle, in the solid phase there has to be tion rate.96 Moreover, possible surface reconstructions as
a one-to-one ratio between the number of Li+ ions and proposed for the {110} and {111} surfaces29,37,97,98 and
the number of Mn eg electrons. Since the average num- the formation of surface layers of different stoichiome-
ber of MnII ions contributing two eg electrons is rather try such as Mn3 O4 99–101 might also be relevant for MnII
small or even negligible at all interfaces, we expect to dissolution. In particular, the Mn3 O4 tetragonal spinel
find about the same number of Li+ ions and MnIII ions, structure, in which MnII ions substitute the Li+ ions at
each containing one eg electron, in the system. Indeed the tetrahedral sites of Lix Mn2 O4 , is an interesting can-
we observe that the number of eg electrons stays ap- didate for the formation of dissolved MnII ions. These
proximately constant during all interface simulations (see MnII ions in addition block the Li+ channels in the spinel
Supplementary Material Figures S2 (a) to (d)). This ob- structure and thus need to be removed during charging
servation provides evidence of the conservation of total of the battery.
charge and number of electrons and confirms the con- In summary, the weak interaction between water and
sistent description of the systems by the HDNNP. Only the {100}Li interface seems to be responsible for only very
small fluctuations in the predictions are observed, since little formation of MnII ions. The outermost Li+ layer
electron hopping processes can give rise to intermediate separates the water molecules from the Mn and O2− ions,
structures in which the geometry-based assignment of the which are important for the dissociation of water and the
oxidation state is unavoidably physically ambiguous.65 In formation of long-living OH− ions. A high coordination
addition, remaining prediction errors of the HDNNS may by O2− ions, i.e., a more bulk-like environment, favors
contribute to these fluctuations as well. the formation of higher Mn oxidation states and leads
to a weaker interaction with water. On the one hand,
Due to the slight excess of Li+ ions in the {100}Li sys-
electron hopping and hence electrical conductivity is in-
tem related to the surface geometry, there are more MnIII
creased in the vicinity of the interface leading to higher
than MnIV ions present in this system. About 409 MnIII
battery performance when using smaller particles sizes.
and 383 MnIV ions are predicted by the HDNNS on av-
On the other hand, the formation of MnII ions is only
erage over the full simulation time of all three {100}Li
observed close to the surface suggesting more durable
interface simulations, which contain all the same number
battery materials when using larger particles.
of Mn ions. Since 414 Li+ ions are present, the error in
the number of eg electrons obtained from the HDNNS
prediction is only about 1.2%. In contrast to the {100}Li
system, the {100}Mn2 O4 system contains more MnIV than C. Structural characterization of the interfaces
MnIII ions. Also in this case the HDNNS prediction is
very accurate yielding about 400 MnIII and 428 MnIV The atomic structure as well as the reactivity of the
ions on average. Compared to the number of 396 Li+ interface are determined by the termination of the solid
ions, the prediction error in the number of eg electrons surface. For instance, we have seen that the Mn coordina-
is again small (1.1%). For the {110}LiMnO2 system 401 tion can strongly affect the formation of OH− ions. The
eg electrons are predicted compared to 408 Li+ ions re- resulting degree of hydroxylation at the interface can be
sulting in an underestimation of 1.8%. Again, the excess expected to be relevant for reactions at the surface such
10
as the OER. Moreover, the structure and dynamics of ence of OH− ions rather far from the surface. The forma-
the liquid in the vicinity of the interface and deviations tion of a small additional O2− peak on top of the surface
of its properties from the bulk liquid are of high interest. with maximum concentrations between 1 and 10 mol l−1
To assess the impact of the interface on the properties is particularly interesting. This peak implies that some
of the liquid, the system has to be sufficiently large to H2 O molecules can be deprotonated twice to partially
ensure the presence of a bulk-like region in the center of complete the octahedral coordination of the Mn ions as
the liquid phase. This bulk-like region is not only impor- shown in Figure 7 (a). This formation of surface exposed
tant for comparing interfacial properties to those of the O2− ions is potentially of interest for catalytic reactions
bulk, but also to obtain converged data for the interfa- due to their low coordination. Furthermore, a MnIV ion
cial properties. Figures 5 (a) to (d) show the averaged is often found close to a surface exposed O2− ion although
atomic distributions in all four systems. The central re- the first solid layer is typically dominated by MnIII ions
gion of the liquid phase is very similar for all different sur- at this surface. Thus, the surface exposed O2− ions have
faces and shows only small fluctuations, which are much an impact on the distribution of MnIII and MnIV ions.
larger in the vicinity of the surfaces. The density of H2 O At the {110}MnO2 interface an H2 O concentration of
in the central 5 Å slice of the liquid phase is 0.946 kg l−1 0.1 to 1 mol l−1 is found in the topmost layer of the solid
(cH2 O = 52.5 mol l−1 ). This density agrees very well with surface, which implies the opposite process. Here, O2−
the value of 0.947 kg l−1 obtained in HDNNP-driven sim- ions are protonated twice thus forming water as shown
ulations of bulk water. Further, the properties of the in Figure 7 (b). A correlation of MnII formation to the
hydrogen bond network are very similar in the centers formation of H2 O molecules in the topmost solid layer
of the liquid in all simulations (Supplementary Mate- is not observed. MnII ions are most often observed in
rial). Consequently, the simulation cells, which all have environments in which the Mn ion is coordinated by two
a water region with a diameter of at least 50 Å, are large H2 O molecules from above instead of typically one OH−
enough to yield bulk properties in the center, which is in ion and one H2 O molecule. The double deprotonation
excellent agreement with previous studies on other solid- and protonation processes can be viewed as surface re-
water interfaces.67,69 An underestimation of the density constructions of the {110} Lix Mn2 O4 surfaces.
compared to the experimental value of 0.997 kg l−1 at On the left side of Figures 6 (a) to (d) the time aver-
298 K and 1 bar102 is common in DFT calculations and aged spatial atomic distributions projected onto the zy
was also observed in a previous study of water yielding plane are shown for each interface. As expected the bulk
0.94 kg l−154 based on the revPBE0-D3103,104 DFT func- solid has a regular pattern reflecting the crystal struc-
tional – we note that our results are based on the PBE0r- ture while the bulk liquid has a diffuse distribution in all
D382,105 DFT functional. simulations. However, at the different solid-liquid inter-
The concentration profile as a function of the distance faces the liquid phase shows various interesting strongly
from the surfaces, which is proportional to the density bound water structural features, which are less mobile
profile with the molar mass as proportionality constant, due to the strong interaction with the surface. An adap-
shows two distinct OH− peaks of about the same size for tion of the interfacial water layers to optimize the inter-
each phase boundary (Figure 5 (a) to (d)). These peaks action to the solid as well as the hydrogen bond network
correspond to protonated O2− ions of the solid and OH− to the bulk liquid has been observed for different metal
ions adsorbed to Mn sites, respectively. Since these two surfaces as well and can yield very specific water struc-
peaks dominate the OH− concentration profile and are of tures depending on the solid surface.106,107 The thickness
about equal height, essentially all protons and hydroxide of the strongly bound water layer depends on the under-
ions formed in the dissociation of water molecules are lying solid surface. For the {100}Li interface the strongly
bound at the solid surface. The OH− concentration is bound water layer has a diameter of about 1.5 to 2 Å
about three orders of magnitude smaller at the {100}Li only, while it is 3 to 4 Å thick for the {100}Mn2 O4 and
interface compared to the other systems. The reason {110}LiMnO2 interfaces. However, the structure at the
is that the OH− ions are not long-living at the {100}Li {100}Mn2 O4 interface is dominated by a two-dimensional
interface. dense water layer on top of the solid, while the struc-
Oscillations of the H2 O concentration in the vicinity ture at the {110}LiMnO2 interface is three-dimensional.
of the {100}Mn2 O4 interface are more pronounced than A pattern similar to the latter one is also observed at
in the vicinity of the {100}Li interface (Figure 5 (a) and the {110}MnO2 interface. Here the strongly bound water
(b)). The depletion layer beyond the first water peak can layer is even 3.5 to 4.5 Å.
be observed in the spatial atomic distributions in Figure To investigate the strongly bound water layers in more
6 (b) as well. The relatively high concentration of H3 O+ detail the right panels of Figures 6 (a) to (d) show the
ions at the same distance as the second OH− peak will spatial atomic distributions in water films of 2.5 Å diam-
be discussed in Section IV D. eter above the surface starting from the H atom closest
The structural deviation of the contact layer from the to the surface projected onto the xy plane. The small
bulk liquid for the {110}LiMnO2 and {110}MnO2 systems strongly bound water layer on top of the {100}Li inter-
is even more pronounced. In the case of the {110}LiMnO2 face forms due to the attractive interactions between the
system, the OH− concentration profile shows the pres- oxygen of H2 O and Li+ ions as well as due to hydro-11
3 3
cO2− cOH− c H2 O c H3 O + cO2− cOH− c H2 O c H3 O +
2 2
log10(c/mol l−1)
log10(c/mol l−1)
1 1
0 0
−1 −1
−2 −2
−3 −3
−40 −30 −20 −10 0 10 20 30 40 −40 −30 −20 −10 0 10 20 30 40
z / Å z / Å
(a) (b)
3 3
cO2− cOH− c H2 O c H3 O + cO2− cOH− c H2 O c H3 O +
2 2
log10(c/mol l−1)
log10(c/mol l−1)
1 1
0 0
−1 −1
−2 −2
−3 −3
−40 −30 −20 −10 0 10 20 30 40 −40 −30 −20 −10 0 10 20 30 40
z / Å z / Å
(c) (d)
FIG.
FIG. 5. 5: Decadic
Decadic logarithm
logarithm of the
of the timetime averaged
averaged concentration
concentration c of different
c of different oxygen oxygen
species species as a function
as a function of the z
of the z coordinate
coordinate for the (a) {100} , (b) {100}
for the (a) {100}Li , (b) {100}Mn2 O4 , (c) {110}LiMnO
Li Mn , (c) {110}
2 42 , and (d) {110}MnO
O LiMnO , and (d) {110}
2 2 Lix Mn2 O4 -water 2
MnO Li x Mn 2 O 4 -water interface
interface systems. The region of
systems.
the Lix Mn2The region
O4 slab of the Lix Mn
is highlighted 2 O4gray
by the slabbackground.
is highlightedTheby thepoint
zero grayofbackground. The
z has been set zerocenter
to the pointofofthe z has
waterbeen set
slabs.
to the center of the water slabs.
gen bond formation between the hydrogen of H2 O and for the {110}LiMnO2 and {110}MnO2 interfaces. At the
−
O2−Toions
investigate the pseudo-crystalline
at the surface (Figure 6 (a)). Awater pattern layers
can be in {110}
boundLiMnO
to specific
2 sites and
interface most thus
OH less mobile
ions of than the water
the first layer
more
observeddetail
at the
the right panels
interface butof the
Figures 6 (a) to (d)atshow
concentrations the molecules.
of the liquid Moreover,
bridge the they
Mnare ablewhich
sites, to form arestrong
arrangedhydro-in
the spatial
strongly atomic
bound distributions
water sites are in water
lower thanfilms of 2.5
those forÅ the
di- gen bonds
rows in theand firstcan order
solid layerthe(e.g., ≈ 5 Å in Figure
watery molecules. Therefore,
6 (c)
ameter above the(lower
other interfaces surface starting
opacity from
of the theliquid
first H atom layerclos-
in they
as have
well a large impact
as Figures 7 (a) and on the formation
8 (a)). Most Hof2 Othe pseudo-
molecules
− to the Li+ ions
est
the to thepanels
right surfaceofprojected
Figure 6 onto the xy
(a) than plane.
in (b) The small
to (d)). Con- crystalline
in waterare
the first layer layer.
alignedTheinHrows2 O/OH close distribution in
pseudo-crystalline
sequently, the H2 Owater moleculeslayeratonthe top{100}of the {100}Li are
Li interface in- the first
with layer ofpointing
H atoms the liquid O2− ions
to phase does of notthe follow
solida regu-
(e.g.,
terface forms than
more mobile due to thethe attractive
various waterinteractions
species at the between
other ylar≈pattern
1 Å in at the {100}
Figure 6 (c)). Mn2In interface
O4 the (Figure
first layer of the 6 (b) as
solid
− III
the
interfaces, of H2 O and Li+toions
oxygen corresponding the as well asinteraction
weaker due to hydro- be- well as
rows of Figure
alternating O2− andthe
4). Hence, OH Mn ions/Mn areIV formed (e.g.,
distribution
gen bond formation
tween water {100}Li surface
and the between the hydrogen discussed of above.
H2 O and yin≈the
−1first
Å inlayer
Figure of 6the solid
(c)). O2− phase
excessis disordered
can lead toasMn IV
well
O2−As ions at the surface
mentioned in Section (Figure
IV B 6OH −
(a)). A pattern
ions are formed can (Figure
ions 4). topmost solid layer.
in the
be observed
at the {100}Mnat 2the
O4 , interface
{110} LiMnO2but , the
and concentrations
{110} MnO2 inter-at Thetheorder
In first in
solidthelayer of the−{110}
H2 O/OH distribution
MnO2 interface increases
an
the 2− −
facespseudo-crystalline
and cover the solid water
surface sites
to are lower
a large than those
fraction (Fig- for the {110}
alternating pattern
LiMnO2 and
of O {110}
and MnO2OH interfaces.
rows is At the
formed,
for
uresthe other
6 (b) to interfaces
(d)). These OH−opacity
(lower ions are of rather
the first liquid
strongly {110}LiMnO
whereby O2− 2
interface
ions bridge mostthe −
OHunderlying
ions of the Mn firstsiteslayer
and
−
layer
boundintothe rightsites
specific panels
andof thusFigure 6 (a) than the
less mobile in (b)
water to of the
the OHliquid ionsbridge the Mn
are above thesites, which
Li sites ≈ 3 Å and
areyarranged
(e.g., in
(d)). Consequently,
molecules. Moreover, the theyHare2 O able
molecules
to formatstrongthe {100}
hydro- Li ≈ 7inÅthe
yrows first solid
in Figure 6 (d)layer as (e.g.,
well as y ≈Figures
5 Å in Figure
7 (b) and 6 (c)8
interface
gen bondsare andmore
can mobile
order the thanwaterthe molecules.
various water species
Therefore, as wellInassome
(b)). Figures 7 (a) andthe
simulations 8 (a)).
H2 O Most H2 O and
molecules OH−
molecules
at thehave
they other interfaces,
a large impact corresponding
on the formation to theofweaker inter-
the strongly in theinfirst
ions the layer are aligned
first liquid layer inarerows close tointhe
arranged Li+ ions
alternating
{100} − 2−
action
bound between
water layer.waterThe andHthe2 O/OH Li surface
distribution discussed
in the x ≈
with H atoms pointing to O
rows (e.g., 2 to 3 Å and x ≈ions of the solid (e.g.,
5 to 6 Å in Figure 6
above.
first layer of the liquid phase does not follow a regular y ≈ 1 Å in Figure 6 (c)). In the first layer of the solid
(d)).
−
pattern at the {100}
As mentioned Mn2 O4 interface
in Section IV B OH −
(Figureions6are(b) formed
as well rows
Theof oxygen
alternating atomsO2−of and the OHwater ions are formed
species in the (e.g.,
first
III IV 2− IV
as Figure
at the {100}4). Mn
Hence,
2 O4
, the
{110} Mn LiMnO2 /Mn, and distribution
{110} MnO2 in the
inter- y ≈ −1layer
liquid Å in generally
Figure 6 (c)). tend Oto continue
excess can theleadoxygen to Mnface
first layer
faces of the the
and cover solid phase
solid is also
surface todisordered (Figure
a large fraction 4).
(Fig- ions in the
centered topmost
cubic (fcc) solid
latticelayer.
of the solid yielding an ener-
The
ures order
6 (b) in theThese
to (d)). OH−−ions
H2 O/OH distribution
are rather increases
strongly getically
In the favored
first solid coordination
layer of the of {110}
the LiMnO and2 Mn ions (see
interface an12
(a)
(b)
(c)
(d)
FIG. 6. Spatial atomic distributions projected onto the zy plane of the (a) {100}Li , (b) {100}Mn2 O4 , (c) {110}LiMnO2 , and
(d) {110}MnO2 Lix Mn2 O4 -water interface systems are shown on the left. On the right the spatial atomic distributions up to
2.5 Å from the interface projected onto the xy plane are represented with a ball model of the non-equilibrated vacuum solid
surface in the background for reference. The time averaged concentration of each atomic species is represented by a linearly
increasing opacity. In the case of oxygen, each of the species differing in hydrogen content is plotted individually. The spatial
distributions are stacked on top of each other in the order from bottom to top H (yellow), Li (green), Mn (violet), O2− (red),
O in H2 O (blue), and O in OH− (turquoise). The spatial distributions of Li, Mn, and O2− are not shown in the xy projections.
Supplementary Material Figures S7 (a) and (b) for repre- face. However, the strongly bound water layer cannot be
sentations of the oxygen lattice only). The second liquid assigned to a specific lattice structure or ice polymorph,
layer is most pronounced in the case of the {110}MnO2 since in most cases the OH− ions at the surface do not
interface. The view on the yz plane still seems to agree form a sufficiently regular pattern.
with the fcc lattice (Figure 8 (b)) but a view on the
xz plane shows that the second layer does not match In conclusion, with increasing OH− concentration com-
the fcc lattice (Supplementary Material Figure S8). The plex structural patterns can form which also affect the
same observation is obtained for the {110}LiMnO2 inter- oxidation states of the underlying Mn ions. Interactions
between the solid and the liquid lead to favored positionsYou can also read
