Density Functional Theory Modeling of MnO2 Polymorphs as

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C: Energy Conversion and Storage; Energy and Charge Transport 2

Density Functional Theory Modeling of MnO Polymorphs as Cathodes for Multivalent Ion Batteries Taylor R Juran, Joshua Young, and Manuel Smeu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00918 • Publication Date (Web): 29 Mar 2018 Downloaded from http://pubs.acs.org on March 30, 2018

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The Journal of Physical Chemistry

Density Functional Theory Modeling of MnO2 Polymorphs as Cathodes for Multivalent Ion Batteries Taylor R Juran, Joshua Young, and Manuel Smeu∗ Department of Physics, Binghamton University, SUNY, Binghamton, NY E-mail: [email protected]

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Abstract Multivalent ion batteries (MVIBs) provide an inexpensive and energy dense alternative to Li-ion batteries when portability of the battery is not of primary concern. However, it is difficult to find cathode materials that provide optimal battery characteristics such as energy density, adequate charge/discharge rates, and cyclability when paired with a multivalent ion. To address this, we investigate six MnO2 polymorphs as cathodes for MVIBs using density functional theory calculations. We find voltages as high as 3.7 V, 2.4 V, 2.7 V, 1.8 V, and 1.0 V for Li, Mg, Ca, Al, and Zn, respectively, and calculate the volume change due to intercalation. We then focus specifically on Ca, and compute the energy barriers which are associated with diffusion of the ion throughout the materials. Our findings show that the α-phase displays the most rapid diffusion kinetics for a Ca ion, with a diffusion barrier as low as 190 meV. We then investigate the potential for the five polymorphs exhibiting the highest voltage to intercalate additional atoms, and demonstrate that it is energetically favorable for each to accept at least one additional Ca ion; furthermore, two of the phases can accept more than two Ca ions. However, in each case there is also a corresponding drop in the voltage as further atoms are intercalated. We also utilize a crystal-chemistry approach to detail the structural evolution of each phase by computing the bond valence sum and effective coordination of the Mn4+ ions upon intercalation of increasing numbers of Ca ions. Finally, by computing the electronic density of states, Bader charges, and real space charge density, we describe how the additional electrons from the Ca ions are distributed throughout the unit cell. These insights provide guidance in selecting a MnO2 polymorph with the traits necessary for the realization of MVIBs.

Introduction Advances in multivalent ion batteries (MVIBs) are opening new opportunities for energy dense alternatives to Li-ion batteries (LIBs). In addition, MVIBs possess several superior properties compared to LIBs, including reduced cost, low environmental impact, and im2


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proved safety, making them a promising alternative. Progress in MVIBs has been primarily limited by the inability to find a cathode material that provides a high energy density, rate capability and cyclability. 1,2 The Chevrel phase Mo6 X8 (X = S, Se, Te) is one of the more prominently studied MVIB cathodes, but it suffers with respect to its voltage and capacity. 3,4 In the quest for a MVIB with an energy density greater than that of the Chevrel phase, MnO2 polymorphs have been proposed as a promising candidate. 5–35 Offering a high theoretical voltage and capacity reaching up to 2.8 V and 308 mAh/g, respectively (for MgMnO2 ), these materials make for an excellent cathode material when intercalated with multivalent ions. 8,36 In addition to a favorable energy density, the large number of MnO2 polymorphs offer structural versatility, and many of the phases are abundant and consequently inexpensive. 8 While MnO2 polymorphs have been studied with several anode pairings, 5–35,37–49 MnO2 polymorphs intercalated with Ca and Al have not received much attention. It is hopeful that utilizing metallic Ca and Al anodes with MnO2 -based cathodes will provide batteries with a higher energy density than MgMnO2 batteries, similar to the impact of intercalating the Chevrel phase with Ca and Al. 4,7,50 Ca-based batteries are often neglected due to the difficulty in plating the Ca anode, and in finding appropriate cathodes and electrolytes. Yet, if these points are addressed, Ca-ion batteries are expected to yield a higher energy density than Mg-ion batteries due to Ca producing a higher voltage, and could potentially be made out of materials that are abundant in Earth’s crust. 2,3,51 While LiMnO2 batteries have been investigated for decades, 37–40 more recently MnO2 polymorph cathodes combined with Mg and Zn anodes have generated significant interest. 5–35,42,43 To the best of our knowledge a comprehensive ab intio study has not yet been reported on the pairing of MnO2 polymorphs with anodes including M = Li, Mg, Ca, Zn, and Al metals. Herein we investigate six MnO2 phases: pyrolusite (β), ramsdellite (R), hollandite (α), intergrowth (γ), spinel (λ), and layered (δ), which are all typical polymorphs considered for energy storage and other applications. 52–60 We use density functional theory (DFT), and

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more specifically the non-empirical ‘strongly constrained and appropriately normed’ (SCAN) meta-generalized gradient approximation (meta-GGA) functional. 61 SCAN has been previously determined by Kitchaev et al. as an adequate functional to study the aforementioned six MnO2 polymorphs, due to its ability to correctly determine β-MnO2 as the ground state, and for other criteria including band gap and structural parameters, which are in agreement with experimental data. 54,60 Our work explores the electronic properties associated with the intercalation of various ions (M = Li, Mg, Ca, Al, Zn) within these six most common MnO2 polymorphs. These properties include the calculation of voltage (via total energies) and diffusion barriers as the ions M diffuse through the different MnO2 crystal structures, as well as the electronic structure and the effect of intercalating multiple ions into the cathodes.

Figure 1: MnO2 polymorphs. The orange and blue octahedra surround spin up and down Mn atoms, respectively. The red atoms represent O. Pictured are the lowest energy configurations. 62

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Computational Methods The Vienna ab initio Simulation Package (VASP) 63–65 was used to perform DFT calculations, 66 using the projector-augmented-wave (PAW) method. 67 Electronic interactions were treated with the non-empirical SCAN meta-GGA 61 functional. The kinetic energy cutoff was set to 600 eV. Γ-centered Monkhorst-pack k -point grids were tested for each of the six polymorphs and the forces were sufficiently converged within 1 meV per atom.1 Due to computational expense, the energy cutoff was set to 450 eV for supercells, and the k -point grids were reduced accordingly. Experimental data demonstrates that all of the MnO2 polymorphs adopt an antiferromagnetic (AFM) spin ordering, 68–71 which led us to test all of the possible AFM spin configurations for the six MnO2 polymorphs considered here. The lowest energy configurations found with the SCAN functional are shown in Fig. 1; we found all six polymorphs to adopt an AFM magnetic spin configuration, in agreement with experiment and calculations done by Kitchaev et al. 60,68–71 These configurations were used for all calculations after this point. Full structure relaxations were performed for bulk metals (M = Li, Mg, Ca, Zn, Al), each of the six empty MnO2 polymorphs, and each of the six polymorphs intercalated with each metal M. The empty MnO2 polymorph structures were based on the space groups specified for each polymorph in Ref. 60. Intercalation sites were selected to be in areas maximizing nearest neighbor distances. Full structure relaxations were performed with PBE 72 and SCAN 61 functionals. Our battery models consisted of a pure metal anode and a MnO2 polymorph cathode. Thus, the electrochemical process can be described as:

M + MnO2 → MMnO2 .

(1)

The voltage is determined from the electronic structure calculations based on the follow1

7×7×7 for α-MnO2 , 5×5×5 for β-MnO2 , 7×7×7 for δ-MnO2 , 3×3×3 for γ-MnO2 , 3×3×3 for λ-MnO2 , 7×7×7 for R-MnO2 .

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ing energy difference: E(M MnO2 ) − E(MnO2 ) − E(M ) V =− , Nelectrons

(2)

where E (M MnO2 ) is the energy of the MnO2 polymorph intercalated with an ion, E (MnO2 ) is the energy of the MnO2 polymorph, E (M ) is the energy per atom of the metal anode, and Nelectrons is the number of electrons transferred with the cation. 50 This voltage is an approximation in the sense that the exact voltage is dependent on the Gibbs free energy, instead of the change in internal energy which we consider here. The voltage approximation is based on the assumption that the volume and entropy effects are negligible here. 73 Inclusion of volume and entropy effects would account for a mere difference of 0.1 V or less. 73 We utilized the climbing image nudged elastic band (CI-NEB) method to determine energy barriers associated with ion diffusion throughout the cathodes. 74 A supercell is used for these calculations. To determine the preferred arrangement when multiple ions are intercalated, we performed a full structural and ionic relaxation for each possible configuration of Ca atoms in the polymorphs, taking the lowest energy phase in each case as the preferred configuration. The voltage was then determined by comparing the energy of that structure with the relaxed phase containing one less Ca ion, in a manner similar to Equation 2. Atomic structures were visualized and the bond lengths used for the bond valence sum and effective coordination analysis were extracted using the VESTA software package. 62

Results and Discussion Voltage Equation 2 was used to compute the voltage for each ion (M = Li, Mg, Ca, Zn, Al) intercalated within each of the six MnO2 polymorphs. Figure 2 shows the voltages computed for

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Figure 2: Voltages for each MnO2 polymorph (α, β, δ, γ, λ, R) intercalated with each ion (M = Li, Mg, Ca, Al, Zn) considered here. the anode and cathode pairs considered here (the numerical values are also provided in Supplementary Information Table S1). Let us first consider the trends observed as we change the cathode material to each of the six different polymorphs. λ-MnO2 yields the highest voltages, suggesting this phase would provide an excellent energy density. The weakest voltages are produced by γ-MnO2 suggesting that the γ-phase will be less suitable as a battery cathode. As the ion being intercalated within the cathode material is changed, we find that the voltages follow the order of Li > Ca > Mg > Al > Zn (with the exception of γ); this trend agrees with the previous work done by Juran et al., where the intercalation of these same ions in the Chevrel phase was studied. 4 Interestingly, the γ-phase produces a higher voltage when intercalated with Al than Mg or Ca, in contrast to the other polymorphs. At this time, it is not clear why the γ-phase voltage trend differs from that of the others. This is beyond the scope of this study, but may motivate future investigations. Looking closer at the voltages produced by each metal ion, we see that Li ions yield an average voltage ranging from 1.47 − 3.67 V, in agreement with experimental data. 37,75 Mg 7



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ions yield an average voltage ranging from 0.54 − 2.44 V, which again matches experimental data. 12,14,15,17–19,23,26 Ca ions offer an average voltage range of 0.58 − 2.70 V, which is generally higher than the range seen with Mg. Al and Zn produce much weaker voltages with average voltage ranges of 0.45 − 1.80 V and 0.59 − 1.06 V, respectively.2 From the polymorphs producing the highest voltages (e.g., λ, δ), the intercalation of a given ion yields a higher voltage than the voltage from intercalating the same ion in the Chevrel phase. 4,50 Table 1: Percent volume change for MnO2 polymorph cathodes. Ion Li Mg Ca Al Zn

α -1 -2 0 -2 -1

β 18 43 68 32 44

δ 9 12 37 21 22

γ 3 8 34 12 9

λ 3 13 17 10 9

R 4 10 20 12 16

Cathode Volume Change due to Intercalation The cathode bulk volume change due to intercalation was calculated as: % Vol. Change =

Vol.(M MnO2 ) − Vol.(MnO2 ) Vol.(MnO2 )

× 100%,

(3)

where Vol. is the abbreviation for volume, and M = Li, Mg, Ca, Al, Zn. The different polymorphs yielded varying degrees of volume change due to intercalation, as seen in Table 1. The α-phase is particularly interesting due to the cathode experiencing a slight contraction instead of expansion upon intercalation with all ions considered here, except for Ca, which causes no appreciable volume change. Some of the polymorphs studied here experience substantial volume change, which must be taken into consideration when fabricating a battery in order to avoid cathode strain and eventual cracking. From here on this study will focus on the intercalation of Ca metals into these MnO2 polymorphs as it consistently produced the highest voltage from the multivalent ions considered. 2

Note, voltages that appear negative actually indicate that the intercalation of the ion is not favorable in that cathode.

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As seen in Table 1, MnO2 polymorphs undergo large changes in volume with Ca ions, as compared to other metal cations, owing to the large size of Ca. Because of this, we discuss how the crystal structure of each phase evolves as a Ca atom is intercalated by investigating the structural distortions each polymorph undergoes. In particular, we focus on changes in the Mn-O bonding environment using two crystal-chemistry descriptors. In all of the MnO2 polymorphs investigated here, the Mn4+ cations are surrounded by 6 O2− anions, forming MnO6 octahedra with an effective coordination number of 6. Upon insertion of a large Ca atom, however, these polyhedra become distorted, altering the crystal structure and lowering the effective coordination of the Mn cations. These structural distortions are further reflected in the bond valence of the Mn ions, which we computed using the bond valence sum (BVS) method. 76 The bond valence (BV) of an ion is given by:

BV = e

R0 −R β

,

(4)

where R is the measured (or, in this case, calculated) Mn-O bond length, R0 is the ideal Mn-O bond length, and β is an empirical parameter (typically 0.37 Å). The sum of the BV of each Mn-O bond thus gives an estimate of the oxidation state of the Mn ion in a given coordination environment. By comparing the computed bond valence of Mn in each of the polymorphs upon Ca ion intercalation and comparing it to its nominal valence (4+ in these polymorphs), we are able to quantify how well the anions continue to coordinate the cation upon distortion of the polyhedra. Consider for example the β-MnO2 phase, which displays small pores in between corner and edge connected MnO6 octahedra. Among all of the polymorphs, it undergoes the largest change in volume upon insertion of a first Ca atom (∼ 68%). This results in a distortion of the polyhedra, resulting in a drop of the effective coordination of the Mn atoms from 6 to 4.26, and the bond valence from 3.73 to 2.72. The α-phase, on the other hand, undergoes nearly no change in volume, as it displays large hollow voids which can well-coordinate intercalated

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Ca ions. Indeed, we find that the effective coordination of the Mn hardly changes at all upon insertion of a first Ca atom, dropping from 6 to 5.77; the bond valence also does not change significantly (3.94 to 3.85). Each of the other investigated phases undergoes structural changes in between the magnitude of these two phases. In the δ-phase, for example, the volume increases by 37%, while the edge-connected polyhedra undergo a buckling and elongation, with a corresponding drop in the effective coordination (6 to 4.36) and Mn bond valence (3.84 to 2.85). On the other hand, the λ-phase undergoes a volume expansion only half that of δ-MnO2 , despite showing a similar voltage; the polyhedral network in the λ-phase also becomes less distorted when a Ca ion is inserted, displaying an effective coordination of 5.89 and a bond valence of 3.30, both close to their values prior to intercalation. Finally, the volume of the R-phase swells by approximately 20%, while the MnO6 octahedra behave in two different ways. Upon intercalation of the first Ca atom, the octahedra surrounding the insertion site undergo a lowering of the effective coordination to 4.68 and bond valence to 2.92. Interestingly, however, the polyhedra further from the Ca ion are barely affected, and display an effective coordination of only 5.92 and bond valence of 3.80.

Diffusion Barriers Here, Ca diffusion kinetics are compared as the ion is intercalated within the six MnO2 polymorphs. Figure 3 shows the lowest energy diffusion pathway for a Ca atom through an α-MnO2 supercell, calculated via the climbing image nudged elastic band method (CINEB) 74 and the SCAN 61 functional. A supercell is used to ensure all unique diffusion pathways are considered. Initial and final positions are used to estimate a direct path between them using eight images (intermediate atomic positions); the coordinates of these images are then relaxed using the CI-NEB method to find the lowest-energy direct path from the initial to final position of the ion. The energy barrier associated with this path represents that encountered by an ion attempting to diffuse from the initial site to the final site. Figure 3 displays the lowest energy diffusion barrier path for the diffusion of a Ca ion 10


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Figure 3: The lowest energy barrier for the diffusion of a Ca ion through an α-MnO2 1×1×2 supercell. Each Ca ion (light blue) represents the Ca position through the NEB path. Other atoms are represented as in Fig. 1. through an α-MnO2 polymorph cathode, while those for the other polymorphs are shown in Supplementary Figure S1. Our calculations revealed that diffusion of Ca through αMnO2 would encounter a 190 meV barrier, which is comparable to ion diffusion barriers in existing secondary batteries. 77–79 Diffusion through the other cathodes corresponds to higher barriers: 280 meV for R-MnO2 , 550 meV for diffusion through δ-MnO2 , and 1860 meV for diffusion through γ-MnO2 ; note that these values were calculated with the PBE 72 functional. Cathodes with higher energy barriers such as the γ-phase should be expected to have slower diffusion kinetics than those with lower barrier energies such as the α-phase. Both the λand β-phases were unsuitable for Ca ion diffusion, based on the inability of the NEB method to identify a direct path for ion diffusion despite our best attempts. Note that while the λ-phase yielded the highest voltage for intercalating Ca ions, it did not allow for the diffusion of a Ca ion; it did, however, allow for the diffusion of a Li ion with a barrier of 430 meV (Supplemental Figure S2). This highlights the importance of diffusion barrier calculations since the voltage alone is not the sole criterion for an adequate ion-cathode pair. Therefore, it is not likely that a calcium ion battery using a λ-MnO2 cathode would produce a successful battery. This examination provides insight to choosing a MnO2 polymorph with optimal 11



diffusion kinetics.

Intercalation of Multiple Ca Ions We next investigate the potential for higher Ca ion capacity in those MnO2 polymorphs that display a high voltage (greater than 1.5 V, corresponding to α, β, δ, λ, and R) by inserting additional Ca atoms into each phase. Because these structures have multiple crystallographic positions on which a Ca can sit, we considered multiple arrangements of atoms to find the lowest energy configuration in each case. We find that insertion of a second Ca atom is energetically favorable in all five polymorphs; however, in agreement with previous results using different cathode materials, 4,50 there is a considerable drop in voltage in each case (Figure 4a). Despite this, several of the polymorphs still display relatively high voltages; for example, the λ-, α-, and R-MnO2 phases all exhibit voltages over 1 V (1.55, 1.55, and 1.31 V, respectively) upon intercalation of a second Ca atom, while the β-phase drops to 0.88 V. Interestingly, the δ-phase experiences the largest drop in voltage of all polymorphs (down to 0.79 V), despite having one of the largest when only one Ca ion is inserted. Finally, we also find that the R and α-phases can potentially accept a third Ca ion, with another corresponding drop in the voltage to 0.52 and 0.62 V. Table 2: The total number of Ca ions that can be intercalated in α-, β-, δ-, λ-, and R-MnO2 , normalized to both the number of MnO2 formula units (f.u.) and the unit cell volume of each polymorph, and specific and volumetric capacities of each cathode. Polymorph Ca ions Ca ions/f.u. Ca ions/Å3 α 3 0.375 0.014 β 2 1 0.036 δ 2 1 0.029 λ 2 0.5 0.015 R 3 0.75 0.025

Capacity mAh/g Capacity mAh/cm3 197 801 422 1780 422 1602 251 979 344 1335

Although it is clear that the α- and R-phases can intercalate more Ca ions than the others, a potentially more useful metric is the number of Ca ions that can be intercalated, 12


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normalized to the number of MnO2 formula units (f.u.) or volume of a given unit cell. We computed these quantities for each of the 5 aforementioned polymorphs, and the results are summarized in Table 2. Interestingly, we find that the β- and δ-phases are able to accept the most Ca ions relative to their size, with R close in magnitude. The α-MnO2 phase, on the other hand, can accommodate the least owing to the large size of the unit cell. The β-, δ- and R-MnO2 phases yield the highest capacities (both specific and volumetric), and the other polymorphs considered are also comparable to existing technologies. We also find that the volume change as additional Ca ions are inserted is, in most cases, less than upon intercalation of the first atom. The α-phase, which undergoes the smallest volume change with one Ca atom, only undergoes a very slight increase to 1.6% (compared to 0 Ca atoms intercalated) when a second Ca ion is inserted. This is again reflected in the effective coordination (5.67) and bond valence (3.84) of the Mn atoms, which remain close to their nominal values of 6 and 4. The β- and R-phases undergo modest volume increases (68% to 90% and 20% to 30%, respectively) in the presence of a second Ca. However, the bonding environment becomes significantly more distorted in β, with the effective coordination dropping to 2.20 and bond valence to 1.51; thus, although intercalation of a second Ca is energetically favorable, the large structural changes this phase undergoes likely make it a poor candidate for a cathode material. In the R-phase, the previously undistorted MnO6 octahedra now become similarly distorted to the first environment, with both polyhedra displaying similar effective coordinations (4.75 and 4.99) and a somewhat similar bond valence (2.63 and 1.97). The δ- and λ-phases, on the other hand, undergo the largest volume increases of these phases of 16.4% and 15.5%, respectively. As before, the λ-phase undergoes a smaller distortion of the polyhedral network (effective coordination of 4.14 and bond valence of 2.76) than the δ-phase (3.27 and 1.63 for those same parameters). Again, the α- and R-phases can accept more than two Ca atoms per unit cell. Upon intercalation of a third Ca atom, the volume changes by 15% for α and 57% for R when compared to the bulk structures. Structural distortions now start appearing in the α-phase;

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(a)

α β δ λ R

2.5 2 1.5 1 0.5 0

90 Volume change (%)

3

Voltage (V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

75 60 45 30 15 0

1 2 3 Number of Ca ions

(b)

1 2 3 Number of Ca ions

Figure 4: Evolution of the (a) voltage and (b) percent volume change as multiple Ca ions are intercalated into the unit cell of various MnO2 polymorphs. although one coordination environment remains relatively the same (effective coordination of 5.77, bond valence of 3.53), another one becomes distorted (effective coordination of 3.53, bond valence of 2.59). While stability upon intercalation is beyond the scope of this work, these results can be compared to the work by Kitchaev et. al, which investigates the stability of these materials upon intercalation of ions, including the Ca ion, which found that the αphase is stabilized with Na, Ca, and K. 60 Additionally, they showed that both the α- and δ-phases are stable upon hydration; 60 it would be interesting to consider the voltage, energy barriers, and volume change incurred upon intercalation of Ca into these hydrated phases.

Electronic Structure To gain further insights into ion intercalation in the various MnO2 polymorphs, we investigate the electronic structure of each phase and how it evolves as the number of Ca atoms per unit 14


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cell increases. We first computed the projected density of states (PDOS) of all six crystal structures, and find that five of the phases are semiconducting with band gaps ranging from 0.54 to 1.24 eV. However, we find the β-phase is metallic owing to the systematic underestimation of band gaps within DFT; previous results have shown that the use of advanced functionals or employing a Hubbard U correction can reproduce the small 0.4 eV band gap. 60 In each phase the bottom of the conduction band is primarily made up of Mn 3d states with small amounts of O 2p states, while the top of the valence band consists of nearly equal amounts of each. As a demonstrative example, we first consider Ca intercalation in the δ-phase, which exhibits a high voltage of 2.7 V. The bulk phase, as mentioned previously, is semiconducting with a band gap of 1.15 eV (Figure 5a). Adding one Ca atom (resulting in a lower voltage) puts two additional electrons into the system, which fill empty Mn and O states; this can be seen in Figure 5b, in which there is a significant decrease in the number of states at the bottom of the conduction band and a corresponding increase in states at the top of the valence band. Furthermore, there is an increase in O 2p states relative to Mn 3d states, implying that more charge becomes localized around the O atoms. The addition of the second Ca atom, and thus two more electrons, fills more empty states and results in yet more filled states just below the Fermi level (Figure 5c). Although the density of states gives insights into how the MnO2 phases accommodate the Ca atoms, it provides no information about the spatial localization of the extra electrons introduced. For this, we performed a Bader charge analysis on the δ-phase, which shows an increase in the electron density around both the Mn and O atoms upon insertion of the first Ca atom (Supplementary Table S4); the charge around the Mn atoms increases by approximately 0.19e, while those O atoms closer to the Ca atoms receive slightly more additional charge than those further (0.32e and 0.27e, respectively). This increase can also be seen in the charge density (Figure 5d), with a larger quantity of charge being seen around the O atoms close to the Ca ion. Upon insertion of the second Ca atom in the δ-MnO2

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(a) 0 Ca

DOS (states/eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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6 4 2 0 -2 -4 -6 (b) 1 Ca 6 4 2 0 -2 -4 -6 (c) 2 Ca 6 4 2 0 -2 -4 -6 -4 -3 -2 -1 0 1 2 3 4 Energy (eV)

Mn 3d O 2p

Ca

Mn

O

(d)

(e)

Figure 5: The atom-resolved density of states with (a) 0, (b) 1, and (c) 2 intercalated Ca ions and the real space charge density of with (d) 1 and (e) 2 intercalated Ca ions in δ-MnO2 as computed using the SCAN functional. phase, further additional charge is given to the Mn (0.47e) and O (0.52e) atoms. This is again reflected in an increase in the charge density surrounding the O atoms (Figure 5e). We next performed this same analysis for the other MnO2 phases with voltages above 1.5 V; the Bader charges can be found in Supplementary Tables S2-S6 while the electronic structure and charge density are shown in Supplementary Figures S3-S6. Similar behavior to the δ-phase is found in the β-phase, with intercalating Ca atoms spreading charge throughout the unit cell, with slightly more appearing on the closer O atoms. In contrast to the DOS of the δ polymorph, however, the β system becomes significantly more insulating with one Ca atom. When a second one is intercalated, the band gap again disappears. 16


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In the λ-phase, the Bader charges again reveal that upon intercalation of the first metal atom, the four O atoms closest to the Ca receive significantly more excess charge (0.22e) than those further away (0.08e). Both the O and Mn atoms receive smaller amounts of charge than in the δ-phase. This is again reflected in the distribution of the charge density. Interestingly, upon intercalation of the Ca ion, the two electrons again fill empty Mn d and O p states at the bottom of the conduction band, but turn the system metallic. Insertion of the second Ca atom more evenly distributes the excess electrons throughout the unit cell, and again turns the system insulating. Although the R- and α-phases can accommodate additional Ca ions, the mechanisms for intercalation are largely the same as the other phases, with additional electrons filling empty Mn 3d and O 2p states. The additional charge then spreads throughout the unit cell starting from the site at which each ion intercalates. Interestingly, however, while the magnitude of the charge transfer to the Mn and O atoms (as reflected in the Bader charges, Supplementary Tables S2 and S6) is approximately the same in the R-phase as in the other phases, it is comparatively much lower in the α-phase; even with 3 intercalated Ca ions, the largest change on a Mn atom is only 0.18e, while the largest change on an O atom is 0.38e. This may likely be due to the large voids present in the α-phase, as previously described.

Summary In this work, we demonstrated that MnO2 phases have the potential to make excellent cathodes for MVIBs, as certain MnO2 polymorphs consistently produce higher potential differences when compared to the Chevrel phase, independent of the intercalating agent. We computed the volume change associated with the intercalation of several ions into six MnO2 polymorphs, and found that the α-phase undergoes the least amount of expansion. The swelling was further investigated and quantified using a crystal-chemistry approach to detail changes in the MnO6 coordination environments upon ion intercalation. After this point our

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study focused solely on CaMnO2 batteries, and we explored the energy barriers associated with Ca ion diffusion; once again the α phase displayed the lowest diffusion barriers of all the polymorphs. We next showed that each of the considered phases can intercalate at least one additional Ca ion, with two (α and R) able to accommodate up to three. Finally, we investigated the electronic properties of these battery materials to elucidate how the cells accommodate the additional charge provided by intercalated ions. In conclusion, we find that the several MnO2 phases display different properties, and that selection of the best one requires balancing voltage, ion capacity, diffusion ability, and structural stability. We find the α-phase to best exhibit this balance, although the R-phase can accommodate more Ca ions per volume. We anticipate that this work will be instrumental in the design of new MVIBs, while also demonstrating the usefulness of the newly-developed SCAN functional in theoretical analyses of battery materials.

Acknowledgement This work was supported as part of the Multidisciplinary GAANN in Smart Energy Materials, a Graduate Areas of National Need, funded by the U.S. Department of Education, under Award #P 200A150135.

Supporting Information Available Voltages for each MnO2 polymorph intercalated with each ion, energy barriers for Ca ion diffusion through other MnO2 phases, energy barrier for Li ion diffusion in λ-MnO2 , Bader charges of each MnO2 phase, atomically resolved density of states for each MnO2 phase. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Voltage, stability and diffusion barrier differences between sodium-ion and lithium-ion intercalation materials. Energy Environ. Sci. 2011, 4, 3680.

(a) 0 Ca

DOS (states/eV)

6 4 2 0 -2 -4 -6 (b) 1 Ca 6 4 2 0 -2 -4 -6 (c) 2 Ca 6 4 2 0 -2 -4 -6 -4 -3 -2 -1 0 1 2 3 4 Energy (eV)

Mn 3d O 2p (a) 0 Ca

Mn

Ca

6 4 2 0 -2 -4 -6 (b) 1 Ca 6 4 2 0 -2 -4 -6 (c) 2 Ca 6 4 2 0 -2 -4 -6 -4 -3 -2 -1 0 1 2 3 4 Energy (eV)

Energy (eV)

DOS (states/eV)

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(d)

O

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Mn

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Mn

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Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 220 3

DOS (states/eV)

0.2

0 -2 -4 -6 (b) 1 Ca 6 4 2 0 -2 -4 -6 (c) 2 Ca 6 4 2 0 -2 -4 -6 -4 -3 -2 -1 0 1 2 3 4 Energy (eV)

(d)

O

Mn 3d O 2p

Ca

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O

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Density Functional Theory Modeling of MnO2 Polymorphs as

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