Highly Pseudocapacitive Storage Design Principles of Heteroatom‐Doped Graphene Anode in Calcium‐Ion Batteries

Pseudocapacitive storage of multivalent ions, especially Ca2+, in heteroatom‐doped carbon nanomaterials is promising to achieve both high energy and power densities, but there is the lack of pseudocapacitive theories that enable rational design of the materials for calcium‐ion batteries. Herein, the general design principles are established for the anode materials of the batteries via density functional theory calculations and experimental verifications of a series of heteroatom‐doped graphene as an efficient pseudocapacitive anode. A novel descriptor Φ is proposed to correlate the intrinsic properties of dopants with the pseudocapacitive storage properties of the carbon‐based anode. The design principle and descriptor have the predictive ability to screen out the best dual‐doped graphene anode with 10 times higher Ca2+ storage capability than that of sole‐doped one, and exceed the current best Ca2+ storage anode materials.


Introduction
The urgent need to integrate such intermittent renewable energies as solar, tidal and wind energies into large-scale power grid has triggered the development of batteries with both high-performance and affordable cost. [1,2]Calcium-ion batteries (CIBs), as potential alternatives to lithium-ion batteries (LIBs), stand out from other multivalent-ion batteries (MIBs) (Mg 2+ , DOI: 10.1002/adfm.202305610Zn 2+ , Al 3+ , etc.) with excellent physiochemical nature and cost advantages, mainly consisting of non-toxicity, stable valence states, relatively small charge density, low redox potential, high specific capacity, earth-abundance and low cost (Table S1, Supporting Information). [3,4]owever, unlike LIBs, CIBs are still in their infancy. [5]Until now, despite many potential cathode materials available, [6][7][8][9][10][11][12][13][14][15][16][17][18] few anode materials work for CIBs. [19]here are two key problems that need to be solved urgently for designing excellent anode, including i) sluggish solid-state diffusion kinetic mainly due to stronger electrostatic adsorption and transport resistance as a result of heavier atomic weight of 40 g mol −1 , larger ionic radius of 1 Å, and higher valence state, and ii) low capacity and cycle stability typically originating from expansion/contraction during Ca 2+ intercalation/deintercalation. [20]ne of the promising solutions to the above issues is to use pseudocapacitive materials that have unique advantages with both superior energy and power densities. [21]The transition from intercalation-type anode to surface-induced pseudocapacitive anode would be a noticeable effective design strategy for divalent www.advancedsciencenews.com www.afm-journal.deCa 2+ even other multivalent ions storage to overcome the above mentioned two key problems.[24][25][26][27][28] Graphene is a typical 2D sheet of sp 2 -hybridized carbon, which is earth-abundant, cost-effective, eco-friendly, thermally and chemically stable, electrically conductive with extraordinary strength and toughness, corrosion-resistance and extremely high specific surface area. [29]These features endow it with excellent potential for anode in CIBs.In addition, graphene can be modified via the introduction of various dopants, defects and vdW heterojunction to achieve extraordinary extrinsic pseudocapacitive contribution. [30,31][35][36][37][38][39] Moreover, in-depth intrinsic physical principle determining the impact of different dopants on pseudocapacitive contribution has not well been elucidated, [40] which restricts reclamation of application potential of such carbon-based pseudocapacitive anode materials in both monovalent-and multivalent-ion batteries.
To rationally design high-performance carbon-based anode for CIBs, it is necessary to develop pseudocapacitive theory to correlate the carbon nanostructures with the pseudocapacitive properties.[43][44] In this study, we first proposed a pseudocapacitive theory to describe pseudocapacitive behaviors of heteroatom-doped carbon nanomaterials.The effect of different dopants on charge storage in CIBs was systematically studied via the first-principle calculation and experiment.A novel descriptor was established to predict charge storage properties of single-/co-doped-graphene anode including capacity and power density.The predicted results were verified by the focused experiments.The proposed pseudocapacitive theory may open a new window for pseudocapacitive charge storage.

Active Sites and Phase Transition Mechanism for Ca 2+ Storage
Three basic models, graphene sheet, zigzag and armchair graphene nanoribbons (Figure S1, Supporting Information), were developed.These model structures were then doped with p-block element X (X = B, P, Sb, Si, N, O, S, I, Br, Cl, and F) to form more than 40 different doping configurations (Figure 1a) for Ca 2+ storage.During the charging process, calcium ions in electrolyte were driven by external electric field to combine the electrons from external circuit to deposit on the doped-graphene surface.The adsorption was calculated by using the density functional theory methods.The change of adsorption energy ΔG was calculated before and after Ca 2+ adsorption (Calculation methods, Supporting Information) on more than 200 possible sites (Figure S2-5, Supporting Information).The results indicated that the introduction of dopants and the presence of nanoribbon defects lowered the adsorption energy barriers of hollow sites near dopants and edges.More significantly, these active sites, which have the lowest adsorption energy barrier and are the starting points for Ca 2+ storage on each doped model, were identified from all possible sites, as shown in Figure 1b.However, it's worth noting that the active site for Ca 2+ storage is not equal to the optimal site (See below for details).In order to further explore the Ca 2+ storage mechanism, more Ca atoms were added continuously to the surface of each doped model to simulate the structural evolution process of Ca ions storage, as shown in Figure 1d.As Ca atoms were continuously added on graphene surface, at first, Ca ion was chemisorbed on the site with the lowest adsorption energy barrier, and then the next site with the second low adsorption energy barrier was occupied by Ca ion, finally the transition from surfaceinduced 2D adsorption to 3D bulk phase occurred upon the coverage  approaching 1, which can be demonstrated by both the trend of Gibbs free energy change (Figure 1c) and spontaneous evolution of layered structure (Figure 1d).It worth noting that basically, both phase transition and bending of substrate, as can be seen in Figure 1d, are responsible for the release of higher energy mainly resulting from Ca-Ca and Ca-substrate interactions.

Relationship Between the Doping Structures and Energy and Power Densities
According to the DFT calculations, the energy barriers for Ca 2+ storage on the surface of the doped graphene anode are different at different storage sites.The calcium ions are stored in a way that Ca 2+ ions are chemisorbed at active sites with adsorption energy in the order from low to high energy.After the first calcium layer is formed, calcium ions will deposit on it to form bulk Ca deposition.Thus, there is the transition from 2D surface adsorption (i.e., pseudocapacitive mechanism) to 3D layered phase (corresponding to battery-type mechanism).For the initial Ca layer deposition, we propose a theoretical model of energy level filling theory for calcium ion storage (ELFT-CIS) on heterogenous anode surface.Briefly, as shown in Figure 2a-c, there are different regions with various Ca 2+ adsorption potential barrier ΔG i on practical surface of doped-graphene anode, which can be thought as different energy levels with different energy i in Ca 2+ storage process.For each energy level i, there are a i Ca 2+ storage sites in total, n i of which are occupied by chemisorbed Ca 2+ .Thus, the Ca 2+ storage is considered as the energy level filling process, in which the sites at each level i are filled in the order of the adsorption energy from low to high.On the basis of the calcium filling mechanism proposed above, the specific capacity C 0/site , energy density E 0/site and power density P 0/site per unit Ca 2+ storage site can be derived to establish the relationship between doped microstructure and electrochemical performance at atomic level (Calculation methods, Supporting Information), as follows. ), ΔG min < 0 (1) where E 0/site , ΔG max , ΔG min , k B and T are the energy density (unit, eV site −1 ), the maximum of adsorption energy for Ca (unit, eV), the minimum of adsorption energy for Ca (unit, eV), the Boltzmann constant (≈1.38 × 10 −23 J K −1 ), the absolute temperature (≈300 K), the electron charge and the external potential (unit, V), respectively.
The above relationship provides design principle for simultaneously increasing the energy-and the power-density of heteroatom-doped graphene anode for CIBs.Both the energy and power densities strongly depend on the minimum of Gibbs free energy change ΔG min before and after Ca 2+ adsorption or minimum adsorption energy.As ΔG min can be changed by doping as well as external electric potential U, absolute temperature T, and concentration and pH value of electrolyte, it provides a theoretical base for the improvement of both energy and power densities.Specifically, more negative ΔG min as a result of stronger interaction between Ca 2+ and electrode surface was conducive to storage due to exothermic reaction without external driving conditions such as higher electric potential U, but not beneficial for release of Ca ions into electrolyte.While more positive Gibbs free energy change ΔG min originating from weaker interaction between Ca 2+ and electrode surface was not conducive to Ca 2+ storage owing to endothermic reaction, but beneficial for Ca 2+ release.Therefore, only the interaction that is neither too strong nor too weak can contribute to the most excellent charge/discharge performance, which will lead to a volcano plot , as shown in Figure 2d,e; Figure S6 (Supporting Information).The line at left refers to stronger interaction which is the charge storage forbidden area where the Ca ions cannot be released, while the line at right represents the weaker Ca 2+ adsorption, which is the effective area for charge storage, but requires harsh external conditions as Ca 2+ adsorption on pristine graphene restson higher electric potential to overcome higher energy barrier (red dots in Figure 2d,e).Only when the minimum of Gibbs free energy change ΔG min reaches to zero (the summit of the volcano plot), can charge/discharge performance of the anode approach the ideal value (purple and red arrows in in Figure 2d,e), which is able to realize via modification of atomic and electronic structure for the anode.Thus, the design principle was established for all pseudocapacitive materials beyond Conway's pseudocapacitive theory (Table S2, Supporting Information).It deserves to note that specific capacitance C 0/site , energy density E 0/site and power density P 0/site should be zero for ΔG i <0 (or ΔG max <0) from perspective of practical application due to the failed discharge process.For 0<ΔG i <ΔG max , as long as ΔG i ≤ 2eU< ΔG max is satisfied under given potential U, charging process can proceed.For ΔG max <2eU, the capacity of the electrode reaches saturation.

Physics-Based Descriptor for the Design of Heteroatom-Doped Graphene Anode
Although the relationship between |ΔG min | (and other parameters) and energy and power densities has been derived and can be used to calculate the energy storage capability of the doped graphene anode based on the DFT calculations, it is more convenient to correlate the storage capability to the intrinsic properties of the dopants, which also provide in-depth understanding of the pseudocapacitive mechanism.We have proposed an innovative descriptor consisting of three intrinsic physical parameters of dopants, which is described by where, A X , R X , and E X are the electronegativity, radius and electron affinity of dopants X, respectively, and A C , R C , and E C are the electronegativity, radius and electron affinity of carbon atom, respectively.This descriptor Φ can well describe the interaction between Ca 2+ and the heteroatom-doped graphene anode and further quantify the complicated interfacial effects on the charge storage.
As shown in Figure 3a  and electrochemical performance (C 0/site , E 0/site , and P 0/site ) with the increase of descriptor Φ upon Ca 2+ storage on p-block element X (X = B, P, Sb, Si, N, O, S, I, Br, Cl, and F) doped graphene anodes, as shown in Figure 3b; Figure S7 (Supporting Information).Specifically, the closer the descriptor Φ to the top of the volcano plot, the better the electrochemical performance of such doped structure.Consequently, based on this guidance of descriptor Φ, the electrochemical performances on graphene doped with X anodes for CIBs continuously climb to the peak of the volcano plot, as shown in Figure 3c,d; Figure S8 (Supporting Information).Thus, Sb-doped graphene located on the top of volcano plot should have the best electrochemical performance among all metal-free single-heteroatom-doped graphene according to the predictions from |ΔG min |.It should be mentioned that the electrochemical performance of F-and S-doped structures are not well predicted by descriptor Φ, as marked by red dotted circle and green shadow in Figure 3a,b.This is mainly due to the fact that F element has the largest electronegativity and is one of the most reactive elements.So, it could form different doping structures.In our study, we generated only a limited number of possible models to represent the F-doping structures.There might be F-doped structures with lower adsorption energy that were not included in this study.This might result in the deviation of the DFT prediction for F-doping from the volcano relationship.Similar situation may also exist for S-doped structures.Anyway, although F-and S-doping predictions deviate from the volcano relationship, we still think that this does not limit the predictive ability of the descriptor.This point is supported by our experiment that the capacitance versus descriptor Φ follows the similar volcano trend (Figure 6d).The doped graphene prepared in the experiment contained all possible doping configurations.

Origin of Pseudocapacitive Storage of the Heteroatom-Doped Graphene
According to the above proposed design principle, the higher Ca 2+ storage capacity, energy density and power density can be achieved by optimizing |ΔG min | toward zero, which can be realized via climbing to the summit of the volcano plot originating from the relationship between |ΔG min | descriptor Φ.Since ΔG min is related to bonding strength, the magnitude of ΔG min is a measure of adsorption strength.
Thus, the descriptor Φ composed of radius R, electronegativity A and electron affinity E can reveal the essence of ΔG min .Therefore, differential charge density and Bader charge transfer for each optimal doped structure with chemisorbed Ca were calculated (Figure 4a,b; Figure S16-18, Supporting Information).We found that the amount of charge transfer from Ca atom to dopedgraphene substrate versus the descriptor forms volcano relationship(Figure 4c).
To explore the dependence of the ΔG min on the electronic structure of X-G substrate, first, we calculated the change of density of states (DOS) after and before Ca chemisorbed on each optimal X-G model (Figure 4d; Figure S20, Supporting Information).The DOS distribution of substrate with Ca shifts to the left compared with that of original one, that is, the direction of lower energy, which can be ascribed to more stable structure than that before Ca adsorption.To further explore the interaction of electronic states between Ca atom and substrate in the process of bond formation, six different DOSs were defined to find the relationship between DOS and ΔG min (Figure S22 and 23, Supporting Information).The results show a volcano relationship between DOS3 of each sole-doped graphene and descriptor Φ (Figure 4e), which can be explained effectively according to molecular orbital theory.As illustrated in Figure 4f, Ca 2+ with electron orbital  1 interacts with Ca 2+ storage site with electron orbital  2 , and their electron orbitals are hybridized and spilt into bond orbital corresponding to DOS below Fermi level and antibond orbital corresponding to DOS above Fermi level.Whereas, the bond strength between Ca and storage site is determined by the filling degree of anti-bond orbital, which depends on the level of anti-bond orbital energy.Empty or excess of anti-bond orbital will lead to inappropriate adsorption strength, which is either too strong or too weak.Thus, DOS3 controls the level of anti-bond orbital energy, [45] and thus determine bond strength, which can serve as the indicator for materials bonding properties.Specifically, with a higher location of the DOS3, the antibonding states move higher with a lower occupancy, which leads to a stronger interaction between Ca and doped-graphene surface, and vice versa.

Focused Experiments of Doped-Graphene Anode For CIBs
To verify design principle and intrinsic descriptor Φ proposed above, six X-heteroatom-doped graphene samples (X-G) (X = B, P, Sb, Si, N, and S) were synthesized by sintering the mixture of pure graphene and heteroatom precursors (see Materials synthesis in Experimental Section).As shown in Figure 5a; Figure S9 (Supporting Information), wrinkled layered structure with certain pore and similar morphologies in all doped graphene samples were observed from the scanning electron microscopy (SEM).This relatively consistent morphology can be further confirmed via typical transmission electron microscopy (TEM) images, as shown in Figure 5b; Figure S10 (Supporting Information), implying that morphology of the pure graphene was well preserved without noticeable morphological change and residues of the precursors.The energy dispersive spectroscopy (EDS) and XPS survey spectrum of the X-G samples showed the existence of carbon and dopants elements coming from graphene matrix and heteroatoms precursors (Figure 5c,d; Figure S11, Supporting Information), which confirmed the successful synthesis of different doped graphene samples.Moreover, from the XPS spectra, the atomic percentage of heteroatoms doped into graphene for each doped sample was obtained, ranging from 0.8% to 23%, which was in line with atomic content change trend of EDS results (Table S4, Supporting Information).In addition, nitrogenadsorption studies were indicative of all samples with large and similar surface areas except for very few samples (Figure 5f; Figure S13, Supporting Information).Overall, it is reasonable to assume that the differences in the Ca ions storage performance of various doped graphene samples is mainly attributed to their doping structures.
To further analyze bonding structures of the X-G materials, the high resolution XPS spectra was used to analyze the X-G bond types.According to peak deconvolutions for the reported respective single doped graphenes, [46,48] the six heteroatoms were chemically replaced or grafted onto carbon atoms at edge or central of the graphene matrix, yielding different species in-or out-of the graphene basal plane, shown in Figure 5e; Figure S12 (Supporting Information).Specifically, Sb-G sam-ple has formed C-Sb bond (Figure 5e), which is consistent with previous work. [45]B-G sample consists of two boron containing species including B-3C and edge B-2C-O species (without regard to B 2 O 3 precursor residue), while N-G sample has three nitrogen species consisting of central graphitic nitrogen (g-N) and edge pyridinic (py-N) and pyrrolic N (pr-N) in the graphene plane.Both P-3C(-O)-type phosphorus and edge C-S-C sulfur doping configuration can be tested in P-G and S-G samples, respectively.More significantly, all these above doped graphene species were verified by high resolution XPS spectra, and included in the DFT calculation (Figure S16 and 17, Supporting Information).

Experimentally Validated Relationship and Descriptor
To validate relationship derived from fundamental considerations, and physics-based descriptor Φ, electrochemical properties of these as-prepared X-G samples were evaluated by galvanostatic charge/discharge (GCD) tests in saturated CaCl 2 aqueous electrolyte (Figure 6a; Figure S14, Supporting Information).GCD results clearly show that the doped graphene samples exhibit strong pseudocapacitive characteristics, [41] depending on the types of the dopants (Figure 6b).Thus, the specific capacitance C m of each doped sample was calculated from galvanostatic charge-discharge curves (Figure 6a; Table S4, Supporting Information).Considering their similar microstructure under the same characterization conditions, it is reasonable to assume that the observed differences in specific capacitance for the X-G samples originates only from pseudocapacitive mechanism, as described theoretically by Equation 1 and 2 (Figure 3c,d).
To compare with the theoretical predictions, the specific capacitance per site, C 0/site * (eV −1 site −1 ) was further calculated based on the measured specific capacitance C m (Note S1, Table S4 and Figure S12,S16, and 17, Supporting Information).The calculated results C 0/site * versus ΔG min are shown in Figure 6c, in which theoretical C 0/site * is also plotted and shows the similar trend.The capacitance C 0/site * was also used to confirm the proposed descriptor Φ, which also followed the similar volcano trend govern by descriptor Φ (Figure 6d).According to the analysis using both the descriptor and ΔG min , Sb-doped graphene is identified as the best dopants among these dopants used in this study.

Rational Design of Co-Doped-Graphene Anode For CIBs
From the above investigation, it is clear that the pseudocapacitive Ca 2+ storage capability of anode material can be improved by intrinsic factors (e.g., tuning ΔG min toward zero) or extrinsic factors (heteroatom doping concentration and the number of exposed Ca 2+ storage sites for a certain mass loading).Thus, we propose two strategies to further enhance Ca 2+ storage ability on doped-graphene anode.The first design strategy is to optimize ΔG min closer to zero by multi-doped strategy.Since Sb was the best dopant among the dopants used in this study, it was selected to combine with other p-block elements to form dual-doped graphene (X-Sb-G) anode (Figure S15, Supporting Information).We have built all possible 189 X-Sb-G models and calculated all the possible 649 sites via DFT calculation to screen out the optimal Ca adsorption sites for each X-Sb-G model, and then determine ΔG min of each dual-doped optimal structure (Figure S17, Supporting Information).It was found that ΔG min correlates with the descriptor Φ, in the form of an invert-volcano relationship (Figure 7a), which is consistent with the predictions for catalytic activity of dual-doped graphene for fuel cells. [49]Thus, the larger the difference in descriptor between the two dopants, the better the pseudocapacitive performance of the dual-doped anode for Ca ions storage (red dotted arrow in Figure 7a).As a result, we found that Ca 2+ ions storage ability for B-Sb-G (ΔG min = 0.0043 eV) and O-Sb-G (ΔG min = 0.0262 eV) dual-doped anodes have surpassed that of all sole-doped anode including the optimal Sb-G (ΔG min = 0.0420 eV) one from its values of ΔG min (Table S3, Supporting Information).The capacitance per unit Ca 2+ storage site C 0/site was roughly evaluated to increase from 95 eV −1 site −1 of Sb-G anode to 930 eV −1 site −1 of B-Sb-G anode according to equation C = Q 2 /ΔG (Q is equal to 2e for Ca 2+ ), which is almost a ten-fold increase.
The origin of the invert-volcano plot for X-Sb-G anode materials can be understood from the synergistic effect of  S4, Supporting Information).d) Volcano relationship resulting from descriptor Φ validated by normalized electrochemical results (Table S4, Supporting Information).Here, the black and blue marks in d) refer to synthesized and non-synthesized experimental samples.All electrochemical measurements were employed in saturated CaCl 2 solution at ambient temperature and pressure.
dual-doped graphene.It is expected that larger difference may lead to stronger interaction between Sb and X, and stronger synergetic effect.Interestingly, despite more charge transfer based on synergistic effect of dual-doped graphene (Figure 7d,e; Figure S19, Supporting Information), this effect can no longer be well explained from the charge transfer viewpoint according to Gauss's law, as shown little irregular invert-volcano plot between charge transfer and descriptor Φ in Figure 7b, which may originate from complexity of synergy.Therefore, starting from molecular orbital theory, DOS distribution after and before Ca chemisorbed on optimal dual-doped structures was calculated to extract 6 different DOS descriptors (Figure S21 and S24, Supporting Information).The results showed that DOS1, namely the weighted DOS center of dual-doped graphene below Fermi level can well conform to descriptor Φ (Figure 7c; Figure S22, Supporting Information), which is mainly due to the weighted DOS capable of capturing the contribution of different dopants.This suggests that descriptor Φ is a universal one.
The second strategy to enhance the calcium storage capability is to increase the concentration of heteroatom dopants.The relationship between the storage ability and the heteroatom concentration can be roughly described as C T = μ/μ 0 C 0/site , where  is the heteroatom doping concentration,  0 is the doping concentration of doped-graphene model in this DFT calculation (≈2 at% −3 at.%) and C 0/site is the capacitance per unit Ca 2+ storage site (unit, eV −1 site −1 ).Thus, upon doping concentration greater than 10 at.% (This has been achieved experimentally), the capacitance per unit Ca 2+ storage site C 0/site can be increased by 3 to 5 times.With these two strategies, the co-doped-graphene anode can exhibit a capacity comparable to and even beyond that of the batterytype metal Au anode in CIBs, as shown in Figure 7f., which can be achieved via dual-doped graphene B-Sb-G and O-Sb-G obtained experimentally (Note S2, Supporting Information).More significantly, the designed co-doped-graphene anode has also an unmatched power density beyond all other battery-type anode due to intrinsic merit of pseudocapacitive anode.

Conclusions
We have established, for the first time, a universal design principle beyond Conway's pseudocapacitive theory to describe charge storage mechanisms of pseudocapacitive materials via the theoretical calculation and experimental characterization.A novel descriptor Φ based on intrinsic physical properties of dopants was proposed and confirmed in the experiment.This descriptor correlates the doping structures with the capacitive properties, enabling rational design of the pseudocapacitive materials.Under the guidance of the descriptor Φ, volcano and invert-volcano plots were established for sole-and dual-doped graphene anode, respectively, from which two design strategies were proposed to promote pseudocapacitive Ca 2+ storage capacity of the doped-graphene anode to the level higher than the state-of-the-art Ca 2+ storage anode materials.Finally, the origin of descriptor Φ, namely a medium for quantitatively capturing  S3, Supporting Information). [4,47].
complex electronic interactions at the microscopic level was discussed.The developed theory provides a theoretical base for rational design of new anode materials for various metallic ion batteries.
Structural Characterization: The X-ray photoelectron spectra (XPS) were measured on Thermo Scientific Escalab 250Xi XPS equipment.The incident radiation was monochromatic Al K X-rays (1486.6 eV).Nitrogensorption isotherms were collected on micromeritics apparatus (ASAP 2020 Plus 2.00) at 77 K and specific surface area was calculated via Brunauer-Emmett-Teller (BET) equation.Scanning electron microscopy (SEM) imaging was conducted on a Thermo Scientific Helios 5 CX.Energy dispersive spectroscopy (EDS) was obtained at the same time as SEM measurement.Transmission electron microscopy (TEM) as well as highresolution transmission electron microscopy (HRTEM) were conducted on Talos F200S G2.
Electrochemical Measurements: Working electrodes were prepared by pressing a slurry of mixture that contained heteroatom-doped graphene (X-G) (80 wt.%), acetylene black (10 wt.%), and polytetrafluoroethylene polyvinylidene difluoride (PVDF) (10 wt.%) onto a piece of conductive carbon paper (1 × 1.5 cm 2 ), with a mass loading of the active material ≈6 mg (Table S4, Supporting Information).The coated electrodes were dried in a vacuum oven at 80 °C for 12 h.The electrochemical performance was tested at room temperature by using a three-electrode system in a saturated CaCl 2 aqueous electrolyte.An Ag/AgCl electrode and a Pt wire were used as the reference and counter electrodes, respectively.Constant-current charge/discharge tests were conducted on a CHI 660E electrochemical workstation (Shanghai Chenhua).The gravimetric capacitance of a working electrode was calculated based on previous report. [34][36] The Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) was used to model the electronic exchange correlation energy. [34]The projector augmented wave (PAW) method was used to describe the ionic cores. [35]The cutoff energy was set to be 400 eV for the plane-wave expansion after testing a series of different cutoff energies.The K-points were set to be 4 × 4 × 1 and 4 × 1 × 1 for the graphene nanosheet and nanoribbons, respectively.Denser K-points of 12 × 12 × 1, 12 × 1 × 1 and 1 × 12 × 1 for sheet, zigzag and armchair nanoribbon models were set to calculate the DOS serving as characterization of electronic structure.
Computational Models: Based on different configurations of heteroatom-doped graphene demonstrated experimentally and theoretically (Figure 1a), pure graphene sheet, armchair and zigzag nanoribbon models were constructed to function as substrates doped with dopants (Figure S1, Supporting Information).The graphene sheet model was periodic on both the x and y directions consisting of 48 carbon atoms with an infinite large supercell sheet model, and zigzag and armchair nanoribbon models consisting of 48 and 36 carbons, respectively were periodic only on the x direction, and H atoms were added to saturate carbon dangle bonds on y direction.All dual-doped graphene models (X-Y-G) were constructed via all possible combination configurations of two sole-doped configurations.(Figure S15, Supporting Information).For each dual-doped graphene model configuration, the all possible Ca 2+ storage sites were tested by DFT calculation to search for the best site on such dual-doped graphene configuration (Figure S15, Supporting Information).

Figure 1 .
Figure 1.Calcium adsorption and charge storage mechanism.a) Summary of the heteroatom-doping configuration: (clockwise) pr-N(S b ), py-N(S b ), g-N(S b ), N(S b )-O, py-O, C─O─C, C≐O, C─OH, P-3C-O, P-3C, P-2C-2O, py-P, g-C(S i ), z-C(S i ) and a-C(S i ), th-S, py-S, C-S-C, S-2C-2O, th-S-2O, B-3C, C-B-2O, B≐C, py-B, B-O, z and a-(F, Cl, Br, and I) and g-(F, Cl, Br,and I).orange/grey, blue, pink, light cadet blue, yellow, red, purple, and white balls represent C(S i ), N(S b ), B, P, S, O, F (Cl, Br and I), and H atoms, respectively.b) The most negative adsorption energy (ΔG min ) of Ca atom on each doped graphene substrate with various configurations.c) The change of Gibbs free energy (ΔG) as the function of the number (n) of Ca atoms chemisorbed on optimal doped substrates or capacity for each optimal doped graphene anode substrate.d) Structural evolution upon Ca atoms chemisorbed continuously on armchair-graphene nanoribbon substrate as the best one in pure graphene.

Figure 2 .
Figure 2. The theoretical model of energy level filling theory for calcium ions storage (ELFT-CIS) and resulting volcano trend proposed by us.a) Schematic of charge/discharge for calcium-ion batteries (CIBs).b) Atomic schematic of divalent Ca 2+ stored (or chemisorbed) on doped-graphene anode with different energy regions during charging.c) The schematic of energy level filling model in which Ca 2+ storage regions with various adsorption energy correspond to different energy level in the order of energy from low to high analogous to the fill of electrons in different bands.Volcano curves originating from d) energy density E 0/site and e. parameter related to power density (P 0/site / k 0 C Ca ) as a function of the minimum Gibbs free change ΔG min , which led to volcano trend (insets refer to ideal electrochemical performance closely related to ΔG min of 0 eV).Here, , k 0 , and C Ca are constant, as mentioned in Calculation Methods in Supporting Information.

Figure 3 .
Figure 3.The volcano relationships established by intrinsic descriptor Φ.The volcano relationship related to a) the absolute value of the minimum Gibbs free energy change |ΔG min |, b) normalized logarithm of energy density log(E 0/site ) and specific capacity log(C 0/site ) to descriptor Φ. c) and d) Climbing to the submits of pseudo-volcano curves (namely parameter related to energy density(log(E 0/site )) and power density (log(P 0/site / k 0 C Ca ))curves) by optimization of the minimum Gibbs free energy change ΔG min based on intrinsic descriptor Φ.

Figure 4 .
Figure 4. Charge transfer and electronic structure origins of Ca stored on doped-graphene anode surface.a) atomic structure of the optimal Sb-doped graphene (py-Sb) and b) corresponding differential charge density and Bader charge transfer.c) Bader charge transfer from Ca for each optimal dopedgraphene as the function of intrinsic descriptor Φ. d) DOS change after and before Ca chemisorbed on B-3C doped-graphene surface.e) the volcano relationship between DOS3 and descriptor Φ. f) Energy level diagram that illustrates orbital hybridization of optimal Ca 2+ storage sites and Ca 2+ .E F refers to Fermi level of X-G-Li substrate, and  and * indicate bonding and anti-bonding states, respectively.Blue color indicates positive charge and yellow color indicates negative values of electrons quantities.The isosurface value is set to 0.003 e Bohr −3 .

Figure 5 .
Figure 5. Characterization of microstructures for doped-graphene samples.a) SEM image, b) TEM image, c) EDS measurement and elemental mapping of Sb-doped graphene sample.d) and e) Survey spectrum and high-resolution XPS spectra of Sb-doped graphene sample.f) Nitrogen adsorption isotherms and BET surface areas for Sb-doped graphene sample.

Figure 6 .
Figure 6.Verified DFT calculation and electrochemical measurements.a) and b) galvanostatic charge-discharge curves of Sb-doped graphene samples and specific capacitance as the function of current density for all doped graphene samples based on mass of active materials.c) energy level filling theory for calcium ions storage (ELFT-CIS) and resulting volcano trend validated by normalized electrochemical results (TableS4, Supporting Information).d) Volcano relationship resulting from descriptor Φ validated by normalized electrochemical results (TableS4, Supporting Information).Here, the black and blue marks in d) refer to synthesized and non-synthesized experimental samples.All electrochemical measurements were employed in saturated CaCl 2 solution at ambient temperature and pressure.

Figure 7 .
Figure 7. Invert-volcano relationship govern by intrinsic descriptor Φ and differential charge density distribution and Bader charge transfer on optimal B-Sb-codoped graphene model with Ca chemisorbed on the best storage site.The invert-volcano relationship related to a) the absolute value of the minimum Gibbs free energy change |ΔG min |, b) Bader charge transfer from Ca and c) DOS1 to intrinsic descriptor Φ for each optimal dual-doped graphene model (X-Sb-G).d) atomic structure of the optimal B-Sb-codoped graphene (B-Sb-G) and e) corresponding differential charge density and Bader charge transfer the charge transfer.Blue color indicates positive charge and yellow color indicates negative values of electrons quantities.The isosurface value is set to 0.003 e Bohr −3 .f) Comparison between predicted capacity of pseudocapacitive doped-graphene anode and Au anode as landmark achievements in references (NoteS3, Supporting Information).[4,47].