Article pubs.acs.org/JPCC
Configuration-Interaction Full-Multiplet Calculation to Analyze the Electronic Structure of a Cyano-Bridged Coordination Polymer Electrode Yusuke Nanba,† Daisuke Asakura,*,† Masashi Okubo,*,† Yoshifumi Mizuno,† Tetsuichi Kudo,† ̅ Haoshen Zhou,*,† Kenta Amemiya,‡ Jinghua Guo,§ and Kozo Okada∥ †
Energy Technology Research Institute, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan ‡ Photon Factory, IMSS, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan § Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ∥ The Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan S Supporting Information *
ABSTRACT: To understand the electronic-structure changes of electrode materials during the charge/discharge processes is one of the most important fundamental aspects to improve the battery performance. Soft X-ray absorption spectroscopy (XAS) was used to study a bimetallic NiFe Prussian blue analogue electrode. XA spectra were obtained during the charge/discharge and were analyzed by the configurationinteraction full-multiplet (CIFM) calculation, in which the strong charge transfer due to the σ/π-donation and backdonation of cyanide was taken into account. The CIFM calculation revealed that the metal-to-ligand charge transfer (MLCT) played an important role in the electronic state of Ni−N bond. The Fe3+−C bond in the charged state is dominated by both the MLCT and ligand-to-metal charge transfer (LMCT), whereas only the MLCT strongly affects the Fe2+−C bond in the discharged state.
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INTRODUCTION
However, to perform the theoretical analysis of XAS more precisely, the second-generation (G2) bases such as dn‑2L2, dnLL, dn+2L2 should also be considered, especially for the electronic structure with strong MLCT/LMCT. The theoretical analysis including the G2 bases can be performed with the configuration-interaction full-multiplet (CIFM) calculation, which we have developed.10−12 Recently, the electrode performance of Prussian blue analogues (PBAs) has been reported to provide the high power, low cost, and durable rechargeable batteries.13−19 PBAs generally have a perovskite structure bridged by cyanide: AyMα[Mβ(CN)6]1‑z·□z·nH2O (A = alkali metal; Mα and Mβ = TMs; □ = [Mβ(CN)6] vacancy; hereafter denoted as MαMβPBA). The electronic structure of the MnFe-PBA electrode during the charge/discharge has been studied by XAS with the CTM calculation previously.20 However, PBAs are well-known to have the electronic structure with strong MLCT/LMCT duo to the σ/π donation and back-donation abilities of the cyanide
Li-ion rechargeable batteries, powering the most portable electric devices, have been investigated intensively,1−4 because the application to grid-scale energy storage demands higher performances such as higher power, higher energy, and lower cost. The electronic-structure change of electrode materials during the charge/discharge is one of the most important fundamental issues to improve the battery performance. Soft X-ray absorption spectroscopy (XAS) is a powerful technique for an element-selective observation of 3d electronic structure of transition metals (TMs) similarly to X-ray photoelectron spectroscopy and X-ray emission spectroscopy.5 XAS in combination with the charge transfer multiplet (CTM) calculation could clarify not only the oxidation state of TMs but also the magnitude of ligand-to-metal charge transfer (LMCT) and metal-to-ligand charge transfer (MLCT).6,7 Thus, XAS with the analysis of the multiplet theory could reveal the electronic structure of electrode materials. For example, XA spectra for LixFePO4 were analyzed in detail by the CTM calculation, in which the first-generation (G1) bases such as dn, dn−1L, and dn+1L are taken into account.8,9 Note that L and L denote the ligand electron and hole, respectively. © 2012 American Chemical Society
Received: October 18, 2012 Revised: October 31, 2012 Published: October 31, 2012 24896
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for C−C, N−N, and C−N ((ppσ)CC, (ppσ)NN, and (ppσ)CN), and the one-electron C 2p and N 2p levels (εC and εN) to obtain the MO energy in the Fe(CN)6 and Ni(NC)6 clusters. The detail of C 2p−N 2p MO has been described in the previous studies.10−12 The CIFM calculation gives the energy levels with the bonding- and antibonding-type characters [εBP(γ) and εABP(γ)]. H2 in eq 1 includes the multipole part of the TM 3d-TM 3d and TM 3d-TM 2p Coulomb interactions that are not described in eq 2 and the spin−orbit interactions for TM 3d and TM 2p orbitals. We evaluated the Slater integrals using Cowan’s code21 and reduced them to 85% to take into account the configuration interaction. The XA spectrum was calculated using the Fermi golden rule22 expressed as
ligand. Therefore, the CIFM calculation with the G2 bases is indispensable to analyze the XA spectra more precisely. Here, we report the XAS study on the electronic structure of the NiFe-PBA electrode15 during the charge/discharge, which is theoretically analyzed with the CIFM calculation including the G2 bases.
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EXPERIMENTAL SECTION NiFe-PBA was synthesized by the precipitation method. The Xray diffraction (XRD) pattern was recorded with Bruker D8 advance. The chemical composition was determined by the standard elemental analysis. For electrochemical experiments, NiFe-PBA (75 wt %), acetylene black (20 wt %), and polytetrafluoroethylene (5 wt %) were ground into a paste, and used as the working electrode. Li metal was used as the reference and counter electrodes. For the electrolyte, a 1 M LiClO4 EC-DEC solution was used. The cutoff voltages were 4.3 V for charging (Li-ion extraction) and 2.0 V for discharging (Li-ion insertion), respectively. XAS measurements were performed at BL-7A of the Photon Factory (PF). The total electron-yield (TEY) detection mode was employed. The resolution was E/ΔE ∼ 1500. The base pressure of experimental chamber was maintained at the order of 10−8 Torr. All the XAS measurements were performed at room temperature.
I=
i
∑ [εd(γ ) − Q ∑ (1 − np,mσ ′)]nd ,γσ m,σ′
∑ εp,mσ np,mσ + U ∑ nd ,γ↑nd ,γ↓ m,σ
∑
+
(4)
RESULTS AND DISCUSSION The XRD pattern showed the peaks indexed into the cubic phase (F4̅3m, a = 10.232 Å, V = 1071.4 Å3) without impurity. The chemical composition was characterized by the standard elemental analysis of C, N, and H to be K0.1Ni[Fe(CN)6]0.7·□0.3·4.7H2O. This result indicated that NiFe-PBA contains 30% [Fe(CN)6] defect. It should be noted that NiFePBA contains K-ion, which can be extracted from the framework. However, the amount is so small that we neglected the contribution in this study. Figure 1 shows the charge/discharge curves for Lix(NiFePBA). 0.63 Li-ions per formula were inserted/extracted almost
where
+
+ Eg )
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THEORY The CIFM calculation for the electronic states of Fe and Ni atoms in LixNiFe-PBA was carried out by assuming the octahedral Fe(CN)6 and Ni(NC)6 clusters. The Hamiltonian is given by H = H0 + H1 + H2 (1)
γ ,σ
i
Here, |g⟩ and |f⟩ are the ground (initial) and final states of the XA spectrum, and the corresponding energies represent Eg and Ef. T denotes the electric dipole transition operator. In the numerical calculation, the wave function was obtained by the Lanczos method.23 The theoretical line spectra thus obtained were convoluted, using Lorentzian and Gaussian functions (with each width of 0.25 eV).
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H0 =
∑ | fi|T |g |2 δ(E − E f
γ
(U ′ − Jδσσ ′)nd , γσ nd , γ ′ σ ′ (2)
γ>γ′,σ ,σ′
and H1 =
∑ εP(jγ ) nP ,jγσ + ∑ Vpd(jγ )(dγσ† Pjγσ + hc) j,γ ,σ
j,γ ,σ
(3)
d†γσ
Here, represents the TM 3d electron creation operator, in which γ is eg or t2g symmetry in Oh and σ is ↑ or ↓ spin. The number operators for TM 3d and TM 2p are nd,γσ and np,mσ, respectively, where m is the magnetic quantum number. The first term in eq 2 represents the TM 3d states with εd(γ) being the one-electron energy level and Q being the Coulomb attraction caused by TM 2p core hole. The second term describes the TM 2p states, and the third and last terms are the Coulomb and exchange interactions between TM 3d electrons, respectively. H1 in eq 1 includes the C 2p−N 2p molecular orbital (MO) and the hybridization between TM 3d and MO. The first and second terms in eq 3 indicate the MO states and TM 3d-MO hybridization, respectively. P†jγσ represents the creation operator for the jth C 2p−N 2p MO with symmetry γ and spin σ. The number operator for MO is nP,jγσ. We used the transfer integrals
Figure 1. Charge−discharge curve for NiFe-PBA at the first cycle.
reversibly. The amount of inserted Li-ions (x = 0.63) is almost consistent with the amount of the redox couple of [FeIII(CN)6]3−/[FeII(CN)6]4− in NiFe-PBA. For XAS measurements, we prepared samples of as-synthesized (NiFe-PBA, before Li-ion insertion), fully Li-ion inserted (Li0.63NiFe-PBA), and fully Li-ion extracted (Li0NiFe-PBA) states. 24897
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Table 1. Electronic-Structure Parameters of [NiII(NC)6]4−, [MnII(NC)6]4−, [FeIII(CN)6]3−, and [FeII(CN)6]4− Clusters and the Calculated MO Energies (εBP(γ) and εABP(γ)) and Hybridization Strengths between TM 3d States and MOs (VB(γ) and VAB(γ)) (in eV)
Figure 2 shows Ni L2,3-edge XA spectra of LixNiFe-PBA. All the spectra have an intense main peak at about 854 eV with a
Δ (pdσ)a U J Q 10Dq (ppσ)CCa (ppσ)NNa (ppσ)CNa εC εN VAB(eg) VAB(t2g) VB(t2g) VB(eg) εABP(eg) εABP(t2g) εBP(t2g) εBP(eg) b
Figure 2. Observed Ni L2,3-egde XA spectra of LixNiFe-PBA. Theoretical spectrum of the [NiII(NC)6]4− cluster for NiFe-PBA and that of the ionic Ni2+ state are also shown. The theoretical spectra were convoluted from the line spectra, using Lorentzian and Gaussian functions (with each width of 0.25 eV).
[Ni(NC)6]4−
[Mn(NC)6]4−
[Fe(CN)6]3−
[Fe(CN)6]4−
3.6 −1.5 7.4 0.86 7.0 0.8
0.9 −1.5 5.6 0.72 5.0 0.6
0.8 −2.3 6.9 0.86 4.0 4.2 1.0
2.2 −2.2 6.7 0.77 4.0 3.6 1.0
0.8 8.0 0.0 −2.5 1.7 0.6 −1.2 −1.9 7.29 0.91 −4.41 −8.79
0.8 8.0 0.0 −2.5 1.7 0.6 −1.2 −1.9 7.29 0.91 −4.41 −8.79
8.0 0.0 −2.5 3.1 1.7 −1.2 2.5 7.59 0.22 −3.97 −8.84
8.0 0.0 −2.5 3.0 1.6 −1.2 2.4 7.59 0.22 −3.97 −8.84
(pdπ)/(pdσ) = −1.0/2.2, (ppπ)/(ppσ) = −0.25.24 bThe definition of the CT energy Δ is different for each cluster (see the Supporting Information). a
shoulder structure at about 856 eV (hereafter denoted as S1) for the L3 edge, and a broad peak at about 871.5 eV for the L2 edge. It should be noted that a small satellite structure was observed at about 860.5 eV (hereafter denoted as S2) for all samples. All the spectra were nearly the same, which suggested that the electronic state of Ni is unchanged during Li-ion insertion/extraction. The CIFM calculation for a [NiII(NC)6]4− cluster was carried out to analyze the spectra. The spectra for an isolated Ni2+ under the crystal field (10Dq = 0.8 eV) was also calculated for comparison. Both calculated results in Figure 2 reproduced the S1 structure for the L3 edge well. However, the calculation for an isolated Ni2+ could not reproduce the S2 structure, whereas that for a [NiII(NC)6]4− cluster successfully shows a small satellite structure. This result clearly suggests that the S2 structure should be attributed to the excitation process involving the LMCT/MLCT. In general, the S2 structure could be explained by the transition from d8LL to cd9LL or that from d7L to cd8L.25,26 Note that c, L, and L denote a core hole of the Ni 2p orbital, an antibonding NC-MO occupied with a transferred electron, and a bonding NC-MO occupied with a created hole, respectively. LL corresponds to the band excitation between the bonding and antibonding MOs in CN. The former transition depends on the (ppσ)CN value, whereas the latter one depends on the Δ value. Because the calculated S2 structure depends on the (ppσ)CN value strongly, this structure is mainly caused by the transition from d8LL to cd9LL. Table 1 shows the electronic structure parameters of the [NiII(NC)6]4− cluster used in the CIFM calculation, which includes charge transfer (CT) energy Δ, Coulomb interaction U, and exchange interaction J. The crystal-field splitting, 10Dq, of 0.8 eV and transfer integral for Ni−N, (pdσ), of −1.5 eV are close to the previous reported values for Ni oxide and dihalides (10Dq = 1.0 eV and (pdσ) = −1.2 to −1.3 eV).27−30 The
transfer integral for C−N, (ppσ)CN, of 8.0 eV is remarkably large, which suggests the large energy separation between the bonding and antibonding MOs. |V/Δ| is well-known as a good indicator for the degree of LMCT or MLCT, because both larger V and smaller Δ (thus larger |V/Δ|) should result in the stronger CT.11,12 In the [NiII(NC)6]4− cluster, |V/Δ| for LMCT (0.147) is smaller than that for MLCT (0.240), which suggests that MLCT plays an important role rather than LMCT. The definition of CT energies is described in the Supporting Information. The weak LMCT could be explained by the fully occupied 3d(t2g) orbitals in Ni high-spin (HS) d8 electron configuration. Table 2 shows the relative weights of each configuration in the ground state obtained from the CIFM calculation. The second-generation (G2) bases were used to diagonalize the Hamiltonian for the ground state. Note that, where electron configurations like d8, d7L, and d9L are called the firstgeneration (G1) bases, d6L2, d8LL, and d10L2 electron Table 2. Weight Percent of Each Electron Configuration in the Ground State and Average 3d Electron Number ⟨nd⟩ of [NiII(NC)6]4−, [MnII(NC)6]4−, [FeIII(CN)6]3−, and [FeII(CN)6]4− Clusters n
d dn+1L dn−1L dn+2L2 dnLL dn−2L2 n ⟨nd⟩ 24898
[Ni(NC)6]4−
[Mn(NC)6]4−
[Fe(CN)6]3−
[Fe(CN)6]4−
75.8 3.1 18.6 0.0 1.8 0.6 8 7.83
81.9 11.7 4.8 0.4 1.1 0.1 5 5.08
56.9 17.9 16.2 0.9 7.3 0.7 5 5.02
44.6 5.4 39.2 0.1 6.1 4.6 6 5.57
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affected by (ppσ)CN, the satellite could be ascribed to the transition from d5LL to cd6LL. Table 1 shows the electronic structure parameters of the [FeIII(CN)6]3− and [FeII(CN)6]4− clusters used in the CIFM calculation. The transfer integrals for Fe−C, (pdσ), of −2.3 and −2.2 eV are about twice as large as that of the iron oxide and dihalides (−1.0 to −1.4 eV).28−30 Large 10Dq for both clusters (4.2 and 3.6 eV) suggests the LS state. The large transfer integral, (ppσ)CN, of 8.0 eV indicates the large energy separation between bonding and antibonding MOs. As mentioned above, |V/Δ| is a good indicator for the degree of LMCT/MLCT. |V/Δ| for LMCT in the [FeIII(CN)6]3− cluster (0.387) is comparable to that for MLCT (0.315), which suggests the coexistence of both LMCT and MLCT in the [FeIII(CN)6]3− cluster. In contrast, as for the [FeII(CN)6]4− cluster, |V/Δ for LMCT (0.182) is much smaller than for MLCT (0.696), which suggests that MLCT is preferred rather than LMCT. The fully occupied 3d(t2g) orbital should suppress LMCT in the [FeII(CN)6]4− cluster. Table 2 shows the relative weights of each configuration in the ground state obtained from the CIFM calculation. The G2 bases in the [FeIII(CN)6]3− cluster include the d5[(t2g)5], d6L, d4L, d7L2, d5LL, and d3L2 electron configurations, whereas those in the [FeII(CN)6]4− cluster include d6 [(t2g)6], d7L, d5L, d8L2, d6LL, and d4L2 electron configurations. As shown in Table 2, the weights of d4L and d6L in the [FeIII(CN)6]3− cluster are almost the same, due to the coexistence of both LMCT and MLCT. In contrast, the dominant weight of d6 and d5L (83.8% in total) for the [FeII(CN)6]4− cluster was obtained, because of the dominant MLCT. The Fe and Mn L2,3-edge XAS have already been reported previously.20 Here, the CT effect and resulting electronic configurations for the [NiII(NC)6]4− and [MnII(NC)6]4− clusters are compared on the basis of the CIFM calculation. Figure 4 shows the Mn L2,3-edge XA spectrum of MnFePBA. The observed spectrum shows three peaks at about 642, 643, and 645 eV for the L3 edge, and two peaks at about 652 and 654 eV for the L2 edge.20 The CIFM calculation was carried out for the [MnII(NC)6]4− cluster (blue line in Figure 4), which reproduced experimentally observed peaks.
configurations together with the G1 bases are called the G2 bases. These bases were based on HS d8 electron configuration [(t2g)6(eg)2]. As shown in Table 2, the weight of d8 and d7L is significantly dominant (94.4% in total), due to the strong MLCT in the [NiII(NC)6]4− cluster. Figure 3 shows Fe L2,3-edge XA spectra of LixNiFe-PBA. The spectrum of NiFe-PBA shows three peaks at about 706, 710,
Figure 3. Observed Fe L2,3-edge XA spectra of LixNiFe-PBA. Theoretical spectra of the [FeIII(CN)6]3− and [FeII(CN)6]4− clusters for NiFe-PBA are also shown. The theoretical spectra were convoluted from the line spectra, using Lorentzian and Gaussian functions (with each width of 0.25 eV).
and 712 eV for the L3 edge and two peaks at about 723 and 726 eV for the L2 edge. It should be noted that a small satellite structure was observed at about 718 eV for NiFe-PBA and Li0NiFe-PBA. The observed spectrum is similar to that of K3[FeIII(CN)6], indicating the Fe3+ at low-spin (LS) state.6,7 After Li-ion is inserted (Li0.63NiFe-PBA), the peaks at about 706 and 718 eV disappear, whereas the peaks at about 710, 712, 723, and 726 eV shift to about 709, 711, 722, and 724 eV. The spectrum is similar to that of K4[FeII(CN)6].6,7 According to ref 5, the peak at about 706 eV, which almost disappeared upon Liion insertion, can be ascribed to the states consisting mainly of Fe 3d(t2g) orbital. The other peaks in the L3 region for 708− 713 eV could be attributed to the unoccupied Fe 3d(eg) states. Thus, the Fe atoms were reduced as Fe3+ LS → Fe2+ LS by Liion insertion. Furthermore, the Fe L2,3-edge spectrum almost returned to the initial shape after Li-ion extraction, indicating that the nearly reversible redox reaction of Fe occurs during Liion insertion/extraction. A small shoulder structure at about 710.5 eV implied that a small fraction of Fe2+ should remain in Li0NiFe-PBA. The CIFM calculation for [FeIII(CN)6]3− and [FeII(CN)6]4− clusters was carried out to analyze the spectra. The blue and red lines in Figure 3 show the calculated results for [FeIII(CN)6]3− and [FeII(CN)6]4−, respectively. The calculated spectrum for the [FeIII(CN)6]3− cluster shows an intense peak at about 706 eV as well as peaks around 709−713 eV, which reproduced the experimental L3-edge structure well for NiFe-PBA and Li0NiFePBA. Two main peaks for the calculated L3-edge in the [FeII(CN)6]4− cluster were consistent with the experimental L3 edge. A small satellite structure at about 718 eV for NiFe-PBA and Li0NiFe-PBA was also reproduced. Because the small satellite structure in the calculated spectrum was strongly
Figure 4. Observed Mn L2,3-edge XA spectrum of MnFe-PBA.15 Theoretical spectrum of the [MnII(NC)6]4− cluster is also shown. The theoretical spectra were convoluted from the line spectra, using Lorentzian and Gaussian functions (with each width of 0.25 eV). 24899
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Table 1 shows the electronic structure parameters of the [MnII(NC)6]4− cluster used in the CIFM calculation. The 10Dq value of 0.6 eV and transfer integral for Mn−N, (pdσ), of −1.5 eV are similar to those in the [NiII(NC)6]4− cluster. However, in contrast to the case for the [NiII(NC)6]4− cluster, |V/Δ| for LMCT (0.297) is much larger than that for MLCT (0.081), which suggests that LMCT plays an important role rather than MLCT in the [MnII(NC)6]4− cluster. Table 2 shows the relative weights of each configuration in the ground state obtained from the CIFM calculation. The G2 bases in the [MnII(NC)6]4− cluster include the d5[(t2g)3(eg)2], d6L, d4L, d7L2, d5LL, and d3L2 electron configurations. As shown in Table 2, the weight of d5 and d6L (93.6% in total) for the [MnII(NC)6]4− cluster was obtained, due to the dominant LMCT. Figure 5 shows the schematic illustration of the CT between TM 3d(t2g) orbital and CN 2pπ (2pπ*) for NiFe- and MnFe-
Article
ASSOCIATED CONTENT
S Supporting Information *
Description of the CT energy in each cluster. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: D.A.,
[email protected]; M.O., m-okubo@ aist.go.jp;H.Z.,
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was done under the approval of the Photon Factory Program Advisory Committee (Proposal No. 2010G038). This work was also conducted on the basis of the MOU between AIST, Japan, and LBNL, DOE, USA. M.O. was financially supported by Industrial Technology Research Grant Program in 2010 from New Energy and Industrial Development Organization (NEDO). J.H.G.’s work at the ALS is supported by the U.S. Department of Energy under Contract No. DEAC02-05CH11231.
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REFERENCES
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Figure 5. CTs from TM 3d(t2g) orbital to antibonding-type 2pπ MO and from bonding-type 2pπ MO to TM 3d(t2g) orbital for (a) NiFePBA and (b) MnFe-PBA. The deduced Fermi levels (EF) are also depicted.
PBA. Here, CN 2pπ (2pπ*) represents the MO(t2g) with the bonding-type (antibonding-type) character. For NiFe-PBA, there are the MLCTs from Ni 3d(t2g) orbitals and no LMCT to Ni 3d(t2g) ones. The electron on Ni 3d(t2g) orbitals can move to CN 2pπ* for NiFe-PBA, whereas there are the CTs from Mn 3d up-spin orbitals (t2g,↑) and to Mn 3d down-spin orbitals (t2g,↓) for MnFe-PBA.
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CONCLUSION The CIFM calculation of XAS was applied to the study on the electronic structure change of NiFe-PBA during the Li-ion insertion/extraction (discharge/charge) process. Ni was determined to be the Ni2+ HS state regardless of the Li-ion concentration. In contrast, Fe L2,3-edge XA spectra revealed that Li-ion insertion resulted in the redox of Fe3+ LS ⇔ Fe2+ LS states. Furthermore, the CIFM calculation clarified the contribution of MLCT and LMCT to the Fe−C and Ni−N bonds. MLCT dominates the electronic configuration of the Ni−N and Fe2+−C bonds, whereas both MLCT and LMCT are important for the electronic configuration of the Fe3+−C bond. 24900
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