For many metabolites, the major barrier between cytosol and mitochondrial matrix is the inner membrane of mitochondria, the site of the respiratory electron transport chain. In consequence, it houses numerous transporters which facilitate the controlled exchange of metabolites, ions, and even proteins between these cellular compartments. While their import into the organelle can be studied with isolated mitochondria or mitoplasts, the analysis of their export from the matrix into the intermembrane space or even the cytosol demands for more sophisticated approaches. Among those, inside-out inner membrane vesicles are particularly useful, since they allow the direct presentation of the potential export substrates to the membrane without prior import into the organelle. Here we present a protocol for the isolation of such inside-out vesicles of the inner membrane of plant mitochondria based on repeated freeze/thaw-cycles of freshly prepared mitoplasts. Electron microscopy and Western analysis could show that the majority of the vesicles have single envelope membranes in an inside-out topology. The vesicles are furthermore physiologically active, as demonstrated by assays measuring the enzymatic activities of Complex I (NADH dehydrogenase), Complex V (ATP synthase) and the mitochondrial processing peptidase (MPP) associated with Complex III. Hence, the method presented here provides a good basis for further studies of the inner mitochondrial membrane and mitochondrial export processes. Plant mitochondria provide a multitude of metabolic reactions and functions which are essential for the cell . The analysis of such processes was strongly supported by the establishment of methods enabling the isolation of intact plant mitochondria and mitochondrial fractions . The innPhaseolus aureus) (Pisum sativum). We have characterized and validated the vesicles obtained with respect to their morphology, membrane topology and integrity, as well as by determining the enzymatic activities of IMM protein complexes of the respiratory electron transport chain. Due to the inevitable loss of soluble components like cytochrome c during vesicle preparation, these would have to be added externally if the activity of the entire electron transport chain is to be determined. We think that these inside-out vesicles might be helpful for numerous potential applications, including the analysis of mitochondrial calcium homeostasis or the export of proteins from the matrix to the intermembrane space (IMS).The first plant IMM vesicles described were generated by sonication of mitochondria isolated from mung bean ( aureus) . Since t aureus) . With su aureus) . However aureus) . With thPrinciplesThe isolation of intact mitochondria from plant tissue is based on a combination of differential centrifugation and density gradient centrifugation. For more information about the principles of isolating plant mitochondria, see SolutionsSIM (sucrose isolation medium)Store at 4°C25 mM HEPES/KOH, pH 8.0350 mM Sucrose2 mM Ethylenediaminetetraacetic acid (EDTA)Supplementation on the day of isolation:0.6% (w/v) Polyvinylpyrrolidone K-25 (PVP)0.2% (w/v) Bovine serum albumin (BSA)10 mM Dithiothreitol (DTT)0.2 mM Phenylmethylsulfonyl fluoride (PMSF)5 x SRM (5x sorbitol resuspension medium)Autoclave and store at 4°C0.25 M HEPES/KOH, pH 8.01.65 M Sorbitol1 x SRM+PMSFPrepare fresh on the day of use20% (v/v) 5xSRM (see above)0.2 mM PMSFPercoll gradient solutions (store at 4°C)50% Percoll 34% Percoll 18% Percoll5xSRM 20% (v/v) 20% (v/v) 20% (v/v)Percoll 50% (v/v) 34% (v/v) 18% (v/v)Preparatory work• Cut the nylon mesh (100 μm pore size) and Miracloth (22-25 μm) to size.• Precool all solutions and equipment to 4°C or on ice.Pisum sativum var. Feltham First) and let the seedlings grow for 7–10 d under constant temperature (18–22°C) and light regime (16/8 h light/dark cycle).• Sow pea  by adding the supplements.• Prepare four Percoll step gradients  in 30 ml Corex tubes and keep them on ice.NOTE.To prevent unwanted turbulence, place a flat piece of cork in the Corex tubes onto which the Percoll solutions, and later also the organelle suspension, are pipetted in sequence.• Soak soft brush with 1 x SRM+PMSF• Harvest 80-120 g pea seedlings without roots and keep them on ice until use.Protocol (timing: 3-4 h)The following protocol was modified based on the isolation procedure described by 1. Homogenize the harvested plant material with approximately 400 ml SIM for 5 x 2 sec in a Waring blender.2. Filter the homogenate through one layer of nylon mesh and two layers of Miracloth into two 250 ml centrifuge beakers placed on ice.NOTE.For higher yield, it is advisable to carefully squeeze the filters with the plant debris.g (4°C).3. Centrifuge for 5 min at 2,000 4. Carefully pour the supernatant (containing mitochondria) into two new precooled 250 ml centrifuge beakers.NOTE.The sediment will easily detach from the walls.g (4°C).5. Centrifuge for 10 min at 6,000 6. Pour the supernatant (containing mitochondria) into two new precooled 250 ml centrifuge beakers.NOTE.In order to prevent spillover of the chloroplast-containing sediment, pour the supernatant off in one go but stop as soon as detached sediment fractions approach the rim of the beaker.g (4°C).7. Centrifuge for 10 min at 16,000 8. Discard the supernatant while retaining the sediment (containing mitochondria).9. Use the soft brush to carefully resuspend each sediment in 2 ml 1 x SRM+PMSF.NOTE.To avoid the formation of lumps during resuspension, the sediment should initially be resuspended in a smaller volume.10. Distribute the organelle suspension equally onto the four Percoll gradients.g (4°C) with low acceleration and deceleration.11. Centrifuge for 45 min at 12,000 NOTE. Intact mitochondria will accumulate in the interphase between 50% and 34% Percoll.12. Remove the upper phases with a Pasteur pipette taking care not to take any mitochondria.13. Carefully collect the interphase containing the mitochondria and transfer it to new precooled 30 ml Corex tubes.g (4°C).14. Fill the Corex tubes to approximately 25 ml with 1 x SRM+PMSF, mix carefully and centrifuge for 10 min at 12,000 15. Remove and discard approximately 50% of the supernatant.16. Repeat steps 14 and 15 until a solid sediment has formed and the supernatant remains clear.17. Discard the supernatant entirely and resuspend the sediment in a few milliliters of 1 x SRM+PMSF.18. Combine the mitochondrial suspensions in a single Corex tube.g (4°C).19. Centrifuge for 5 min at 12,000 20. Discard the supernatant, resuspend the sediment in 1 ml 1 x SRM+PMSF and transfer the suspension to a 1.5 ml Eppendorf tube.g (4°C).21. Centrifuge for 5 min at 16,000 22. Resuspend the sediment in 100 μl 1 x SRM+PMSF.23. Determine the protein concentration of the mitochondria suspension by Bradford assay.ALTERNATIVE.Alternatively, a simpler Percoll gradient consisting of 13 ml 34% Percoll and 5 ml 18% Percoll can be used. In this case, the mitochondria are found together with starch granules and other high-density particles at the bottom of the Corex tube after centrifugation. This procedure is faster and usually leads to higher yields at the expense of some impurities with high-density particles.Principles2, which masks membrane charges, allows the cristae regions to stack and thus supports the formation of inside-out vesicles FB1 (fractionation buffer 1)Store in aliquots at -20°C10 mM HEPES/KOH, pH 8.060 mM SucroseFB2 (fractionation buffer 2)Store in aliquots at -20°C20 mM HEPES/KOH, pH 8.0600 mM SucroseOn the day of isolation• Supplement FB1 and FB2 with 1mM PMSF each.Protocol (timing: ~45 min)g (4°C).1. Centrifuge the suspension of isolated mitochondria corresponding to 0.5–1 mg protein for 5 min at 16,000 2. Resuspend the sediment in FB1 .3. Incubate the suspension for 15 min on ice.NOTE.During osmolysis, the outer membrane of the mitochondria is disrupted, ultimately leading to mitoplast formation.4. Add FB2 in a 1:1 ratio and incubate for 10 min on ice.g (4°C).5. Centrifuge for 15 min at 16,000 6. Resuspend the sedimented mitoplasts in 1 x SRM .2 to 20 mM.7. For further fractionation, supplement the assays with MgCl8. Shock-freeze the suspension in liquid nitrogen for 20 sec and let it thaw while holding the tubes in your hands.9. Repeat step 8 twice.NOTE.2 supports an inverted membrane orientation .ation ;.PrinciplesTransmission electron microscopy (TEM) is a suitable method to determine the morphology, quality, and purity of the isolated vesicles. For this purpose, it is necessary to fix the samples with glutaraldehyde (preservation of ultrastructure) and osmium tetroxide (preservation of ultrastructure and staining of membranes). Then the vesicles are immobilized with agar, dehydrated with ethanol and infiltrated with an epoxy resin. After polymerization of the resin, the samples are ultra-thin sectioned, transferred to TEM grids, post-stained with heavy metals, and analyzed by electron microscopy.Solutions0.1 M SCB (Sodium cacodylate buffer), pH 7.2FixativePrepare fresh on the day of use0.2 M SCB, pH 7.2(TOXIC)!6% (w/v) Glutaraldehyde 0.33 M SorbitolSER (Spurr epoxy resin) (y resin) (TOXIC)! according to the manufacturer’s manual and store it at -20°C after testing.Prepare epoxy resin  Protocol(TOXIC)!, incubate at room temperature for 30–60 min with gentle shaking and store overnight at 4°C for fixation.1. Supplement vesicles corresponding to 100 μg protein with one volume of freshly prepared fixative g (4°C).2. Centrifuge for 15 min at 22,000 3. Discard the supernatant and resuspend the sediment in 4% agar (dissolved freshly in 0.1 M SCB) to immobilize the vesicles.4. Cut the solidified agar into small pieces and transfer them into a 5 ml sample tube containing 0.1 M SCB.5. Wash 6 times for 8 min each with 0.1 M SCB.4 (dissolved in 0.1 M SCB).6. Discard the supernatant and add 1% OsO7. Incubate for 60 min at room temperature.2O.8. Wash twice for 10 min each with H9. Discard the supernatant and dehydrate the samples stepwise with (a) 10% EtOH, (b) 30% EtOH, and (c) 50% EtOH for 30 min each.10. Discard the supernatant and add 1% uranyl acetate (dissolved in 70% EtOH).11. Incubate for 30 min at room temperature.NOTE.If necessary, the samples can be stored for several days in 70% EtOH at 4°C.12. Discard the supernatant and dehydrate the samples further, once with 90% EtOH and twice with 100% EtOH (for 30 min each).13. Remove the supernatant and incubate the samples stepwise at room temperature as follows:(a) 25% SER (diluted with 100% EtOH) for 3 h(b) 50% SER (diluted with 100% EtOH) for 4 h(c) 75% SER (diluted with 100% EtOH) overnight14. Discard the supernatant and incubate the samples in 1 ml SER for 6 h at room temperature.15. Discard the supernatant and incubate the samples in 1 ml SER for 18 h at 70°C to achieve polymerization.16. Prepare sections from the samples using an ultramicrotome and transfer them to copper grids covered with a Cedukol film .17. Stain the sections at 25°C for 60 min with 1% uranyl acetate and 10 min with 3% lead citrate using an automatic section stainer.18. Analyze the sections by TEM.NOTE.Considering numerous extended incubation steps, the actual TEM analysis usually takes place 8–10 days after starting the procedure.ResultsThe electron micrographs of the vesicle fraction reveal the presence of a variety of structures Figure 2PrinciplesOne approach to determine the orientation of the membrane vesicles rests on treatment of such vesicles with highly concentrated solutions of mild chaotropic salts  to release membrane-attached proteins and protein complexes (Solutions1 x SRM (see above)4 x LSB (4 x Laemmli sample buffer)Store in aliquots at -20°C250 mM TRIS/HCl, pH 6.88% (w/v) SDS40% (w/v) Glycerol20% (w/v) 2-Mercaptoethanol0.016% (w/v) Coomassie G-250Protocol (timing: ~1 h for steps 1–6)g (vesicles) or 5 min at 16,000 g (mitochondria and mitoplasts).1. Collect two aliquots each of mitochondria, mitoplasts and IMM vesicles (each corresponding to 100 μg protein) in Eppendorf tubes and centrifuge at 4°C for either 15 min at 22,000 2. Discard the supernatants and carefully resuspend the sediments in either 50 μl 1 x SRM or 50 μl 1 x SRM supplemented with 2 M NaBr .3. Incubate on ice for 5 min.g (vesicles) or 5 min at 16,000 g (mitochondria and mitoplasts).4. Centrifuge at 4°C for either 15 min at 22,000 5. Transfer the supernatants to fresh Eppendorf tubes containing 50 μl 4 x LSB each  by SDS-PAGE.8. After electrophoresis, blot the proteins onto a PVDF membrane and perform a standard Western analysis using suitable antibodies.Results1 subunit beta of mitochondrial ATP synthase (AtpB), which is exposed to the matrix side of the IMM, to determine the topology of the IMM vesicles prepared. In an inside-out orientation of the vesicles, treatment with 2 M NaBr leads to the dissociation of the F1 subcomplex from the membrane-spanning Fo subcomplex of ATP synthase (Complex V) and thus to the accumulation of AtpB in the supernatant , which in plant mitochondria is associated with Complex III .Principles+, which is traced photometrically by the decrease of absorption at its maximum, 340 nm. However, while Complex I provides the predominant NADH oxidizing activity, plant mitochondria have at least three further membrane-bound NADH dehydrogenases. One is found in the outer membrane  to inhibit Complex III and Complex IV, respectively. As an electron acceptor, ferricyanide is instead present in excess amounts to prevent any backreaction.Solutions1 x SRM (see above)100 mM NADH100 mM potassium ferricyanideC1 bufferStore in aliquots at -20°C20% (v/v) 5 x SRM (see above)(TOXIC)!240 μM Potassium cyanide (TOXIC)!4 μM Antimycin A Protocol (timing: ~7 min per measurement)The following protocol was modified based on enzyme activity measurements described by (TOXIC)!, and mitochondria, mitoplasts or IMM vesicle suspension corresponding to 150 μg protein into a 1 ml cuvette and measure the blank value at 340 nm.1. Add 800 μl 1 x SRM, 200 μl C1 buffer 2. Start the reaction by adding 1.6 μl 100 mM NADH and 10 μl 100 mM ferricyanide.3. Record the absorption at 340 nm for at least 5 min.ResultsWhen mitochondria or mitoplasts are analyzed, a constant and almost linear decrease in absorption at 340 nm is observed until, after approximately 5 min, the blank value is reached  Protocol (timing: ~15 min per measurement)1. Add mitochondria, mitoplasts or vesicles corresponding to 100 μg protein to 1 ml C5 buffer that is preheated to 25°C.2. Transfer the suspension to a 1 ml cuvette placed in a photometer and incubate for 5 min.3. Set to zero at 492 nm and record the data for 1 min.4. Add 50 μl 20 mM ATP, mix thoroughly and continue recording the extinction at 492 nm for 4 min.5. Add 2 μl 0.5 mM Gramicidin, mix thoroughly and continue recording the extinction at 492 nm for at least 3 min.ResultsAs shown in Also in the presence of mitoplasts, a decrease in AO absorption at 492 nm after addition of ATP and its recovery in the presence of Gramicidin is found, though both to a significantly lower extent .PrinciplesMitochondrial processing peptidase (MPP) removes presequences from nuclearly encoded mitochondrial precursor proteins after their import into the mitochondrial matrix. In plant mitochondria, MPP is associated with Complex III of the respiratory electron transport chain and exposes its active site to the matrix . Thus, wSolutionsLSB (see above)0.5 M EDTAProtease solutionPrepare fresh on the day of use2 mg/ml Thermolysin225 mM CaCl2 x IB (2 x import buffer)Store in aliquots at -20°C30 mM HEPES/KOH, pH 7.4600 mM Sucrose2PO410 mM KH0.1% (w/v) BSASIB (supplemented import buffer)Prepare fresh on the day of use50% (v/v) 2 x IB (see above)24 mM MgCl4 mM Methionine4 mM ATP1 mM GTP0.2 mM ADP5 mM DL-Malic acid5 mM DTT10 mM Potassium acetate2 mM NADH310 mM NaHCOFixing solution50% (v/v) Methanol10% (v/v) Acetic acidPreparatory workin vitro transcription followed by in vitro translation in the presence of 35S methionine. For details, see • Prepare radiolabeled mitochondrial precursor proteins by Protocol (timing: ~1 h 30 min for steps 1–12)The following protocol was modified based on the protein transport assays described by in vitro translation assay to 90 μl SIB.1. Add mitochondria or vesicle suspension corresponding to 100 μg protein and 10 μl 2. Incubate for 20 min at 25°C.g (mitochondria) or 15 min at 22,000 g (vesicles).3. Centrifuge at 4°C for 5 min at 16,000 4. Carefully remove supernatant and resuspend each sediment in 200 μl 1 x IB.5. Divide the samples into two 90 μl aliquots each and discard the rest.6. While one aliquot of each sample remains untreated, the second aliquot is supplemented with 10 μl protease solution.7. Incubate for 30 min on ice.8. Stop protease activity by adding 3 μl 0.5 M EDTA.g (mitochondria) or 15 min at 22,000 g (vesicles).9. Centrifuge at 4°C for 5 min at 16,000 10. Discard supernatant and resuspend each sediment with 100 μl 1 x SRM.g (mitochondria) or 15 min at 22,000 g (vesicles).11. Centrifuge at 4°C for 5 min at 16,000 12. Discard supernatant and resuspend each sediment in 30 μl 2 x LSB.13. Heat samples for 2 min at 95°C, centrifuge briefly and analyze by SDS-PAGE.14. After electrophoresis, incubate the gel for 30 min in fixing solution.15. Dehydrate the gel in vacuum at 80°C maximum  using a gel dryer .NOTE.To visualize the position of unlabelled molecular weight marker in the autoradiogram, a small amount of in vitro translation assay in LSB can be dotted with a pipette tip onto the marker bands.16. Expose for 0.5–3 days to a phosphor imager screen .NOTE.For exposure times exceeding 3 days, the screens should be placed in a radiation-shielding lead chamber to reduce background caused by ambient radiation.NOTE.Instead of phosphor imager screens, conventional X-ray films can alternatively be used for exposure. However, due to the lower sensitivity of such films, exposure times will probably be considerably longer.ResultsIn the experiment shown in The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.LE carried out most of the experimental work except electron microscopy which was performed by GH. BB and RK designed the experiments and supervised the project. LE, BB, and RK wrote the manuscript. All authors contributed to the article and approved the submitted version.


Despite having a slightly lower capacity than Ca–Ge, Mg–Ge shows an approximately 150% smaller volume expansion ratio (231% vs. 389%) and three orders of magnitude higher ion diffusivity (3.0 × 10−8 vs. 1.1 × 10−11 cm2 s−1) than Ca–Ge. Furthermore, ion diffusion in Mg–Ge occurs at a rate comparable to that of monovalent ions, such as Li+, Na+, and K+. The outstanding performance of the Mg–Ge system may originate from the coordination number of the Ge host atoms and the smaller atomic size of Mg. Therefore, Ge anodes could be applied in multivalent-ion batteries using Mg2+ as the carrier ion because its properties can compete with or surpass monovalent ions. Here, we report that the maximum capacity, volume expansion ratio, and ion diffusivities of the alloying electrode materials can be understood using atomic-scale structural properties, such as the host–host and host–ion coordination numbers, as valuable indicators.Germanium, a promising electrode material for high-capacity lithium ion batteries (LIBs) anodes, attracted much attention because of its large capacity and remarkably fast charge/discharge kinetics. Multivalent-ion batteries are of interest as potential alternatives to LIBs because they have a higher energy density and are less prone to safety hazards. In this study, we probed the potential of amorphous Ge anodes for use in multivalent-ion batteries. Although alloying Al and Zn in Ge anodes is thermodynamically unstable, Mg and Ca alloys with Ge form stable compounds, Mg In ai and Na ,51,52. A2+ and Ca2+ cations. We found that the Mg–Ge and Ca–Ge alloys were most stable at compositions of Mg2.3Ge and Ca2.4Ge, respectively, and showed the highest capacities of 1697 and 1771 mA·h·g–1, respectively. Although the Mg2.3Ge alloy has a slightly lower specific capacity than Ca2.4Ge (~4%), it exhibits a ~150% smaller volume expansion ratio and a three orders of magnitude-higher ion diffusivity than Ca2.4Ge, while demonstrating comparable or superior values to those of Li4.0Ge, Na1.5Ge, and K1.2Ge. We found that the values of the average coordination numbers of CNhost–host and CNhost–ion are decisive descriptors for comprehending the specific capacity, volume expansion, and ion diffusivity of alloy-based negative electrode materials. The findings of this study suggest that the Mg2+ cation has the highest potential among the multivalent ions for use as a promising carrier ion in Ge anodes, and the performance of Mg–Ge alloys is comparable to that of monovalent ions.We performed FPMD simulations to gain insights into the chemical bonding and structural changes that occur when amorphous Ge material alloys with the multivalent Mg22s1, 2p63s1, 3p64s1, 3s23p1, 2p63s2, 3p64s2, 3d104s2, and 4s24p2, respectively. In our study, we constructed a periodic cubic super cell with 40 Ge atoms 40 × x M atoms for each amorphous MxGe  structure. A 3 × 3 × 3 k-point mesh was used for the Brillouin zone integration. The simulation procedure for amorphous MxGe  alloys consists of two steps: (1) volume relaxation and (2) energy evaluation. First, for a given ion concentration (x), the volume of MxGe was determined using the liquid quench method. Initially, the cubic supercells containing 40 × x M and 40 Ge atoms were randomly generated with estimated dimensions. This structure underwent a heating process , followed by equilibration (at 2000 K for 3 ps), and was finally quenched  /x), the volumes occupied by M in MxGe were 21.76, 34.88, 13.73, 29.94, and 63.32 Å3 for MgxGe, CaxGe, LixGe, NaxGe, and KxGe, respectively. The corresponding ratios for volume expansion (defined as (V − V0)/V0 × 100%) for Mg2.3Ge and Ca2.4Ge are 231% and 386% for Mg2.3Ge and Ca2.4Ge, respectively, as shown in 2.3Ge showed a favorably lower volume expansion ratio (231%) compared with Li4.0Ge (253%). However, the volume expansion of magnesiated Ge could result in capacity degradation during cycling because the discharge–charge volume expansion ratio remains high. This challenge may be overcome by advanced electrode architectures, such as nanostructures, nanopores, and composite electrodes, as demonstrated in Ge anode systems [–1 and low volume expansion ratio of 231% in the Mg2.3Ge alloy suggest that Mg2.3Ge could be utilized as a next-generation anode material in LIBs. systems ,62,63,642.3Ge and Ca2.4Ge. These results indicate that the volume of MxGe was determined by the total combined volume occupied by the M cations and Ge anions. The data points for Ge near −2.0 e are from isolated Ge–Ge pairs. While most of the Ge atoms are surrounded by the relatively larger Ca atoms with positive charges, the Ge atoms in the Ge–Ge pairs accept fewer electrons from Ca atoms, leading to the deviated data points shown in xGe alloys as originating from (1) the ionic concentration, (2) the difference in atomic volume between M and Ge ions, and (3) the charge distribution between M and Ge ions.0.5Ge amorphous alloys  at T = 300 K, as shown in dms) values linearly increased with time t for both Mg and Ca ions  with respect to the inverse temperature, as shown in We investigated the M-ion diffusivities in M Ca ions , thereby0.5Ge alloys at room temperature. The calculated ion diffusivities (D) are 3.0 × 10–8 and 1.1 × 10–11 cm2·s–1 for Mg ions in Mg0.5Ge and Ca ions in Ca0.5Ge at T = 300 K, respectively, as shown in 0.5Ge and in the monovalent Li0.5Ge, Na0.5Ge, and K0.5Ge alloys. This result contradicts the prevailing view that the diffusion of multivalent ions is significantly lower than that of monovalent ions, as in the Ni2O4, Mn2O4, V2O5, and Ti2S4 systems. Furthermore, the Mg ion diffusivity in amorphous Ge was even one order of magnitude superior to the Mg ion diffusivity (2.3 × 10–9 cm2·s–1) in Mg0.5Si [0.5Ge, Ca0.5Ge, Li0.5Ge, Na0.5Ge, and K0.5Ge are shown in We suggest that Mg ions diffuse considerably more rapidly than Ca ions in M Mg0.5Si . This dixGe, CaxGe LixGe, NaxGe, and KxGe. The specific capacity of Mg2.3Ge was somewhat lower (~4%) than that of Ca2.4Ge, which exhibited the highest capacity. However, Mg2.3Ge showed a relatively small volume expansion ratio (~150%) compared to Ca2.4Ge. In addition, the Mg ions in Mg2.3Ge diffused more rapidly than the Ca ions in Ca2.4Ge by three orders of magnitude. These findings suggest that the Mg–Ge alloys have significantly better cycling performance and rate capability than Ca–Ge alloys. xGe , showing that (1) the order of specific capacity is Ca > Mg > Li > Na > K, (2) the volume expansion ratio has the increasing order of Na < Mg < Li < K < Ca, and (3) the order of ion transport is Li > Mg > K > Na > Ca. Compared to alloys between Ge and monovalent ions, Ge–Mg alloys showed a moderately high specific capacity, low volume expansion ratio, and fast ion transport. Accordingly, Mg2+ is a more promising carrier ion than Ca2+ for the amorphous Ge electrode in MIBs because of its superior electrochemical properties that can even compete with monovalent ions.2.3Ge and Ca2.4Ge to their specific capacities, volume expansion ratio, and ion diffusivities. We determined the specific capacities as 1697 for MgxGe and 1771 mA·h·g–1 for CaxGe from the highest concentration (xmax = 2.3 for Mg and 2.4 for Ca) at the most favorable formation energies as plotted in C) calculation is included in the xmax plays an important role in determining the specific capacities because both MgxGe and CaxGe have the same charge and molecular weight per structural formula unit.We attempted to relate the structural properties in Mgxmax, were related to the number of carrier ions that could be coordinated to the Ge host anions. The average host ion coordination numbers for Mg2.3Ge and Ca2.4Ge were CNGe–Mg = 2.56 and CNGe–Ca = 2.64, respectively, in line with a somewhat smaller capacity of Mg2.3Ge than of Ca2.4Ge. This relationship was consistent for monovalent ions as well as for these multivalent ions. Ge–Li = 3.62 in Li4.0Ge, CNGe–Na = 2.36 in Na1.5Ge, and CNGe–K = 1.90 in K1.2Ge. The CNGe–M  values have the order Li (3.62) > Ca (2.64) > Mg (2.56) > Na (2.36) > K (1.90), which was analogous to the order of xmax: Li (4.0) > Ca (2.4) > Mg (2.3) > Na (1.5) > K (1.2). Considering the different ne for monovalent (1 × xmax) and divalent (2 × xmax) ions, we can obtain the order of capacity (Ca > Mg > Li > Na > K) from the order of maximum ion concentrations (xmax). Furthermore, the CN values are CNGe–Ge = 4.24 in Mg2.3Ge and CNGe–Ge = 0.71 in Ca2.4Ge, as shown in We found that the highest concentrations, xGe was also analyzed in terms of the xmax values. While the ion concentrations at the maximum charging for MgxGe (xmax = 2.3) and CaxGe (xmax = 2.4) were similar, a noticeable difference was observed in the volumes accommodated by Mg and Ca at 21.76 for Mg and 34.88 Å3 for Ca, resulting in a considerably lower volume expansion ratio of 231% for Mg2.3Ge compared to 386% for Ca2.4Ge. The contrasting difference in the volumes accommodated by Mg and Ca may originate from the difference in the atomic radii between Mg (1.50 Å) and Ca (1.80 Å). Notably, we found that the order of the volume occupied by M in MxGe  was K (63.32 Å3) > Ca (34.88 Å3) > Na (29.94 Å3) > Mg (21.76 Å3) > Li (13.73 Å3), which was consistent with the order of the atomic radii: K (2.20) > Ca (1.80) ≈ Na (1.80) > Mg (1.50) > Li (1.45 Å).The relationship between the volume extension ratios and the volumes accommodated by the M ions in M0.5Ge (3.03 × 10−8 cm2·s–1) than in Ca0.5Ge (1.13 × 10−11 cm2·s–1). A weaker interaction between the carrier ions and the host ions creates conditions where ions can more easily break ion–host bonds and travel through the host structure. The strength of the M–Ge bond seemed to be related to the coordination number of Ge (CNGe–Ge) in MxGe at x = 0.5. The CNGe–Ge values , respectively, implying that the bond strength of M–Ge  follows the order of Ca > Li > K > Na ~ Mg, consistent with the order of the thermodynamic driving forces for alloy formation (Ca > Li > K > Mg > Na). Assuming that the interaction between ion and host atoms is the primary factor that determines the formation energy of MxGe, the observed analogous trends strongly support the discussion that the strength of the bond between ion and host Ge atoms is highly correlated with the CNGe–Ge values. Along with the aforementioned discussion on CNGe–M, we conclude that the CNhost–host and CNhost–ion values can be used as important indicators for evaluating the electrochemical performance of alloy-based anode materials, including the formation energy, specific capacity, volume expansion ratio, and ion diffusivity.The relationship between the M–Ge bond strength  and the coordination number of CN3+, Mg2+, Ca2+, Zn2+, and using first-principles calculations, we demonstrated that Mg2+ and Ca2+ can work stably as multivalent carrier ions for amorphous Ge anodes. Furthermore, Mg2+ has better cycle stability and rate capability than Ca2+. Specifically, Mg2.3Ge demonstrates a capacity of 1697 mA·h·g–1, a volume expansion ratio of 231%, and an ion diffusivity of 3.0 × 10–8 cm2·s–1; these values are equivalent to or superior to those of Li4.0Ge, Na1.5Ge, and K1.2Ge. The strong correlation between the electrochemical performance and structural properties of Ge alloys with monovalent and multivalent ions offers comprehensive insight into alloying mechanisms. The findings of this study suggest that Ge anodes could be used in practical multivalent-ion batteries, as Mg2+ emerged as the most promising multivalent ion for amorphous Ge anodes and showed comparable or even better performance than traditional monovalent ions. Moreover, we also found that the CN values of the host atoms (CNhost–host) and ions (CNhost–ion) can be used to understand the relationship between the structural properties and electrochemical performance of alloying anode materials. The results presented here will serve as a helpful reference for experimental researchers working on the development of alloying anode materials for multivalent-ion batteries. Moreover, our results demonstrate a new class of materials that can overcome the skyrocketing demands for battery capacities while also revealing an effective theoretical methodology for the development of alloying electrodes, which are among the most promising electrode materials for next-generation batteries [By investigating multivalent ions such as Alatteries ,66.


Their outstandingability to absorb and release oxygen at relatively low temperaturesof 250–400 °C holds promise of saving energy comparedto current industrial methods. Unfortunately, the low temperatureof operation also implies slow kinetics of oxygen exchange in thesematerials, which would make them inefficient in applications suchas chemical looping air separation. Here, we show that the oxidationkinetics of RMnO3 can be improved through Ti4+-doping as well as by increasing the rare earth cation size. Therate of oxygen absorption of nanocrystalline RMnx1–TixO3  was investigated by thermogravimetricanalysis, X-ray absorption near-edge structure, and high-temperatureX-ray diffraction (HT-XRD) with in situ switching of atmosphere fromN2 to O2. The kinetics of oxidation increasesfor larger R and even more with Ti4+ donor doping, as bothinduce expansion of the ab-plane, which reduces theelectrostatic repulsion between oxygen in the lattice upon oxygenion migration. Surface exchange rates and activation energies of oxidationwere determined from changes in lattice parameters observed throughHT-XRD upon in situ switching of atmosphere.Hexagonal manganites, RMnO The emergingpotential for using oxygen in oxy-combustion technology for CO2 capture may also further increase the demand in the comingyears.2 Today, the bulk supply of oxygenis made through the highly energy-demanding process of cryogenic distillation.4 In recent years, air separation by oxygen absorption has been studiedas a promising energy-efficient alternative for oxygen production.5 These methods are usually referred to as chemicallooping air separation (CLAS) and utilize materials with reversibleoxygen storage and release properties, known as “oxygen storagematerials” (OSMs),6 in an eitherpressure swing- or temperature swing-based method. A suitable materialfor CLAS can rapidly absorb and release large amounts of oxygen, preferablyat lower temperatures to reduce energy costs, and must not degradeover time.2Oxygen gas is imperative to a number ofdiverse applications, suchas medical treatments, and production of steel, polymer materials,and pharmaceuticals.7 Perovskite-type oxides (ABO3−δ), such as LaxSrx1–MO3 ,CaMnO3, or SrFeO3-based materials, are possibleOSMs due to their high oxygen storage capacities (OSC) and as theirproperties can be fine-tuned due to having broad cation compositionalflexibility.13 These materials, which are widely studied transition metal-basedoxygen carriers, utilize oxygen vacancies for the storage and transportof oxygen and allow for reversible switching between a reduced ABO3−δ state and an oxidized ABO3 statedepending on temperature and partial pressure of oxygen, pO2. These oxygen transport properties also make perovskiteoxides promising material candidates within applications such as solidoxide fuel cells and metal–air batteries.15 Generally, bulk transport of oxygen is rate-limiting for particleslarger than ∼1 μm, while the catalytic splitting or formationof the O2 molecule on the surface is rate-limiting forsmaller particles.16 As oxygen vacanciesin perovskites have limited mobility, temperatures as high as 600–800°C are generally required to achieve sufficiently rapid oxygenexchange.17 At such elevated temperatures, these materialsare prone to degradation and kinetic demixing.18 The OSC and oxygen exchange kinetics can be improved bydoping on the A-site, B-site, or both.19 Compared toSr0.8Ca0.2FeO3 and CaMnO3, Sr0.8Ca0.2Fe0.4Co0.6O3−δ and Ca0.8Sr0.2MnO3 show faster surface oxygen exchange kinetics, shortertimes required for oxidation, and smaller activation energy for bulkoxygen diffusion.19 Similar kinetics have also beenfound for SrFeO3-based materials21 making both material systems good candidates for CLAS at lower temperatures.Possible oxygen carriersinclude transition metal oxides, rangingfrom binary manganese, iron, and copper oxides to complex ternarymetal oxides.3+δ ,are possible OSMs due to their large OSCs at lower temperatures.26 RMnO3 oxides can crystallize in one of two crystal structuresdepending on the size of the R3+ cation, with smaller cations(rR3+ ≤ rHo3+) favoring the layered hexagonal structureof interest here with space group P63cm (rR3+ ≥ rDy3+) favors theorthorhombic perovskite Pnma structure.27 The hexagonal P63cm structure is less close-packed than the Pnma perovskite structure, and excess oxygen is accommodatedas interstitials in the hexagonal polymorph, in contrast to cationvacancies in the perovskite structure.30 Calculated energy barriersfor migration of interstitial oxygen through an interstitialcy mechanismare about 0.4–0.6 eV and lower compared to most oxygen vacancymigration barriers found in perovskites,33 enabling significant transport of oxygen interstitialsat temperatures even below 200 °C. Unfortunately, at such lowtemperatures, these materials suffer from slow oxidation kineticsin bulk form. Even nanocrystalline samples, which generally show muchfaster oxidation kinetics than bulk materials,34 show reduced OSC with faster cooling rates.40 The maximum OSC of hexagonal manganites has been improved by R-sitedopants.41 However, improving the kinetics of oxygen exchangeis crucial for potential industrial applications. E.g. doping YMnO3+δ with larger R cations results in oxygen contentsas high as δ = 0.45 at slow cooling rates in oxygen atmosphere.35 Unfortunately, as these compositions have relativelyslow redox kinetics, only a portion of the full capacity can be utilizedwithin the timeframes needed for efficient temperature or pressureswing CLAS. Nanocrystalline Y0.95Pr0.05MnO3 has been shown to only need minutes to reduce from δ= 0.2 to δ = 0.0 in air at T > 270 °C,while reoxidation to δ = 0.2 requires several hours, as thisoccurs at a lower temperature where the redox kinetics are slower.37 Similar oxidation timeframes have also beenreported for undoped YMnO3 and HoMnO3.36 Larger R cations do seem to affect the redox kinetics, as usingR larger than Dy3+ has resulted in improved oxidation ratesfor R0.25Y0.75MnO3 and Y0.6Tb0.2Ce0.2MnO3,41 and donor doping can increase both the OSCand the thermal stability of interstitial oxygen in hexagonal manganites.43 Ti4+ donor dopingof the Mn sublattice44 has been reportedto increase the absorption of oxygen and thermal stability of Oi in hexagonal manganites,42 and thereare also indications that Ti4+-doping can improve the oxygenexchange kinetics.40 Ti4+ asa donor dopant is charge compensated by formal reduction of Mn3+ to Mn2+ at high temperatures or low pO2 where there is limited absorption of oxygen interstitials.At lower temperatures and higher pO2,Ti4+ is charge compensated by oxygen interstitials.40 The rate-limiting step for cyclic processeslike CLAS is oxidation, and the oxidation kinetics of hexagonal manganitesmust be improved to enable commercial applications.Hexagonal manganites, RMnOup P63cm 1, while x1–TixO3  by thermogravimetry and high-temperatureX-ray diffraction (HT-XRD) and X-ray absorption spectroscopy within situ switching of atmosphere. The oxidation kinetics are improvedwith the increasing size of R3+ and with 15% Ti4+ donor doping. Larger R3+ and particularly Ti4+ doping cause an expansion of the ab-plane and alower ferroelectric Curie temperature, and both effects are suggestedto improve the oxygen bulk transport. Surface exchange rates and activationenergies were calculated from lattice parameter changes, using chemicalexpansion to gauge the oxygen content. The surface exchange kineticsare similar to literature reports on state-of-the-art materials measuredat significantly higher temperatures. Finally, we discuss future avenuesfor further improving the oxidation kinetics of hexagonal manganitesby aliovalent doping.Here, we study the oxidation kinetics of RMnx1–TixO3 sampleswere prepared using a previously reported modified citric acid synthesisroute.46 Metal acetates Ho(CH3CO2)3·xH2O (AlfaAesar),Dy(CH3CO2)3·xH2O (AlfaAesar), and Mn(CH3CO2)3·xH2O (Riedel-de-Haën)were each dissolved in a mixture of citric acid (99% Sigma-Aldrich)and deionized water with a molar ratio of cation to citric acid of1:20 for Ho3+, 1:35 for Dy3+, and 1:5 for Mn3+. The precursor solutions were stirred on a hot plate setto 150 °C until clear. For the Ti4+ precursor solution,titanium(IV) isopropoxide (TTIP) (Sigma-Aldrich) was added to citricacid dissolved in deionized water, with a molar ratio of cation tocitric acid of 1:6.3, and stirred on a hot plate set to 60 °Cuntil clear. The cation precursors were mixed in stoichiometric amounts,and ethylene glycol (EG) (Merck) was added with a 1:1 molar ratiobetween EG and citric acid. The solutions were stirred on a hot plateset to 150 °C until a viscous gel was formed, which was thendried at 120 °C for 3 days. The dried gels were heated to 400°C and kept for 3 h and subsequently calcined at 600 °Cfor 6 h. The calcined amorphous powders were then crystallized attemperatures ranging from 850 to 950 °C in N2 atmospherefor 1 h. Some of the samples were pre-annealed in 5% H2 in N2 atmosphere at temperatures ranging from 250 to300 °C prior to crystallization to achieve phase pure powders.40Nanocrystalline RMn47 All samples were refined within the P63cm space group. The DyMnO3 sample contains 14 molar% Dy2O3, inferredfrom Rietveld refinement. Oxygen stoichiometry as a function of temperaturewas analyzed by thermogravimetric analysis (TGA) using a Netzsch STA449C Jupiter with 30 mL min–1 O2 gasflow. The samples were heated to and subsequently cooled from 800°C using heating rates of 5, 10, and 20 °C min–1. Calculations of δ were based on a reference point chosenat the lowest mass at T > 700 °C where allMnis assumed to be found as Mn3+, corresponding to δ= 0 and δ = 0.075 for undoped and Ti-doped samples, respectively.Prior to the TGA measurements, all samples were heated to 600 °Cfor 10 h in N2 atmosphere to remove excess oxygen.To investigate phase purity and latticeparameters, XRD was performed using a Bruker D8 Focus with Cu Kαradiation. Lattice parameters and average crystallite size of thedifferent powders 1 were de3 and HoMn0.85Ti0.15O3. For the STEM image acquisition, a beam semi-convergenceangle of 27 mrad and collection angles of 67–155 mrads wereused.The morphology of the samples was studied using transmissionelectronmicroscopy (TEM) imaging, performed on an aberration-corrected JeolJEM ARM200F equipped with a cold field emission gun operated at 200kV. Bright-field TEM and scanning TEM (STEM) images were acquiredand are shown in –1 gas flow, which was verified using a Pfeiffer Vacuum Omnistar spectrometer.For diffraction measurements, a wavelength of 0.338591 Å anda Dexela 2923 area detector were used. A Hitachi Vortex single-elementsilicon drift detector was used to measure the XANES fluorescencesignal. Absorption measurements were done in fluorescence mode, asthe transmission for Mn was weak due to the heavy rare earth elementsattenuating the signal. XANES measurements were performed prior to,and after, each XRD measurement. In addition, each sample was measuredonce using XANES with in situ switching of atmosphere at a temperaturechosen for each sample to display reasonable kinetics. Prior to thesynchrotron measurements, all samples were heated to 600 °C inN2 atmosphere to remove any excess oxygen from the structure.The samples were heated 500 °C in N2 atmosphere inbetween each measurement. TOPAS 5 operating in launch mode was usedfor Pawley refinement of lattice parameters. Larch48 was used for the normalization of XANES measurements.HT-XRD and X-ray absorption near-edge structure(XANES) measurementswith in situ switching of atmosphere were carried out at the BM31beamline of the Swiss-Norwegian Beamlines (SNBL) at the European SynchrotronRadiation Facility (ESRF) in Grenoble, France. A few milligrams ofeach sample were each placed in a capillary with quartz wool on eachside. All experiments were performed using 10 mL min2 atmosphere, are shown in 3 increases from ∼30 to ∼60 °C when increasingthe rate from 1 to 5 °C min–1. No differencesin the kinetics of oxidation between HoMnO3 and DyMnO3 can be inferred from the TGA measurements.The changes in oxygen stoichiometry as a functionof temperature,measured by TGA at different heating and cooling rates in O0.85Ti0.15O3 and DyMn0.85Ti0.15O3, compared to ∼150 and ∼200°C for HoMnO3 and DyMnO3, respectively.This indicates that Ti4+ donor doping greatly improvesthe kinetics of oxidation as well as that it stabilizes oxygen interstitialsto higher temperatures.In contrast to the undoped materials, the Ti-dopedmaterials 3b,d show3+ to Mn4+, when exposed to O2 atmosphere. NormalizedX-ray absorption near-edge structure (XANES) spectra of the Mn K-edgemeasured before and after oxidation at 300 °C are shown in Figures S2–S4.The spectra collected after oxidation, noted “O2” in 2. As shown by the Mn2O3 andMnO2 references, with the Mn K-edge of MnO2 beingat higher energies than that of Mn2O3, thisshift indicates an oxidation process from Mn3+ to Mn4+, which is the expected charge compensation mechanism uponabsorption of oxygen. The Ti-doped samples in panels (b) and (d) displaya shift with greater magnitude than the undoped samples, indicatingthat a larger amount of Mn3+ has been oxidized to Mn4+. This corresponds well with the larger oxygen content thatTi-doped samples possess at 300 °C (3 in (a)show the smallest change in absorption edge energies after being exposedto O2, as this composition shows low OSC (δ ≈0.06) at this temperature.All samples display a partial oxidationof Mn, from Mnt 300 °C 3. The sp2 to O2 are shown in XANES spectra measured during oxidation after insitu switchingof the atmosphere from N2 to O2 areshown in Figures S6–S11. All samples showshifts in the position of the (0 0 4) reflection at ∼6.8°2θ toward higher angles during oxidation, reflecting a contractionof the c axis when interstitial oxygen enters MnOplanes. This contraction is attributed to partial rectification ofthe tilting of the MnO5 bipyramids and the smaller radiusof Mn4+ which is charge compensating interstitial O2–. In the Dy-containing samples, shown in panels  and , the single (0 0 4) reflection of the P63cm structure (marked with triangles▲) is replaced by the two (1 0 10) and (0 0 12) reflections(marked with asterisks *) of the new structure with space group R3c during oxidation, respectively. Theappearance of these two reflections demonstrates the transition tothe oxygen-rich structure with space group R3c (δ > 0.28), where the c axisistripled compared to the stoichiometric structure with space group P63cm.40 Another observable in 0.85Ti0.15O3 and DyMn0.85Ti0.15O3 stabilize within 2 min, while DyMnO3 needsover 15 min to fully oxidize. The HoMnO3 sample does notoxidize significantly at 300 °C, as shown inthe TGA measurements in Synchrotron X-ray diffractograms measured at 300°C upon insitu switching of atmosphere from N49 through which the kinetics of oxidation canbe investigated indirectly.50 Lattice parametersof HoMnO3, HoMn0.85Ti0.15O3, and DyMn0.85Ti0.15O3 as a functionof time after switching from N2 to O2 atmosphereat different temperatures are shown in 0.85Ti0.15O3 at additional temperatures includedin Figure S12. For all samples, the oxidationprocess is faster with increasing temperatures, as expected. The netexpansion and contraction of the lattice parameters decrease withincreasing temperature, as the materials oxidize less at higher temperatures.This is most significant for HoMnO3  to the larger Dy3+ (1.027 Å),as seen from the X-ray diffractograms , will then follow an exponential equation:ceq is the equilibrium concentration, ct=0 is the start concentration, kexch is the surface exchange rate coefficient, and d is the average size of the material sample, e.g., filmthickness, or in our case half the particle size. The surface exchangerate k can now be estimated by fitting the refined c lattice parameters presented in S12 to The significant contraction alongthe 3, HoMn0.85Ti0.15O3, and DyMn0.85Ti0.15O3 are presented in 66 The surface exchange rate for HoMnO3 at 300 °C isnot included, as very little oxidation happens in this sample at highertemperatures, and the resulting calculated exchange rate is thereforeunreliable.The calculatedoxygen surface exchange rates for HoMnO0.85Ti0.15O3 and 0.68 eV for DyMn0.85Ti0.15O3. The activation energy for HoMnO3 was not calculated as this sample had only two data points, whichwould result in a high uncertainty in the calculated value. Theseactivation energies are slightly lower than the typical values reportedfor hexagonal Pr0.05Y0.95MnO3 (0.8–0.9eV)67 and for perovskites (∼0.7–1.1eV).69 From 0.85Ti0.15O3 displays an initial expansion followed by a contractionin the ab-plane during oxidation, which differs fromthe other samples that only show expansion. One possible explanationfor this is that the electrostatic attraction between the Ti4+ present in the already expanded ab-plane and thenegatively charged Oi entering the lattice is larger thanthe electrostatic repulsion between planar oxygen and Oi, causing a contraction along the a axis and anincrease in stability of interstitial oxygen in the structure comparedto the undoped samples. Substituting YMnO3 with largerR cations such as Sm3+ can stabilize the oxidized phaseand thus lower the oxygen release rate.38 The TGA data in 4+ and Oi is lowering the rate of oxygen release, and thelack of thermal hysteresis confirms that the kinetics of reductionis still fast.The activation energies calculated from the surfaceexchange ratesfor each sample were found to be 0.54 eV for HoMn3 for CLASshould focus on improving the oxidation kinetics. It is now establishedthat larger R3+ improves both the oxidation rate and OSC,and large rare earth dopants should be included in future studies.The addition of Ti4+ affects both the OSC and the kineticsof oxidation positively, but it also limits these materials to pressureswing applications, as the broad temperature interval for oxidationand reduction is impractical for temperature swing processes. Otheraliovalent dopants may also be beneficial; e.g., Zr4+ onthe Y-sublattice has displayed similar effects as Ti4+ onthe Mn-sublattice for the OSC and thermal stability of Oi,43 but its effect on oxidation kineticsis unknown.For hexagonal manganites to be used for CLAS,both the OSC andthe kinetics of oxidation and reduction must be sufficiently high.While the OSC of hexagonal manganites has become competitive comparedto other material classes, future work on RMnORMnO3 has been studied by thermogravimetric analysisandHT-XRD upon in situ switching of atmosphere from N2 toO2. The rate of oxidation increases for larger R3+ cations and with 15% Ti4+-doping on the Mn sublattice.The OSC of Ti-doped samples is insensitive to the rate of coolingin O2 atmosphere, signifying very fast kinetics of oxidation.Changes in lattice parameters inferred from HT-XRD showed that theoxidation times decrease substantially when Ho3+ is replacedby the larger Dy3+ and even more when substituting 15%Ti4+ on the Mn sublattice. The oxidation of DyMn0.85Ti0.15O3, which showed the fastest kinetics,was completed within only a few seconds at 350 °C in O2 atmosphere. Faster oxidation kinetics were correlated with expansionof the ab-plane caused by the larger ionic radiusof Dy3+ and the Ti4+-doping-induced partialrectification of the tilted MnO5 trigonal bipyramids, whichalso results in a smaller c/a ratio.The change in structure toward the high symmetry P63/mmc phase is also hypothesized toimprove the kinetics of oxygen transport. The changes in lattice parameterswere used to calculate surface exchange rates, which also showed improvementwith larger rare earth cations and with Ti doping.The kinetics of oxidation of nanocrystalline


Electroabsorptionspectroscopy (EA) exploits changes in wave function character of CTstates in response to static electric fields to enhance detectionof CT states via nonlinear optical absorption spectroscopies. A 4 ×4 model Hamiltonian is used to derive splittings of even and odd Frenkel(FR) excited states and changes in wave function character of CT excitedstates in an external electric field. These are used to explain whyFR and CT states yield EA lineshapes which are first and second derivativesof the linear optical absorption spectrum. The model is applied toammonia–borane molecules and pairs of molecules with largeand small B–N separations and CT or FR excited states. EA spectraare obtained from differences in linear optical absorption spectrain the presence or absence of a static electric field and from perturbativesum over states (SOS) configuration interaction singles χ(2) and χ(3) nonlinear susceptibility calculations.Good agreement is found between finite field (FF) and SOS methodsat field strengths similar to those used in EA experiments. EA spectraof three C60/oligothiophene complexes are calculated usingthe SOS method combined with GW/BSE methods. For these C60/oligothiophene complexes, we find several CT states in a narrowenergy range in which charge transfer from the thiophene HOMO levelto several closely spaced C60 acceptor levels yields anEA signal around 10% of the signal from oligothiophene.Creation of charge transfer (CT) states in bulk heterojunctionsystems such as C I5 They are also important in biological systems such as PS II.8 They may be formed following photoexcitation by a photosensitizerand relaxation to a CT state, or they may be created directly by photoabsorption,with a very low absorption cross section. Spectroscopic identificationof CT states at sub-band gap energies remains difficult because ofthe low cross section9 and because thereare other weak absorptions from excitations such as polarons,11 vibrational replicas of the fundamental band, etc. in the same energyrange. Electroabsorption (EA) spectroscopy13 offers a way of enhancing the optical cross section of CT statesrelative to local or Frenkel (FR) excitations by exploiting the largeStark shift of their excited state dipole moments in a static externalelectric field. In EA spectroscopy, changes in the optical absorptionspectrum of a thin film induced by a low frequency applied electricfield are measured. EA can be modeled using the Liptay equation,15 which is a classical approach based on molecular polarizabilityderivatives with respect to external field frequency, or using a quantummechanical sum over states (SOS) nonlinear optical susceptibility.17 The connection between these approaches has been discussed by Saitoand co-workers.18Charge transfer (CT) states,in which the electron and hole ina bound exciton are localized on distinct molecular entities, areimportant intermediate states in creation of carriers in organic photovoltaicsystems.60 complexes. The model is based on a 4 × 4 Hamiltonianwith two FR and two CT excited states.19 EA spectra are commonly fitted to first and second derivative lineshapesof the linear optical absorption spectrum.20 Splittings of FR states induced by the Coulomb interaction in excitedsinglet states and strong changes in wave function character of CTstates induced by an external field are used to explain how firstand second derivative lineshapes arise in EA spectra of model systemsconstructed from ammonia and borane molecules. ΔA(ω) is the change in linear optical absorption spectrum inducedby an external electric field. Calculations of ΔA(ω) are performed for these model systems using FF configurationinteraction singles (CIS) calculations and by the SOS perturbationtheory method. Results from the two approaches are in excellent agreement,validating the use of the SOS approach combined with GW/BSE calculationsto calculate EA spectra for C60/oligothiophene systems.Here we presenta model for EA based on a pair of two level systemswith inversion symmetry, perform finite field (FF) and perturbativesum over states (SOS) calculations for a model ammonia-borane systemto validate the SOS method, and then apply it to EA spectra of oligothiophene-C21 In noncentrosymmetric molecular crystals, an EA signal which islinear in the static electric field may be observed via the linearelectrooptic effect.22 This is governed by a second order χ(2) nonlinearsusceptibility. However, in centrosymmetric or disordered systems,symmetry or averaging over random molecular orientations means thatthe EA signal is governed by a third order, χ(3) susceptibility,21 which is quadratic in the staticelectric field and the linear part vanishes.From a phenomenological viewpoint, changes in polarization inducedby a static external electric field may occur through changes in thepolarizability or via a Stark shift of the excitation energy whenthere is a difference in the dipole moments of the excited and groundstates. The former and latter are generally regarded as the mechanismsby which FR and CT states are observed in EA spectroscopy.24 Reviews by Piliego and Loi,1 Gao andInganäs,2 and Vandewal3 cite direct observation of CT state absorptionand emission by C60 polymer blends. Using electroluminescence(EL) measurements, Tvingstedt and co-workers25 reported EL from poly/phenyl-C61-butyricacid methyl ester (P3HT/PCBM) blends at 1.0 eV and in the range 1.3to 1.4 eV in a poly(p-phenylenevinylene) (PPV)/PCBMblend. Similarly, Faist and co-workers observed emission at 0.89 eVfrom a P3HT/PCBM blend and in the range 0.97 to 1.32 eV in similarpolymer/fullerene blends.9 Veldman andco-workers26 estimated the CT energy inP3HT/PCBM to be 0.99 eV and a range of CT energies in related systemsto lie in the range 1.11 to 2.13 eV. A strong correlation betweenthe energy of the CT state and the open circuit voltage of an organicPV cell made from a particular blend has also been noted.26 Optical signals from sub-band gap states inpolymer–fullerene BHJ systems have been reported at 0.9 eVby photothermal deflection spectroscopy (PDS) in P3HT/PCBM.10 Sanden and co-workers reported peaks in P3HT/PCBMsamples at 0.33, 1.26, and 1.8 eV27 inphotoinduced absorption (PIA) measurements. Signals attributed toCT states in these systems have been observed in EA spectroscopy.29 However, polaron absorption in conjugated polymers also lies inthe range 1.0 to 1.6 eV, where CT states also lie. Polaron opticalabsorption in a conjugated polymer has recently been reinterpreted.11Polythiophene–fullerenesystems are the archetypal donor–acceptorbulk heterojunction (BHJ) organic photovoltaics.60 and similar systemshave been modeled using time-dependent density functional theory (TDDFT)applied to single donor–acceptor pairs.33 We reported EA calculations on tetrathiophene dimers19 and found that the main features arise fromthe main 1Bu1 thiophene FR transitionand the CT state; the former exhibits a first derivative EA line shapeand the latter a second derivative shape. Both are observed in experimenton polycrystalline P3HT.34 Electronic transitionsprobed by optical absorption in C60 in solution37 and in the gas phase38 have been reported,and optical excitations and vibronic interactions in C60 have been analyzed by Negri and co-workers.41 EA spectrafrom C60 thin films have been reported a number of times45 and model Hamiltonian calculations have been used to analyze thesespectra.46 Calculations of two photon absorptionspectra of C60 have also been reported.48CT states in oligothiophene/C3:NH3 adduct anddetails of computational parameters and methods are given in 3:NH3 adduct and its dimerfrom FF and SOS approaches are compared; the linear and nonlinearoptical absorption by gas phase C60 and EA from oligothiophene/C60 systems are presented in 60 systemsare considered in The organization of the remainder of this paper is as follows:the SOS and phenomenological models for EA spectroscopy are outlinedand illustrated using the BHIIII.AA, of a thin film induced by a static external electric field, F, are measured. It can be modeled using the Liptay equation,15fL is a local field factor, F is the quasi-staticelectric field, and A0(ω) is thelinear optical absorption when F = 0 and θ is theangle between the external static and optical frequency electric fields.EAis a spectroscopy in which changes in the linear optical absorptionspectrum, Δ(3),16 withtwo static and one optical frequency input electric fields. The relationshipbetween ΔA(ω) and χ(3) is,18k and n are the optical wavenumber and material refractive index, respectively.The Liptay equation is a classical approach based on first andsecond molecular polarizability derivatives with respect to opticalfield frequency, ω. EA can also be modeled using the imaginarypart of a third order nonlinear susceptibilty, χ18 The Liptay equationis quadratic in the static field. The absence of any linear dependenceon this field arises because macroscopic averages over random molecularorientations in a macroscopic sample result in zero net signal atfirst order in the field.18 However, in a noncentrosymmetriccrystal the leading order response of a sample in an external fieldis the linear electrooptic (or Pockels) effect.17 The linear electrooptic spectrum is obtained from the imaginarypart of,1 = ω, input quasi-static field frequency, ω2, and the resultant polarization frequency, ωσ, satisfy ωσ = ω1 + ω2 ∼ ω, where N is the numberdensity of molecules, ST is a permutation operator which permutes pairs , , in which p, e1, and e2 are unit vectors for the corresponding electric fields.Ωmg is the transition frequencyfor the ground state |g⟩ to excited state |m⟩ minus a small imaginary lifetime factor, iΓ/2. μgm = ⟨g|μ|m⟩ is the transitiondipole moment connecting those states. The overbar on the transitionmoment m = n, i.e., m|μ|n⟩ – ⟨g|μ|g⟩δmn.Saito and co-workers have given a detailed analysis of the correspondenceof these two approaches.17 which describes the EA spectrum18 contains one-photon,σ = ω1 + ω2 + ω3 ∼ ω, The EA spectrum is obtained from the imaginarypart of χ(3), where ω1 = ω is the incident light frequency and ω2 = ω3 ∼ 0, is the quasi-static external fieldfrequency, which has a field strength around 107 V m–1 in experiment. Here ST generates all pairwise permutations of , , , and   spectral lineshapesand the FR or CT character of excited states. We consider the ΔA(ω) spectrum of a pair of BH3 and NH3 molecules that share a common molecular axis, denoted z ((2) susceptibility. Incontrast, the leading nonlinear response of the centrosymmetric systemscontaining dimers shown in (3).In a recent publicationenoted z 1a,b. At enoted z 1b. At laenoted z 1a, howev3–BH3 pairhas occupied σ states composed of local orbitals A and B and unoccupied σ* states composed oforbitals C and D. Linear combinationsof these form the H – 0 (HOMO), H – 1, L + 0 (LUMO) and L + 1 orbitals . Chemist’s notationis used for two-electron integrals (ij|kl), in which orbitals i and j sharethe same electron coordinate and k and l share the other electron coordinate. Diagonal and off-diagonal (ij|ab) two-electron matrix elements havethe following approximate forms,AA|BB)etc. are Coulomb integrals over local orbitals A, B, etc. Transitions in the Hamiltonian are ordered as H – 1 → L + 0, H – 1 → L + 1, H –0 → L + 0, and H –0 → L + 1. Each diagonal element has the same(ij|ab) two electron part and eachnonzero off-diagonal part is the same when intermolecular overlaps⟨A|B⟩ and ⟨C|D⟩ are neglected. The odd/evensymmetry of the molecular wave functions with respect to the centerof inversion means that only four off-diagonal terms in the Hamiltonianare nonzero.19For the model Hamiltonian applied to the ammonia–boranesystem, we assume that each NHorbitals 1. Dimer triplet states. The Hamiltonian for singlet states in this model has theterm 2(ia|jb), in addition to termsin ai–((AA|CC)+(BB|DD))/2 and the degenerate triplet CT state energy is εai–((AA|DD)+(BB|CC))/2. The correspondingwave functions for the first eigenvalue19 are,ai–((AA|DD)+(BB|CC))/219 are,ia|jb) term for singlet states are,A|B⟩ and ⟨C|D⟩ are neglected. The 2(ia|jb) term in the singlet state Hamiltonianincreases the FR2 state energy by 2(AC|BD) and lowers the FR1 state by the same amount. This is the dipole–dipolecoupling of the monomer transition moments. Energies of the CT statesare unchanged by the 2(ia|jb) termin the Hamiltonian equation when overlaps are neglected.The Hamiltonian in F, the interaction Hamiltonianwith a molecular permanent or transition dipole moment, μij, is,E1 and E2 are the energies of pairs of states (FR1 andFR2 or CT1 and CT2) in the absence of the field and μ12 is the dipole transition moment connecting them. Nonzeromatrix elements of – μij.F are,E2 – E1| > |μ12·F|. In contrast, CT states are not split by the Coulomb interactionbut couple strongly to an external field. These conclusions are basedon the assumption of neglect of overlap of wave functions on separatemolecules and pure FR or CT character for the states. Therefore, fora state with strong FR character, large splittings induced by theCoulomb interaction and small splittings induced by an external fieldare expected, while for states with strong CT character, small splittingsinduced by the Coulomb interaction are expected. Large changes inwave function character are also expected for CT states because oftheir small energetic splitting: an external field is expected toinduce strong mixing of the CT1 and CT2 states and thereby induceexcited states with large permanent dipole moments.Inan external field, A(ω) spectral lineshapes for FR and CT states is illustratedin E2 – E1| > |μ12·F| at typical EA experimental field strengths and eigenvectorsfor states of mainly FR character are not stronglymixed by the external field. For states of CT character, there isfull mixing of states. Permanent dipole moments of CT+(F) and CT–(F),The effectof these couplings on excitation energies and ΔWe now consider the implications of these two limitsof interactionof pairs of excited states with an external electric field for theEA spectrum. Changes in the absorption spectrum of a pair of FR oscillatorsare illustrated in The CT2 state 2c has a (2) response is linear in thestatic external field and so averages to zero when a random ensembleof molecular orientations is chosen. Saito and co-workers have presentedorientational averages for the Aθ, Bθ, and Cθ coefficients18 in Cθ coefficient,⟨Cθ⟩, is the mostrelevant,μ| is thechange in permanent dipole moment in an excited state, l, relative to the ground state, g, mgl is a unit vector parallel to the μgl transition dipole moment,and Δm is a unit vector parallel to the excitedstate permanent dipole moment. In the case where there is additionaldipole coupling between excited state, l, and closelyspaced excited state, m, additional terms which replace|Δμ|2 by |μlm|2 and Δm by mlm must be added.18 For the case where θ = 0 (χxxxx(3) or χyyyy(3)) the numerical factor in xxyy(3) or χyyxx(3)) the numericalfactor is 1/5.Molecular configurations used in this section were chosenwithand without inversion symmetry in order to create systems with thefirst nonlinear response at the second or third order in applied fields.In an amorphous BHJ structure inversion symmetry is lacking, however,the χII.CII.C.150 Calculations on ammonia-boranesystems were performed using 6-311G basis sets for B, H and N51 and the CIS method in Exciton. Molecular geometryoptimizations for thiophene and C60 systems were performedwith the B3LYP functional and def2-TZVP basis sets52 using the Gaussian16 code.53 Geometry optimizations with C60 and oligothiophenes includedthe D3BJ dispersion correction in the DFT exchange-correlation functional.54 TDDFT calculations in this work used the Gaussian16code, the ωB97X-D functional56 and def2-TZVPbasis sets. def2-TZVP-RIFIT auxiliary basis sets57 were used for density fitting in GW/BSE calculations inthe Tamm–Dancoff approximation (TDA). GW/BSE calculations onC60 were performed using the aug-cc-pVDZ basis set forC.59 Calculations on thiophene-C60 complexes were performed using smaller, modified def2-TZVP (C) anddef2-SVP (H) and 6-311G* (S) basis sets with some high angular momentumfunctions omitted (Tables S1 to S3) toallow calculations to be performed on large systems. Calculationson C60 were repeated with the modified def2-TZVP basisand excitation frequencies, and linear and nonlinear optical absorptionspectra reproduce well with the smaller basis set . GW/BSE calculations used the following molecularorbital active space ranges: C60 (61 to 697); T6-C60 (175 to 643); T6-C60-T6 (206 to 854); and T10-C60-T10 (423 to 1102). The first 400 excited states were usedin EA spectra calculations. Corresponding cutoff energies for the400th excited state in the three complexes used were 5.7, 6.0, and6.9 eV.The Excitoncode and methods used for GW/BSE calculations in this work have beendescribed elsewhere.II.C.2e or 16e 140 Å from thecoordinate origin on the molecular axis, which yielded electric fieldstrengths of 2.9 × 107 V m–1 or1.2 × 108 V m–1 at the origin. Theformer is comparable to field strengths used in EA experiments. Thelatter is used to demonstrate changes in line shape with field strength,but is probably beyond the range encountered in experiments. The opticalfield is directed along the molecular axis. The static electric fieldresults in splittings of CT state energies of order 50 meV; a linewidth of 40 meV was used in calculating optical absorption spectra.EA spectra were obtained by calculating the optical absorption spectrumusing a CIS method in the presence and absence of this field and subtractingone from the other.Externalelectric fields in FF calculations were generated by placing a chargeof 4II.C.360 from GW@HF/BSE calculationspresented in Optical absorption spectra of C0 arethe interacting and noninteracting particle-hole propagators and K* is the proper interaction kernel. A BSE equation is solvedas an eigenvalue problem in the form,–1. XS and ΛS are eigenvectors and eigenvalues with anindex, S. BSE calculations which use the GW@HF approximationwith screening via the RPA polarizability (Π0 = ΠRPA) overestimate excitation energies in C60 (0 = ΠTDHF), poles of the polarizability shift tolower energy, and BSE excitation energies are underestimated. If thisprocess is iterated once, then stronger screening in ΠTDHF reduces the pole shift to lower energy. Thispolarizability is denoted as ΠscTDHF as it is a partially self-consistent TDHF polarizability. This yieldsbetter agreement than either ΠRPA or ΠTDHF when used in calculatingthe IP-EA gap of C60 and the linear optical absorptionspectrum in a BSE calculation (Sec. III B and III C). Continued iterationof this process would lead to self-consistency in the screened interaction, while retaining HF single-particle eigenvaluesand wave functions in –1.A BSE equation can be represented ass in C60 III.B. IfBSE calculations are summarizedin a – εi, where indices i and a denote occupied and virtual orbitals.The interaction kernel, K*, contains (ia|jb) terms corresponding to electron–holepair hopping. In an HF-TDHF or HF-scTDHF calculation, K* also contains the electron–hole attraction terms, (ij|ab).Matrix elements used in these different approachesto polarizabilityand screening in GW/II.C.460, T6-C60-T6 and T10-C60-T10 complex susceptibilitiesdescribed below were 5.3 × 1026, 3.7 × 1026, and 2.7 × 1026 m–3, respectively,corresponding to a density of approximately 1070 kg m–3, the density of polythiophene. The number density of C60 was 1.4 × 1027 m–3, the densityin bulk C60.60Number densities used for the T6-CIIIIII.AA(ω) calculations for the BH3:NH3 adduct; BH3 and NH3 moleculeswith a BN separation of 5 Å; a pair of BH3:NH3 adducts and a pair of BH3 and NH3 moleculesfrom FF calculations and perturbation theory expressions in A(ω) spectra for BH3 andNH3 molecules separated by 5 Å and a single BH3:NH3 adduct obtained from FF calculations and fromthe χ(2) perturbative expression in 3:NH3 geometry, andwhen the molecules are separated by 5 Å.Results ofΔH – 0 level to the L + 0, L + 2 and L + 10levels. Differences in excited and ground state dipole moments are21.5, 24.9, and 13.1 D, respectively. Each transition has a nonzerotransition dipole moment. Switching to the adduct equilibrium geometry,there are five strong first derivative lineshapes at 10.5, 10.8, 13.3,16.1, and 16.5 eV. Differences in excited and ground state dipolemoments are 2.8, 2.3, 10.1, 3.5, and 0.8 D, respectively. Magnituduesof dipole moment differences are smaller than for CT excitations,as expected.For the latter, there are three strong first derivativelineshapesat 10.1, 12.5, and 15.2 eV. These are NσBσ* CT excitationsmostly from the 3:NH3 adducts has two FR modes in which the transition momentsin either adduct are in phase  or in antiphase. For the mode at 10.5 eV in the adduct,the CIS energies in the adduct pair are 10.4586 and 10.4692 eV. Thetransition dipole moment connecting these states is 6.375 D. Whenan external electric field with strength 2.934 × 107 V m–1 is applied, the −μ12·F interaction energy is 3.89 meV.Diagonalizing the 2 × 2 matrix in A(ω) spectral lineshapeswhich result from this change in static electric field strength areshown in the lower panel of (3) susceptibility in Changes in the optical absorption spectrum of theFR and CT modeswhen an electric field is applied are illustrated in 7 V m–1 the −μ12·F interaction energy is 11.59 meV. Diagonalizingthe 2 × 2 matrix for these CT1 and CT2 states yields energiesof 10.1313 and 10.1545 eV, which compare to 10.1299 and 10.1540 eVfrom the CIS calculation performed in a FF. The eigenvectors are  and . Since the off-diagonal element,11.59 meV, greatly exceeds the difference in diagonal elements, 0.8meV, there is a full rotation of CT1 and CT2 eigenvectors in thiscase to the form given in 7 V m–1 and 1.2 × 108 V m–1. The limitedchange in FF EA spectral line shape is shown in the top panel of For the CT mode at 10.1 eV in the separated molecules,the localoscillator energies are 10.1425 and 10.1433 eV in the absence of anexternal electric field. In a field strength of 2.934 × 10From these results on the ammonia–borane model system, weconclude that there is excellent agreement between FF and perturbativecalculations of second and third order nonlinear responses of asymmetricmonomers and symmetric molecular dimers and that the Hamiltonian in III.B60 from several GW65 and TDDFT66 calculations are available.The experimental IP67 and EA68 values in the gas phase are 7.6 and 2.7 eV,respectively. Single particle HF-scTDHF-GW energy levels and the first11 BSE-TDA excited state energies of gas phase C60 areshown in g, from various GW and TDDFT methods are compared to experiments in tg1, tu1, hu, hg, and gg irreducible representationsof the Ih, icosahedralpoint group. The hu HOMOand tu1 LUMO levels fromthe GW calculation with HF-RPA screening are at −7.35 and −1.82eV with a gap of 5.43 eV. Using HF-scTDHF screening instead in theGW calculation, these levels are at −6.95 and −2.26eV with a gap of 4.69 eV. A TD-ωB97X-D calculation yields avalue, 5.44 eV, similar to that of GW@HF with RPA screening. Thesevalues compare to the experimental Eg of 4.9 eV. The former overestimates the gap by 10.8%,and the latter underestimates it by 4.3%.Predictions of the IP and EA of gas phaseC39 and GW/BSE and TD-ωB97X-D calculations(this work), scGW/BSE61 and TD-BP9869 results arecompared to experimental optical transition data in 1Tu1 level at 3.04 eV and three stronger absorptions at 3.78, 4.84,and 5.88 eV  and two1Tg2 state to be thelowest singlet excited state and to lie just below the 1Tg1 state, in contrastto the reanalysis of experimental data mentioned above.40 These methods predict the same ordering forthe first 9 excited states and good overall agreement in energies predict the energiesIII. scGW60 have mostly focusedon the optically active n1Tu1 states. These are compared in the bottom part of 1Tu1 states in the range of 3.36 to 6.27 eV. CNDO/S states for whichthere is a large oscillator strength from the ground state are inbold in 1Tu1 excited states on the basis of comparisonto results of CNDO/S calculations.39 Experimentshows strong transitions at 3.78, 4.84, and 5.88 eV35,36 in n-hexane  susceptibilities for C60. Susceptibilities in 60  expression in 3 and a magnitude of 9.0× 10–19 m2 V–1, of the order of intensities of lines in –21 m2 V–1.17First of all, we consider overall magnitudes of χes in 60 II.C.4 is60 inthe gas phase Ih pointgroup symmetry lie about 1 eV above the S1 excited state ((3) susceptibilityin 1Ag ground state.In the Ih point group,Cartesian monomials x, y and z transform according to the Tu1 ireducible representation (irrep). The only directproduct with Tu1 whichincludes Ag in the resultingdirect sum is Tu1 itself,Tu1 states are dipole coupled to the groundstate, intermediate states in the 2ph terms in Ag, Tg1, or Hg irreps in the absence of higher order couplingsand the intermediate states in the 1ph terms in Tu1. As expected, χph1(3) shows negative, first derivative lines, which are expected to varyin intensity as the square of intensity of the linear optical absorptionintensity, owing to dependence on the same dipole matrix elements.Analysis of χph2(3) also depends on dipole coupling between Tu1 excited states and Ag, Tg1, and Hg excited states, as noted above. Strong second order resonances canoccur when there is a state belonging to one of these irreps closein energy to a Tu1 state.The lowest dipole allowed excitations in Ced state III. InteIII.D(1), χ(2), and χ(3) linear and nonlinear optical absorptioncalculations were performed for a sexithiophene-C60 complex,T6-C60. Linear absorption and χ(3) calculationswere performed for similar complexes with two sexithiophenes (T6-C60-T6) and two decathiophenes (T10-C60-T10), eachusing the HF-scTDHF-BSE methods described in χTables S7 to S9. TD-ωB97X-D calculationsof CT excitedstate energies were also performed for the T6-C60-T6 andT10-C60-T10 complexes. CT and thiophene oligomer and infinitepolymer chain excited state energies are compared in Coordinates of the complexes are available in 60 local excitons. They lie in ranges1.74 to 1.85 (T6-C60), 1.64 to 1.83 (T6-C60-T6)and 1.83 to 2.00 eV (T10-C60-T10). These values compareto the 1Tg2, 1Tu1 and 1Gg excited stateenergies (1.63 to 1.66 eV) in C60 . Transition moments connecting the groundstate to the CT states at 1.92 and 1.94 eV are parallel to the y (charge transfer) direction and the transition momentto the state at 1.97 eV is parallel to the x direction(thiophene chain) direction. Low energy CT excited states and χ(3) spectra for the two complexes with two oligothiophene strandsbound to C60 are similar to those in T6-C60 withthe addition of transitions from both the H –0 and H – 1 levels. For T6-C60-T6there are four states at 1.98, 2.00, 2.01, and 2.03 eV which are predominantly H – 0 and H – 1 to L + 0 and L + 2. Transition moments tothese states are parallel to y. There are three furtherCT states at 2.05, 2.06, and 2.09 eV which are predominantly H – 0 and H – 1 to L + 1 and transition moments to these states are parallelto x. For T10-C60-T10, the pattern isthe same as that for T6-C60-T6. Excitation energies anddipole matrix elements between states are given in Table S4. Multiple states in a small energy range can leadto nonadiabatic effects,41 but this is beyondthe scope of the present work.For each complex, the first 10 excited states fromHF-scTDHF-BSEare intramolecular C) in C60 III. In T60-T6 and the first12 excited states of T10-C60-T10 in the TD-ωB97X-Dcalculations are CT states. In T10-C60-T10 they are groupedin sixes as transitions from H-0 and H-1 to L+0, L+1 and L+2 (1.15to 1.23 eV) and from H-2 and H-3 to L+0, L+1 and L+2 (1.49 to 1.63eV).The first nine excited statesof T6-CscTDHF – GW/BSE calculations compare to a CT excitedstate energy of 1.69 eV from a GW/BSE calculationon a T10-C60 complex32 and 0.99eV from an estimate based on comparisons of experimental data26 or 1.05 eV in electroluminescence in a P3HT:PCBMblend.25 Omission of screening from theenvironment surrounding the complex and limited basis sets contributeto the difference in predicted CT energies and experiment. However,conclusions regarding the observability of CT states in these systemsusing EA spectroscopy are expected to remain valid as long as relativeintensities of features from the oligothiophene and CT states andposition of the CT state below the main thiophene absorption are correct.Values of CT excited state energies from xxy, yxx, and yyy elements of χ(2) and xxxx and yyyy elements of χ(3) susceptibilities for a single T6 oligomer bound to C60 with C2 symmetry areshown in yyy(2) spectrum, which has an intensity about 10%of the intensity of the signal from T6 in χxxy(2) at 2.88eV, compared to about 1% in the linear absorption spectrum (yyyy(3) spectrum has a second derivative line shape at the CT energy (1.92eV), which has an intensity about 50% of the T6 peak at 2.88 eV. Inthis case, the static and optical frequency fields are parallel. Linearand χ(3) spectra for T6-C60-T6 and T10-C60-T10 and additional elements of the χ(3) spectrum of T6-C60 are shown in Figures S2 to S4. Similar features are observed for each complex: Thelinear absorption spectrum is dominated by the main thiophene absorptionaround 2.8 eV (x (thiophene chain)direction and an isotropic absorption at 4.8 eV from C60. One-photon χ(3) spectra are dominated by the xxxx element at the main thiophene absorption energy, asexpected. The χxxyy(3) and χyyxx(3) one- and two-photonspectra have little intensity at the CT energy .Linear absorption and spectrum 9. The χyd 2.8 eV IV polari(3) spectra for thethree complexesstudied in the CT excited state energy range are shown in yyxx and yyyy elements of χ(3) at 1.93 eV and first and second derivative features in the xxxx and xxyy elements of χ(3) at 1.98 eV for T6-C60. The second derivative yyyy line shape is dominant.Two-photon χTables S4 to S6. For T6-C60 this shows large permanent moments for eachCT excited state and weak couplings between the excited states. Thepattern of zero and nonzero dipole matrix elements shows that thefirst two CT states belong to the A (even) irrepand the third belongs to the B (odd) irrep with respectto C2 rotations about the y axis. Bothof these contribute to the strong yyyy second derivativeline shape at 1.93 eV, which is approximately 10 times stronger thanthe xxyy line at 1.97 eV.Dipole couplings between the ground and CT excitedstates and betweenCT excited states are given in 60-T6 and T10-C60-T10complexes, the number of low energyCT states increases from three to seven. The pattern of dipole couplingsbetween the ground and excited states is similar to the T6-C60 complex, but there are additional strong off-diagonal dipole couplingsbetween excited states 1 and 3 and 2 and 4 in T6-C60-T6(Table S5) and between states 1 and 2 and3 and 4 in T10-C60-T10 (Table S6). This leads to increases in the intensity of the xxyy χ(3) element relative to yyyy in T6-C60-T6 and in T10-C60-T10 xxyy isthe dominant element, by a factor of 5. Thus, χ(3) matrix elements are sensitive tothe molecular structure in oligothiophene/C60 complexes.Furthermore, the strength of the signal from a CT state in a thiophene-C60 complex increases relative to the main thiophene linearoptical absorption peak on going from χ(1) to χ(2) by a factor of 10 or so and by a factor of 50 on goingto the χ(3) response. EA spectroscopy therefore offersa means of significantly enhancing relative strengths of optical absorptionsignals which are weak in linear spectroscopies.When second oligothiophenesare introduced in the T6-CIVIV.A1 Gao and Inganäs,2 and Vandewal3 citedirect observation of CT state absorption and emission by C60 polymer blends. The kinetics of CT excited state dissociation intofree carriers in bilayer devices consisting of C60 andtrimethine cyanine dye (Cy3-P) have been measured in an external fieldof 5 × 107V m–1 by Devižisand co-workers29 using a dynamic EA spectroscopytechnique. Here the dissociation was inferred by monitoring the EAspectrum in the range 400 to 650 nm (3.1 to 1.9 eV) and it was assumedthat free carrier generation screened the external, static electricfield, resulting in a reduction of the measured EA spectral intensity.The lowest energy EA feature in the pure Cy3-P spectrum just above2 eV was also found in the C60 bilayer device but no newfeature in the bilayer device which might be attributed to a CT stateis clearly evident. As noted above, CT states in conjugated polymersystems containing C60 derivatives26 typically lie in the range 1.0 to 1.6 eV.Reviews by Piliego and Loi,10As shown in IV.B3:NH3 molecules, gas phase C60 and three thiophene-C60 complexes.We have investigated prospectsfor spectroscopic identification of CT excited states in the sub-bandgap region of thiophene–fullerene BHJ systems using CIS, GW/BSEand TD-ωB97X-D calculations on a model system consisting ofpairs of BH3:NH3 and BH3:NH3 dimers as adducts and separated molecules were used to demonstrateexcellent agreement between finite field calculations of the changein absorption spectrum, ΔA(ω), and imaginaryparts of the second and third order sum over states perturbation theoryexpressions of Orr and Ward.16 This isimportant for establishing confidence in the results of perturbativecalculations when applied to larger systems where convergence offinite field calculations to the required precision is difficult.A single BH3:NH3 molecular pair lacks inversionsymmetry, and the leading nonlinear response is at second order. Shiftsin transition energies and absorption intensities are very well reproducedby a 2 × 2 model Hamiltonian applied to the centrosymmetric casesin which excited state transition energies are on the diagonal, and−μ12·F dipolarcoupling between excited states and an external electric field arethe off-diagonal elements. Typically one state is optically brightand one is dark. When the magnitude of the off-diagonal matrix elementexceeds the difference in bright and dark state transition energiesthe new eigenstates mix the bright and dark states, resulting in twooptically active lines and an overall second derivative line shapefor the change in optical absorption.CIScalculations on BH60 were calculated usingGW/BSE with a SCF HF starting point and TD-ωB97X-D. When screeningin the BSE calculations on C60 was introduced using a screenedinteraction based on an RPA polarizability, optical absorption energiesare considerably overestimated, and relative intensities of severalpeaks in experiment are not reproduced. TD-ωB97X-D yielded excitation energies similar to those in the GW/BSE calculation withthe RPA polarizability. However, when a partly self-consistent polarizabilitydenoted scTDHF which includes ladder terms is used instead, thereis much better agreement with experiment for both optical absorptionenergies and relative intensities. GW/BSE excited state energies andwave functions from this method are used to calculate χ(3) for gas phase C60.Optical absorption spectrafor C60 complexes usingGW/BSE and scTDHF polarizability. In eachcase, these calculations predict several CT excited state energieswhich cluster together in a narrow energy range. The origin of thisclose spacing of excited states and dipole coupling is excitationfrom the thiophene HOMO level into the LUMO, LUMO+1 and LUMO+2 levels.It is concluded that EA spectroscopy on conjugated polymer–fullerenesystems could be used to identify energies of CT excited states inBHJ devices.Finally, GW/BSE calculationswere performed for three thiophene-C


This is only the second crystal structure report on a ClSeO2− salt. The structure contains an extended planar hydrogen bond net, including a double interaction with both O atoms of the anion (an 2− leads to an elongation of this bond. A good match to a known value for [Me4N][ClSeO2] is found, which fits to the Raman spectroscopic evidence for this long-known salt and to data measured on solutions of the anion in CH3CN. The assignment of the experimental Raman spectrum was corrected by means of the DFT-computed vibrational spectrum, confirming the strong mixing of the symmetry coordinate of the Se–Cl stretch with both ν2 and ν4 modes.The single-crystal X-ray diffraction structure characterizing a new 4-methylbenzamidinium salt of chloroselenite [C This structure is most consistent with type A in d(Se–Cl) = 2.453(1); d(Se–O) = 1.632(2) Å [10H9N2][ClSeO2] is indexed in Chemical Abstracts (Registry number [27380-14-9]), but its crystal structure is apparently only available in an unpublished thesis [ClSeO2] was noteworthy for having anisotropic shielding of >1000 ppm [− ions and SeO2 in several aprotic solvents was originally established using UV-vis absorption spectroscopy [2 in either dilute or concentrated HCl has been attested [2] despite reported attempts to obtain these  number 2380-14-9)632(2) Å H9N2[ClSeattested . Similarin these .n clusters have been evaluated for similar motivations [2 rotational lines remain of interest for astronomic detection [2 itself has also been identified as having electrostatic ‘π-holes’ [2]− . New attention to the higher oxochloroselenates, after a long hiatus, is bearing fruit with the report of an inclusion compound of Cl2 in a tetramethylamino salt of [Se2O2Cl7]3− −, more feasible than ever before.The nature and scope of weak chemical bonds has become a major focus of research in recent years . Chlorosivations  and fundetection ,17,18. Setection ,21,22,23π-holes’ , which mO2Cl7]3− , which hO2Cl7]3− . The theO2Cl7]3− . Less isructural ,29,30 anructural . The app2]− salts, all of which so far are from single-crystal X-ray diffraction (SC-XRD) data. Since the literature is very scattered, the current state of knowledge is briefly reviewed. FSO2− salts are the best represented, with nine known structures, consistent with the accepted wisdom that this is the most stable member of its class  [2− was the first reported structure (CSD refcode: LIHWAA) but it suffers from serious F/O positional disorder [2], Rb[FSO2] [2F] [2N)3S]+, [(Me2N)3SO]+ and [(Me4N)4N]+ salts    and the O2] [2F] . The recctively) . The str2−, ion structures are in the CSD. The oldest structure  containe XEGCAQ  was repo, KIGZEF  and LAQY, KIGZEF , which c, LAYTUC  and by [yed by EtN[BrSO2],, BIRHUF .2− salts, and these are the most structurally diverse of all. The [Ph3PBz]+ salt BZTPPI 2 and all the H-bond parameters fit for standard electrostatic-covalent H-bonding according to the criteria of Jeffrey  2.852(3) and 2.948(3) Å] and even shorter links to the next amidinium ions on both sides in the net [d(D∙∙∙A) 2.852(3) and 2.880(4) Å]. The H-bond acceptor sites at O correspond to negative charge maxima on the computed electrostatic potential surface , which K[FSeO2] . However2  to the bridging Cl∙∙∙Se contacts in the chain structure of [Me4N][ClSeO2] . Other BIRHAL10 ); [NEt4]: BORCAM ); : EWILOO ); [ClSeO2] [OSeCl4]  where t: DPRYSE ) where t4N][ClSeO2] was one of the very salts originally investigated by Milne using Raman spectroscopy [ClSeO2] . In the4 has been described previously [General synthetic methods for thiazyl and selenazyl chemistry are as previously described ,66. The eviously .10H8Cl5N3Se, was exposed to 10 mL of CH2Cl2 and 10 mL of CH3CN and heated in an attempted purification by recrystallization. Upon removing all volatiles, 30 mL of CH3CN was added and the mixture was heated to reflux, ensuring all solids were dissolved, and then filtered hot under nitrogen. After cooling, the filtrate was placed in a −10 °C freezer overnight, producing small amounts of solids which were removed by a second filtration. Subsequent cooling of the filtrate in a −30 °C freezer overnight produced well-formed colorless crystals, which were quickly isolated, dried under high vacuum, and submitted for crystallographic study.Initially, 0.26 g of selenium(IV)-4-NH-dichloroselenatriazine, C2 were collected on a Bruker Platform/SMART 1000 CCD diffractometer at the University of Alberta. Image collection, peak identification, cell and space group determination were controlled using SAINT. Multi-scan absorption correction was undertaken using SADABS. Initial structure solution was performed with SHELXS [Suitable crystals were selected under a microscope, mounted on fine glass capillaries in Paratone™ oil, and cooled using the diffractometer cooling wand. Crystal and refinement data are summarized in h SHELXS . In viewh SHELXS  within th SHELXS . After ah SHELXS . A detaih SHELXS .2, HAR/NoSpherA2 quickly proved to be very successful. The electron density (ED) of each atom was computed using ORCA 5.0 [Rint = 3.28%), the data were obtained on an older sealed-tube diffractometer where the resolution was capped at 0.80 Å. This is probably the origin of the two ghost peaks for the Se atom (Fourier ripples), hindering the overall refinement quality. Hence, in the final refinement cycles the aromatic C-H, distances were restrained to 1.085 Å and N-H distances to 1.040 Å, which are the current best values from neutron refinement in this temperature range [3 group, and the occupancies were frozen in a 50:50 ratio. This structure is not intended for validating the performance of the HAR/NoSpherA2 method : monoclinic, space group P21/c (no. 14), a = 3.9773(3) Å, b = 28.477(2) Å, c = 9.5781(9) Å, β = 91.242(1)°, V = 1084.56(16) Å3, Z = 4, T = 193.15 K, μ(Mo Kα) = 3.685 mm−1, calcD = 1.725 g/cm3, 8245 reflections measured (4.48° ≤ 2θ ≤ 52.84°), 2194 unique  which were used in all calculations. The final R1 was 0.0339 (I ≥ 2σ(I)) and wR2 was 0.0827 . CCDC 2301348.Crystal Data for C2 (gas-phase structure), for which, see Initial geometries for the DFT calculations were obtained from the X-ray coordinates (ignoring the second component of the toluene methyl group disorder). All calculations were performed with Gaussian W16 under GUI control from GaussView 6.0 and were run on an AMD Ryzen Threadripper 16-core 3.75 GHz PC under Windows 10 [2− ions by the characteristic H-bonding from benzamidinium cations. This discovery could have major benefits for isolating stable salts of other halochalcogenite(IV) salts. For example, selectivity of the H-bonding for O is considered likely, which may help prevent O/F positional disorder in FChO2− salts. These cations may also lead to success in obtaining crystalline adducts for the many X/Ch combinations for which there are no SC-XRD data. This work also emphasizes a point, made previously by others, that work in this area should use multiple, mutually integrated, techniques. For example, vibrational spectroscopy, when fully interpreted by adequate levels of computation, should be feasible on the proposed benzamidinium salts, enhancing the reliability of salt characterization and enabling direct comparisons, especially with Raman spectroscopy, to the structures adopted by these ions in solutions. Additionally, 77Se NMR may become invaluable for characterizing the formation of haloselenite ions in solution.The evidence from this paper is that significant Cl–Se bond shortening is induced in ClSeO