Accurate Electron Density Research Articles

Electron density estimation using MPPC-based photon-counting CT for radiation therapy planning

Photon-counting computed tomography (PCCT) has been attracting attention recently, as a potential alternative to the conventional computed tomography (CT). With PCCT, the photon energy can be obtained, and the amount of exposure can be reduced compared with the conventional CT. We developed a detector system composed of a scintillator and multi-pixel photon counter (MPPC). This makes the system simple and inexpensive compared with the semiconductor-based PCCT, like CdTe and CZT. In this study, we propose estimating electron density for radiation therapy planning using a six-threshold MPPC-based photon-counting detector. Electron density is an essential information for determining beam energy in radiation therapy planning. Therefore, accurate electron density estimation is required. The estimation method used in this study is based on the method proposed by Saito et al. (2012) PCCT images of electron-density-known phantoms were acquired, and information of the two out of the six energy bands was used for estimation. As a result, we succeeded in estimating the electron density with an accuracy of 4.59% root-mean-square error. However, the lung phantoms, which had a relatively low electron density, still had a large deviation from the true value. In addition, dual-energy CT and PCCT estimation results were compared. PCCT results has not yet surpassed the accuracy of dual-energy CT (DECT) results; however, the high electron density materials were obtained almost at the same level of accuracy. In future, we will continue to work on more accurate electron density estimation using multiple energy band information.

MV-based relative electron density estimation (iMREDe) for MR-LINAC dose calculation.

MR-LINAC systems have been increasingly utilized for real-time imaging in adaptive treatments worldwide. Challenges in MR representation of air cavities and subsequent estimation of electron density maps impede planning efficiency and may lead to dose calculation uncertainties. To demonstrate the generation of accurate electron density maps using the primary MV beam with a flat-panel imager. The ViewRay MRIdian MR-LINAC system was modeled digitally for Monte Carlo simulations. Iron shimming, the magnetic field, and the proposed flat panel detector were included in the model. The effect of the magnetic field on the detector response was investigated. Acquisition of projections over 360 degrees was simulated for digital phantoms of the Catphan 505 phantom and a patient treated for Head and Neck cancer. Shim patterns on the projections were removed and detector noise linearity was assessed. Electron density maps were generated for the digital patient phantom using the flat-panel detector and compared with actual treatment planning CT generated electron density maps of the same patient. The effect of the magnetic field on the detector point-spread function (PSF) was found to be substantial for field strengths above 50 mT. Shims correction in the projection images using air normalization and in-painting effectively removed reconstruction artifacts without affecting noise linearity. The relative difference between reconstructed electron density maps from the proposed method and electron density maps generated from the treatment planning CT was 11% on average along all slices included in the iMREDe reconstruction. The proposed iMREDe technique demonstrated the feasibility of generating accurate electron densities for the ViewRay MRIdian MR-LINAC system with a flat-panel imager and the primary MV beam. This work is a step towards reducing the time and effort required for adaptive radiotherapy in the current ViewRay MR-LINAC systems.

Accurate determination of plasma temperature and electron density using a reference target: one-point calibration LIBS elemental analysis ofalloy samples.

Elemental analysis of aluminum alloy samples with calibration-free laser-induced breakdown spectroscopy (CF-LIBS) encounters two difficulties: the inconvenience of determining accurate temperature and electron density of the plasma and the influence of self-absorption of the observed aluminum lines. To solve this problem, target-enhanced orthogonal double-pulse laser-induced breakdown spectroscopy in the reheating regime combined with the one-point calibration method was proposed in this work. A mixture of copper powders and K H C O 3 grains was pressed to a pellet and used as the target. Accurate determination of plasma temperature and electron density can be obtained using a reference target. The plasma temperature could be determined with Saha-Boltzmann plot of copper, and the electron density of the plasma could be determined according to the Stark broadening of the H α line of hydrogen. Aluminum alloy samples were analyzed with a relative error of better than 0.02% for a major element. This approach provides a convenient way to determine the temperature and electron density of the plasma more accurately and is able to reduce the influence of self-absorption, which is helpful for realizing quantitative elemental analysis of different samples while using a calibration-free algorithm.

Accuracy of Electron Density Mapping of a Novel kVCBCT System Designed for Planning

A recently developed advanced kVCBCT system, designed for simulation and planning, includes improvements to the imaging panel and reconstruction technique, enabling more accurate electron density mapping than a typical CBCT. This study investigates the accuracy, limitations, and dosimetric impact of this new system. CBCT images were taken of both large (pelvis) and small (head) electron density phantoms with inserts ranging from lung (0.29) to cortical bone (1.69). Images were taken with several pre-set protocols with energies of 125 kVp and 140 kVp. The effects of longitudinal buildup (for scatter due to the cone-beam geometry) and blade position were also investigated. The HU values of each insert were measured over a small region of interest. Several electron density curves were generated - pelvis protocol on the large phantom, head protocol on the small phantom, and average - and imported into a treatment planning system. Dose calculation was performed using each curve and differences were observed. HU to electron density mapping was sensitive to the use of longitudinal buildup and blade position, with differences in the curves observed at both low and high electron densities, due to imager saturation effects not found in typical clinical scenarios. Subsequent studies used both longitudinal buildup and fully opened blades. Under these conditions, mapping was not sensitive to technique or phantom size at low electron densities. At higher values, the curves diverged, with the head protocol showing higher HU values and the pelvis protocol showing lower. The average curve matched very closely with the curve from our standard CT simulator. Dose calculation showed little dependence on the curve chosen, with max point dose differences of 1.2% between the pelvis and average scans, though most of the plan was <0.5% different. Results for the head protocol were similar. The system provides reliable HU values comparable to a CT simulator, though it is important to consider the effects of imager saturation by choosing appropriate scatter and collimation. The calibration is slightly sensitive to the choice of phantom size and beam energy, though these differences led to negligible (<0.5%) differences in dose calculation accuracy.

Impact of a novel multilayer imager on metal artifacts in MV-CBCT

Objective. Megavoltage cone-beam computed tomography (MV-CBCT) imaging offers several advantages including reduced metal artifacts and accurate electron density mapping for adaptive or emergent situations. However, MV-CBCT imaging is limited by the poor efficiency of current detectors. Here we examine a new MV imager and compare CBCT reconstructions under clinically relevant scenarios. Approach. A multilayer imager (MLI), consisting of four vertically stacked standard flat-panel imagers, was mounted to a clinical linear accelerator. A custom anthropomorphic pelvis phantom with replaceable femoral heads was imaged using MV-CBCT and kilovoltage CBCT (kV-CBCT). Bone, aluminum, and titanium were used as femoral head inserts. 8 MU 2.5 MV scans were acquired for all four layers and (as reference) the top layer. Prostate and bladder were contoured on a reference CT and transferred to the other scans after rigid registration, from which the structural similarity index measure (SSIM) was calculated. Prostate and bladder were also contoured on CBCT scans without guidance, and Dice coefficients were compared to CT contours. Main results. kV-CBCT demonstrated the highest SSIMs with bone inserts (prostate: 0.86, bladder: 0.94) and lowest with titanium inserts (0.32, 0.37). Four-layer MV-CBCT SSIMs were preserved with bone (0.75, 0.80) as compared to titanium (0.67, 0.74), outperforming kV-CBCT when metal is present. One-layer MV-CBCT consistently underperformed four-layer results across all phantom configurations. Unilateral titanium inserts and bilateral aluminum insert results fell between the bone and bilateral titanium results. Dice coefficients trended similarly, with four-layer MV-CBCT reducing metal artifact impact relative to KV-CBCT to provide better soft-tissue identification. Significance. MV-CBCT with a four-layer MLI showed improvement over single-layer MV scans, approaching kV-CBCT quality for soft-tissue contrast. In the presence of artifact-producing metal implants, four-layer MV-CBCT scans outperformed kV-CBCT by eliminating artifacts and single-layer MV-CBCT by reducing noise. MV-CBCT with a novel multi-layer imager may be a valuable alternative to kV-CBCT, particularly in the presence of metal.

Combined analysis of laser interferometer and microwave reflectometer for a consistent electron density profile on HL-2A

In order to acquire a consistent and accurate electron density profile for HL-2A tokamak, a combined analysis of the laser interferometer and microwave reflectometer based on the mapping of density profiles to a common equilibrium magnetic coordinate has been proposed. In this approach, the edge density profile measured locally by microwave reflectometer is taken as a supplementary boundary condition in the procedure of inverting line-integrated data from interferometer diagnostic. The density profile inside that boundary is reconstructed by a Gaussian Process Tomography (GPT) method [1] within the Bayesian framework, by which the uncertainty of the result can be quantified via the confidence interval of a posterior probability. In the simulation benchmark, two representative cases of density distribution with different profile shapes, e.g. peaked and flat, are tested and the factors that may affect the accuracy of the results are investigated, providing a useful reference for practical applications. The application of this approach to actual data proves its ability to resolve the dynamic evolution of density profiles. Specifically, the effect of Electron Cyclotron Resonance Heating (ECRH) on electron particle transport observed in HL-2A experiments has been confirmed. The combined analysis approach developed is expected to provide a robust means to study the confinement performance and particle transport on HL-2A, with the focus on the core region.

Machine Learning Electron Density Prediction Using Weighted Smooth Overlap of Atomic Positions.

Having access to accurate electron densities in chemical systems, especially for dynamical systems involving chemical reactions, ion transport, and other charge transfer processes, is crucial for numerous applications in materials chemistry. Traditional methods for computationally predicting electron density data for such systems include quantum mechanical (QM) techniques, such as density functional theory. However, poor scaling of these QM methods restricts their use to relatively small system sizes and short dynamic time scales. To overcome this limitation, we have developed a deep neural network machine learning formalism, which we call deep charge density prediction (DeepCDP), for predicting charge densities by only using atomic positions for molecules and condensed phase (periodic) systems. Our method uses the weighted smooth overlap of atomic positions to fingerprint environments on a grid-point basis and map it to electron density data generated from QM simulations. We trained models for bulk systems of copper, LiF, and silicon; for a molecular system, water; and for two-dimensional charged and uncharged systems, hydroxyl-functionalized graphane, with and without an added proton. We showed that DeepCDP achieves prediction R2 values greater than 0.99 and mean squared error values on the order of 10-5e2 Å-6 for most systems. DeepCDP scales linearly with system size, is highly parallelizable, and is capable of accurately predicting the excess charge in protonated hydroxyl-functionalized graphane. We demonstrate how DeepCDP can be used to accurately track the location of charges (protons) by computing electron densities at a few selected grid points in the materials, thus significantly reducing the computational cost. We also show that our models can be transferable, allowing prediction of electron densities for systems on which it has not been trained but that contain a subset of atomic species on which it has been trained. Our approach can be used to develop models that span different chemical systems and train them for the study of large-scale charge transport and chemical reactions.

Phase jump detection and correction based on the support vector machine

In general, interferometers are used to perform electron density measurements in magnetically confined plasma, where the electron density is dependent on the refractive index of the plasma. Measurements can be made through comparisons of the phase shift variation between the probe and reference laser beam. The plasma electron density should vary continuously during discharge; however, the fringe jump is a step-like change of the apparent electron density caused by a sudden jump of the measured phase shift. The appearance of fringe jump will degrade the interferometric measurements accuracy. This study attempted to solve the fringe jump problem on the polarimeter-interferometer (POINT) diagnostics system of the Experiment Advanced Superconducting Tokamak (EAST) by proposing a support vector machine model for electron density fringe jump detection and correction. The established model can efficiently classify the fringe jump data from the raw measurement data in a manner robust to noise and interference, and subsequently correct the jump. This model greatly improves the correction efficiency and precision of electron density data from the POINT system, and is expected to be embedded into the plasma control system to perform more accurate real-time electron density feedback control. Moreover, the algorithm is not limited to specific fusion devices or interferometer diagnostics, and is applicable to other interferometric measurement systems.

A recipe for cracking the quantum scaling limit with machine learned electron densities

A long-standing goal of science is to accurately simulate large molecular systems using quantum mechanics. The poor scaling of current quantum chemistry algorithms on classical computers, however, imposes an effective limit of about a few dozen atoms on traditional electronic structure calculations. We present a machine learning (ML) method to break through this scaling limit for electron densities. We show that Euclidean neural networks can be trained to predict molecular electron densities from limited data. By learning the electron density, the model can be trained on small systems and make accurate predictions on large ones. In the context of water clusters, we show that an ML model trained on clusters of just 12 molecules contains all the information needed to make accurate electron density predictions on cluster sizes of 50 or more, beyond the scaling limit of current quantum chemistry methods.

Predicting accurate ab initio DNA electron densities with equivariant neural networks

One of the fundamental limitations of accurately modeling biomolecules like DNA is the inability to perform quantum chemistry calculations on large molecular structures. We present a machine learning model based on an equivariant Euclidean neural network framework to obtain accurate ab initio electron densities for arbitrary DNA structures that are much too large for conventional quantum methods. The model is trained on representative B-DNA basepair steps that capture both base pairing and base stacking interactions. The model produces accurate electron densities for arbitrary B-DNA structures with typical errors of less than 1%. Crucially, the error does not increase with system size, which suggests that the model can extrapolate to large DNA structures with negligible loss of accuracy. The model also generalizes reasonably to other DNA structural motifs such as the A- and Z-DNA forms, despite being trained on only B-DNA configurations. The model is used to calculate electron densities of several large-scale DNA structures, and we show that the computational scaling for this model is essentially linear. We also show that this machine learning electron density model can be used to calculate accurate electrostatic potentials for DNA. These electrostatic potentials produce more accurate results compared with classical force fields and do not show the usual deficiencies at short range.

How Good Is the Density-Corrected SCAN Functional for Neutral and Ionic Aqueous Systems, and What Is So Right about the Hartree-Fock Density?

Density functional theory (DFT) is the most widely used electronic structure method, due to its simplicity and cost effectiveness. The accuracy of a DFT calculation depends not only on the choice of the density functional approximation (DFA) adopted but also on the electron density produced by the DFA. SCAN is a modern functional that satisfies all known constraints for meta-GGA functionals. The density-driven errors, defined as energy errors arising from errors of the self-consistent DFA electron density, can hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree-Fock level of theory due to its relatively low computational cost. In this work, we present extensive calculations aimed at determining the accuracy of the DC-SCAN functional for various aqueous systems. DC-SCAN (SCAN@HF) shows remarkable consistency in reproducing reference data obtained at the coupled cluster level of theory, with minimal loss of accuracy. Density-driven errors in the description of ionic aqueous clusters are thoroughly investigated. By comparison with the orbital-optimized CCD density in the water dimer, we find that the self-consistent SCAN density transfers a spurious fraction of an electron across the hydrogen bond to the hydrogen atom (H*, covalently bound to the donor oxygen atom) from the acceptor (OA) and donor (OD) oxygen atoms, while HF makes a much smaller spurious transfer in the opposite direction, consistent with DC-SCAN (SCAN@HF) reduction of SCAN overbinding due to delocalization error. While LDA seems to be the conventional extreme of density delocalization error, and HF the conventional extreme of (usually much smaller) density localization error, these two densities do not quite yield the conventional range of density-driven error in energy differences. Finally, comparisons of the DC-SCAN results with those obtained with the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method show that DC-SCAN represents a more accurate approach to reducing density-driven errors in SCAN calculations of ionic aqueous clusters. While the HF density is superior to that of SCAN for noncompact water clusters, the opposite is true for the compact water molecule with exactly 10 electrons.

Measurement on electron density of high-power and large-volume ICP-heated wind tunnel with HCN laser interferometer

This paper explains the physical behavior of the electron density of high-power and large-volume plasma wind tunnel using a single channel hydrogen cyanide (HCN) laser interferometer. Based on the characteristics of inductively coupled plasma (ICP)-heated wind tunnel, the temperature and pressure distribution of the ICP-heated wind tunnel are obtained from numerical simulations, during which the influence of neutral particles is considered to calculate the accurate electron density. The typical electron density order of ICP-heated wind tunnel is 1018m−3. We discovered that there is a positive correlation between the electron density of argon plasma jet and mass flow rate, while that of air plasma jet decreases slightly. We also found that the peak of electron density appears when the argon is switched to air. Within the voltage range of 6–10 kV, the electron density of argon and air plasma increases slowly. However, when the voltage increases from 10 to 12 kV, the electron density of air plasma increases sharply with the mass flow rate of 15 g/s. Finally, the electron density of argon plasma is much higher than that of air plasma at the same mass flow rate and voltage.

Monitoring Space Weather: Using Automated, Accurate Neural Network Based Whistler Segmentation for Whistler Inversion

AbstractIt is challenging, yet important, to measure the—ever‐changing—cold electron density in the plasmasphere. The cold electron density inside and outside of the plasmapause is a key parameter for radiation belt dynamics. One indirect measurement is through finding the velocity dispersion relation exhibited by lightning induced whistlers. The main difficulty of the method comes from low signal‐to‐noise ratios for most of the ground‐based whistler components. To provide accurate electron density and ‐shell measurements, whistler components need to be detectable in the noisy background, and their characteristics need to be reliably determined. For this reason, precise segmentation is needed on a spectrogram image. Here, we present a fully automated way to perform such an image segmentation by leveraging the power of convolutional neural networks, a state‐of‐the‐art method for computer vision tasks. Testing the proposed method against a manually, and semi‐manually segmented whistler data set achieved 10% relative electron density prediction error for 80% of the segmented whistler traces, while for the shell, the relative error is 5% for 90% of the cases. By segmenting more than 1 million additional real whistler traces from Rothera station Antarctica, logged over 9 years, seasonal changes in the average electron density were found. The variations match previously published findings, and confirm the capabilities of the image segmentation technique.

On the determination of ionospheric electron density profiles using multi-frequency riometry

Abstract. Radio wave absorption in the ionosphere is a function of electron density, collision frequency, radio wave polarisation, magnetic field and radio wave frequency. Several studies have used multi-frequency measurements of cosmic radio noise absorption to determine electron density profiles. Using the framework of statistical inverse problems, we investigated if an electron density altitude profile can be determined by using multi-frequency, dual-polarisation measurements. It was found that the altitude profile cannot be uniquely determined from a “complete” measurement of radio wave absorption for all frequencies and two polarisation modes. This implies that accurate electron density profile measurements cannot be ascertained using multi-frequency riometer data alone and that the reconstruction requires a strong additional a priori assumption of the electron density profile, such as a parameterised model for the ionisation source. Nevertheless, the spectral index of the absorption could be used to determine if there is a significant component of hard precipitation that ionises the lower part of the D region, but it is not possible to infer the altitude distribution uniquely with this technique alone.

Thermodynamic Interpretation of Electron Density and Temperature Description in the Solar Corona

We reach a thermodynamic interpretation of the CODET model and its accurate electron density and temperature prediction, grounded on the physics of hydro magnetism in global equilibrium. The thermodynamic interpretation finds consistency with the model of a magneto-matter medium possessing a 3-D Langmuir structure. That medium is diamagnetic in the context of ideal magnetohydrodynamic (MHD). It is shown that this magneto-matter has unusual characteristics consistent with assuming that the low quiescent solar corona possesses a nature-state, non yet studied. It is further noticed that this is wholly consistent with the CODET model prediction of a polytropic anomalous index for the electron gas of the Sun’s corona. Constitutive properties are derived from this novel state of nature, like magnetic permeability properties and non-dispersive acoustic speed. This non-dispersive acoustic speed is also expected to predict the observed equilibration time for the 1.1 to 1.3R⊙ quiescent corona during the solar minimum from 2008 to 2009.

A Tomographic Method for the Reconstruction of the Plasmasphere Based on COSMIC/ FORMOSAT-3 Data

A tomographic method has been developed for reconstructing the topside ionospheric and plasmaspheric electron density distribution using total electron content (TEC) measurements from global positioning system (GPS) receivers aboard the constellation observing system for meteorology, ionosphere, and climate&#x002F;Formosa Satellite Mission 3 (COSMIC&#x002F;FORMOSAT-3). Since the COSMIC&#x002F;FORMOSAT-3 constellation has an orbit altitude of about 800 km, the integral TEC measurements obtained from the topside GPS navigation data are rather small and imposed relevant challenges to obtaining stable electron density reconstructions. However, the developed method can represent the natural variability of the plasma ambient in terms of latitude, altitude, solar activity, season, and local time when analyzing electron density reconstructions during 2008&#x2013;2013. The method employs independent spatial grids for satellite rising and setting geometries and imposes a set of constraints to stabilize the solution in the presence of noise and ill-conditioned geometry. We further consider background ionosphere and plasmasphere models for electron density initialization and filling data gaps. The quality assessment using TEC and <i>in-situ</i> electron density measurements has shown that the proposed method performs better than the background model, with improvements of about 26&#x0025; in TEC and 20&#x0025; in terms of electron density. Our investigation also reveals the necessity of more accurate background electron density representations and precise TEC measurements in order to have better plasmaspheric specifications at high altitudes.

Inhomogeneous plasma electron density inversion based on Bayesian regularization neural network

Electron density is one of the most important parameters for characterizing plasma properties, so obtaining accurate electron density is a prerequisite for studying the interaction between plasma and the electromagnetic waves. This paper presents the effects of different electron densities on the electric field distribution of a microstrip antenna with a center frequency of 2.45 GHz. Then, on the basis of the integrated model of plasma and the microstrip antenna, the Bayesian regularization neural network (BRNN) is used to retrieve the electron density of inhomogeneous plasma. Furthermore, the performance of the proposed approach is evaluated and analyzed by comparison with Levenberg–Marquardt (LM) and Scaled Conjugate Gradient (SCG) neural networks. The results show that the BRNN provides better performance than LM and SCG neural networks to retrieve plasma electron density based on the electric field intensity at fewer spatial positions. The accurate distribution of the electron density of inhomogeneous plasma can be obtained using BRNN. In addition, the greater the range variation of electron density, the greater the relative inversion error. This study provides an important theoretical basis for the diagnosis of electron density for inhomogeneous plasma in experiments.

A Method for Automatic Scaling of Ionograms and Electron Density Reconstruction

Ionogram scaling is the process of reconstructing electron density with respect to height by using the measurements of a remote sensing instrument known as ionosonde. In this study, a novel two-stage ionogram scaling technique, ionogram scaling and electron density (ISED), is proposed. In the first stage, hidden Markov models (HMMs) are used to identify the actual ionospheric reflections in the ionosonde measurements. In the second stage, an International Reference Ionosphere extended to plasmasphere (IRI-Plas) model-based optimization problem is solved to obtain the vertical profile that generates the best least-squares fit to the reflections identified in the first stage. To show the performance of ISED in a global scale, experiments are conducted on 14812 ionograms recorded at the three different stations that are Pruhonice in Czech Republic, Eielson in USA, and São Luis in Brazil. Application of ISED to raw ionograms indicates 97.6% of the cases, and ISED provides accurate electron density reconstructions, which is an improvement about 8.7% over automatic real-time ionogram scaler with true height (ARTIST), most commonly used ionogram scaling technique.

Spectroscopic diagnostic of electron density for four-level system by collisional excitation model

For accurate electron density diagnostics of plasma, the spectral diagnostics for four-level system instead of three-level system by collision excitation model are investigated. Taking the first four levels of magnesium VIII ion as an example, the relationship of electron density with line ratio is discussed, for a large region of electron density. Results show that when the electron density varies from 1011 cm−3 to 1013 cm−3, the electron density decreases with increasing of line ratio; at a same line ratio, the electron density obtained from the four-level system is smaller than that from the three-level system; at low electron density limit, the line ratio is 2, while at high electron density limit, the line ratio is 0.0467, which are both in good agreement with the theoretical predicted value. This discussion is significant in spectral diagnostics of plasma.

Electron density distribution of LiMn2O4 cathode investigated by synchrotron powder x-ray diffraction* *Project supported by Beijing Natural Science Foundation, China (Grant No. Z190010), the National Key Research and Development Program of China (Grant No. 2019YFA0308500), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB07030200), Key Research Projects of Frontier Science of Chinese Academy of Sciences (Grant

Electron density plays an important role in determining the properties of functional materials. Revealing the electron density distribution experimentally in real space can help to tune the properties of materials. Spinel LiMn2O4 is one of the most promising cathode candidates because of its high voltage, low cost, and non-toxicity, but suffers severe capacity fading during electrochemical cycling due to the Mn dissolution. Real-space measurement of electron distribution of LiMn2O4 experimentally can provide direct evaluation on the strength of Mn–O bond and give an explanation of the structure stability. Here, through high energy synchrotron powder x-ray diffraction (SPXRD), accurate electron density distribution in spinel LiMn2O4 has been investigated based on the multipole model. The electron accumulation between Mn and O atoms in deformation density map indicates the shared interaction of Mn–O bond. The quantitative topological analysis at bond critical points shows that the Mn–O bond is relatively weak covalent interaction due to the oxygen loss. These findings suggest that oxygen stoichiometry is the key factor for preventing the Mn dissolution and capacity fading.