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At least 91 records · Page 5

CAPOS: The bulge Cluster APOgee Survey: III. Spectroscopic tomography of Tonantzintla 2

Here, we performed the first detailed spectral analysis of red giant members of the relatively high-metallicity globular cluster (GC) Tononzintla 2 (Ton 2) using high-resolution near-infrared spectra collected with the Apache Point Observatory Galactic Evolution Experiment II survey (APOGEE-2), obtained as part of the bulge Cluster APOgee Survey. We investigated chemical abundances for a variety of species including the light, odd-Z, α-, Fe-peak, and neutron-capture elements from high S/N spectra of seven giant members. The derived mean cluster metallicity is [Fe/H] = –0.70 ± 0.05, with no evidence for an intrinsic metallicity spread. Ton 2 exhibits a typical α-enrichment that follows the trend for high-metallicity Galactic GCs, similar to that seen in 47 Tucanae and NGC 6380. We find a significant nitrogen spread (> 0.87 dex), and a large fraction of nitrogen-enriched stars that populate the cluster. Given the relatively high-metallicity of Ton 2, these nitrogen-enriched stars are well above the typical Galactic levels, indicating the prevalence of the multiple-population phenomenon in this cluster that also contains several stars with typical low first-generation N abundances. We also identify the presence of [Ce/Fe] abundance spread in Ton 2, which is correlated with the nitrogen enhancement, indicating that the s-process enrichment in this cluster has likely been produced by relatively low-mass asymptotic giant branch stars. Furthermore, we find a mean radial velocity of the cluster, –178.6 ± 0.86 km s –1 , with a small velocity dispersion, 2.99 ± 0.61 km s –1 , which is typical of GCs. We also find a prograde bulge-like orbit for Ton 2 that appears to be radial and highly eccentric. Finally, the considerably nitrogen-enhanced population observed in Ton 2, combined with its dynamical properties, makes this object a potential progenitor for the nitrogen-enriched field stars identified so far toward the bulge region at similar metallicity.

79 ASTRONOMY AND ASTROPHYSICS↗

Accelerating the Structure Exploration of Diverse Bi–Pt Nanoclusters via Physics‐Informed Machine Learning Potential and Particle Swarm Optimization

Bimetallic Bi–Pt nanoclusters exhibit diverse structural motifs, including core-shell, Janus, and mixed alloy configurations, due to the unique bonding characteristics between Bi and Pt atoms. Using density functional theory refinements from ChIMES physically machine-learned potential and CALYPSO particle swarm optimization global searches, 34 Bi20-Pt20 nanoclusters are systematically classified. The results reveal that Bi atoms predominantly occupy surface sites, driven by charge transfer effects. Cohesive energy trends alone prove insufficient for structure differentiation, necessitating a data-driven approach employing principal component analysis and K-means clustering. Furthermore, vibrational, electronic, and infrared spectral analyses provide additional insights into structure-property relationships. The findings offer an original framework for the automated classification and analysis of bimetallic nanoclusters, enhancing the understanding of their stability and functional properties.

bimetallic nanoparticles↗

Spin Decoherence Dynamics of Er 3+ in CeO 2 Films

Developing telecom-compatible spin-photon interfaces is essential towards scalable quantum networks. Erbium ions (Er 3+ ) exhibit a unique combination of a telecom (1.5 mu m) optical transition and an effective spin-1=2 ground state, but identifying a host that enables heterogeneous device integration while preserving long optical and spin coherence remains an open challenge. In this work, we explore the potential of Er 3+ :CeO 2 films on silicon and study the Er 3+ spin coherence, offering low nuclear spin density and the potential for on-chip integration. We demonstrate a 38.8 mu s spin coherence, which can be extended to 176.4 mu s with dynamical decoupling. Pairing experiments with cluster correlation expansion calculations, we identify spectral diffusion induced by bath Er 3+ spin flip-flops as the dominant decoherence mechanism and provide pathways to millisecond-scale coherence.

36 MATERIALS SCIENCE↗

Passivating Nucleobases Bring Charge Transfer Character to Optically Active Transitions in Small Silver Nanoclusters

DNA-wrapped silver nanoclusters (DNA–AgNCs) are known for their efficient luminescence. However, their emission is highly sensitive to the DNA sequence, the cluster size, and its charge state. To get better insights into photophysics of these hybrid systems, simulations based on density functional theory (DFT) are performed. Our calculations elucidate the effect of the structural conformations, charges, solvent polarity, and passivating bases on optical spectra of DNA–AgNCs containing five and six Ag atoms. It is found that inclusion of water in calculations as a polar solvent media results in stabilization of nonplanar conformations of base-passivated clusters, while their planar conformations are more stable in vacuum, similar to the bare Ag5 and Ag6 clusters. Cytosines and guanines interact with the cluster twice stronger than thymines, due to their larger dipole moments. In addition to the base–cluster interactions, hydrogen bonds between bases notably contribute to the structure stabilization. While the relative intensity, line width, and the energy of absorption peaks are slightly changing depending on the cluster charge, conformations, and base types, the overall spectral shape with five well-resolved bands at 2.5–5.5 eV is consistent for all structures. Independent of the passivating bases and the cluster size and charge, the low energy optical transitions at 2.5–3.5 eV exhibit a metal to ligand charge transfer (MLCT) character with the main contribution emerging from Ag-core to the bases. Cytosines facilitate the MLCT character to a larger degree comparing to the other bases. However, the doublet transitions in clusters with the open shell electronic structure (Ag5 and Ag6 + ) result in appearance of additional red-shifted (<2.5 eV) and optically weak band with negligible MLCT character. The passivated clusters with the closed shell electronic structure (Ag5 + and Ag6) exhibit higher optical intensity of their lowest transitions with much higher MLCT contribution, thus having better potential for emission, than their open shell counterparts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Infrared Spectroscopy of Li + Solvation in EmimBF 4 and in Propylene Carbonate: Ab Initio Molecular Dynamics and Experiment

Infrared (IR) spectra of solutions of the lithium salt LiBF 4 in the ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate (EmimBF 4 ) and in the organic solvent propylene carbonate (PC) are studied via infrared spectroscopy and ab initio molecular dynamics (AIMD) simulations. The measurements show that the major effects of LiBF 4 in both solutions, compared to their neat counterparts, are the appearance of a new broad band in the 300-450 cm -1 frequency region and a broadening of the IR structure in the 900-1200 cm -1 region with the development of a new peak at 980 cm -1 . Computational analysis indicates that hindered translational motions of Li + in its solvation cage are mainly responsible for the former, while the latter is due to Li + -induced structural changes and accompanying vibrational frequency shifts of constituent ions and molecules of the solutions. In addition, molecular motions in these and lower frequency regions are generally correlated, disclosing the collective nature of the vibrational dynamics, which involve multiple ions/molecules. Herein, detailed analysis of these features via AIMD simulations of the spectrum and its components arising from auto- and cross-correlations of motions of constituent molecular species, combined with generalized normal modes of the solutions and normal modes of small Li + -containing clusters, is presented. Furthermore, other minor spectral changes caused by the lithium salt as well as the interaction-induced effect on IR spectra are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Identifying Different Classes of Seismic Noise Signals Using Unsupervised Learning

Abstract Proper classification of nontectonic seismic signals is critical for detecting microearthquakes and developing an improved understanding of ongoing weak ground motions. We use unsupervised machine learning to label five classes of nonstationary seismic noise common in continuous waveforms. Temporal and spectral features describing the data are clustered to identify separable types of emergent and impulsive waveforms. The trained clustering model is used to classify every 1 s of continuous seismic records from a dense seismic array with 10–30 m station spacing. We show that dominate noise signals can be highly localized and vary on length scales of hundreds of meters. The methodology demonstrates the complexity of weak ground motions and improves the standard of analyzing seismic waveforms with a low signal‐to‐noise ratio. Application of this technique will improve the ability to detect genuine microseismic events in noisy environments where seismic sensors record earthquake‐like signals originating from nontectonic sources.

Johnson, Christopher W.↗

Proper orthogonal descriptors for efficient and accurate interatomic potentials

Here, we present the proper orthogonal descriptors for efficient and accuracy representation of the potential energy surface. The potential energy surface is represented as a many-body expansion of parametrized potentials in which the potentials are functions of atom positions and parameters. The proper orthogonal decomposition is employed to decompose the parametrized potentials into a set of proper orthogonal descriptors (PODs). Because of the rapid convergence of the proper orthogonal decomposition, relevant snapshots can be sampled exhaustively to represent the atomic neighborhood environment accurately with a small number of descriptors. The proper orthogonal descriptors are used to develop interatomic potentials by using a linear expansion of the descriptors and determining the expansion coefficients from a weighted least-squares regression against a density functional theory (DFT) training set. We present a comprehensive evaluation of the POD potentials on previously published DFT data sets comprising Li, Mo, Cu, Ni, Si, Ge, and Ta elements. The data sets represent a diverse pool of metals, transition metals, and semiconductors. The accuracy of the POD potentials are comparable to that of state-of-the-art machine learning potentials such as the spectral neighbor analysis potential (SNAP) and the atomic cluster expansion (ACE).

97 MATHEMATICS AND COMPUTING↗

Revisiting the Anisotropic Complex Refractive Indices of Sodium Nitrate for Interpretation of the Reflectance Spectrum of Pressed Pellets

Reflectance spectroscopy is notoriously confounding in that the measured spectral response is highly dependent upon the morphology of the sample. Fortunately, all such perturbations are neatly encoded by the complex refractive index of the sample. Herein, we seek to quantitatively model the measured infrared reflectance spectrum of a specularly flat pressed pellet sample of the birefringent compound, sodium nitrate. Single crystals of sodium nitrate were synthesized via a slow evaporation process and spectroscopically analyzed using polarization-dependent infrared single-angle reflectance spectroscopy. The anisotropic complex refractive index was measured from 7500 to 300 cm-1 (1.33 to 33.33 µm). The deduced anisotropic optical constants were found to be consistent with those previously reported. Once measured and validated, the optical constants were applied to model the pressed pellet reflectance spectrum. It was evident that an average of the anisotropic refractive indices was insufficient to account for the measured pellet reflectance. In order to account for contributions of all possible microcrystalline orientations within the pellet, the Python package PYELLI was used to calculate a basis set of orientation-dependent reflection spectra spanning the distinct ? and ? Euler rotations of the uniaxial crystal. When the population of orientations was allowed to vary freely in a spectral fit analysis, the fit-deduced orientations were tightly clustered along f = 45º, hinting at residual anisotropy in the pressed pellet sample. Conversely, an equally valid spectral fit (with marginally worse fit metric) was obtained when the population was constrained to an isotropic distribution of orientations. Subsequent non-zero cross-polarization reflectance measurements likewise suggested anisotropy in the pellet. However, both grazing incidence wide-angle x-ray scattering and scanning electron microscopy measurements revealed that the microcrystal orientations at the surface of the pressed pellet sample were isotropically distributed (and that the average crystallite size was larger than ?/10). Application of the measured complex refractive indices for modeling the reflectance spectrum of the pressed pellet, and rectification of these seemingly contradictory observations will be discussed.

Wilhelm, Michael J.↗

Mechanistic implications of excited high-spin states, spin–spin coupling, and differential [2Fe–2S] + cluster temperature relaxations in the electron-bifurcating NfnABC from Thermococcus sibiricus

Electron bifurcation (EB) is a mechanism of biological energy transduction in which multiple oxidation–reduction (redox) reactions are thermodynamically coupled within a single enzyme, enabling the enzyme to harness the excess free energy from an exergonic process to drive an endergonic process. Because of this unprecedented chemistry, there is interest to translate EB principles to artificial and bioengineered systems, but a hurdle is that knowledge pertaining to the fundamental design principles of EB enzymes remains scarce. Here, we investigated the fundamental physical and electronic properties of electron transfer sites in a spectroscopically uncharacterized member of the BfuABC family of EB enzymes, the NADH-dependent reduced-ferredoxin:NADP + oxidoreductase from Thermococcus sibiricus (Tsi NfnABC). Cryo-EM structures of Tsi NfnABC previously demonstrated that it contains twelve redox cofactors: two flavins (one FAD and one FMN), eight [4Fe–4S] clusters, and two [2Fe–2S] clusters. The FMN, one [4Fe–4S] cluster, and one [2Fe–2S] cluster comprise the bifurcating active site termed the electron-bifurcating flavobicluster (BF-FBC), which is found in all BfuABC family members. By using electron paramagnetic resonance spectroscopy, we identified spectral signatures originating from interactions between the FMN radical and [4Fe–4S] + cluster in the BF-FBC and observed temperature dependent behavior of the BF-FBC's [2Fe–2S] + cluster indicative of moderately slow spin–lattice relaxation. Additionally, we uncovered numerous spectral features corresponding to half-integer, S > ½ spin states of [4Fe–4S] + clusters, including one attributable to the consequences of lysine-ligation of a [4Fe–4S] cluster unique to NfnABC. We contextualize these findings to electron transfer theory and NfnABC's structure. Our insights further the understanding of how enzymes are designed to exert control over electron transfer to conduct thermodynamically challenging reactions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Census of Star Formation in the Outer Galaxy. II. The GLIMPSE360 Field

We have conducted a study of star formation in the outer Galaxy from 65°< l < 265° in the region observed by the GLIMPSE360 program. This Spitzer warm mission program mapped the plane of the outer Milky Way with IRAC at 3.6 and 4.5 μm. We combine the IRAC, Wide-field Infrared Survey Explorer (WISE), and Two Micron All Sky Survey catalogs and our previous results from another outer Galaxy survey and identify a total of 47,338 young stellar objects (YSOs) across the field spanning >180° in Galactic longitude. Using the DBSCAN method on the combined catalog, we identify 618 clusters or aggregations of YSOs having five or more members. We identify 10,476 class I, 29,604 class II, and 7325 anemic class II/class III YSOs. The ratio of YSOs identified as members of clusters was 25,528/47,338, or 54%. We found that 100 of the clusters identified have previously measured distances in the WISE H ii survey. We used these distances in our spectral energy distribution (SED) fitting of the YSOs in these clusters, of which 96 had YSOs with <3σ fits. We used the derived masses from the SED model fits to estimate the initial mass function (IMF) in the inner and outer Galaxy clusters; dividing the clusters by galactocentric distances, the slopes were Γ = 1.87 ± 0.31 above 3 M {sub ⊙} for R {sub Gal} < 11.5 kpc and Γ = 1.15 ± 0.24 above 3 M {sub ⊙} for R {sub Gal} > 11.5 kpc. The slope of the combined IMF was found to be Γ = 1.92 ± 0.42 above 3 M {sub ⊙}. These values are consistent with each other within the uncertainties and with literature values in the inner Galaxy high-mass star formation regions. The slopes are likely also consistent with a universal Salpeter IMF.

79 ASTRONOMY AND ASTROPHYSICS↗

Uncovering acoustic signatures of pore formation in laser powder bed fusion

Abstract We present a machine learning workflow to discover signatures in acoustic measurements that can be utilized to create a low-dimensional model to accurately predict the location of keyhole pores formed during additive manufacturing processes. Acoustic measurements were sampled at 100 kHz during single-layer laser powder bed fusion (LPBF) experiments, and spatio-temporal registration of pore locations was obtained from post-build radiography. Power spectral density (PSD) estimates of the acoustic data were then decomposed using non-negative matrix factorization with custom $$\varvec{k}$$ k -means clustering (NMF $$\varvec{k}$$ k ) to learn the underlying spectral patterns associated with pore formation. NMF $$\varvec{k}$$ k returned a library of basis signals and matching coefficients to blindly construct a feature space based on the PSD estimates in an optimized fashion. Moreover, the NMF $$\varvec{k}$$ k decomposition led to the development of computationally inexpensive machine learning models which are capable of quickly and accurately identifying pore formation with classification accuracy of supervised and unsupervised label learning greater than 95% and 90%, respectively. The intrinsic data compression of NMF k , the relatively light computational cost of the machine learning workflow, and the high classification accuracy makes the proposed workflow an attractive candidate for edge computing toward in-situ keyhole pore prediction in LPBF.

36 MATERIALS SCIENCE↗

A Decentralized Approach for Modeling Organized Convection Based on Thermal Populations on Microgrids

Abstract In this study, a spectral model for convective transport is coupled to a thermal population model on a two‐dimensional horizontal “microgrid,” covering the typical gridbox size of general circulation models. The goal is to explore new ways of representing impacts of spatial organization in cumulus cloud fields. The thermals are considered the smallest building block of convection, with thermal life cycle and movement represented through binomial functions. Thermals interact through two simple rules, reflecting pulsating growth and environmental deformation. Long‐lived thermal clusters thus form on the microgrid, exhibiting scale growth and spacing that represent simple forms of spatial organization and memory. Size distributions of cluster number are diagnosed from the microgrid through an online clustering algorithm, and provided as input to a spectral multiplume eddy‐diffusivity mass flux scheme. This yields a decentralized transport system, in that the thermal clusters acting as independent but interacting nodes that carry information about spatial structure. The main objectives of this study are (a) to seek proof of concept of this approach, and (b) to gain insight into impacts of spatial organization on convective transport. Single‐column model experiments demonstrate satisfactory skill in reproducing two observed cases of continental shallow convection. Metrics expressing self‐organization and spatial organization match well with large‐eddy simulation results. We find that in this coupled system, spatial organization impacts convective transport primarily through the scale break in the size distribution of cluster number. The rooting of saturated plumes in the subcloud mixed layer plays a key role in this process.

54 ENVIRONMENTAL SCIENCES↗

Revealing the Structural Evolution of Green Rust Synthesized in Ionic Liquids by In Situ Molecular Imaging

Abstract Ionic liquids are green solvents that have wide applications in material synthesis, catalysis, and separation. A model switchable ionic liquid (SWIL) consisting of 1,8‐diazabicycloundec‐7‐ene (DBU) and 1‐hexanol with carbon dioxide (CO 2 ) as the trigger gas is chosen to synthesize nanocrystalline green rust. Under anoxic conditions, by adding iron (II) acetate (Fe(C 2 H 3 O 2 ) 2 ) and methanol to the degassed SWIL, a nanoparticulate green rust with carbonate (nano‐GR) is synthesized. More importantly, the molecular structural change of the ionic liquid resulting in green rust crystallines is first characterized using in situ liquid using time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) coupled with the system for analysis at the liquid vacuum interface (SALVI), a vacuum compatible microfluidic reactor in this work. Dimers and ionic clusters consisting ferric and ferrous ions are identified in liquid ToF‐SIMS spectra. Spectral principal component analysis is used to confirm that these ion pairs including dimers and cluster ions are different from nonionic liquids. The results show that liquid ToF‐SIMS can be a useful tool to study complex liquids at the molecular level providing insights into predicative synthesis of nanomaterials using environmentally friendly green solvents and giving unique visualization of the evolving material interface due to nucleation.

Shen, Yanjie↗

Accuracy, transferability, and computational efficiency of interatomic potentials for simulations of carbon under extreme conditions

Large-scale atomistic molecular dynamics (MD) simulations provide an exceptional opportunity to advance the fundamental understanding of carbon under extreme conditions of high pressures and temperatures. However, the fidelity of these simulations depends heavily on the accuracy of classical interatomic potentials governing the dynamics of many-atom systems. Here, this study critically assesses several popular empirical potentials for carbon, as well as machine learning interatomic potentials (MLIPs), in their ability to simulate a range of physical properties at high pressures and temperatures, including the diamond equation of state, its melting line, shock Hugoniot, uniaxial compressions, and the structure of liquid carbon. Empirical potentials fail to accurately predict the behavior of carbon under high pressure–temperature conditions. In contrast, MLIPs demonstrate quantum accuracy, with Spectral Neighbor Analysis Potential (SNAP) and atomic cluster expansion (ACE) being the most accurate in reproducing the density functional theory results. ACE displays remarkable transferability despite not being specifically trained for extreme conditions. Furthermore, ACE and SNAP exhibit superior computational performance on graphics processing unit-based systems in billion atom MD simulations, with SNAP emerging as the fastest. In addition to offering practical guidance in selecting an interatomic potential with a fine balance of accuracy, transferability, and computational efficiency, this work also highlights transformative opportunities for groundbreaking scientific discoveries facilitated by quantum-accurate MD simulations with MLIPs on emerging exascale supercomputers.

36 MATERIALS SCIENCE↗

Modeling the Spectral Diversity of Quasars in the Sixteenth Data Release from the Sloan Digital Sky Survey

Abstract We present a new approach to capturing the broad diversity of emission-line and continuum properties in quasar spectra. We identify populations of spectrally similar quasars through pixel-level clustering on 12,968 high signal-to-noise ratio (S/N) spectra from the Sloan Digital Sky Survey (SDSS) in the redshift range of 1.57 < z < 2.4. Our clustering analysis finds 396 quasar spectra that are not assigned to any population, 15 misclassified spectra, and 6 quasars with incorrect redshifts. We compress the quasar populations into a library of 684 high-S/N composite spectra, anchored in redshift space by the Mg ii emission line. Principal component analysis on the library results in an eigenspectrum basis spanning 1067–4007 Å. We model independent samples of SDSS quasar spectra with the eigenbasis, allowing for a free redshift parameter. Our models achieve a median reduced χ 2 on non–broad absorption line quasar spectra that is reduced by 8.5% relative to models using the eigenspectra from the SDSS spectroscopic pipeline. A significant contribution to the relative improvement is from the ability to reconstruct the range of emission-line variation. The redshift estimates from our model are consistent with the Mg ii emission-line redshift with an average offset that displays 51.4% less redshift-dependent variation relative to the SDSS eigenspectra. Our method for developing quasar spectra models can improve automated classification and predict the intrinsic spectrum in regions affected by intervening absorbers such as Ly α , C iv , and Mg ii , thus benefiting studies of large-scale structure.

79 ASTRONOMY AND ASTROPHYSICS↗

Spectral Peak Enhancement by Combining Trusted Response Elements via Machine Learning (SPECTRE-ML) v0.8.0

SPECTRE-ML (Spectral Peak Enhancement by Combining Trusted Response Elements via Machine Learning) is a machine learning based program for finding optimal clusters of radiation detector segments (i.e., pixels or voxels) in order to improve spectral performance. It provides facilities for pre-processing and analyzing training datasets, running ML algorithms, and evaluating and visualizing outputs. SPECTRE-ML outperforms simpler ad-hoc segmentation methods such as uniform depth clusters, learning detector performance trends such as dead layers, edge effects, and gain shifts. Although extensible to arbitrary highly-segmented spectroscopic radiation detectors, SPECTRE-ML currently focuses on improving spectral performance in highly-segmented CdZnTe (CZT) detectors for International Atomic Energy Agency (IAEA) non-destructive assay (NDA) safeguards tasks.

Vavrek, Jayson↗

Anion Photoelectron Spectroscopy and Ab Initio Studies of the UF – Anion

A synergistic anion photoelectron spectroscopic and ab initio computational study of photodetachment of UF – is reported. The measurement determined a vertical detachment energy of 0.63(03) eV, which is consistent with a spinor-based relativistic coupled-cluster CCSD(T) value of 0.61 eV. The complex spectral features due to excited electronic states and vibrational progressions of UF are analyzed and assigned with the help of spin–orbit-coupled multireference perturbation theory and spinor-based relativistic coupled-cluster calculations. UF and UF – are confirmed to be dominated by ionic bonding. Furthermore, the usefulness of the spinor CCSD(T) approach is demonstrated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Advanced Polymer Characterization: Modular Operations for Spectral Alignment by Iterative Compression (MOSAIC)

Matrix-assisted laser desorption/ionization (MALDI) mass spectrometry encodes structural information across diverse homo- and copolymer ensembles, yet decrypting these spectra requires a systematic analytical approach. We introduce Modular Operations for Spectral Alignment by Iterative Compression (MOSAIC)─a general cipher algorithm that applies modular arithmetic to filter monomer-derived mass contributions and cluster MALDI peaks by nonconstitutional repeating units (non-CRUs). MOSAIC performs sequential modular operations using monomer mass differences as base units to compress complex spectral data, revealing end-group distributions and comonomer incorporation. As a demonstration, we applied MOSAIC to five copolymers formed by two different polymerization mechanisms. Furthermore, the resulting remainder–mass plots clearly resolve polymer homologs with distinct non-CRUs into visually apparent clusters, enabling intuitive assignment of mass spectral features.

Wang, Hanlin M. [University of Illinois at Urbana−↗