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At least 181 records · Page 10

Density Functional Theory Study of Iron–Oxygen Divacancies in Magnetite (Fe 3 O 4 ) and Hematite (Fe 2 O 3 )

Density functional theory (DFT) calculations are employed to investigate the formation energies, charge redistribution, and binding energies of iron–oxygen divacancies in magnetite (Fe 3 O 4 ) and hematite (Fe 2 O 3 ). For magnetite, we focus on the low-temperature phase to explore variations with local environments. Building on previous DFT calculations of the variations in formation energies for oxygen vacancies with local charge and spin order in magnetite, we extend this analysis to include octahedral iron vacancies before analyzing the iron–oxygen divacancies. We also assessed the relative stability of iron–oxygen divacancies by comparing their formation energies with those of individual vacancies. Our findings reveal a significant energetic driving force for the formation of divacancy clusters, particularly in magnetite, where divacancies in the +1 charge state exhibit formation energies comparable to those of neutral iron vacancies under oxidizing conditions. In hematite, the results indicate a strong tendency for oxygen vacancies to bind to iron vacancies. These results highlight the significance of iron–oxygen vacancy complexes in the transport properties of iron oxides, with particular relevance to diffusion mechanisms under irradiation conditions.

36 MATERIALS SCIENCE↗

Cyclometallated Co(III) Complexes with Lowest-Energy Charge Transfer Excited States Accessible with Visible Light

The Co(III) complexes, cis-[Co(ppy) 2 (L)]PF 6 , where ppy = 2-phenylpyridine and L = bpy (2,2′-bipyridine; 1), phen (1,10-phenanthroline; 2), and DAP (1,12-diazaperylene; 3), are reported and their photophysical properties were investigated to evaluate their potential as sensitizers for applications that include solar energy conversion schemes and photoredox catalysis. Calculations show that cyclometallation in the cis-[Co(ppy) 2 (L)]PF 6 series affords strong Co(dπ)/ppy(π) orbital interactions that result in a Co/ppy(π*) highest occupied molecular orbital (HOMO) and a lowest unoccupied molecular orbital (LUMO) localized on the diimine ligand, L(π*). Complexes 1–3 exhibit relatively invariant oxidation potentials, whereas the reduction event is dependent on the identity of the diimine ligand, L, consistent with the theoretical predictions. For 3 a broad Co/ppy(π*) → L(π*) metal/ligand-to-ligand charge transfer (ML-LCT) absorption band is observed in CH 3 CN with a maxima at 507 nm, extending beyond 600 nm. Upon excitation of the 1ML-LCT transition, transient absorption features consistent with the population of a 3 ML-LCT excited state with lifetimes, τ, of 3.0 ps, 4.6 and 42 ps for 1, 2 and 3 in CH 3 CN respectively are observed. Upon irradiation with 505 nm, 3 is able to reduce methyl viologen (MV 2+ ), an electron acceptor commonly in photocatalytic schemes. Here, to our knowledge, 3 represents the first heteroleptic molecular Co(III) complex that combines cyclometallation with a diimine ligand with lowest-lying metal-to-ligand charge transfer excited states able to undergo photoinduced charge transfer with low-energy green light. As such, the structural design of 3 represents an important step toward d6 photosensitizers based on earth abundant metals.

Energy↗

The Role of Surface Hydroxyls in Dehydration and Dehydrogenation of Formic Acid on Fe 3 O 4 (001)

Understanding the role of surface structure and hydroxylation in catalytic reactions on metal oxide surfaces is important for developing a mechanistic insight into the complex interface processes. Here, we investigate the reactivity of formic acid on reconstructed Fe 3 O 4 (001) using a combination of X-ray photoelectron spectroscopy, infrared reflection absorption spectroscopy, temperature-programmed reaction spectroscopy, low energy electron diffraction, and electronic structure calculations. We find that formic acid initially dissociates at low temperatures (< 80 K) into bidentate formate and a hydroxyl up to an initial dosed coverage of two HCOOH per Fe 3 O 4 (001) unit cell. At higher temperatures (> 450 K), formate largely decomposes along the dehydration pathway, producing CO and H 2 O, with dehydrogenation to CO 2 being a minority side reaction. As a first step, water formation leads to surface oxygen extraction via the Mars-van Krevelen mechanism. Computational studies reveal formate embedded in oxygen vacancies as a key intermediate in the CO formation mechanism. CO formation proceeds via two reaction pathways with desorption that peaks at 530 K on the hydroxyl-rich surface and 560 K on the hydroxyl-deficient surface. Atomic hydrogen coadsorption experiments and ab initio calculations reveal that the presence of surface hydroxyls reduces the CO formation barrier. Furthermore, these results highlight the complex interactions between substrate and intermediate species occurring during reactions on metal oxide surfaces.

Adsorption↗

Assembly and Repair of the Photosystem II Reaction Center

This project investigated the biochemical and biophysical mechanisms governing assembly and repair of Photosystem II (PSII), the membrane protein complex responsible for solar-driven water oxidation in oxygenic photosynthesis. The work focused on three integrated areas: (1) protein–protein interactions that facilitate PSII assembly in cyanobacterial biogenesis centers, (2) the chemical mechanism of photo-assembly of the Mn 4 CaO 5 oxygen-evolving complex (OEC), and (3) mechanisms that target PSII reaction centers for degradation and repair in photosynthetic organisms. Using electron paramagnetic resonance spectroscopy, protein biochemistry, molecular genetics, quantitative mass spectrometry, and computational modeling, the project demonstrated that proton release events limit early steps of OEC assembly and that chloride and calcium ions facilitate Mn oxidation and intermediate stabilization. Complementary studies identified chaperone recruitment mechanisms in cyanobacterial PSII biogenesis centers and translation and protease factors involved in PSII turnover in Chlamydomonas. Together, these results establish proton management and coordinated protein quality control as central design principles in PSII assembly and repair and provide mechanistic insight relevant to biological and artificial photosynthetic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elucidating the role of Cr migration in Ni-Cr exposed to molten FLiNaK via multiscale characterization

Structural materials used in nuclear reactor environments are subjected to coupled extremes such as high temperature, irradiation, and corrosion which act in concert to degrade their functional performance. Connecting alloy microstructure such as grain boundaries, and accumulating point defects with corrosion attack and pore morphology is critical to understanding underlying mechanisms. We uncover the compositional variations and morphology at multiple length scales in corrosion-damaged Ni-Cr alloy after exposure to oxidants in molten fluoride salts. A complex network of dense corrosion pores is detected by surface-level SEM observations. The corrosion pores take on a 1-dimensional morphology and are enriched with Ni and depleted of Cr 1–5 µm from the pore surface. STEM-EDS and 4D-STEM strain maps acquired simultaneously highlight the local variations in composition and structure of a ≤ 200 nm Cr-rich layer identified from a cross-section taken at the bottom of an isolated corrosion pore between the Ni-Cr alloy matrix and the embedded salt. However, the absence of an observed interface between the Ni-Cr alloy matrix and the FCC-structured Cr-rich layer suggests that Cr plating from the salt did not transpire. These findings support a proposed Cr lattice diffusion mechanism rather than Cr-precipitation from the salt to accommodate temperature transient conditions during sample cooling. Through the development of a 1D phase field model, these results are rationalized by formation energies for the Ni- and Cr-oxidation into the molten salt. This study reveals the locally altered microstructure caused by high temperature corrosion in non-steady-state molten salt nuclear reactor environments.

36 MATERIALS SCIENCE↗

Olefin Coupling Catalyzed by (Pybox)Os Complexes via Osmacyclopentane Intermediates: Comparison with Isoelectronic (Phebox)Ir

(Pybox)Os is found to catalyze alkene hydrovinylation, effecting the dimerization of ethylene, tail-to-tail coupling of propene and 1-butene, and cross-coupling of ethylene with higher α-olefins. This reactivity contrasts with the previously reported dehydrogenative coupling of ethylene to give butadiene catalyzed by the isoelectronic fragment (Phebox)Ir. The reaction mechanism was investigated through computational and experimental means. Both the Os- and Ir-catalyzed reactions proceed through a [2 + 2 + 1] cyclization of the corresponding bis-olefin complex to yield an experimentally observed metallacyclopentane intermediate. In both cases, the metallacyclopentane undergoes β- H elimination, via a dechelated κ 2 -pincer-ligated intermediate, to yield a σ−π-but-3-enyl hydride complex or derivative. Both the greater reactivity and the distinct chemoselectivity of the Os system relative to the Ir system are attributable to C−H reductive elimination by the σ−π-but-3-enyl hydride having a barrier for Os much lower than that for Ir. This lower barrier to C−H elimination for Os is unexpected given that the thermodynamic driving force for elimination is much less for Os than for Ir. Computational studies of model complexes were conducted, comparing (Pybox)Os(L)(CH 3 )(H) with the isoelectronic (Phebox)Ir(L)(CH 3 )(H). The results indicate that the more facile kinetics with Os relative to Ir may be general for C−H elimination from six-coordinate d 6 complexes of the two metals, as well as for the microscopic reverse, i.e., C−H addition to the corresponding four-coordinate d 8 species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe–2S] Systems: A Benchmark Study of the [Fe 2 S 2 (SCH 3 ) 4 ] 2–,3–,4– , [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S- p -tol) 4 ] 2– , and [Fe 2 S 2 (S- o -xyl) 4 ] 2– Complexes

Iron–sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Here, using a [2Fe–2S] model complex with Fe II and Fe III oxidation states, which leads to different charges, i.e., [Fe 2 S 2 (SMe) 4 ] 2–,3–,4– , we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree–Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S-o-tol) 4 ] 2– , and [Fe 2 S 2 (S-o-xyl) 4 ] 2– , via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the Fe III /Fe III → Fe II /Fe III (4.27 eV) and Fe II /F III → Fe II /F II (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Probing the Framework Metal Dependent Properties of Actinide-Centered Polyoxoalkoxide Sandwich-Type Complexes

Development of a simple and scalable synthesis of (TBA) 3 [W 5 O 18 MoNO] provides for the formation of the mixed-metal lacunary polyoxoalkoxide, (TBA) 2 [W 4 O 13 (OMe) 4 MoNO][Na(MeOH)]. This complex was used to synthesize a series of polyoxoalkoxide sandwich-type complexes with the general formula (TBA) 2 [M{W 4 O 13 (OMe) 4 MoNO} 2 ], where M = Zr(IV), Hf(IV), Th(IV), U(IV), and Np(IV). Compared to the analogous all-molybdenum complexes, the series have drastically different optical and redox properties. The results indicate that framework metal substitution acts as a tool for “orbital engineering”, with Density Functional Theory (DFT) calculations revealing that the major consequence of incorporation of tungsten into the complexes is localization of LUMO and LUMO+1 on the molybdenum centers remaining in the molecule. The change in the distribution of the frontier orbitals translates to discrepancies in the electronic properties of the series. Given the rarity of polyoxometalate complexes featuring a U(V) ion, one electron oxidation of (TBA) 2 [U(IV){W 4 O 13 (OMe) 4 MoNO} 2 ] was pursued. Isolation of the corresponding U(V) centered sandwich-type complex is reported, only the second example of U(V)-polyoxometalate complex described to date.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thiol-based pathways in the thylakoid lumen and their role in photoprotection

The long-term goal of this research is to elaborate the catalysis of thiol-disulfide transactions in the thylakoid lumen, a compartment required for transducing energy via photophosphorylation. The molecular identity of the redox players catalyzing thiol-disulfide exchanges, their relevant targets of action in vivo and how thiol-disulfide chemistry in general controls photosynthesis are the experimental questions this research aims to address. Through previous work, we documented the requirement of catalyzed disulfide formation and reduction for the biogenesis of two photosynthetic enzymes, namely Photosystem II and the cytochrome b6f complex. We established that dedicated trans-thylakoid pathways operate in these processes by delivering reducing and oxidizing power to cysteine-containing subunits of the photosynthetic complexes, which are localized in the lumen compartment. Here we focused on CCDA, CCS4 and CCS5/HCF164, the components of the disulfide-reducing pathway which maintains the heme binding cysteines of apoforms of plastid cytochrome c in the reduced form prior to covalent heme ligation. We showed that CCS4 and CCS5 operate in functionally redundant pathways for the supply of reducing power and postulate a role for CCS4 in recruiting the source of reductants to CCDA or controlling the CCDA-dependent transduction of reducing equivalents. We also demonstrate the disulfide reducing pathway operates to counter thiol oxidation of the heme-binding cysteines by disulfide forming enzyme LTO1 in the thylakoid lumen.

59 BASIC BIOLOGICAL SCIENCES↗

Flash Communication: Flexibility of a Biologically Inspired Ligand Framework for Intramolecular C–H Activation

High-valent iron complexes play a crucial role in the oxidation of organic substrates, especially in C–H bond functionalization reactions in biology. This paper investigates the reactivity of nonporphyrin tripodal ligands featuring a secondary coordination sphere, focusing on their prospective ability to stabilize high-valent iron-oxo species. Using NMR spectroscopy and X-ray crystallography, we detail the formation of an Fe(III)-alkoxide complex through intramolecular C–H bond activation, providing insight into the potential transient formation of a high-valent iron-oxo intermediate. While attempts to observe an Fe(IV)-oxo complex were unsuccessful, our findings underscore the significance of the ligand electronic environment in stabilizing reactive iron species for C–H bond activation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interfacial Void Formation and Self-Healing in Oxide Scales on Al-containing High-Entropy Alloy

The exceptional high-temperature oxidation resistance of Al-containing high-entropy alloys (HEAs) is often attributed to the formation of a protective α-Al 2 O 3 scale. However, the dynamic, atomic-scale mechanisms governing the stability of this scale—including interfacial void formation and the often-postulated but rarely visualized “self-healing” capacity—remain poorly understood. Herein, we reveal the complex evolution of the triple-layer oxide scale on an Al 10 CoCrFeNi HEA through combined electron microscopy and diffraction study. We show that interfacial voids are an inherent consequence of the scaling process, originating from two distinct mechanisms: the Kirkendall effect at the interface between the γ-Al 2 O 3 /α-Al 2 O 3 and alloy driven by cationic diffusion imbalance and volumetric contraction due to phase transformations at the spinel/Cr 2 O 3 interface. Crucially, we provide microstructural evidence consistent with an intrinsic self-healing response. This process is driven by coupled inward diffusion of oxygen and outward diffusion of metal cations, leading to the in-situ formation of transient θ-Al 2 O 3 and spinel phases that partially fill and seal the voids. Here, these results provide atomic-scale insights into the phase evolution, defect formation, and self-repair of oxide scales in HEAs—highlighting pathways to enhance their oxidation resistance in extreme environments.

High-entropy alloy↗

A Ce 4+ Aluminum Hydride Complex

Complexes of reducing hydride ligands by high-oxidation state cerium are unknown due to the fundamental mismatch in their redox chemistry. Herein we report the synthesis, characterization, and reactivity of the first example of a Ce 4+ aluminum hydride complex. Synthetic strategies adapted from the preparation of Ce 4+ alkyl complexes facilitated the isolation of [Ce 4+ (κ 2 -H 3 AlC(TMS) 3 )(NP( t Bu) 3 ) 3 ] (CeHAl). The bonding and structure of this complex is characterized by single-crystal XRD, NMR, and UV–vis–NIR spectroscopy, and DFT computations. The fundamental reactivity profile is evaluated by cyclic voltammetry and small-molecule reactions.

anions↗

Complex-Concentrated Anion Doping Enables Ultra-Stable Lattice Oxygen and Structural Integrity in Lithium-Rich Layered Oxide Cathodes

Lithium- and manganese-rich layered oxides (LMR) stand out as next-generation lithium-ion cathode chemistries, which harness both transition-metal and lattice-oxygen redox processes to deliver exceptional capacity and energy density. However, their full potential is hindered by intrinsic oxygen instability and structural degradation, resulting in pronounced voltage fade and capacity decay. Here, we present a complex-concentrated anion-doping paradigm in which multiple anions, F, Br, and S, are incorporated into the oxygen sublattice to enhance oxygen-redox and structural stability. X-ray absorption spectroscopy and aberration-corrected scanning transmission electron microscopy confirm ultra-stable local oxygen coordination environments during long-term cycling, with detrimental phase transformations and oxygen-loss-induced cavitation dramatically inhibited. Notably, we show that the characteristic LiTM6 transition metal (TM) honeycomb ordering is preserved even after electrochemical cycling. Concurrently, this strategy yields an unprecedented volume change of only 0.63% upon charging to 4.8 V vs. Li+/Li, achieving the first zero-strain LMR cathode. The resulting LMR cathode delivers ultralow voltage fade (1 mV per cycle during the first 100 cycles and becomes negligible in subsequent cycles) and outstanding energy retention (93% after 200 cycles) in a pouch cell configuration. Our complex-concentrated anion-doping concept establishes a broadly applicable strategy for resolving chemo-mechanical failure mechanisms in ceramic intercalation electrodes for next-generation energy storage.

Li-ion batteries↗

Comparison of Ce( iv )/Th( iv )-alkynyl complexes and observation of a trans -influence ligand series for Ce( iv )

Organometallic cerium(iv) complexes have been challenging to isolate and characterize due to the strongly oxidizing nature of the cerium(iv) cation. Herein, we report two cerium(iv) alkynyl complexes, [Ce(TriNOx)(C[triple bond, length as m-dash]C-SiMe3)] (1-CeTMS) and [Ce(TriNOx)(C[triple bond, length as m-dash]C-Ph)] (1-CePh) (TriNOx3- = tris(2-tert-butylhydroxylaminato)benzylamine), that include terminal alkyne moieties. The isostructural thorium analogue [Th(TriNOx)(C[triple bond, length as m-dash]C-SiMe3)] (1-ThTMS) was also synthesized and compared with 1-CeTMS in bond distance, 13C-NMR spectra, vibrational spectra and electronic structure. The Ce-C bond distances were 2.501(3) Å for 1-CePh and 2.513(5) Å for 1-CeTMS on the shorter end of the few reported CeIV-C single bonds (2.478(3)-2.705(2) Å), possibly indicating significant Ce 5d- and 4f-orbital involvement. 13C-NMR spectroscopy was also consistent with Ce-C covalency, with significantly deshielded resonances ranging from 185-213 ppm. Such 13C-NMR shifts demonstrate a strong influence from spin-orbit coupling (SOC) effects, corroborated by computational studies. Raman analysis showed ν C[triple bond, length as m-dash]C stretching frequencies of 2000 cm-1 (1-CeTMS) and 2052 cm-1 (1-CePh), indicating the cerium(iv)-alkynyl interaction, compared to the parent HC[triple bond, length as m-dash]CPh (IR = 2105 cm-1 and Raman = 2104 cm-1). L3-edge X-ray absorption measurements revealed a predominant Ce(iv) electronic configuration, and magnetic measurements revealed temperature-independent paramagnetism. Electrochemical studies similarly revealed the electron donating ability of the alkynyl ligands, stronger than either fluoride or imido ligands for the Ce(iv)(TriNOx)-framework, with a cerium(iv/iii) reduction potential of E pc = -1.58 to -1.66 V vs. Fc/Fc+. Evidence for a trans-influence has been observed by evaluating a series including previously reported [CeIV(TriNOx)X]+/0 complexes with axial ligands X = THF, I-, Br-, Cl-, F-, -C[triple bond, length as m-dash]C-Ph, -C[triple bond, length as m-dash]C-SiMe3, -NH(3,5-(CF3)2-Ar), -OSiPh3, -N(M(L))(3,5-(CF3)2-Ar) [M(L) = Li(TMEDA), K(DME)2 or Cs(2,2,2-crypt)]. These data stand in contrast with previous reports of an inverse trans-influence at cerium(iv) and point to differences in involvement of cerium 4f- versus 5d-orbitals in the electronic structures of the complexes.

Yang, Qiaomu↗

Structural and spectroscopic characterization of a Tb(IV) polyoxometalate

There has been a renaissance in high valent lanthanide chemistry, which has resulted in the first examples of tetravalent praseodymium (Pr) and terbium (Tb) in molecular systems. These feats have been achieved with tailored ligands that facilitate tetravalent lanthanide stability in non-aqueous conditions. The next step in realizing the potential of high valent lanthanide chemistry is moving towards complexes that are stable in ambient and aqueous conditions. In this investigation, we advance this paradigm by obtaining definitive evidence of Tb(IV) in a molecular system under aqueous conditions utilizing the lacunary Wells-Dawson polyoxometalate, K 10 P 2 W 17 O 61 •20H 2 O. Herein we present the single crystal structure of K 16 Tb(IV)(P 2 W 17 O 61 ) 2 •39.85H 2 O (Tb(IV)W 34 ) as well as extensive spectroscopic evidence obtained via UV–Vis-NIR, X-ray absorption near edge spectroscopy, continuous wave X-band electron paramagnetic resonance spectroscopy and SQUID magnetometry measurements to confirm the oxidation state of Tb in W 34 complexes as +4.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Venturing Past Uranium: Synthesis of a Np(IV) Polyoxomolybdate–Alkoxide Sandwich Complex

The synthesis of a Np(IV) polyoxomolybdate– alkoxide sandwich complex, (TBA) 2 [Np{Mo 5 O 13 (OMe) 4 NO} 2 ] (TBA = tetrabutylammonium), is reported. This compound represents a rare example of a neptunium polyoxometalate cluster isolated outside of water, allowing for characterization of its electrochemical properties in nonaqueous solvents. Complexation of An(IV) cations fine-tunes the redox properties of the cluster, with the observed four reversible reductive events varying slightly both in potential and peak separation depending on the actinide present. The new Np(IV) complex also shows an irreversible event assigned to oxidation of Np(IV) to Np(V). New methodology for facile 17 O enrichment of (TBA) 2 [Mo 5 O 13 (OMe) 4 NO][Na(MeOH)] is presented, which provides a simple pathway to 17 O enriched analogues of the sandwich complexes discussed (Zr(IV), Hf(IV), Th(IV), U(IV), U(V), Np(IV)). 17 O NMR spectroscopy subsequently provides insights into both the nature of metal–oxygen bonding, as well as the influence of unpaired f-electrons on the local environment of the oxygen nuclei.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Regularization via f -Divergence: An Application to Multi-Oxide Spectroscopic Analysis

In this paper, we explore the application of convolutional neural networks (CNNs) for predicting the chemical composition of complex geologic samples in a simulated Martian atmospheric environment. Specifically, we aim to characterize oxide weight percentages (wt.%) of rock samples analyzed by remote Laser-Induced Breakdown Spectroscopy (LIBS), framing the problem as a multi-target regression task . Neural networks trained on LIBS spectra are prone to overfitting due to high spectral complexity, limited labeled data, and measurement noise. While regularization is critical for improving generalization, common methods (e.g., ℓ 2 regularization) impose constraints not directly tied to data distribution properties. We propose a novel regularization method based on a specific ƒ-divergence induced by a graph-based estimator, designed to constrain the distributional discrepancy between predictions and targets. This regularizer serves a dual purpose: (a) mitigating overfitting by enforcing a constraint on the distributional difference between predictions and noisy targets, and (b) acting as an auxiliary loss that penalizes large divergences. To enable backpropagation, we develop a differentiable approximation of this particular ƒ-divergence, making the method feasible for neural networks. Experiments on ChemCam and SuperCam LIBS calibration spectra show that mathematical equation-divergence regularization outperforms or matches standard regularization methods (ℓ 1 , ℓ 2 , dropout) and the classical baseline, partial least squares (PLS). Combining ƒ-divergence regularization with standard regularization yields further performance gains, indicating that distributional regularization is useful in this context giving a promising direction for robust model training in planetary science applications. Source code is publicly available at Klein and Li (2025), https://doi.org/10.11578/dc.20250530.7.

58 GEOSCIENCES↗