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At least 253 records · Page 14

Leveraging Intramolecular π-Stacking to Access an Exceptionally Long-Lived 3 MC Excited State in an Fe(II) Carbene Complex

The ability to manipulate excited-state decay cascades using molecular structure is essential to the application of abundant-metal photosensitizers and chromophores. Ligand design has yielded some spectacular results elongating charge-transfer excited state lifetimes of Fe(II) coordination complexes, but triplet metal-centered ( 3 MC) excited states - recently demonstrated to be critical to the photoactivity of isoelectronic Co(III) polypyridyls - have to date remained elusive, with temporally isolable examples limited to the picosecond regime. Here, with this report, we show how strong-field donors and intramolecular π-stacking can conspire to stabilize a long-lived 3 MC excited state for a remarkable 4.1 ± 0.3 ns in fluid solution at ambient temperature. Analysis of variable-temperature time-resolved absorption data using theoretical models ranging from Arrhenius to semiclassical Marcus theory, combined with computational modeling and X-ray crystallography, reveal a Jahn−Teller stabilized excited state with a high activation barrier for ground-state recovery. The net result is a chromophore with a 3 MC excited-state lifetime that is orders of magnitude longer than anything yet observed for an Fe(II) complex.

carbene compounds↗

Probing Excited-State Dynamics of Transmon Ionization

The fidelity and quantum nondemolition character of the dispersive readout in circuit QED are limited by unwanted transitions to highly excited states at specific photon numbers in the readout resonator. This observation can be explained by multiphoton resonances between computational states and highly excited states in strongly driven nonlinear systems, analogous to multiphoton ionization in atoms and molecules. In this work, we utilize the multilevel nature of high-𝐸 𝐽 /𝐸 𝐶 transmons to probe the excited-state dynamics induced by strong drives during readout. With up to ten resolvable states, we quantify the critical photon number of ionization, the resulting state after ionization, and the fraction of the population transferred to highly excited states. Moreover, using pulse shaping to control the photon number in the readout resonator in the high-power regime, we tune the adiabaticity of the transition and verify that transmon ionization is a Landau-Zener-type transition. We further extend these methods to a typical transmon with 𝐸 𝐽 /𝐸 𝐶 ≈ 55 and probe the offset-charge dependence of ionization dynamics in a timed-resolved manner. Our experimental results agree well with the theoretical prediction from a semiclassical driven transmon model and may guide future exploration of strongly driven nonlinear oscillators.

cavity quantum electrodynamics↗

Steric augmentation of three-coordinate Cu( I ) β-diketiminate isocyanide chromophores to achieve microsecond excited-state lifetime

Copper(I) complexes are promising alternatives to noble metal-based photosensitizers. A recently developed class of three-coordinate copper(I) charge-transfer chromophores, pairing β-diketiminate ligands with aryl isocyanides, exhibits excited-state lifetimes that are responsive to the steric profile of the isocyanide, reaching a value of nearly 300 nanoseconds when a substituted m-terphenyl isocyanide was used. In this work, we show that extreme steric augmentation of the β-diketiminate and m-terphenyl isocyanide ligands can lead to further improvements in excited-state lifetime, with one example surpassing 1 µs. This study includes a series of eight compounds of the general formula Cu(RNacNac)(CN-Ar X2 ), where RNacNac is the substituted β-diketiminate and CN-Ar X2 is the substituted m-terphenyl isocyanide. All eight compounds are crystallographically characterized, and their excited-state properties are thoroughly evaluated by a combination of steady-state and time-resolved photoluminescence studies. This combined structural/photophysical approach unveils a correlation between common steric parameters, derived from buried volume (%V bur ) and solid angle analysis, and the excited-state lifetime. Our investigation reveals that the steric profile of the β-diketiminate has a much larger impact on the steric profile and lifetime, whereas the m-terphenyl isocyanide substituents have an unsystematic and subtle influence on these two correlated parameters. Nevertheless, judicious pairing of the two ligands is critical for achieving long excited-state lifetimes.

Kumar, Ashish [University of Houston, TX (United S↗

Braiding for the win: Harnessing braiding statistics in topological states to play quantum games

Nonlocal quantum games provide proof of principle that quantum resources can confer an advantage at certain tasks. They also provide a compelling way to explore the computational utility of phases of matter on quantum hardware. In a recent paper [O. Hart et al., Phys. Rev. Lett. 134, 130602 (2025)], we demonstrated that a toric code resource state conferred advantage at a certain nonlocal game, which remained robust to small deformations of the resource state. In this paper we demonstrate that this robust advantage is a generic property of resource states drawn from topological or fracton ordered phases of quantum matter. To this end, we illustrate how several other states from paradigmatic topological and fracton ordered phases can function as resources for suitably defined nonlocal games, notably the three-dimensional toric-code phase, the X-cube fracton phase, and the double-semion phase. The key in every case is to design a nonlocal game that harnesses the characteristic braiding processes of a quantum phase as a source of contextuality. We unify the strategies that take advantage of mutual statistics by relating the operators to be measured to order and disorder parameters of an underlying generalized symmetry-breaking phase transition. Additionally, by connecting the win probability to twist products, we show that success at the game serves as a many-body entanglement witness. Namely, if the players implement a perfect quantum strategy on large length scales, the quantum state they share cannot be connected to a trivial product state via a constant-depth local unitary circuit. Lastly, we massively generalize the family of games that admit perfect strategies when codewords of homological quantum error-correcting codes are used as resources.

Fractons↗

Precision measurement of lifetime and branching ratios of the 4⁢𝑓 13⁡ 5⁢𝑑⁢6⁢𝑠 1 ⁢[5/2] 5/2 state in Yb + ions

We report spectroscopic and time-resolved experimental observations to characterize the [Xe]⁢4⁢𝑓 13 ⁡( 2 𝐹$^𝑜_{5/2}$)⁢5⁢𝑑⁢6⁢𝑠⁡( 1 𝐷)⁢ 1 ⁢[5/2]$^𝑜_{5/2}$ state in 172 Yb + ions. We access this state from the metastable 4⁢𝑓 14 ⁡5⁢𝑑⁡( 2 𝐷 3/2,5/2 ) manifold and observe an unexpectedly long lifetime of 𝜏 = 37.9⁢(9) ⁢µ⁢s that allows visible Rabi oscillations and resolved-sideband spectroscopy. Using a combination of coherent population dynamics, high-fidelity detection and heralded state preparation, and optical pumping methods, we measure the branching ratios to the 2 𝐷 3/2 , 2 𝐷 5/2 , and 2 𝑆 1/2 states to be 0.359⁢(2), 0.639(2), and 0.0023⁢(16), respectively. The branching ratio to the 4⁢𝑓 13⁡ 6⁢𝑠 2 ⁡( 2 𝐹 7/2 ) is compatible with zero within our experimental resolution. We also report measurements of Landé 𝑔-factor of the 1 ⁢[5/2]$^𝑜_{5/2}$ state. Further, the branching ratio of the 2 𝐷 5/2 to 2 𝑆 1/2 decay in 172 Yb + was measured to be 0.188(3), improving its relative uncertainty by an order of magnitude. Our measurements provide experimental benchmarks for better understanding the atomic structure of Yb + ions, which still lacks accurate numerical descriptions, and the use of high-lying excited states for partial detection and qubit manipulation in the omg architecture.

74 ATOMIC AND MOLECULAR PHYSICS↗

Combined Machine Learning and Molecular Dynamics Reveal Two States of Hydration of a Single Functional Group of Cationic Polymeric Brushes

The state of hydration of a macromolecular system regulates a plethora of different properties of such a system. In this article, we develop a novel machine learning (ML) approach, based on the unsupervised clustering algorithm, for probing the hydration behavior of the {N(CH 3 ) 3 } + functional group of the PMETAC [Poly(2-(methacryloyloxy)ethyl trimethylammonium chloride] polyelectrolyte (PE) brush system. The PE brushes and the brush-supported water molecules and counterions (chloride ions) are first described using all-atom molecular dynamics (MD) simulations. The simulation data is subsequently used in our ML framework to identify that (1) the {N(CH 3 ) 3 } + functional groups of the PMETAC brushes have two distinct hydration states with one state (state 1) being characterized by less structured water molecules and the other state (state 2) being characterized by more structured water molecules and (2) an enhancement in the brush grafting density leads to the progressive dissapparenace of state 2. An increase in the grafting density increases the number of chloride counterions in a given volume around the {N(CH 3 ) 3 } + functional group and increases the number of shared water molecules between the {N(CH 3 ) 3 } + and Cl - . The chloride counterions are associated with a hydration layer with much less structured water molecules. Therefore, with an increase in the grafting density, an increase in the percentage of shared water molecules leads to the prevalence of the hydration state [of the {N(CH 3 ) 3 } + moiety] with less structured water molecules. Finally, we explain how the present findings are commensurate with two key previous related results, namely a significantly large chloride ion mobility inside the PMETAC brush layer and the {N(CH 3 ) 3 } + -Cl - average distance remaining independent of the PMETAC brush grafting density. Furthermore, we anticipate that the combined ML-MD-simulation approach proposed in this study can be adapted to probe other soft matter systems to reveal new insights of the underlying mechanisms of emergent phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Excited state electronic structure of dimethyl disulfide involved in photodissociation at ∼200 nm

Dimethyl disulfide (DMDS), one of the smallest organic molecules with an S–S bond, serves as a model system for understanding photofragmentation in polypeptides and proteins. Prior studies of DMDS photodissociation excited at ∼266 nm and ∼248 nm have elucidated the mechanisms of S–S and C–S bond cleavage, which involve the lowest excited electronic states S 1 and S 2 . Far less is known about the dissociation mechanisms and electronic structure of relevant excited states of DMDS excited at ∼200 nm. Herein we present calculations of the electronic structure and properties of electronic states S 1 –S 6 accessed when DMDS is excited at ∼200 nm. Our analysis includes a comparison of theoretical and experimental UV spectra, as well as theoretically predicted one-dimensional cuts through the singlet and triplet potential energy surfaces along the S–S and C–S bond dissociation coordinates. Finally, we present calculations of spin–orbit coupling constants at the Franck–Condon geometry to assess the likelihood of ultrafast intersystem crossing. We show that choosing an accurate yet computationally efficient electronic structure method for calculating the S 0 –S 6 potential energy surfaces along relevant dissociation coordinates is challenging due to excited states with doubly excited character and/or mixed Rydberg-valence character. Our findings demonstrate that the extended multi-state complete active space second-order perturbation theory (XMS-CASPT2) balances this computational efficiency and accuracy, as it captures both the Rydberg character of states in the Franck–Condon region and multiconfigurational character toward the bond-dissociation limits. In conclusion, we compare the performance of XMS-CASPT2 to a new variant of equation of motion coupled cluster theory with single, double, and perturbative triple corrections, EOM-CCSD(T)(a)*, finding that EOM-CCSD(T)(a)* significantly improves the treatment of doubly excited states compared to EOM-CCSD, but struggles to quantitatively capture asymptotic energies along bond dissociation coordinates for these states.

Rishi, Varun↗

A molecular ground electronic state with an occupied 5g spinor—The superheavy (E125)F molecule

Fully relativistic calculations, primarily at the 4-component coupled-cluster singles and doubles with perturbative triples [CCSD(T)] level of theory with the Dirac–Coulomb (DC) Hamiltonian, have been carried out for the superheavy (E125)F molecule using large Gaussian basis sets. The electronic ground state is determined to have an [Og]8s 2 5g 1 6f 3 configuration on E125 with an Ω = 6 ground state and an 8p electron largely donated to F. A Mulliken population analysis indicates that the ground state is mainly ionic with a partial charge of +0.79 on E125 and a single sigma bond involving the F 2p and E125 8p spinors. The occupied g spinor is not involved in the bonding. With the largest basis set used in this work, the (0 K) dissociation energy was calculated at the DC-CCSD(T) level of theory to be 7.02 eV. Analogous calculations were also carried out for the E125 atom, both the neutral and its cation. The lowest energy electron configuration of E125 + , [Og]$8s$$^{2}_{1/2}$$5g$$^{1}_{7/2}$$6f$$^{3}_{5/2}$ with a J = 6 ground state, was found to be similar to that in (E125)F, while the neutral E125 atom has an [Og]$8s$$^{2}_{1/2}$$5g$$^{1}_{7/2}$$6f$$^{2}_{5/2}$$7d$$^{1}_{3/2}$$8p$$^{1}_{1/2}$ ground state electron configuration with a J = 17/2 ground state. The ionization energy (IE) of E125 is reported for the first time and is calculated to be 4.70 eV at the DC-CCSD(T) level of theory. Non-relativistic calculations were also carried out on the E125 atom and the (E125)F molecule. Here, the non-relativistic ground state of the E125 atom was calculated to have a 5g 5 ground state with an IE of just 3.4 eV. The net effect of relativity on (E125)F is to stabilize its bonding.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Diagonal state designs with reconfigurable real-time circuits

Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple and efficient diagonal state 3-design based on real-time evolutions under 2-local Hamiltonians. Our construction is inspired by the classical Girard-Hutchinson trace estimator in that it involves the stochastic preparation of many random-phase states. Though the exact Girard-Hutchinson states are not tractably implementable on a quantum computer, we can construct states that match the statistical moments of the Girard-Hutchinson states with real-time evolution. Importantly, our random states are all generated using the same Hamiltonians for real-time evolution, with the randomness arising solely from stochastic variations in the durations of the evolutions. In this sense, the circuit is fully reconfigurable and thus suited for near-term realizations on both digital and analog platforms. Moreover, we show how to extend our construction to achieve diagonal state designs of arbitrarily high order.

Shen, Yizhi [LBL, Berkeley] (ORCID:000000024160548↗

Learning energy-based representations of quantum many-body states

Efficient representation of quantum many-body states on classical computers is a problem of practical importance. An ideal representation of a quantum state combines a succinct characterization informed by the structure and symmetries of the system along with the ability to predict the physical observables of interest. Several machine-learning approaches have been recently used to construct such classical representations, which enable predictions of observables and account for physical symmetries. However, the structure of a quantum state typically gets lost unless a specialized is employed based on prior knowledge of the system. Moreover, most such approaches give no information about what states are easier to learn in comparison with others. Here, we propose a generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Based on the prior information on a family of quantum states, the energy function can be specified by a small number of parameters using an explicit low-degree polynomial or a generic parametric family such as neural nets and can naturally include the known symmetries of the system. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables. Importantly, the structure of the learned energy function provides a natural explanation for the difficulty of learning an energy-based representation of a given class of quantum states when measured in a certain basis. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Defect-induced displacement of topological surface state in quantum magnet MnBi2Te4

The topological magnet MnBi2⁢Te4 (MBT), with gapped topological surface state, is an attractive platform for realizing quantum anomalous Hall and axion insulator states. However, the experimentally observed surface state gaps fail to meet theoretical predictions, although the exact mechanism behind the gap suppression has been debated. Recent theoretical studies suggest that intrinsic antisite defects push the topological surface state away from the MBT surface, closing its gap and making it less accessible to scanning probe experiments. Here, we report on the local effect of defects on the MBT surface states and demonstrate that high defect concentrations lead to a displacement of the surface states well into the MBT crystal, validating the theorized mechanism. The local and global influence of antisite defects on the topological surface states are studied with samples of varying defect densities by combining scanning tunneling microscopy, angle-resolved photoemission spectroscopy, and density functional theory. Our findings identify a combination of increased defect density and reduced defect spacing as the primary factors underlying the displacement of the surface states and suppression of surface gap, guiding further development of topological quantum materials.

Lupke, Felix [Carnegie Mellon University (CMU)]↗

Barotropic instability of basic states with a realistic jet and a wave

The stability of basic states consisting of a jet similar to the stratospheric polar night jet and a traveling wave with a single zonal wavenumber is examined in a linearized nondivergent barotropic model on a sphere. Basic state waves are chosen to resemble observed traveling and stationary features in the winter stratosphere. Results are presented for disturbance growth rates, propagation characteristics, and energy conversion as a function of the basic state wave amplitude. The effects of small amplitude basic state waves on unstable disturbances arising from a zonally symmetric jet are discussed; results are shown where a small amplitude basic state wave dramatically affects the stability characteristics. Evidence is shown that the presence of a traveling wave may favor the appearance of disturbances that include other zonal wavenumbers which move with the basic state wave; this result is discussed in relation to the origin of observed quasi-nondispersive features in the polar winter stratosphere. Results for a stationary wavenumber 1 basic state wave suggest that a distorted polar vortex may be unstable to disturbances that would lead to further distortion. An unstable disturbance for a basic state with an eastward moving wavenumber 2 has components which resemble, in period and location, traveling waves that are observed in the winter stratosphere.

Manney, Gloria L.↗

A theoretical study of the low-lying states of Ti2 and Zr2

The low-lying states of Ti2 and the valence isoelectronic Zr2 are examined theoretically by means of a multireference configuration-interaction (MRCI) method. MRCI calculations demonstrate that two of the Zr2 states are very low-lying and that the resulting vertical excitation is consistent with the optical spectrum of Zr2. The ground state is predicted for Ti2 on the basis of valence correlation with the MRCI method and the average coupled-pair functional technique. Calculations of the inner-shell correlation effects are estimated and found to lower the 3Delta g state to a ground state, and another to a very low-lying state. The ground state of Ti2 is assigned to 3Delta g since it is lower than the other state at all levels of correlation and is derived from the same atomic asymptote. This conclusion is supported by the lack of an electron-spin resonance signal but contradicts the absence of subcomponents on the Raman spectral lines.

Bauschlicher, Charles W., Jr.↗

Performance and state-space analyses of systems using Petri nets

The goal of any modeling methodology is to develop a mathematical description of a system that is accurate in its representation and also permits analysis of structural and/or performance properties. Inherently, trade-offs exist between the level detail in the model and the ease with which analysis can be performed. Petri nets (PN's), a highly graphical modeling methodology for Discrete Event Dynamic Systems, permit representation of shared resources, finite capacities, conflict, synchronization, concurrency, and timing between state changes. By restricting the state transition time delays to the family of exponential density functions, Markov chain analysis of performance problems is possible. One major drawback of PN's is the tendency for the state-space to grow rapidly (exponential complexity) compared to increases in the PN constructs. It is the state space, or the Markov chain obtained from it, that is needed in the solution of many problems. The theory of state-space size estimation for PN's is introduced. The problem of state-space size estimation is defined, its complexities are examined, and estimation algorithms are developed. Both top-down and bottom-up approaches are pursued, and the advantages and disadvantages of each are described. Additionally, the author's research in non-exponential transition modeling for PN's is discussed. An algorithm for approximating non-exponential transitions is developed. Since only basic PN constructs are used in the approximation, theory already developed for PN's remains applicable. Comparison to results from entropy theory show the transition performance is close to the theoretic optimum. Inclusion of non-exponential transition approximations improves performance results at the expense of increased state-space size. The state-space size estimation theory provides insight and algorithms for evaluating this trade-off.

Watson, James Francis, III↗

Low-state disks and low-beta disks

Stellar black hole candidates (BHCs) exhibit bimodal spectral states. We calculate nonthermal disk spectra, demonstrating that a large photon index (alpha (sub x) approximately 2-3) observed in the soft (high) state is due to a copious soft photon supply, whereas soft photon starvation leads to a smaller index (alpha (sub x) approximately 1.5-2) in the hard (low) state. Thus, the absence of the soft component flux in the low state cannot be due to obscuration. A possible disk configuration during the low state is discussed. We proposed that a low-state disk may be a low-beta disk in which magnetic pressure may exceed gas pressure becuase of the suppression of field escape by a strong shear. As a result, disk material will take the form of blobs constricted by mainly toroidal magnetic fields. Fields are dissipated mainly by occasional reconnection events with a huge energy release. This will account for large-amplitude, aperiodic X-ray variations (flickering) and high-energy radiation with small alpha(sub x) from hard state BHCs and possibly from active galactic nuclei. Further, we propose a hysteretic relation between the mass-flow rate and plasma-beta, a ratio of gas pressure to magnetic pressure, for the spectral evolution of transient BHCs. The disk is in the low-beta state in quiescence and early rise. The low-beta disk is optically thin and affected by advection. A hard-to-soft transition occurs before the peak luminosity, since there is no advection-dominated branch at higher luminosities. An optically thick, high-beta disk appears at small radii. In the decay phase of the light curve, the standard-type disk becomes effectively optically thin, when a soft-hard transition is triggered. High-beta plasmas in the main body shrink to form minute blobs, and low-beta coronal plasma fills interblob space.

Mineshige, Shin↗

Quasi-Periodic Oscillations in Black Hole Candidates as an Indicator of Transition Between Low and High States

By comparing positions on a spectral color-color diagram from 10 black hole candidates (BHCS) observed with Ginga (1354-64, 1826-24, 1630-47, LMC X-1, LMC X-3, GS 2000+25, GS 2023+33, GS 1124-68, Cyg X-1, and GX 339-4) with the observed broadband noise (BBN) (0.001-64 Hz) and quasi-periodic oscillation (QPO) variability, we find that the "very high state" is spectrally intermediate to the soft/high state and hard/low state. We find a transition point in spectral hardness where the dependence of the BHC QPO centroid frequency (of GS 1124-68 and GX 339-4) on spectral hardness switches from a correlation to an anticorrelation; where the BBN variability switches from high state to low state; and where the spectral hardness of the QPO relative to that of the BBN variability is a maximum. This coincidence of changing behavior in both the QPO and the broadband variability leads us to hypothesize that the QPO is due to interaction between the physical components which dominate the behaviors of BHCs when they occupy the hard/low and soft/high states. We conclude that these QPOs should be observed from BHCs during transition between these two states. Comparison with QPO and BBN behavior observed during the 1996 transition of Cyg X-1 supports this hypothesis. We also report 1-3 Hz QPOs observed in GS 2000+25 and Cyg X-1 in the hard/low state, and we compare these to the QPOs observed in GS 1124-68 and GX 339-4.

Rutledge, Robert E.↗

The Low-Lying Electronic States of LiB

The spectroscopic constants for the triplet and singlet states of LiB below about 30 000/ cm are determined using an internally contracted multireference configuration interaction approach in conjunction with [6s 5p 3d 2f] atomic natural orbital basis sets. The ground state is (sup 3)Pi as found in previous work. No excited triplet states are found to be ideal for characterizing the ground state; the (1)(sup 3)Sigma(sup -) state has a transition energy that is too small for many experimental approaches and the (2)(sup 3)Pi and (3)(sup 3)Pi states have bond lengths that are significantly longer than the ground state, resulting in transition intensities that are spread out over many vibrational levels of the ground state.

Ricca, Alessandra↗

SNC Oxygen Fugacity Recorded in Pyroxenes and its Implications for the Oxidation State of the Martian Interior: An Experimental and Analytical Study

Knowledge of the oxidation state of a magma is critical as it is one of the parameters which controls the nature and composition of the resulting crystals. In terrestrial magmatic systems, oxygen fugacity (fo2) is known to vary by over nine orders of magnitude. With variations of this magnitude, understanding the compositional differences, phase changes, and crystallization sequence variations, caused by the magma fo2, is essential in deciphering the origin of all igneous rocks. Magmatic oxidation state is of great importance in that it reflects the degree of oxidation of the source region and can provide insight into magmatic processes, such as metasomatism, degassing, and assimilation, which may have changed them. Carmichael [1991] argues that most magmas are unlikely to have their redox states altered from those of their source region. This assumption allows for estimation of the oxidation state of planetary interiors. Conversely, it is known that the fo2 of the magma can be affected by other processes, which occur outside of the source region and therefore, the oxidation state may record those too. Processes which could overprint source region fugacities include melt dehydrogenation or other volatile loss, water or melt infiltration, or assimilation of oxidized or reduced wallrock. Understanding which of these processes is responsible for the redox state of a magma can provide crucial information regarding igneous processes and other forces active in the region. The composition of the SNC basalts and their widely varying proposed oxidation states raise some interesting questions. Do the SNC meteorites have an oxidized or reduced signature? What was the oxygen fugacity of the SNC source region at the time of melt generation? Is the fugacity calculated for the various SNC samples the fugacity of the magma source region or was it overprinted by later events? Are there different oxidation states in the Martian interior or a single one? This proposal seeks to address all of these questions.

McCanta, M. C.↗