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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

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↗
DOE OSTI2024

Unconventional quantum oscillations and evidence of nonparabolic electronic states in quasi-two-dimensional electron system at complex oxide interfaces

The simultaneous occurrence of electric-field controlled superconductivity and spin-orbit interaction makes two-dimensional electron systems (2DES) constructed from perovskite transition metal oxides promising candidates for the next generation of spintronics and quantum computing. It is, however, essential to understand the electronic bands thoroughly and verify the predicted electronic states experimentally in these 2DES to advance technological applications. Here, we present insights into the electronic states of the 2DES at oxide interfaces through comprehensive investigations of Shubnikov–de Haas oscillations in three different systems: EuO/KTaO 3 , LaAlO 3 /SrTiO 3 , and amorphous-LaAlO 3 /KTaO 3 . To accurately resolve these oscillations, we conducted transport measurements in high magnetic fields up to 60 T and low temperatures down to 100 mK. For 2D confined electrons at these interfaces, we observed a progressive increase of oscillations frequency and cyclotron mass with the magnetic field. We interpret these universal and intriguing findings by considering the existence of nontrivial electronic bands, for which the 𝐸−𝑘 dispersion incorporates both linear and parabolic relations. In addition to providing experimental evidence for nonparabolic electronic states in KTaO 3 and SrTiO 3 2DES, the unconventional oscillations presented in this study establish a paradigm for quantum oscillations in 2DES based on perovskite transition metal oxides, where the oscillation frequencies in 1/𝐵 exhibit quadratic dependence on the magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Ab initio exploration of low–lying electronic states of linear and bent MNX + (M = Ca, Sr, Ba, Ra; X = O, S, Se, Te, Po) and their origins

High-level multireference and coupled cluster quantum calculations were employed to analyze low-lying electronic states of linear-MNX + and side-bonded-M[NX] + (M = Ca, Sr, Ba, Ra; X = O, S, Se, Te, Po) species. Their full potential energy curves (PECs), dissociation energies (D e s), geometric parameters, excitation energies (T e s), and harmonic vibrational frequencies (ω e s) are reported. The first three chemically bound electronic states of MNX + and M[NX] + are 3 Σ – , 1 Δ, 1 Σ + and 3 A", 1 A', 1 A", respectively. The 3 Σ – , 1 Δ, 1 Σ + of MNX + originate from the M + ( 2 D) + NX( 2 Π) fragments, whereas the 3 A", 1 A', 1A" states of M[NX] + dissociate to M + ( 2 S) + NX( 2 Π) as a result of avoided crossings. The MNX + and M[NX] + are real minima on the potential energy surface and their interconversions are possible. The M 2+ NX – /M 2+ [NX] – ionic structure is an accurate representation for their low-lying electronic states. The D e s of MNX + species were found to depend on the dipole moment (μ) of the corresponding NX ligands and a linear relationship between these two parameters was observed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Establishing coherent momentum-space electronic states in locally ordered materials

Rich momentum-dependent electronic structure naturally arises in solids with long-range crystalline symmetry. Reliable and scalable quantum technologies rely on materials that are either not perfect crystals or non-crystalline, breaking translational symmetry. This poses the fundamental questions of whether coherent momentum-dependent electronic states can arise without long-range order, and how they can be characterized. Here we investigate Bi 2 Se 3 , which exists in crystalline, nanocrystalline, and amorphous forms, allowing direct comparisons between varying degrees of spatial ordering. Through angle-resolved photoemission spectroscopy, we show for the first time momentum-dependent band structure with Fermi surface repetitions in an amorphous solid. The experimental data is complemented by a model that accurately reproduces the vertical, dispersive features as well as the replication at higher momenta in the amorphous form. These results reveal that well-defined real-space length scales are sufficient to produce dispersive band structures, and that photoemission can expose the imprint of these length scales on the electronic structure.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Doping Effects on Multivalence States, Electronic Structure, and Optical Band Gap in LaCrO 3 under Varied Atmospheres: An Integrated Experimental and Density Functional Theory Study

Doping effects on the valence state, electronic structure, and optical band and the effects on electrical conductivity were studied on the doped lanthanum chromite (LaCrO 3 ) system. The specific compositions studied were La 1–x Ca x CrO 3 (LCCx), La 1–x Sr x CrO 3 (LSCx), and La 0.8 Sr 0.2 Cr 1–x Mn x O 3 (LSCMx) (0.1 ≤ x ≤ 0.4). The powders were synthesized using a modified Pechini sol–gel method, and the ceramic samples were densified using a reactive sintering method resulting in densities >96% theoretical. X-ray photoelectron spectroscopy (XPS) was completed to characterize the defect states and cationic valence compensation as a result of divalent (Ca 2+ or Sr 2+ ) and trivalent (Mn 3+ ) substitutions. XPS was completed for samples tested in oxidizing and reducing atmospheres (up to 1500 °C), which provided insights into the oxidation state transitions induced by the Ca 2+ and Sr 2+ dopants. The work notably demonstrated, for the first time, the oxidation/reduction transitions of Cr 4+ to Cr 3+ in Sr 2+ /Mn 3+ co-doped samples under reducing atmospheres. Reflectance UV–vis spectrophotometry optical band gap measurements were also completed for the same materials; a decrease in the optical band gap (2.81–3.12 eV) was shown with increased substitution, suggesting electronic structure modifications in the LaCrO 3 perovskite. Density functional theory calculations validated experimental trends, predicting a diminishing band gap with a rising dopant concentration. The transition in Cr oxidation states was attributed to the presence of divalent/trivalent cations. These findings contribute some insights into methods to tune the LaCrO 3 electrical properties for various low- and high-temperature applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

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↗
DOE OSTI2026

Modulating Mid-Gap Electronic States Through Site-Selective Modification in B-Pbx/B'-CuyV2O5/CdS Heterostructures for Photocatalytic Hydrogen Evolution

We interfaced ..beta..-Pbx/..beta..'-CuyV2O5 compounds, with varying stoichiometries of precisely positioned Pb-ions (x) and Cu-ions (y) in interstitial sites along a tunnel-structured ?-V2O5 framework, with cysteine-capped CdS (cysCdS) quantum dots (QDs) to yield heterostructured photocatalysts. ..beta..-Pbx/..beta..'-CuyV2O5 compounds exhibit midgap electronic states with orbital contributions from both Cu 3d and stereochemically active Pb 6s states that show distinctive light-initiated reactivity with photoexcited QDs. ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures were prepared by linker-assisted assembly (LAA). Scanning and transmission electron microscopy, energy-dispersive X-ray spectroscopy, and Raman spectroscopy revealed that cysCdS QDs were deposited onto surfaces of ..beta..-Pbx/..beta..'-CuyV2O5 via LAA. HAXPES revealed that the site-selective positioning of Pb-ions and Cu-ions promoted close energetic alignment of the midgap states of ..beta..-Pbx/..beta..'-CuyV2O5 compounds with the valence-band maximum of cysCdS QDs. Transient absorption spectroscopy revealed that photogenerated holes were transferred from CdS QDs to midgap states of ..beta..-Pbx/..beta..'-CuyV2O5 compounds on time scales <50 ps. Finally, photoelectrochemical and photochemical experiments revealed that ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures promoted the photocatalytic reduction of H+ to H2. In photoelectrochemical experiments, under oxidative conditions, for all ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures, H2 was evolved at a Pt counter electrode while a sacrificial donor was oxidized at the heterostructure-functionalized working electrode. In contrast, under reductive conditions, for ..beta..-Pb0.152V2O5/CdS and ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures, H2 was evolved at the working electrode. In photochemical experiments, dispersed ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures promoted the reduction of H+ to H2 under white-light illumination; ..beta..'-Cu0.55V2O5/CdS and ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures, for which midgap states have Cu 3d orbital character, generated 2-fold more H2 than ..beta..-Pb0.152V2O5/CdS heterostructures. Cu-ion insertion thus appends additional acceptor surface states that improve ligand-mediated hole transfer from photoexcited QDs, but such states are intrinsically limited in mediating hole transport to the substrate as a result of the low mobility of holes in narrow Cu 3d-states. Our results reveal that the density and orbital character of midgap states of ..beta..-Pbx/..beta..'-CuyV2O5 compounds, tunable through recently developed site-selective ion insertion strategies, determine efficiencies of charge-transfer and charge-transport mechanisms that underpin photocatalysis.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Investigation of Key Electronic States in Layered Mixed Chalcogenides With a d 0 Transition Metal as Li-Ion Cathodes

Lithium-rich transition metal chalcogenides are witnessing a revival as candidates for Li-ion cathode materials, spurred by the boost in their capacities from transcending conventional redox processes based on cationic states and tapping into additional chalcogenide states. A particularly striking case is Li 2 TiS 3-y Se y , which features a d 0 metal. While the end members are expectedly inactive, substantial capacities are measured when both Se and S are present. Using X-ray absorption spectroscopy, it is shown that the electronic structure of Li 2 TiS 3-y Se y is not a simple combination of the end members. The data confirm previous hypotheses that, in Li 2 TiS 2.4 Se 0.6 , this behavior is underpinned by concurrent and reversible redox of only S and Se, and identify key electronic states. Moreover, wavelet transforms of the extended X-ray absorption fine structure provide direct evidence of the formation of short Se–Se units upon charging. The study uncovers the underpinnings of this intriguing reactivity and highlights the richness of redox chemistry in complex solids.

25 ENERGY STORAGE↗
DOE OSTI2024

An under-approximation of entropy for elemental multiconfigurational ground state electronic structures

A combinatorial approach has been applied to the allowable permutations of quantum electronic configurations under the constraints of Hund's rule for established ground state configurations toward an under-approximation of electronic structure entropy. Combined with a previously reported over-approximation, the approximations are used in conjunction in an attempt to bracket the upper and lower entropy limits for multiconfigurational ground state electronic structure entropy and compared to known standard molar entropies for the elements. This formality has been used for the application of a classical statistical mechanics methodology to be applied to the discrete sets of quantum mechanical states of Pu in order to calculate orbital occupancies in Pu's multiconfigurational ground state. Without consideration of the relative energies of various possible electronic configurations contributing to the multiconfigurational ground state, the calculations are performed under a general energy degeneracy assumption weighted to the number of permutations for specific configurations. The number of configurations assumed to significantly contribute is gradually constrained in order to approach a low-order approximation of orbital occupancies in Pu that are then compared to experimental and other calculated results from the literature.

Beaux, II, Miles F. (ORCID:000000032192626X)↗
DOE OSTI2025

Differential Ligation Alters Electronic State and Coupling Signals of Iron-Sulfur Clusters in Flavin-Based Electron Bifurcation

Flavin-based electron bifurcation (FBEB) is employed by microorganisms for controlling pools of redox equivalents by reversibly splitting electron pairs into high- and low-energy levels from an initial midpoint potential. Our ability to harness this phenomenon is crucial for biocatalytic design which is limited by our understanding of energy coupling in the bifurcation system. In Pyrococcus furiosus, FBEB is carried out by the NADH-dependent ferredoxin:NADP+-oxidoreductase (NfnSL), coupling the uphill reduction of ferredoxin in NfnL to the downhill reduction of NAD+ in NfnS from oxidation of NADPH. Flanking the bifurcating flavin are two site-differentiated iron-sulfur clusters; the nearest is a glutamate-ligated [4Fe-4S] cluster in NfnL. Recent biochemical experiments substituting the native glutamate with cysteine led to loss of coupling between the uphill and downhill pathways, in contrast to the tight thermodynamic coupling in the native system. To understand how this decoupling is biochemically manifested by the cysteine-substituted [4Fe-4S] in NfnL, we employed electron paramagnetic resonance (EPR) spectroscopy to identify changes in electronic architecture and square wave voltammetry (SWV) to probe thermodynamic shifts produced by the substitution. We observed notable g-value shifts in the EPR for the cysteine-substituted iron-sulfur cluster in addition to significant downward shifts in the redox potential, as well as the disappearance of several low-field signals observed in the native NfnSL complex. These results suggest the site-differentiated glutamate residue facilitates higher spin states in the [4Fesingle bond4S] cluster to bridge energetic gaps in electron transfer to the bifurcating flavin in the native complex, preventing unwanted short-circuiting seen in the cysteine-substituted complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Direct and Inverse Photoelectron Spectroscopy Evidence for a Revised Picture of Electronic States of Negative Polarons in n‐Doped C 60

Abstract Determining the electronic levels associated with polarons, the fundamental charge carriers in organic semiconductors, is key to understanding the charge transport properties of these materials. Recent findings challenge the traditional view of these electronic levels by highlighting the importance of intra‐molecular Coulomb interactions in polarons. Experimental evidence was previously presented for a revised model of the negative polaron in the case of the polymer semiconductor poly(NDI2OD‐T 2 ); there, the addition of an excess electron was seen to lead to the emergence of a singly occupied state within the energy gap of the undoped material and an unoccupied state above the edge of the conduction states . Here, focus is on a small‐molecule semiconductor, C 60 , and spectral evidence is provided of a similar picture for the new states appearing upon polaron formation. Specifically, direct and inverse photoemission spectroscopy is used to investigate the density of states in C 60 films n‐doped with two dimeric dopants. The Coulomb interaction energy (Hubbard U ) of the C 60 anion is experimentally determined to be ≈1.1 eV, a value that aligns closely with theoretical predictions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bridge connectivity effects on photoinduced ground-state electron spin polarization

Transient electron paramagnetic resonance (TREPR) spectroscopy has been used to probe photoinduced electron spin polarization in the recovered ground states of four radical-elaborated (CAT)Pt(bpy) donor-acceptor complexes (CAT = catechol; bpy = 4,4'-di-tert-butyl-2,2'-bipyridine). These complexes are comprised of one or two S = 1/2 nitronyl nitroxide radicals attached through different phenylethynyl bridges to the 3- or 3,6 positions of the CAT donor. In this paper, we demonstrate the effects of substitution patterns on the magnitude of the TREPR signal, thereby guiding future design principles for generating and understanding the origin of photoinduced electron spin polarization in these and related chromophores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Graphene-driven correlated electronic states in one dimensional defects within WS2

Tomonaga-Luttinger liquid (TLL) behavior in one-dimensional systems has been predicted and shown to occur at semiconductor-to-metal transitions within two-dimensional materials. Reports of one-dimensional defects hosting a Fermi liquid or a TLL have suggested a dependence on the underlying substrate, however, unveiling the physical details of electronic contributions from the substrate require cross-correlative investigation. Here, we study TLL formation within defectively engineered WS2 atop graphene, where band structure and the atomic environment is visualized with nano angle-resolved photoelectron spectroscopy, scanning tunneling microscopy and spectroscopy, and non-contact atomic force microscopy. Correlations between the local density of states and electronic band dispersion elucidated the electron transfer from graphene into a TLL hosted by one-dimensional metal (1DM) defects. It appears that the vertical heterostructure with graphene and the induced charge transfer from graphene into the 1DM is critical for the formation of a TLL.

Rossi, Antonio↗
DOE OSTI2026

Correlating Surface Processing of Nb Superconducting RF Cavities with the Evolution of Surface Electronic States

Superconducting-radio frequency (RF) cavities provide an efficient way to accelerate particle beams with extremely high acceleration gradients while generating very small power dissipation. The few nanometers of the surface play a critical role in defining the RF performance of superconducting Nb based cavities. Over the past two decades, several pioneering surface treatment and processing methods have emerged, enabling remarkable improvements in superconducting cavity performance by simultaneously achieving high quality factors with increasing maximum acceleration gradients. These processing approaches include chemical polishing, distinct multi-step thermal treatments under ultra-high vacuum (UHV) conditions over low to high temperature regimes, as well as high-temperature treatments under controlled nitrogen atmospheres. Beyond their macroscopic impact on RF performance, these methods produce distinct surface oxide configurations characterized by different valence states, oxide thicknesses, chemical uniformity, and oxygen concentration profiles extending into the near-surface bulk of niobium. In this work, we are trying to understand how the surface-processing methods and the resulting oxide/oxygen profiles affect the electronic structure of surface and the mechanism of superconductivity. Using a combination of X-ray photoemission and X-ray absorption spectroscopies, we investigate how the valence-band structure and the electronic density of states (DoS) near the Fermi level evolve under different surface treatments. By employing tunable photon energies across multiple elemental absorption edges, we use resonant photoemission to disentangle and identify the elemental contributions to specific valence-band features. Our observations show that different surface-processing methods lead to distinct temperature evolutions of the DoS and valence-band states near the Fermi level. Our results suggest variations in different Nb-O orbital hybridizations in distinct processes and point towards the possibility of different underlying mechanisms of superconductivity governed by surface chemistry and oxide configuration. We also correlate these distinct superconducting mechanisms with RF cavity performance, specifically focusing on measured surface resistance, the nature of the Q-slope, and quench fields observed in superconducting RF measurements. These results will enable us to identify the potential limiting factors and relevant controllable parameters that can be further optimized to improve the performance of superconducting RF cavities.

Tripathi, Malvika [Fermilab] (ORCID:00000001989251↗
DOE OSTI2025

Automated Construction of Artificial Lattice Structures with Designer Electronic States

Manipulating matter with a scanning tunneling microscope (STM) enables the creation of atomically defined artificial structures that host designer quantum states. However, the time-consuming nature of the manipulation process, coupled with the sensitivity of the STM tip, constrains the exploration of diverse configurations and limits the size of the designed features. In this study, we present a reinforcement learning (RL)-based framework for creating artificial structures by spatially manipulating carbon monoxide (CO) molecules on a copper substrate by using the STM tip. The automated workflow combines molecule detection and manipulation, employing deep-learning-based object detection to locate CO molecules and linear assignment algorithms to allocate these molecules to designated target sites. We initially perform molecule maneuvering based on randomized parameter sampling for sample bias, tunneling current set point, and manipulation speed. This data set is then structured into an action trajectory used to train an RL agent. The model is subsequently deployed on the STM for real-time fine-tuning of the manipulation parameters during structure construction. Our approach incorporates path-planning protocols coupled with active drift compensation to enable atomically precise fabrication of structures with significantly reduced human input while realizing larger-scale artificial lattices with the desired electronic properties. Furthermore, using our approach, we demonstrate the automated construction of an extended artificial graphene lattice and confirm the existence of a characteristic Dirac point in its electronic structure. Further challenges regarding the RL-based structural assembly scalability are discussed.

Algorithms↗
DOE OSTI2025

Excited electronic states of Na 2 and K 2 : The potential for long-lived “reservoir” states leading to collision induced population inversions

Potential energy curves (PECs) for the spin-free (ΛS) and spin–orbit (Ω) states associated with the four lowest-lying dissociation channels of Na 2 and K 2 were calculated at the SA-CASSCF/SO-CASPT2/aug-cc-pwCVQZ-DK level. The PECs of Na 2 were consistent with the experimental data and with the FS-CCSD (2,0) calculations, reproducing the double-well and the “shelf” character for some of the potentials of the excited states. For K 2 , the PECs behaved in a similar way and the spectroscopic parameters for the ground and the excited states are in good agreement with the available experimental values. The dissociation energy of K 2 was predicted to be D e = 4454 cm −1 , within an agreement of 5 cm −1 with the experiments. For Na 2 , D e = 5789 cm −1 compared to the experimental value of 6022 cm −1 . The inclusion of spin–orbit coupling effects resulted in avoided crossings, which affect the PECs. Spin–orbit changes the predicted curves for some excited Ω states arising from ΛS states that overlap each other, affecting their associated vibrational frequencies and bond distances. Here, the current studies of the low-lying states in K 2 reveal a similar structure to those of Na 2 , which suggests the accessibility of long-lived energy storing reservoir states and possible population inversions in K 2 following prior experimental work on the reaction of halogen atoms with Na 3 to produce excited states of Na 2 .

Ab-initio methods↗