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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 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Is organic photovoltaics promising for indoor applications?

This work utilizes organic photovoltaics (OPV) for indoor applications, such as powering small electronic devices or wireless connected Internet of Things. Three representative polymer-based OPV systems, namely, poly(3-hexylthiophene-2,5-diyl), poly[N-9′-heptadecanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2-thienyl-2′, 1′,3′-benzothiadiazole)], and poly[[4,8-bis[(2-ethylhexyl)oxy]benzo[1,2-b:4,5-b′]dithiophene-2,6-diyl] [3-fluoro-2-[(2-ethylhexyl)carbonyl]thieno[3,4-b]thiophenediyl]], were selected as the donor materials in blend with fullerene derivatives for comparison under low light level condition using fluorescent lamps. PCDTBT based devices are found to be the best performing system, generating 13.9 μW/cm{sup 2} corresponding to 16.6% power conversion efficiency at 300 lx, although PTB7 based devices show the highest efficiency under one sun conditions. This high performance suggests that OPV is competitive to the other PV technologies under low light condition despite much lower performance under one sun condition. Different properties of these devices are studied to explain the competitive performance at low light level. A low energy consuming method for maximum power point tracking is introduced for the operation of the OPV devices. Finally, a 14 cm × 14 cm OPV module with 100 cm{sup 2} active area is demonstrated for real applications. These findings suggest that OPV, in particular, PCDTBT based devices, could be a promising candidate for indoor applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Investigation of phonon transport and thermal boundary conductance at the interface of functionalized SWCNT and poly (ether-ketone)

Carbon nanostructures such as carbon nanotube (CNT), graphene, and carbon fibers can be used as fillers in amorphous polymers to improve their thermal properties. In this study, the effect of covalent bonding of CNT with poly(ether ketone) (PEK) on interfacial thermal interactions is investigated using non-equilibrium molecular dynamics simulations. The number of covalent bonds between (20, 20) CNT and PEK is varied in the range of 0–80 (0%–6.25%), and the thermal boundary conductance is computed. The analysis reveals that covalent functionalization of CNT atoms can enhance the thermal boundary conductance by an order of magnitude compared to the non-functionalized CNT-PEK interface at a high degree of CNT functionalization. Besides strengthening the thermal coupling, covalent functionalization is also shown to modify the phonon spectra of CNT. The transient spectral energy analysis shows that the crosslinks cause faster energy exchange from CNT to PEK in different frequency bands. The oxygen atom of hydroxyl group of PEK contributes energy transfer in the low frequency band, while aromatic and carbonyl carbon atoms play a more significant role in high frequency bands. In addition, by analyzing the relaxation time of the spectral temperature of different frequency bands of CNT, it is revealed that with increasing number of bonds, both lower frequency vibrational modes and higher frequency modes efficiently couple across the CNT-PEK interface and contribute in thermal energy transfer from CNT to the matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Guided ion beam and theoretical studies of the bond energy of SmS +

Previous work has shown that atomic samarium cations react with carbonyl sulfide to form SmS + + CO in an exothermic and barrierless process. To characterize this reaction further, the bond energy of SmS + is determined in the present study using guided ion beam tandem mass spectrometry. Reactions of SmS + with Xe, CO, and O 2 are examined. Results for collision-induced dissociation processes with all three molecules along with the endothermicity of the SmS + + CO → Sm + + COS exchange reaction are combined to yield D 0 (Sm + –S) = 3.37 ± 0.20 eV. The CO and O 2 reactions also yield a SmSO + product, with measured endothermicities that indicate D 0 (SSm + –O) = 3.73 ± 0.16 eV and D 0 (OSm + –S) = 1.38 ± 0.27 eV. The SmS + bond energy is compared with theoretical values characterized at several levels of theory, including CCSD(T) complete basis set extrapolations using all-electron basis sets. Multireference configuration interaction calculations with explicit spin-orbit calculations along with composite thermochemistry using the Feller-Peterson-Dixon method and all-electron basis sets were also explored for SmS+, and for comparison, SmO, SmO + , and EuO

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Nascent energy distribution of the Criegee intermediate CH 2 OO from direct dynamics calculations of primary ozonide dissociation

Here, ozonolysis produces chemically activated carbonyl oxides (Criegee intermediates, CIs) that are either stabilized or decompose directly. This branching has an important impact on atmospheric chemistry. Prior theoretical studies have employed statistical models for energy partitioning to the CI arising from dissociation of the initially formed primary ozonide (POZ). Here, we used direct dynamics simulations to explore this partitioning for decomposition of c -C 2 H 4 O 3 , the POZ in ethylene ozonolysis. A priori estimates for the overall stabilization probability were then obtained by coupling the direct dynamics results with master equation simulations. Trajectories were initiated at the concerted cycloreversion transition state, as well as the second transition state of a stepwise dissociation pathway, both leading to a CI (H 2 COO) and formaldehyde (H 2 CO). The resulting CI energy distributions were incorporated in master equation simulations of CI decomposition to obtain channel-specific stabilized CI (sCI) yields. Master equation simulations of POZ formation and decomposition, based on newhigh-level electronic structure calculations, were used to predict yields for the different POZ decomposition channels. A non-negligible contribution of stepwise POZ dissociation was found, and new mechanistic aspects of this pathway were elucidated. By combining the trajectory-based channel-specific sCI yields with the channel branching fractions, an overall sCI yield of (48 +/- 5)% was obtained. Non-statistical energy release was shown to measurably affect sCI formation, with statistical models predicting significantly lower overall sCI yields (~30%). Within the range of experimental literature values (35%-54%), our trajectory-based calculations favor those clustered at the upper end of the spectrum. Published by AIP Publishing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Self-assembling of formic acid on the partially oxidized p (2×1) Cu(110) surface reconstruction at low coverages

Carbon dioxide (CO 2 ) reduction for synthetic fuel generation could be an integral part of a sustainable energy future. Copper (Cu) is the leading electrocatalyst for CO 2 reduction to produce multiple C-containing products such as C1 and C2 hydrocarbons and oxygenates. Understanding the mechanisms leading to their production could help optimize these pathways further. Adsorption studies of the many possible intermediates on well-characterized surfaces are crucial to elucidating these mechanisms. In this work, we explore the adsorption configurations of formic acid (HCOOH) on the surface of the partially oxidized p (2 × 1) reconstruction of the Cu(110) surface, using low-temperature scanning tunneling and atomic force microscopy, in conjunction with density functional theory modeling. We find that HCOOH adsorbs favorably on the CuO chain comprising the reconstruction. The adsorption interactions involve dative bonding of the carbonyl O to the oxidized Cu and hydrogen bonding of the OH group to the surface O or to an adjacently adsorbed HCOOH molecule. Furthermore, cooperative adsorption of the molecules occurs, forming two- to three-molecule-long oligomer chains, facilitated by intermolecular hydrogen bonding and mutual polarization of the CuO acid-base adsorption sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Probing the interplay between geometric and electronic-structure features via high-harmonic spectroscopy

We present molecular-frame measurements of the recombination dipole matrix element (RDME) in CO 2 , N 2 O, and carbonyl sulfide (OCS) molecules using high-harmonic spectroscopy. Both the amplitudes and phases of the RDMEs exhibit clear imprints of a two-center interference minimum, which moves in energy with the molecular alignment angle relative to the laser polarization. Here, we find that whereas the angle dependence of this minimum is consistent with the molecular geometry in CO 2 and N 2 O, it behaves very differently in OCS; in particular, the phase shift which accompanies the two-center minimum changes sign for different alignment angles. Our results suggest that two interfering structural features contribute to the OCS RDME, namely, (i) the geometrical two-center minimum and (ii) a Cooper-like, electronic-structure minimum associated with the sulfur end of the molecule. We compare our results to ab initio calculations using time-dependent density functional theory and present an empirical model that captures both the two-center and the Cooper-like interferences. We also show that the yield from unaligned samples of two-center molecules is, in general, reduced at high photon energies compared to aligned samples, due to the destructive interference between molecules with different alignments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Experimental and theoretical studies of the doubly substituted methyl-ethyl Criegee intermediate: Infrared action spectroscopy and unimolecular decay to OH radical products

In this work the infrared (IR) action spectrum of the doubly substituted methyl-ethyl Criegee intermediate (MECI) is observed in the CH stretch overtone region with detection of OH products. The MECI exhibits four conformers, all of which undergo unimolecular decay via a 1,4 H-atom transfer mechanism, followed by the rapid release of OH products. Conformers with different orientations of the carbonyl oxide group with respect to the methyl and ethyl substituents (i.e., anti and syn ) decay via distinct transition state barriers (16.1 kcal mol –1 and 15.4 kcal mol –1 , respectively). The observed IR action spectrum is in good agreement with the predicted anharmonic IR absorption spectrum, but exhibits significant congestion, which is attributed to couplings between spectroscopic bright states and nearby dark states. Energy-dependent OH appearance rates are measured upon IR excitation of the strongest features in the IR action spectrum and are found to be on the order of 10 6 –10 7 s –1 . The experimental rates are in good agreement with computed Rice–Ramsperger–Kassel–Marcus rates for the unimolecular decay of MECI at these energies, which incorporate quantum mechanical tunneling and sophisticated hindered rotor treatments, as well as high-level theoretical calculations of the TS barrier heights, rovibrational properties, and torsional barriers associated with the MECI conformers. Master equation modeling is used to predict thermal rates for the unimolecular decay of anti - and syn -MECI of 473 s –1 and 660 s –1 , respectively. Comparison with other previously studied Criegee intermediate systems provides insights into substituent effects on unimolecular decay under both energy-dependent and thermal conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Looking at the bigger picture: Identifying the photoproducts of pyruvic acid at 193 nm

Here, photodissociation of pyruvic acid (PA) was studied in the gas-phase at 193 nm using two complementary techniques. The time-sliced velocity map imaging arrangement was used to determine kinetic energy release distributions of fragments and estimate dissociation timescales. The multiplexed photoionization mass spectrometer setup was used to identify and quantify photoproducts, including isomers and free radicals, by their mass-to-charge ratios, photoionization spectra, and kinetic time profiles. Using these two techniques, it is possible to observe the major dissociation products of PA photodissociation: CO 2 , CO, H, OH, HCO, CH 2 CO, CH 3 CO, and CH 3 . Acetaldehyde and vinyl alcohol are minor primary photoproducts at 193 nm, but products that are known to arise from their unimolecular dissociation, such as HCO, H 2 CO, and CH 4 , are identified and quantified. A multivariate analysis that takes into account the yields of the observed products and assumes a set of feasible primary dissociation reactions provides a reasonable description of the photoinitiated chemistry of PA despite the necessary simplifications caused by the complexity of the dissociation. These experiments offer the first comprehensive description of the dissociation pathways of PA initiated on the S 3 excited state. Most of the observed products and yields are rationalized on the basis of three reaction mechanisms: (i) decarboxylation terminating in CO 2 + other primary products (~50%); (ii) Norrish type I dissociation typical of carbonyls (~30%); and (iii) O—H and C—H bond fission reactions generating the H atom (~10%). The analysis shows that most of the dissociation reactions create more than two products. This observation is not surprising considering the high excitation energy (~51 800 cm –1 ) and fairly low energy required for dissociation of PA. We find that two-body fragmentation processes yielding CO 2 are minor, and the expected, unstable primary co-fragment, methylhydroxycarbene, is not observed because it probably undergoes fast secondary dissociation and/or isomerization. Norrish type I dissociation pathways generate OH and only small yields of CH 3 CO and HOCO, which have low dissociation energies and further decompose via three-body fragmentation processes. Experiments with d 1 -PA (CH 3 COCOOD) support the interpretations. The dissociation on S 3 is fast, as indicated by the products’ recoil angular anisotropy, but the roles of internal conversion and intersystem crossing to lower states are yet to be determined.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition

Here, in this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Photodissociation dynamics of methyl vinyl ketone oxide: A four-carbon unsaturated Criegee intermediate from isoprene ozonolysis

The electronic spectrum of methyl vinyl ketone oxide (MVK-oxide), a four-carbon Criegee intermediate derived from isoprene ozonolysis, is examined on its second π* ← π transition, involving primarily the vinyl group, at UV wavelengths (λ) below 300 nm. A broad and unstructured spectrum is obtained by a UV-induced ground state depletion method with photoionization detection on the parent mass (m/z 86). Electronic excitation of MVK-oxide results in dissociation to O ( 1 D) products that are characterized using velocity map imaging. Electronic excitation of MVK-oxide on the first π* ← π transition associated primarily with the carbonyl oxide group at λ > 300 nm results in a prompt dissociation, and yields broad total kinetic energy release (TKER) and anisotropic angular distributions for the O ( 1 D) + methyl vinyl ketone products. By contrast, electronic excitation at λ ≤ 300 nm results in bimodal TKER and angular distributions, indicating two distinct dissociation pathways to O ( 1 D) products. Furthermore, one pathway is analogous to that at λ > 300 nm, while the second pathway results in very low TKER and isotropic angular distributions indicative of internal conversion to the ground electronic state and statistical unimolecular dissociation.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Ultrafast infrared transient absorption spectroscopy of gas-phase Ni(CO) 4 photodissociation at 261 nm

Here, we employ ultrafast mid-infrared transient absorption spectroscopy to probe the rapid loss of carbonyl ligands from gas-phase nickel tetracarbonyl following ultraviolet photoexcitation at 261 nm. Here, nickel tetracarbonyl undergoes prompt dissociation to produce nickel tricarbonyl in a singlet excited state; this electronically excited tricarbonyl loses another CO group over tens of picoseconds. Our results also suggest the presence of a parallel, concerted dissociation mechanism to produce nickel dicarbonyl in a triplet excited state, which likely dissociates to nickel monocarbonyl. Mechanisms for the formation of these photoproducts in multiple electronic excited states are theoretically predicted with one-dimensional cuts through the potential energy surfaces and computation of spin–orbit coupling constants using equation of motion coupled cluster methods (EOM-CC) and coupled cluster theory with single and double excitations (CCSD). Bond dissociation energies are calculated with CCSD, and anharmonic frequencies of ground and excited state species are computed using density functional theory (DFT) and time-dependent density functional theory (TD-DFT).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

The effect of polymer stiffness on magnetization reversal of magnetorheological elastomers

Ultrasoft magnetorheological elastomers (MREs) offer convenient real-time magnetic field control of mechanical properties that provides a means to mimic mechanical cues and regulators of cells in vitro. Here, we systematically investigate the effect of polymer stiffness on magnetization reversal of MREs using a combination of magnetometry measurements and computational modeling. Poly-dimethylsiloxane-based MREs with Young’s moduli that range over two orders of magnitude were synthesized using commercial polymers Sylgard™ 527, Sylgard 184, and carbonyl iron powder. The magnetic hysteresis loops of the softer MREs exhibit a characteristic pinched loop shape with almost zero remanence and loop widening at intermediate fields that monotonically decreases with increasing polymer stiffness. A simple two-dipole model that incorporates magneto-mechanical coupling not only confirms that micrometer-scale particle motion along the applied magnetic field direction plays a defining role in the magnetic hysteresis of ultrasoft MREs but also reproduces the observed loop shapes and widening trends for MREs with varying polymer stiffnesses.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Relativistic and magnetic Breit effects for the reaction Sg + 6CO → Sg(CO)6 and Sg(OC)6: Prediction of the existence and atomization energy of the isomer Sg(OC)6

Our ab initio all-electron fully relativistic Dirac–Fock (DF) and Dirac–Fock–Breit–Gaunt (DFBG) and nonrelativistic (NR) Hartree–Fock (HF) calculations for seaborgium hexacarbonyl Sg(CO)6 predict atomization energies (Ae) of 68.81, 69.28, and 67.69 eV, respectively, at the corresponding optimized octahedral geometry. However, our DF, DFBG, and NR HF calculations for the isomer Sg(OC)6 yield atomization energies of 64.30, 64.77, and 62.62 eV, respectively, at the optimized geometry for this species. The optimized Sg–C and C–O bond distances (in Å) for octahedral Sg(CO)6 using our DF (NR) calculations are 2.15 (2.32) and 1.11 (1.11), respectively. However, the optimized Sg–O and O–C bond distances (in Å) for the isomer octahedral Sg(OC)6 obtained with our DF (NR) calculations are 2.80 (2.73) and 1.10 (1.11), respectively. Our prediction of the greater stability of Sg(CO)6 isomer at both the relativistic (DF and DFBG) and the NR HF levels of theory lends further support to the detection of Sg(CO)6 in the state-of-the-art gas-phase experimental studies of the carbonyl complex of seaborgium reported by Even et al. [Science 345(6203), 1491 (2014)].

Materials Science↗
DOE OSTI2024

Molecular structures of residual solvent in polyacrylonitrile based electrolytes: Implications for conductivity and stability

Lithium-ion batteries increasingly play significant roles in modern technologies; however, increased energy density also raises concerns about electrolyte safety. Traditional electrolytes that use volatile organic solvents face risks of thermal runaways and fires from electrode shorting. In response, polymer-based solid electrolytes have been developed for replacement. Polyacrylonitrile (PAN) is a promising fire-resistant component for electrolyte fabrication, but its limited solubility necessitates using low-volatility solvents, which are notoriously difficult to remove in subsequent drying processes. Here, we use femtosecond two-dimensional infrared spectroscopy to provide an in-depth understanding of how residual solvent from processing affects the molecular structures and dynamics within a polymer electrolyte. To this end, linear and nonlinear infrared spectroscopies are employed to interrogate the molecular interactions in PAN-based electrolytes containing various contents of N,N-dimethylformamide (DMF). We show that the amount of DMF within the PAN electrolyte affects the Li+ structure. Further, the coordination can proceed through the carbonyl group and/or the amide nitrogen to form antiparallel structures with the nitrile groups of PAN through dipole–dipole interactions. The free motion of DMF is drastically inhibited upon interaction with Li+ and PAN, which decreases the ionic conductivity and potentially affects the stability (resistance toward removal and chemical decomposition). These findings have implications for the design and processing of solid polymer electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Reversible catalytic dehydrogenation of alcohols for energy storage

Significance Catalytic hydrogenation and dehydrogenation reactions are extremely important in organic chemistry and recently for energy storage in the form of chemical bonds. Although catalysts are known which catalyze both reactions, the rates and conditions required for the two are frequently very different due to the differences associated with the bonds to be activated (C–H/O–H/N–H and C = O/C = N/H–H). The use of a bifunctional catalyst would substantially simplify the design of processes related to energy storage. In this work, organometallic complexes of iron and iridium are shown to act as catalysts for reversible dehydrogenation of alcohols to carbonyl compounds. This finding opens a pathway to the development of catalysts for direct reversible electrochemical dehydrogenation of organic fuels in energy generation and storage reactions.

25 ENERGY STORAGE↗
DOE OSTI2017

Photoactivation mechanism of a carotenoid-based photoreceptor

Photoprotection is essential for efficient photosynthesis. Cyanobacteria have evolved a unique photoprotective mechanism mediated by a water-soluble carotenoid-based photoreceptor known as orange carotenoid protein (OCP). OCP undergoes large conformational changes in response to intense blue light, and the photoactivated OCP facilitates dissipation of excess energy via direct interaction with allophycocyanins at the phycobilisome core. However, the structural events leading up to the OCP photoactivation remain elusive at the molecular level. Here we present direct observations of light-induced structural changes in OCP captured by dynamic crystallography. Difference electron densities between the dark and illuminated states reveal widespread and concerted atomic motions that lead to altered protein–pigment interactions, displacement of secondary structures, and domain separation. Based on these crystallographic observations together with site-directed mutagenesis, we propose a molecular mechanism for OCP light perception, in which the photochemical property of a conjugated carbonyl group is exploited. We hypothesize that the OCP photoactivation starts with keto–enol tautomerization of the essential 4-keto group in the carotenoid, which disrupts the strong hydrogen bonds between the bent chromophore and the protein moiety. Subsequent structural changes trapped in the crystal lattice offer a high-resolution glimpse of the initial molecular events as OCP begins to transition from the orange-absorbing state to the active red-absorbing state.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Selective deuteration illuminates the importance of tunneling in the unimolecular decay of Criegee intermediates to hydroxyl radical products

Significance Ozonolysis of volatile biogenic and anthropogenic alkenes is a significant source of hydroxyl radicals, a key oxidant in the troposphere. A critical step in the generation of hydroxyl radicals is a hydrogen-atom transfer reaction involving a carbonyl oxide species, known as the Criegee intermediate. In this study, experiment and statistical theory reveal that selective deuteration of a Criegee intermediate results in deuterium atom transfer and slows the release of hydroxyl- d radicals. A large kinetic isotope effect is found at energies near the classical barrier to reaction and under thermal conditions relevant to the atmosphere. This demonstrates that quantum mechanical tunneling significantly enhances the rate of production of hydroxyl radicals in alkene ozonolysis reactions under atmospheric conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Imaging the Renner–Teller effect using laser-induced electron diffraction

Structural information on electronically excited neutral molecules can be indirectly retrieved, largely through pump–probe and rotational spectroscopy measurements with the aid of calculations. Here, we demonstrate the direct structural retrieval of neutral carbonyl disulfide (CS 2 ) in the B ~ 1 B 2 excited electronic state using laser-induced electron diffraction (LIED). We unambiguously identify the ultrafast symmetric stretching and bending of the field-dressed neutral CS 2 molecule with combined picometer and attosecond resolution using intrapulse pump–probe excitation and measurement. We invoke the Renner–Teller effect to populate the B ~ 1 B 2 excited state in neutral CS 2 , leading to bending and stretching of the molecule. Our results demonstrate the sensitivity of LIED in retrieving the geometric structure of CS 2 , which is known to appear as a two-center scatterer.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗