Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “GROUND STATES”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Resonances of A = 4T = 1 isospin triplet states within the ab initio no-core Gamow shell model

Here, the A = 4 nuclei, i.e., 4 H, 4 He, and 4 Li , establish an interesting isospin T = 1 isobaric system. 4 H and 4 Li are unbound broad resonances, whereas 4 He is deeply bound in its ground state but unbound in all its excited states. The present situation is that experiments so far have not given consistent data on the resonances. Few-body calculations have well studied the scatterings of the 4N systems. In the present work, we provide many-body calculations of the broad resonance structures, in an ab initio framework with modern realistic interactions. It occurs that, indeed, 4 H, 4 Li, and excited 4 He are broad resonances, which is in accordance with experimental observations. The calculations also show that the first 1 - excited state almost degenerates with the 2 - ground state in the pair of mirror isobars of 4 H and 4 Li, which may suggest that the experimental data on energy and width are the mixture of the ground state and the first excited state. The T = 1 isospin triplet formed with an excited state of 4 He and ground states of 4 H and 4 Li is studied, focusing on the effect of isospin symmetry breaking.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Generalized single excitation configuration interaction: an investigation into the impact of the inclusion of non-orthogonality on the calculation of core-excited states

In this paper, we investigate different non-orthogonal generalizations of the configuration interaction with single substitutions (CIS) method for the calculation of core-excited states. Fully non-orthogonal CIS (NOCIS) has been described previously for species with singlet and doublet ground states, and this paper reports the extension to molecules in their triplet ground state. In addition to NOCIS, we present a novel method, one-center NOCIS (1C-NOCIS), for open-shell molecules which is intermediate between NOCIS and the computationally less demanding static exchange approximation (STEX). We explore this hierarchy of spin-pure methods for core excitations of molecules with singlet, doublet, and triplet ground states. We conclude that, while NOCIS provides the best results and preserves the spatial symmetry of the wavefunction, 1C-NOCIS retains much of the accuracy of NOCIS at a dramatically reduced cost. For molecules with closed-shell ground states, STEX and 1C-NOCIS are identical.

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

Study of the ferromagnetic quantum phase transition in Ce 3– x Mg x Co 9

The Ce 3-x Mg x Co 9 system evolves from a Pauli paramagnetic ground state for x = 0 to a ferromagnetic ground state for x≈0.80 in single-phase, polycrystalline samples [Lamichhane, V. Taufour, A. Palasyuk, Q. Lin, S.L. Budko, and P.C. Canfield, Ce3-xMgxCo9 : transformation of a Pauli paramagnet into a strong permanent magnet, Phys. Rev. Appl. 9 (2018), p. 024023]. In order to better understand this behaviour, single-crystalline samples of Ce 3-x Mg x Co 9 for x = 0.01, 0.16, 0.24, 0.35, 0.43 and 0.50 were grown using the flux growth technique, and electrical transport and magnetic properties were studied. The T C-x phase diagram we infer shows that the system has a quantum phase transition near x = 0.35, transforming to a ferromagnetic ground state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Revealing the electronic structure of the current-induced metastable state in 1T-TaS 2

Among the key features for next-generation memory devices is the need for high-contrast switching between metallic and insulating states with fast switching speed and long lifetime. However, materials exhibiting such properties are rare, and their electronic structure is often poorly understood. Here, by combining state-of-the-art devices with angle-resolved photoemission spectroscopy, we study the emergence of a metastable metallic state from the insulating ground state in the charge-density wave (CDW) material 1T-TaS 2 after applying short current pulses. Analysis of the electronic structure suggests a picture in which 1T-TaS 2 transforms from a band insulator in the commensurate CDW ground state to a correlated metal in the metastable state. Moreover, the optically induced metastable state reveals a strong similarity to the current-induced one. This work provides an extensive characterization of metastable order in 1T-TaS 2 and proves how studying electronic properties under in-operando conditions is a critical step for next-generation devices.

Huber, Maximilian [Lawrence Berkeley National Labo↗
DOE OSTI2022

Analysis of spin frustration in an Fe III 7 cluster using a combination of computational, experimental, and magnetostructural correlation methods

The synthesis, structure, and magnetic properties are reported for [Fe 7 O 3 (O 2 C t Bu) 9 (mda) 3 (H 2 O) 3 ] ( 1 ), where mdaH 2 is N -methyldiethanolamine. 1 was prepared from the reaction of [Fe 3 O(O 2 C t Bu) 6 (H 2 O) 3 ](NO 3 ) with mdaH 2 in a 1:~3 ratio in MeCN. The core of 1 consists of a central octahedral Fe III ion held within a non-planar Fe 6 loop by three μ 3 -O 2- and three μ 2 -RO - arms from the three mda 2- chelates. Variable-temperature dc and ac magnetic susceptibility studies revealed dominant antiferromagnetic coupling, leading to a ground state spin of S = 5 / 2 . The ground state was confirmed by a fit of magnetization data collected in the 0.1–7.0 T and 1.8–10.0 K ranges. The four Fe 2 pairwise exchange parameters ( J 1 - J 4 ) were estimated by independent methods: theoretical calculations using either broken symmetry energy differences (-46.3, -16.2, -3.9, and - 28.1 cm -1 , respectively) or Green’s function approximation methods (-41.4, -14.8, -13.2, and - 24.7 cm -1 ), and a magnetostructural correlation (MSC) previously developed for high nuclearity Fe III /O complexes (-39.5, -13.8, -6.7, and - 23.5 cm -1 ). Additionally, the J 1 - J 4 obtained from the MSC and theoretical methods were used with the program PHI to both simulate χ M T vs T as well as to serve as reasonable input values to fit the experimental data (-41.0, -11.4, -5.0, and - 27.3 cm -1 ). Analysis of the J ij led to identification of the spin frustration effects operative and the resultant spin vector alignments at each Fe III ion, thus allowing for the rationalization of the experimental ground state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Spin-orbital correlations from complex orbital order in MgV 2⁢ O 4

MgV 2 ⁢O 4 is a spinel based on magnetic V 3+ ions, which host both spin (𝑆 = 1) and orbital (𝑙 eff = 1) moments. Owing to the underlying pyrochlore coordination of the magnetic sites, the spins in MgV 2 ⁢O 4 only antiferromagnetically order once the frustrating interactions imposed by the 𝐹⁡𝑑⁢$\overline{3}$⁢𝑚 lattice are broken through an orbitally-driven structural distortion at T 𝑆 ≃ ⁢60 K. Consequently, a Néel transition occurs at T 𝑁 ≃ ⁢40 K. Low-temperature spatial ordering of the electronic orbitals is fundamental to both the structural and magnetic properties; however, considerable discussion on whether it can be described by complex or real orbital ordering is ambiguous. We apply neutron spectroscopy to resolve the nature of the orbital ground state and characterize hysteretic spin-orbital correlations using x-ray and neutron diffraction. Neutron spectroscopy finds multiple excitation bands and we parametrize these in terms of a multilevel (or excitonic) theory based on the orbitally degenerate ground state. Meaningful for the orbital ground state, we report an “optical-like” mode at high energies that we attribute to a crystal-field-like excitation from the spin-orbital 𝑗 eff = 2 ground-state manifold to an excited 𝑗 eff =1 energy level. We parametrize the magnetic excitations in terms of a Hamiltonian with spin-orbit coupling and local crystalline electric field distortions resulting from deviations from perfect octahedra surrounding the V 3+ ions. We suggest that this provides compelling evidence for complex orbital order in MgV 2⁢ O 4 . We then apply the consequences of this model to understand hysteretic effects in the magnetic diffuse scattering where we propose that MgV 2⁢ O 4 displays a high-temperature orbital memory of the low-temperature spin order.

Frustrated magnetism↗
DOE OSTI2022

Stable excited dication: trapping on the S 1 state of formaldehyde dication after strong field ionization

Combined theoretical and experimental work examines the dynamics of dication formaldehyde produced by strong field ionization. Trajectory surface hopping dynamics on the first several singlet electronic states of the formaldehyde dication are used to examine the relaxation pathways and dissociation channels, while kinetic energy distributions after strong field ionization of formaldehyde and deuterated formaldehyde are used to confirm the theoretical predictions. Here, we find that the first excited state of the formaldehyde dication is stable, neither decays to the ground state nor dissociates, even though the ground state and higher lying states are directly dissociative. The stability of the first excited state is explained by its symmetry which does not allow for radiative or nonradiative transitions to the ground state and by large barriers to dissociate on the excited state surface.

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

Regulating Exciton–Phonon Coupling to Achieve a Near‐Unity Photoluminescence Quantum Yield in One‐Dimensional Hybrid Metal Halides

Abstract Low‐dimensional hybrid metal halides are emerging as a highly promising class of single‐component white‐emitting materials for their unique broadband emission from self‐trapped excitons (STEs). Despite substantial progress in the development of these metal halides, many challenges remain to be addressed to obtain a better fundamental understanding of the structure–property relationship and realize the full potentials of this class of materials. Here, via pressure regulation, a near 100% photoluminescence quantum yield (PLQY) of broadband emission is achieved in a corrugated 1D hybrid metal halide C 5 N 2 H 16 Pb 2 Br 6 , which possesses a highly distorted structure with an initial PLQY of 10%. Compression reduces the overlap between STE states and ground state, leading to a suppressed phonon‐assisted non‐radiative decay. The PL evolution is systematically demonstrated to be controlled by the pressure‐regulated exciton–phonon coupling which can be quantified using Huang–Rhys factor S . Detailed studies of the S ‐PLQY relation for a series of 1D hybrid metal halides (C 5 N 2 H 16 Pb 2 Br 6 , C 4 N 2 H 14 PbBr 4 , C 6 N 2 H 16 PbBr 4 , and (C 6 N 2 H 16 ) 3 Pb 2 Br 10 ) reveal a quantitative structure–property relationship that regulating S factor toward 28 leads to the maximum emission.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Photophysical Properties and Electronic Structure of Hydroporphyrin Dyads Exhibiting Strong Through-Space and Through-Bond Electronic Interactions

Electronic interactions between tetrapyrroles are utilized in natural photosynthetic systems to tune the light-harvesting and energy/charge-transfer processes in these assemblies. Such interactions also can be employed to tailor the electronic properties of tetrapyrrolic dyads and larger arrays for use in materials science and biomedical research. Here we have utilized static and time-resolved optical spectroscopy to characterize the optical absorption and emission properties of a set of chlorin and bacteriochlorin dyads with varied degrees of through-bond (TB) and through-space (TS) interactions between the constituent macrocycles. The dyads consist of two chlorins or two bacteriochlorins joined by a linker that utilizes a triple-double-triple bond (enediyne) motif in which the double bond portion is a ester-substituted ethylene or o-phenylene unit. The photophysical studies are coupled with density functional theory (DFT) calculations to probe the ground-state molecular orbital (MO) characteristics of the dyads and time-dependent calculations (TDDFT) to elucidate excited-state properties. The latter include electronic characteristics of the singlet excited state manifold and the absorption transitions to these states from the electronic ground state. Comparison of the MO and calculated spectral properties of each dyad with the linker present versus disrupted (by eliminating the double-bond portion) gives insight into the relative contributions of TB versus TS interactions to the electronic properties of the dyads. The results show that the TB and TS contributions are additive (constructively interfere), which is not always the case for molecular dyads. Most of the dyads have shorter lifetimes of the lowest singlet excited state compared to the parent monomer, which derives from increased S 1 → S 0 internal conversion. The enhancement is greater for the dyads in benzonitrile than in toluene. Furthermore, the studies provide insights into the nature of the electronic interactions between the constituents in the tetrapyrrole arrays and how these interactions dictate the spectral properties and excited-state decay characteristics.

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

Reduction of efficiency droop in c -plane InGaN/GaN light-emitting diodes using a thick single quantum well with doped barriers

We report on c-plane InGaN/GaN single quantum well (QW) light-emitting diodes (LEDs) of different well widths (3 or 9 nm) with and without doped barriers. QW barriers were doped with the aim of reducing the internal electric field (F QW ) in the QW to increase the electron-hole overlap, therefore increasing the recombination rates and resulting in the reduction of the efficiency droop. We, indeed, observed, through biased photocurrent spectroscopy, a reduction in F QW with doped barriers, with F QW being in the same direction of the p-n junction field at zero bias as opposed to the junction field for LEDs without doped barriers. Even with the improvement in the ground state wavefunction overlap, the ground state transition rate remains low for thick QWs. Transitions through excited states were observed for both thick QW LEDs with and without doped barriers. Here, the thick QW LED without doped barriers displayed low external quantum efficiency (EQE), likely as a result of the carrier overflow due to the poor confinement of carriers in the excited states. On the other hand, for LEDs with doped barriers, the flatter band in the QW resulting from the lower F QW reduces the energy separation between the eigenstates, leading to better confinement of carriers in the excited states. With doped barriers, we demonstrated a low efficiency droop 9-nm-thick single QW LED with a peak EQE of 42% at 40 A/cm 2 and an EQE of 36% at 400 A/cm 2 .

42 ENGINEERING↗
DOE OSTI2022

Spatiotemporal evolution of emission and absorption signatures in a laser-produced plasma

Here we report spatiotemporal evolution of emission and absorption signatures of Al species in a nanosecond (ns) laser-produced plasma (LPP). The plasmas were generated from an Inconel target, which contained ~0:4 wt. % Al, using 1064 nm, ≈6 ns full width half maximum pulses from an Nd:YAG laser at an Ar cover gas pressure of ≈34 Torr. The temporal distributions of the Al I (394.4 nm) transition were collected from various spatial points within the plasma employing time-of-flight (TOF) emission and laser absorption spectroscopy, and they provide kinetics of the excited state and ground state population of the selected transition. The emission and absorption signatures showed multiple peaks in their temporal profiles, although they appeared at different spatial locations and times after the plasma onset. The absorption temporal profiles showed an early time signature representing shock wave propagation into the ambient gas. We also used emission and absorption spectral features for measuring various physical properties of the plasma. The absorption spectral profiles are utilized for measuring linewidths, column density, and kinetic temperature, while emission spectra were used to measure excitation temperature. A comparison between excitation and kinetic temperature was made at various spatial points in the plasma. Our results highlight that the TOF measurements provide a resourceful tool for showing the spatiotemporal LPP dynamics with higher spatial and temporal resolution than is possible with spectral measurements but are difficult to interpret without additional information on excitation temperatures and linewidths. The combination of absorption and emission TOF and spectral measurements thus provides a more complete picture of LPP spatiotemporal dynamics than is possible using any one technique alone.

(140.3440) Laser-induced breakdown, (280.4788) Opt↗
DOE OSTI2026

Connecting collisional and photofragmentation resonances in the ungerade symmetry states of H 2

A recently developed energy-dependent frame transformation theory that incorporates both ionisation and dissociation channels of the H 2 molecule, is extended to treat the ungerade states that occur both in dissociative recombination and as the final state in ground state photoabsorption. The theoretical treatment includes the rotational degrees of freedom and is benchmarked against a two-dimensional model that can be solved with high accuracy and also compared with photoabsorption experiments. Analysis of the resulting spectra demonstrates how the same resonances appear in very different observables, often with quite different line shapes.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Magnetic glassiness in noncentrosymmetric Sm 7 Pd 3 : Interplay of magnetic frustration, long-range order, and frozen domains

Here, we present a comprehensive investigation of the intricate spin dynamics in the noncentrosymmetric compound Sm 7 ⁢Pd 3 , revealing the coexistence of spin-glass, domain-glass, and ferromagnetic (FM) behaviors. Magnetic field-dependent measurements indicate large coercivity, suggesting ferromagnetic domain formation below the Curie temperature (𝑇 C ≈ 173 K), while temperature-dependent magnetization data point to antiferromagnetic (AFM) coupling, highlighting the competition between FM and AFM interactions. Detailed ac susceptibility, isothermal remanent magnetization, and aging effect measurements demonstrate the presence of two distinct types of glassiness in the sample, and their possible origins are discussed extensively. Magnetization measurements reveal the mixing of the 𝐽 = 5/2 ground state of Sm 3+ with the excited 𝐽 = 7/2 multiplet, lying 965 K above. The specific heat data show further crystalline electric field splitting of the 𝐽 = 5/2 state into a ground-state doublet and a fourfold-degenerate excited state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Quantum Spin Torque Driven Transmutation of an Antiferromagnetic Mott Insulator

The basic model of spin-transfer torque (STT) in antiferromagnetic spintronics considers the exchange of angular momentum between quantum spins of flowing electrons and noncollinear-to-them localized spins treated as classical vectors. These vectors are assumed to realize Néel order in equilibrium, ↑ ↓ ∙∙∙ ↑ ↓, and their STT-driven dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation. However, many experimentally employed materials (such as archetypal NiO) are strongly electron-correlated antiferromagnetic Mott insulators (AFMIs) whose localized spins form a ground state quite different from the unentangled Néel state | ↑ ↓ ∙∙∙ ↑ ↓$\rangle$. The true ground state is entangled by quantum spin fluctuations, leading to the expectation value of all localized spins being zero, so that LLG dynamics of classical vectors of fixed length rotating due to STT cannot even be initiated. Instead, a fully quantum treatment of both conduction electrons and localized spins is necessary to capture the exchange of spin angular momentum between them, denoted as quantum STT. We use a recently developed time-dependent density matrix renormalization group approach to quantum STT to predict how injection of a spin-polarized current pulse into a normal metal layer coupled to an AFMI overlayer via exchange interaction and possibly small interlayer hopping—mimicking, e.g., topological-insulator/NiO bilayer employed experimentally—will induce a nonzero expectation value of AFMI localized spins. This new nonequilibrium phase is a spatially inhomogeneous ferromagnet with a zigzag profile of localized spins. The total spin absorbed by AFMI increases with electron-electron repulsion in AFMIs, as well as when the two layers do not exchange any charge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Numerical simulations of noisy quantum circuits for computational chemistry

The opportunities afforded by near-term quantum computers to calculate the ground-state properties of small molecules depend on the structure of the computational ansatz as well as the errors induced by device noise. Here we investigate the behavior of these noisy quantum circuits using numerical simulations to estimate the accuracy and fidelity of the prepared quantum states relative to the ground truth obtained by conventional means. We implement several different types of ansatz circuits derived from unitary coupled cluster theory for the purposes of estimating the ground-state energy of sodium hydride using the variational quantum eigensolver algorithm. We show how relative error in the energy and the fidelity scale with the levels of gate-based noise, the internuclear configuration, the ansatz circuit depth, and the parameter optimization methods.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Twisted bilayer graphene. VI. An exact diagonalization study at nonzero integer filling

Using exact diagonalization, we research the projected Hamiltonian with the Coulomb interaction in the eight flat bands of first magic angle twisted bilayer graphene. Employing the U(4) [U(4) × U(4)] symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent that allows for study around ν = ±3,±2,±1 fillings. In the first chiral limit w 0 /w 1 = 0, where w 0 (w 1 ) is the A A (AB) stacking hopping, we find that the ground states at these fillings are extremely well-described by Slater determinants in a so-called Chern basis, and the exactly solvable charge ±1 excitations found in Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] are the lowest charge excitations up to system sizes 8 × 8 (for restricted Hilbert space) in the chiral-flat limit. We also find that the flat metric condition (FMC) used by Bernevig et al. [Phys. Rev. B 103, 205411 (2021)], Song et al. [Phys. Rev. B 103, 205412 (2021)], Bernevig et al. [Phys. Rev. B 103, 205413 (2021)], Lian et al. [Phys. Rev. B 103, 205414 (2021)], and Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] for obtaining a series of exact ground states and excitations holds in a large parameter space. For ν = -3, the ground state is the spin and valley polarized Chern insulator with ν C = ±1 at w 0 /w 1 ≲ 0.9 (0.3) with (without) FMC. At ν = -2, we can only numerically access the valley polarized sector, and we find a spin ferromagnetic phase when w 0 /w 1 ≳ 0.5 t where t ϵ [0,1] is the factor of rescaling of the actual TBG bandwidth, and a spin singlet phase otherwise, confirming the perturbative calculation [Lian. et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. The analytic FMC ground state is, however, predicted in the intervalley coherent sector which we cannot access [Lian et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. For ν = -3 with/without FMC, when w 0 /w 1 is large, the finite-size gap Δ to the neutral excitations vanishes, leading to phase transitions. Further analysis of the ground state momentum sectors at ν = -3 suggests a competition among (nematic) metal, momentum M M (π) stripe and K M -CDW orders at large w 0 /w 1 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Persistence of collectivity in the low-lying states of 30,31 Na inside the 𝑁 = 20 island of inversion

Near the 𝛽-stability line, nuclei with magic numbers are expected to exhibit spherical ground states. However, mass measurements of neutron-rich nuclei near the 𝑁 = 20 island of inversion have indicated an excess in the binding energies. These results, together with subsequent spectroscopic studies and theoretical works, point to the structural evolution from normal configurations to intruder-deformed configurations characterized by particle-hole excitations across the shell gap. Despite evidence of intruder-dominant ground states for the 30,31 Na isotopes in the vicinity of 𝑁 = 20, a question remains as to whether the deformation persists into the ground-state bands beyond the first excited states. Here, in this work, we report on a heavy-ion inelastic scattering measurement performed with GRETINA, the TRIPLEX device, and the S800 spectrograph to study the low-lying excitations in neutron-rich 30,31 Na . The observed gamma rays for the (4 + ) → (3 + ), (3 + ) → 2$^+_{g.s.}$, and (4 + ) → 2$^+_{g.s.}$ decays in 30 Na and for the (7/2 + ) → (5/2 + ) and (5/2 + )→3/2$^+_{g.s.}$ decays in 31 Na were used to extract the reduced transition probabilities 𝐵⁡(𝐸⁢2↑). We report the first measurement of the 𝐵⁡(𝐸⁢2↑) between the 3/2$^+_{g.s.}$ and the (7/2 + ) states in 31 Na . The results from this study are compared to shell-model calculations, confirming the persistence of large collectivity in the low-lying excited states consistent with the formation of the well-deformed ground-state bands in 30,31 Na .

collective models↗
DOE OSTI2021

Artificial Neural Networks as Mappings between Proton Potentials, Wave Functions, Densities, and Energy Levels

We report artificial neural networks (ANNs) have become important in quantum chemistry. Herein, applications to nuclear quantum effects, such as zero-point energy, vibrationally excited states, and hydrogen tunneling, are explored. ANNs are used to solve the time-independent Schrödinger equation for single- and double-well potentials representing hydrogen-bonded molecular systems capable of proton transfer. ANN mappings are trained to predict the lowest five proton vibrational energies, wave functions, and densities from the proton potentials and to predict the excited state proton vibrational energies and densities from the proton ground state density. For the inverse problem, ANN mappings are trained to predict the proton potential from the proton vibrational energy levels or the proton ground state density. This latter mapping is theoretically justified by the first Hohenberg-Kohn theorem establishing a one-to-one correspondence between the external potential and the ground state density. ANNs for two- and three-dimensional systems are also presented to illustrate the straightforward extension to higher dimensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗