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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Deciphering between enhanced light emission and absorption in multi-mode porphyrin cavity polariton samples

Abstract It remains unclear how the collective strong coupling of cavity-confined photons to the electronic transitions of molecular chromophore leverages the distinct properties of the polaritonic constituents for future technologies. In this study, we design, fabricate, and characterize multiple types of Fabry-Pérot (FP) mirco-resonators containing copper(II) tetraphenyl porphyrin (CuTPP) to show how cavity polariton formation affects radiative relaxation processes in the presence of substantial non-Condon vibronic coupling between two of this molecule’s excited electronic states. Unlike the prototypical enhancement of Q state radiative relaxation of CuTPP in a FP resonator incapable of forming polaritons, we find the light emission processes in multimode cavity polariton samples become enhanced for cavity-exciton energy differences near those of vibrations known to mediate non-Condon vibronic coupling. We propose the value of this detuning is consistent with radiative relaxation of Herzberg-Teller polaritons into collective molecular states coupled to the cavity photon coherently. We contrast the feature stemming from light emission from the HT polariton state with those that occur due to polariton-enhanced light absorption. Our results demonstrate the landscape of molecular and photonic interactions enabled by cavity polariton formation using complex chromophores and how researchers can design resonators to leverage these interactions to characterize and control polaritonic properties.

Odewale, Elizabeth O.↗
DOE OSTI2021

In Situ Identification of NNH and N 2 H 2 by Using Molecular-Beam Mass Spectrometry in Plasma-Assisted Catalysis for NH 3 Synthesis

In this work, ammonia synthesis at 533 K and atmospheric pressure was investigated in a coaxial dielectric barrier discharge (DBD) plasma reactor without packing and with porous γ-Al 2 O 3 , 5 wt % Ru/γ-Al 2 O 3 , or 5 wt % Co/γ-Al 2 O 3 catalyst particles. Gas-phase species were monitored in situ using an electron impact molecular-beam mass spectrometer (EI-MBMS). Gas-phase species NNH and N 2 H 2 were first identified under common conditions of plasma-assisted ammonia synthesis and were present at levels comparable to that of NH 3 in the plasma discharge. Concentrations of NNH, N 2 H 2 , and NH in a reactor packed with γ-Al 2 O 3 or other particles were lower than those observed in an empty reactor, while the concentration of NH 3 increased. These observations point to the importance of NNH and N 2 H 2 in plasma-assisted surface reactions in ammonia synthesis. Reaction pathways of direct adsorption of gas-phase NNH and N 2 H 2 on solid surfaces and subsequent reactions were proposed. This study demonstrated that in situ identification of gas-phase species via EI-MBMS provides a powerful approach to study the kinetics of plasmaassisted catalysis.

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

Angularly resolved photoionization dynamics in atoms and molecules combining temporally and spectrally resolved experiments at ATTOLab and Synchrotron SOLEIL

We report results for XUV-IR two-photon ionization of Ar, Ne, NO, and O2, where an XUV attosecond pulse train is superimposed with a synchronized IR pulse, obtained at the ATTOLab laser facility using electron–ion coincidence 3D momentum spectroscopy. Temporally resolved photoelectron angular distributions providing angle-resolved time-delays for np ionization of Ar and Ne, achieved by reconstruction of attosecond beating by interference of two-photon transitions through a unified formalism (Joseph et al. in J Phys B At Mol Opt Phys 53:184007, 2020), are summarized. For inner valence XUV-IR dissociative photoionization of NO and O2 molecules, we report electron–ion kinetic energy correlation diagrams and disentangle the dissociative photoionization processes relying on parallel XUV experiments at Synchrotron SOLEIL. For ionization into the NO+(c3Π) ionic state, extending the formalism developed for single-photon ionization, we focus on photoelectron angular distributions averaged on the delay between the XUV and the IR field in the field frame, molecular frame, and electron frame of reference.

Joseph, J↗
DOE OSTI2020

Calculation of electron-ion temperature equilibration rates and friction coefficients in plasmas and liquid metals using quantum molecular dynamics

In this work, we discuss a method to calculate with quantum molecular dynamics simulations the rate of energy exchanges between electrons and ions in two-temperature plasmas, liquid metals, and hot solids. Promising results from this method were recently reported for various materials and physical conditions. Like other ab initio calculations, the approach offers a very useful comparison with the experimental measurements and permits an extension into conditions not covered by the experiments. The energy relaxation rate is related to the friction coefficients felt by individual ions due to their nonadiabatic interactions with electrons. Each coefficient satisfies a Kubo relation given by the time integral of the autocorrelation function of the interaction force between an ion and the electrons. These Kubo relations are evaluated using the output of quantum molecular dynamics calculations in which electrons are treated in the framework of finite-temperature density functional theory. The calculation presents difficulties that are unlike those encountered with the Kubo formulas for the electrical and thermal conductivities. In particular, the widely used Kubo-Greenwood approximation is inapplicable here. Indeed, the friction coefficients and the energy relaxation rate diverge in this approximation since it does not properly account for the electronic screening of electron-ion interactions. The inclusion of screening effects considerably complicates the calculations. We discuss the physically motivated approximations we applied to deal with these complications in order to investigate a widest range of materials and physical conditions. Unlike the standard method used for the electronic conductivities, the Kubo formulas are evaluated directly in the time domain and not in the energy domain, which spares one from needing to introduce an extraneous undetermined numerical parameter to account for the discrete character of the numerical density of states. We highlight interesting properties of the energy relaxation rate not shared by other electronic properties, in particular its self-averaging character. We then present a detailed parametric and convergence study with the numerical parameters, including the system size, the number of bands and k-points, and the physical approximations for the dielectric function and the exchange-correlation energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Probing Electronic Coherence between Core-Level Vacancies at Different Atomic Sites

The detailed understanding of electronic coherence in quantum systems requires measurements on the attosecond timescale. Attosecond x-ray pulses enable the study of electronic coherence in core-excited molecular systems. Here we report on the coherent motion of electrons in the 1,1-difluoroethylene ion following ionization of the K shell of the two nonequivalent carbon sites with a subfemtosecond x-ray pulse. Using the angular streaking technique to track the Auger-Meitner decay, we observe temporal modulations of the emission, indicating the electronic coherence of the core-excited ionic states, and extract a 6.5 ± 0.8 fs average lifetime of the core-level vacancies. A quantum-mechanical model is employed to interpret the measurement, and we find the observed temporal modulations are independent of charge density oscillations. This work opens a new regime of coherent electronic motion, beyond charge migration, where electronic coherence manifests in the nonlocal quantum correlation between atomic sites while charge density oscillation is absent. Our results broaden the landscape of electronic coherence in molecular systems. Published by the American Physical Society 2025

Wang, Jun (ORCID:000000031962895X)↗
DOE OSTI2024

Excited-State and Nonadiabatic Molecular Dynamics Methods with Broad Applicability

Electronically excited states play a pivotal role in the capture, transformation, storage, and emission of radiative energy. Despite much recent progress for small model systems, excited state properties and dynamics in many larger molecular devices and materials have remained elusive for experiment and theory. Nonadiabatic transitions between electronic states turn radiative energy into heat and are particularly difficult to control. This project aims to develop new electronic structure and nonadiabatic molecular dynamics (NAMD) methods to simulate, predict, and ultimately control the flow and transformation of excitation energy in a wide-range of light-driven molecular devices such as dyes, photocatalysts, and fluorescence emitters.

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

Inverse Trans Influence and Uranium-Arene σ-Bonding Drive Molecular Geometry: Ligand Modification from Hard to Soft Flips the Oxide from Axial to Equatorial

A rare example of an equatorially bound terminal uranium(V) oxo complex in a chelating sulfur-based ligand environment, namely [(mes( Me,Ad ArS) 3 )U V (O eq )(THF)] (2), is presented. Octahedrally coordinated 2 is obtained by reaction of the mesitylene-anchored tris-thiophenolate-coordinated uranium(III) complex [U III ((SAr Ad,Me ) 3 mes)] (1) with the oxygen-atom transfer reagent N 2 O. The observed, equatorially bound oxo ligand in 2 is in stark contrast to its known tris-aryloxide analog, [(mes( Me,Ad ArO) 3 )U V (O ax )(THF)] (A), where the oxo ligand occupies the typically observed axial coordination site. Complexes 1 and 2 are characterized by single-crystal X-ray diffraction analyses and spectroscopic and magnetochemical methods, including 1 H NMR, UV/vis/NIR electronic absorption, as well as EPR spectroscopy and SQUID magnetometry, thus confirming the C S symmetry and the pentavalent oxidation state of 2. Encompassing quantum chemical calculations (DFT and CASPT2) on 2 and its tris-phenolate analog A, support and rationalize the structural and electronic differences. The molecular orbital pictures show that a stabilizing σ-bonding interaction arising from the U–O eq inverse trans influence (ITI) is present in 2 but missing in A. In 2, the sulfur 3p orbitals are closer in energy to the uranium 5f manifold than the arene π-system, leading to an ITI, while U–arene σ- or δ-bonding is not observed. Although the arene orbitals remain separated from the uranium 5f orbitals in A, the absence of an ITI allows the arene a 2u orbital to engage in a σ-type interaction with the metal. Thus, incorporating a tris-thiophenolate to an arene anchor introduces a new design concept in molecular f-element chemistry. This approach stabilizes an equatorially bound U(V) oxo center, contrasting with its tris-phenolate counterpart, where oxo coordination is axial. The observed geometric divergence, driven by competing ITI and U–arene interactions, not only tunes electronic structure but also leads to differentiated reactivity: only the phenolate analogs activate H 2 O, while the thiolates do not.

Hydrocarbons↗
DOE OSTI2021

A molecular design approach towards elastic and multifunctional polymer electronics

Next-generation wearable electronics require enhanced mechanical robustness and device complexity. Besides previously reported softness and stretchability, desired merits for practical use include elasticity, solvent resistance, facile patternability and high charge carrier mobility. Here, we show a molecular design concept that simultaneously achieves all these targeted properties in both polymeric semiconductors and dielectrics, without compromising electrical performance. This is enabled by covalently-embedded in-situ rubber matrix (iRUM) formation through good mixing of iRUM precursors with polymer electronic materials, and finely-controlled composite film morphology built on azide crosslinking chemistry which leverages different reactivities with C–H and C=C bonds. The high covalent crosslinking density results in both superior elasticity and solvent resistance. When applied in stretchable transistors, the iRUM-semiconductor film retained its mobility after stretching to 100% strain, and exhibited record-high mobility retention of 1 cm 2 V -1 s -1 after 1000 stretching-releasing cycles at 50% strain. The cycling life was stably extended to 5000 cycles, five times longer than all reported semiconductors. Furthermore, we fabricated elastic transistors via consecutively photo-patterning of the dielectric and semiconducting layers, demonstrating the potential of solution-processed multilayer device manufacturing. The iRUM represents a molecule-level design approach towards robust skin-inspired electronics.

42 ENGINEERING↗
DOE OSTI2023

A quantitative assessment of (bacterio)chlorophyll assignments in the cryo-EM structure of the Chloracidobacterium thermophilum reaction center

Chlorophylls and bacteriochlorophylls are the primary pigments used by photosynthetic organisms for light-harvesting, energy transfer, and electron transfer. Many molecular structures of (bacterio)chlorophyll-containing protein complexes are available, some of which contain mixtures of different (bacterio)chlorophyll types. Differentiating these, which sometimes are structurally similar, is challenging but is required for leveraging structural data to gain functional insight. The reaction center complex from Chloroacidobacterium thermophilum has a hybrid (bacterio)chlorophyll antenna system containing both chlorophyll a and bacteriochlorophyll a molecules. The recent availability of its cryogenic electron microscopy (cryo-EM) structure provides an opportunity for a quantitative analysis of their identities, and chemical environments. Here, we describe a theoretical basis for differentiating chlorophyll a and bacteriochlorophyll a in a cryo-EM map, and apply the approach to the experimental cryo-EM maps of the (bacterio)chlorophyll sites of the chloroacidobacterial reaction center. The comparison reveals that at ~2.2-Å resolution, chlorophyll a and bacteriochlorophyll a are easily distinguishable, but the orientation of the bacteriochlorophyll a acetyl moiety is not; however, the latter can confidently be assigned by identifying a hydrogen bond donor from the protein environment. Furthermore, this study reveals the opportunities and challenges in assigning (bacterio)chlorophyll types in structural biology, the accuracy of which is vital for downstream investigations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Ab initio generalized Langevin equation

We introduce a machine learning–based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori–Zwanzig formalism, under the constraint of the fluctuation–dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Leveraging Sequential Doping of Semiconducting Polymers to Enable Functionally Graded Materials for Organic Thermoelectrics

With the ability to modulate electronic properties through molecular doping coupled with ease in processability, semiconducting polymers are at the forefront in enabling organic thermoelectric devices for thermal energy management. In contrast to uniform thermoelectric material properties, an alternative route focuses on functionally graded materials (FGMs) where one spatially controls and optimizes transport properties across the length of a thermoelectric material. While primarily studied in the context of inorganic materials, the concept of FGMs for organic thermoelectrics has not been explored. Herein, we introduce how molecular doping of semiconducting polymers enables spatial compositional control of thin-film FGMs. Specifically, we utilize sequential vapor doping of poly[2,5-bis(3-tetradecylthiophen-2-yl) thieno [3,2-b]thiophene] (PBTTT) with the small molecule acceptor 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4TCNQ) to fabricate the simplest form of FGMs – double- segmented thin films. The two thin-film segments are of equal length (7.5 mm), but each set to different doping levels. Our study focuses on understanding the thermoelectric properties (Seebeck coefficient, α, and electronic conductivity, σ) and structural properties (through X-ray scattering, UV-vis-NIR spectroscopy, and Raman spectroscopy) within and across the two segments. We observe the presence of a small diffuse interfacial region of 0.5 – 1 mm between the two segments where the doping level and transport properties vary continuously. Despite the diffuse interface, the measured effective Seebeck coefficient (αeff) across the two segments is simply the average of α within each segment. Importantly, this experimental result is consistent with reported mathematical models describing αeff in graded thermoelectric materials. Finally, our results demonstrate the facile fabrication and characterization of functionally graded organic thermoelectric materials, providing guidelines for further development on more complex FGMs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

PYSEQM

PYSEQM is a package for performing semi-empirical quantum mechanical (SEQM) simulations on molecular systems utilizing PyTorch. SEQM simulations determine molecular properties (energy, electron density, dipole moment, ect.) by solving an approximate Schrödinger equation for the motions of electrons in a molecule. The use of PyTorch provides three specific advantages. First, it allows the calculations to be offloaded to GPU accelerators, giving an order of magnitude increase in speed. Second, back propagation is used to get atomic forces (derivative of the total energy with respect to atomic position) at the same computational cost as the energy calculation itself. Finally, the use of PyTorch makes for a natural interface to modern machine learning methods, which can be used to adjust the semi-empirical parameters build into SEQM methods. Additionally, PYSEQM implements various other optimizations for performing quantum mechanics based molecular dynamics, including SP2 for rapid GPU based solution of the self-consistent field algorithm, and the extended Lagrangian method for rapid QM-MD.

Nebgen, Benjamin↗
DOE OSTI2022

Microcavity-Modified Emission from Rare-Earth Ion-Based Molecular Complexes

Despite the remarkable optical properties of rare-earth ion materials, their applications as light sources and in quantum technologies are often hindered by their long lifetimes and weak emission. Leveraging the natural compatibility of rare-earth ion molecular complexes with photonic structures, here we modify their photoluminescence properties by coupling them to a flexible open Fabry-Perot cavity. The full in situ tunability of the Fabry-Perot cavity allows fine control over its cavity modes and the achievement of resonant coupling between the rare-earth ion emission and the cavity modes. This configuration allows us to achieve a maximum photoluminescence enhancement factor of 30 and accelerate the decay rate up to two orders of magnitude. Our pump-power-dependent spectroscopic studies of the emitter-cavity system suggest that the cavity-modified emission is primarily caused by amplified spontaneous emission. These results suggest that integrating rare-earth ion molecular complexes with photonic structures could be a viable approach for the effective tuning of their optical properties. This natural compatibility, together with their versatile molecular structures and the resultant electronic states, renders rare-earth ion molecular complexes a potential alternative material platform for lighting and quantum applications.

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

Multiscale and Multimodal Characterization of 2D Titanium Carbonitride MXene

Here, a comprehensive study on the prototype solid solution phase carbonitride MXene Ti 3 CN is conducted using nuclear magnetic resonance, electron spin resonance, total and quasi-elastic neutron scattering, combined with density functional theory-based electronic structure and molecular dynamic calculations. The combination of experiment and theory lead toward rational atomic structural models of Ti 3 CN. The remnant Al ions from the etching process significantly tune the interlayer spacing, distinct from the more typical MXene, Ti 3 C 2 , prepared similarly. Neutron scattering indicates the surface terminations of Ti 3 CN display high oxygen and fluorine concentrations and rather low hydroxyl and hydrogen concentrations. Calculations show that the structure including both the residual Al ions and mixed surface terminations give the best agreement with the measurements. The water molecules in Ti 3 CN are highly immobile, in strong contrast to those in Ti 3 C 2 . The analysis of the electronic structure suggests that the nitride MXene displays higher conductivity than the carbides. Finally, the absence of hydroxyl groups in terminations, the solid-solution in the anion sites, the remnants within layers, and immobile water altogether make the carbonitrides a unique series in the MXene family, implying a further exploration of their exotic properties and applications in energy storage.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Simulation of 24,000 Electron Dynamics: Real-Time Time-Dependent Density Functional Theory (TDDFT) with the Real-Space Multigrids (RMG)

Here, we present the theory, implementation, and benchmarking of a real-time time-dependent density functional theory (RT-TDDFT) module within the RMG code, designed to simulate the electronic response of molecular systems to external perturbations. Our method offers insights into nonequilibrium dynamics and excited states across a diverse range of systems, from small organic molecules to large metallic nanoparticles. Benchmarking results demonstrate excellent agreement with established TDDFT implementations and showcase the superior stability of our time integration algorithm, enabling long-term simulations with minimal energy drift. The scalability and efficiency of RMG on massively parallel architectures allow for simulations of complex systems, such as plasmonic nanoparticles with thousands of atoms. Future extensions, including nuclear and spin dynamics, will broaden the applicability of this RT-TDDFT implementation, providing a powerful toolset for studies of photoactive materials, nanoscale devices, and other systems where real-time electronic dynamics is essential.

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

Plasma decay in hydrocarbons and hydrocarbon- and H 2 O-containing mixtures excited by high-voltage nanosecond discharge at elevated gas temperatures

Plasma decay after a high-voltage nanosecond discharge was experimentally and numerically studied in pure hydrocarbons (C 2 H 6 and C 3 H 8 ), and H 2 O:N 2 and C 3 H 8 :O 2 mixtures for pressures in the range 2–4 Torr and gas temperatures from 300 to 600 K. In a stoichiometric C 3 H 8 :O 2 mixture, plasma decay was also studied in a repetitively pulsed discharge for varing numbers of discharge pulses (varying degrees of fuel oxidation). The rate of plasma decay was determined from the temporal evolution of electron density measured using the microwave interferometer. It was observed that gas heating to 600 K leads to a decrease in the rate of plasma decay in all cases. The effect of heating on plasma decay was most profound in the H 2 O:N 2 mixture (after a single discharge pulse) and in the C 3 H 8 :O 2 mixture for high degrees of fuel oxidation. A kinetic scheme was developed to numerically simulate the plasma decay in hydrocarbons and combustible mixtures. Numerical analysis showed that, under the conditions studied, plasma decay was controlled by dissociative electron recombination with simple molecular and cluster ions. Gas heating led to a decrease in the rate of the electron-ion recombination and the rate of conversion of molecular ions to cluster ions. As a result, the gas temperature increase caused a decrease in the fraction of cluster ions for which the recombination coefficients are an order of magnitude higher than the recombination coefficients for molecular ions. The influence of gas heating on the decrease of the amount of cluster ions was more important when the ion composition was dominated by hydrated H 3 O + (H 2 O) k ions. The rates of the formation of these ions are extremely sensitive to any variations in gas temperature. A result, in agreement with our observations, gas heating led to an anomalous decrease in the rates of plasma decay in the H 2 O:N 2 mixture, as well as in the C 3 H 8 :O 2 mixture when H 2 O molecules were produced due to fuel oxidation.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2024

Symmetry Breaking in the Lowest-Lying Excited-State of CCl4: Valence Shell Spectroscopy in the 5.0–10.8 eV Photon Energy Range

We report absolute high-resolution vacuum ultraviolet (VUV) photoabsorption cross-sections of carbon tetrachloride (CCl4) in the photon energy range 5.0–10.8 eV (248–115 nm). The molecular spectrum and electronic structure have been comprehensively investigated together with quantum chemical calculations, providing geometries, bond lengths, vertical excitation energies and oscillator strengths. The major electronic excitations have been assigned to valence and Rydberg transitions which are also accompanied by vibrational excitation assigned to degenerate stretching, v3′t2 and degenerate deformation v4′t2 modes. The rather complex nuclear dynamics along the degenerate deformation mode, v4′t2, have been thoroughly investigated by Time-Dependent Density Functional Theory (TD-DFT) method. The relevant Jahn–Teller distortion operative within the lowest-lying electronic excited-state is shown here for the first time in order to yield a weak absorption feature at 6.156 eV. Further calculations on the potential energy curves for the singlet excited-states along the C–Cl stretching coordinate show the relevance of efficient C–Cl bond excision.

Biochemistry & Molecular Biology↗
DOE OSTI2022

Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗