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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

Applied Dynamical Systems↗
DOE OSTI2014

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the number of relaxation modes or “folding pathways” that contribute to the evolution of the state populations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Effect of the size of nanoparticles on their dissolution within metal-glass nanocomposites under sustained irradiation

We investigate the dissolution law of metallic nanoparticles (NPs) under sustained irradiation. The system is composed of isolated spherical gold NPs (4–100 nm) embedded in an amorphous silica host matrix. Samples are irradiated at room temperature in the nuclear stopping power regime with 4 MeV Au ions for fluences up to 8 × 10{sup 16 }cm{sup −2}. Experimentally, the dependence of the dissolution kinetics on the irradiation fluence is linear for large NPs (45–100 nm) and exponential for small NPs (4–25 nm). A lattice-based kinetic Monte Carlo (KMC) code, which includes atomic diffusion and ballistic displacement events, is used to simulate the dynamical competition between irradiation effects and thermal healing. The KMC simulations allow for a qualitative description of the NP dissolution in two main stages, in good agreement with the experiment. Moreover, the perfect correlation obtained between the evolution of the simulated flux of ejected atoms and the dissolution rate in two stages implies that there exists an effect of the size of NPs on their dissolution and a critical size for the transition between the two stages. The Frost-Russell model providing an analytical solution for the dissolution rate, accounts well for the first dissolution stage but fails in reproducing the data for the second stage. An improved model obtained by including a size-dependent recoil generation rate permits fully describing the dissolution for any NP size. This proves, in particular, that the size effect on the generation rate is the principal reason for the existence of two regimes. Finally, our results also demonstrate that it is justified to use a unidirectional approximation to describe the dissolution of the NP under irradiation, because the solute concentration is particularly low in metal-glass nanocomposites.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Quantum simulations of hadron dynamics in the Schwinger model using 112 qubits

Hadron wave packets are prepared and time evolved in the Schwinger model using 112 qubits of IBM’s 133-qubit Heron quantum computer ibm_torino. The initialization of the hadron wave packet is performed in two steps. First, the vacuum is prepared across the whole lattice using the recently developed SC-ADAPT-VQE algorithm and workflow. SC-ADAPT-VQE is then extended to the preparation of localized states, and used to establish a hadron wave packet on top of the vacuum. This is done by adaptively constructing low-depth circuits that maximize the overlap with an adiabatically prepared hadron wave packet. Due to the localized nature of the wavepacket, these circuits can be determined on a sequence of small lattices using classical computers, and then robustly scaled to prepare wave packets on large lattices for simulations using quantum computers. Time evolution is implemented with a second-order Trotterization. To reduce both the required qubit connectivity and circuit depth, an approximate quasilocal interaction is introduced. This approximation is made possible by the emergence of confinement at long distances, and converges exponentially with increasing distance of the interactions. Using multiple error-mitigation strategies, up to 14 Trotter steps of time evolution are performed, employing 13,858 two-qubit gates (with a CNOT depth of 370). The propagation of hadrons is clearly identified, with results that compare favorably with Matrix Product State simulations. Finally, prospects for a near-term quantum advantage in simulations of hadron scattering are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Triangle Method for Dense ReLU Layers [SWR-25-72]

This software is an implementation of the methods for initializing and training neural networks to be more efficient per parameter, described more fully below and in the related publication: In theory, depth should make a ReLU network EXPONENTIALLY more efficient by enabling it to produce an exponential number of piecewise linear sections in its output. This reasoning is largely based on the work of mathematicians that have hand-constructed networks that make good use of depth. In practice however, even very deep ReLU networks that have been randomly initialized will behave identically to their shallow counterparts - missing an entire exponential dimension of efficiency. The triangle method is a first attempt at realizing the exponential potential of deep networks. Instead of randomly setting weights, we force pairs of neurons in each layer learn to build triangles (i.e. functions from [0,1] -> [0,1] that look like triangles). This is a very efficient pattern for generating lots of linear pieces because composing two triangular functions doubles the number of pieces with each composition. The triangle method is more than just a different initialization, it is a new paradigm of training. Instead of making direct updates to the matrix weights, we do an extra step of backpropagation to collect the derivatives of the loss function with respect to the shapes of the triangles, training them to tilt left or right. This process essentially holds the networks hand throughout the loss landscape and forces it to always use depth effectively by producing triangular shapes internally. This can produce several orders of magnitude of improvement on convex one-dimensional regression problems. Much more theoretical work is needed to realize its full potential beyond this context, but the implementation in this repository will still work in arbitrary numbers of dimensions. The file Triangle_Method.py is a generalized form of the method that will build each neuron its own custom 1-d convex activation function (with exponential efficiency). Example usage on one dimensional problems can be found in Example_Usage.ipynb and an example of using this in a real neural network can be found in Example_VGG16_CIFAR10.ipynb.

Milkert, Max [National Renewable Energy Laboratory↗
DOE OSTI2023

Two-dimensional isometric tensor networks on an infinite strip

The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of TNS that allows for efficient simulation of such systems on finite square lattices. The isoTNS ansatz requires the identification of an “orthogonality column” of tensors, within which one-dimensional matrix product state (MPS) methods can be used for calculation of observables and optimization of tensors. Here we extend isoTNS to infinitely long strip geometries and introduce an infinite version of the Moses Move algorithm for moving the orthogonality column around the network. Using this algorithm, we iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. In addition, we demonstrate that the local observables can be evaluated efficiently. Lastly, we introduce an infinite time-evolving block decimation algorithm (iTEBD 2 ) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Modeling curved interfaces without element‐partitioning in the extended finite element method

Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h ‐refinement ( p =1,2,…,5) and exponential rates of convergence with p ‐refinement ( p =1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian p th‐order spectral finite element meshes.

Chin, Eric B.↗
DOE OSTI2018

The Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice

We prove the Pfaffian Sign Theorem for the dimer model on a triangular lattice embedded in the torus. More specifically, we prove that the Pfaffian of the Kasteleyn periodic-periodic matrix is negative, while the Pfaffians of the Kasteleyn periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic matrices are all positive. The proof is based on the Kasteleyn identities and on small weight expansions. As an application, we obtain an asymptotic behavior of the dimer model partition function with an exponentially small error term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Simulating large one-dimensional neutral-atom quantum systems

While abstract models of quantum computation assume a closed system of two-level states, practical quantum devices inevitably couple to the environment in some way, creating sources of noise. Understanding the tolerance to noise of specific quantum algorithms run on specific devices is important for determining the feasibility of quantum computing in the current noisy intermediate-scale quantum era. Of particular interest is understanding the noise sensitivity of these devices as more qubits are added to the system. Classical simulations are a useful tool to understand the effects of this noise, but direct classical simulations of open quantum systems are burdened by an exponentially growing cost in the number of qubits and a large local Hilbert space dimension. For onedimensional, shallow circuits, using tensor networks can replace this exponential cost with a linear one and simulate far wider systems than what would normally be available. In this paper, we describe a tensor network simulation of a neutral atom quantum system under the presence of noise, while introducing a purity-preserving truncation technique that compromises between the simplicity of the matrix product state and the positivity of the matrix product density operator. We apply this simulation to a near-optimized iteration of the quantum approximate optimization algorithm on a transverse field Ising model in order to investigate the influence of large system sizes on the performance of the algorithm. We find that while circuits with a large number of qubits fail more often under noise that depletes the qubit population, their outputs on a successful measurement are just as robust under Rydberg atom dissipation or qubit dephasing as smaller systems. However, such circuits might not perform as well under coherent multiqubit errors such as Rydberg atom crosstalk. We also find that the optimized parameters are especially robust to noise, suggesting that a noisier quantum system can be used to find the optimal parameters before switching to a cleaner system for measurements of observables.

Allen, James↗
DOE OSTI2010

Tomography, control, and characterization of entanglement in a three-level atomic system

We study the quantum correlations of the radiation emitted by three-level atoms (cascade type) interacting with two driving fields. In the linear regime, and in the Weisskopf-Wigner approximation, we show that the atomic and the two-photon density matrix are equivalent to each other. This facilitates the tomography of the two-mode state to be realized by measurements on either the atomic system or the emitted fields. While, in general, one needs 4{sup N} measurements for the tomography of an N-photon state, we show that one needs (N+1){sup 2}-1 observables for the tomography of photons emitted by an atomic system. Thus there is an exponential reduction in the number of observables for the reconstruction of the class of N-photon states emitted by atoms. We show that the driving field strengths and detunings provide the control parameters for the preparation of a specific target state. Finally, we study the characterization of entanglement of the two-photon state. We observe that a characterization of entanglement in terms of a single parameter is not possible when the system is in a mixed state; therefore, we provide a description in terms of the newly introduced probability distribution for entanglement, in various regimes of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree–Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree–Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Elucidation of the physical factors that control activated transport of penetrants in chemically complex glass-forming liquids

Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics, and biophysics. Many angstrom- and nanometer-scale features enter due to the highly variable shape, size, interaction, and conformational flexibility of the penetrant and matrix species, leading to a dramatic diversity of penetrant dynamics. Based on a minimalist model of a spherical penetrant in equilibrated dense matrices of hard spheres, a recent microscopic theory that relates hopping transport to local structure has predicted a novel correlation between penetrant diffusivity and the matrix thermodynamic dimensionless compressibility, S 0 ( T ) (which also quantifies the amplitude of long wavelength density fluctuations), as a consequence of a fundamental statistical mechanical relationship between structure and thermodynamics. Moreover, the penetrant activation barrier is predicted to have a factorized/multiplicative form, scaling as the product of an inverse power law of S 0 ( T ) and a linear/logarithmic function of the penetrant-to-matrix size ratio. This implies an enormous reduction in chemical complexity that is verified based solely on experimental data for diverse classes of chemically complex penetrants dissolved in molecular and polymeric liquids over a wide range of temperatures down to the kinetic glass transition. The predicted corollary that the penetrant diffusion constant decreases exponentially with inverse temperature raised to an exponent determined solely by how S 0 ( T ) decreases with cooling is also verified experimentally. Our findings are relevant to fundamental questions in glassy dynamics, self-averaging of angstrom-scale chemical features, and applications such as membrane separations, barrier coatings, drug delivery, and self-healing.

Science & Technology - Other Topics↗
DOE OSTI2019

Two-Exponential Rossi-Alpha Analysis of Copper- and Polyethylene-Reflected Plutonium

The prompt neutron decay constant $\mathcal{α}$, which is used to infer reactivity, is estimated using the Rossi-alpha technique that is predicated on fitting Rossi-alpha histograms. The histograms are traditionally fit with a one-exponential model; however, recent work has proposed a two-exponential model to account for reflector-induced phenomenon. Recent work also validated the two-exponential model for shields, a subset of reflectors, but not for reflectors in general. Ultimately, it is desirable to validate the two-exponential model for the general shield. This work will investigate if previous 3 He measurements of plutonium reflected by copper and polyethylene, and replacement measurements where the plutonium is replaced by 252 Cf are suitable for validating the new model. Since the 3 He detectors ( 3 He gas proportional counters embedded in a polyethylene matrix) inherently contain moderating/reflector material (to increase detection efficiency), this work also investigates the use of organic scintillation detectors that can directly detect fast, fission neutrons.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2017

Lattice QCD exploration of parton pseudo-distribution functions

Here, we demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equal-time matrix element ${\cal M} (Pz_3, z_3^2)$ as a function of the Ioffe time $\nu = Pz_3$ and the distance $z_3$. The next step is to divide ${\cal M} (Pz_3, z_3^2)$ by the rest-frame density ${\cal M} (0, z_3^2)$. Our lattice calculation shows a linear exponential $z_3$-dependence in the rest-frame function, expected from the $Z(z_3^2)$ factor generated by the gauge link. Still, we observe that the ratio ${\cal M} (Pz_3 , z_3^2)/{\cal M} (0, z_3^2)$ has a Gaussian-type behavior with respect to $z_3$ for 6 values of $P$ used in the calculation. This means that $Z(z_3^2)$ factor was canceled in the ratio. When plotted as a function of $\nu$ and $z_3$, the data are very close to $z_3$-independent functions. This phenomenon corresponds to factorization of the $x$- and $k_\perp$-dependence for the TMD ${\cal F} (x, k_\perp^2)$. For small $z_3 \leq 4a$, the residual $z_3$-dependence is explained by perturbative evolution, with $\alpha_s/\pi =0.1$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Paradigm for approaching the forbidden spontaneous phase transition in the one-dimensional Ising model at a fixed finite temperature

The Ising model describes collective behaviors such as phase transitions and critical phenomena in various physical, biological, economical, and social systems. It is well known that spontaneous phase transition at finite temperature does not exist in the Ising model with short-range interactions in one dimension. Yet, little is known about whether this forbidden phase transition can be approached arbitrarily closely—at fixed finite temperature. Here I use symmetry analysis of the transfer matrix to reveal the existence of spontaneous ultranarrow phase crossover (UNPC) at finite temperature in one class of one-dimensional Ising models on decorated two-leg ladders, in which the crossover temperature T 0 is determined solely by on-rung interactions and decorations, while the crossover width 2 δ T is independently, exponentially reduced ( δ T = 0 means a genuine phase transition) by on-leg interactions and decorations. These findings establish a simple ideal paradigm for realizing an infinite number of one-dimensional Ising systems with spontaneous UNPC at desirable T 0 , which would be characterized in routine laboratory measurements as a genuine first-order phase transition with large latent heat thanks to the ultranarrow δ T (say less than one nanokelvin), paving a way to push the limit in our understanding of phase transitions and the dynamical actions of frustration arbitrarily close to the forbidden regime. Published by the American Physical Society 2024

1-dimensional systems↗
DOE OSTI2010

A semi-analytical model for heat and mass transfer in geothermal reservoirs to estimate fracture surface-are-to-volume ratios and thermal breakthrough using thermally-decaying and diffusing tracers

A semi-analytical model was developed to conduct rapid scoping calculations of responses of thermally degrading and diffusing tracers in multi-well tracer tests in enhanced geothermal systems (EGS). The model is based on an existing Laplace transform inversion model for solute transport in dual-porosity media. The heat- and mass-transfer calculations are decoupled and conducted sequentially, taking advantage of the fact that heat transfer between fractures and the rock matrix is much more rapid than mass transfer and therefore mass transfer will effectively occur in a locally isothermal system (although the system will be nonisothermal along fracture flow pathways, which is accounted for by discretizing the flow pathways into multiple segments that have different temperature histories). The model takes advantage of the analogies between heat and mass transfer, solving the same governing equations with k{sub m}/({rho}C{sub p}){sub w} being substituted for {phi}D{sub m} in the equation for fracture transport and k{sub m}/({rho}C{sub p}){sub m} being subsituted for D{sub m} in the equation for matrix transport; where k = thermal conductivity (cal/cm-s-K), {rho} = density (g/cm{sup 3}), C{sub p} = heat capacity (at constant pressure) (cal/g-K), {phi} = matrix porosity, and D = tracer diffusion coefficient (cm{sup 2}/s), with the subscripts w and m referring to water and matrix, respectively. A significant advantage of the model is that it executes in a fraction of second on a single-CPU personal computer, making it very amenable for parameter estimation algorithms that involve repeated runs to find global minima. The combined thermal-mass transport model was used to evaluate the ability to estimate when thermal breakthrough would occur in a multi-well EGS configuration using thermally degrading tracers. Calculations were conducted to evaluate the range of values of Arrhenius parameters, A and E{sub {alpha}} (pre-exponential factor, 1/s, and activation energy, cal/mol) required to obtain interpretable responses of thermally-degrading tracers that decay according to the rate constant k{sub d} = Ae{sup -E{sub {alpha}}/RT}, where k{sub d} = decay rate constant (1/s), R = ideal gas constant (1.987 cal/mol-K), and T = absolute temperature (K). It is shown that there are relatively narrow ranges of A and E{sub {alpha}} that will result in readily interpretable tracer responses for any given combination of ambient reservoir temperature and working fluid residence time in a reservoir. The combined model was also used to simulate the responses of conservative tracers with different diffusion coefficients as a way of estimating fracture surface-area-to-volume ratios (SA/V) in multi-well EGS systems. This method takes advantage of the fact that the differences in breakthrough curves of tracers with different matrix diffusion coefficients are a function of SA/V. The model accounts for differences in diffusion coefficients as a function of temperature so that tracer responses obtained at different times can be used to obtain consistent estimates of SA/V as the reservoir cools down. Some single-well applications of this approach are simulated with a numerical model to demonstrate the potential to evaluate the effectiveness of EGS stimulations before a second well is drilled.

58 GEOSCIENCES↗
DOE OSTI2016

Dielectric relaxation in 0-3 PVDF-Ba(Fe{sub 1/2}Nb{sub 1/2})O{sub 3} composites

(1-x)PVDF-xBa(Fe{sub 1/2}Nb{sub 1/2})O{sub 3} ceramic-polymer composites with x = 0.025, 0.05, 0.10, 0.15 were prepared using melt-mixing technique. The crystal symmetry, space group and unit cell dimensions were determined from the XRD data of Ba(Fe{sub 1/2}Nb{sub 1/2})O{sub 3} using FullProf software, whereas crystallite size and lattice strain were estimated using Williamson-Hall approach. The distribution of Ba(Fe{sub 1/2}Nb{sub 1/2})O{sub 3} particles in the PVDF matrix were examined on the cryo-fractured surfaces using a scanning electron microscope. Cole-Cole and pseudo Cole-Cole analysis suggested the dielectric relaxation in this system to be of non-Debye type. Filler concentration dependent real and imaginary parts of dielectric constant as well as ac conductivity data followed definite trends of exponential growth types of variation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

Strongly correlated mechanisms of a photoexcited radical reaction from the anti-Hermitian contracted Schroedinger equation

Photoexcited radical reactions are critical to processes in both nature and materials, and yet they can be challenging for electronic structure methods due to the presence of strong electron correlation. Reduced-density-matrix (RDM) methods, based on solving the anti-Hermitian contracted Schroedinger equation (ACSE) for the two-electron RDM (2-RDM), are examined for studying the strongly correlated mechanisms of these reactions with application to the electrocyclic interconversion of allyl and cyclopropyl radicals. We combine recent extensions of the ACSE to excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)] and arbitrary spin states [A. E. Rothman, J. J. Foley IV, and D. A. Mazziotti, Phys. Rev. A 80, 052508 (2009)]. The ACSE predicts that the ground-state ring closure of the allyl radical has a high 52.5 kcal/mol activation energy that is consistent with experimental data, while the closure of an excited allyl radical can occur by disrotatory and conrotatory pathways whose transition states are essentially barrierless. Comparisons are made with multireference second- and third-order perturbation theories and multireference configuration interaction. While predicted energy differences do not vary greatly between methods, the ACSE appears to improve these differences when they involve a strongly and a weakly correlated radical by capturing a greater share of single-reference correlation that increases the stability of the weakly correlated radicals. For example, the ACSE predicts a -39.6 kcal/mol conversion of the excited allyl radical to the ground-state cyclopropyl radical in comparison to the -32.6 to -37.3 kcal/mol conversions predicted by multireference methods. In addition, the ACSE reduces the computational scaling with the number of strongly correlated orbitals from exponential (traditional multireference methods) to quadratic. Computed ground- and excited-state 2-RDMs are nearly N-representable.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗