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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Electronic properties of ThC − and ThC

The present study investigates the properties of low-lying states of ThC − and ThC using correlated wave function theories. To this end, we employed multireference calculations and various coupled-cluster approaches in combination with large correlation-consistent basis sets. These methods were applied to examine potential energy curves (PECs), electron configurations, energetics, spectroscopic constants, and spin–orbit coupling effects for 9 states of ThC − and 18 states of ThC. The ground states of ThC − and ThC were identified as single-reference 2 Σ + 1/2 (I) and $^3Σ^+_{0^-} (\textrm{I})$, respectively. Electron detachment from the 7s orbital of the Th center in ThC − [ 2 Σ + (I); 1σ 2 2σ1 3 σ2 1 π 4 ] yields ThC [ 3 Σ + (I); 1σ 2 2σ 1 3σ 1 1π 4 ]. The calculated adiabatic detachment energy (ADE) and vertical detachment energy (VDE) for this process are 1.591 and 1.604 eV, respectively. Furthermore, the dissociation energy (D 0 ) of ThC [$^3Σ^+_{0^-} (\textrm{I})$] is predicted to be 5.099 eV. The standard enthalpy of formation, $ΔH^{°}_{\textrm{f}}$ (298 K), of ThC is estimated to be 822.52 ± 6 kJ mol −1 .

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green’s functions

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green’s function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green’s function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green’s function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green’s function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green’s function approach and other Green’s function approaches in the numerical exact limit.

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

A molecular ground electronic state with an occupied 5g spinor—The superheavy (E125)F molecule

Fully relativistic calculations, primarily at the 4-component coupled-cluster singles and doubles with perturbative triples [CCSD(T)] level of theory with the Dirac–Coulomb (DC) Hamiltonian, have been carried out for the superheavy (E125)F molecule using large Gaussian basis sets. The electronic ground state is determined to have an [Og]8s 2 5g 1 6f 3 configuration on E125 with an Ω = 6 ground state and an 8p electron largely donated to F. A Mulliken population analysis indicates that the ground state is mainly ionic with a partial charge of +0.79 on E125 and a single sigma bond involving the F 2p and E125 8p spinors. The occupied g spinor is not involved in the bonding. With the largest basis set used in this work, the (0 K) dissociation energy was calculated at the DC-CCSD(T) level of theory to be 7.02 eV. Analogous calculations were also carried out for the E125 atom, both the neutral and its cation. The lowest energy electron configuration of E125 + , [Og]$8s$$^{2}_{1/2}$$5g$$^{1}_{7/2}$$6f$$^{3}_{5/2}$ with a J = 6 ground state, was found to be similar to that in (E125)F, while the neutral E125 atom has an [Og]$8s$$^{2}_{1/2}$$5g$$^{1}_{7/2}$$6f$$^{2}_{5/2}$$7d$$^{1}_{3/2}$$8p$$^{1}_{1/2}$ ground state electron configuration with a J = 17/2 ground state. The ionization energy (IE) of E125 is reported for the first time and is calculated to be 4.70 eV at the DC-CCSD(T) level of theory. Non-relativistic calculations were also carried out on the E125 atom and the (E125)F molecule. Here, the non-relativistic ground state of the E125 atom was calculated to have a 5g 5 ground state with an IE of just 3.4 eV. The net effect of relativity on (E125)F is to stabilize its bonding.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2024

A new “gold standard”: Perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework for dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the “gold standard” CCSD(T) method, which bolsters the baseline CCSD with the effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes are leveraged to evaluate energy corrections associated with triple excitations, leading to the UCCSD[T] method. In terms of quantum computing, this correction represents an entirely classical post-processing step that improves the energy estimate by accounting for triple excitation effects without necessitating new quantum algorithm developments or increasing demand for quantum resources. The rationale behind this choice is shown to be rigorous by studying the properties of finite-order UCC energy functionals, and our efforts do not support the addition of the fifth-order contributions as in the (T) correction. We assess the performance of these approaches on a collection of small molecules and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories.

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

Integrating subsystem embedding subalgebras and coupled cluster Green’s function: a theoretical foundation for quantum embedding in excitation manifold

Here, in this study, we introduce a novel approach to coupled-cluster Green's function (CCGF) embedding by seamlessly integrating conventional CCGF theory with the state-of-the-art sub-system embedding sub-algebras coupled cluster (SES-CC) formalism. This integration focuses primarily on delineating the characteristics of the sub-system and the corresponding segments of the Green's function, defined explicitly by active orbitals. Crucially, our work involves the adaptation of the SES-CC paradigm, addressing the left eigenvalue problem through a distinct form of Hamiltonian similarity transformation. This advancement not only facilitates a comprehensive representation of the interaction between the embedded sub-system and its surrounding environment but also paves the way for the quantum mechanical description of multiple embedded domains, particularly by employing the emergent quantum flow algorithms. Our theoretical underpinnings further set the stage for a generalization to multiple embedded sub-systems. This expansion holds significant promise for the exploration and application of non-equilibrium quantum systems, enhancing the understanding of system–environment interactions. In doing so, the research underscores the potential of SES-CC embedding within the realm of quantum computations and multi-scale simulations, promising a good balance between accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantum many-body linear algebra, Hamiltonian moments, and a coupled-cluster inspired framework

Here, we propose a general strategy to develop quantum many-body approximations of primitives in linear algebra algorithms. As a practical example, we introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments and demonstrate its application in various linear algebra algorithms for ground state estimation. Through numerical examples, we illustrate the difference between the ground-state energies arising from quantum many-body linear algebra and those from the analogous many-body perturbation theory. Our results support the general idea of designing quantum many-body approximations outside of perturbation theory, providing a route to new algorithms and approximations.

Algorithms and data structure↗
DOE OSTI2025

Repartitioning the Hamiltonian in many-body second-order Brillouin–Wigner perturbation theory: Uncovering new size-consistent models

Second-order Møller-Plesset perturbation theory is well-known as a computationally inexpensive approach to the electron correlation problem that is size-consistent with a size-consistent reference but fails to be regular. On the other hand, the less well-known many-body version of Brillouin-Wigner perturbation theory has the reverse properties: it is regular but fails to be size-consistent when used with the standard MP partitioning. Consequently, its widespread use remains limited. In this work, we analyze the ways in which it is possible to use alternative non-MP partitions of the Hamiltonian to yield variants of BW2 that are size-consistent as well as regular. We show that there is a vast space of such BW2 theories and also show that it is possible to define a repartitioned BW2 theory from the ground state density alone, which regenerates the exact correlation energy. We also provide a general recipe for deriving regular, size-consistent, and size-extensive partitions from physically meaningful components, and we apply the result to small model systems. The scope of these results appears to further set the stage for a revival of BW2 in quantum chemistry.

Ab initio perturbation↗
DOE OSTI2025

Benchmarking third-order cluster perturbation theory for electronically excited states

In this study, we investigate the reliability of cluster perturbation (CP) theory applied to the calculation of electronically excited states through a comprehensive benchmark. In CP theory, perturbative corrections are added to the properties of a parent excitation space, which converge toward the properties of a target excitation space. For the CPS(D-n) model, perturbative corrections through order n are added to the coupled cluster singles (CCS) excitation energies to target the coupled cluster singles and doubles (CCSD) excitation energies. Through a comparative analysis of excitation energy calculations across a diverse set of molecules and wavefunction methods, we present a comprehensive evaluation of the accuracy of the third-order CPS(D) model, CPS(D-3), in calculating excitation energies. Further, our findings demonstrate that CPS(D-3) is a reliable alternative to established methods, particularly CCSD, while systematically overestimating the excitation energies compared to high-level coupled cluster methods such as CC3. These results highlight the strengths and limitations of CPS(D-3), as well as the promising directions for its future development.

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

Structure of odd-mass Ne, Na, and Mg nuclei

The island of inversion is a region of neutron-rich nuclei around 31 Na that are deformed in their ground states. In this region, less is known about the energy levels of odd-mass nuclei, how they evolve with increasing neutron numbers, and how they can be organized into rotational bands. We perform ab initio coupled-cluster calculations of spectra in odd-mass Ne, Na, and Mg nuclei based on an interaction of chiral effective field theory. In conclusion, our results confirm some tentative spin and parity assignments, predict the structure of nuclei near the neutron dripline, and inform us about rotational bands in this region of the nuclear table.

20 ≤ A ≤ 38↗
DOE OSTI2025

The reaction NH 2 + CH 2 O: Kinetic measurements and computational studies

The reaction of amidogen with formaldehyde is relevant to astrochemistry and couples nitrogen and carbon chemistry in flames. The first measurements of the temperature dependence of the rate constant k were made, over 409–643 K, and are summarized as k = 7.1 × 10 −12 exp(−18.2 kJ mol −1 /RT) cm 3 molecule −1 s −1 with a confidence interval of ±20%. These results address a controversy over the presence of a significant barrier in the addition/elimination pathway leading to the production of formamide between theoretical models that include the zero-point energy of all modes at the transition state and a model that excludes transitional modes. The latter would lead to a negligible barrier, which is inconsistent with the experiments. Contrary to earlier claims, CCSDT(Q)-corrected energies combined with transition state theory yield quantitative accord with the measurements.

Astrochemistry↗
DOE OSTI2025

Exploring the nexus of many-body theories through neural network techniques: the tangent model

Abstract In this paper, we present a physically informed neural network (NN) representation of the effective interactions associated with coupled-cluster downfolding models to describe chemical systems and processes. The NN representation not only allows us to evaluate the effective interactions efficiently for various geometrical configurations of chemical systems corresponding to various levels of complexity of the underlying wave functions, but also reveals that the bare and effective interactions are related by a tangent function of some latent variables. We refer to this characterization of the effective interaction as a tangent model. We discuss the connection between this tangent model for the effective interaction with the previously developed theoretical analysis that examines the difference between the bare and effective Hamiltonians in the corresponding active spaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A static quantum embedding scheme based on coupled cluster theory

Here, we develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller–Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid second-order Møller–Plesset (MP2) and CC works by Nooijen [J. Chem. Phys. 111, 10815 (1999)] and Bochevarov and Sherrill [J. Chem. Phys. 122, 234110 (2005)]. We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for N=N bond breaking in azomethane and for the central C–C bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver.

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

The approximate second order coupled-cluster method based on a size-consistent Brillouin–Wigner partitioning

We present a variant of the approximate second order coupled-cluster method (CC2) with a two-parameter size-consistent Brillouin–Wigner (BW-s) partitioning instead of a Møller–Plesset (MP) partitioning for the unperturbed Hamiltonian, which we refer to as BWs-CC2. The computational complexity of this model scales identically to CC2 with molecular size. Conventional CC2 and its regularized BWs-CC2 variants, as well as conventional MP2 and two of its regularized BW-s2 variants, were assessed on a 535 element database spanning thermochemistry, non-covalent interactions, barrier heights, and isomerization energies. To ensure a well-defined model chemistry, the assessment was performed using internally stable spin-polarized Hartree–Fock (HF) orbitals in the finite aug-cc-pVQZ basis without counterpoise corrections. As a result of using stable orbitals, contrary to conventional wisdom, we find that CC2 substantially outperforms MP2 on molecules with significantly spin contaminated reference orbitals without a significant increase in error on systems with a spin-pure reference, showing the value of its single substitutions. While no single choice of regularization parameters can be optimal for all datasets, we find that BWs-CC2 generally outperforms both CC2 and BW-s2 with a single judicious parameter choice. Additional tests on dipole moments and bond lengths of diatomics provide further support for the utility of this choice. Furthermore, the main outliers and poorest performing cases are associated with large amounts of spin-contamination in the HF reference, which is indicative of systems with either strong correlation or extensive artificial symmetry breaking. Overall, these findings argue that the perception of the quality of the CC2 ground state should be reevaluated and that it can be further improved upon by the soundly based BWs-CC2 variant with the recommended parameter choice.

Correlation energy↗
DOE OSTI2024

Prediction of photodynamics of 200 nm excited cyclobutanone with linear response electronic structure and ab initio multiple spawning

Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S 2 ). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. Herein we use both time dependent density functional theory (TDDFT) and equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory for the underlying electronic structure theory. We find that the lifetime of the S 2 state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted ultrafast electron diffraction spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.

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

The accuracies of effective interactions in downfolding coupled-cluster approaches for small-dimensionality active spaces

Here, this paper evaluates the accuracy of the Hermitian form of the downfolding procedure using the double unitary coupled cluster (DUCC) ansatz on the benchmark systems of linear chains of hydrogen atoms, H6 and H8. The computational infrastructure employs the occupation-number-representation codes to construct the matrix representation of arbitrary second-quantized operators, allowing for the exact representation of exponentials of various operators. The tests demonstrate that external amplitudes from standard single-reference coupled cluster methods that sufficiently describe external (out-of-active-space) correlations reliably parameterize the Hermitian downfolded effective Hamiltonians in the DUCC formalism. The results show that this approach can overcome the problems associated with losing the variational character of corresponding energies in the corresponding SR-CC theories.

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

The bond energy of UN + : Guided ion beam studies of the reactions of U + with N 2 and NO

In this work, a guided ion beam tandem mass spectrometer was used to study the reactions of U + with N 2 and NO. Reaction cross sections were measured over a wide range of energy for both systems. In each reaction, UN + is formed by an endothermic process, thereby enabling the direct measurement of the threshold energy and determination of the UN + bond dissociation energy. For the reaction of U + + N 2 , a threshold energy (E 0 ) of 4.02 ± 0.11 eV was measured, leading to D 0 (UN + ) = 5.73 ± 0.11 eV. The reaction of U + + NO yields UO + through an exothermic, barrierless process that proceeds with 94 ± 23% efficiency at the lowest energy. Analysis of the endothermic UN + cross section in this reaction provides E 0 = 0.72 ± 0.11 eV and, therefore, D 0 (UN + ) = 5.78 ± 0.11 eV. Averaging the values obtained from both reactions, we report D 0 (UN + ) = 5.76 ± 0.13 eV as our best value (uncertainty of two standard deviations). Combined with precise literature values for the ionization energies of U and UN, we also derive D 0 (UN) = 5.86 ± 0.13 eV. Both bond dissociation energies agree well with high-level theoretical treatments in the literature. The formation of UN + in reaction of U + with NO also exhibits a considerable increase in reaction probability above ~3 eV. Theory suggests that this may be consistent with the formation of UN + in excited quintet spin states, which we hypothesize are dynamically favored because the number of 5f electrons in reactants and products is conserved.

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

Ultrafast Correlation Energy Estimator

A virtually no-cost method is proposed that can compute the correlation energies of general, covalently bonded, organic, and inorganic molecules (including conjugated π-electron systems) with a well-defined dominant Lewis structure at the accuracy of 99.5% of the near-exact values determined by the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] in the complete-basis-set (CBS) limit. This Correlation Energy Per Bond (CEPB) method assigns a partial correlation energy to each bond type (characterized by the identities of the two atoms forming the bond and its integer bond order) and to a lone pair, regardless of the bond length, bond angle, sp-hybridization, π-electron conjugation, ionicity, noncovalent interactions, etc. At its current stage, the method is mainly suitable for near-equilibrium geometries. The correlation energies per bond are determined by a fit to the CCSD(T)/CBS benchmarks. It can neither improve the equilibrium structures nor discern conformers or positional isomers, yet its accuracy for reaction energies rivals that of the second-order Møller–Plesset perturbation theory, which is far more expensive. Its promising performance underscores the possibility that surprisingly compact, chemically intuitive molecular fragments exist into which correlation energies can be partitioned, leading to various ultrafast correlation-energy estimators tailored to different purposes.

Binding energy↗
DOE OSTI2024

Ab initio computations of strongly deformed nuclei near Zr 80

Nuclei around N ≈ Z ≈ 40 are strongly deformed and exhibit coexistence of shapes. These phenomena have challenged nuclear models. Here, we perform ab initio coupled-cluster computations of low-lying collective states and electromagnetic quadrupole transitions of the even-even nuclei 72 Kr, 76,78 Sr, 78,80 Zr, and 84 Mo starting from chiral nucleon-nucleon and three-nucleon forces. Our calculations reproduce the coexistence of oblate and prolate shapes in these nuclei, yield rotational bands and strong electromagnetic transitions, but are not accurate for some observables and nuclei. Finally, these results highlight the advances and challenges of ab initio computations of heavy deformed nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗