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DOE OSTI2023

Coupled-cluster theory for strong entanglement in nuclei

Atomic nuclei can exhibit shape coexistence and multireference physics that enters in their ground states, and accurately capturing the ensuing correlations and entanglement is challenging. Here, we address this problem by applying single-reference coupled-cluster theory based on spherical and deformed reference states and the tailored coupled-cluster method. The latter combines configuration interactions to capture static correlations with coupled-cluster theory for dynamic correlations. We compute the atomic nuclei 12 C, 28 Si, and 56 Ni and find that the tailored coupled-cluster method and the single-reference approach based on a deformed Hartree-Fock state yield the most accurate results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Energetic and Spectroscopic Properties of Astrophysically Relevant MgC 4 H Radicals Using High-Level Ab Initio Calculations

Considering the importance of magnesium-bearing hydrocarbon molecules (MgC n H; n = 2, 4, and 6) in the carbon-rich circumstellar envelopes (e.g., IRC+10216), a total of 28 constitutional isomers of MgC 4 H have been theoretically investigated using density functional theory (DFT) and coupled-cluster methods. The zero-point vibrational energy corrected relative energies at the ROCCSD(T)/cc-pCVTZ level of theory reveal that the linear isomer, 1-magnesapent-2,4-diyn-1-yl (1, 2 Σ + ), is the global minimum geometry on the MgC 4 H potential energy surface. The latter has been detected both in the laboratory and in the evolved carbon star, IRC+10216. The calculated spectroscopic data for 1 match well with the experimental observations (error ~ 0.78%) which validates our theoretical methodology. Plausible isomerization processes happening among different isomers are examined using DFT and coupled-cluster methods. CASPT2 calculations have been performed for a few isomers exhibiting multireference characteristics. The second most stable isomer, 1-ethynyl-1λ 3 -magnesacycloprop-2-ene-2,3-diyl (2, 2 A 1 , μ = 2.54 D), is 146 kJ mol –1 higher in energy than 1 and possibly the next promising candidate to be detected in the laboratory or in the interstellar medium in future.

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 OSTI2023

A parallel, distributed memory implementation of the adaptive sampling configuration interaction method

The many-body simulation of quantum systems is an active field of research that involves several different methods targeting various computing platforms. Many methods commonly employed, particularly coupled cluster methods, have been adapted to leverage the latest advances in modern high-performance computing. Selected configuration interaction (sCI) methods have seen extensive usage and development in recent years. However, the development of sCI methods targeting massively parallel resources has been explored only in a few research works. Here, we present a parallel, distributed memory implementation of the adaptive sampling configuration interaction approach (ASCI) for sCI. In particular, we will address the key concerns pertaining to the parallelization of the determinant search and selection, Hamiltonian formation, and the variational eigenvalue calculation for the ASCI method. Load balancing in the search step is achieved through the application of memory-efficient determinant constraints originally developed for the ASCI-PT2 method. The presented benchmarks demonstrate near optimal speedup for ASCI calculations of Cr 2 (24e, 30o) with 10 6 , 10 7 , and 3 × 10 8 variational determinants on up to 16 384 CPUs. Importantly, to the best of the authors’ knowledge, this is the largest variational ASCI calculation to date.

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

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

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

Excited states in variational Monte Carlo using a penalty method

Here, in this article, the authors present a technique using variational Monte Carlo to solve for excited states of electronic systems. This technique is based on enforcing orthogonality to lower energy states, which results in a simple variational principle for the excited states. Energy optimization is then used to solve for the excited states. This technique is applied to the well-characterized benzene molecule, in which ~10 000 parameters are optimized for the first 12 excited states. Agreement within ~0.2 eV is obtained with higher scaling coupled cluster methods; small disagreements with experiment are likely due to vibrational effects.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Linear-Scaling Local Natural Orbital-Based Full Triples Treatment in Coupled-Cluster Theory

We present an efficient, asymptotically linear-scaling implementation of the canonically O(N 8 ) coupled-cluster method with singles, doubles, and full triples excitations (CCSDT) method. We apply the domain-based local pair natural orbital (DLPNO) approach for computing CCSDT amplitudes. Our method, called DLPNO–CCSDT, uses the converged coupled-cluster amplitudes from a preceding DLPNO–CCSD(T) computation as a starting point for the solution of the CCSDT equations in the local natural orbital basis. To simplify the working equations, we t1-dress our two-electron integrals and Fock matrices, allowing our equations to take on the form of CCDT. With appropriate parameters, our method can recover more than 99.99% of the total canonical CCSDT correlation energy. In addition, we demonstrate that our method consistently yields sub-kJ mol –1 errors in relative energies when compared to canonical CCSDT, and, likewise, when computing the difference between CCSDT and CCSD(T). Finally, to highlight the low scaling of our algorithm, we present timings on linear alkanes (up to 30 carbons and 730 basis functions) and water clusters (up to 131 water molecules and 3144 basis functions).

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

Rank-reduced coupled-cluster. III. Tensor hypercontraction of the doubles amplitudes

In this work, we develop a quartic-scaling implementation of coupled-cluster singles and doubles (CCSD) based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our rank-reduced (RR) coupled-cluster method to incorporate higher-order tensor factorizations. The THC factorization of the doubles amplitudes accounts for most of the gain in computational efficiency as it is sufficient, in conjunction with a Cholesky decomposition of the ERIs, to reduce the computational complexity of most contributions to the CCSD amplitude equations. Further THC factorization of the ERIs reduces the complexity of certain terms arising from nested commutators between the doubles excitation operator and the two-electron operator. We implement this new algorithm using graphical processing units and demonstrate that it enables CCSD calculations for molecules with 250 atoms and 2500 basis functions using a single computer node. Furthermore, we show that the new method computes correlation energies with comparable accuracy to the underlying RR-CCSD method.

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

Geometric phase in coupled cluster theory

It has been well-established that the topography around conical intersections between excited electronic states is incorrectly described by coupled cluster and many other single reference theories (the intersections are “defective”). Despite this, we show both analytically and numerically that the geometric phase effect (GPE) is correctly reproduced upon traversing a path around a defective excited-state conical intersection (CI) in coupled cluster theory. The theoretical analysis is carried out by using a non-Hermitian generalization of the linear vibronic coupling approach. Interestingly, the approach qualitatively explains the characteristic (incorrect) shape of the defective CIs and CI seams. Moreover, the validity of the approach and the presence of the GPE indicate that defective CIs are local (and not global) artifacts. This implies that a sufficiently accurate coupled cluster method could predict nuclear dynamics, including geometric phase effects, as long as the nuclear wavepacket never gets too close to the conical intersections.

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

Theoretical prediction of magnetic exchange coupling constants from broken-symmetry coupled cluster calculations

Exchange coupling constants ( J ) are fundamental to the understanding of spin spectra of magnetic systems. In this study, we investigate the broken-symmetry (BS) approaches of Noodleman and Yamaguchi in conjunction with coupled cluster (CC) methods to obtain exchange couplings. J values calculated from CC in this fashion converge smoothly toward the full configuration interaction result with increasing level of CC excitation. We compare this BS-CC scheme to the complementary equation-of-motion CC approach on a selection of bridged molecular cases and give results from a few other methodologies for context.

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

Ab initio study and assignment of electronic states in molecular RaCl

Radium compounds have attracted recently considerable attention due to both development of experimental techniques for high-precision laser spectroscopy of molecules with short-lived nuclei and amenability of certain radium compounds for direct cooling with lasers. Currently, radium monofluoride (RaF) is one of the most studied molecules among the radium compounds, both theoretically and recently also experimentally. Complementary studies of further diatomic radium derivatives are highly desired to assess the influence of chemical substitution on diverse molecular parameters, especially on those connected with laser cooling, such as vibronic transition probabilities, and those related to violations of fundamental symmetries. Here in this article high-precision ab initio studies of electronic and vibronic levels of diatomic radium monochloride (RaCl) are presented. Recently developed approaches for treating electronic correlation with Fock-space coupled cluster methods are applied for this purpose. Theoretical results are compared to an early experimental investigation by Lagerqvist and used to partially reassign the experimentally observed transitions and molecular electronic levels of RaCl. Effective constants of $\mathscr{P}$-odd hyperfine interaction W a and $\mathscr{P, T}$-odd scalar-pseudoscalar nucleus-electron interaction Ws in the ground electronic state of RaCl are estimated within the framework of a quasirelativistic Zeroth-Order Regular Approximation approach and compared to parameters in RaF and RaOH.

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

Atomic isotropic hyperfine properties for second row elements (Al–Cl)

Isotropic hyperfine properties have been obtained for the second row elements Al–Cl using a systematic composite approach consisting of a sequence of core/valence correlation consistent basis sets, up through aug-cc-pCV7Z, along with configuration interaction and coupled cluster methods. The best nonrelativistic final values for the atomic ground states (in MHz) are -1.80 27 Al ( 2 P o 1/2 ), -24.31 29 Si ( 3 P 0 ), 63.70 31 P ( 4 So 3/2 ), 20.77 33 S ( 3 P 2 ), and 35.42 35 Cl ( 2 P o 3/2 ). We find a large K shell contribution to the spin density at the nucleus that is almost canceled by the L and M shell contributions. The spin density in atomic units is approximately linear with respect to the atomic number.

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

An Attractive Way to Correct for Missing Singles Excitations in Unitary Coupled Cluster Doubles Theory

Coupled cluster methods based exclusively on double excitations are comparatively “cheap” and interesting model chemistries, as they are typically able to capture the bulk of the dynamic electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron-pair-restricted T 2 operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent to which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Here, our analysis includes the derivations of finite-order UCC energy functionals, which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing single excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron-pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.

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

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Finally, best practices for the maintenance and distribution of GAMESS are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Local Pair Natural Orbital-Based Coupled-Cluster Theory through Full Quadruples (DLPNO–CCSDTQ)

In this work, we implement a local pair natural orbitalbased coupled-cluster method through the full treatment of quadruple excitations (CCSDTQ). The domain-based local pair natural orbital (DLPNO) approach, which has successfully been applied to lower levels of coupled-cluster theory, is utilized in our algorithm, and thus our algorithm is called DLPNO-CCSDTQ. For simplicity in the working equations and in the implementation, we t 1 -dress the twoelectron integrals as well as Fock matrix elements. Our method can recover CCSDTQ-CCSDT and CCSDTQ-CCSDT(Q) energy differences on the order of 0.01−0.05 kcal mol −1 , even at a loose quadruples natural orbital (QNO) occupation number cutoff of 3.33 × 10 −6 . To highlight the capabilities of our code and its potential future applications, we showcase computations that would be intractable with canonical CCSDTQ, such as the benzene dimer, (H 2 O) 17 , and adamantane. With sufficient computing resources, computations up to 15 heavy atoms (40 atoms overall) may be feasible for fully bonded 3D systems.

Cluster chemistry↗
DOE OSTI2022

Diffusion Monte Carlo evaluation of disiloxane linearisation barrier

The disiloxane molecule is a prime example of silicate compounds containing the Si-O-Si bridge. The molecule is of significant interest within the field of quantum chemistry, owing to the difficulty in theoretically predicting its properties. Herein, the linearisation barrier of disiloxane is investigated using a fixed-node diffusion Monte Carlo (FNDMC) approach, which is one of the most reliable ab initio methods in accounting for the electronic correlation. Calculations utilizing the density functional theory (DFT) and the coupled cluster method with single and double substitutions, including noniterative triples (CCSD(T)) are carried out alongside FNDMC for comparison. It is concluded that FNDMC successfully predicts the disiloxane linearisation barrier and does not depend on the completeness of the basis-set as much as DFT or CCSD(T), thus establishing its suitability.

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

Three-dimensional potential energy surfaces of ArNO ($\tilde{X}$ 2 Π)

Until now, the potential energy surfaces (PESs) of the ArNO complex found in the literature were two-dimensional, with the NO interatomic distance being fixed. In this work, we present the first accurate three-dimensional ground state X 2 Π PESs (both A ' and A ") of ArNO computed at the CCSD(T)/CBS level of theory. The equilibrium geometries and the well depths ( D e ) are compared to several other electronic structure methods. We found that using the multireference method, MRCI-F12 makes the surfaces much shallower (by 25%) and the depth of the surfaces does not agree with experimental data. The explicitly correlated coupled-cluster method underestimates the well depth as well. Analytic representations for both A ' and A " surfaces were fit to 4380 ab initio points to within 2.71 cm -1 .A three-dimensional Numerov propagator method in Delves coordinates is used to compute the bound state spectrum up to J tot = 6.5. The recommended dissociation energies are D 0 = 97.2 cm -1 for the adiabatic ground state and D e = 133.7 (128.1) cm -1 for A ' ( A ")

36 MATERIALS SCIENCE↗
DOE OSTI2019

Global Sensitivity Analysis of Bulk Properties of an Atomic Nucleus

We perform a global sensitivity analysis of the binding energy and the charge radius of the nucleus 16 O to identify the most influential low-energy constants in the next-to-next-to-leading order chiral Hamiltonian with two- and three-nucleon forces. For this purpose, we develop a subspace-projected coupled-cluster method using eigenvector continuation [Frame D. et al., Phys. Rev. Lett. 121, 032501 (2018)]. With this method, we compute the binding energy and charge radius of 16 O at more than 106 different values of the 16 low-energy constants in one hour on a standard laptop computer. For relatively small subspace projections, the root-mean-square error is about 1% compared to full-space coupled-cluster results. We find that 58(1)% of the variance in energy can be apportioned to a single contact term in the 3 S 1 wave, whereas the radius depends sensitively on several low-energy constants and their higher-order correlations. The results identify the most important parameters for describing nuclear saturation and help prioritize efforts for uncertainty reduction of theoretical predictions. The achieved acceleration opens up an array of computational statistics analyses of the underlying description of the strong nuclear interaction in nuclei across the Segrè chart.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗