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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Toward more accurate adiabatic connection approach for multireference wavefunctions

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space self-consistent field and density matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approximations: (i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and (ii) extended random phase approximation (ERPA). This work investigates the effect of removing the “fixed-RDM” approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact reference AC integrands are generated from the DMRG full configuration interaction solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving the accuracy of existing AC approximations.

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

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Equation-of-motion internally contracted multireference unitary coupled-cluster theory

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we introduce a novel equation-of-motion (EOM) extension of the internally contracted multireference unitary coupled-cluster framework (ic-MRUCC), termed EOM-ic-MRUCC. EOM-ic-MRUCC follows the transform-then-diagonalize approach, in analogy to its non-unitary counterpart. By employing a projective approach to optimize the ground state, the method retains additive separability and proper scaling with system size. We show that excitation energies are size-intensive if the EOM operator satisfies the “killer” and the projective conditions. Furthermore, we propose to represent changes in the reference state upon electron excitation via projected many-body operators that span the active orbitals and show that the EOM equations formulated in this way are invariant with respect to active orbital rotations. We test the EOM-ic-MRUCC method truncated to single and double excitations by computing the potential energy curves for several excited states of a BeH2 model system, the HF molecule, and water undergoing symmetric dissociation. Across these systems, our method delivers accurate excitation energies and potential energy curves within 5 mE h (∼0.14 eV) from full configuration interaction. Here, we find that truncating the Baker–Campbell–Hausdorff series to fourfold commutators contributes negligible errors (on the order of 10 −5 E h or less), offering a practical route to highly accurate excited-state calculations with reduced computational overhead.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Degenerate coupled-cluster theory

A size-extensive, converging, black-box, ab initio coupled-cluster (ΔCC) ansatz is introduced that computes the energies and wave functions of states from any degenerate or nondegenerate Slater-determinant references with any numbers of α- and β-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Møller–Plesset perturbation (ΔMP) theory. For ionized and electron-attached references, it is a coupled-cluster Green’s function, although the present theory is convergent toward the full-configuration-interaction limits, while the Feynman–Dyson many-body Green’s function (MBGF) theory generally is not. Its single-excitation instance is a projection Hartree–Fock theory as per the Thouless theorem, which may be useful for core ionizations, high-spin states, and possibly electron affinities. Additionally, a new multireference coupled-cluster theory for a general model space is developed. This quasidegenerate coupled-cluster (QCC) theory is exactly converging, but not black-box, and intended for strong correlation. Determinant-based, general-order algorithms of ΔCC and QCC theories are implemented and compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with ΔMP and MBGF theories up to the nineteenth order. An algebraic, optimal-scaling algorithm of the ΔCC theory is computer-synthesized at the levels of single excitations (ΔCCS) and of single and double excitations (ΔCCSD). As a result, the order of performance is QCC ≈ ΔCC > EOM-CC > CI at the same order or QCC ≈ ΔCC > ΔMP > MBGF at the same cost scaling.

Hirata, So [University of Illinois at Urbana-Champ↗
DOE OSTI2026

NuLattice: Ab initio computations of atomic nuclei on lattices

Here, we introduce NuLattice, a Python software package for ab initio computations of atomic nuclei on lattices. The computational tools consist of Hartree Fock, the coupled cluster method, the in-medium similarity renormalization group, and full configuration interaction. At present, the employed interactions are from pion-less effective field theory at leading order and consist of two-body and three-body contacts. We present results for light nuclei 2 H, 3,4 He, 8 Be, 12 C, and 16 O. NuLattice algorithms exploit the sparsity and locality of lattice interactions, and as a result computations can be run on laptops.

Rothman, Maxwell [Univ. of Tennessee, Knoxville, T↗
DOE OSTI2023

A Systematic, Polynomial-Cost Approach to Exact Correlation Energies (Final Technical Report)

The full configuration interaction (FCI) wave function provides the exact solution to the Schrödinger equation in a given basis set. While FCI is intractable due to exponential computational costs, the many-body expansion (or the method of increments) can reduce scaling to a low-order polynomial with system size. This project entailed advances in the incremental FCI (iFCI) approach, designed to allow iFCI to reach larger system sizes and maintain its intrinsic high accuracy. This document describes advances in solvers for iFCI, strategies to treat multiple charge and spin states, and virtual state management methods to reduce memory requirements. Overall, this project allows iFCI to correlate (for the first time) 142 valence electrons in 444 orbitals in a realistic model of a transition metal complex.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Quantum Computing for Energy-Related Applications

Growing interest in quantum computing and simulations have created opportunities for its deployment to improve processes pertaining to energy production, distribution, and consumption. While quantum computing is considered as a paradigm shift in our basic understanding of physical computation, effective implementation of quantum computing in energy applications also depends on progress and development in the dimensions of both quantum computing hardware and quantum computing algorithms. To fully address the status and future challenges of quantum information science (QIS) applied within the energy sector, in this presentation, we firstly summarize recent advancements on the applications of quantum computing to energy infrastructure and materials, complex energy system processes, advanced manufacturing, and energy system security. Then, we will demonstrate the results of quantum computing both on a simulator and a quantum device accessing from OLCF. Our first example is to use the variational quantum eigensolver (VQE) with a unitary coupled cluster with singles and doubles (UCCSD) ansatz to simulate a series of LixHyq molecules (q=-1, 0, +1). The obtained results showed that the quantum computing VQE-UCCSD is comparable to classical CCSD for small systems like LiH with respect to full configuration interaction (FCI). Targeting on CO2 capture application, our second example is to use VQE to quantify molecular vibrational energies and reaction pathways between CO2 and a simplified amine-based solvent model—NH3 to form H2NCOOH. This research showcases quantum computing applications in the study of CO2 capture reactions.

Duan, Yuhua↗
NASA NTRS1987

Full CI benchmark calculations on N2, NO, and O2 - A comparison of methods for describing multiple bonds

Full configuration interaction (CI) calculations on the ground states of N2, NO, and O2 using a DZP Gaussian basis are compared with single-reference SDCI and coupled pair approaches (CPF), as well as with CASSCF multireference CI approaches. The CASSCF/MRCI technique is found to describe multiple bonds as well as single bonds. Although the coupled pair functional approach gave chemical accuracy (1 kcal/mol) for bonds involving hydrogen, larger errors occur in the CPF approach for the multiple bonded systems considered here. CI studies on the 1Sigma(g +) state of N2, including all single, double, triple, and quadruple excitations show that triple excitations are very important for the multiple bond case, and accounts for most of the deficiency in the coupled pair functional methods.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1987

An initio calculations on C2, Si2, and SiC

Full-configuration-interaction (FCI) calculations have been performed for the Z 1Sigma(g)(+), a 3Pi(u), and b 3Sigma(g)(-) states of C2 and the X 3Sigma(g)(-) and A 3Pi(u) states of Si2 in valence double-zeta plus polarization one-particle basis sets. By carrying out the CASSCF multireference singles plus doubles CI (MRCI) procedure in a very large Gaussian basis set and correcting for errors with the FCI, the triplet-triplet separation in C2 is reproduced to within 47/cm. Analogous calculations on Si2 definitively determine the ground state to be 3Sigma(g)(-); the 3Pi(u) state is only 440 + or - 100/cm higher in energy. For the SiC molecule, which has never been observed spectroscopically but is believed to be an important component in carbon stars and to be present in interstellar space, the A 3Sigma(-) state is nearly 4000/cm above the X 3Pi ground state.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1989

Accurate quantum chemical calculations

An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1994

Electronic spectroscopy of diatomic molecules

This article provides an overview of the principal computational approaches and their accuracy for the study of electronic spectroscopy of diatomic molecules. We include a number of examples from our work that illustrate the range of application. We show how full configuration interaction benchmark calculations were instrumental in improving the understanding of the computational requirements for obtaining accurate results for diatomic spectroscopy. With this understanding it is now possible to compute radiative lifetimes accurate to within 10% for systems involving first- and second-row atoms. We consider the determination of the infrared vibrational transition probabilities for the ground states of SiO and NO, based on a globally accurate dipole moment function. We show how we were able to assign the a(sup "5)II state of CO as the upper state in the recently observed emission bands of CO in an Ar matrix. We next discuss the assignment of the photoelectron detachment spectra of NO and the alkali oxide negative ions. We then present several examples illustrating the state-of-the-art in determining radiative lifetimes for valence-valence and valence-Rydberg transitions. We next compare the molecular spectroscopy of the valence isoelectronic B2, Al2, and AlB molecules. The final examples consider systems involving transition metal atoms, which illustrate the difficulty in describing states with different numbers of d electrons.

Partridge, Harry↗
DOE OSTI2022

Atomic structure considerations for the low-temperature opacity of Xenon

Here, we have begun a preliminary investigation into the opacity of Xe at low temperatures (<50 eV). The emissivity and opacity of Xe is a crucial factor in determining the utility of Xe in EUV lithography, with numerous industrial applications. To this end, we have been exploring the accuracy of some approximations used in opacity models for the relevant ion stages of Xe (6 times ionized through 20 times ionized). Due to the complexity of Xe atomic structure, one needs to use full configuration-interaction to properly describe the strong mixing in the various n=4 sub-shells that give rise to the Δn=0 and Δn=1 transitions that dominate the opacity spectrum at low temperatures. Since calculations that include full configuration-interaction for large numbers of configurations quickly become computationally prohibitive, we have explored hybrid calculations, in which full configuration-interaction is retained for the most important transitions, while intermediate coupling is employed for all other transitions. After verifying atomic structure properties, local-thermodynamic-equilibrium (LTE) opacities are generated using the ATOMIC code at selected temperatures and densities and compared to various experimental results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1991

Quantum mechanical calculations to chemical accuracy

The accuracy of current molecular-structure calculations is illustrated with examples of quantum mechanical solutions for chemical problems. Two approaches are considered: (1) the coupled-cluster singles and doubles (CCSD) with a perturbational estimate of the contribution of connected triple excitations, or CCDS(T); and (2) the multireference configuration-interaction (MRCI) approach to the correlation problem. The MRCI approach gains greater applicability by means of size-extensive modifications such as the averaged-coupled pair functional approach. The examples of solutions to chemical problems include those for C-H bond energies, the vibrational frequencies of O3, identifying the ground state of Al2 and Si2, and the Lewis-Rayleigh afterglow and the Hermann IR system of N2. Accurate molecular-wave functions can be derived from a combination of basis-set saturation studies and full configuration-interaction calculations.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1986

On the electron affinity of the oxygen atom

The electron affinity (EA) of oxygen is computed to be 1.287 eV, using 2p electron full configuration-interaction (CI) wave functions expanded in a 6s5p3d2f Slater-type orbital basis. The best complete active space self-consistent field - multireference CI (CASSCF-MRCI) result including only 2p correlation is 1.263 eV. However, inclusion of 2s intrashell and 2s2p intershell correlation increases the computed EA to 1.290 at the CASSCF-MRCI level. At the full CI basis set limit, the 2s contribution to the electron affinity is estimated to be as large as 0.1 eV. This study clearly establishes the synergistic effect between the higher excitations and basis set completeness on the electron affinity when the 2s electrons are correlated.

Bauschlicher, C. W., Jr.↗
DOE OSTI2022

Nucleon-pair truncation of the shell model for medium-heavy nuclei

Background: Establishing computationally tractable models of atomic nuclei is a long-time goal of nuclear structure physics. A flexible framework which easily includes excited states and many-body correlations is the configuration-interaction shell model (SM), but the exponential growth of the basis means one needs an efficient truncation scheme, ideally one that includes both deformation and pairing correlations. Purpose: Here, we propose an efficient truncation scheme of the SM: starting from a pair condensate variationally defined by Hartree-Fock single-particle states and the particle-number conserved Bardeen-Cooper-Schrieffer (NBCS) approximation, we carry out projection of states with good angular momentum. Methods: After generating Hartree-Fock single-particle states with Kramers degeneracy in a SM space, we optimize the pair amplitudes in the NBCS by minimizing the energy, and then use linear algebra projection (LAP) of states with good angular momentum. Both NBCS and LAP are computationally fast. Results: Our calculations yield good agreement with full configuration-interaction SM calculations for low-lying states of transitional and rotational nuclei with axially symmetric and triaxial deformation in medium- and heavy-mass regions: 44,46,48 Ti, 48,50 Cr, 52 Fe, 60,62,64 Zn, 66,68 Ge, 68 Se, and 108,110 Xe. We predict low-lying states of 112–114 Ba and 116–120 Ce, nuclei difficult to reach by large-scale SM calculations. Conclusions: Both pair correlation and the configuration mixing between different intrinsic states play a key role in reproducing collectivity and shape coexistence, demonstrating the utility of this truncation scheme of the SM to study transitional and deformed nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Piecewise interaction picture density matrix quantum Monte Carlo

The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact N-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC (IP-DMQMC) method that overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation, thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.

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

How effective is the Brink–Axel hypothesis for astrophysical weak rates?

We explore the effectiveness of the Brink–Axel hypothesis (BAH) for the computation of stellar electron capture (EC) and β-decay (BD) rates, namely that the transition strength function depends only upon the transition energy and not upon the details of the initial state. For this purpose, we calculated Gamow–Teller (GT) strength distributions for a selection of sd-shell nuclides, using two different microscopic models, namely the proton–neutron quasiparticle random phase approximation and the full configuration-interaction shell model, taking into account the first 100 states of both the initial and final nuclides. The GT transition strengths among these levels evolve with initial state energy. These transition strength functions we folded into weak-interaction mediated rates in stellar matter, specifically EC and BD rates, for a range of densities 10 g cm –3 ≤ ρ ≤ 10 11 g cm –3 and range of temperatures 1 GK ≤ T ≤ 30 GK. When transitions from excited states were approximated using the BAH, augmented by so-called 'back-resonance' transitions, the rates were affected by up to three orders of magnitude or more at high temperatures and densities. Furthermore the BAH is not a reliable approximation for the calculation of stellar rates, especially in high temperature–density environments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Nucleon-pair approximation for nuclei from spherical to deformed regions

Here we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provide a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (denoted by S D G pairs) reproduce the nuclear shape evolution in the N = 26 isotones, Ca 46 , Ti 48 , Cr 50 , and Fe 52 , and yield good agreement with full configuration-interaction calculations of low-lying states in medium-heavy transitional and deformed nuclei: Ti 44 – 48 , Cr 48 , Cr 50 , Fe 52 , Zn 60 – 64 , Ge 64 , 66 , Mo 84 , and Xe 108 – 112 . Finally, using the S D G I -pair approximation we describe low-lying states of Ba 112 , 114 , cases difficult to reach by conventional configuration-interaction methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗