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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Taming the virtual space for incremental full configuration interaction

Incremental full configuration interaction (iFCI) closely approximates the FCI limit with polynomial cost through a many-body expansion of the correlation energy, providing highly accurate total energies within a given basis set. To extend iFCI beyond previous basis set limitations, this work introduces a novel natural orbital (NO) screening approach, incremental NO full configuration interaction (iNO-FCI). By consideration of the importance of virtual orbital selection in the convergence of iFCI, iNO-FCI maximizes the consistency between orbitals selected for each correlated body. iNO-FCI employs a principle of cancellation of errors and ensures that the same set of virtual NOs is used for interdependent terms. Here, this strategy significantly reduces computational cost without compromising precision. Computational savings of up to 95% are demonstrated, allowing access to larger basis sets that were previously computationally prohibitive. iNO-FCI is herein introduced and benchmarked for several difficult test cases involving double-bond dissociation, biradical systems, conjugated π systems, and the spin gap of a Cu-based transition metal complex.

Correlation energy↗
DOE OSTI2025

Many-Body Basis Set Amelioration Method for Incremental Full Configuration Interaction

Incremental full configuration interaction (iFCI) is a polynomial-cost electronic structure method that systematically approaches the FCI limit by employing the method of increments to solve the Schrödinger equation through a many-body expansion. This article introduces the many-body basis set amelioration (MBBSA) method, which is designed to allow iFCI to be applicable to larger atomic orbital basis sets. MBBSA uses a series of inexpensive iFCI calculations to approximate the correlation energy that would be found using a more expensive, highly accurate iFCI calculation. Here, when compared to standard iFCI computations on smaller molecules in triple-zeta and larger basis sets, MBBSA provides approximations to the total and relative energies within chemical accuracy. MBBSA exhibits a reduced cost of between 60-92% when compared to standard iFCI calculations, with larger systems experiencing the largest benefit. Tests of MBBSA on two reactions that involve highly correlated systems, the automerization of cyclobutadiene and a Criegee intermediate reaction, show that MBBSA has practical utility for studying realistic chemistries.

Basis sets↗
DOE OSTI2023

Exchange correlation potentials from full configuration interaction in a Slater orbital basis

Ryabinkin–Kohut–Staroverov (RKS) theory builds a bridge between wave function theory and density functional theory by using quantities from the former to produce accurate exchange-correlation potentials needed by the latter. In this work, the RKS method is developed and tested alongside Slater atomic orbital basis functions for the first time. To evaluate this approach, full configuration interaction computations in the Slater orbital basis are employed to give quality input to RKS, allowing full correlation to be present along with correct nuclei cusps and asymptotic decay of the wavefunction. SlaterRKS is shown to be an efficient algorithm to arrive at exchange-correlation potentials without unphysical artifacts in moderately-sized basis sets. Furthermore, enforcement of the nuclear cusp conditions will be shown to be vital for the success of the Slater-basis RKS method. As a result, examples of weakly and strongly correlated molecular systems will demonstrate the main features of SlaterRKS.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Hybrid gausslet/Gaussian basis sets

We introduce hybrid gausslet/Gaussian basis sets, where a standard Gaussian basis is added to a gausslet basis in order to increase accuracy near the nuclei while keeping the spacing of the grid of gausslets relatively large. The Gaussians are orthogonalized to the gausslets, which are already orthonormal, and approximations are introduced to maintain the diagonal property of the two electron part of the Hamiltonian so that it continues to scale as the second power of the number of basis functions rather than the fourth. We introduce several corrections to the Hamiltonian designed to enforce certain exact properties, such as the values of certain two-electron integrals. We also introduce a simple universal energy correction that compensates for the incompleteness of the basis stemming from the electron–electron cusps based on the measured double occupancy of each basis function. We perform a number of Hartree Fock and full configuration interaction (full-CI) test calculations on two electron systems and Hartree Fock on a ten-atom hydrogen chain to benchmark these techniques. The inclusion of the cusp correction allows us to obtain complete basis set full-CI results for the two electron cases at the level of several micro-Hartrees, and we see similar apparent accuracy for Hartree Fock on the ten-atom hydrogen chain.

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

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH) 4 H]- model employing state-of-the-art ab initio methods

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (ΔE) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ΔE estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree–Fock included (0%–54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ΔE is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn–Sham orbitals gives results within 4–11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ~5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

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

The many-body electronic interactions of Fe(II)–porphyrin

Fe(II)–porphyrin complexes exhibit a diverse range of electronic interactions between the metal and macrocycle. Herein, the incremental full configuration interaction method is applied to the entire space of valence orbitals of a Fe(II)–porphyrin model using a modest basis set. A novel visualization framework is proposed to analyze individual many-body contributions to the correlation energy, providing detailed maps of this complex’s highly correlated electronic structure. Furthermore, this technique is used to parse the numerous interactions of two low-lying triplet states ( 3 A 2 g and 3 E g ) and to show that strong metal d–d and macrocycle π–π orbital interactions preferentially stabilize the 3 A 2 g state. d–π interactions, on the other hand, preferentially stabilize the 3 E g state and primarily appear when correlating six electrons at a time. Ultimately, the Fe(II)–porphyrin model’s full set of 88 valence electrons are correlated in 275 orbitals, showing the interactions up to the 4-body level, which covers the great majority of correlations in this system.

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

Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. As a result, the normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Thermal mean-field theories

Several closely related ab initio thermal mean-field theories for fermions, both well-established and new ones, are compared with one another at the formalism level and numerically. The theories considered are Fermi–Dirac theory; thermal Hartree–Fock (HF) theory; two modifications of the thermal single-determinant and the first-order finite-temperature many-body perturbation theory based on a zero-temperature or thermal HF reference. Furthermore, thermal full-configuration-interaction theory is used as the benchmark.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data

In this work, we present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.

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

Ground state property calculations of LiH n complexes using IBM Qiskit’s quantum simulator

In this study, the variational quantum eigensolver (VQE) on a quantum simulator is used in calculating ground state electronic structure properties of the LiH n , n = 1–3, complexes including their singly charged ions. Results calculated using classical electronic structure algorithms are also included. We investigate the use of the unitary coupled cluster with singles and doubles (UCCSD) Ansatz using VQE within Qiskit and compare results to full configuration interaction (FCI) calculations. Computed ground state energies, electron affinities, ionization potentials, and dipole moments are considered. We report the first-of-its-kind simulated quantum computing results of selected LiH n species and use the parity orbital to qubit mapping scheme. We find that VQE/UCCSD results are comparable to classical coupled clusters with singles and doubles for all considered systems with respect to FCI. A VQE calculation cost evaluation is included in which we evaluate performance using both Jordan–Wigner and parity orbital to qubit mapping schemes. We also discuss some of the current limitations of utilizing VQE for the study of chemical systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Electronic structure theory with molecular point group symmetries on quantum annealers

Quantum computation has the potential to revolutionize quantum chemistry through major speedups in computation times and an exponential reduction in computational resources. Here, we combine the symmetry-adapted Jordan–Wigner encoding based on the full Boolean symmetry group $\mathbb{Z}$$^{k}_{2}$ with our new implementation of the Xia–Bian–Kais (XBK) method for improving the efficiency of electronic structure theory calculations on quantum annealers, particularly by reducing the number of qubits needed to achieve the same accuracy. By providing a more extensive symmetry-adapted encoding (SAE) than previous work, we are able to simulate molecules larger than those previously reported that have been studied using methods developed for quantum annealers and without using an active space. We calculated the potential energy surfaces of H 2 , LiH, He 2 , H 2 O, O 2 , N 2 , Li 2 , F 2 , CO, BH 3 , NH 3 , and CH 4 , with the largest molecule in the STO-6G basis set requiring 16 qubits with our SAE, and compared them with full configuration interaction results. The application of SAE to the XBK method provides an exponential reduction in the size of the Hilbert space and scales well with the size of the problem. It does not introduce significant additional errors for even or large values of a key variational parameter that determines the number of ancilla qubits used in the XBK method’s Hamiltonian embedding, or for certain molecules such as He 2 and H 2 O. Here, we provide an explanation for this behavior and a recommendation on the usage of our method. In addition, we briefly discuss the potential of extracting electronic excited states from our method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

An Ab Initio Electronic Structure Investigation of the Ground and Excited States of ScH + , YH + , and LaH +

Multireference configuration interaction (MRCI), Davidson-corrected MRCI (MRCI+Q), coupled-cluster singles, doubles, and perturbative triples [CCSD(T)], and frozen-core full configuration interaction (fcFCI) calculations were carried out using large, correlation-consistent basis sets to investigate the excited states of the Sc atom and the spin–free and spin–orbit coupled potential energy profiles, energetics, spectroscopic constants, and electron populations of low-lying states of MH + (M = Sc, Y, La). The core electron correlation effects, complete basis set effects, and spin–orbit coupling effects were also evaluated. The first four electronic states of all MH + are 1 2 Δ, 1 2 Σ + , 1 2 Π, and 2 2 Σ + with 1σ 2 1δ 1 , 1σ 2 2σ 1 , 1σ 2 1π 1 , and 1σ 2 3σ 1 single-reference electron configurations, respectively. These states of MH + can be represented by the M 2+ H – ionic structure. The ground states of ScH + , YH + , and LaH + are 1 2 Δ 3/2 , 1 2 Σ + 1/2 , and 1 2 Δ 3/2 with 55.45, 60.54, and 62.34 kcal/mol bond energies, respectively. The core electron correlation was found to be vital for gaining accurate predictions on the ground and excited state properties of MH + . The spin–orbit coupling effects are minor for ScH + but become substantial moving to YH + and LaH + . Overall, the results of this work are in good agreement with the limited set of experimental findings of MH + available in the literature and will be of use for future investigations. Furthermore, the theoretical approaches, findings, and trends reported here are expected to aid studies of similar species.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Removing Basis Set Incompleteness Error in Finite-Temperature Electronic Structure Calculations: Two-Electron Systems

We investigate the basis-set-size dependence for quantities related to interacting electrons in the canonical ensemble. Calculations are performed using exact diagonalization (finite temperature full configuration interaction method) on two-electron model systems–the uniform electron gas (UEG) and the helium atom. Our data reproduce previous observations of a competition for how the internal energy converges between the ground-state correlation energy and the high-temperature kinetic energy. We explore how this can be related to component parts of the internal energy including kinetic, exchange, and correlation energies and show there is surprising nuance in how this can be broken down into mostly monotonically converging quantities. We also show that separation of the free energy into a free energy with/without correlation allows for monotonic convergence with basis set size due to the variational principle. We find that the free energy convergence matches the previously observed convergence properties of the internal energy. We discuss the free energy divergence that happens when converging a finite basis analytical hydrogen atom to the complete basis set limit and compare this to the energies of a helium atom in a large periodic box. Reducing the box size, we saw convergence trends for the helium atom that were similar to the UEG.

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

Solving the nuclear pairing model with neural network quantum states

In this work, we present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the groundstate wave function. A memory-efficient version of the stochastic reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian. We benchmark this approach against widely used nuclear many-body methods by solving a model used to describe pairing in nuclei for different types of interaction and different values of the interaction strength. Despite its polynomial computational cost, our method outperforms coupled-cluster and provides energies that are in excellent agreement with the numerically-exact full configuration interaction values.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Vibrational levels of a generalized Morse potential

A Generalized Morse Potential (GMP) is an extension of the Morse Potential (MP) with an additional exponential term and an additional parameter that compensate for MP’s erroneous behavior in the long range part of the interaction potential. Because of the additional term and parameter, the vibrational levels of the GMP cannot be solved analytically, unlike the case for the MP. We present several numerical approaches for solving the vibrational problem of the GMP based on Galerkin methods, namely, the Laguerre Polynomial Method (LPM), the Symmetrized LPM, and the Polynomial Expansion Method (PEM), and apply them to the vibrational levels of the homonuclear diatomic molecules B 2 , O 2 , and F 2 , for which high level theoretical near full configuration interaction (CI) electronic ground state potential energy surfaces and experimentally measured vibrational levels have been reported. Overall, the LPM produces vibrational states for the GMP that are converged to within spectroscopic accuracy of 0.01 cm –1 in between 1 and 2 orders of magnitude faster and with much fewer basis functions/grid points than the Colbert–Miller Discrete Variable Representation (CN-DVR) method for the three homonuclear diatomic molecules examined in this study.

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

Dissipative ground state preparation in ab initio electronic structure theory

Dissipative engineering is a powerful tool for quantum state preparation, and has drawn significant attention in quantum algorithms and quantum many-body physics in recent years. In this work, we introduce a novel approach using the Lindblad dynamics to efficiently prepare the ground state for general ab initio electronic structure problems on quantum computers, without variational parameters. These problems often involve Hamiltonians that lack geometric locality or sparsity structures, which we address by proposing two generic types of jump operators for the Lindblad dynamics. Type-I jump operators break the particle number symmetry and should be simulated in the Fock space. Type-II jump operators preserves the particle number symmetry and can be simulated more efficiently in the full configuration interaction space. For both types of jump operators, we prove that in a simplified Hartree-Fock framework, the spectral gap of our Lindbladian is lower bounded by a universal constant. For physical observables such as energy and reduced density matrices, the convergence rate of our Lindblad dynamics with Type-I jump operators remains universal, while the convergence rate with Type-II jump operators only depends on coarse grained information such as the number of orbitals and the number of electrons. To validate our approach, we employ a Monte Carlo trajectory-based algorithm for simulating the Lindblad dynamics for full ab initio Hamiltonians, demonstrating its effectiveness on molecular systems amenable to exact wavefunction treatment.

Quantum chemistry↗
DOE OSTI2026

Definitive Assessment of the Accuracy, Variationality, and Convergence of Relativistic Coupled Cluster and Density Matrix Renormalization Group in 100-Orbital Space

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this paper, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

Chemical calculations↗