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All sources NASA NTRS DOE 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↗

NASA NTRS1988

Full configuration interaction benchmark calculations for TiH

Full configuration interaction (FCI) results for the 3F and 5F states of Ti and the 4Phi and 2Delta states of TiH are presented. While the coupled pair functional (CPF) or modified CPF approaches are found to work well for the 4Phi state of TiH, they do not perform as well for the 2Delta state. Although for mu, the CASSCF/MRCI methods do well for the 2Delta state, when the active space is expanded outside the normal valence definition, the dipole moment is only brought into agreement with the FCI results by natural orbital iterations.

Bauschlicher, Charles W., Jr.↗

NASA NTRS1986

Benchmark full configuration-interaction calculations on H2O, F, and

Full configuration-interaction calculations are reported, and compared to other methods, for H2O at its equilibrium geometry and at two geometries with the H-O bonds stretched. Since the percentage of the self-consistent field (SCF) reference in the full configuration-interaction (FCI) wave function decreases greatly with the bond elongation, the accuracy of techniques based on a single reference do not compare well with the FCI results. However, the results from a complete active space SCF/multireference configuration-interaction (CASSCF/MRCI) treatment are in good agreement with the FCI. Correlation effects in F compared to Ne are far more similar than for Fcompared to Ne, despite F- and Ne being isoelectronic. Since the importance of higher than double excitations is more important for F- than F, a very high percentage of the correlation must be obtained to accurately compute the electron affinity. In a CASSCF/MRCI treatment the higher than quadruple excitations contribute 0.02 eV to the electron affinity (EA), even for modest basis sets.

Bauschlicher, C. W., Jr.↗

NASA NTRS1986

Benchmark full configuration-interaction calculations on H2O, F- and F

Full configuration-interaction calculations are reported, and compared to other methods, for H2O at its equilibrium geometry and at two geometries with the H-O bonds stretched. Since the percentage of the self-consistent field (SCF) reference in the full configuration-interaction (FCI) wave function decreases greatly with the bond elongation, the accuracy of techniques based on a single reference do not compare well with the FCI results. However, the results from a complete active space SCF/multireference configuration-interaction (CASSCF/MRCI) treatment are in good agreement with the FCI. Correlation effects in F compared to Ne are far more similar than for F- compared to Ne, despite F- and Ne being isoelectronic. Since the importance of higher than double excitations is more important for F- than F, a very high percentage of the correlation must be obtained to accurately compute the electron affinity. In a CASSCF/MRCI treatment the higher than quadruple excitations contribute 0.02 eV to the electron affinity (EA), even for modest basis sets.

Bauschlicher, C. W., Jr.↗

NASA NTRS1986

Benchmark full configuration-interaction calculations on HF and NH2

Full configuration-interaction (FCI) calculations are performed at selected geometries for the 1-sigma(+) state of HF and the 2-B(1) and 2-A(1) states of NH2 using both DZ and DZP gaussian basis sets. Higher excitations become more important when the bonds are stretched and the self-consistent field (SCF) reference becomes a poorer zeroth-order description of the wave function. The complete active space SCF - multireference configuration-interaction (CASSCF-MRCI) procedure gives excellent agreement with the FCI potentials, especially when corrected with a multi-reference analog of the Davidson correction.

Bauschlicher, C. W., Jr.↗

NASA NTRS1986

Benchmark full configuration-interaction calculations on HF and NH2

Bauschlicher, C. W., Jr.↗

NASA NTRS1986

Benchmark Full Configuration-Interaction Calculations on HF and NH2

Full configuration-interaction (FCI) calculations are performed at selected geometries for the (sup 1)Sigma(+) state of HCF and the (sup 2)B(sub 1) and (sup 3)A(sub 1) states NH2 using both DZ and DZP Gaussian basis sets. Higher excitations become more important when the bonds are stretched and the SCF reference becomes a poorer zeroth-order description of the wave function. The CASSCF-MRCI procedure gives excellent agreement with the FCI potentials, especially when corrected with a multireference analog of the Davidson correction.

Bauschlicher, Charles W., Jr.↗

NASA NTRS1988

Full configuration-interaction study of the ionic-neutral curve crossing in LiF

Full configuration-interaction (FCI) calculations are used to assess the relative ability of methods for truncating the n-particle expansion in describing the ionic-neutral curve crossing between the two lowest Sigma(+) states of LiF. While the FCI calculations yield a smooth dipole moment function, MRCI calculations based on CASSCF orbitals optimized for the lowest state at all r values yield a discontinuous dipole moment function. However, when the orbitals are optimized using a state-averaged CASSCF procedure, with equal weights for the ionic and neutral solutions, both the CASSCF and MRCI dipole moment functions are smooth and in reasonable agreement with the FCI. No single-reference-based method is found to work satisfactorily. Potential curves for the lowest two Sigma(+) states are determined in both the adiabatic and diabatic representations using a large atomic natural orbit Gaussian basis set and a state-averaged CASSCF/MRCI treatment of electron correlation.

Bauschlicher, Charles W., Jr.↗

NASA NTRS1988

Full configuration-interaction benchmark calculations for AlH

Full CI and CASSCF/SOCI theoretical computations are presented for the X 1Sigma(+), A 1Pi, and C 1Sigma(+) states of AlH. The aim is to establish benchmark data to calibrate methods which describe valence-Rydberg transitions in other molecules. The results are presented in extensive tables and graphs and compared with published theoretical and experimental values, and the conditions under which CASSCF/SOCI calculations accurately reproduce the FCI results are defined.

Bauschlicher, Charles W., Jr.↗

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 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 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↗

DOE OSTI2026

Analysis of Fourth-, Fifth-, and Infinite-Order Triple Excitations in Unitary Coupled Cluster Theory

Here, in this work, we introduce a perturbative correction to the unitary coupled cluster method with single and double excitations (UCCSD) that incorporates the effects of missing triple excitations through fifth-order in many-body perturbation theory (MBPT). Referred to as UCCSD[T-5], this method is benchmarked alongside the previously developed UCCSD[T] to lend insight into the behavior of perturbative triples corrections relative to UCCSDT, which inherently provides an infinite-order treatment of triple excitations, as well as full configuration interaction (FCI). Two key findings emerge from this analysis. First, UCCSD[T] consistently yields ground-state energies in closest agreement with FCI, outperforming both UCCSD[T-5] and UCCSDT. Second, UCCSD[T-5] largely emulates the behavior of UCCSDT, suggesting a close relationship between fifth- and infinite-order triple-excitation contributions. Given the growing interest in UCC ansätze for quantum computing and the limitations of current quantum hardware, these results highlight the potential of classically computed perturbative corrections within UCC theory to capture triple-excitation effects without the additional quantum resources required by the UCCSDT ansatz.

Windom, Zachary W. [Oak Ridge National Laboratory ↗

DOE OSTI2025

Exploiting a Shortcoming of Coupled-Cluster Theory: The Extent of Non-Hermiticity as a Diagnostic Indicator of Computational Accuracy

The fundamental non-Hermitian nature of the forms of the coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present paper shows how this can be used to an advantage. Specifically, the non-symmetric nature of the reduced one-particle density matrix (in the molecular orbital basis) is advocated as a diagnostic indicator of computational quality. In the limit of the full coupled-cluster theory [which is equivalent to full configuration interaction (FCI)], the electronic wave function and correlation energy are exact within a given one-particle basis set, and the symmetric character of the exact density matrix is recovered. The extent of the density matrix asymmetry is shown to provide a measure of “how difficult the problem is” (like the well-known T 1 diagnostic), but its variation with the level of theory also gives information about “how well this particular method works”, irrespective of the difficulty of the problem at hand. The proposed diagnostic is described and applied to a select group of small molecules, and an example of its overall utility for the practicing quantum chemist is illustrated through its application to the beryllium dimer (Be 2 ). Future application of this idea to excited states, open-shell systems, and symmetry-breaking problems and an extension of the method to the two-particle density are then proposed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗