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A. Eugene DePrince III

Publications and source records attributed to A. Eugene DePrince III.

At least 19 recordsLinked to original sources
arXiv2026

A constructive solution to the $n$-representability problem

We present a solution to the fermionic quantum marginal problem by constructing the complete family of two-body witnesses at each level of a weighted sum-of-squares hierarchy. Our construction combines positive-semidefinite Gram matrices with explicit linear nullspace constraints that exactly cancel all higher-body contributions, replacing the search for individual representability conditions with a systematic algebraic procedure. Beyond the completeness proof, we demonstrate the construction numerically by solving the associated semidefinite program and recovering the exact ground-state energy of a Richardson Hamiltonian in the three-fermion sector. We further prove that higher-degree particle-number multipliers are unnecessary when the full sum-of-squares generating algebra is used. These results establish a unified constructive framework for verifying the physicality of a candidate two-particle reduced density matrix through a complete characterization of all two-body witnesses.

quant-ph↗
arXiv2026

Dynamic Response Functions for Cavity Quantum Electrodynamics Hartree-Fock Theory

Frequency-dependent linear and quadratic response functions are implemented for a cavity quantum electrodynamics (QED) generalization of Hartree-Fock (HF) theory. Dynamic electric dipole polarizability, optical rectification hyperpolarizability, and second harmonic generation hyperpolarizability tensors are evaluated for molecules strongly coupled to a single-mode optical cavity, and the results are benchmarked against the same tensors obtained from real-time time-dependent QED-HF simulations. Substantial cavity-induced changes to the frequency-dependent properties are observed for certain perturbing frequencies at large electron-photon coupling strengths. We also find special perturbing frequencies at which there is no cavity effect, regardless of the coupling strength.

physics.chem-ph↗
arXiv2026

Near-frustration-free electronic structure Hamiltonian representations and lower bound certificates

Hamiltonian representations based on the sum-of-squares (SOS) hierarchy provide rigorous lower bounds on ground-state energies and facilitate the design of efficient classical and quantum simulation algorithms. This work presents a unified framework connecting SOS decompositions with variational two-particle reduced density matrix (v2RDM) theory. We demonstrate that the ``weighted'' SOS ansatz naturally recovers the dual of the v2RDM program, enabling the strict enforcement of symmetry constraints such as particle number and spin. We provide explicit SOS constructions for the Hubbard model and electronic structure Hamiltonians, ranging from spin-free approximations to full rank-2 expansions. We also highlight theoretical connections to block-invariant symmetry shifts. Numerical benchmarks on molecular systems and Iron-Sulfur clusters validate these near frustration-free representations, demonstrating their utility in improving spectral gap amplification and reducing block encoding costs in quantum algorithms.

quant-ph↗
arXiv2026

Spectral amplification for ground-state energy estimation of electronic structure in first quantization

We demonstrate an asymptotic gate complexity improvement in first-quantized ground-state energy estimation of electronic structure Hamiltonians in a plane wave basis by employing the sum-of-squares spectral gap amplification protocol. The improvement relies on identifying a sum-of-squares representation of the Hamiltonian which provides a lower bound certificate and low cost block encoding that leads to a provably lower quantum phase estimation gate cost. This is achieved by using a sum-of-squares operator generated by the total charge density operator resulting in a block encoding normalization improvement of $λ= \mathcal{O}\left(ηΔ^{-1.5}+η^{1.5}Δ^{-1} \right)$ compared to prior work $λ= \mathcal{O}(ηΔ^{-2}+η^2Δ^{-1})$ where $η$ is the number of electrons and $Δ$ is the simulation grid spacing. The asymptotic reduction in block encoding normalization and similar block encoding costs to prior work is demonstrated to reduce resource estimates for materials and chemical systems by a factor of $2 - 44\times$ corresponding to the lowest cost estimates for ab initio materials simulation.

quant-ph↗
arXiv2026

Time-Dependent Relativistic Two-Component Equation-of-Motion Coupled-Cluster for Open-Shell Systems: TD-EA/IP-EOMCC

We present a combined imaginary-time/real-time time-dependent (TD) approach for evaluating linear absorption spectra of open-shell systems at the electron attachment (EA) and ionization potential (IP) equation-of-motion coupled-cluster (EOMCC) levels of theory and within the exact two-component relativistic framework. The absorption lineshape is given by the Fourier transform of the electric dipole autocorrelation function, which is obtained from a real-time simulation. Approximations of the lowest-energy EA- and IP-EOMCC eigenstates, which are required as initial states for the real-time simulation, are generated by propagating a Koopmans EA/IP state in imaginary time. TD-EA/IP-EOMCC linear absorption spectra of open-shell atomic (Na, K, Rb, F, Cl, and Br) and diatomic (SiH and ClO) systems closely reproduce those obtained from standard TD-EA/IP procedures carried out in the frequency domain. We find that the existence of low-lying states with non-negligible overlap with the Koopmans determinant impacts the length of the imaginary-time propagation required to obtain an initial state that produces correct absolute energies and peak height intensities in spectra extracted from the subsequent real-time TD-EA/IP-EOMCC calculations.

physics.chem-ph↗
arXiv2026

Cavity Quantum Electrodynamics Ring Coupled Cluster and the Random Phase Approximation

It is well known that the ground-state correlation energy from the particle-hole channel of the random phase approximation (RPA) is formally equivalent to that from a simplified coupled cluster doubles (CCD) model that includes only ring diagram contraction contributions in the residual equations [{\em J. Chem. Phys.} {\bf 129}, 231101 (2008)]. We generalize this analytic result to the cavity quantum electrodynamics (QED) case and demonstrate the numerical equivalence of QED-RPA and a QED ring-CCD model that accounts for double electron excitations, coupled single electron excitations / single photon creation, and double photon creation.

physics.chem-ph↗
arXiv2026

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 work, 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.

physics.chem-ph↗
arXiv2025

Relativistic Core-Valence-Separated Molecular Mean-Field Exact-Two-Component Equation-of-Motion Coupled Cluster Theory: Applications to L-edge X-ray Absorption Spectroscopy

L-edge X-ray absorption spectra for first-row transition metal complexes are obtained from relativistic equation-of-motion singles and doubles coupled-cluster (EOM-CCSD) calculations that make use of the core-valence separation (CVS) scheme, with scalar and spin--orbit relativistic effects modeled within the molecular mean-field exact two-component (X2C) framework. By incorporating relativistic effects variationally at the Dirac--Coulomb--Breit (DCB) reference level, this method delivers accurate predictions of L-edge features, including energy shifts, intensity ratios, and fine-structure splittings, across a range of molecular systems. Benchmarking against perturbative spin--orbit treatments and relativistic TDDFT highlights the superior performance and robustness of the CVS-DCB-X2C-EOM-CCSD approach, including the reliability of basis set recontraction schemes. While limitations remain in describing high-density spectral regions, our results establish CVS-DCB-X2C-EOM-CCSD as a powerful and broadly applicable tool for relativistic core-excitation spectroscopy.

physics.chem-ph↗
arXiv2025

Extension of the CC($P$;$Q$) Formalism to the Electron Attachment and Ionization Potential Equation-of-Motion Coupled-Cluster Frameworks

We combine the electron attachment (EA) and ionization potential (IP) equation-of-motion (EOM) coupled-cluster (CC) approaches with the CC($P$;$Q$) formalism. The resulting methodologies are used to describe the electronic states of several open-shell molecules, with the goal of approximating high-level EA/IP-EOMCC energetics corresponding to a full treatment of 3-particle-2-hole (3$p$-2$h$) and 3-hole-2-particle (3$h$-2$p$) excitations on top of CC with singles and doubles (CCSD). We show that the active-orbital-based EA/IP-EOMCC CC($P$;$Q$) approaches, abbreviated as EA/IP-CC(t;3), achieve sub-millihartree accuracies relative to the parent EA-EOMCCSD(3$p$-2$h$)/IP-EOMCCSD(3$h$-2$p$) data using reduced computational effort, while improving upon their completely renormalized EA/IP-CR-EOMCC(2,3) counterparts.

physics.chem-ph↗
arXiv2025

Static Electric Dipole Polarizability and Hyperpolarizability Tensors from Mean-Field Cavity Quantum Electrodynamics Approaches

First-order electric dipole response functions are implemented for cavity quantum electrodynamics (QED) generalizations of Hartree-Fock (HF) and Kohn-Sham density functional theory (DFT) in order to assess the degree to which static molecular response properties are impacted by interactions between electronic degrees of freedom and an optical cavity mode. Isotropically averaged static electric dipole polarizability tensors from QED-HF and QED-DFT are found to be somewhat insensitive to the presence of the cavity under realistic single-molecule coupling strengths. In contrast, the first hyperpolarizability tensor computed using QED-HF can be significantly modified by the cavity, depending on the relative orientation of the molecule and cavity mode polarization axis. For example, compared to the isolated molecule case, the isotropically averaged hyperpolarizability for $p$-nitroaniline decreases by more than 20% when the molecule is coupled to a single-mode optical cavity with a coupling strength of $|λ| = 0.05$ a.u. and when the cavity mode is polarized along the principal molecular axis. On the other hand, with this coupling strength and polarization, the isotropically averaged static dipole polarizability from QED-HF or QED-DFT decreases by only $\approx$ 2--5%, depending on the choice of DFT functional.

physics.chem-ph↗
arXiv2025

Relativistic Two-component Double Ionization Potential Equation-of-Motion Coupled Cluster with the Dirac--Coulomb--Breit Hamiltonian

We have implemented relativistic formulations of DIP-EOMCCSD and DIP-EOMCCSDT within the 1eX2C and DC-, DCG-, and DCB-X2C frameworks. Direct comparisons against full 4c-DIP-EOMCCSD calculations show excellent agreement with DC(G)-X2C-DIP-EOMCCSD, suggesting, at least for the systems studied herein, two-electron relativistic effects are well-described by the mean-field treatment in mmfX2C, and remaining relativistic two-electron and electron-positron correlation effects are negligible. A subsequent basis set study on vertical double IPs for noble gas and diatomic species has shown that DCB-X2C-DIP-EOMCCSD tends to overestimate double IP values in the limit of a complete one-electron basis, by more than 0.25 eV, on average. For atomic systems, we were able to demonstrate that a composite scheme whereby the dominant correlation effects are captured by large-basis DCB-X2C-DIP-EOMCCSD and remaining high-order correlation effects are approximately modeled via small-basis DCB-X2C-DIP-EOMCCSDT brings the double IP values into excellent agreement with experiment; for Xe atom, for example, absolute errors in double IP values from this approach are less than 0.02 eV. However, we found the ANO-RCC family of basis sets used in our composite approach to have poor convergence behavior in terms of DCB-X2C-DIP-EOMCC calculations, as the estimates computed using the non-relativistic DIP-EOMCC approach at the large basis set limit indicates a larger 0.1--0.2 eV error relative to experimental data.

physics.chem-ph↗
arXiv2025

Comparing Perturbative and Commutator-Rank-Based Truncation Schemes in Unitary Coupled-Cluster Theory

Unitary coupled cluster (UCC) theory offers a promising Hermitian alternative to conventional coupled cluster (CC) theory, but its practical implementation is hindered by the non-truncating nature of the Baker-Campbell-Hausdorff (BCH) expansion of the similarity-transformed Hamiltonian ($\bar{H}$). To address this challenge, various truncation strategies have been developed to approximate $\bar{H}$ in a compact and reliable manner. In this work, we compare the numerical performance of approximate UCC with single and double excitations (UCCSD) methods that employ many-body perturbation theory (MBPT) and commutator rank based truncation schemes. Our results indicate low-order MBPT-based schemes, such as UCC(2) and UCC(3), yield reasonable results near equilibrium, but they become unreliable at stretched geometries. Higher-order MBPT-based schemes do not necessarily improve performance, as the UCCSD(4) and UCCSD(5) amplitude equations sometimes lack solutions. In contrast, commutator-rank-based truncations exhibit greater numerical stability, with the Bernoulli representation of the BCH expansion enabling more rapid convergence to the UCCSD limit compared to the standard BCH formulation.

physics.chem-ph↗
arXiv2025

Automated Quantum Chemistry Code Generation with the p$^\dagger$q Package

This article summarizes recent updates to the p$^\dagger$q package, which is a C++ accelerated Python library for generating equations and computer code corresponding to singly-reference many-body quantum chemistry methods such as coupled-cluster (CC) and equation-of-motion (EOM) CC theory. Since 2021, the functionality in \pq has expanded to include boson operators, coupled fermion-boson operators, unitary cluster operators, non-particle-conserving EOM operators, spin tracing, multiple single-particle subspaces, and more. Additional developments allow for the generation of C++ and Python code that minimizes floating-point operations via contraction order optimization, sub-expression elimination, and the fusion of similar terms.

physics.chem-ph↗
arXiv2025

Fast quantum simulation of electronic structure by spectrum amplification

The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings of the Hamiltonian. A natural challenge of these methods is the degree to which block-encoding costs can be reduced. We address this challenge through the technique of spectrum amplification, which magnifies the spectrum of the low-energy states of Hamiltonians that can be expressed as sums of squares. Spectrum amplification enables estimating ground-state energies with significantly improved cost scaling in the block encoding normalization factor $Λ$ to just $\sqrt{2ΛE_{\text{gap}}}$, where $E_{\text{gap}} \ll Λ$ is the lowest energy of the sum-of-squares Hamiltonian. To achieve this, we show that sum-of-squares representations of the electronic structure Hamiltonian are efficiently computable by a family of classical simulation techniques that approximate the ground-state energy from below. In order to further optimize, we also develop a novel factorization that provides a trade-off between the two leading Coulomb integral factorization schemes -- namely, double factorization and tensor hypercontraction -- that when combined with spectrum amplification yields a factor of 4 to 195 speedup over the state of the art in ground-state energy estimation for models of Iron-Sulfur complexes and a CO$_{2}$-fixation catalyst.

quant-ph↗
arXiv2025

Two-component relativistic equation-of-motion coupled cluster for electron ionization

We present an implementation of relativistic ionization-potential (IP) equation-of-motion coupled-cluster (EOMCC) with up to 3-hole--2-particle (3h2p) excitations that makes use of the molecular mean-field exact two-component (mmfX2C) framework and the full Dirac--Coulomb--Breit Hamiltonian. The closed-shell nature of the reference state in an X2C-IP-EOMCC calculation allows for accurate predictions of spin-orbit splittings in open-shell molecules without breaking degeneracies, as would occur in an excitation-energy EOMCC calculation carried out directly on an unrestricted open-shell reference. We apply X2C-IP-EOMCC to the ground and first excited state of the HCCX$^+$ (X = Cl, Br, I) cations, where it is demonstrated that a large basis set (\emph{i.e.}, quadruple-zeta quality) and 3h2p correlation effects are necessary for accurate absolute energetics. The maximum error in calculated adiabatic IPs is on the order of 0.1 eV, whereas spin-orbit splittings themselves are accurate to $\approx 0.01$ eV, as compared to experimentally obtained values.

physics.chem-ph↗
arXiv2024

Quantum Simulation of Realistic Materials in First Quantization Using Non-local Pseudopotentials

This paper improves and demonstrates the usefulness of the first quantized plane-wave algorithms for the quantum simulation of electronic structure, developed by Babbush et al. and Su et al. We describe the first quantum algorithm for first quantized simulation that accurately includes pseudopotentials. We focus on the Goedecker-Tetter-Hutter (GTH) pseudopotential, which is among the most accurate and widely used norm-conserving pseudopotentials enabling the removal of core electrons from the simulation. The resultant screened nuclear potential regularizes cusps in the electronic wavefunction so that orders of magnitude fewer plane waves are required for a chemically accurate basis. Despite the complicated form of the GTH pseudopotential, we are able to block encode the associated operator without significantly increasing the overall cost of quantum simulation. This is surprising since simulating the nuclear potential is much simpler without pseudopotentials, yet is still the bottleneck. We also generalize prior methods to enable the simulation of materials with non-cubic unit cells, which requires nontrivial modifications. Finally, we combine these techniques to estimate the block-encoding costs for commercially relevant instances of heterogeneous catalysis (e.g. carbon monoxide adsorption on transition metals) and compare to the quantum resources needed to simulate materials in second quantization. We conclude that for computational cells with many particles, first quantization often requires meaningfully less spacetime volume.

quant-ph↗
arXiv2024

The orientation dependence of cavity-modified chemistry

Recent theoretical studies have explored how ultra-strong light--matter coupling can be used as a handle to control chemical transformations. {\em Ab initio} cavity quantum electrodynamics (QED) calculations demonstrate that large changes to reaction energies or barrier heights can be realized by coupling electronic degrees of freedom to vacuum fluctuations associated with an optical cavity mode, provided that large enough coupling strengths can be achieved. In many cases, the cavity effects display a pronounced orientational dependence. In this Perspective, we highlight the critical role that geometry relaxation can play in such studies. As an example, we consider recent work [Nat.~Commun.~{\bf 14}, 2766 (2023)] that explored the influence of an optical cavity on Diels-Alder cycloaddition reactions and reported large changes to reaction enthalpies and barrier heights, as well as the observation that changes in orientation can inhibit the reaction or select for one reaction product or another. Those calculations used fixed molecular geometries optimized in the absence of the cavity and fixed relative orientations of the molecules and the cavity mode polarization axis. Here, we show that, when given a chance to relax in the presence of the cavity, the molecular species reorient in a way that eliminates the orientational dependence. Moreover, in this case, we find that qualitatively different conclusions regarding the impact of the cavity on the thermodynamics of the reaction can be drawn from calculations that consider relaxed versus unrelaxed molecular structures.

physics.chem-ph↗
arXiv2024

Relativistic coupled cluster with completely renormalized and perturbative triples corrections

We have implemented noniterative triples corrections to the energy from coupled-cluster with single and double excitations (CCSD) within the 1-electron exact two-component (1eX2C) relativistic framework. The effectiveness of both the CCSD(T) and the completely renormalized (CR) CC(2,3) approaches are demonstrated by performing all-electron computations of the potential energy curves and spectroscopic constants of copper, silver, and gold dimers in their ground electronic states. Spin-orbit coupling effects captured via the 1eX2C framework are shown to be crucial for recovering the correct shape of the potential energy curves, and the correlation effects due to triples in these systems changes the dissociation energies by about 0.1--0.2 eV or about 4--7\%. We also demonstrate that relativistic effects and basis set size and contraction scheme are significantly more important in Au$_2$ than in Ag$_2$ or Cu$_2$.

physics.chem-ph↗