arXiv subjects

Zachary W. Windom

Publications and source records attributed to Zachary W. Windom.

9 recordsLinked to original sources

arXiv2026

A note on the accuracy of spin-densities from Kohn-Sham Density Functional Theory

Quantifying the magnetic properties of open-shell molecules is a common task in chemistry and is increasingly performed in silico using Kohn-Sham density functional theory (KS-DFT). Previous work demonstrates that the predictive accuracy of a few functionals for one such property - hyperfine coupling constants (HFCCs) - is possible, implying that such approximations must yield accurate spin-densities at the nucleus. However, the ability of such functionals to globally predict accurate spin-densities of comparable quality to rigorous ab initio coupled cluster theory, for example, is dubious, despite this being a fundamental quantity for KS-DFT. This work intends to explore the matter by evaluating moments of the spin-density, $\langle r^n \rangle = \int ρ(r)r^n dτ$, $n=-2,\cdots,2,3$, for second-, third-, and fourth-row atoms to compare various KS-DFT functionals against CCSD. Our results broadly indicate that the tested functionals experience significant deviations with respect to CCSD spin-densities in regions up to 1 Bohr away from the nuclei, with most errors occurring in the immediate vicinity of the nucleus. We find evidence of extreme errors by some functionals for individual $α$/$β$ spin-densities, although several ultimately end up benefiting from significant error cancellation once the corresponding global spin-density is formed. Nevertheless, a comparison between CAM-B3LYP and the Quantum Theory Project (QTP)-family of DFT functionals based on Correlated Orbital Theory conditions across all error metrics demonstrates that QTP00 more accurately reproduces the global spin-density as well as HFCCs, generally offering results in better agreement with CCSD. In line with previous work, we also corroborate the success of PBE0 and the TPSS-family of functionals for HFCCs, further finding that both approximations generally yield spin-densities that are amongst the best.

physics.chem-ph↗

arXiv2026

Integrating Julia-ITensors into the Tensor Network Quantum Virtual Machine (TNQVM)

The Tensor Network Quantum Virtual Machine (TNQVM) is a high-performance classical circuit simulation backend for the eXtreme-scale ACCelerator (XACC) framework that leverages the Intelligent Tensor (ITensor) library for tensor network--based quantum circuit simulation. However, TNQVM's original C++ ITensor backend is tied to an older integrated release, limiting access to newer tensor network algorithms, diagnostics, and performance improvements available in the actively developed Julia-based ITensors ecosystem. We introduce JuliaITensorTNQVM, an interoperability layer that bridges TNQVM's C++ visitor infrastructure and the Julia-ITensors runtime through a C-compatible application binary interface. This design preserves the existing XACC/TNQVM programming model while enabling access to modern tensor network capabilities, including entanglement entropy diagnostics exposed directly to XACC. We evaluate the implementation through two studies: a Page-curve verification protocol using Haar-random states, and QAOA MaxCut simulations on 3-regular graphs. Within these tested regimes, results are consistent with expected entanglement behavior and established scaling trends, supporting JuliaITensorTNQVM as a practical modernization path for tensor network simulation in TNQVM.

quant-ph↗

arXiv2025

Analysis of fourth-, fifth-, and infinite-order triple excitations in unitary coupled cluster theory

In this work, we introduce a correction to the unitary coupled cluster method with single and double excitations (UCCSD) that incorporates the effects of missing triple excitations through a treatment that is correct through fifth-order in many-body perturbation theory (MBPT), which we refer to as UCCSD[T-5]. We then benchmark the performance of UCCSD[T-5] alongside the previously developed fourth-order UCCSD[T], comparing both against the infinite-order treatment of triples in UCCSDT as well as full configuration interaction (FCI). Two key findings emerge from this analysis. First, the fourth-order correction in UCCSD[T] consistently provides the closest agreement with FCI in estimating ground state energies, outperforming both UCCSD[T-5] and UCCSDT. Second, the inclusion of fifth-order corrections as in UCCSD[T-5] largely recovers the infinite-order triples limit in UCCSDT. With the growing interest in UCC ansätze for quantum computing and the constraints imposed by current quantum hardware, these results underscore the potential of using classically computed perturbative corrections within UCC theory to salient triple excitation effects without requiring the additional quantum resources as would be demanded by the UCCSDT ansatz.

physics.chem-ph↗

arXiv2025

Toward the "platinum standard" of quantum chemistry on quantum computers: perturbative quadruple corrections in unitary coupled cluster theory

We propose a non-iterative, post hoc correction to the unitary coupled cluster theory with single, double, and triple excitations (UCCSDT) ansatz, which considers the leading-order effects of neglected quadruple excitations. We present two ways to derive this quadruples correction to UCCSDT, henceforth referred to as [Q-6], which leads to an improvement in the correlation energy shown to be correct through sixth-order in many-body perturbation theory (MBPT). A comparison between the UCC-based [Q-6] correction proposed in this work and analogous, "platinum" standard quadruples corrections proposed in conventional coupled cluster (CC) theory recognizes that [Q-6] is distinct from prior corrections since it is constructed entirely from internally connected components. Although Trotterized (t) and full operator variants of UCCSDT exhibit errors in scans of small molecule potential energy surfaces (PESs) that routinely exceed 1.6 mH, we find that t/UCCSDT[Q-6] is nevertheless able to achieve chemical accuracy as measured by the mean-unsigned error (MUE).

physics.chem-ph↗

arXiv2024

An "ultimate" coupled cluster method based entirely on $T_2$

Electronic structure methods built around double-electron excitations have a rich history in quantum chemistry. However, it seems to be the case that such methods are only suitable in particular situations and are not naturally equipped to simultaneously handle the variety of electron correlations that might be present in chemical systems. To this end, the current work seeks a computationally efficient, low-rank, "ultimate" coupled cluster method based exclusively on $T_2$ and its products which can effectively emulate more "complete" methods that explicitly consider higher-rank, $T_{2m}$ operators. We introduce a hierarchy of methods designed to systematically account for higher, even order cluster operators - like $T_4, T_6, \cdots, T_{2m}$ - by invoking tenets of the factorization theorem of perturbation theory and expectation-value coupled cluster theory. It is shown that each member within this methodological hierarchy is defined such that both the wavefunction and energy are correct through some order in many-body perturbation theory (MBPT), and can be extended up to arbitrarily high orders in $T_2$. The efficacy of such approximations are determined by studying the potential energy surface of several prototypical systems that are chosen to represent both non-dynamic, static, and dynamic correlation regimes. We find that the proposed hierarchy of augmented $T_2$ methods essentially reduce to standard CCD for problems where dynamic electron correlations dominate, but offer improvements in situations where non-dynamic and static correlations become relevant. A notable highlight of this work is that the cheapest methods in this hierarchy - which are correct through fifth-order in MBPT - consistently emulate the behavior of the $\mathcal{O}(N^{10})$ CCDQ method, yet only require a $\mathcal{O}(N^{6})$ algorithm by virtue of factorized intermediates.

physics.chem-ph↗

arXiv2024

Factorized Quadruples and a Predictor of Higher-Level Correlation in Thermochemistry

Coupled cluster theory has had a momentous impact on the ab initio prediction of molecular properties, and remains a staple ingratiate in high-accuracy thermochemical model chemistries. However, these methods require inclusion of at least some connected quadruple excitations, which generally scale at best as $\mathcal{O}(N^9)$ with the number of basis functions. It very difficult to predict, a priori, the effect correlation past CCSD(T) has on a give reaction energies. The purpose of this work is to examine cost-effective quadruple corrections based on the factorization theorem of many-body perturbation theory that may address these challenges. We show that the $\mathcal{O}(N^7)$, factorized CCSD(TQ${}_\text{f}$) method introduces minimal error to predicted correlation and reaction energies as compared to the $\mathcal{O}(N^9)$ CCSD(TQ). Further, we examine the performance of Goodson's continued fraction method in the estimation of CCSDT(Q)${}_Λ$ contributions to reaction energies, as well as a "new" method related to %TAE[(T)] that we refer to as a scaled perturbation estimator. We find that the scaled perturbation estimator based upon CCSD(TQ${}_\text{f}$)/cc-pVDZ is capable of predicting CCSDT(Q)${}_Λ$/cc-pVDZ contributions to reaction energies with an average error of 0.07 kcal mol${}^{-1}$ and a RMST of 0.52 kcal mol${}^{-1}$ when applied to a test-suite of nearly 3000 reactions. This offers a means by which to reliably ballpark how important post-CCSD(T) contributions are to reaction energies while incurring no more than CCSD(T) formal cost and a little mental math.

physics.chem-ph↗

arXiv2024

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 dynamical 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 in which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. 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 singles 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.

quant-ph↗

arXiv2024

An assessment of frozen natural orbitals and band gaps using equation of motion coupled cluster theory: a case study on polyacene and trans-polyacetylene

Frozen natural orbitals (FNOs) are used to augment IP/EA-EOM-CCSD calculations targeting the band gap of trans-polyacetylene and polyacene. We show the resulting electron affinities (EAs), ionization potentials (IPs), and extrapolated band gaps incur errors that are largely tunable to a desired accuracy, yet require many orders of magnitude fewer core-hours as compared to the corresponding full calculation. The relationship between various FNO truncation schemes and (cc-pV$n$Z) basis set is also examined.

physics.chem-ph↗

arXiv2024

A new "gold standard": perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework in dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the "gold standard" CCSD(T) method, which bolsters the baseline CCSD with effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes, which can be obtained on a quantum computer, are leveraged by a classical computer to evaluate energy corrections associated with triple excitations - leading to the UCCSD[T] and UCCSD(T*) methods. The rationale behind these choices is shown to be rigorous by studying the properties of finite-order UCC energy functionals. Although our efforts do not support the addition of the fifth-order contribution as in the (T) correction, comparisons are nevertheless made using a hybrid UCCSD(T) approach. We assess the performance of these approaches on a collection of small molecules, and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories.

physics.chem-ph↗