Zachary W. Windom

Correlated Orbital Theory (COT) provides an exact one-particle framework by imposing rigorous physical constraints on Kohn–Sham eigenvalues and, as a consequence, directly incorporates essential electron correlation into molecular orbitals. This approach paves the way toward a new class of approximations within Kohn–Sham Density Functional Theory (KS-DFT). However, since all existing quantum theory project functionals are derived from CAM-B3LYP, we pose the question: Can COT improve the hybrid versions of different exchange-correlation functionals as well? To that end, we explore two optimization strategies for adjusting the existing parameters within PBE0, TPSS0, and LC-PBE0: (i) the ionization potential condition and (ii) the HOMO–LUMO condition. In this sense, we critically assess how these functionals address the “Devil’s Triangle” of KS-DFT: self-interaction error, integer discontinuity, and one-particle spectra. We further examine how the COT influences the description of two challenging properties, charge transfer and reaction barrier heights. Overall, enforcing both COT conditions systematically enhances the performance of functionals within the PBE family, although the description of reaction barriers still leaves room for improvement.

We propose a non-iterative, post-hoc correction to the unitary coupled cluster theory with the single, double, and triple excitations (UCCSDT) Ansatz, which considers the leading-order effects of neglected quadruple excitations. We present two ways to derive this correction, henceforth referred to as [Q-6], which leads to an improvement in the correlation energy shown to be truncated to sixth-order in many-body perturbation theory. A comparison between the UCC-based [Q-6] correction proposed in this work and analogous, “platinum standard” quadruple corrections proposed in conventional coupled cluster 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 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.

Correlated orbital theory (COT) is an exact one-particle treatment that adds essential electron correlation into its molecular orbitals, potentially reducing correlated treatments of response properties to one-particle coupled-perturbed Hartree–Fock- or Kohn–Sham-like calculations. Such a computation is vastly simpler than the usual ab initio correlated approach that would add correlation typically with EOM-CC after a perturbed mean-field solution. The question then is, how well can this be accomplished via the Quantum Theory Project (QTP) exchange–correlation (XC) functionals that are meant to emulate the rigorous COT framework? This paper addresses this question for response properties by making comparisons between such orbital-specific calculations and those from well-correlated EOM-CC solutions for static polarizabilities, nuclear magnetic resonance coupling constants, and chemical shifts. The simple orbital-specific version provides an accurate realization of the correlated EOM-CC results, but now in a mode that facilitates an orbital-by-orbital interpretation. Here, we compare 33 XC functionals from the different Jacob’s ladder rungs always against the EOM-CCSD results. Thus, the smallest mean absolute deviation for the static polarizability comes from LC-QTP XC, 0.28 a.u. Regarding the total nuclear spin–spin coupling constants, QTP01 performs best, %Error = 10.63% (QTP02 and LC-QTP are second and third best). Finally, the XC that stood out in the chemical shift analysis was TPSS0, which presented the best result for the majority of the chemical shifts. However, considering the overall performances based on linear fitting of all isotope data points, five functionals are recommended for a chemical shift study: TPSS0, ωB97X, QTP00, QTP01, and QTP02, all presenting R2 = 0.96.

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 T2 and its products that can effectively emulate more “complete” methods that explicitly consider higher-rank, T2m, operators. We introduce a hierarchy of methods designed to systematically account for higher, even order cluster operators, such as T4, T6, …, T2m, by invoking tenets of the factorization theorem of many-body perturbation theory (MBPT) 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 MBPT and can be extended up to arbitrarily high orders in T2. The efficacy of such approximations are determined by studying the potential energy surface of several closed and open-shell molecules. We find that the proposed hierarchy of augmented T2 methods essentially reduces 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 O(N10) CCDQ method, yet only require a O(N6) algorithm by virtue of factorized intermediates.

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 for 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 the 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 are leveraged to evaluate energy corrections associated with triple excitations, leading to the UCCSD[T] method. In terms of quantum computing, this correction represents an entirely classical post-processing step that improves the energy estimate by accounting for triple excitation effects without necessitating new quantum algorithm developments or increasing demand for quantum resources. The rationale behind this choice is shown to be rigorous by studying the properties of finite-order UCC energy functionals, and our efforts do not support the addition of the fifth-order contributions as in the (T) correction. 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.

EA-EOM-CCSD electron affinities and LUMO energies of various Kohn–Sham density functional theory (DFT) methods are calculated for an a priori IP benchmark set of 64 small, closed-shell molecules. The purpose of these calculations was to investigate whether the QTP KS-DFT functionals can emulate EA-EOM-CC with only a mean-field approximation. We show that the accuracy of DFT—relative to CCSD—improves significantly when elements of correlated orbital theory are introduced into the parameterization to define the QTP family of functionals. In particular, QTP(02), which has only a single range separation parameter, provides results accurate to a MAD of <0.15 eV for the whole set of 64 molecules compared to EA-EOM-CCSD, far exceeding the results from the non-QTP family of density functionals.

Iterative diagonalization of large matrices to search for a subset of eigenvalues that may be of interest has become routine throughout the field of quantum chemistry. Lanczos and Davidson algorithms hold a monopoly, in particular, owing to their excellent performance on diagonally dominant matrices. However, if the eigenvalues happen to be clustered inside overlapping Gershgorin disks, the convergence rate of both strategies can be noticeably degraded. In this work, we show how Davidson, Jacobi–Davidson, Lanczos, and preconditioned Lanczos correction vectors can be formulated using the reduced partitioning procedure, which takes advantage of the inherent flexibility promoted by Brillouin–Wigner perturbation (BW-PT) theory’s resolvent operator. In doing so, we establish a connection between various preconditioning definitions and the BW-PT resolvent operator. Using Natural Localized Molecular Orbitals (NLMOs) to construct Configuration Interaction Singles (CIS) matrices, we study the impact the preconditioner choice has on the convergence rate for these comparatively dense matrices. We find that an attractive by-product of preconditioning the Lanczos algorithm is that the preconditioned variant only needs 21%–35% and 54%–61% of matrix-vector operations to extract the lowest energy solution of several Hartree–Fock- and NLMO-based CIS matrices, respectively. On the other hand, the standard Davidson preconditioning definition seems to be generally optimal in terms of requisite matrix-vector operations.

Interest in ab initio property prediction of π-conjugated polymers for technological applications places significant demand on “cost-effective” and conceptual computational methods, particularly effective, one-particle theories. This is particularly relevant in the case of Kohn–Sham Density Functional Theory (KS-DFT) and its new competitors that arise from correlated orbital theory, the latter defining the QTP family of DFT functionals. This study presents large, ab initio equation of motion-coupled cluster calculations using the massively parallel ACESIII to target the fundamental bandgap of two prototypical organic polymers, trans-polyacetylene (tPA) and polyacene (Ac), and provides an assessment of the new quantum theory project (QTP) functionals for this problem. Further results focusing on the 1Ag (1Ag), 1Bu (1B2u), and 3Bu (3B2u) excited states of tPA (Ac) are also presented. By performing calculations on oligomers of increasing size, extrapolations to the thermodynamic limit for the fundamental and all excitation gaps, as well as estimations of the exciton binding energy, are made. Thermodynamic-limit results for a combination of “optimal” and model geometries are presented. Calculated results for excitations that are adequately described using a single-particle model illustrate the benefits of requiring a KS-DFT functional to satisfy the Bartlett ionization potential theorem.

Significant effort has been devoted to benchmarking isotropic hyperfine coupling constants for both wavefunction and density-based approaches in recent years, as accurate theoretical predictions aid the fitting of experimental model Hamiltonians. However, literature examining the predictive quality of a Density Functional Theory (DFT) functional abiding by the Bartlett IP condition is absent. In an attempt to rectify this, we report isotropic hyperfine coupling constant predictions of 24 commonly used DFT functionals on a total of 56 radicals, with the intent of exploring the successes and failures of the Quantum Theory Project (QTP) line of DFT functionals (i.e., CAM-QTP00, CAM-QTP01, CAM-QTP02, and QTP17) for this property. Included in this benchmark study are both small and large organic radicals as well as transition metal complexes, all of which have been studied to some extent in prior work. Subsequent coupled-cluster singles and doubles (CCSD) and CCSD withperturbative triples [CCSD(T)] calculations on small and large organic radicals show modest improvement as compared to prior work and offer an additional avenue for evaluation of DFT functional performance. We find that the QTP17 and CAM-QTP00 functionals consistently underperform, despite being parameterized to satisfy an IP eigenvalue condition primarily focused on inner shell electrons. On the other hand, the CAM-QTP01 functional is the most accurate functional in both organic radical datasets. Furthermore, both CAM-QTP01 and CAM-QTP02 are the most accurate functionals tested on the transition metal dataset. A significant portion of functionals were found to have comparable errors (within 5–15 MHz), but the hybrid class of DFT functionals maintains a consistently optimal balance between accuracy and precision across all datasets.