Rodney J. Bartlett

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.

We present a new exchange–correlation (XC) functional inspired by correlated orbital theory and designed to enhance the accuracy of core-electron ionization energy predictions as measured by x-ray photoelectron spectroscopy. This functional, referred to as cQTP25, differs from other Quantum Theory Project (QTP) functionals by optimizing the range-separation parameters through a targeted restriction of the orbital space to core 1s electrons only. We benchmarked cQTP25 against a diverse set of XC functionals spanning multiple rungs of Jacob’s ladder in Density Functional Theory (DFT). The performance was evaluated primarily using the relation IP1s = −ɛ1s, but for completeness, we also computed core ionization potentials using the ΔDFT method. All calculations accounted for both non-relativistic and relativistic corrections. Overall, within Koopmans’s framework, the QTP functionals perform best, and specifically cQTP25. The exception is the ΔDFT analysis, where M11, ωB97X, and BHandHLYP are more accurate and cQTP25 ranks fourth.

Accurate predictions of ionization potentials and electron affinities are essential for guiding the design of organic photovoltaic materials. In this study, we revisit a set of twenty molecules that have been explored in earlier studies and extend the analysis using our approaches: (1) CC theory in its ionization potentials (IPs)/electron affinities (EAs)-equation-of-motion (EOM)/coupled-cluster singles and doubles (CCSD) forms to offer a direct measure of IPs and EAs and (2) Kohn–Sham density functional theory (DFT) using the QTP family compared to a broad range of exchange–correlation functionals (from simple local density approximation/generalized gradient approximation forms through hybrid and range-separated variants). For consistency with prior calculations, one-shot G0W0 corrections are applied to each QTP result. To reduce the cost of coupled-cluster computations, we also investigate both standard and tailored frozen natural orbital (FNO) truncations. Our results confirm that local and semi-local DFT functionals exhibit significant errors, whereas global hybrids and range-separated hybrids offer improved accuracy. The QTP functionals stand out by matching or exceeding the performance of all other functionals. G0W0 on top of DFT starting points further refines orbital energies, bringing them into close agreement with coupled-cluster results. Tailored FNO truncations preserve coupled-cluster accuracy while reducing the virtual space by nearly half. Timing tests on anthracene demonstrate that QTP00 and G0W0@QTP00 workflows almost achieve coupled-cluster quality predictions in under a day, compared with week-long runtimes for full EA-EOM/CCSD.

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 (QTP) functionals are derived from CAM-B3LYP, we pose the question: Can COT improve the hybrid versions of different exchange-correlation (XC) 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 (IP) 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.

The metal K pre-edge spectra of 3d transition metal tetrachlorides (MCl4, M = Ti, Fe, Co, Ni, and Cu) are obtained using the equation of motion coupled cluster (EOM-CC) approach. These spectra are primarily influenced by two key contributions to the oscillator strength—the electric dipole and quadrupole transition moments—due to the possible mixing of 3d and 4p orbitals in transition metal atoms. The EOM-CC singles and doubles method incorporating a recently implemented formalism that includes all the second-order contributions to oscillator strength [i.e., beyond the customary dipole approximation, Park et al., J. Chem. Phys. 155, 094103 (2021)] provides a powerful tool for computing excitation energies and oscillator strengths. This approach enables accurate interpretation of experimental spectra and facilitates predictions when experimental data are unavailable. In the present study, we demonstrate how these new extensions to the EOM-CC method can be utilized to compute metal K pre-edge spectra and determine the orbital characteristics of MCl4 complexes.

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.

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 O(N-9) with the number of basis functions. It is very difficult to predict, a priori, the effect correlation of past CCSD(T) on a given reaction energy. The purpose of this work is to examine cost-effective quadruple corrections based on the factorization theorem of the many-body perturbation theory that may address these challenges. We show that the O(N-7) factorized CCSD(TQ(f)) method introduces minimal error to predicted correlation and reaction energies as compared to the O(N-9) CCSD(TQ). Further, we examine the performance of Goodson's continued fraction method in the estimation of CCSDT(Q)(Lambda) 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(f))/cc-pVDZ is capable of predicting CCSDT(Q)(Lambda)/cc-pVDZ contributions to reaction energies with an average error of 0.07 kcal mol(-1) and an L2D 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.