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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 ( N 10 ) CCDQ method, yet only require a O ( N 6 ) algorithm by virtue of factorized intermediates. [ABSTRACT FROM AUTHOR]

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 ( N 10 ) CCDQ method, yet only require a O ( N 6 ) algorithm by virtue of factorized intermediates. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

It is known that some non-dynamic effects of electron correlation can be included in coupled cluster theory using a tailoring technique that separates the effects of non-dynamic and dynamic correlations. Recently, the simple pCCD (pair coupled cluster doubles) wavefunction was shown to provide good results for some non-dynamic correlation problems, such as bond-breaking, in a spin-adapted way with no active space selection. In this paper, we report a study of excited states using "tailored coupled cluster singles and doubles," to attempt to use pCCD as a kernel for more complete coupled-cluster singles and doubles (CCSD) results for excited states. Several excited states are explored from those primarily due to single excitations to those dominated by doubly excited states and from singlet–triplet splittings for some diradical states. For the first two situations, tailored pCCD-TCCSD offers no improvement over equation of motion-CCSD. However, when we explore the singlet–triplet gap of diradical molecules that are manifestly multi-reference, a pCCD kernel provides improved results, particularly with generalized valence bond orbitals. [ABSTRACT FROM AUTHOR]

The core excitation energies and related principal ionization energies are obtained for selected molecules using several density functionals and compared with benchmark equation-of-motion coupled cluster (EOM-CC) results. Both time-dependent and time-independent formulations of excitation spectra in the time-dependent density functional theory and the EOM-CC are employed to obtain excited states that are not always easily accessible with the time-independent method. Among those functionals, we find that the QTP(00) functional, which is only parameterized to reproduce the five IPs of water, provides excellent core IPs and core excitation energies, consistently yielding better excitation and ionization energies. We show that orbital eigenvalues of KS density functional theory play an important role in determining the accuracy of the excitation and photoelectron spectra. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Solution of dark, doubly excited states using equation-of-motion coupled-cluster (EOM-CC) usually equires at least triple excitations or even quadruples beyond the standard singles and doubles (EOM-CCSD) for an appropriate treatment. A new route to obtain these doubly excited states using EOM-CCSD is demonstrated. Traditionally, EOM-CC is performed on a closed shell reference state that has a well-described single reference CC wavefunction. In this Communication, we attempt to use low spin open-shell states such as the MS = 0 triplet and open-shell singlet as a reference state. Using this intermediate excited state as a reference state provides us with the benefit of obtaining a doubly excited state, as a single excitation at the cost of EOM-CCSD. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present the time-independent (TI) and time-dependent (TD) equation of motion coupled-cluster (EOM-CC) oscillator strengths not limited to those obtained by the dipole approximation. For the conventional TI-EOM-CC, we implement all the terms in the multipole expansion through second order that contributes to the oscillator strength. These include contributions such as magnetic dipole, electric quadrupole, electric octupole, and magnetic quadrupole. In TD-EOM-CC, we only include the quadrupole moment contributions. This augments our previous work [Y. C. Park, A. Perera, and R. J. Bartlett, J. Chem. Phys. 151, 164117 (2019)]. The inclusion of the quadrupole contributions (and all the other contributions through second order in the case of TI-EOM-CCSD) enables us to obtain the intensities for the pre-edge transitions in the metal K-edge spectra, which are dipole inactive. The TI-EOM-CCSD and TD-EOM-CCSD spectra of Ti4+ atoms are used to showcase the implementation of the second-order oscillator strengths. The origin of 1s → e and 1s → t2 in core spectra from iron tetrachloride and titanium tetrachloride is discussed and compared with the experiment. [ABSTRACT FROM AUTHOR]

A linearly approximated explicitly correlated coupled-cluster singles and doubles model for the Fock-space coupled-cluster method has been formulated and implemented. An extension of the Fock-space wave operators is introduced in order to treat the short-range correlation effects for excited and doubly electron-attached states. We show that an effective reduction in the number of active virtuals can also be obtained by improving how the short-range correlation is treated. Numerical results to gauge the performance for valence and Rydberg excitation energies, double ionization potentials, and double electron attachment energies of several molecules are obtained. Statistical measures of the errors in excitation energies show that the explicitly correlated results are within 0.1 eV from the complete basis set limit already at the double-ζ level unless the excitation energies are too close to the ionization thresholds. Similar accuracy is seen for the double ionization potentials and double electron attachment energies. [ABSTRACT FROM AUTHOR]

Atmospheric formic acid is severely underpredicted by models. A recent study proposed that this discrepancy can be resolved by abundant formic acid production from the reaction (1) between hydroxyl radical and methanediol derived from in-cloud formaldehyde processing and provided a chamber-experiment-derived rate constant, k1 = 7.5 × 10-12 cm³ s-1. High-level accuracy coupled cluster calculations in combination with E,J-resolved two-dimensional master equation analyses yield k1 = (2.4 ± 0.5) × 10-12 cm3 s-1 for relevant atmospheric conditions (T = 260-310 K and P = 0-1 atm). We attribute this significant discrepancy to HCOOH formation from other molecules in the chamber experiments. More importantly, we show that reversible aqueous processes result indirectly in the equilibration on a 10 min. time scale of the gas-phase reaction HCHO + H2O - HOCH2OH (2) with a HOCH2OH to HCHO ratio of only ca. 2%. Although HOCH2OH outgassing upon cloud evaporation typically increases this ratio by a factor of 1.5-5, as determined by numerical simulations, its in-cloud reprocessing is shown using a global model to strongly limit the gas-phase sink and the resulting production of formic acid. Based on the combined findings in this work, we derive a range of 1.2-8.5 Tg/y for the global HCOOH production from cloud-derived HOCH2OH reacting with OH. The best estimate, 3.3 Tg/y, is about 30 times less than recently reported. The theoretical equilibrium constant Keq (2) determined in this work also allows us to estimate the Henry's law constant of methanediol (8.1 × 105 M atm-1 at 280 K). [ABSTRACT FROM AUTHOR]

A full configuration interaction calculation (FCI) ultimately defines the innate molecular orbital description of a molecule. Its density matrix and the natural orbitals obtained from it quantify the difference between having N-dominantly occupied orbitals in a reference determinant for a wavefunction to describe N-correlated electrons and how many of those N-electrons are left to the remaining virtual orbitals. The latter provides a measure of the multi-determinantal character (MDC) required to be in a wavefunction. MDC is further split into a weak correlation part and a part that indicates stronger correlation often called multi-reference character (MRC). If several virtual orbitals have high occupation numbers, then one might argue that these additional orbitals should be allowed to have a larger role in the calculation, as in MR methods, such as MCSCF, MR-CI, or MR-coupled-cluster (MR-CC), to provide adequate approximations toward the FCI. However, there are problems with any of these MR methods that complicate the calculations compared to the uniformity and ease of application of single-reference CC calculations (SR-CC) and their operationally single-reference equation-of-motion (EOM-CC) extensions. As SR-CC theory is used in most of today's "predictive" calculations, an assessment of the accuracy of SR-CC at some truncation of the cluster operator would help to quantify how large an issue MRC actually is in a calculation, and how it might be alleviated while retaining the convenient SR computational character of CC/EOM-CC. This paper defines indices that identify MRC situations and help assess how reliable a given calculation is. [ABSTRACT FROM AUTHOR]