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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]

We revisit the connection between equation-of-motion coupled cluster (EOM-CC) and random phase approximation (RPA) explored recently by Berkelbach [J. Chem. Phys. 149, 041103 (2018)] and unify various methodological aspects of these diverse treatments of ground and excited states. The identity of RPA and EOM-CC based on the ring coupled cluster doubles is established with numerical results, which was proved previously on theoretical grounds. We then introduce new approximations in EOM-CC and RPA family of methods, assess their numerical performance, and explore a way to reap the benefits of such a connection to improve on excitation energies. Our results suggest that addition of perturbative corrections to account for double excitations and missing exchange effects could result in significantly improved estimates. [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]

The advanced concepts in electronic structure (ACES) programs are products of the Bartlett research group at the University of Florida. They consist of ACES II, which is serial, and ACES III and Aces4, which are massively parallel. All three programs are publically available free of charge. The focus of the ACES implementations is coupled cluster theory and many-body-perturbation theory. We give an overview of the ACES programs, discuss the many features of the program systems, and document the number of benchmarks. [ABSTRACT FROM AUTHOR]

This paper presents core excitation spectra from coupled-cluster (CC) theory obtained from both a time-independent and a new time-dependent formalism. The conventional time-independent CC formulation for excited states is the equation-of-motion (EOM-CC) method whose eigenvalues and eigenvectors describe the core excited states. An alternative computational procedure is offered by a time-dependent CC description. In that case, the dipole transition operator is expressed in the CC effective Hamiltonian form and propagated with respect to time. The absorption spectrum is obtained from the CC dipole autocorrelation function via a Fourier transformation. Comparisons are made among the time-dependent results obtained from second-order perturbation theory, to coupled cluster doubles and their linearized forms (CCD and LCCD), to CC singles and doubles (CCSD) and the linearized form (LCCSD). In the time-independent case, considerations of triples (EOM-CCSDT) and quadruples (EOM-CCSDTQ) are used to approach sub-electron volt accuracy. A particular target is the allyl radical, as an example of an open-shell molecule. As the results have to ultimately be the same, the two procedures offer a complementary approach toward analyzing experimental results. [ABSTRACT FROM AUTHOR]

The similarity transformed equation-of-motion coupled-cluster method (STEOM-CCSD) for excited states is extended to treat spin-orbit coupling interactions (SOIs) using the spin-orbit mean field approximation of the Breit-Pauli Hamiltonian. Two possible schemes to include the spin-orbit splittings of excited states within the STEOM-CCSD model are formulated. They are identified as "diagonalize-then-perturb" and "perturb-then-diagonalize" approaches. The second approach is more suited for cases where SOI is larger, and the first approach breaks down. With the aid of the standard many-body diagrammatic techniques, expressions for all the necessary matrix elements can be derived. These new formulations are implemented in the ACES III suite of parallel coupled cluster programs, and benchmark studies are performed. Numerical tests for several atoms and molecules show a good agreement of calculated spin-orbit splittings to experiment, while also documenting the numerical differences between the two approaches. [ABSTRACT FROM AUTHOR]

The ionization potential (IP) of a molecule quantifies the energy required to remove an electron from the system. As such, it is a fundamental quantity in the context of redox chemistry, charge transfer, and molecular electronics. The accurate theoretical prediction of this property is therefore highly desirable for virtual materials design. Furthermore, vertical IPs are of interest in the development of many-body Green's function methods like the GW formalism, as well as density functionals and semiempirical methods. In this contribution, we report over 1468 vertical valence IPs calculated with the IP variant of equation-of-motion coupled cluster theory with singles and doubles (IP-EOM-CCSD) covering 155 molecules. The purpose of this is two-fold: First, the quality of the predicted IPs is compared with respect to experiments and higher-order coupled cluster theory. This confirms the overall high accuracy and robustness of this method, with some outliers which are discussed in detail. Second, a large set of consistent theoretical reference values for vertical valence IPs are generated. This addresses a lack of reliable reference data for lower-lying valence IPs, where experimental data are often unavailable or of dubious quality. The benchmark set is then used to assess the quality of the eigenvalues predicted by different density functional approximations (via Bartlett's IP-eigenvalue theorem) and the extended Koopmans' theorem approach. The QTP family of functionals are found to be remarkably accurate, low-cost alternatives to IP-EOM-CCSD. [ABSTRACT FROM AUTHOR]

A low-scaling method is presented for the equation-of-motion coupled-cluster theory with single and double (EOM-CCSD) excitations and its second-order many-body perturbation theory [EOM-MBPT(2)] approximations. For a simple description of an excited state, the particular orbitals, ϕ Ĩ and ϕ à , are selected from the natural transition orbitals (NTOs, ϕ), where Ĩ and à refer to NTO occupied and virtual orbital indices. They are chosen based on the largest eigenvalues of the transition density matrix. We expect the ϕ Ĩ and ϕ à pair to be dominant in representing excited states in EOM calculations. Therefore, the double excitation vector, R2 which scale as ∼O2V2, can be modified to keep only a few dominant excitations. Our work indicates that the most important contributions of the R2 vector define smaller subspaces that scale as ∼OV, ∼O2V, and ∼OV2, where O and V refer to the occupied and virtual orbitals in the NTO basis. Thus, the scaling for the EOM part becomes ∼M5. The energy changes due to R2 truncation are small (the mean average deviation from untruncated EOM-CCSD is ∼0.03 eV). We show that this approach works relatively well with various types of NTOs, ranging from configuration singles to time-dependent density functional theory making ∼M5 scaling calculations possible with the use of MBPT(2) as the reference state. [ABSTRACT FROM AUTHOR]

The long-range dispersion C6 coefficient for the SF6 dimer is experimentally measured using a technique that uses the expansion of a supersonic pulse jet into a vacuum. A dynamic model of the jet enables us to correlate the position of the maximal peak in the time-of-flight spectrum with the initial conditions of the experiment and the parameters of the intermolecular interaction potential. Due to the low temperature of the jet target, the C6 coefficient can be extracted directly from the experimental results. Theoretical calculation of the C6 dispersion coefficient is also performed by using linearly approximated explicitly correlated coupled-cluster singles and doubles (CCSD(F12)) method with the subsequent utilization of the Casimir-Polder formula. Good agreement of experimental and theoretical results confirms the reliability of results. [ABSTRACT FROM AUTHOR]

The ˙OH-initiated oxidation of methyl hydroperoxide, which plays an important role in the atmospheric chemistry of methane, was theoretically characterized using high-accuracy composite amHEAT-345(Q) coupled-cluster calculations followed by a two-dimensional E,J resolved master equation analysis. The reaction is found to proceed through two distinct hydrogen-bonded pre-reactive complexes leading to two product channels, in accord with the experimental observations: (i) ˙OH + CH3OOH → CH3OO˙ + H2O with a yield of 0.8 ± 0.1, and (ii) ˙OH + CH3OOH → HCHO + ˙OH + H2O with a yield of 0.2 ± 0.1. The calculated reaction enthalpies are within 0.2 kcal mol−1 of the benchmark ATcT values. Overall thermal rate coefficients obtained from first principles are found to be in the low-pressure limit at atmospheric pressure; the total rate coefficient can be expressed over the T = 200–450 K range as k(T) = 5.0 × 10−12 × T−0.152 × exp(287/T) cm3 s−1, strongly supporting the experimental results of Vaghjiani and Ravishankara (J. Phys. Chem. 1989, 93, 1948), with which this expression agrees within ca. 15%. The current results show that (i) is the principal reaction channel and support the view that, due to its inherently fast transformations, CH3OOH is an important redistribution species for HOx˙ radicals in the Earth's atmosphere. [ABSTRACT FROM AUTHOR]

Knowledge of postfire residuals in boreal forest landscapes is increasingly important for ecological applications and forest management. While many studies provide useful insight, knowledge of stand-scale postfire residual occurrence and variability remains fragmented and untested as formal hypotheses. We examined the spatial variability of stand-scale postfire residuals in boreal forests and tested hypotheses of their spatial associations. Based on the literature, we hypothesized that preburn forest cover characteristics, site conditions, proximity to water and fire edge, and local fire intensity influence the spatial variability of postfire residuals. To test these hypotheses, we studied live-tree and snag residuals in 11 boreal Ontario forest fires, using 660 sample points based on high resolution photography (1:408) captured immediately after the fires. The abundance of residuals varied considerably within and among these fires, precluding attempts to generalize estimates. Based on a linear mixed-effects model, our data did not support the hypotheses that preburn forest cover characteristics, site conditions, and proximity to water significantly affect the spatial variability of stand-scale residuals. The results do indicate, however, that stand-scale residual variability is associated with local fire intensity (strongly) and distance to fire edge (weakly). La connaissance des residus apres feu dans les paysages forestiers boreaux prend de plus en plus d'importance pour les applications ecologiques et l'amenagement forestier. Meme si plusieurs etudes fournissent des renseignements utiles, la connaissance de la presence et de la variabilite des residus apres feu a (echelle du peuplement demeure fragmentee et n'a pas ete testees sous forme d'hypotheses formelles. Nous avons etudie la variabilite spatiale des residus apres feu a (echelle du peuplement en foret boreale et nous avons teste des hypotheses reliees a leurs relations spatiales. S'appuyant sur la litterature, nous avons pose l'hypothese que la variabilite spatiale des residus apres feu est influencee par les caracteristiques du couvert anterieur au feu, les conditions de la station, la proximite de Peau et de la limite du feu, et l'intensite locale du feu. Pour tester ces hypotheses, nous avons etudie les arbres vivants et les chicots residuels a la suite de feux survenus dans 11 peuplements boreaux de l'Ontario a l'aide des photographies a haute resolution (1 : 408) de 660 points d'echantillonnage prises immediatement apres le feu. L'abondance des residus variait considerablement a l'interieur et entre les feux, excluant toute tentative de generaliser les estimations. En se basant sur un modele lineaire a effets mixtes, nos donnees n'ont pas confirme les hypotheses selon lesquelles les caracteristiques du couvert anterieur au feu, les conditions de la station et la proximite de l'eau influencent la variabilite spatiale des residus a l'echelle du peuplement. Cependant, les resultats indiquent que la variabilite residuelle a l'echelle du peuplement est associee a l'intensite locale du feu (lien fort) et a la distance de la limite du feu (lien faible). [Traduit par la Redaction], Introduction Forest fires are frequent in boreal North America, burning over 7 x [10.sup.-6] ha annually in Canada alone (Van Wagner 1988), and are considered a major cause of forest [...]

The structure, spectra, and rearrangement mechanisms of P[H.sub.2][F.sub.3], the first member of the P[H.sub.n][F.sub.5-n] series and a prototype for molecules that undergo rotational isomerism, are analyzed. The results have identified the spectral fingerprints that could distinguish various rotational isomers that could form a powerful basis for the characterization of various rotational isomers of P[H.sub.2][F.sub.3] when used along with high resolution measurements.

The accuracy of the density of wave function methods and Kohn-Sham (KS) density functionals is studied using moments of the density, = fp(r) rnd τ = F0∞ 4лr2 p(r)rndr, where n = -1, -2, 0, 1, 2, and 3 provides information about the short- and long-range behavior of the density. Coupled cluster (CC) singles, doubles, and perturbative triples (CCSD(T)) is considered as the reference density. Three test sets are considered: boron through neon neutral atoms, two and four electron cations, and 3d transition metals. The total density and valence only density are distinguished by dropping appropriate core orbitals. Among density functionals tested, CAMQTP00 and !B97x show the least deviation for boron through neon neutral atoms. They also show accurate eigenvalues for the HOMO indicating that they should have a more correct long-range behavior for the density. For transition metals, some density functional approximations outperform some wave function methods, suggesting that the KS determinant could be a better starting point for some kinds of correlated calculations. By using generalized many-body perturbation theory (MBPT), the convergence of second-, third and fourth-order KS-MBPT for the density is addressed as it converges to the infinite-order coupled cluster result. For the transition metal test set, the deviations in the KS density functional theory methods depend on the amount of exact exchange the functional uses. Functionals with exact exchange close to 25% show smaller deviations from the CCSD(T) density. [ABSTRACT FROM AUTHOR]

Coupled cluster (CC) theory is widely accepted as the most accurate and generally applicable approach in quantum chemistry. CC calculations are usually performed with single Slater-determinant references, e.g., canonical Hartree-Fock (HF) wavefunctions, though any single determinant can be used. This is an attractive feature because typical CC calculations are straightforward to apply, as there is no potentially ambiguous user input required. On the other hand, there can be concern that CC approximations give unreliable results when the reference determinant provides a poor description of the system of interest, i.e., when the HF or any other single determinant ground state has a relatively low weight in the full CI expansion. However, in many cases, the reported "failures" of CC can be attributed to an unfortunate choice of reference determinant, rather than intrinsic shortcomings of CC itself. This is connected to well-known effects like spin-contamination, wavefunction instability, and symmetry-breaking. In this contribution, a particularly difficult singlet/triplet splitting problem in two phenyldinitrene molecules is investigated, where CC with singles, doubles and perturbative triples [CCSD(T)] was reported to give poor results. This is analyzed by using different reference determinants for CCSD(T), as well as performing higher level CCSDT-3 and CCSDT calculations. We show that doubly electron attached and doubly ionized equation-of-motion (DEA/DIP-EOM) approaches are powerful alternatives for treating such systems. These are operationally single-determinant methods that adequately take the multi-reference nature of these molecules into account. Our results indicate that CC remains a powerful tool for describing systems with both static correlation and dynamic correlation, when pitfalls associated with the choice of the reference determinant are avoided. [ABSTRACT FROM AUTHOR]

A method of calculation of excited states with spin-orbit couplings, which utilizes left and right eigenvectors of equation-of-motion coupled-cluster singles and doubles model has been formulated and implemented. The spin-orbit interactions are introduced by using the spin-orbit mean field approximation of the Briet-Pauli Hamiltonian. In order to evaluate all the necessary matrix elements, a scheme based on the diagrammatic representation of the second-quantized form of the spin-orbit interaction operator and the standard rules of second-quantized algebra is presented. We posit that this scheme is general and much simpler to use than the often used rules derived for the configuration state functions by using theWigner-Eckart theorem. We show that the spin-orbit coupled states (i.e., target relativistic states) must satisfy specific conditions in order to classify them according to the double group symmetry. This interrelation between the structure of the target relativistic states and its double group symmetry is discussed in detail. An algorithm to classify the target states according to the irreducible representation of the double group symmetry is offered and implemented. Numerical tests for several atoms and molecules show good agreement of predicted and experimental spin-orbit splittings of the target excited states. [ABSTRACT FROM AUTHOR]

We present a parallel implementation to compute electron spin resonance g-tensors at the coupledcluster singles and doubles (CCSD) level which employs the ACES III domain-specific software tools for scalable parallel programming, i.e., the super instruction architecture language and processor (SIAL and SIP), respectively. A unique feature of the present implementation is the exact (not approximated) inclusion of the five one- and two-particle contributions to the g-tensor [i.e., the mass correction, one- and two-particle paramagnetic spin-orbit, and one- and two-particle diamagnetic spin-orbit terms]. Like in a previous implementation with effective one-electron operators [J. Gauss et al., J. Phys. Chem. A 113, 11541-11549 (2009)], our implementation utilizes analytic CC second derivatives and, therefore, classifies as a true CC linear-response treatment. Therefore, our implementation can unambiguously appraise the accuracy of less costly effective one-particle schemes and provide a rationale for their widespread use. We have considered a large selection of radicals used previously for benchmarking purposes including those studied in earlier work and conclude that at the CCSD level, the effective one-particle scheme satisfactorily captures the two-particle effects less costly than the rigorous two-particle scheme. With respect to the performance of density functional theory (DFT), we note that results obtained with the B3LYP functional exhibit the best agreement with our CCSD results. However, in general, the CCSD results agree better with the experimental data than the best DFT/B3LYP results, although in most cases within the rather large experimental error bars. [ABSTRACT FROM AUTHOR]

Simplifications or modifications of coupled cluster methods such as the CCSD (coupled cluster singles and doubles) model often perform better than the original method in providing the total energy, equilibrium geometries, and harmonic vibration frequencies for the ground state. Three such methods that have been recently proposed include 2CC, parameterized CCSD generalizations, and distinguishable cluster singles and doubles (DCSD) approach. In this paper, we lay the theoretical foundation needed to treat excited states via the equation of motion (EOM) approach using these ground state CC methods. As these ground state approximations to CCSD share its property of being exact for two-electron systems, so will their excited state extensions. These methods are tested for two complementary benchmark sets of excited states for a wide range of organic molecules with focus on singlet and triplet excited states of both valence and Rydberg nature. We also test these methods for doubly excited states, taking CH+ as an example to test their performance at equilibrium and stretched bond geometries. Finally, we assess if any of these methods perform consistently better than EOM CCSD. [ABSTRACT FROM AUTHOR]

Three-bond 15N-31P coupling constants, J(super 3h)(N15-31P), across N-H...O-P hydrogen bonds is measured in model cationic and anionic complexes by applying equation-of-motion coupled cluster singles and doubles (EOM-CCSD) calculations.

A method of calculation of static polarizabilities with wavefunctions, corresponding to linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] model, has been formulated and implemented. For the proper description of the response of system on applied electric field, modified ansatz is introduced for geminal part of cluster operators. Such extension of CCSD(F12) model provides balanced description of both perturbed and unperturbed wave functions, what leads to the increase of the accuracy of target polarizabilities. As a part of algorithm, explicitly correlated version of coupled-perturbed CCSD equations has also been derived and implemented. Numerical tests conducted for the set of eight molecules show good agreement between static polarizabilities, calculated with developed explicitly correlated approach and corresponding complete basis set results in regular CCSD already at triple-ζ level. [ABSTRACT FROM AUTHOR]

The accurate determination of the preferred Si12C12 isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for the opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies, and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC3 to Si12C12. It is found that post-MBPT(2) correlation energy plays a significant role in obtaining converged relative isomer energies, suggesting that predictions using low rung density functional methods will not have adequate accuracy. Utilizing the best composite coupled-cluster energy that is still computationally feasible, entailing a 3-4 SCF and coupled-cluster theory with singles and doubles extrapolation with triple-ζ (T) correlation, the closo Si12C12 isomer is identified to be the preferred isomer in the support of previous calculations [X. F. Duan and L. W. Burggraf, J. Chem. Phys. 142, 034303 (2015)]. Additionally we have investigated more pragmatic approaches to obtaining accurate silicon carbide isomer energies, including the use of frozen natural orbital coupled-cluster theory and several rungs of standard and double-hybrid density functional theory. Frozen natural orbitals as a way to compute post-MBPT(2) correlation energy are found to be an excellent balance between efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Obtaining the correct potential energy curves for the dissociation of multiple bonds is a challenging problem for ab initio methods which are affected by the choice of a spin-restricted reference function. Coupled cluster (CC) methods such as CCSD (coupled cluster singles and doubles model) and CCSD(T) (CCSD + perturbative triples) correctly predict the geometry and properties at equilibrium but the process of bond dissociation, particularly when more than one bond is simultaneously broken, is much more complicated. New modifications of CC theory suggest that the deleterious role of the reference function can be diminished, provided a particular subset of terms is retained in the CC equations. The Distinguishable Cluster (DC) approach of Kats and Manby [J. Chem. Phys. 139, 021102 (2013)], seemingly overcomes the deficiencies for some bond-dissociation problems and might be of use in quasi-degenerate situations in general. DC along with other approximate coupled cluster methods such as ACCD (approximate coupled cluster doubles), ACP-D45, ACP-D14, 2CC, and pCCSD(α, β) (all defined in text) falls under a category of methods that are basically obtained by the deletion of some quadratic terms in the double excitation amplitude equation for CCD/CCSD (coupled cluster doubles model/coupled cluster singles and doubles model). Here these approximate methods, particularly those based on the DC approach, are studied in detail for the nitrogen molecule bond-breaking. The N2 problem is further addressed with conventional single reference methods but based on spatial symmetry-broken restricted Hartree-Fock (HF) solutions to assess the use of these references for correlated calculations in the situation where CC methods using fully symmetry adapted SCF solutions fail. The distinguishable cluster method is generalized: 1) to different orbitals for different spins (unrestricted HF based DCD and DCSD), 2) by adding triples correction perturbatively (DCSD(T)) and iteratively (DCSDT-n), and 3) via an excited state approximation through the equation of motion (EOM) approach (EOM-DCD, EOM-DCSD). The EOM-CC method is used to identify lower-energy CC solutions to overcome singularities in the CC potential energy curves. It is also shown that UHF based CC and DC methods behave very similarly in bond-breaking of N2, and that using spatially broken but spin preserving SCF references makes the CCSD solutions better than those for DCSD. [ABSTRACT FROM AUTHOR]