High-level Coupled-cluster Methods Research Articles

Benchmark Study of Core-Ionization Energies with the Generalized Active Space-Driven Similarity Renormalization Group.

X-ray photoelectron spectroscopy (XPS) is a powerful experimental technique for probing the electronic structure of molecules and materials; however, interpreting XPS data requires accurate computational methods to model core-ionized states. This work proposes and benchmarks a new approach based on the generalized active space-driven similarity renormalization group (GAS-DSRG) for calculating core-ionization energies and treating correlation effects at the perturbative and nonperturbative levels. We tested the GAS-DSRG across three data sets. First, the vertical core-ionization energies of small molecules containing first-row elements are evaluated. GAS-DSRG achieves mean absolute errors below 0.3 eV, which is comparable to high-level coupled cluster methods. Next, the accuracy of GAS-DSRG is evaluated for larger organic molecules using the CORE65 data set, with the DSRG-MRPT3 level yielding a mean absolute error of only 0.34 eV for 65 core-ionization transitions. Insights are provided into the treatment of static and dynamic correlation, the importance of high-order perturbation theory, and notable differences from density functional theory in the predicted energy ordering of core-ionized states for specific molecules. Finally, vibrationally resolved XPS spectra of diatomic molecules (CO, N2, and O2) are simulated, showing excellent agreement with experimental data.

Excited-state downfolding using ground-state formalisms

Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau reference determinants, paving the way for applications of quantum computing in excited-state chemistry. This study focuses on doubly excited states for which canonical equation-of-motion CC approaches struggle to describe unless one includes higher-than-double excitations. The downfolding technique results in state-specific effective Hamiltonians that, when diagonalized in their respective active spaces, provide ground- and excited-state total energies (and therefore excitation energies) comparable to high-level CC methods. The performance of this procedure is examined with doubly excited states of H2, Methylene, Formaldehyde, and Nitroxyl.

Computational Study on Chemoselective Difunctionalization of Unactivated Alkenes with Radical-mediated Remote Functional Group Migration.

A computational study of the radical-mediated chemoselective difunctionalization of the tertiary alcohol substituted aliphatic alkenes is carried out employing density functional theory (DFT) and high-level coupled-cluster methods, such as coupled-cluster singles and doubles with perturbative triples [DLPNO-CCSD(T)]. Our results indicate that the cyclic vinyl radical plays an important role in the progression of the reactions. Our computations demonstrated that the chemoselective difunctionalization of unactivated alkenes with radical-mediated remote functional group migration is suitable for the 5- and 6-exo-dig cyclization, as opposite to 3- and 4-exo-dig cyclization suffering from cyclic intermediate with high energy. Our results show that the migration of nitrile group is more preferable than that of alkynyl group for the molecules including both cyano group and alkynyl group. For the 5- and 6-exo-dig cyclization, the rate-determining step is the homolysis of the C-C σ-bond in the cyclic intermediate, which results in the hydroxyl alkyl radical.

Linear-Scaling Systematic Molecular Fragmentation Approach for Perturbation Theory and Coupled-Cluster Methods.

The coupled-cluster (CC) singles and doubles with perturbative triples [CCSD(T)] method is frequently referred to as the “gold standard” of modern computational chemistry. However, the high computational cost of CCSD(T) [O(N7)], where N is the number of basis functions, limits its applications to small-sized chemical systems. To address this problem, efficient implementations of linear-scaling coupled-cluster methods, which employ the systematic molecular fragmentation (SMF) approach, are reported. In this study, we aim to do the following: (1) To achieve exact linear scaling and to obtain a pure ab initio approach, we revise the handling of nonbonded interactions in the SMF approach, denoted by LSSMF. (2) A new fragmentation algorithm, which yields smaller-sized fragments, that better fits high-level CC methods is introduced. (3) A modified nonbonded fragmentation scheme is proposed to enhance the existent algorithm. Performances of the LSSMF-CC approaches, such as LSSMF-CCSD(T), are compared with their canonical versions for a set of alkane molecules, CnH2n+2 (n = 6–10), which includes 142 molecules. Our results demonstrate that the LSSMF approach introduces negligible errors compared with the canonical methods; mean absolute errors (MAEs) are between 0.20 and 0.59 kcal mol–1 for LSSMF(3,1)-CCSD(T). For a larger alkanes set (L12), CnH2n+2 (n = 50–70), the performance of LSSMF for the second-order perturbation theory (MP2) is investigated. For the L12 set, various bonded and nonbonded levels are considered. Our results demonstrate that the combination of bonded level 6 with nonbonded level 2, LSSMF(6,2), provides very accurate results for the MP2 method with a MAE value of 0.32 kcal mol–1. The LSSMF(6,2) approach yields more than a 26-fold reduction in errors compared with LSSMF(3,1). Hence, we obtain substantial improvements over the original SMF approach. To illustrate the efficiency and applicability of the LSSMF-CCSD(T) approach, we consider an alkane molecule with 10,004 atoms. For this molecule, the LSSMF(3,1)-CCSD(T)/cc-pVTZ energy computation, on a Linux cluster with 100 nodes, 4 cores, and 5 GB of memory provided to each node, is performed just in ∼24 h. As a second test, we consider a biomolecular complex (PDB code: 1GLA), which includes 10,488 atoms, to assess the efficiency of the LSSMF approach. The LSSMF(3,1)-FNO–CCSD(T)/cc-pVTZ energy computation is completed in ∼7 days for the biomolecular complex. Hence, our results demonstrate that the LSSMF-CC approaches are very efficient. Overall, we conclude the following: (1) The LSSMF(m, n)-CCSD(T) methods can be reliably used for large-scale chemical systems, where the canonical methods are not computationally affordable. (2) The accuracy of bonded level 3 is not satisfactory for large chemical systems. (3) For high-accuracy studies, bonded level 5 (or higher) and nonbonded level 2 should be employed.

From Molecules with a Planar Tetracoordinate Carbon to an Astronomically Known C5H2 Carbene

Ethynylcyclopropenylidene (2), an isomer of C5H2, is a known molecule in the laboratory and has recently been identified in Taurus Molecular Cloud-1 (TMC-1). Using high-level coupled-cluster methods up to the CCSDT(Q)/CBS level of theory, it is shown that two isomers of C5H2 with a planar tetracoordinate carbon (ptC) atom, (SP-4)-spiro[2.2]pent-1,4-dien-1,4-diyl (11) and (SP-4)-spiro[2.2]pent-1,4-dien-1,5-diyl (13), serve as the reactive intermediates for the formation of 2. Here, a theoretical connection has been established between molecules containing ptC atoms (11 and 13) and a molecule (2) that is present nearly 430 light years away, thus providing evidence for the existence of ptC species in the interstellar medium. The reaction pathways connecting the transition states and the reactants and products have been confirmed by intrinsic reaction coordinate calculations at the CCSDT(Q)/CBS//B3LYP-D3BJ/cc-pVTZ level. While isomer 11 is non-polar (μ = 0), isomers 2 and 13 are polar, with dipole moment values of 3.52 and 5.17 Debye at the CCSD(T)/cc-pVTZ level. Therefore, 13 is also a suitable candidate for both laboratory and radioastronomical studies.

Accuracy of the distinguishable cluster approximation for triple excitations for open-shell molecules and excited states.

The distinguishable cluster approximation for triple excitations has been applied to calculate thermochemical properties and excited states involving closed-shell and open-shell species, such as small molecules, 3d transition metal atoms, ozone, and an iron-porphyrin model. Excitation energies have been computed using the ΔCC approach by directly optimizing the excited states. A fixed-reference technique has been introduced to target selected spin-states for open-shell molecular systems. The distinguishable cluster approximation consistently improves coupled cluster with singles doubles and triples results for absolute and relative energies. For excited states dominated by a single configuration state function, the fixed-reference approach combined with high-level coupled-cluster methods has a comparable accuracy to the corresponding equation-of-motion coupled-cluster methods with a negligible amount of spin contamination.

A computational study of the reaction mechanism of 2,2-azobis(isobutyronitrile)-initiated oxidative cleavage of geminal alkenes.

A computational study of 2,2-azobis(isobutyronitrile) (AIBN)-initiated aerobic oxidative cleavage of alkenes is carried out employing density functional theory (DFT) and high-level coupled-cluster methods, such as coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. Our computations show that the barriers for the formation of dioxetane derivatives suggested by Xu and co-workers (J. Org. Chem., 2014, 79, 7220-7225) for the reaction mechanism of aerobic oxidative cleavage of alkenes are computed to be higher than 65 kcal mol-1. This barrier is relatively high under the reaction conditions. Our results for the Xu mechanism indicate that the reaction does not proceed via the formation of a dioxetane ring under the reaction conditions. Our results demonstrate that the reaction of aerobic oxidative cleavage of geminal alkenes in the presence of AIBN is initiated by the peroxyl radical 9, contrary to the isobutyronitrile radical 2. Our results show that the 2-(2-hydroxyl-1,1-diarylethoxy)-2-methylpropanenitrile radical (15) does not appear throughout the reaction scheme and the reaction progresses over the 2-(2-hydroxyl-2,2-diarylethoxy)-2-methylpropanenitrile radical (13) rather than the 2-(2-hydroxyl-1,1-diarylethoxy)-2-methylpropanenitrile radical (15). Our results are in agreement with the experimental results for the aerobic oxidative cleavage of the geminal disubstituted alkenes. Our results also demonstrate that the epoxide derivatives can be formed as an intermediate under the reaction conditions. This reaction is not applicable for pyridine derivatives due to the conversion of vinylpyridine derivatives to N-oxide derivatives.

A computational study for the reaction mechanism of metal-free cyanomethylation of aryl alkynoates with acetonitrile.

A computational study of metal-free cyanomethylation and cyclization of aryl alkynoates with acetonitrile is carried out employing density functional theory and high-level coupled-cluster methods, such as coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. Our results indicate that the reaction of aryl alkynoates with acetonitrile in the presence of tert-butyl peroxybenzoate (TBPB) under metal-free conditions tends to proceed through cyanomethylation, spirocyclization and ester migration of the kinetically favoured coumarin derivatives. 1,2-Ester migration in the spiro-radical intermediate 10 does not proceed via the formation of the carboxyl radical 11 suggested by Sun and co-workers. Our results also demonstrate that the t-butoxy radical is substantially responsible the formation of the cyanomethyl radical by the abstraction of a hydrogen atom from acetonitrile.

Computational Study for the Reaction Mechanism of N-Hydroxyphthalimide-Catalyzed Oxidative Cleavage of Alkenes.

A computational study of N-hydroxyphthalimide-catalyzed aerobic oxidative cleavage of alkenes is carried out employing density functional theory and high-level coupled-cluster methods, such as coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. Our results demonstrate that the reaction proceeds through the alkoxyl radicals, as opposed to the mechanism suggested by Jiao and co-workers (Org. Lett. 2012, 14, 4158-4161), in which the reaction proceeds via formation of the dioxetane ring. The barriers for the formation of dioxetane derivatives are computed to be higher than 50 kcal mol-1, while the barriers for the formation of alkoxyl radicals are as low as 13 kcal mol-1. Our results also demonstrate that epoxide derivatives can be formed as intermediates or byproducts under the reaction conditions.

Theoretical Studies of SiC4H2 Isomers Delineate Three Low-Lying Silylidenes Are Missing in the Laboratory.

Eleven isomers of SiC4H2 lying within 50 kcal mol-1 have been theoretically investigated using density functional theory and high-level coupled-cluster methods. Among them, four isomers, 1-ethynyl-3-silacycloprop-1(2)-en-3-ylidene (1), diethynylsilylidene (2), 1-sila-1,2,3,4-pentatetraenylidene (4), and 1,3-butadiynylsilylidene (5), have already been identified in the laboratory. The current investigation reports three low-lying (<1 eV) silylidenes [2-methylenesilabicyclo[1.1.0]but-1(3)-en-4-ylidene (3), 4-sila-2-methylenebicyclo[1.1.0]but-1(3)-en-4-ylidene (6), and 3-ethynyl-1-silapropadienylidene (7)] and three high-lying (>1 eV) silylidenes [2-sila-(didehydrovinylidene)cyclopropene (8), an isomer with a planar tetracoordinate carbon (ptC) atom (10), and 1-ethynyl-1-silapropadienylidene (11)], which remain elusive in the laboratory to date. Isomer 9 also contains a ptC atom, which turned out to be a transition state at all levels. Though all isomers are polar (μ ≠ 0), rotational spectrum is available only for 4. Using matrix isolation, three isomers (1, 2, and 5) have been trapped in the laboratory at 10 K. Considering the astrochemical relevance of silicon-carbide clusters in the interstellar medium, the current theoretical data demand new molecular spectroscopic studies on SiC4H2. Surprisingly, unlike the isovalent C5H2 isomers, where the bent carbenes are yet to be identified in the laboratory, the bent silylidenes (2 and 5) have been trapped in the case of SiC4H2. In both the cases, molecules with transannular C-C and/or Si-C bonds remain elusive, though they lie in the low-lying region. Using suitable precursors, whether these peculiar geometries (especially 3 and 6) would be identified or not in the laboratory needs to be addressed by molecular spectroscopists. The present investigation documents structural and spectroscopic information of SiC4H2 isomers, which may compliment future molecular spectroscopic observations including radioastronomical searches.

Diffusion quantum Monte Carlo calculations with a recent generation of effective core potentials for ionization potentials and electron affinities

Pseudopotentials are an essential ingredient in diffusion quantum Monte Carlo (DMC) calculations to increase efficiency substantially. A new generation of effective core potentials (ccECP) has been recently developed for DMC calculations. In this paper, performance of DMC using ccECP potentials on total energies, ionization potentials (IPs) and electron affinities (EAs) of some second- and third-row atoms and molecules is investigated systematically with different types of trial wave functions. DMC results are compared with those of high-level coupled-cluster methods extrapolated to complete basis set limit (CC-CBS). Error of ccECP potentials on IPs and EAs is also evaluated through a comparison with those from all-electron calculations. Our results show that mean errors in DMC energies with the ccECP potentials are smaller than those with the pseudopotentials developed by Burkatzki, Filippi, and Dolg (BFD), when the same type of trial wave functions is adopted. Mean absolute deviations (MADs) on IPs of DMC compared with those of CC-CBS are about 1.6 kcal/mol with single-determinant-Jastrow trial wave functions, and 1 kcal/mol with multideterminant-Jastrow trial wave functions using either ccECP or BFD potentials. MADs on EAs with DMC using the ccECP potentials are about 1 kcal/mol and slightly larger than those with the BFD potentials. Our results show that ccECP potentials are able to provide reliable IPs and EAs in DMC calculations. Accuracy of IPs and EAs from DMC calculations using ccECP potentials is similar to that with the BFD potentials, although mean error in total DMC energies with ccECP potentials is smaller. Furthermore, error of ccECP potentials in DMC calculations on IPs and EAs is smaller than that of BFD potentials compared with all-electron results.

Molecular interactions in electron-groups embedding generalized valence bond picture

Theoretical description of molecular interactions remains a challenge for computational chemistry. In particular, systems dominated by static correlation, in which bonds are stretched or twisted, are often beyond capabilities of methods based on a single-electron approximation, being usually a method of choice. For interacting multireference systems, it is necessary to apply either high-level coupled-cluster methods (which however include multireference effects only partially) or base the theoretical description on a multireference wavefunction. Popular multireference methods like CASPT2 (complete active space perturbation theory) do not provide satisfactory results since they may suffer from problems with size consistency and poor accuracy. Recently we have shown that combining a simple multireference wavefunction, perfect-pairing generalized valence bond (GVB) with extended random phase approximation in embedding framework (EERPA) leads to a method EERPA-GVB providing accurate results for challenging multireference systems. In this paper, good performance of EERPA-GVB is confirmed by its application to van der Waals and hydrogen-bonded complexes. In addition, we show that the decomposition of the EERPA-GVB correlation energy into contributions from pairs of geminals can provide useful insight into the investigated interactions.

High-Level Ab Initio Calculations of Intermolecular Interactions: Heavy Main-Group Element π-Interactions.

This work reports high-level ab initio calculations and a detailed analysis on the nature of intermolecular interactions of heavy main-group element compounds and π systems. For this purpose we have chosen a set of benchmark molecules of the form MR3 , in which M=As, Sb, or Bi, and R=CH3 , OCH3 , or Cl. Several methods for the description of weak intermolecular interactions are benchmarked including DFT-D, DFT-SAPT, MP2, and high-level coupled cluster methods in the DLPNO-CCSD(T) approximation. Using local energy decomposition (LED) and an analysis of the electron density, details of the nature of this interaction are unraveled. The results yield insight into the nature of dispersion and donor-acceptor interactions in this type of system, including systematic trends in the periodic table, and also provide a benchmark for dispersion interactions in heavy main-group element compounds.

Thioformaldehyde S-Sulfide, Sulfur Analogue of the Criegee Intermediate: Structures, Energetics, and Rovibrational Analysis.

The ephemeral Criegee intermediate, first postulated over 70 years ago, has only recently been isolated in the gas phase. The sulfur analogue of this canonical zwitterion, thioformaldehyde S-sulfide, has eluded similar analysis; however, argon matrix isolation has been achieved ( Angew. Chem., Int. Ed. 2001 , 40 , 393 - 396 ). Here thioformaldehyde S-sulfide and its valence isomer dithiirane are examined with high-level coupled-cluster methods, including the minimum-energy pathway for interconversion. Relative enthalpies calculated from extrapolated energies at the complete basis set limit of the full CCSDTQ method are reported. Isomerization from thioformaldehyde S-sulfide to the lower-lying dithiirane (-7.2 kcal mol-1) is predicted to include a 27.0 kcal mol-1 barrier. Harmonic and anharmonic vibrational frequencies are also predicted using second-order vibrational perturbation theory. These results should aid in future gas-phase identification.

Conformational properties of 1-cyano-1-silacyclohexane, C5H10SiHCN: Gas electron diffraction, low-temperature NMR and quantum chemical calculations

The conformational preference of the cyano group of the 1-cyano-1-silacyclohexane was studied experimentally by means of gas electron diffraction (GED) and dynamic nuclear magnetic resonance (DNMR) as well as by quantum chemical (QC) calculations applying high-level coupled cluster methods as well as DFT methods. According to the GED experiment, the compound exists in the gas-phase as a mixture of two conformers possessing the chair conformation of the six-membered ring and Cs symmetry while differing in the axial or equatorial position of the substituent (axial = 84(12) mol %/equatorial = 16(12) mol %) at T = 279(3) K, corresponding to an A value (Gax – Geq) of −1.0(4) kcal mol−1. Gas-phase CCSD(T) calculations predict an A value of −0.72 kcal mol−1 at 279 K. In contrast, the low-temperature 13C NMR experiments resulted in an axial/equatorial ratio of 35/65 mol % at 120 K corresponding to an A value of 0.14 kcal mol−1. An average value for ΔG#e→a = 5.6 ± 0.1 kcal mol−1 was obtained for the temperature range 110–145 K. The dramatically different conformational behaviour in the gas-phase (GED) compared to the liquid phase (DNMR) suggests a strong solvation effect. According to natural bond orbital analysis the axial conformer of the title compound is an example of stabilization of a form, which is not favored by electrostatic effects and is favored predominantly by steric and conjugation effects.

Theoretical Study of Reaction of Ketene with Water in the Gas Phase: Formation of Acetic Acid?

Production of acetic acid via gas-phase hydration of ketene by water (uncatalyzed and in the presence of an additional water molecule) was theoretically characterized using high-level coupled-cluster methods, followed by a two-dimensional master equation analysis to compute thermal reaction rate constants. The results show that the formation of acetic acid quite likely occurs in high-temperature combustion of biomass, but that the rate of formation should be negligible under ambient atmospheric conditions.

On the Photodetachment from the Green Fluorescent Protein Chromophore

Motivated by the discrepancies in recent experimental and theoretical studies of photodetachment from isolated model chromophores of the green fluorescent protein (GFP), this study reports calculations of the electron detachment energies and photoelectron spectra of the phenolate and deprotonated p-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI) anions. The spectra were computed using double-harmonic parallel normal mode approximation. High-level coupled-cluster methods as well as density functional theory were used to compute vertical and adiabatic detachment energies of the phenolate anion serving as a model system representing anionic GFP-like chromophores (HBDI). The benchmark calculations reveal that the basis set has significant effect on the computed detachment energies, whereas the results are less sensitive to the level of electron correlation treatment. At least aug-cc-pVTZ basis set is required. The best ωB97X-D and CCSD(T) estimates of phenolate's adiabatic detachment energy are 2.12 and 2.19 eV; these values are very close to the experimental value, 2.253 eV [Gunion et al. Int. J. Mass Spectrom. Ion Proc. 1992, 117, 601]. The best estimate of the vertical detachment energy of deprotonated HBDI is 2.76 eV, which supports bound character of the bright excited state in the Franck-Condon region. The most intense transition in the computed photoelectron spectra of both phenolate and deprotonated HBDI is the 0-0 S0-D0 transition, which is 0.11 eV below vertical detachment energy. Therefore, the position of the maximum of the photoelectron spectrum does not represent vertical detachment energy, and the direct comparison between theory and experiment must involve spectrum modeling.

The Beryllium Pentamer: Trailing an Uneven Sequence of Dissociation Energies

Recent high-resolution spectroscopic studies by Merritt, Bondybey, and Heaven (Science 2009, 324, 1548) have heightened the anticipation that small beryllium clusters will soon be observed in the laboratory. Beryllium clusters are important discrete models for the theoretical study of metals. The trigonal bipyramidal Be(5) molecule is studied using high-level coupled cluster methods. We obtain the optimized geometry, atomization and dissociation energies, and vibrational frequencies. The c~CCSDT(Q) method is employed to compute the atomization and dissociation energies. In this approach, complete basis set (CBS) extrapolations at the CCSD(T) level of theory are combined with an additive correction for the effect of iterative triple and perturbative quadruple excitations. Harmonic vibrational frequencies are obtained using analytic gradients computed at the CCSD(T) level of theory. We report an atomization energy of 129.6 kcal mol(-1) at the trigonal bipyramid global minimum geometry. The Be(5)→Be(4)+Be dissociation energy is predicted to be 39.5 kcal mol(-1). The analogous dissociation energies for the smaller beryllium clusters are 64.0 kcal mol(-1) (Be(4)→Be(3)+Be), 24.2 kcal mol(-1) (Be(3)→Be(2)+Be), and 2.7 kcal mol(-1) (Be(2)→Be+Be). The trigonal bipyramidal Be(5) structure has an equatorial-equatorial bond length of 2.000 Å and an axial-equatorial distance of 2.060 Å. Harmonic frequencies of 730, 611, 456, 583, 488, and 338 cm(-1) are obtained at the CCSD(T)/cc-pCVQZ level of theory. Quadruple excitations are found to make noticeable contributions to the energetics of the pentamer, which exhibits a significant level of static correlation.

Symmetry breaking in the cyclic C3C2H radical

We have employed high-level coupled cluster methods including connected triple excitations to study the possibility of symmetry-breaking in the (2)B(2) ground state of the c-C(3)C(2)H radical. Specifically, we find that spin-restricted open-shell Hartree-Fock (ROHF) reference orbitals yield a C(2v) structure, whereas spin-unrestricted Hartree-Fock (UHF) and Brueckner orbitals lead to a symmetry-broken C(s) minimum-energy geometry. Equation-of-motion coupled cluster singles and doubles method for ionized states yields a C(s) structure with a double-zeta basis set, but not with a triple-zeta basis set. Through a detailed analysis of the orbital instability/near-instability behavior of each type of Hartree-Fock reference, we have determined that the UHF reference wave function is more reliable than the ROHF reference in this case and that the Born-Oppenheimer potential surface for c-C(3)C(2)H exhibits a symmetry broken C(s) global minimum. This result is supported by excited-state computations, which indicate that a second-order (pseudo) Jahn-Teller interaction is responsible for the symmetry-breaking.

Hartree−Fock Orbital Instabilities and Symmetry-Breaking in ScO2: Is aCsEquilibrium Structure Viable?

We have applied high-level coupled cluster methods, in conjunction with a variety of reference molecular orbitals and basis sets, to consider the possibility that the equilibrium geometry of the ground state of ScO 2 breaks C 2 v symmetry. The force constants for the antisymmetric stretching vibration (b 2 symmetry) have been computed across a domain of Sc-O bond distances and O-Sc-O bond angles at the spin-restricted open-shell Hartree-Fock (ROHF) and spin-unrestricted Hartree-Fock (UHF) levels of theory in order to investigate the importance of artifactual orbital instability envelopes on the properties computed with correlated wave functions. In most cases, Hartree-Fock instability regions are located far from the pertinent optimized geometries, suggesting that the corresponding harmonic vibrational frequencies should be free from artifactual orbital effects. Nevertheless, ROHF- and UHF-based coupled cluster models disagree qualitatively on the symmetry of ScO 2 , and Brueckner orbital based methods give variable results with respect to basis set and level of electron correlation. Although full coupled cluster single-, double-, and triple-excitation results indicate symmetry breaking with smaller basis sets, extrapolation of the results to larger basis sets is inconclusive. The current results indicate with certainty only a flat symmetry-breaking potential. Furthermore, although all methods considered here predict that C s optimized structures lie lower in energy than their C 2 v counterparts, the highest levels of theory predict very low effective barriers to interconversion of equivalent C s minimalow enough that the zero-point vibrational energy (even when computed with anharmonicity corrections) lies above the barrier leading to an overall dynamical C 2 v symmetry.