2v Structure Research Articles

Identification of the spintronic NiGaVN center in c-GaN and its qubit applications

The presence of NiGa center in cubic gallium nitride (c-GaN), a candidate material for qubit applications, has been proven through first-principles calculation and theoretical analysis. The NiGa center is composed of a nitride-vacancy (VN) and an adjacent substitutional nickel atom (NiGa) at the gallium site, possessing the same C 3v structure with the negatively charged nitrogen-vacancy center (NV– center) as the diamond. The NiGa center is a spin-triplet, existing in n-type c-GaN. Combined with the group theory, the molecular orbitals (MOs), and the electron distribution of the center were analyzed. Furthermore, regarding the optical properties of the NiGa center and maintaining spin-conserving, the electron occupation number in the MOs a 1(2) and exy could be changed, which opens up the prospects for spin manipulation in the NiGa center. As a result, the zero-phonon line is found to be relatively low (at about 0.575 eV), which means the optical excitation can be achieved at lower energy. The Stokes and anti-Stokes shifts are shown to be 240 and 153 meV, respectively. Therefore, the findings of this study provide an important basis for quantum computing and networks. In particular, combining the results of the magnetic coupling and hyperfine interaction to achieve the best characteristics of the spintronic center makes it promising for qubit application.

DFT study of molecular properties , potential energy surface and Stability of the dioxide of the group 12 M(O2): M=Zn, Cd and Hg

Two potential energy surfaces PESs in the lowest energy multiplicities triplet 3 A'' and singlet 1 A' for the dioxide of heavy metals of the group 12 Zn(O 2 ), Cd(O 2 ) and Hg(O 2 ) have been studied through DFT methods with the B3LYP functional. The core electrons of Zn (30 electrons), Cd (48 electrons) and Hg (60 electrons) are represented by pseudopotential ECP and the valences electrons are explicitly treated with the quasi-relativistic basis MWB and the full relativist basis AVTZ-PP. Both linear C ∞v and D ∞h or bent C s and cyclic C 2v structures of M(O 2 )have been considered in this work. The different pathways of dissociation and formation of M(O 2 ) and their dissociative limits M+O 2 and MO+O have been examined to discuss the stability of these molecules. Structural, spectroscopic and thermodynamic properties of stationary points are presented and compared with previous theoretical and experimental studies.

Combined crossed molecular beams and computational study on the N(2D) + HCCCN(X1Σ+) reaction and implications for extra-terrestrial environments

The reaction of the nitrogen atom (N) in its first electronically excited state (2D) with cyanoacetylene (HC3N) has been investigated under single-collision conditions by using the crossed molecular beam method with mass spectrometric detection at a collision energy of 31 kJ mol−1. With the support of electronic structure calculations, we found that this reaction proceeds via the barrierless addition of the N(2D) atom to the carbon–carbon triple bond of HC3N, followed by the formation of a cyclic intermediate adduct HC(N)CCN, which dissociates to C(N)CCN + H products or isomerises to a more stable intermediate HNCCCN by H-migration and ring-opening processes. The long-lived HNCCCN complex produces the linear 3Σg – ground state dicyanocarbene (NCCCN) radical plus atomic hydrogen through a barrierless unimolecular dissociation accompanied by a negligible competitive channel forming the NCCCN radical (1A1) with a bent C 2v structure plus H. The main product of this neutral-neutral reaction is the 3NCCCN radical that could be a potential precursor to form other nitriles (C2N2, C3N) or more complex organic species in planetary atmospheres, such as that of Titan and Pluto, in cometary comas, and in UV irradiated interstellar environments.

Electronic structures and geometries of the XF3 (X = Cl, Br, I, At) fluorides.

The potential energy surfaces of the group 17 XF3 (X = Cl, Br, I, At) fluorides have been investigated for the first time with multiconfigurational wave function theory approaches. In agreement with experiment, bent T-shaped C(2v) structures are computed for ClF3, BrF3, and IF3, while we predict that an average D(3h) structure would be experimentally observed for AtF3. Electron correlation and scalar relativistic effects strongly reduce the energy difference between the D(3h) geometry and the C(2v) one, along the XF3 series, and in the X = At case, spin-orbit coupling also slightly reduces this energy difference. AtF3 is a borderline system where the D(3h) structure becomes a minimum, i.e., the pseudo-Jahn-Teller effect is inhibited since electron correlation and scalar-relativistic effects create small energy barriers leading to the global C(2v) minima, although both types of effects interfere.

Relativistic coupled-cluster calculations on XeF6: Delicate interplay between electron-correlation and basis-set effects

A systematic relativistic coupled-cluster study is reported on the harmonic vibrational frequencies of the O(h), C(3v), and C(2v) conformers of XeF6, with scalar-relativistic effects efficiently treated using the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). Atomic natural orbital type basis sets recontracted for the SFX2C-1e scheme have been shown to provide rapid basis-set convergence for the vibrational frequencies. SFX2C-1e as well as complementary pseudopotential based computations consistently predicts that both O(h) and C(3v) structures are local minima on the potential energy surface, while the C(2v) structure is a transition state. Qualitative disagreement between the present results for the O(h) structure and those from CCSD(T)-F12b calculations [Peterson et al., J. Phys. Chem. A 116, 9777 (2012)], which yielded a triply degenerate imaginary frequency for the O(h) structure, is attributed here to the high sensitivity of the computed harmonic frequencies of the t(1u) bending modes to the basis-set effects of triples contributions.

The Use of Explicitly Correlated Methods on XeF6 Predicts a C3v Minimum with a Sterically Active, Free Valence Electron Pair on Xe

Explicitly correlated CCSD(T)-F12b calculations show that the lowest energy conformer of XeF(6) is the C(3v) structure with a stereoactive lone pair. The C(3v) structure is 1.08 kcal/mol below the C(2v) structure and 1.80 kcal/mol below the O(h) structure without vibrational corrections. The C(2v) conformer is a transition state connecting the different C(3v) minima on the pseudorotation potential energy surface, and the O(h) structure is a higher-order saddle point leading to the C(2v) transition states. The calculated vibrational frequencies for the C(3v) structure best fit the experimental frequencies. The calculated heats of formation for XeF(6), -62.1 ± 1.4 kcal/mol at 0 K and -64.0 ± 1.4 kcal/mol at 298 K, are the best available values and show that there are serious issues with the experimental values. The results show that the explicitly correlated CCSD(T)-F12b method can be used to address important electronic structure issues with smaller basis sets.

Quantum chemical studies on the enantiomerization mechanism of several [Zn(py)3(tach)]2+ derivatives

The enantiomerization mechanism of the trigonal-prismatic [Zn(py)(3)(tach)](2+) complex and several derivatives has been studied by applying DFT calculations (B3LYP/LANL2DZp). The enantiomerization pathways of [Zn(py(3)tach-X)](2+) (X = C, Si, Ge, N, P, As, O, S and Se) start from a distorted trigonal-prismatic C(3) symmetric ground state via an ideal trigonal-prismatic C(3v) structure to end up in a C(3)' symmetric image of the ground state. The activation energy and structural data of the complexes depend on electronic and steric factors. The activation barriers of the complexes decrease in the order [Zn(py(3)tach-Ge)](2+) > [Zn(py(3)tach-Si)](2+) > [Zn(py(3)tach-As)](2+) > [Zn(py(3)tach-Se)](2+) > [Zn(py(3)tach-P)](2+) > [Zn(py(3)tach-S)](2+) > [Zn(py(3)tach-C)](2+) > [Zn(py(3)tach-N)](2+) > [Zn(py(3)tach-O)](2+).

Formation and Characterization of Two Interconvertible Side-On and End-On Bonded Beryllium Ozonide Complexes

The reactions of beryllium atoms with dioxygen were reinvestigated by matrix isolation infrared absorption spectroscopy. Besides the previously reported linear OBeO and cyclic Be(2)O(2) molecules, two interconvertible beryllium ozonide complexes were prepared and characterized. The BeOBe(η(2)-O(3)) complex was formed on annealing, which is characterized to be a side-on bonded ozonide complex with a planar C(2v) structure. The BeOBe(η(2)-O(3)) complex isomerized to the BeOBe(η(1)-O(3)) isomer under visible light excitation, which is an end-on bonded ozonide complex with planar C(s) symmetry. These two isomers are interconvertible; that is, visible light induces the conversion of the side-on bonded complex to the end-on bonded isomer, and vice versa on annealing. In addition, evidence is also presented for the linear BeOBeOBe cluster.

Planarization of B7− and B12− Clusters by Isoelectronic Substitution: AlB6− and AlB11−

Small boron clusters have been shown to be planar from a series of combined photoelectron spectroscopy and theoretical studies. However, a number of boron clusters are quasiplanar, such as B(7)(-) and B(12)(-). To elucidate the nature of the nonplanarity in these clusters, we have investigated the electronic structure and chemical bonding of two isoelectronic Al-doped boron clusters, AlB(6)(-) and AlB(11)(-). Vibrationally resolved photoelectron spectra were obtained for AlB(6)(-), resulting in an accurate electron affinity (EA) for AlB(6) of 2.49 ± 0.03 eV. The photoelectron spectra of AlB(11)(-) revealed the presence of two isomers with EAs of 2.16 ± 0.03 and 2.33 ± 0.03 eV, respectively. Global minimum structures of both AlB(6)(-) and AlB(11)(-) were established from unbiased searches and comparison with the experimental data. The global minimum of AlB(6)(-) is nearly planar with a central B atom and an AlB(5) six membered ring, in contrast to that of B(7)(-), which possesses a C(2v) structure with a large distortion from planarity. Two nearly degenerate structures were found for AlB(11)(-) competing for the global minimum, in agreement with the experimental observation. One of these isomers with the lower EA can be viewed as substituting a peripheral B atom by Al in B(12)(-), which has a bowl shape with a B(9) outer ring and an out-of-plane inner B(3) triangle. The second isomer of AlB(11)(-) can be viewed as an Al atom interacting with a B(11)(-) cluster. Both isomers of AlB(11)(-) are perfectly planar. It is shown that Al substitution of a peripheral B atom in B(7)(-) and B(12)(-) induces planarization by slightly expanding the outer ring due to the larger size of Al.

Infrared Spectra of the Ethynyl Metal Hydrides Produced in Reactions of Laser-Ablated Mn and Re Atoms with Acetylene

The ethynyl metal hydride molecules (HM-C≡CH) are identified in the matrix infrared spectra from reactions of laser-ablated Mn and Re atoms with acetylene using D and (13)C isotopic substitution and density functional computed frequencies. The assignment of strong M-H as well as C≡C bond stretching product absorptions suggests oxidative C-H insertion during reagent codeposition and subsequent photolysis. The unique linear structure calculated for HMn-C≡CH is parallel to C(3v) structures found recently for Mn complexes including CH(3)-MnF.

Endohedral Beryllium Atoms in Ten-Vertex Germanium Clusters: Effect of a Small Interstitial Atom on the Cluster Geometry

Ten-vertex clusters are unusually versatile because polyhedra with 3-, 4-, and 5-fold symmetry are possible and are found in experimentally known structures. Such clusters therefore provide useful probes for subtle effects on cluster structure such as changing the electron count or introducing an interstitial atom. In this connection, DFT shows that one of the smallest possible interstitial atoms, namely beryllium, has relatively little effect on the structures of Be@Ge(10)(z) (z = +2, 0, -2, -4) clusters. Thus the same C(3v) and D(4d) polyhedra are found as the lowest energy structures for the isoelectronic pairs Be@Ge(10)(2+)/Ge(10) and Be@Ge(10)/Ge(10)(2-). Even for the more complicated potential energy surfaces of the Be@Ge(10)(2-)/Ge(10)(4-) and Be@Ge(10)(4-)/Ge(10)(6-) systems, the lowest energy structures are remarkably similar. Thus the same C(2v) structures are the global minima for both Be@Ge(10)(2-) and Ge(10)(4-). Similarly, the same slipped pentagonal prism structures are the global minima for both Be@Ge(10)(4-) and Ge(10)(6-).

Theoretical Study of the Low Lying States of Ga2X (X = P, As)

Since the low lying electronic states of Ga(2)X (X = P, As) are nearly degenerate, an accurate determination of the electronic structure of these states was incomplete in the previous works. In this study, the geometry optimization and vibrational frequency calculation have been performed at the various levels of theory, using the effective core pseudopotentials of the Ga and As atoms and the associated cc-pVTZ basis sets. The ground state of Ga(2)P is found to be the (2)A' state correlating with the (2)B(2) state in C(2v) structure, which lies 0.031 eV above the global minimum at the RCCSD(T) level. The equilibrium of the (2)A(1) state is optimized above that of the (2)B(2) state, and the (2)B(1) state, predicted previously as the ground state, has a stable minimum above the optimized geometries of the former states. Concerning the low lying states of Ga(2)As, our results confirm in general the previous studies. Because all the states of both compounds can be considered monoconfigurational around their equilibrium, the RCCSD(T) method is well adapted to acurrately describe both systems. In turn, we have applied our obtained information to analyze the Ga(2)P(-) and Ga(2)As(-) anion photoelectron spectra, to which it remains difficult to appropriately assign the low lying states of Ga(2)P and Ga(2)As. As a consequence, our analysis supports the previous assignment for Ga(2)P, but contrasts partially to that for Ga(2)As.

ChemInform Abstract: Ab initio MO Study of Diverse Si3H3+ Isomers.

Structures and energies of many Si 3 H 3 + isomers were investigated theoretically at the MP2/6-31G ∗ level. The global minimum was the classical aromatic planar D 3h structure (5). Isodesmic equations indicate the resonance stabilization energy to be half that of the analogous cyclopropenyl cation. The next lowest energy minimum, with a divalent silicon and a bridging hydrogen, also exhibits the 2π aromaticity. Five planar Si 3 H 3 + isomers display cyclic three-center-two-electron (3c-2e) delocalization, and eight minima have 3c-2e Si-H-Si bridged bonds. The planar tetracoordinated silicon and five-coordinated silicon also are represented. Eleven other minima were found within a 46 kcal/mol range. An H-bridged C 3v structure, derived from B 3 H 6 + , is 42.1 kcal/mol above the global minimum. However, for Ge, Sn, and Pb these A 3 H 3 + forms are more stable than the classical structures (5, J. Am. Chem. Soc. 1995, 117, 11361). In contrast to Si 3 H 3 + , C 3 H 3 + has only four isomers in the 189 kcal/mol range. The silicon analogues of the C 3 H 3 + acyclic structures, the prop-2-en-1-yl-3-ylidene cation and the 1-propynyl cation, are not favorable.

Photochemical and thermal isomerizations of C 2h and C 2v forms of para-benzoquinone dioxime: A matrix-isolation study

The C 2h and C 2v isomers of para-benzoquinone dioxime were studied using matrix isolation technique combined with infrared spectroscopy. The energies of these two forms were theoretically estimated (at the MP2 and CASSCF) to be nearly equal, with the C 2h isomer slightly more stable (by 1–2 kJ mol −1). Both C 2h and C 2v forms were observed in low-temperature Ar matrices. It was experimentally found that the population ratio of the two isomers depends on the conditions of preparation of the solid para-benzoquinone dioxime sample used for deposition of the matrix. UV irradiation of the matrix-isolated para-benzoquinone dioxime led to a photochemical transformation of the C 2v isomer into the C 2h form. These findings allowed separation of the infrared spectra of the two isomers. The assignment of the C 2v structure to the substrate of the phototransformation as well as identification of the C 2h photoproduct structure was achieved by comparison of the experimental IR spectra with the spectra theoretically predicted at the DFT(B3LYP)/6-31++G(d,p) level. Complementarily to the experimental observation of the C 2v → C 2h photoisomerization, the methods of computational photochemistry were employed to calculate potential energy surfaces of the ground (S 0) and the first excited singlet (S 1) electronic states of para-benzoquinone. These calculations, carried out at the CASSCF level, resulted in localization of a conical intersection between the S 0 and S 1 states. At the optimized geometry of the conical intersection point, one of the hydroxylimino groups was found to adopt a perpendicular orientation with respect to the six-membered ring, whereas the other hydroxylimino group remained coplanar with the ring.

Matrix isolation studies on the co-condensation reactions of molecular SiO and GeO: the characterisation of the novel cyclic species SiGeO2, Si2GeO3 and SiGe2O3

Matrix isolation IR studies, together with DFT calculations, have established that the co-condensation of molecular SiO and GeO in low temperature (12 K) nitrogen matrices leads to the formation of the novel silicon germanium oxide species SiGeO(2), Si(2)GeO(3) and SiGe(2)O(3) analogous to the known dimer and trimer species M(2)O(2) and M(3)O(3) (M = Si, Ge). Controlled diffusion studies in the temperature range 20-34 K result in a significant increase in trimer formation, which implies a very low activation energy for this oligomerisation step. Characteristic IR modes are assigned for all three novel mixed oxide molecules, and the DFT calculations establish that these species have cyclic C(2v) structures and provide estimates for their geometrical parameters. The significance of these results is noted in the light of current interest in the properties of mixed Si/Ge oxide systems.

Helical C2 Structure of Perfluoropentane and the C2v Structure of Perfluoropropane

Saturated hydrocarbons have structures with completely staggered bonds and dihedral angles of 180 degrees . Substituting hydrogen by fluorine results in a slight shift from 180 degrees , giving rise to a helical structure. X-ray diffraction studies on fibers and computational studies on perfluoroalkanes estimate a dihedral angle of about 17 degrees from the trans position. The rotational spectra of perfluoropentane and its three (13)C isotopomers have been observed and assigned using a pulsed-jet Fourier transform microwave spectrometer. The rotational constants for the parent species are A 990.6394(3) MHz, B 314.0002(1) MHz, and C 304.3703(1) MHz, respectively. The determination of an exact dihedral angle has been challenging, as the helical twist has proven to be quite sensitive to the structural inputs and constraints. A series of r(0) structures incorporating various model constraints and a Kraitchman analysis gives a range of 13-19 degrees for the torsional angle. An objective approach, which only assumes overall C(2) symmetry, is to scale the principal coordinates from ab initio models by the square root of the ratio of the observed second moments to the computed second moments. The scaled structures of computed models at various levels of theory reproduce the parent second moments exactly and the (13)C second moments very well, giving a dihedral angle of 17 +/- 1 degrees from trans. The microwave spectrum of perfluoropropane has also been observed and assigned. The rotational constants are A 1678.5982(9) MHz, B 900.1968(10) MHz, and C 955.3216(11) MHz, respectively. Unlike longer perfluoroalkanes, perfluoropropane has a nonhelical, C(2v) structure. Computations are in excellent agreement with experimental results.

Infrared Spectra and Density Functional Calculations of the SUO2 Molecule

Reactions of laser-ablated U atoms with SO(2) molecules gave the very stable U(VI) molecule, SUO(2), as the major product. Infrared absorptions for two new O=U=O stretching modes were observed in solid argon and neon. The band assignments were confirmed by appropriate (34)SO(2), S(18)O(2), and S(16,18)O(2) isotopic shifts. B3LYP and BPW91 density functional calculations were performed to determine molecular structure, vibrational frequencies, and isotopic shifts. The C(2v) structure is analogous to those computed for UO(3) and US(3). Minor products were identified as SUO, the SUO(2)(+) cation, and the (SO(2))(SUO(2)) adduct.

Assignment of photoelectron spectra of (TiO2)n with n=1–3

This paper reports a comprehensive study of (TiO(2))(n) (n=1-3) clusters on their structures, vertical electron affinities (VEA) and adiabatic electron affinities (AEA), and excited states that are further correlated with experimental photoelectron spectra (PES). Local density functional and time-dependent density functional methods (TTDFT) with 6-31G(d) basis set are used. For (TiO(2))(n) with n=1 and 3, the ground-state geometries are found to have C(2v) and C(s) structures, respectively, in both neutral and anionic charge states. For neutral (TiO(2))(2), the most stable structure corresponds to a C(2h) conformation. For anionic (TiO(2))(2)(-), two isomers with C(2h) and C(2v) symmetries are identified to be nearly isoenergetic. This conclusion is supported by reoptimization at CCSD/6-31G(d) level and single-point calculation at CCSD(T)/6-311+G(d) level. Hence, they are competitive candidates for the ground-state structure of (TiO(2))(2)(-). For TiO(2) and (TiO(2))(3), the calculated VEA and AEA values agree well with the experimental data. For (TiO(2))(2), the VEA and AEA obtained with the C(2v) structure agree well with the experimental data while those with the C(2h) structure do not. The subsequent assignment of PES indicates that it is the C(2v) isomer of (TiO(2))(2)(-) that represents the structure from which the photoexcitation in experimental PES takes place. TDDFT is used to determine the excited states of (TiO(2))(n) (n=1-3) and the calculated excitation energies are in good agreement with PES experiment.

A study of the ground and excited states of Al3 and Al3−. I. 488 nm anion photoelectron spectrum

The vibrationally resolved, 488 nm anion photoelectron spectrum of aluminum trimer displays transitions from two electronic states of Al(3)(-) to four states of Al(3). Franck-Condon analyses of the spectra in the independent harmonic oscillator, parallel mode approximation provide information concerning equilibrium bond length and bond angle differences among the observed states. The electron affinity of Al(3) is measured to be 1.916+/-0.004 eV. In the X (2)A(1)(') Al(3) ground state, fundamental symmetric stretching (nu(1)) and bending (nu(2)) vibrational frequencies are 357+/-10 and 240+/-10 cm(-1). In the X (1)A(1)(') Al(3)(-) ground state, these values are 365+/-15 and 257+/-15 cm(-1), and the equilibrium bond lengths are the same as those of Al(3) to within 0.02 A. The transition between the Al(3)(-) and Al(3) ground states displays only weak activity in the bending mode, consistent with essentially D(3h) structures for both states. An excited (3)B(2) Al(3)(-) state at 0.409+/-0.004 eV (T(0)) has vibrational frequencies of 330+/-20 (nu(1)) and 200+/-10 cm(-1) (nu(2)). This C(2v) state has a 65+/-1 degree apex bond angle and its two equal bond lengths are within 0.01 A of the ground state value. Liquid nitrogen cooling of the downstream portion of the approximately 60 cm long, 0.4-0.7 Torr flow tube anion source increases the observed relative population of this excited triplet state among the sampled anions, evidently slowing its relaxation to the singlet ground state. A (2)A(2)(") excited state of Al(3) lies 0.192+/-0.004 eV above the ground state and has frequencies of 315+/-15 (nu(1)) and 197+/-10 cm(-1) (nu(2)) and bonds 0.10+/-0.03 A longer than in the ground state. A (4)A(2) Al(3) excited state at 0.300+/-0.004 eV displays 315+/-15 (nu(1)) and 140+/-10 cm(-1) (nu(2)) vibrational frequencies. The Franck-Condon analysis of this state, which is accessed only from the (3)B(2) anion, indicates a C(2v) structure with a 69+/-2 degree apex bond angle and bonds 0.06+/-0.02 A longer than in the ground state. A (2)B(2) Al(3) excited state at 0.706+/-0.005 eV is also accessed from the (3)B(2) anion. The lack of vibrational features observable over overlapping transitions indicates similar structures for the (2)B(2) and (3)B(2) states. Primary stretching force constants (mdyn/A) are reported for the Al(3)(-) (0.70+/-0.06) and Al(3) (0.63+/-0.04) ground states and for three excited states. In the following paper, computational predictions for the ground and excited states of Al(3)(-) and Al(3) are reported and compared with these results.

The Gas Phase HO-Initiated Oxidation of Furan: A Theoretical Investigation on the Reaction Mechanism

The reaction mechanism of the gas-phase HO-initiated oxidation of furan has been investigated by means of high level theoretical methods. The reaction is a complex process that begins with the formation of a pre-reactive hydro- gen bonded complex, previous to the addition of the HO radical to furan, forming the 2 and 3-HO-adducts. In the pre- reactive complex, the hydrogen bond is formed by interaction between the hydrogen of the hydroxyl radical and the π sys- tem of furan and its stability is computed to be 1.6 kcal·mol -1 (including the BSSE corrections). The 2 and 3-HO-adducts are computed to be 30.5 and 12.5 kcal·mol -1 respectively, more stable than the reactants. The transition state leading to the formation of the 2-HO-adduct lies below the energy of the separate reactants (0.5 kcal·mol -1 ) and the transition state pro- ducing the 3-HO-adduct that is computed to lie 3.4 kcal·mol -1 above the sum of the energies of furan and hydroxyl radical. There are four reaction paths for the ring-opening of the 2-HO-adduct, leading to the formation of different conformers of 4-hydroxybutenaldehyde radical. The most stable of these conformers presents a cyclic symmetric (C 2V ) structure and can be characterized as a low-barrier hydrogen bond. The geometry optimizations and characterizations done in this work were carried out at MP2/6-311G(d,p), MP2/6-311+G(2df,2p) and QCISD/6-311G(d,p) levels of theory, whereas the rela- tive energies are obtained at CCSD(T)/cc-pVTZ level of theory.