Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order M?ller-Plesset perturbation theory, fourth-order M?ller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values.     

Two-electron reduced density matrices from the anti-Hermitian contracted Schrodinger equation: enhanced energies and properties with larger basis sets

Two-electron reduced density matrices (2-RDMs) have recently been directly determined from the solution of the anti-Hermitian contracted Schrodinger equation (ACSE) to obtain 95%-100% of the ground-state correlation energy of atoms and molecules, which significantly improves upon the accuracy of the contracted Schrodinger equation (CSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. Two subsets of the CSE, the ACSE and the contraction of the CSE onto the one-particle space, known as the 1,3-CSE, have two important properties: (i) dependence upon only the 3-RDM and (ii) inclusion of all second-order terms when the 3-RDM is reconstructed as only a first-order functional of the 2-RDM. The error in the 1,3-CSE has an important role as a stopping criterion in solving the ACSE for the 2-RDM. Using a computationally more efficient implementation of the ACSE, the author treats a variety of molecules, including H2O, NH3, HCN, and HO3-, in larger basis sets such as correlation-consistent polarized double- and triple-zeta. The ground-state energy of neon is also calculated in a polarized quadruple-zeta basis set with extrapolation to the complete basis-set limit, and the equilibrium bond length and harmonic frequency of N2 are computed with comparison to experimental values. The author observes that increasing the basis set enhances the ability of the ACSE to capture correlation effects in ground-state energies and properties. In the triple-zeta basis set, for example, the ACSE yields energies and properties that are closer in accuracy to coupled cluster with single, double, and triple excitations than to coupled cluster with single and double excitations. In all basis sets, the computed 2-RDMs very closely satisfy known N-representability conditions.     

Strongly correlated barriers to rotation from parametric two-electron reduced-density-matrix methods in application to the isomerization of diazene

Recently, parameterization of the two-electron reduced density matrix (2-RDM) has made possible the determination of electronic energies with greater accuracy and lower cost than traditional electron-pair theories including coupled cluster with single and double excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. We examine the method's performance for strongly correlated barriers to rotation; in particular, we study two distinct pathways in the isomerization of diazene (N(2)H(2)) from cis to trans: (i) a strongly correlated rotational pathway and (ii) a moderately correlated inversion pathway. While single reference wavefunction methods predict that the rotational barrier is higher than the inversional barrier, the parametric 2-RDM method predicts that the rotational barrier is lower than the inversional barrier by 3.1 kcal/mol in the extrapolated basis set limit. The parametric 2-RDM results are in agreement with those from multireference methods including multireference perturbation theory and the solution to the anti-Hermitian contracted Schro?dinger equation. We report energies, optimized structures, and natural orbital occupation numbers for three diazene minima and two transition states.     

Treating molecules in arbitrary spin states using the parametric two-electron reduced-density-matrix method

Minimizing the electronic energy with respect to a parameterized two-electron reduced density matrix (2-RDM) is known as a parametric variational 2-RDM method. The parametric 2-RDM method with the M 2-RDM parametrization [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)] is extended to treat molecules in arbitrary spin states. Like its singlet counterpart, the M parametric 2-RDM method for arbitrary spin states is derived using approximate N-representability conditions, which allow it to capture more correlation energy than coupled cluster with single and double excitations at a lower computational cost. We present energies, optimized bond lengths, potential energy curves, and occupation numbers for a set of molecules in a variety of spin states using the M and K parametric 2-RDM methods as well as several wavefunction methods. We show that the M parametric 2-RDM method can describe bond breaking of open-shell molecules like triplet B(2) and singlet and triplet OH(+) even in the presence of strong correlation. Finally, the computed 2-RDMs are shown to be nearly N-representable at both equilibrium and non-equilibrium geometries.     

Parametric two-electron reduced-density-matrix method applied to computing molecular energies and properties at nonequilibrium geometries

A parametric approach to the variational calculation of the two-electron reduced density matrix (2-RDM) for many-electron atoms and molecules has recently been developed in which the 2-RDM is parametrized to be both size consistent and nearly N-representable [C. Kollmar, J. Chem. Phys. 125, 084108 (2006); A. E. DePrince and D. A. Mazziotti, Phys. Rev. A 76, 049903 (2007)]. The parametric variational 2-RDM method is applied to computing ground-state molecular energies and properties at nonequilibrium geometries in significantly larger basis sets than previously employed. We study hydrogen abstraction from the hydroxide groups of H(2)O, NH(3)OH, and CH(3)OH. The 2-RDM method, parametrized by single and double excitations, shows significant improvement over coupled-cluster methods with similar excitations in predicting the shape of potential energy curves and bond-dissociation energies. Previous work completes the parametrization of the energy and 2-RDM by a system of n(2)h(2) normalization constraints, where n and h are the number of occupied and unoccupied orbitals, respectively. In the present paper, however, we show that the constraints can be eliminated by incorporating them into the energy and 2-RDM functions and, hence, the constrained optimization of the ground-state energy can be reformulated as an unconstrained optimization. The 2-RDMs from the parametric method are very nearly N-representable, and as measured by an l(2) norm, they are more accurate than the 2-RDMs from configuration interaction truncated at single and double excitations by an order of magnitude.     

Assessment of the accuracy of density functionals for prediction of relative energies and geometries of low-lying isomers of water hexamers

Water hexamers provide a critical testing ground for validating potential energy surface predictions because they contain structural motifs not present in smaller clusters. We tested the ability of 11 density functionals (four of which are local and seven of which are nonlocal) to accurately predict the relative energies of a series of low-lying water hexamers, relative to the CCSD(T)/aug'-cc-pVTZ level of theory, where CCSD(T) denotes coupled cluster theory with an interative treatment of single and double excitations and a quasi-perturbative treatment of connected triple excitations. Five of the density functionals were tested with two different basis sets, making a total of 16 levels of density functional theory (DFT) tested. When single-point energy calculations are carried out on geometries obtained with second-order M?ller-Plesset perturbation theory (MP2), only three density functionals, M06-L, M05-2X, and M06-2X, are able to correctly predict the relative energy ordering of the hexamers. These three functionals predict that the range of energies spanned by the six isomers is 3.2-5.6 kcal/mol, whereas the other eight functionals predict ranges of 1.0-2.4 kcal/mol; the benchmark value for this range is 3.1 kcal/mol. When the hexamers are optimized at each level of theory, all methods are able to reproduce the MP2 geometries well for all isomers except the boat and bag isomers, and DFT optimization changes the energy ordering for seven of the 16 methods tested. The addition of zero-point energy changes the energy ordering for all of the density functionals studied except for M05-2X and M06-2X. The variation in relative energies predicted by the different methods highlights the necessity for exercising caution in the choice of density functionals used in future studies. Of the 11 density functionals tested, the most accurate results for energies were obtained with the PWB6K, MPWB1K, and M05-2X functionals.     

Determining the energy gap between the cis and trans isomers of HO3- using geometry optimization within the anti-Hermitian contracted Schrödinger and coupled cluster methods

The cis and trans isomers of the HO3- anion, which are important in proposed mechanisms for ozonization, are studied computationally. Relative energies, geometries, and normal-mode frequencies are calculated with anti-Hermitian contracted Schr?dinger equation (ACSE) and coupled cluster methods. Both the ACSE method and the coupled cluster method with single and double excitations (CCSD) are applied in a correlation-consistent polarized double-zeta basis set (cc-pVDZ). Using coupled cluster with singles, doubles, and perturbative triples (CCSD(T)), we treat the problem with larger basis sets than those in previous work, including correlation-consistent polarized quadruple-zeta basis sets with (aug-cc-pVQZ) and without (cc-pVQZ) diffuse functions, which permit extrapolation of the cis and trans energies to the complete-basis-set limit. The cis isomer is found to be lower in energy than the trans isomer by -3.5 kcal/mol, which is 50% larger in magnitude than the best previous result of -2.2 kcal/mol. The bond lengths between the O2 and OH fragments of the cis- and trans-HO3 are calculated to be 1.713 and 1.857 A, respectively, where both bond lengths are significantly longer than the 1.464 A O-O bond in hydrogen peroxide. In this paper, we extend the ACSE method [Mazziotti, D. A. J. Chem. Phys. 2007, 126, 184101], which computes the two-electron reduced density matrix directly, to include geometry optimization by a Newton's method with numerical derivatives. Calculation of the cis- and trans-HO3- isomers by the ACSE yields energies, geometries, and frequencies that are closer to those from CCSD(T) than those from CCSD.     

Elementary constituents of microdevices: the Ge2H fragment

Highly correlated ab initio electronic structure theory has been used to systematically investigate the linear (X 2Pi) GeGeH and H-bridged (X 2B1 and A 2A1) GeHGe structures and the isomerization transition state (A 2A') connecting X 2Pi with A 2A1. The equilibrium structures and physical properties have been predicted employing self-consistent field, configuration interaction with single and double excitations, coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triple excitations [CCSD(T)]. Four correlation-consistent polarized valence-[cc-pVXZ and aug-cc-pVXZ (X=T and Q)] type basis sets were used in the study. For the H-bridged GeHGe isomer, the X 2B1 ground state is predicted to lie only 0.74 [0.95 with zero-point vibrational energy (ZPVE) corrections] kcal mol-1 below the A 2A1 excited state at the CCSD(T) level of theory with the augmented correlation-consistent polarized valence quadruple zeta (aug-cc-pVQZ) basis set. The X 2B1 state of the H-bridged GeHGe isomer lies 8.6 kcal mol-1 below the X 2Pi ground state of the linear GeGeH isomer. The forward isomerization barrier from the linear ground state to the A 2A' transition state is predicted to be 3.7 kcal mol-1. The reverse isomerization barrier between the A 2A1 GeHGe structure and the X 2Pi GeGeH structure is predicted to be 11.6 (10.8 with the ZPVE corrections) kcal mol-1 at the aug-cc-pVQZ CCSD(T) level of theory.     

Accurate energetics of small molecules containing third-row atoms Ga-Kr: a comparison of advanced ab initio and density functional theory

Advanced ab initio [coupled cluster theory through quasiperturbative triple excitations (CCSD(T))] and density functional (B3LYP) computational chemistry approaches were used in combination with the standard and augmented correlation consistent polarized valence basis sets [cc-pVnZ and aug-cc-pVnZ, where n=D(2), T(3), Q(4), and 5] to investigate the energetic and structural properties of small molecules containing third-row (Ga-Kr) atoms. These molecules were taken from the Gaussian-2 (G2) extended test set for third-row atoms. Several different schemes were used to extrapolate the calculated energies to the complete basis set (CBS) limit for CCSD(T) and the Kohn-Sham (KS) limit for B3LYP. Zero point energy and spin orbital corrections were included in the results. Overall, CCSD(T) atomization energies, ionization energies, proton affinities, and electron affinities are in good agreement with experiment, within 1.1 kcal/mol when the CBS limit has been determined using a series of two basis sets of at least triple zeta quality. For B3LYP, the overall mean absolute deviation from experiment for the three properties and the series of molecules is more significant at the KS limit, within 2.3 and 2.6 kcal/mol for the cc-pVnZ and aug-cc-pVnZ basis set series, respectively.     

Combustion chemistry: important features of the C3H5 potential energy surface, including allyl radical, propargyl + H2, allene + H, and eight transition states

The C(3)H(5) potential energy surface (PES) encompasses molecules of great significance to hydrocarbon combustion, including the resonantly stabilized free radicals propargyl (plus H(2)) and allyl. In this work, we investigate the interconversions that take place on this PES using high level coupled cluster methodology. Accurate geometries are obtained using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)] combined with Dunning's correlation consistent quadruple-ζ basis set cc-pVQZ. The energies for these stationary points are then refined by a systematic series of computations, within the focal point scheme, using the cc-pVXZ (X = D, T, Q, 5, 6) basis sets and correlation treatments as extensive as coupled cluster with full single, double, and triple excitation and perturbative quadruple excitations [CCSDT(Q)]. Our benchmarks provide a zero-point vibrational energy (ZPVE) corrected barrier of 10.0 kcal mol(-1) for conversion of allene + H to propargyl + H(2). We also find that the barrier for H addition to a terminal carbon atom in allene leading to propenyl is 1.8 kcal mol(-1) lower than that for the addition to a central atom to form the allyl radical.     

Electronic excited-state energies from a linear response theory based on the ground-state two-electron reduced density matrix

Ground-state two-particle reduced density matrices (2-RDMs) are used to calculate excited-state energy spectra. Solving the Schrodinger equation for excited states dominated by single excitations from the ground-state wavefunction requires the ground-state 2- and 3-RDMs. The excited states, however, can be obtained without a knowledge of the ground-state 3-RDM by two methods: (i) cumulant expansion methods which build the 3-RDM from the 2-RDM, and (ii) double commutator methods which eliminate the 3-RDM. Previous work [Mazziotti, Phys. Rev. A 68, 052501 (2003)] examined the accuracy of excited states extracted from ground-state 2-RDMs, which were calculated by full configuration interaction or the variational 2-RDM method. In this work we employ (i) advances in semidefinite programming to treat the excited states of water and hydrogen fluoride and chains of hydrogen atoms, and (ii) the addition of partial three-particle N-representability conditions to compute more accurate ground-state 2-RDMs. With the hydrogen chains we examine the metal-to-insulator transition as measured by the band gap (the difference between the ground-state and the first excited-state energies), which is difficult for excited-state methods to capture.     

Computational study of the reactions of methanol with the hydroperoxyl and methyl radicals. 1. Accurate thermochemistry and barrier heights

The reactions of CH(3)OH with the HO(2) and CH(3) radicals are important in the combustion of methanol and are prototypes for reactions of heavier alcohols in biofuels. The reaction energies and barrier heights for these reaction systems are computed with CCSD(T) theory extrapolated to the complete basis set limit using correlation-consistent basis sets, both augmented and unaugmented, and further refined by including a fully coupled treatment of the connected triple excitations, a second-order perturbative treatment of quadruple excitations (by CCSDT(2)(Q)), core-valence corrections, and scalar relativistic effects. It is shown that the M08-HX and M08-SO hybrid meta-GGA density functionals can achieve sub-kcal mol(-1) agreement with the high-level ab initio results, identifying these functionals as important potential candidates for direct dynamics studies on the rates of these and homologous reaction systems.     

The fluorobenzene-argon S(1) excited-state intermolecular potential energy surface

We evaluate the first excited-state (S1) intermolecular potential energy surface for the fluorobenzene-Ar van der Waals complex using the coupled cluster method and the augmented correlation-consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. To calculate the S(1) interaction energies, we use ground-state interaction energies evaluated with the same basis set and the coupled cluster singles and doubles (CCSD) including connected triple excitations [CCSD(T)] model and interaction and excitation energies evaluated at the CCSD level. The surface minima are characterized by the Ar atom located above and below the fluorobenzene ring at a distance of 3.5060 A with respect to the fluorobenzene center of mass and at an angle of 5.89 degrees with respect to the axis perpendicular to the fluorobenzene plane. The corresponding interaction energy is -425.226 cm(-1). The surface is used in the evaluation of the intermolecular level structure of the complex, and the results are compared to the experimental data available and to those found in previous theoretical papers on ground-state potentials for similar complexes.     

Toward subchemical accuracy in computational thermochemistry: focal point analysis of the heat of formation of NCO and [H,N,C,O] isomers

In continuing pursuit of thermochemical accuracy to the level of 0.1 kcal mol(-1), the heats of formation of NCO, HNCO, HOCN, HCNO, and HONC have been rigorously determined using state-of-the-art ab initio electronic structure theory, including conventional coupled cluster methods [coupled cluster singles and doubles (CCSD), CCSD with perturbative triples (CCSD(T)), and full coupled cluster through triple excitations (CCSDT)] with large basis sets, conjoined in cases with explicitly correlated MP2-R12/A computations. Limits of valence and all-electron correlation energies were extrapolated via focal point analysis using correlation consistent basis sets of the form cc-pVXZ (X=2-6) and cc-pCVXZ (X=2-5), respectively. In order to reach subchemical accuracy targets, core correlation, spin-orbit coupling, special relativity, the diagonal Born-Oppenheimer correction, and anharmonicity in zero-point vibrational energies were accounted for. Various coupled cluster schemes for partially including connected quadruple excitations were also explored, although none of these approaches gave reliable improvements over CCSDT theory. Based on numerous, independent thermochemical paths, each designed to balance residual ab initio errors, our final proposals are DeltaH(f,0) ( composite function )(NCO)=+30.5, DeltaH(f,0) ( composite function )(HNCO)=-27.6, DeltaH(f,0) ( composite function )(HOCN)=-3.1, DeltaH(f,0) ( composite function )(HCNO)=+40.9, and DeltaH(f,0) ( composite function )(HONC)=+56.3 kcal mol(-1). The internal consistency and convergence behavior of the data suggests accuracies of +/-0.2 kcal mol(-1) in these predictions, except perhaps in the HCNO case. However, the possibility of somewhat larger systematic errors cannot be excluded, and the need for CCSDTQ [full coupled cluster through quadruple excitations] computations to eliminate remaining uncertainties is apparent.     

High-level ab initio computations of structures and interaction energies of naphthalene dimers: origin of attraction and its directionality

The intermolecular interaction energies of naphthalene dimers have been calculated by using an aromatic intermolecular interaction model (a model chemistry for the evaluation of intermolecular interactions between aromatic molecules). The CCSD(T) (coupled cluster calculations with single and double substitutions with noniterative triple excitations) interaction energy at the basis set limit has been estimated from the second-order M?ller-Plesset perturbation interaction energy near saturation and the CCSD(T) correction term obtained using a medium-size basis set. The estimated interaction energies of the set of geometries explored in this work show that two structures emerge as being the lowest energy, and may effectively be considered as isoenergetic on the basis of the errors inherent in out extrapolation procedure. These structures are the slipped-parallel (Ci) structure (-5.73 kcal/mol) and the cross (D2d) structure (-5.28 kcal/mol). The T-shaped (C2v) and sandwich (D2h) dimers are substantially less stable (-4.34 and -3.78 kcal/mol, respectively). The dispersion interaction is found to be the major source of attraction in the naphthalene dimer. The electrostatic interaction is substantially smaller than the dispersion interaction. The large dispersion interaction is the cause of the large binding energies of the cross and slipped-parallel dimers.     

Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method

The variational two-electron reduced-density-matrix (2-RDM) method allows for the computation of accurate ground-state energies and 2-RDMs of atoms and molecules without the explicit construction of an N-electron wave function. While previous work on variational 2-RDM theory has focused on calculating full configuration-interaction energies, this work presents the first application toward approximating multiconfiguration self-consistent-field (MCSCF) energies via low-rank restrictions on the 1- and 2-RDMs. The 2-RDM method with two- or three-particle N-representability conditions reduces the exponential active-space scaling of MCSCF methods to a polynomial scaling. Because the first-order algorithm [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] represents each form of the 1- and 2-RDMs by a matrix factorization, the RDMs are readily defined to have a low rank rather than a full rank by setting the matrix factors to be rectangular rather than square. Results for the potential energy surfaces of hydrogen fluoride, water, and the nitrogen molecule show that the low-rank 2-RDM method yields accurate approximations to the MCSCF energies. We also compute the energies along the symmetric stretch of a 20-atom hydrogen chain where traditional MCSCF calculations, requiring more than 17x10(9) determinants in the active space, could not be performed.     

Thermodynamics of titanium and vanadium reduction in non-aqueous environment calculated at various levels of theory

Reduction of titanium and vanadium compounds is a process accompanying the activation of coordinative olefin polymerization catalysts. Four density functional theory (DFT) functionals, coupled cluster with single, double, and perturbative triple excitations method CCSD(T) as well as complete active-space second-order perturbation theory method CASPT2 with a complete active-space self-consistent field CASSCF reference wave function were applied to investigate the thermodynamics of titanium and vanadium reduction. The performance of these theoretical methods was assessed and compared with experimental values. The calculations indicate that vanadium(IV) chloride is more easily reduced by trimethylaluminum than the corresponding titanium compound; the energies of reaction calculated at the CCSD(T) level are equal -57.21 and -33.10 kcal/mol, respectively. The calculations deal with the redox reactions of metal chlorides in the gas phase, rather than solvated ions in the aqueous solution. This approach may be more appropriate for olefin polymerization, usually carried out in nonpolar solvents.     

Quantum chemical assessment of the binding energy of CuO+

We present a detailed theoretical investigation on the dissociation energy of CuO(+), carried out by means of coupled cluster theory, the multireference averaged coupled pair functional (MR-ACPF) approach, diffusion quantum Monte Carlo (DMC), and density functional theory (DFT). At the respective extrapolated basis set limits, most post-Hartree-Fock approaches agree within a narrow error margin on a D(e) value of 26.0 kcal mol(-1) [coupled-cluster singles and doubles level augmented by perturbative triples corrections, CCSD(T)], 25.8 kcal mol(-1) (CCSDTQ via the high accuracy extrapolated ab initio thermochemistry protocol), and 25.6 kcal mol(-1) (DMC), which is encouraging in view of the disaccording data published thus far. The configuration-interaction based MR-ACPF expansion, which includes single and double excitations only, gives a slightly lower value of 24.1 kcal mol(-1), indicating that large basis sets and triple excitation patterns are necessary ingredients for a quantitative assessment. Our best estimate for D(0) at the CCSD(T) level is 25.3 kcal mol(-1), which is somewhat lower than the latest experimental value (D(0) = 31.1 ± 2.8 kcal mol(-1)[semicolon] reported by the Armentrout group) [Int. J. Mass Spectrom. 182/183, 99 (1999)]. These highly correlated methods are, however, computationally very demanding, and the results are therefore supplemented with those of more affordable DFT calculations. If used in combination with moderately-sized basis sets, the M05 and M06 hybrid functionals turn out to be promising candidates for studies on much larger systems containing a [CuO](+) core.     

1-Germavinylidene (Ge═CH2), germyne (HGeCH), and 2-germavinylidene (H2Ge═C) molecules and isomerization reactions among them: anharmonic rovibrational analyses

Theoretical investigations of three equilibrium structures and two associated isomerization reactions of the GeCH(2) - HGeCH - H(2)GeC system have been systematically carried out. This research employed ab initio self-consistent-field (SCF), coupled cluster (CC) with single and double excitations (CCSD), and CCSD with perturbative triple excitations [CCSD(T)] wave functions and a wide variety of correlation-consistent polarized valence cc-pVXZ and cc-pVXZ-DK (where X = D, T, Q) basis sets. For each structure, the total energy, geometry, dipole moment, harmonic vibrational frequencies, and infrared intensities are predicted. Complete active space SCF (CASSCF) wave functions are used to analyze the effects of correlation on physical properties and energetics. For each of the equilibrium structures, vibrational second-order perturbation theory (VPT2) has been utilized to obtain the zero-point vibration corrected rotational constants, centrifugal distortion constants, and fundamental vibrational frequencies. The predicted rotational constants and anharmonic vibrational frequencies for 1-germavinylidene are in good agreement with available experimental observations. Extensive focal point analyses, including CCSDT and CCSDT(Q) energies and basis sets up to quintuple zeta, are used to obtain complete basis set (CBS) limit energies. At all levels of theory employed in this study, the global minimum of the GeCH(2) potential energy surface (PES) is confirmed to be 1-germavinylidene (GeCH(2), 1). The second isomer, germyne (HGeCH, 2) is predicted to lie 40.4(41.1) ± 0.3 kcal mol(-1) above the global minimum, while the third isomer, 2-germavinylidene (H(2)GeC, 3) is located 92.3(92.7) ± 0.3 kcal mol(-1) above the global minimum; the values in parentheses indicate core-valence and zero-point vibration energy (ZPVE) corrected energy differences. The barriers for the forward (1→2) and reverse (2→1) isomerization reactions between isomers 1 and 2 are 48.3(47.7) ± 0.3 kcal mol(-1) and 7.9(6.6) ± 0.3 kcal mol(-1), respectively. On the other hand, the barriers of the forward (2→3) and reverse (3→2) isomerization reactions between isomers 2 and 3 are predicted to be 55.2(53.2) ± 0.3 kcal mol(-1) and 3.3(1.6) ± 0.3 kcal mol(-1), respectively.