Anharmonic Zero-point Vibrational Energy Research Articles

Anharmonic rotational and vibrational spectroscopic constants of NH2CH2OH

The recent experimental identification of aminomethanol (NH2CH2OH) and its synthesis under simulated interstellar conditions suggests that it may be formed, and thus observable, in the interstellar medium. To aid in its possible detection, this work presents high-level theoretical, anharmonic vibrational and rotational spectroscopic data for the three lowest-energy conformers of NH2CH2OH. All three conformers fall within 0.80 kcal mol−1 of each other at the CCSD(T)-F12b/cc-pCVTZ-F12 level, with an anharmonic zero-point vibrational energy correction. Additionally, all three conformers are shown to have multiple vibrational frequencies with intensities greater than 100 km mol−1. The most notable of these are the symmetric O-C-N stretch of the lower-energy C1 conformer at 976.4 cm−1, the C-O stretch of the Cs conformer at 964.9 cm−1, and the antisymmetric O-C-N stretch of the higher-energy C1 conformer at 1099.0 cm−1. While much of the vibrational spectra of the three overlap, these features should help to separate them. Finally, all three conformers have non-zero dipole moments on the order of 1 D, suggesting that they may be observable by rotational spectroscopy, as well. In all cases, the computational data provided herein will help to facilitate future experimental and observational studies on this key molecule in the formation of extraterrestrial amino acids.

The heavy Carbene analogues SbH2 + and BiH2 +. Convergent quantum mechanical studies*

In 2021 Olaru, Mebs, and Beckmann reported the synthesis of remarkable cationic carbene analogues P R 2 + and As R 2 + . This work followed the same group's synthesis of Sb R 2 + and Bi R 2 + . To better understand these important systems, Sb H 2 + and Bi H 2 + have been studied with high level ab initio quantum mechanical methods. Geometries were optimised with the CCSDT(Q) method with the cc-pwCVTZ-PP basis set using small core pseudopotentials. Fundamental vibrational frequencies were computed to provide theoretical predictions for future synthetic studies. Relative energies with respect to P n + + H 2 ( Pn = Sb , Bi ) were determined at the CCSDT/CBS level of theory via the Focal Point Analysis method, and anharmonic zero-point vibrational energy and higher order contributions were also computed. For Sb H 2 + , we obtained R = 1.697 Å and θ = 90.8 ∘ with S b + + H 2 → Sb H 2 + reaction enthalpy of ΔH = − 18.71 kcal mol − 1 . For Bi H 2 + , the analogous results were R = 1.774 Å, θ = 89.7 ∘ , and ΔH = − 7.64 kcal mol − 1 for B i + + H 2 → Bi H 2 + .

The torsional states of methyl hydroperoxide molecule calculated using anharmonic zero point vibrational energy

The 2D surfaces of potential energy, kinematic coefficients, components of the dipole moment, the heights of potential barriers, the energies of stationary torsional states, and the tunneling frequencies of hydroxyl and methyl groups in the methyl hydroperoxide molecule were calculated at MP2/CBS and CCSD(T)/Aug-cc-pVTZ levels of theory. Additionally, calculations of the 2D surface of zero point vibrational energy of the molecule in the harmonic and anharmonic approximations were performed at MP2/Aug-cc-pVTZ level of theory. The zero point vibrational energy calculated in two approximations is summed up with the potential energy of the methyl hydroperoxide molecule, calculated at two levels of theory, and the resulting four outcomes of the refined potential energy are used to calculate the energies of stationary torsional states and tunneling frequencies. The results obtained are compared with the experimental and theoretical data presented in the literature to evaluate the efficiency of taking into account the zero point vibrational energy when examining the internal rotation in molecules.

Hydrogen bonding in the mixed HF/HCl dimer: Is it better to give or receive?

The ClH⋯FH and FH⋯ClH configurations of the mixed HF/HCl dimer (where the donor⋯acceptor notation indicates the directionality of the hydrogen bond) as well as the transition state connecting the two configurations have been optimized using MP2 and CCSD(T) with correlation consistent basis sets as large as aug-cc-pV(5 + d)Z. Harmonic vibrational frequencies confirmed that both configurations correspond to minima and that the transition state has exactly one imaginary frequency. In addition, anharmonic vibrational frequencies computed with second-order vibrational perturbation theory (VPT2) are within 6 cm-1 of the available experimental values and deviate by no more than 4 cm-1 for the complexation induced HF frequency shifts. The CCSD(T) electronic energies obtained with the largest basis set indicate that the barrier height is 0.40 kcal mol-1 and the FH⋯ClH configuration lies 0.19 kcal mol-1 below the ClH⋯FH configuration. While only modestly attenuating the barrier height, the inclusion of either the harmonic or anharmonic zero-point vibrational energy effectively makes both minima isoenergetic, with the ClH⋯FH configuration being lower by only 0.03 kcal mol-1 . © 2018 Wiley Periodicals, Inc.

Estimating the intrinsic limit of the Feller-Peterson-Dixon composite approach when applied to adiabatic ionization potentials in atoms and small molecules

Benchmark adiabatic ionization potentials were obtained with the Feller-Peterson-Dixon (FPD) theoretical method for a collection of 48 atoms and small molecules. In previous studies, the FPD method demonstrated an ability to predict atomization energies (heats of formation) and electron affinities well within a 95% confidence level of ±1 kcal/mol. Large 1-particle expansions involving correlation consistent basis sets (up to aug-cc-pV8Z in many cases and aug-cc-pV9Z for some atoms) were chosen for the valence CCSD(T) starting point calculations. Despite their cost, these large basis sets were chosen in order to help minimize the residual basis set truncation error and reduce dependence on approximate basis set limit extrapolation formulas. The complementary n-particle expansion included higher order CCSDT, CCSDTQ, or CCSDTQ5 (coupled cluster theory with iterative triple, quadruple, and quintuple excitations) corrections. For all of the chemical systems examined here, it was also possible to either perform explicit full configuration interaction (CI) calculations or to otherwise estimate the full CI limit. Additionally, corrections associated with core/valence correlation, scalar relativity, anharmonic zero point vibrational energies, non-adiabatic effects, and other minor factors were considered. The root mean square deviation with respect to experiment for the ionization potentials was 0.21 kcal/mol (0.009 eV). The corresponding level of agreement for molecular enthalpies of formation was 0.37 kcal/mol and for electron affinities 0.20 kcal/mol. Similar good agreement with experiment was found in the case of molecular structures and harmonic frequencies. Overall, the combination of energetic, structural, and vibrational data (655 comparisons) reflects the consistent ability of the FPD method to achieve close agreement with experiment for small molecules using the level of theory applied in this study.

Radicals derived from acetaldehyde and vinyl alcohol.

Vinyl alcohol and acetaldehyde are isoelectronic products of incomplete butanol combustion. Along with the radicals resulting from the removal of atomic hydrogen or the hydroxyl radical, these species are studied here using ab initio methods as complete as coupled cluster theory with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)], with basis sets as large as cc-pV5Z. The relative energies provided herein are further refined by including corrections for relativistic effects, the frozen core approximation, and the Born-Oppenheimer approximation. The effects of anharmonic zero-point vibrational energies are also treated. The syn conformer of vinyl alcohol is predicted to be lower in energy than the anti conformer by 1.1 kcal mol-1. The alcoholic hydrogen of syn-vinyl alcohol is found to be the easiest to remove, requiring 84.4 kcal mol-1. Five other radicals are also carefully considered, with four conformers investigated for the 1-hydroxyvinyl radical. Beyond energetics, we have conducted an overhaul of the spectroscopic literature for these species. Our results also provide predictions for fundamental modes yet to be reported experimentally. To our knowledge, the ν3 (3076 cm-1) and ν4 (2999 cm-1) C-H stretches for syn-vinyl alcohol and all but one of the vibrational modes for anti-vinyl alcohol (ν1-ν14) are yet to be observed experimentally. For the acetyl radical, ν6 (1035 cm-1), ν11 (944 cm-1), ν12 (97 cm-1), and accounting for our changes to the assignment of the 1419.9 cm-1 experimental mode, ν10 (1441 cm-1), are yet to be observed. We have predicted these unobserved fundamentals and reassigned the experimental 1419.9 cm-1 frequency in the acetyl radical to ν4 rather than to ν10. Our work also strongly supports reassignment of the ν10 and ν11 fundamentals of the vinoxy radical. We suggest that the bands assigned to the overtones of these fundamentals were in fact combination bands. Our findings may be useful in constructing improved combustion models of butanol and in spectroscopically characterizing these molecules further.

Application of a convergent, composite coupled cluster approach to bound state, adiabatic electron affinities in atoms and small molecules.

Benchmark quality adiabatic electron affinities for a collection of atoms and small molecules were obtained with the Feller-Peterson-Dixon composite coupled cluster theory method. Prior applications of this method demonstrated its ability to accurately predict atomization energies/heats of formation for more than 170 molecules. In the current work, the 1-particle expansion involved very large correlation consistent basis sets, ranging up to aug-cc-pV9Z (aug-cc-pV10Z for H and H2), with the goal of minimizing the residual basis set truncation error that must otherwise be approximated with extrapolation formulas. The n-particle expansion begins with coupled cluster calculations through iterative single and double excitations plus a quasiperturbative treatment of "connected" triple excitations (CCSD(T)) pushed to the complete basis set limit followed by CCSDT, CCSDTQ, or CCSDTQ5 corrections. Due to the small size of the systems examined here, it was possible in many cases to extend the n-particle expansion to the full configuration interaction wave function limit. Additional, smaller corrections associated with core/valence correlation, scalar relativity, anharmonic zero point vibrational energies, and non-adiabatic effects were also included. The overall root mean square (RMS) deviation was 0.005 eV (0.12 kcal/mol). This level of agreement was comparable to what was found with molecular heats of formation. A 95% confidence level corresponds to roughly twice the RMS value or 0.01 eV. While the atomic electron affinities are known experimentally to high accuracy, the molecular values are less certain. This contributes to the difficulty of gauging the accuracy of the theoretical results. A limited number of electron affinities were determined with the explicitly correlated CCSD(T)-F12b method. After extending the VnZ-F12 orbital basis sets with additional diffuse functions, the F12b method was found to accurately reproduce the best F/F(-) value obtained with standard methods, but it underestimated the CH3/CH3 (-) value by 0.01 eV.

Isomerism of Cyanomethanimine: Accurate Structural, Energetic, and Spectroscopic Characterization

The structures, relative stabilities, and rotational and vibrational parameters of the Z-C-, E-C-, and N-cyanomethanimine isomers have been evaluated using state-of-the-art quantum-chemical approaches. Equilibrium geometries have been calculated by means of a composite scheme based on coupled-cluster calculations that accounts for the extrapolation to the complete basis set limit and core-correlation effects. The latter approach is proved to provide molecular structures with an accuracy of 0.001-0.002 Å and 0.05-0.1° for bond lengths and angles, respectively. Systematically extrapolated ab initio energies, accounting for electron correlation through coupled-cluster theory, including up to single, double, triple, and quadruple excitations, and corrected for core-electron correlation and anharmonic zero-point vibrational energy, have been used to accurately determine relative energies and the Z-E isomerization barrier with an accuracy of about 1 kJ/mol. Vibrational and rotational spectroscopic parameters have been investigated by means of hybrid schemes that allow us to obtain rotational constants accurate to about a few megahertz and vibrational frequencies with a mean absolute error of ∼1%. Where available, for all properties considered, a very good agreement with experimental data has been observed.

Examining the ground and first excited states of methyl peroxy radical with high-level coupled-cluster theory

Peroxy radicals (RO2) are intermediates in fuel combustion, where they engage in efficiency-limiting autoignition reactions. They also participate in atmospheric chemistry leading to the formation of unwanted tropospheric ozone. Advances in spectroscopic techniques have allowed for the possibility of employing the lowest () electronic transition of RO2 as a tool to selectively monitor these species, enabling accurate kinetic values to be obtained. Herein, high-level ab initio methods are employed to systematically refine spectroscopic predictions for the methyl peroxy radical (CH3O2), one of the most abundant peroxy radicals in the atmosphere. In particular, vibrationally corrected geometries and anharmonic vibrational frequencies for both the ground () and first excited () state are predicted using coupled-cluster theory with up to perturbative triples [CCSD(T)] and large atomic natural orbital basis sets. Equation-of-motion coupled-cluster theory is utilised to compute vertical transition properties; a radiative lifetime of 4.7 ms is suggested for the excited state. Finally, we predict the adiabatic excitation energy (T0) via systematic extrapolation to the complete basis limit of coupled-cluster with up to full quadruples (CCSDTQ). After accounting for several approximations, and including an anharmonic zero-point vibrational energy correction, we match experiment for this transition to within 9 cm−1.

Anharmonic zero point vibrational energies: Tipping the scales in accurate thermochemistry calculations?

Anharmonic zero point vibrational energies (ZPVEs) calculated using both conventional CCSD(T) and MP2 in combination with vibrational second-order perturbation theory (VPT2) are compared to explicitly correlated CCSD(T)-F12 and MP2-F12 results that utilize vibrational configuration interaction (VCI) theory for 26 molecules of varying size. Sequences of correlation consistent basis sets are used throughout. It is found that the explicitly correlated methods yield results close to the basis set limit even with double-zeta quality basis sets. In particular, the anharmonic contributions to the ZPVE are accurately recovered at just the MP2 (or MP2-F12) level of theory. Somewhat surprisingly, the best vibrational CI results agreed with the VPT2 values with a mean unsigned deviation of just 0.09 kJ/mol and a standard deviation of just 0.11 kJ/mol. The largest difference was observed for C(4)H(4)O (0.34 kJ/mol). A simplified version of the vibrational CI procedure that limited the modal expansion to at most 2-mode coupling yielded anharmonic corrections generally within about 0.1 kJ/mol of the full 3- or 4-mode results, except in the cases of C(3)H(8) and C(4)H(4)O where the contributions were underestimated by 1.3 and 0.8 kJ/mol, respectively (34% and 40%, respectively). For the molecules considered in this work, accurate anharmonic ZPVEs are most economically obtained by combining CCSD(T)-F12a/cc-pVDZ-F12 harmonic frequencies with either MP2/aug-cc-pVTZ/VPT2 or MP2-F12/cc-pVDZ-F12/VCI anharmonic corrections.

The lowest-lying electronic singlet and triplet potential energy surfaces for the HNO–NOH system: Energetics, unimolecular rate constants, tunneling and kinetic isotope effects for the isomerization and dissociation reactions

The lowest-lying electronic singlet and triplet potential energy surfaces (PES) for the HNO-NOH system have been investigated employing high level ab initio quantum chemical methods. The reaction energies and barriers have been predicted for two isomerization and four dissociation reactions. Total energies are extrapolated to the complete basis set limit applying focal point analyses. Anharmonic zero-point vibrational energies, diagonal Born-Oppenheimer corrections, relativistic effects, and core correlation corrections are also taken into account. On the singlet PES, the (1)HNO → (1)NOH endothermicity including all corrections is predicted to be 42.23 ± 0.2 kcal mol(-1). For the barrierless decomposition of (1)HNO to H + NO, the dissociation energy is estimated to be 47.48 ± 0.2 kcal mol(-1). For (1)NOH → H + NO, the reaction endothermicity and barrier are 5.25 ± 0.2 and 7.88 ± 0.2 kcal mol(-1). On the triplet PES the reaction energy and barrier including all corrections are predicted to be 7.73 ± 0.2 and 39.31 ± 0.2 kcal mol(-1) for the isomerization reaction (3)HNO → (3)NOH. For the triplet dissociation reaction (to H + NO) the corresponding results are 29.03 ± 0.2 and 32.41 ± 0.2 kcal mol(-1). Analogous results are 21.30 ± 0.2 and 33.67 ± 0.2 kcal mol(-1) for the dissociation reaction of (3)NOH (to H + NO). Unimolecular rate constants for the isomerization and dissociation reactions were obtained utilizing kinetic modeling methods. The tunneling and kinetic isotope effects are also investigated for these reactions. The adiabatic singlet-triplet energy splittings are predicted to be 18.45 ± 0.2 and 16.05 ± 0.2 kcal mol(-1) for HNO and NOH, respectively. Kinetic analyses based on solution of simultaneous first-order ordinary-differential rate equations demonstrate that the singlet NOH molecule will be difficult to prepare at room temperature, while the triplet NOH molecule is viable with respect to isomerization and dissociation reactions up to 400 K. Hence, our theoretical findings clearly explain why (1)NOH has not yet been observed experimentally.

General Perturbative Approach for Spectroscopy, Thermodynamics, and Kinetics: Methodological Background and Benchmark Studies.

A general second-order perturbative approach based on resonance- and threshold-free computations of vibrational properties is introduced and validated. It starts from the evaluation of accurate anharmonic zero-point vibrational energies for semirigid molecular systems, in a way that avoids any singularity. Next, the degeneracy corrected second-order perturbation theory (DCPT2) is extended to a hybrid version (HDCPT2), allowing for reliable computations even in cases where the original formulation faces against severe problems, including also an automatic treatment of internal rotations through the hindered-rotor model. These approaches, in conjunction with the so-called simple perturbation theory (SPT) reformulated to treat consistently both energy minima and transition states, allow one to evaluate degeneracy-corrected partition functions further used to obtain vibrational contributions to properties like enthalpy, entropy, or specific heat. The spectroscopic accuracy of the HDCPT2 model has been also validated by computing anharmonic vibrational frequencies for a number of small-to-medium size, closed- and open-shell, molecular systems, within an accuracy close to that of well established but threshold-dependent perturbative-variational models. The reliability of the B3LYP/aug-N07D model for anharmonic computations is also highlighted, with possible improvements provided by the B2PLYP/aug-cc-pVTZ models or by hybrid schemes. On a general grounds, the overall approach proposed in the present work is able to provide the proper accuracy to support experimental investigations even for large molecular systems of biotechnological interest in a fully automated manner, without any ad hoc scaling procedure. This means a fully ab initio evaluation of thermodynamic and spectroscopic properties with an overall accuracy of about, or better than, 1 kJ mol(-1), 1 J mol(-1) K(-1) and 10 cm(-1) for enthalpies, entropies, and vibrational frequencies, respectively.

Accurate thermochemistry and spectroscopy of the oxygen-protonated sulfur dioxide isomers

Despite the promising relevance of protonated sulfur dioxide in astrophysical and atmospheric fields, its thermochemical and spectroscopic characterization is very limited. High-level quantum-chemical calculations have shown that the most stable isomer is the cis oxygen-protonated sulfur dioxide, HOSO(+), while the trans form is about 2 kcal mol(-1) less stable; even less stable (by about 42 kcal mol(-1)) is the S-protonated isomer [V. Lattanzi et al., J. Chem. Phys., 2010, 133, 194305]. The enthalpy of formation for the cis- and trans-HOSO(+) is presented, based on the well tested HEAT protocol [A. Tajti et al., J. Chem. Phys., 2004, 121, 11599]. Systematically extrapolated ab initio energies, accounting for electron correlation through coupled cluster theory, including up to single, double, triple and quadruple excitations, have been corrected for core-electron correlation, anharmonic zero-point vibrational energy, diagonal Born-Oppenheimer and scalar relativistic effects. As a byproduct, proton affinity of sulfur dioxide and atomization energies have also been obtained at the same levels of theory. Vibrational and rotational spectroscopic properties have been investigated by means of composite schemes that allow us to account for truncation of basis set as well as core correlation. Where available, for both thermochemistry and spectroscopy, very good agreement with experimental data has been observed.

Thermochemistry of the HOSO Radical, a Key Intermediate in Fossil Fuel Combustion

Despite the key role of the HOSO radical in the combustion of sulfur-rich fuels, the thermochemistry of this simple species is not well-established. Due to the extraordinary sensitivity of the potential energy surface to basis set and electron correlation methods in ab initio computations, there is no consensus in the literature regarding the structure of the global minimum syn-HOSO. A definitive enthalpy of formation for HOSO is presented, based on systematically extrapolated ab initio energies, accounting for electron correlation primarily through coupled cluster theory, including up to single, double, and triple excitations with a perturbative correction for connected quadruple excitations [CCSDT(Q)]. These extrapolated valence electronic energies have been corrected for core-electron correlation, harmonic and anharmonic zero-point vibrational energy, and non-Born-Oppenheimer and scalar relativistic effects. Our final recommended enthalpy of formation is Delta(f)H(0)(o)(syn-HOSO) = -58.0 kcal mol(-1). The planar anti-HOSO transition state lies 2.28 kcal mol(-1) above the syn-HOSO minimum, while predicted reaction enthalpies for H + SO(2) --> HOSO, HOSO --> OH + SO, HOSO + H --> H(2) + SO(2), and OH + HOSO --> SO(2) + H(2)O are -38.6, 68.0, -64.4, and -80.1 kcal mol(-1), respectively. We provide incontrovertible evidence for a quasi-planar structure of the syn-HOSO radical, with a remarkably flat torsional energy surface, based on CCSD(T) geometries and harmonic vibrational frequencies energies with up to quintuple-zeta quality basis sets. The energy separation between planar syn-HOSO and the nonplanar global minimum is a mere 5 cm(-1) at the cc-pV(T+D)Z CCSD(T) level of theory. Computed fundamental vibrational frequencies for syn-HOSO and syn-DOSO based on a full quartic force-field evaluated at the cc-pV(T+d)Z CCSD(T) level of theory are in agreement with available experimental data. The present results confirm a previously tentative assignment of a band at 1050 cm(-1) to the HOS bending mode.

Thermochemistry of Key Soot Formation Intermediates: C3H3 Isomers

Accurate standard enthalpies of formation for allene, propyne, and four C3H3 isomers involved in soot formation mechanisms have been determined through systematic focal point extrapolations of ab initio energies. Auxiliary corrections have been applied for anharmonic zero-point vibrational energy, core electron correlation, the diagonal Born-Oppenheimer correction (DBOC), and scalar relativistic effects. Electron correlation has been accounted for via second-order Z-averaged perturbation theory (ZAPT2) and primarily through coupled-cluster theory, including single, double, and triple excitations, as well as a perturbative treatment of connected quadruple excitations [ROCCSD, ROCCSD(T), ROCCSDT, and UCCSDT(Q)]. The correlation-consistent hierarchy of basis sets, cc-pVXZ (X = D, T, Q, 5, 6), was employed. The CCSDT(Q) corrections do not exceed 0.12 kcal mol(-)1 for the relative energies of the systems considered here, indicating a high degree of electron correlation convergence in the present results. Our recommended values for the enthalpies of formation are as follows: Delta(f)H(o)(0)(propargyl) = 84.76, Delta(f)H(o)(0) (1-propynyl) = 126.60, Delta(f)H(o)(0) (cycloprop-1-enyl) = 126.28, Delta(f)H(o)(0)(cycloprop-2-enyl) = 117.36, Delta(f)H(o)(0)(allene) = 47.41, and Delta(f)H(o)(0)(propyne) = 46.33 kcal mol(-1), with estimated errors no larger than 0.3 kcal mol(-1). The corresponding C3H3 isomerization energies are about 1 kcal mol(-1) larger than previous coupled-cluster results and several kcal mol(-1) below those previously obtained using density functional theory.

Structure and spectral features of H+(H2O)7: Eigen versus Zundel forms

The two dimensional (2D) to three dimensional (3D) transition for the protonated water cluster has been controversial, in particular, for H(+)(H(2)O)(7). For H(+)(H(2)O)(7) the 3D structure is predicted to be lower in energy than the 2D structure at most levels of theory without zero-point energy (ZPE) correction. On the other hand, with ZPE correction it is predicted to be either 2D or 3D depending on the calculational levels. Although the ZPE correction favors the 3D structure at the level of coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] using the aug-cc-pVDZ basis set, the result based on the anharmonic zero-point vibrational energy correction favors the 2D structure. Therefore, the authors investigated the energies based on the complete basis set limit scheme (which we devised in an unbiased way) at the resolution of the identity approximation Moller-Plesset second order perturbation theory and CCSD(T) levels, and found that the 2D structure has the lowest energy for H(+)(H(2)O)(7) [though nearly isoenergetic to the 3D structure for D(+)(D(2)O)(7)]. This structure has the Zundel-type configuration, but it shows the quantum probabilistic distribution including some of the Eigen-type configuration. The vibrational spectra of MP2/aug-cc-pVDZ calculations and Car-Parrinello molecular dynamics simulations, taking into account the thermal and dynamic effects, show that the 2D Zundel-type form is in good agreement with experiments.

Protonated carbonyl sulfide: Prospects for the spectroscopic observation of the elusive HSCO+ isomer

Spurred by the apparent conflict between ab initio predictions and infrared spectroscopic evidence regarding the relative stability of isomers of protonated carbonyl sulfide, key stationary points on the isomerization surface of HOCS(+) have been examined via systematic extrapolations of ab initio energies. Electron correlation has been accounted for using second-order Møller-Plesset perturbation theory and coupled cluster theory through triple excitations [CCSD, CCSD(T), and CCSDT] in conjunction with the correlation consistent hierarchy of basis sets, cc-pVXZ (X=D,T,Q,5,6). HSCO(+) is predicted to lie lower in energy than HOCS(+) by 4.86 kcal mol(-1), computed using the focal point extrapolation scheme of Allen and co-workers [J. Chem. Phys. 99, 4638 (1993)] with corrections for anharmonic zero-point vibrational energy, core correlation, non-Born-Oppenheimer, and scalar relativistic effects. A transition state has been located, constituting the barrier to isomerization of HSCO(+) to HOCS(+), lying 68.9 kcal mol(-1) higher in energy than HSCO(+). This is well above predicted exothermicity [DeltaH(r) (o)(0 K)=48.1 kcal mol(-1), cc-pVQZ CCSD(T)] for the reaction considered in the experiments (HSCO(+)+H(2)-->OCS+H(3) (+)). Though proton tunneling will lead to a lower effective barrier, this prediction is consistent with the lack of HSCO(+) in electrical discharges in H(2)OCS, since the relative populations of HOCS(+) and HSCO(+) will depend on the experimental details of the protonation route rather than the relative thermodynamic stability of the isomers. Anharmonic vibrational frequencies and vibrationally corrected rotational constants from cc-pVTZ CCSD(T) cubic and quartic force constants are provided, to aid in the spectroscopic observation of the energetically favorable but apparently elusive HSCO(+) isomer.

Estimation, Computation, and Experimental Correction of Molecular Zero-Point Vibrational Energies

For accurate thermochemical tests of electronic structure theory, accurate true anharmonic zero-point vibrational energies ZPVE(true) are needed. We discuss several possibilities to extract this information for molecules from density functional or wave function calculations and/or available experimental data: (1) Empirical universal scaling of density-functional-calculated harmonic ZPVE(harm)s, where we find that polyatomics require smaller scaling factors than diatomics. (2) Direct density-functional calculation by anharmonic second-order perturbation theory PT2. (3) Weighted averages of harmonic ZPVE(harm) and fundamental ZPVE(fund) (from fundamental vibrational transition frequencies), with weights (3/4, 1/4) for diatomics and (5/8,3/8) for polyatomics. (4) Experimental correction of the PT2 harmonic contribution, i.e., the estimate ZPVE(true)PT2 + (ZPVE(fund)expt - ZPVE(fund)PT2) for ZPVE(true). The (5/8,3/8) average of method 3 and the additive correction of method 4 have been proposed here. For our database of experimental ZPVE(true), consisting of 27 diatomics and 8 polyatomics, we find that methods 1 and 2, applied to the popular B3LYP and the nonempirical PBE and TPSS functionals and their one-parameter hybrids, yield polyatomic errors on the order of 0.1 kcal/mol. Larger errors are expected for molecules larger than those in our database. Method 3 yields errors on the order of 0.02 kcal/mol, but requires very accurate (e.g., experimental, coupled cluster, or best-performing density functional) input harmonic ZPVE(harm). Method 4 is the best-founded one that meets the requirements of high accuracy and practicality, requiring as experimental input only the highly accurate and widely available ZPVE(fund)expt and producing errors on the order of 0.05 kcal/mol that are relatively independent of functional and basis set. As a part of our study, we also test the ability of the density functionals to predict accurate equilibrium bond lengths and angles for a data set of 21 mostly polyatomic molecules (since all calculated ZPVEs are evaluated at the correspondingly calculated molecular geometries).

Accurate ab initio determination of spectroscopic and thermochemical properties of mono- and dichlorocarbenes

The best technically feasible values for the triplet-singlet energy gap and the enthalpies of formation of the HCCl and CCl2 radicals have been determined through the focal-point approach. The electronic structure computations were based on high-level coupled cluster (CC) methods, up to quadruple excitations (CCSDTQ), and large-size correlation-consistent basis sets, ranging from aug-cc-pVDZ to aug-cc-pV6Z, followed by extrapolation to the complete basis set limit. Small corrections due to core correlation, relativistic effects, diagonal Born-Oppenheimer correction, as well as harmonic and anharmonic zero-point vibrational energy corrections have been taken into account. The final estimates for the triplet-singlet energy gap, T0(ã), are 2170+/-40 cm-1 for HCCl and 7045+/-60 cm-1 for CCl2, favoring the singlet states in both cases. Complete quartic force fields in internal coordinates have been computed for both the X and ã states of both radicals at the frozen-core CCSD(T)/aug-cc-pVQZ level. Using these force fields vibrational energy levels of {HCCl, DCCl, CCl2} up to {6000, 5000, 7000} cm-1 were calculated both by second-order vibrational perturbation theory (VPT2) and variationally. These results, especially the variational ones, show excellent agreement with the experimentally determined energy levels. The enthalpies of formation of HCCl (X1A') and CCl2(X1A1), at 0 K, are 76.28+/-0.20 and 54.54+/-0.20 kcal mol-1, respectively.

HEAT: High accuracy extrapolated ab initio thermochemistry

A theoretical model chemistry designed to achieve high accuracy for enthalpies of formation of atoms and small molecules is described. This approach is entirely independent of experimental data and contains no empirical scaling factors, and includes a treatment of electron correlation up to the full coupled-cluster singles, doubles, triples and quadruples approach. Energies are further augmented by anharmonic zero-point vibrational energies, a scalar relativistic correction, first-order spin-orbit coupling, and the diagonal Born-Oppenheimer correction. The accuracy of the approach is assessed by several means. Enthalpies of formation (at 0 K) calculated for a test suite of 31 atoms and molecules via direct calculation of the corresponding elemental formation reactions are within 1 kJ mol(-1) to experiment in all cases. Given the quite different bonding environments in the product and reactant sides of these reactions, the results strongly indicate that even greater accuracy may be expected in reactions that preserve (either exactly or approximately) the number and types of chemical bonds.