Chemical accuracy in ab initio thermochemistry and spectroscopy: current strategies and future challenges

The ionization energy (IE) of NiC and the 0 K bond dissociation energies (D(0)) and heats of formation at 0 K (ΔH(o)(f0)) and 298 K (ΔH(o)(f298)) for NiC and NiC(+) are predicted by the wavefunction based CCSDTQ(Full)/CBS approach and the multireference configuration interaction (MRCI) method with Davidson correction (MRCI+Q). The CCSDTQ(Full)/CBS calculations presented here involve the approximation to the complete basis set (CBS) limit at the coupled cluster level up to full quadruple excitations along with the zero-point vibrational energy (ZPVE), high-order correlation, core-valence electronic (CV), spin-orbit coupling (SO), and scalar relativistic effect (SR) corrections. The present calculations provide the correct symmetry predictions for the ground states of NiC and NiC(+) to be (1)∑(+) and (2)∑(+), respectively. The CCSDTQ(Full)/CBS IE(NiC)=8.356 eV is found to compare favorably with the experimental IE value of 8.372 05±0.000 06 eV. The predicted IE(NiC) value at the MRCI+Q/cc-pwCV5Z level, including the ZPVE, SO, and SR effects is 8.00 eV, which is 0.37 eV lower than the experimental value. This work together with the previous experimental and theoretical investigations supports the conclusion that the CCSDTQ(Full)/CBS method is capable of providing reliable IE predictions for 3d-transition metal carbides, such as FeC and NiC. Furthermore, the CCSDTQ(Full)/CBS calculations give the prediction of D(0)(Ni-C)-D(0)(Ni(+)-C)=0.688 eV, which is also consistent with the experimental determination of 0.732 21±0.000 06 eV, whereas the MRCI+Q calculations (with relativistic and CV effects) predict a significantly lower value of 0.39 eV for D(0)(Ni-C)-D(0)(Ni(+)-C). The analysis of the correction terms shows that the CV and valence-valence electronic correlations beyond CCSD(T) wavefunction and the relativistic effect make significant contributions to the calculated thermochemical properties of NiC/NiC(+). For the experimental D(0) and ΔH(o)(f0) values of NiC/NiC(+), which are not known experimentally, we recommend the CCSDTQ(Full)/CBS predictions [D(0)(Ni-C)=4.048 eV, D(0)(Ni(+)-C)=3.360 eV, ΔH(o)(f0)(NiC)=749.0 kJ/mol, and ΔH(o)(f0)(NiC(+))=1555.1 kJ/mol].

The coupled-cluster approach, including single and double excitations and perturbative corrections for triple excitations, is capable of predicting molecular electronic energies and enthalpies of formation of small molecules in the gas phase with very high accuracy (specifically, with error bars less than 5 kJmol-1), provided that the electronic wavefunction is dominated by the Hartree-Fock configuration. This capability is illustrated by calculations on molecules containing O-H and O-F bonds, namely OH, FO, H2O, HOF, and F2O. To achieve this very high accuracy, it is imperative to account for electron-correlation effects in a quantitative manner, either by using explicitly correlated two-particle basis functions (R12 functions) or by extrapolating to the limit of a complete basis. Besides taking into account harmonic zero-point vibrational energies, it is also necessary to account for anharmonic corrections to the zero-point vibrational energies, to include the core orbitals into the coupled-cluster calculations, and to account for spin-orbit corrections and scalar relativistic effects. These additional corrections constitute small but significant contributions in the range of 1-4 kJmol-1 to the enthalpies of formation of the aforementioned molecules. The highly accurate coupled-cluster results, obtained by employing R12 functions and by including various corrections, are compared with standard Kohn-Sham density-functional calculations as well as with the Gaussian-2 and complete-basis-set model chemistries.

The OH radical reaction with Br2 and the subsequent reaction HOBr + Br are of exceptional importance to atmospheric chemistry and environmental chemistry. The entrance complex, transition state, and exit complex for both reactions have been determined using the coupled-cluster method with single, double, and perturbative triple excitations CCSD(T) with correlation consistent basis sets up to size cc-pV5Z and cc-pV5Z-PP. Coupled cluster effects with full triples (CCSDT) and full quadruples (CCSDTQ) are explicitly investigated. Scalar relativistic effects, spin-orbit coupling, and zero-point vibrational energy corrections are evaluated. The results from the all-electron basis sets are compared with those from the effective core potential (ECP) pseudopotential (PP) basis sets. The results are consistent. The OH + Br2 reaction is predicted to be exothermic 4.1 ± 0.5 kcal/mol, compared to experiment, 3.9 ± 0.2 kcal/mol. The entrance complex HO···BrBr is bound by 2.2 ± 0.2 kcal/mol. The transition state lies similarly well below the reactants OH + Br2. The exit complex HOBr···Br is bound by 2.7 ± 0.6 kcal/mol relative to separated HOBr + Br. The endothermicity of the reaction HOBr + Br → HBr + BrO is 9.6 ± 0.7 kcal/mol, compared with experiment 8.7 ± 0.3 kcal/mol. For the more important reverse (exothermic) HBr + BrO reaction, the entrance complex BrO···HBr is bound by 1.8 ± 0.6 kcal/mol. The barrier for the HBr + BrO reaction is 6.8 ± 0.9 kcal/mol. The exit complex (Br···HOBr) for the HBr + BrO reaction is bound by 1.9 ± 0.2 kcal/mol with respect to the products HOBr + Br.

We present a composite procedure based on explicitly correlated CCSD(T)-F12 calculations for accurate energetic predictions for carbon chain molecules HCnH encompassing both the even (HC2kH) and odd series (HC2k-1H), with the shorter members playing a key role in the evolution of cosmic carbon compounds in both circumstellar envelopes and interstellar medium. This approach considers the contributions of core-valence correlation, scalar relativistic effect, spin-orbit coupling, and zero-point vibrational energy in an additive manner. The computed ionization energies demonstrate outstanding agreement (±0.07 eV) up to a chain size of k = 6 and the literature heats of formation for k ≤ 2 are reproduced with "chemical accuracy" of 1 kcal mol-1. Among the various corrections included, the importance of core-valence correlation effect has been highlighted in the thermochemical calculations for carbon chain growth. The thermochemical trend toward infinite length is also highlighted by extrapolation of ionization energy and triplet-singlet splitting at the CCSD(T) level for k up to 15. The correlation between the end-group effect and the even-odd parity effect observed for HCnH chains has been established with the aid of intrinsic bond orbital localization.

Silylidene (SiCH2) and its isomers: Anharmonic rovibrational analyses for silylidene, silaacetylene, and silavinylidene

The ionization energies of VCH2 and VCH3, the various 0 K bond dissociation energies (D0s) in their neutrals and cations, and their respective heats of formation at 0 and 298 K are computed by the single-reference, wave function-based CCSDTQ/CBS procedure. The core of the composite method is the approximation to the complete basis set (CBS) limit at the coupled cluster (CC) level which includes up to full quadruple excitations. The zero-point vibrational energy, core-valence correlation, spin-orbit coupling, and scalar relativistic effects have their contributions incorporated in an additive manner. For the species in the current study, this protocol requires geometry optimizations and harmonic frequency calculations practically no higher than the CCSD(T)/aug-cc-pwCVTZ and CCSD(T)/aug-cc-pVTZ levels, respectively. The present calculations successfully predict D0(V+-CH3) = 2.126 eV and D0(V+-CH2) = 3.298 eV in remarkable agreement with the data recently measured by a spin-orbit state selected V+ + CH4 collision experiment (Phys. Chem. Chem. Phys. 2021, 23, 273-286). The good accord encourages the use of CCSDTQ/CBS protocol in thermochemical predictions of various feasible product channels identified in methane activation by transition metal species.

The bond dissociation energies (BDEs), fluoride and fluorocation affinities, and electron affinities of SeF(n) (n = 1-6), SeOF(n) (n = 0-4), and SeO(2)F(n) (n = 0-2) have been predicted with coupled cluster CCSD(T) theory extrapolated to the complete basis set limit. To achieve near chemical accuracy, additional corrections were added to the complete basis set binding energies based on frozen core coupled cluster theory energies. These included corrections for core-valence effects, scalar relativistic effects, for first-order atomic spin-orbit effects, and vibrational zero point energies. The adiabatic BDEs contain contributions from product reorganization energies and, therefore, can be much smaller than the diabatic BDEs and can vary over a wide range. For thermochemical calculations, the adiabatic values must be used, whereas for bond strength and kinetic considerations, the diabatic values should be used when only small displacements of the atoms without change of the geometry of the molecule are involved. The adiabatic Se-F BDEs of SeF(n) (n = 1-6) are SeF(6) = 90, SeF(5) = 27, SeF(4) = 93, SeF(3) = 61, SeF(2) = 86, and SeF = 76 kcal/mol, and the corresponding diabatic values are SeF(6) = 90, SeF(5) = 88, SeF(4) = 93, SeF(3) = 74, SeF(2) = 86, and SeF = 76 kcal/mol. The adiabatic Se-O BDEs of SeO(n) (n = 1-3), SeOF(n) (n = 1-4), and SeO(2)F(n) (n = 1,2) range from 23 to 107 kcal/mol, whereas the diabatic ones range from 62 to 154 kcal/mol. The adiabatic Se-F BDEs of SeOF(n) (n = 1-4) and SeO(2)F(n) (n = 1,2) range from 20 to 88 kcal/mol, whereas the diabatic ones range from 73 to 112 kcal/mol. The fluoride affinities of SeF(n), (n = 1-6), SeO(n), (n = 1-3), SeOF(n), (n = 1-4), and SeO(2)F(n) (n = 1,2) range from 15 to 121 kcal/mol, demonstrating that the Lewis acidity of these species covers the spectrum from very weak (SeF(6)) to very strong (SeO(3)) acids. The electron affinities which are a measure of the oxidizing power of a species, span a wide range from 1.56 eV in SeF(4) to 5.16 eV in SeF(5) and for the free radicals are much higher than for the neutral molecules. Another interesting feature of these molecules and ions stems from the fact that many of them possess both a Se free valence electron pair and a free unpaired valence electron, raising the questions of their preferred location and their influence on the Se-F and Se═O bond strengths.

To resolve a significant uncertainty in the heat of vaporization of silicona fundamental parameter in gas-phase thermochemistryΔH°f,0 [Si(g)] has been determined from a thermochemical cycle involving the precisely known experimental heats of formation of SiF4(g) and F(g) and a benchmark calculation of the total atomization energy (TAE0) of SiF4 using coupled-cluster methods. Basis sets up to [8s7p6d4f2g1h] on Si and [7s6p5d4f3g2h] on F have been employed, and extrapolations for residual basis set incompleteness applied. The contributions of inner-shell correlation (−0.08 kcal/mol), scalar relativistic effects (−1.88 kcal/mol), atomic spin−orbit splitting (−1.97 kcal/mol), and anharmonicity in the zero-point energy (+0.04 kcal/mol) have all been explicitly accounted for. Our benchmark TAE0 = 565.89 ± 0.22 kcal/mol leads to ΔH°f,0 [Si(g)] = 107.15 ± 0.38 kcal/mol (ΔH°f,298 [Si(g)] = 108.19 ± 0.38 kcal/mol): between the JANAF/CODATA value of 106.5 ± 1.9 kcal/mol and the revised value proposed by Grev and Schaefer [ J. Chem. Phys. 1992, 97, 8389], 108.1 ± 0.5 kcal/mol. The revision will be relevant for future computational studies on heats of formation of silicon compounds. Among standard computational thermochemistry methods, G2 and G3 theory exhibit large errors, while CBS-Q performs relatively well, and the very recent W1 theory reproduces the present calibration result to 0.1 kcal/mol.

Dipole-bound anionic states of CH3CN, C3H2, and (HF)2 were studied using highly correlated electronic structure methods and extended one-electron basis sets. The electron detachment energies were calculated using the coupled cluster method with single, double, and noniterative triple excitations. Geometrical relaxation of the molecular framework upon electron attachment and the difference in the harmonic zero-point vibrational energies between the neutral and the dipole-bound anionic species were calculated at the MP2 level of theory. We demonstrate that the dispersion interaction between the loosely bound electron and the electrons of the neutral molecule is an important component of the electron binding energy, comparable in magnitude to the electrostatic electron–dipole stabilization. The geometrical relaxation upon electron attachment and the change in the zero-point vibrational energy is important for the weakly bound HF dimer. The predicted values of the vertical electron detachment energies for the dipole bound states of CH3CN and C3H2 of 112 and 188 cm−1, respectively, are in excellent agreement with the recent experimental results of 93 and 171±50 cm−1, respectively. For (HF)2−, the predicted value of adiabatic electron detachment energy is 396 cm−1, whereas the experimental vertical detachment energy is 508±24 cm−1. The possibility of formation of the neutral dimer in an excited vibrational state is considered. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 183–191, 1997

Geometry parameters, frequencies, heats of formation, and bond dissociation energies are predicted for the simple alkaline earth (Be, Mg and Ca) fluorides, chlorides, oxides, and hydroxides at the coupled cluster theory [CCSD(T)] level including core-valence correlation with the aug-cc-pwCVnZ basis sets up to n = 5 in some cases. Additional corrections (scalar relativistic effects, vibrational zero-point energies, and atomic spin-orbit effects) were necessary to accurately calculate the total atomization energies and heats of formation. The calculated geometry parameters, frequencies, heats of formation, and bond dissociation energies are compared with the available experimental data. For a number of these alkaline earth compounds, the experimental geometries and energies are not reliable. MgF(2) and BeF(2) are predicted to be linear and CaF(2) is predicted to be bent. BeOH is predicted to be bent, whereas MgOH and CaOH are linear. The OBeO angle in Be(OH)(2) is not linear, and the molecule has C(2) symmetry. The heat of formation at 298 K for MgO is calculated to be 32.3 kcal/mol, and the bond dissociation energy at 0 K is predicted to be 61.5 kcal/mol.

Geometry parameters, frequencies, heats of formation, and bond dissociation energies are predicted for simple alkali metal compounds (hydrides, chlorides, fluorides, hydroxides and oxides) of Li, Na, and K from coupled cluster theory [CCSD(T)] calculations including core-valence correlation with the aug-cc-pwCVnZ basis set (n = D, T, Q, and 5). To accurately calculate the heats of formation, the following additional correction were included: scalar relativistic effects, atomic spin-orbit effects, and vibrational zero-point energies. For calibration purposes, the properties of some of the lithium compounds were predicted with iterative triple and quadruple excitations via CCSDT and CCSDTQ. The calculated geometry parameters, frequencies, heats of formation, and bond dissociation energies were compared with all available experimental measurements and are in excellent agreement with high-quality experimental data. High-level calculations are required to correctly predict that K(2)O is linear and that the ground state of KO is (2)Sigma(+), not (2)Pi, as in LiO and NaO. This reliable and consistent set of calculated thermodynamic data is appropriate for use in combustion and atmospheric simulations.

Methyl isocyanide, CH3NC, is a key compound in astrochemistry and astrobiology. A combined theoretical and experimental investigation of the single photon ionization of gas phase methyl isocyanide and its fragmentation pathways is presented. Vacuum ultraviolet (VUV) synchrotron radiation based experiments are used to measure the threshold photoelectron photoion coincidence (TPEPICO) spectra between 10.6 and 15.5 eV. This allowed us to experimentally determine the adiabatic ionization energy (AIE) and fragment ion appearance energies (AE) of gas-phase methyl isocyanide. Its AIE has been measured with a precision never achieved before. It is found to be AIEexp = 11.263 ± 0.005 eV. We observe a vibrational progression upon ionization corresponding to the population of vibrational levels of the ground state of the methyl isocyanide cation. In addition, four fragment ion appearance energies (AEs) were measured to be AE (m/z 40) = 12.80 ± 0.05 eV, AE (m/z 39) = 13.70 ± 0.05, AE (m/z 15) = 13.90 ± 0.05 eV, AE (m/z 14) 13.85 ± 0.05 eV, respectively. In order to interpret the experimental data, we performed state-of-the-art computations using the explicitly correlated coupled cluster approach. We also considered the zero-point vibrational energy (ZPVE), core-valence (CV) and scalar relativistic (SR) effects. The results of theoretical calculations of the AIE and AEs are in excellent agreement with the experimental findings allowing for assignment of the fragmentations to the loss of neutral H, H2, CN and HCN upon ionization of CH3NC. The computations show that in addition to the obvious bond breakings, some of the corresponding ionic fragments result from rearrangements - upon photon absorption - either before or after electron ejection.

The ionization energies (IEs) of TiO and TiO2 and the 0 K bond dissociation energies (D0) and the heats of formation at 0 K (ΔH°f0) and 298 K (ΔH°f298) for TiO/TiO+ and TiO2/TiO2+ are predicted by the wave-function-based CCSDTQ/CBS approach. The CCSDTQ/CBS calculations involve the approximation to the complete basis set (CBS) limit at the coupled cluster level up to full quadruple excitations along with the zero-point vibrational energy (ZPVE), high-order correlation (HOC), core-valence (CV) electronic, spin-orbit (SO) coupling, and scalar relativistic (SR) effect corrections. The present calculations yield IE(TiO) = 6.815 eV and are in good agreement with the experimental IE value of 6.819 80 ± 0.000 10 eV determined in a two-color laser-pulsed field ionization-photoelectron (PFI-PE) study. The CCSDT and MRCI+Q methods give the best predictions to the harmonic frequencies: ωe (ωe+) = 1013 (1069) and 1027 (1059) cm-1 and the bond lengths re (re+) = 1.625 (1.587) and 1.621 (1.588) Å, for TiO (TiO+) compared with the experimental values. Two nearly degenerate, stable structures are found for TiO2 cation: TiO2+(C2v) structure has two equivalent TiO bonds, while the TiO2+(Cs) structure features a long and a short TiO bond. The IEs for the TiO2+(C2v)←TiO2 and TiO2+(Cs)←TiO2 ionization transitions are calculated to be 9.515 and 9.525 eV, respectively, giving the theoretical adiabatic IE value in good agreement with the experiment IE(TiO2) = 9.573 55 ± 0.000 15 eV obtained in the previous vacuum ultraviolet (VUV)-PFI-PE study of TiO2. The potential energy surface of TiO2+ along the normal vibrational coordinates of asymmetric stretching mode (ω3+) is nearly flat and exhibits a double-well potential with the well of TiO2+ (Cs) situated around the central well of TiO2+(C2v). This makes the theoretical calculation of ω3+ infeasible. For the symmetric stretching (ω1+), the current theoretical predictions overestimate the experimental value of 829.1 ± 2.0 cm-1 by more than 100 cm-1. This work together with the previous experimental and theoretical investigations supports the conclusion that the CCSDTQ/CBS approach is capable of providing reliable IE and D0 predictions for TiO/TiO+ and TiO2/TiO2+ with error limits less than or equal to 60 meV. The CCSDTQ/CBS calculations give the predictions of D0(Ti+-O) - D0(Ti-O) = 0.004 eV and D0(O-TiO) - D0(O-TiO+) = 2.699 eV, which are also consistent with the respective experimental determination of 0.008 32 ± 0.000 10 and 2.753 75 ± 0.000 18 eV.

Computational thermochemistry: Automated generation of scale factors for vibrational frequencies calculated by electronic structure model chemistries

Atomization energies at 0 K and heats of formation at 0 and 298 K are predicted for the neutral and ionic N(x)F(y) and O(x)F(y) systems using coupled cluster theory with single and double excitations and including a perturbative triples correction (CCSD(T)) method with correlation consistent basis sets extrapolated to the complete basis set (CBS) limit. To achieve near chemical accuracy (±1 kcal/mol), three corrections to the electronic energy were added to the frozen core CCSD(T)/CBS binding energies: corrections for core-valence, scalar relativistic, and first order atomic spin-orbit effects. Vibrational zero point energies were computed at the CCSD(T) level of theory where possible. The calculated heats of formation are in good agreement with the available experimental values, except for FOOF because of the neglect of higher order correlation corrections. The F(+) affinity in the N(x)F(y) series increases from N(2) to N(2)F(4) by 63 kcal/mol, while that in the O(2)F(y) series decreases by 18 kcal/mol from O(2) to O(2)F(2). Neither N(2) nor N(2)F(4) is predicted to bind F(-), and N(2)F(2) is a very weak Lewis acid with an F(-) affinity of about 10 kcal/mol for either the cis or trans isomer. The low F(-) affinities of the nitrogen fluorides explain why, in spite of the fact that many stable nitrogen fluoride cations are known, no nitrogen fluoride anions have been isolated so far. For example, the F(-) affinity of NF is predicted to be only 12.5 kcal/mol which explains the numerous experimental failures to prepare NF(2)(-) salts from the well-known strong acid HNF(2). The F(-) affinity of O(2) is predicted to have a small positive value and increases for O(2)F(2) by 23 kcal/mol, indicating that the O(2)F(3)(-) anion might be marginally stable at subambient temperatures. The calculated adiabatic ionization potentials and electron affinities are in good agreement with experiment considering that many of the experimental values are for vertical processes.