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

Theoretical Study of the Isotope Effect in Optical Rotation

In this work, the isotope effect in optical rotation (OR) is examined by exploring structure-property relationships for H → D substitutions in chiral molecules. While electronic effects serve as the dominant source of optical activity, there is a non-negligible contribution from nuclear vibrations, which changes with isotopic substitution. We employ a test set of 50 small organic molecules: three-membered rings with varying heteroatoms (PCl, PH, S, NCl, NH, O, and NBr) and functional groups (Me, F), and simulations were run at the B3LYP/aug-cc-pVDZ level of theory. The objectives of this work are to determine locations of isotopic substitution that result in significant changes in the vibrational correction to the OR and to evaluate which vibrational modes and electronic response are the major contributors to the isotope effect. Molecules with more polarizable heteroatoms in the ring (e.g., S and P) have the largest change in the vibrational correction compared to the unsubstituted parent molecules. In many cases, isotopic substitution made to the hydrogens on the opposite side of the ring from the functional group provides the largest change in the OR. H/D wagging modes and C vibrations (for D-C centers) are the largest contributors to the isotope effect. This is explained with a molecular orbital decomposition analysis of the OR. The relevant vibrational modes affect the orbital transitions that are already significant at the equilibrium geometry. However, this effect is only large when polarizable heteroatoms are involved because the electron density surrounding them is diffuse enough to feel the subtle effect of change in mass due to isotopic substitution on the relevant vibrational modes.

High accuracy barrier heights, enthalpies, and rate coefficients for chemical reactions

Quantitative chemical reaction data, including activation energies and reaction rates, are crucial for developing detailed kinetic mechanisms and accurately predicting reaction outcomes. However, such data are often difficult to find, and high-quality datasets are especially rare. Here, we use CCSD(T)-F12a/cc-pVDZ-F12//ωB97X-D3/def2-TZVP to obtain high-quality single point calculations for nearly 22,000 unique stable species and transition states. We report the results from these quantum chemistry calculations and extract the barrier heights and reaction enthalpies to create a kinetics dataset of nearly 12,000 gas-phase reactions. These reactions involve H, C, N, and O, contain up to seven heavy atoms, and have cleaned atom-mapped SMILES. Our higher-accuracy coupled-cluster barrier heights differ significantly (RMSE of ∼5 kcal mol-1) relative to those calculated at ωB97X-D3/def2-TZVP. We also report accurate transition state theory rate coefficients [Formula: see text] between 300 K and 2000 K and the corresponding Arrhenius parameters for a subset of rigid reactions. We believe this data will accelerate development of automated and reliable methods for quantitative reaction prediction.

Fast Predictions of Reaction Barrier Heights: Toward Coupled-Cluster Accuracy

Quantitative estimates of reaction barriers are essential for developing kinetic mechanisms and predicting reaction outcomes. However, the lack of experimental data and the steep scaling of accurate quantum calculations often hinder the ability to obtain reliable kinetic values. Here, we train a directed message passing neural network on nearly 24,000 diverse gas-phase reactions calculated at CCSD(T)-F12a/cc-pVDZ-F12//ωB97X-D3/def2-TZVP. Our model uses 75% fewer parameters than previous studies, an improved reaction representation, and proper data splits to accurately estimate performance on unseen reactions. Using information from only the reactant and product, our model quickly predicts barrier heights with a testing MAE of 2.6 kcal mol^-1 relative to the coupled-cluster data, making it more accurate than a good density functional theory calculation. Furthermore, our results show that future modeling efforts to estimate reaction properties would significantly benefit from fine-tuning calibration using a transfer learning technique. We anticipate this model will accelerate and improve kinetic predictions for small molecule chemistry.

Critical benchmarking of popular composite thermochemistry models and density functional approximations on a probabilistically pruned benchmark dataset of formation enthalpies

First-principles calculation of the standard formation enthalpy, ΔH_f° (298 K), in such a large scale as required by chemical space explorations, is amenable only with density functional approximations (DFAs) and certain composite wave function theories (cWFTs). Unfortunately, the accuracies of popular range-separated hybrid, "rung-4" DFAs, and cWFTs that offer the best accuracy-vs-cost trade-off have until now been established only for datasets predominantly comprising small molecules; their transferability to larger systems remains vague. In this study, we present an extended benchmark dataset of ΔH_f° for structurally and electronically diverse molecules. We apply quartile-ranking based on boundary-corrected kernel density estimation to filter outliers and arrive at probabilistically pruned enthalpies of 1694 compounds (PPE1694). For this dataset, we rank the prediction accuracies of G4, G4(MP2), ccCA, CBS-QB3, and 23 popular DFAs using conventional and probabilistic error metrics. We discuss systematic prediction errors and highlight the role an empirical higher-level correction plays in the G4(MP2) model. Furthermore, we comment on uncertainties associated with the reference empirical data for atoms and the systematic errors stemming from these that grow with the molecular size. We believe that these findings will aid in identifying meaningful application domains for quantum thermochemical methods.

On the choice of coordinates in anharmonic theoretical vibrational spectroscopy: Harmonic vs. anharmonic coupling in vibrational configuration interaction

By a suitable choice of coordinates, the computational effort required for calculations of anharmonic vibrational spectra can be reduced significantly. By using suitable localized-mode coordinates obtained from an orthogonal transformation of the conventionally used normal-mode coordinates, anharmonic couplings between modes can be significantly reduced. However, such a transformation introduces harmonic couplings between the localized modes. To elucidate the role of these harmonic couplings, we consider the vibrational self-consistent field (VSCF)/vibrational configuration interaction (VCI) calculations for both few-mode model systems and for ethene as a molecular test case. We show that large harmonic couplings can result in significant errors in localized-mode L-VSCF/L-VCI calculations and study the convergence with respect to the size of the VCI excitation space. To further elucidate the errors introduced by harmonic couplings, we discuss the connection between L-VSCF/L-VCI and vibrational exciton models. With the help of our results, we propose an algorithm for the localization of normal modes in suitable subsets that are chosen to strictly limit the errors introduced by the harmonic couplings while still leading to maximally localized modes.

Efficient Estimation of Formation Enthalpies for Closed-Shell Organic Compounds with Local Coupled-Cluster Methods

Efficient estimation of the enthalpies of formation for closed-shell organic compounds via atom-equivalent-type computational schemes and with the use of different local coupled-cluster with single, double, and perturbative triple excitation (CCSD(T)) approximations was investigated. Detailed analysis of established sources of uncertainty, inclusive of contributions beyond frozen-core CCSD(T) and errors due to local CCSD(T) approximations and zero-point energy anharmonicity, suggests the lower limit of about 2 kJ·mol-1 for the expanded uncertainty of the proposed estimation framework. Among the tested computational schemes, the best-performing cases demonstrate expanded uncertainty of about 2.5 kJ·mol-1, based on the analysis against 44 critically evaluated experimental values. Computational efficiency, accuracy commensurable with that of a typical experiment, and absence of the need for auxiliary reactions and additional experimental data offer unprecedented advantages for practical use, such as prompt validation of existing measurements and estimation of missing values, as well as resolution of experimental conflicts. The utility of the proposed methodology was demonstrated using a representative sample of the most recent experimental measurements.

Anomalous description of the anharmonicity of bending motions of carbon–carbon double bonded molecules with the MP2 method: ethylene as a case study

In this work, we report anomalous descriptions of bending modes of the smallest carbon–carbon double bonded molecule ethylene with the MP2 method.

Doppler-limited high-resolution spectrum and VPT2 assisted assignment of the C-H stretch of CH2Br2

The Doppler limited non-saturated rotationally resolved infrared spectra of the symmetric and asymmetric CH-stretch bands of CH₂Br₂ have been measured. A continuous wave cavity ringdown setup with a widely tunable Mid-IR-OPO laser light source yielded a single-shot minimum absorption of 4.9×10^-8cm^-1. In contrast to the heavily congested ν₁ band, the ν₆ band showed partially resolved rotational features that may serve as suitable absorption targets in future environmental detection schemes for CH₂Br₂. A straightforward, VPT2 (second-order vibrational perturbation theory) assisted quantum-chemical approach for assigning the rotational structure has been tested using different model chemistries. The molecular structures, anharmonic frequencies and the structural changes upon vibrational excitation of CH₂Br₂ have been investigated. The predicted changes of the anharmonic rotational constants have been used together with available spectroscopic ground state constants to simulate the rovibrational structures of the ν₁ and ν₆ bands of CH₂Br₂. A refined analysis of the ν₆ band is presented yielding accurate values for the band origin and the rotational constants. A fit of the line positions of 312 prominent transitions of the three isotopologues revealed a low standard error of 0.00056cm^-1, hence within the absolute 0.0009cm^-1 wavelength accuracy of the used spectrometer setup. A combined analysis of the predicted line strengths and positions of the strong Q sub-branches of the ν₆ band has been performed to test the ability of the different density functionals for VPT2 prediction of anharmonic molecular constants. The M06/6-311++G(d,p) model chemistry turned out to yield reliable state-dependent rotational constants that are accurate enough to reproduce the overall rotational structure even without fitting.

On the benefits of localized modes in anharmonic vibrational calculations for small molecules

Anharmonic vibrational calculations can already be computationally demanding for relatively small molecules. The main bottlenecks lie in the construction of the potential energy surface and in the size of the excitation space in the vibrational configuration interaction (VCI) calculations. To address these challenges, we use localized-mode coordinates to construct potential energy surfaces and perform vibrational self-consistent field and L-VCI calculations [P. T. Panek and C. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all vibrational modes of two prototypical test cases, the ethene and furan molecules. We find that the mutual coupling between modes is reduced when switching from normal-mode coordinates to localized-mode coordinates. When using such localized-mode coordinates, we observe a faster convergence of the n-mode expansion of the potential energy surface. This makes it possible to neglect higher-order contributions in the n-mode expansion of the potential energy surface or to approximate higher-order contributions in hybrid potential energy surfaces, which reduced the computational effort for the construction of the anharmonic potential energy surface significantly. Moreover, we find that when using localized-mode coordinates, the convergence with respect to the VCI excitation space proceeds more smoothly and that the error at low orders is reduced significantly. This makes it possible to devise low-cost models for obtaining a first approximation of anharmonic corrections. This demonstrates that the use of localized-mode coordinates can be beneficial already in anharmonic vibrational calculations of small molecules and provides a possible avenue for enabling such accurate calculations also for larger molecules.

Anharmonic Theoretical Vibrational Spectroscopy of Polypeptides

Because of the size of polypeptides and proteins, the quantum-chemical prediction of their vibrational spectra presents an exceptionally challenging task. Here, we address one of these challenges, namely, the inclusion of anharmonicities. By performing the expansion of the potential energy surface in localized-mode coordinates instead of the normal-mode coordinates, it becomes possible to calculate anharmonic vibrational spectra of polypeptides efficiently and reliably. We apply this approach to calculate the infrared, Raman, and Raman optical activity spectra of helical alanine polypeptides consisting of up to 20 amino acids. We find that while anharmonicities do not alter the band shapes, simple scaling procedures cannot account for the different shifts found for the individual bands. This closes an important gap in theoretical vibrational spectroscopy by making it possible to quantify the anharmonic contributions and opens the door to a first-principles calculation of multidimensional vibrational spectra.

An Evaluation of Gas Phase Enthalpies of Formation for Hydrogen-Oxygen (HxOy) Species

We have compiled gas phase enthalpies of formation for nine hydrogen-oxygen species (HxOy) and selected recommended values for H, O, OH, H2O, HO2, H2O2, O3, HO3, and H2O3. The compilation consists of values derived from experimental measurements, quantum chemical calculations, and prior evaluations. This work updates the recommended values in the NIST-JANAF (1985) and Gurvich et al. (1989) thermochemical tables for seven species. For two species, HO3 and H2O3 (important in atmospheric chemistry) and not found in prior thermochemical evaluations, we also provide supplementary data consisting of molecular geometries, vibrational frequencies, and torsional potentials which can be used to compute thermochemical functions. For all species, we also provide supplementary data consisting of zero point energies, vibrational frequencies, and ion reaction energetics.

The electronic donation and frequency shifts on the YCCH⋯BH₄⁻ boron-bonded complexes (Y=H, CH₃, CF₃ and CCl₃)

In this theoretical work, the tetrahydroborate ion (BH4(-)) was used as proton acceptor in the formation of the YCC-H⋯BH4(-) complexes (Y=H, CH3, CCl3 and CF3). Using B3LYP/6-311++G(d,p) level of theory, the results of structure corroborate with the analyses of infrared spectra showing that the changes in the bond lengths are in good agreement with the frequency shifts of the HCC-H, H3CCC-H, Cl3CCC-H and F3CCC-H proton donors. Based on the calculations carried out by the Quantum Theory of Atoms in Molecules (QTAIM), the reductions of electronic density corroborate with the red shifts in the frequencies of the C-H bonds. In addition to that, the C-H bonds are polarized because the contributions of s orbital diminish whereas of p increase. In line with this, the variations on the atomic radii computed via QTAIM calculations show that carbon outweigh hydrogen as follows (ΔrC>ΔrH). This scenario is indirectly supported by the Bent's rule of the chemical bonding. Although the interaction energies (corrected with BSSE and ZPE) vary between -19 and -67 kJ mol(-1), these complexes interact without covalent character.

Pushing the limits in accurate vibrational structure calculations: anharmonic frequencies of lithium fluoride clusters (LiF)n, n = 2-10

The vibrational spectra of a series of small lithium fluoride clusters, i.e. (LiF)n, n = 2-10, were studied by vibrational configuration interaction (VCI) calculations relying on potential energy surfaces including three-mode coupling terms and being obtained from explicitly correlated local coupled cluster calculations. Due to the account for anharmonicity effects, the simulated spectra allow for a direct comparison with experimental data and may thus help to identify clusters in the experiments. Even structurally closely related clusters can clearly be distinguished by infrared spectroscopy. The largest system in this study required more than 1000 basis functions in the electronic structure calculations and more than 10(7) configurations in the vibrational structure calculations and became computationally feasible only due to a combination of different approximations and highly parallelized algorithms.

To π or not to π – how does methanol dock onto anisole?

Supersonic jet spectroscopy reveals that methanol opts against aromatic docking onto anisole despite a very close competition.

Towards black-box calculations of tunneling splittings obtained from vibrational structure methods based on normal coordinates

Multidimensional potential energy surfaces obtained from explicitly correlated coupled-cluster calculations and further corrections for high-order correlation contributions, scalar relativistic effects and core-correlation energy contributions were generated in a fully automated fashion for the double-minimum benchmark systems OH3(+) and NH3. The black-box generation of the potentials is based on normal coordinates, which were used in the underlying multimode expansions of the potentials and the μ-tensor within the Watson operator. Normal coordinates are not the optimal choice for describing double-minimum potentials and the question remains if they can be used for accurate calculations at all. However, their unique definition is an appealing feature, which removes remaining errors in truncated potential expansions arising from different choices of curvilinear coordinate systems. Fully automated calculations are presented, which demonstrate, that the proposed scheme allows for the determination of energy levels and tunneling splittings as a routine application.