Frequency Scale Factors for Some Double-Hybrid Density Functional Theory Procedures: Accurate Thermochemical Components for High-Level Composite Protocols

Accurate Structures and Rotational Constants of Steroid Hormones at DFT Cost: Androsterone, Testosterone, Estrone, β-Estradiol, and Estriol

A comprehensive analysis of the structural, conformational, and spectroscopic properties in the gas phase has been performed for five prototypical steroid hormones, namely, androsterone, testosterone, estrone, β-estradiol, and estriol. The revDSD-PBEP86 double-hybrid functional in conjunction with the D3BJ empirical dispersion and a suitable triple-ζ basis set provides accurate conformational energies and equilibrium molecular structures, with the latter being further improved by proper account of core-valence correlation. Average deviations within 0.1% between computed and experimental ground state rotational constants are reached when adding to those equilibrium values vibrational corrections obtained at the cost of standard harmonic frequencies thanks to the use of a new computational tool. Together with the intrinsic interest of the studied hormones, the accuracy of the results obtained at DFT cost for molecules containing about 50 atoms paves the way toward the accurate investigations of other flexible bricks of life.

Quantum chemistry meets high-resolution spectroscopy for characterizing the molecular bricks of life in the gas-phase

Computation of accurate geometrical structures and spectroscopic properties of large flexible molecules in the gas-phase is tackled at an affordable cost using a general exploration/exploitation strategy. The most distinctive feature of the approach is the careful selection of different quantum chemical models for energies, geometries and vibrational frequencies with the aim of maximizing the accuracy of the overall description while retaining a reasonable cost for all the steps. In particular, a composite wave-function method is used for energies, whereas a double-hybrid functional (with the addition of core-valence correlation) is employed for geometries and harmonic frequencies and a cheaper hybrid functional for anharmonic contributions. A thorough benchmark based on a wide range of prototypical molecular bricks of life shows that the proposed strategy is close to the accuracy of state-of-the-art composite wave-function methods, and is applicable to much larger systems. A freely available web-utility post-processes the geometries optimized by standard electronic structure codes paving the way toward the accurate yet not prohibitively expensive study of medium- to large-sized molecules by experimentally-oriented researchers.

Theoretical Kinetic Study on Hydrogen Abstraction Reactions from n-Pentane by NO2

The interaction of fuel with NOx chemistry is important for the construction of the reaction mechanism and engine application. In this work, the reaction pathways of nC5H12 + NO2 were studied by high-level electronic structure calculations (DLPNO-CCSD(T)-F12/cc-pVTZ-F12//B2PLYPD3/cc-pVTZ). The rate constants were calculated by using the multistructural canonical transition-state theory with the Eckart tunneling method (TST/MS-T/ET). The studied condition is in a wide temperature range of 298-2400 K. The influence of MS-T anharmonicity and tunneling effect will be clarified for these site-specific H-abstraction pathways. The result reflects the large deviation introduced by the treatment of MS-T anharmonicity, especially at a high temperature. For the same type of reactions, the rate constants of H-abstraction both occurring at the secondary carbon are not almost identical. The branching ratios show that abstraction from the secondary site forming cis-HONO (R2c) contributes 36-78% to nC5H12 consumption in the temperature range of 298-2400 K. The current results show that the multistructural torsional anharmonicity has a crucial influence on the accurate estimation of branching ratios.

Accurate Thermochemical and Kinetic Parameters at Affordable Cost by Means of the Pisa Composite Scheme (PCS)

A new strategy for the computation at an affordable cost of geometrical structures, thermochemical parameters, and rate constants for medium-sized molecules in the gas phase is proposed. The most distinctive features of the new model are the systematic use of cc-pVnZ-F12 basis sets, the addition of MP2 core-valence correlation in geometry optimizations by a double-hybrid functional, the separate extrapolation of MP2 and post-MP2 contributions, and the inclusion of anharmonic contributions in zero-point energies and thermodynamic functions. A thorough benchmark based on a wide range of prototypical systems shows that the new scheme outperforms the most well-known model chemistries without the need for any empirical parameter. Additional tests show that the computed zero-point energies and thermal contributions can be confidently used for obtaining accurate thermochemical and kinetic parameters. Since the whole computational workflow is translated in a black-box procedure, which can be followed with standard electronic structure codes, the way is paved for the accurate yet not prohibitively expensive study of medium- to large-sized molecules also by nonspecialists.

Molecular Geometries and Vibrational Contributions to Reaction Thermochemistry Are Surprisingly Insensitive to the Choice of Basis Sets

Calculation of molecular geometries and harmonic vibrational frequencies are pre-requisites for thermochemistry calculations. Contrary to conventional wisdom, this paper demonstrates that quantum chemical predictions of the thermochemistry of many gas and solution phase chemical reactions appear to be very insensitive to the choice of basis sets. For a large test set of 80 diverse organic and transition-metal-containing reactions, variations in reaction free energy based on geometries and frequencies calculated using a variety of double and triple-zeta basis sets from the Pople, Jensen, Ahlrichs, and Dunning families are typically less than 4 kJ mol^-1, especially when the quasiharmonic oscillator correction is applied to mitigate the effects of low-frequency modes. Our analysis indicates that for many organic molecules and their transition states, high-level revDSD-PBEP86-D4 and DLPNO-CCSD(T)/(aug-)cc-pVTZ single-point energies usually vary by less than 2 kJ mol^-1 on density functional theory geometries optimized using basis sets ranging from 6-31+G(d) to aug-pcseg-2 and aug-cc-pVTZ. In cases where these single-point energies vary significantly, indicating sensitivity of molecular geometries to the choice of basis set, there is often substantial cancellation of errors when the reaction energy or barrier is calculated. The study concludes that the choice of basis set for molecular geometry and frequencies, particularly those considered in this study, is not critical for the accuracy of thermochemistry calculations in the gas or solution phase.

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

Scytonemin redox status in a filamentous cyanobacterium visualized by an excitation-laser-line-scanning spontaneous Raman scattering spectral microscope

Some cyanobacteria produce a UVA-absorbing pigment, scytonemin, at extracellular sheaths. Although scytonemin-containing dark sheaths are recognizable through optical microscopes and its redox changes have been known for decades, there has been no report to obtain images of both oxidized and reduced scytonemins at subcellular resolution. Here, we show that a spontaneous Raman scattering spectral microscopy based on an excitation-laser-line-scanning method unveil 3D subcellular distributions of both the oxidized and reduced scytonemins in a filamentous cyanobacterium. The redox changes of scytonemin were supported by comparison in the Raman spectra between the cyanobacterial cells, solid-state scytonemin and quantum chemical normal mode analysis. Distributions of carotenoids, phycobilins, and the two redox forms of scytonemin were simultaneously visualized with an excitation wavelength at 1064 nm that is virtually free from the optical screening by the dark sheaths. The redox differentiation of scytonemin will advance our understanding of the redox homeostasis and secretion mechanisms of individual cyanobacteria as well as microscopic chemical environments in various microbial communities. The line-scanning Raman microscopy based on the 1064 nm excitation is thus a promising tool for exploring hitherto unreported Raman spectral features and distribution of nonfluorescent molecules embedded below nontransparent layers for visible light, while avoiding interference by autofluorescence.

Model Chemistry Recommendations for Scaled Harmonic Frequency Calculations: A Benchmark Study

Despite the widespread popularity of scaled harmonic frequency calculations to predict experimental fundamental frequencies in chemistry, sparse benchmarking is available to guide users on the appropriate level of theory and basis set choices (model chemistry) or deep understanding of expected errors. An updated assessment of the best approach for scaling to minimize errors is also overdue. Here, we assess the performance of over 600 popular, contemporary, and robust model chemistries in the calculation of scaled harmonic frequencies, evaluating different scaling factor types and their implications in the scaled harmonic frequencies and model chemistry performance. We can summarize our results into three main findings: (1) Using model-chemistry-specific scaling factors optimized for three different frequency regions (low (<1,000 cm^-1), mid (1,000-2,000 cm^-1), and high (>2,000 cm^-1)) results in substantial improvements in the agreement between the scaled harmonic and experimental frequencies compared to other choices. (2) Larger basis sets and more robust levels of theory generally lead to superior performance; however, the particular model chemistry choice matters and poor choices lead to significantly reduced accuracies. (3) Outliers are expected in routine calculations regardless of the model chemistry choice. Our benchmarking results here do not consider the intensity of vibrational transitions; however, we draw upon previous benchmarking results for dipole moments that highlight the importance of diffuse functions (i.e., augmented basis sets) in high-quality intensity predictions. In terms of specific recommendations, overall, the highest accuracy model chemistries are double-hybrid density functional approximations with a non-Pople augmented triple-ζ basis set, which can produce median frequency errors down to 7.6 cm^-1 (DSD-PBEP86/def2-TZVPD), which is very close to the error in the harmonic approximation, i.e., the anharmonicity error. Double-ζ basis sets should not be used with double-hybrid functionals as there is no improvement compared to hybrid functional results (unlike for double-hybrid triple-ζ model chemistries). Note that 6-311G* and 6-311+G* basis sets perform like a double-ζ basis set for vibrational frequencies. After scaling, all studied hybrid functionals with non-Pople triple-ζ basis sets will produce median errors of less than 15 cm^-1, with the best result of 9.9 cm^-1 with B97-1/def2-TZVPD. Appropriate matching of double-ζ basis sets with hybrid functionals can produce high-quality results, but the precise choice of functional and basis set is more important. The B97-1, TPSS0-D3(BJ), or ωB97X-D hybrid density functionals with 6-31G*, pc-1, or pcseg-1 are recommended for fast routine calculations, all delivering median errors of 11-12 cm^-1. Note that dispersion corrections are not easily available for B97-1; given its strong performance here, we recommend these be added to major programs in coming updates.

High-Level Quantum Chemistry Reference Heats of Formation for a Large Set of C, H, N, and O Species in the NIST Chemistry Webbook and the Identification and Validation of Reliable Protocols for Their Rapid Computation

A recent study has examined the accuracy of NIST heats of formation for a set of C, H, and O-containing species with a proposed low-cost quantum chemistry approach. In the present study, we have used high-level methods such as W1X-2 to obtain these data more rigorously, which we have then used to assess the NIST and the previously computed values. We find that many of these NIST data that are as suggested to be unreliable by the previous study are indeed inconsistent with our high-level reference values. However, we also find substantial deviations for the previously computed values from our benchmark. Thus, we have assessed the performance of alternative low-cost methods. In our assessment, we have additionally examined C, H, N, and O-containing species for which heats of formation are available from the NIST database. We find the ωB97M-V/ma-def2-TZVP, DSD-PBEP86/ma-def2-TZVP, and CCSD(T)-F12b/aug'-cc-pVDZ methods to be adequate for obtaining heats of formation with the atomization approach, once their atomic energies are optimized with our benchmark. Notably, the low-cost ωB97M-V method yields values that agree to be within 10 kJ mol^-1 for more than 90% of the (∼1500) species. A higher 20 kJ mol^-1 threshold captures 98% of the data. The outlier species typically contain many electron-withdrawing (nitro) groups. In these cases, the use of isodesmic-type reactions rather than the atomization approach is more reliable. Our assessment has also identified significant outliers from the NIST database, for which experimental re-determination of the heats of formation would be desirable.

VIBFREQ1295: A New Database for Vibrational Frequency Calculations

High-throughput approaches for producing approximate vibrational spectral data for molecules of astrochemistry interest rely on harmonic frequency calculations using computational quantum chemistry. However, model chemistry recommendations (i.e., a level of theory and basis set pair) for these calculations are not yet available and, thus, thorough benchmarking against comprehensive benchmark databases is needed. Here, we present a new database for vibrational frequency calculations (VIBFREQ1295) storing 1295 experimental fundamental frequencies and CCSD(T)(F12*)/cc-pVDZ-F12 ab initio harmonic frequencies from 141 molecules. VIBFREQ1295's experimental data was complied through a comprehensive review of contemporary experimental data, while the ab initio data was computed here. The chemical space spanned by the molecules chosen is considered in-depth and is shown to have good representation of common organic functional groups and vibrational modes. Scaling factors are routinely used to approximate the effect of anharmonicity and convert computed harmonic frequencies to predicted fundamental frequencies. With our experimental and high-level ab initio data, we find that a single global uniform scaling factor of 0.9617(3) results in median differences of 15.9(5) cm^-1. A far superior performance with a median difference of 7.5(5) cm^-1 can be obtained, however, by using separate scaling factors (SFs) for three regions: frequencies less than 1000 cm^-1 (SF = 0.987(1)), between 1000 and 2000 cm^-1 (SF = 0.9727(6)), and above 2000 cm^-1 (SF = 0.9564(4)). This sets a lower bound for the performance that could be reliably obtained using scaling of harmonic frequency calculations to predict experimental fundamental frequencies. VIBFREQ1295's most important purpose is to provide a robust database for benchmarking the performance of any vibrational frequency calculations. VIBFREQ1295 data could also be used to train machine-learning models for the prediction of vibrational spectra and as a reference and data starting point for more detailed spectroscopic modeling of particular molecules. The database can be found as part of the Supporting Information for this paper or in the Harvard DataVerse at https://doi.org/10.7910/DVN/VLVNU7.

ATOMIC-2 Protocol for Thermochemistry

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2_um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2_um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2_um analyses.

Secondary kinetic deuterium isotope effects on unimolecular cleavage reactions: Zero-point vibrational energy and qualitative RRKM theory

Secondary kinetic isotope effects arise as the result of transition-state zero-point vibrational energy differences. Unimolecular simple cleavage reactions of gas-phase ions in mass spectrometers allow detailed studies of isotope effects on competing reactions, particularly when examined in intramolecular competition experiments where interpretation requires very few simplifying assumptions. The zero-point energy differences reflect changes of isotope sensitive vibrational properties, and both α- and β-secondary deuterium isotope effects are related to the sp ³  → sp ² hybridization changes that accompany bond cleavage. Deuterium substitution three bonds or more removed from the bond broken also gives rise to isotope effects, but their origin is less easily interpreted. The magnitude and variation of the observed effects depend not only on zero-point energy differences; a number of additional factors play a role. The influence of the critical energy, the excess energy, the size of the reactant, and the presence of competing reactions can be rationalized within a simple, qualitative RRKM framework. The distinction between kinetic and thermodynamic isotope effects is not always obvious.

Accurate Thermochemistry for Main-Group Elements up to Xenon with the Wn-P34 Series of Composite Methods

In the present study, we introduce the accurate Wn-P34 quantum chemistry composite methods with applicability to heavy p-block elements up to xenon. For a set of thermochemical properties for prototypical third- and fourth-row species and for a diverse set of small light-main-group species, they show accuracies of ∼3 kJ mol^-1 or better. Overall, the Wn-P34 methods are comparable in accuracy to Wn, with a widened applicability to heavier elements. We have used Wn-P34 to compile the P34 set of accurate thermochemical values for heavy p-block species, and we have applied this set to assess a wide range of lower-cost methods. The results of our assessment show that the G4(MP2)-XK composite method provides adequate treatments for these species, but several widely used double-hybrid density functional theory (DH-DFT) methods show uncharacteristically large deviations. In contrast, we find it presently surprising that some pure and hybrid DFT methods such as TPSS and SCANh perform quite well. We hope that our findings and new tools would facilitate the application of computational chemistry for heavy elements, of which the properties are yet to be broadly explored.

Polycyclic aromatic hydrocarbons: from small molecules through nano-sized species towards bulk graphene

We have examined the use of systematic bond-separation reactions and purposely constructed chemistry-preserving isodesmic reactions for the thermochemical calculation of aromatic hydrocarbon species. The bond-separation approach yields somewhat disappointing accuracy even when the reaction energies are obtained with generally robust composite and double-hybrid (DH) density functional theory (DFT) methods. In contrast, for the purposely constructed reactions, we find a dramatic improvement in the accuracy for energies calculated with all methods examined. Notably, for medium-sized aromatic hydrocarbons, we find that an effective approach for formulating a well-balanced reaction is to split the target species into two halves with an aromatic overlapping region. Overall, the G4(MP2)-XK, MPW2PLYP, MN15, PBE, and DC-DFTB3 methods are reasonable within their respective classes of methods for the calculation of bond-separation as well as chemistry-preserving isodesmic reactions. We have further computed per-carbon atomization energy (AE) for a series of D_6h benzene-type molecules, and thus obtained a formula for extrapolation to the graphene limit [AE_n = 711.5 × (1 - 1/n^0.640) kJ mol^-1, where n = number of carbons]. It suggests that nano-graphene with a length larger than 10 nm would resemble properties of bulk graphene, and conversely, downsizing a nano-graphene beyond this point may lead to considerably altered properties from the bulk.

Density Functional Geometries and Zero-Point Energies in Ab Initio Thermochemical Treatments of Compounds with First-Row Atoms (H, C, N, O, F)

Density functionals are often used in ab initio thermochemistry to provide optimized geometries for single-point evaluations at a high level and to supply estimates of anharmonic zero-point energies (ZPEs). Their use is motivated by relatively high accuracy at a modest computational expense, but a thorough assessment of geometry-related error seems to be lacking. We have benchmarked 53 density functionals, focusing on approximations of the first four rungs and on relatively small basis sets for computational efficiency. Optimized geometries of 279 neutral first-row molecules (H, C, N, O, F) are judged by energy penalties relative to the best available geometries, using the composite model ATOMIC/B5 as energy probe. Only hybrid functionals provide good accuracy with root-mean-square errors around 0.1 kcal/mol and maximum errors below 1.0 kcal/mol, but not all of them do. Conspicuously, first-generation hybrids with few or no empirical parameters tend to perform better than highly parameterized ones. A number of them show good accuracy already with small basis sets (6-31G(d), 6-311G(d)). As is standard practice, anharmonic ZPEs are estimated from scaled harmonic values. Statistics of the latter show less performance variation among functionals than observed for geometry-related error, but they also indicate that ZPE error will generally dominate. We have selected PBE0-D3/6-311G(d) for the next version of the ATOMIC protocol (ATOMIC-2) and studied it in more detail. Empirical expressions have been calibrated to estimate bias corrections and 95% uncertainty intervals for both geometry-related error and scaled ZPEs.

Combined experimental and theoretical study on photoionization cross sections of benzonitrile and o/m/p-cyanotoluene

Photoionization cross sections (PICSs) for the products of the reaction from CN with toluene, including benzonitrile and o/m/p-cyanotoluene, were obtained at photon energies ranging from ionization thresholds to 14 eV by tunable synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS). Theoretical calculations based on the frozen-core Hartree-Fock approximation and Franck-Condon simulations were carried out to cross-verify the measured PICS. The results show that the photoionization cross sections of benzonitrile and cyanotoluene isomers are similar. The generalized charge decomposition analysis was used to investigate the components of the highest occupied molecular orbital (HOMO) and HOMO-1. It was found that the HOMO and HOMO-1 of benzonitrile and cyanotoluene isomers are dominated by the features of the benzene ring, indicating that the substitution of CN and methyl has a minor influence on the PICS of the studied molecules. The reported PICS on benzonitrile and cyanotoluene isomers in the present work could contribute to the near-threshold PIMS experiments and determine the ionization and dissociation rates in interstellar space for these crucial species. The theoretical analysis on characteristics of molecular orbitals provides clues to estimating the PICS of similar substituted aromatic compounds.

Hydride Affinities for Main-Group Hydride Reductants: Assessment of Density Functionals and Trends in Reactivities

In the present study, we have examined hydride affinities relevant to a range of group 13 and group 14 reductants. We use the high-level W1X-G0, G4(MP2)-XK, and DSD-PBEP86 methods to obtain the RHA42 set of accurate reductant hydride affinities. Assessment of DFT methods with the RHA42 set shows that all functionals that we have examined are fairly accurate. Overall, we find ωB97X-V to be the most accurate. The MN12-SX screened-exchange functional and the nonhybrid B97-D3BJ method also perform well, and they may provide a lower-cost means for obtaining hydride affinities. The trend in the hydride affinities suggests an increased reducing power when one moves down the periodic table, e.g., with TlH₃ being a stronger reductant than BH₃. We also find that group 13 hydrides are stronger reductants than the group 13 analogues. In general, substitution of a hydrogen, e.g., BH₂⁺ → BHMe⁺, and the formation of dimer, e.g., BH₂⁺ → B₂H₅⁺, also lead to stronger reductants. A notable observation is the small hydride affinities for silyl cations, which are indicative of the potential of silanes as strong reducing agents. In particular, poly(methylhydrosiloxane) (PMHS) cations are associated with especially small hydride affinities owing to the presence of intramolecular oxygen atoms that can stabilize the cation center. We have further found the germanium analogues of the silanes to be more reactive, and they may further widen the scope of main-group hydride reducing agents.

Fullerene Thermochemical Stability: Accurate Heats of Formation for Small Fullerenes, the Importance of Structural Deformation on Reactivity, and the Special Stability of C60

We have used quantum chemistry computations, in conjunction with isodesmic-type reactions, to obtain accurate heats of formation (HoFs) for the small fullerenes C₂₀ (2358.2 ± 8.0 kJ mol^-1), C₂₄ (2566.2 ± 7.6), and the lowest-energy isomers of C₃₂ (2461.1 ± 15.4), C₄₂ (2629.0 ± 20.5), and C₅₄ (2686.2 ± 25.3). As part of this endeavor, we have also obtained accurate HoFs for several medium-sized molecules, namely 216.6 ± 1.4 for fulvene, 375.5 ± 1.5 for pentalene, 670.8 ± 2.9 for acepentalene, and 262.7 ± 2.5 for acenaphthylene. We combine the energies of the small fullerenes and previously obtained energies for larger fullerenes (from C₆₀ to C₆₀₀₀) into a full picture of fullerene thermochemical stability. In general, the per-carbon energies can be reasonably approximated by the "R+D" model that we have previously developed [Chan et al. J. Chem. Theory Comput. 2019, 15, 1255-1264], which takes into account Resonance and structural Deformation factors. In a case study on C₅₄, we find that most of the high-deformation-energy atoms correspond to the sites of the C-Cl bond in the experimentally captured C₅₄Cl₈. In another case study, we find that C₆₀ has the lowest value for the maximum local-deformation energy when compared with similar-sized fullerenes, which is consistent with its "special stability". These results are indicative of structural deformation playing an important role in the reactivity of fullerenes.

Aqueous-Phase Conformations of Lactose, Maltose, and Sucrose and the Assessment of Low-Cost DFT Methods with the DSCONF Set of Conformers for the Three Disaccharides

In the present study, we have examined a range of quantum chemistry methods for the calculation of conformers for lactose, maltose, and sucrose. We find that the DSD-PBE-P86/aug'-cc-pVTZ//B3-LYP-D3BJ/6-311+G(2d,p) protocol yields good relative energies in comparison with reference CCSD(T)/CBS//B3-LYP-D3BJ/maug-cc-pVTZ values. We have surveyed a total of ∼550 conformers for the three disaccharides with the chosen DSD-PBE-P86 method in conjunction with continuum aqueous solvation. In each case, the lowest free energy conformer is characterized by hydrogen bond(s) between the two rings. Another finding is that the major contributors to the overall variations in aqueous free energies are the electronic energies and the solvation energies. To facilitate investigations of larger systems, we have compiled the DSCONF set of conformers for the three disaccharides, and we have assessed lower cost methods with this set. We find MS1-D3/6-31+G(2d,p) to be cost-effective and accurate for both geometry optimization and the calculation of relative energies for disaccharides. In addition, we note that MS1-D3 has previously been found to yield good relative energies for the WATER27 set of water clusters. We thus deem this method to be appropriate for the study of saccharide conformations in both gas phase and aqueous solution.

New theoretical insights into the reaction kinetics of toluene and hydroxyl radicals

This work provides theoretical insights into the kinetics of toluene + OH, focusing on the anharmonic effect and the accuracy of barrier heights.

The CUAGAU Set of Coupled-Cluster Reference Data for Small Copper, Silver, and Gold Compounds and Assessment of DFT Methods

We have obtained benchmark data for a set of small molecular systems of Cu, Ag, and Au using coupled-cluster methods. Using this collection of reference data (that we termed the CUAGAU set) for assessing DFT-type methods, we find the MN15-L nonhybrid DFT to be cost-effective for geometry optimization [mean absolute deviation (MAD) in bond length = 0.20 Å], with an accuracy that is comparable to that for the double-hybrid (DH) DFT method DSD-PBEP86 (MAD = 0.19 Å). For the computation of thermochemical properties, among "conventional" (non-MP2-based) DFT methods, the best performance is found for the global-hybrid meta-GGA functional MN15, with an MAD of 11.4 kJ mol^-1. We also find the nonhybrid method B97M-rV to have a reasonable performance (MAD = 14.4 kJ mol^-1), and it may serve as a cost-effective means for qualitative study. If we look beyond conventional functionals, we find DSD-PBEP86 (MAD = 7.3 kJ mol^-1) to be more accurate than even MN15. Nonetheless, this level of accuracy is still not sufficient for quantitative studies. In this regard, high-level wave function methods such as composite procedures that are based on coupled cluster are still indispensable for obtaining reliable reference data for transition-metal species.

A Simple Model for Relative Energies of All Fullerenes Reveals the Interplay between Intrinsic Resonance and Structural Deformation Effects in Medium-Sized Fullerenes

Fullerenes are sheets of sp² carbon atoms wrapped around to form spheres. With this simple consideration, we have in the present study devised and (with over 3600 DFT data points) successfully validated a simple model, termed R+D, for estimating the relative energies of fullerenes. This model contains a resonance component to account for the intrinsic differences between the π-energies of different fullerenes, and a deformation component for treating the distortions from planarity. Notably, we find that both terms (and they alone) are required to obtain good relative energies, which lends support to the formulation of the R+D model. An interesting finding is that for some medium-sized IPR fullerenes, their isomers show similar variations in the two components. We deduce that these fullerenes may represent a good opportunity for tuning molecular properties for practical applications. We hope that the promising results of the present study will encourage further investigations into fullerenes from a fundamental perspective.

Thermochemistry of Guanine Tautomers Re-Examined by Means of High-Level CCSD(T) Composite Ab Initio Methods

We obtained accurate gas-phase tautomerization energies for a set of 14 guanine tautomers by means of high-level thermochemical procedures approximating the CCSD(T) energy at the complete basis set (CBS) limit. For the five low-lying tautomers, we use the computationally demanding W1-F12 composite method for obtaining the tautomerization energies. The relative W1-F12 tautomerization enthalpies at 298K are: 0.00 (1), 2.37 (2), 2.63 (3), 4.03 (3′), and 14.31 (4) kJmol−1. Thus, as many as four tautomers are found within a small energy window of less than 1.0kcalmol−1 (1kcalmol−1=4.184kJmol−1). We use these highly accurate W1-F12 tautomerization energies to evaluate the performance of a wide range of lower-level composite ab initio procedures. The Gn composite procedures (G4, G4(MP2), G4(MP2)-6X, G3, G3B3, G3(MP2), and G3(MP2)B3) predict that the enol tautomer (3) is more stable than the keto tautomer (2) by amounts ranging from 0.36 (G4) to 1.28 (G3(MP2)) kJmol−1. We also find that an approximated CCSD(T)/CBS energy calculated as HF/jul-cc-pV{D,T}Z+CCSD/jul-cc-pVTZ+(T)/jul-cc-pVDZ results in a root-mean-square deviation (RMSD) of merely 0.11kJmol−1 relative to the W1-F12 reference values. We use this approximated CCSD(T)/CBS method to obtain the tautomerization energies of 14 guanine tautomers. The relative tautomerization enthalpies at 298K are: 0.00 (1), 2.20 (2), 2.51 (3), 4.06 (3′), 14.30 (4), 25.65 (5), 43.78 (4′), 53.50 (6′), 61.58 (6), 77.37 (7), 82.52 (8′), 86.02 (9), 100.70 (10), and 121.01 (8) kJmol−1. Using these tautomerization enthalpies, we evaluate the performance of standard and composite methods for the entire set of 14 guanine tautomers. The best-performing procedures emerge as (RMSDs are given in parentheses): G4(MP2)-6X (0.51), CCSD(T)+ΔMP2/CBS (0.52), and G4(MP2) (0.64kJmol−1). The worst performers are CCSD(T)/AVDZ (1.05), CBS-QB3 (1.24), and CBS-APNO (1.38kJmol−1).

DFT computations on vibrational spectra: Scaling procedures to improve the wavenumbers

The performance of ab initio and density functional theory (DFT) methods in calculating the vibrational wavenumbers in the isolated state was analyzed. To correct the calculated values, several scaling procedures were described in detail. The two linear scaling equation (TLSE) procedure leads to the lowest error and it is recommended for scaling. A comprehensive compendium of the main scale factors and scaling equations available to date for a good accurate prediction of the wavenumbers was also shown. Examples of each case were presented, with special attention to the benzene and uracil molecules and to some of their derivatives. Several DFT methods and basis sets were used. After scaling, the X3LYP/DFT method leads to the lowest error in these molecules. The B3LYP method appears closely in accuracy, and it is also recommended to be used. The accuracy of the results in the solid state was shown and several additional corrections are presented.

Barriometry – an enhanced database of accurate barrier heights for gas-phase reactions

The kinetics of many reactions are critically dependent upon the barrier heights for which accurate determination can be difficult. More than 100 accurate barriers are obtained with the high-level W3X-L composite procedure.

Vibrational analysis of dibenzo-18-crown-6. Effect of dispersion correction on the calculated vibrational spectra

We report for the first time a detailed vibrational analysis of dibenzo-18-crown-6, db18c6. The experimental IR and Raman spectra of db18c6 were measured. The assignment of the fundamental vibrational frequencies of db18c6 was aided by using scaled quantum mechanical force fields calculated at the B3LYP/6-311G** and CAM-B3LYP/6-311G** levels. Comparison between the experimental and calculated spectra of some of the important conformations of db18c6 led to the conclusion that db18c6 in the solid phase exists in a C₂ conformation that is similar to that predicted by X-ray, for also the solid phase. The effect of inclusion of the atom pair-wise dispersion correction to the B3LYP method, known as the B3LYP-D3 method, on the calculated IR and Raman spectra of db18c6 at the B3LYP level was also investigated. It was concluded that the effect of inclusion of the dispersion correction on the calculated vibrational frequencies and intensities is negligible.

How to computationally calculate thermochemical properties objectively, accurately, and as economically as possible

We have developed the WnX series of quantum chemistry composite protocols for the computation of highly-accurate thermochemical quantities with advanced efficiency and applicability. The W1X-type methods have a general accuracy of ~3–4 kJ mol−1 and they can currently be applied to systems with ~20–30 atoms. Higher-level methods include W2X, W3X and W3X-L, with the most accurate of these being W3X-L. It can be applied to molecules with ~10–20 atoms and is generally accurate to ~1.5 kJ mol−1. The WnX procedures have opened up new possibilities for computational chemists in pursue of accurate thermochemical values in a highly-productive manner.