Accurate Geometries of Large Molecules at DFT Cost by Semiexperimental and Coupled Cluster Templating Fragments

Accurate geometries of small semirigid molecules in the gas phase are available thanks to high-resolution spectroscopy and accurate quantum chemical approaches. These results can be employed for validating cheaper low-level quantum chemical models or correcting the corresponding structures of large molecules. On these grounds, in this work, a large panel of semiexperimental equilibrium structures already available in the literature is used to confirm the average error (1 mÅ for bond lengths and 2 mrad for valence angles) of a version of the Pisa composite schemes (PCS2), which is applicable to molecules containing up to about 20 atoms. Then, the geometries of 30 additional medium-sized systems were optimized at the PCS2 level to cover a more balanced chemical space containing moieties poorly represented in SE compilations. The final database is available on a public domain Web site (https://www.skies-village.it/databases/) and can be employed for correcting structures of larger molecules obtained by hybrid or double-hybrid density functionals in the framework of the templating molecule approach. Several examples show that corrections based on the structures of building blocks taken from this database reduce the error of the B3LYP geometrical parameters of large molecules by nearly an order of magnitude without increasing the computational cost. Furthermore, the results of different density functional theory (DFT) or wave function (e.g., MP2) models can be improved in the same way by simply computing both the whole molecule and suitable building blocks at the chosen level. Then, whenever reference structures of some building blocks containing up to about 20 atoms are not available, they can be purposely optimized at the PCS2 level by employing reasonable computer resources. Therefore, a new DFT-cost tool is now available for the accurate characterization of large molecules by experiment-oriented scientists.

Plain Capping for Improved Accuracy of Approximate One- and Two-Electron Densities at Two-Particle Coalescence Points

The values of the one-electron and intracule densities at two-particle coalescence points that enter the expressions for relativistic corrections to energies of Coulombic systems cannot be efficiently computed with sufficient accuracy from approximate wave functions expressed in terms of cuspless basis functions such as the explicitly correlated Gaussians. A new approach to alleviation of this problem, called plain capping, is proposed. Unlike those offered by the previously published formalisms, such as the expectation value identities and integral transforms, the accuracy improvements effected by the plain capping are attained with negligible computational effort and minimum programming. In the case of the on-top two-electron densities, whose accurate computation is particularly costly, the plain capping constitutes the only viable means of error reduction available at present.

Accurate Vibrational and Ro-Vibrational Contributions to the Properties of Large Molecules by a New Engine Employing Curvilinear Internal Coordinates and Vibrational Perturbation Theory to Second Order

The unbiased comparison between theory and experiment requires approaches more sophisticated than the basic harmonic-oscillator rigid-rotor model, for taking into account vibrational averaging effects and ro-vibrational couplings in molecules of increasing size. Second-order vibrational perturbation theory based on curvilinear internal coordinates (ICs) offers a remarkable compromise between accuracy and computational cost, thanks to the reduction of mode-mode couplings with respect to their counterparts based on Cartesian coordinates. Therefore, we have developed, implemented, and validated a general engine employing ICs, which allows the accurate evaluation of vibrational averages and ro-vibrational couplings for molecules containing up to about 50 atoms beyond the harmonic approximation. After validation of the new tool for relatively small molecules, the effectiveness of ICs has been demonstrated for some flexible and/or quite large molecular bricks of life.

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium

A vibrational electronic-thermofield coupled cluster (VE-TFCC) approach is developed to calculate thermal properties of non-adiabatic vibronic coupling systems. The thermofield (TF) theory and a mixed linear exponential ansatz based on second-quantized Bosonic construction operators are introduced to propagate the thermal density operator as a "pure state" in the Bogoliubov representation. Through this compact representation of the thermal density operator, the approach is basis-set-free and scales classically (polynomial) as the number of degrees of freedoms (DoF) in the system increases. The VE-TFCC approach is benchmarked with small test models and a real molecular compound (CoF4- anion) against the conventional sum over states (SOS) method and applied to calculate thermochemistry properties of a gas-phase reaction: CoF3 + F- → CoF4-. Results shows that the VE-TFCC approach, in conjunction with vibronic models, provides an effective protocol for calculating thermodynamic properties of vibronic coupling systems.

Accurate structures and rotational constants of bicyclic monoterpenes at DFT cost by means of the bond-corrected Pisa composite scheme (BPCS)

The structural, conformational, and spectroscopic properties in the gas phase of 20 bicyclic monoterpenes and monoterpenoids have been analyzed by a new accurate, reduced-cost computational strategy. In detail, the revDSD-PBEP86 double-hybrid functional in conjunction with the D3BJ empirical dispersion corrections and a suitable triple-zeta basis set provides accurate geometrical parameters, whence equilibrium rotational constants, which are further improved by proper account of core-valence correlation. Average deviations within 0.1% between computed and experimental rotational constants are reached when taking into account the vibrational corrections obtained by the B3LYP functional in conjunction with a double-zeta basis set in the framework of second-order vibrational perturbation theory. In addition to their intrinsic interest, the studied terpenes further extend the panel of systems for which the proposed strategy has provided accurate results at density functional theory cost. Therefore, a very accurate yet robust and user-friendly tool is now available for systematic investigations of the role of stereo-electronic effects on the properties of large systems of current technological and/or biological interest by experimentally oriented researchers.

Energetics of the OH radical H-abstraction reactions from simple aldehydes and their geminal diol forms

CONTEXT

Carbonyl compounds, especially aldehydes, emitted to the atmosphere, may suffer hydration in aerosols or water droplets in clouds. At the same time, they can react with hydroxyl radicals which may add or abstract hydrogen atoms from these species. The interplay between hydration and hydrogen abstraction is studied using density functional and quantum composite theoretical methods, both in the gas phase and in simulated bulk water. The H-abstraction from the aldehydic and geminal diol forms of formaldehyde, acetaldehyde, glycolaldehyde, glyoxal, methylglyoxal, and acrolein is studied to determine whether the substituent has any noticeable effect in the preference for the abstraction of one form or another. It is found that abstraction of the H-atom adjacent to the carbonyl group gives a more stable radical than same abstraction from the geminal diol in the case of formaldehyde, acetaldehyde, and glycolaldehyde. The presence of a delocalizing group in the Cα (a carbonyl group in glyoxal and methylglyoxal, and a vinyl group in acrolein), reverts this trend, and now the abstraction of the H-atom from the geminal diol gives more stable radicals. A further study was conducted abstracting hydrogen atoms from the other different positions in the species considered, both in the aldehydic and geminal diol forms. Only in the case of glycolaldehyde, the radical formed by H-abstraction from the -CH2OH group is more stable than any of the other radical species. Abstraction of the hydrogen atom in one of the hydroxyl groups in the geminal diol is equivalent to the addition of the •OH radical to the aldehyde. It leads, in some cases, to decomposition into a smaller radical and a neutral molecule. In these cases, some interesting theoretical differences are observed between the results in gas phase and (simulated) bulk solvent, as well as with respect to the method of calculation chosen.

METHODS

DFT (M06-2X, B2PLYP, PW6B95), CCSD(T), and composite (CBS-QB3, jun-ChS, SCVECV-f12) methods using Dunning basis sets and extrapolation to the CBS limit were used to study the energetics of closed shell aldehydes in their keto and geminal-diol forms, as well as the radical derived from them by hydrogen abstraction. Both gas phase and simulated bulk solvent calculations were performed, in the last case using the Polarizable Continuum Model.

Toward Accurate Quantum Chemical Methods for Molecules of Increasing Dimension: The New Family of Pisa Composite Schemes

The new versions of the Pisa composite scheme introduced in the present paper are based on 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, the computation of accurate electronic energies has been further improved introducing more reliable complete basis set extrapolations and estimation of core-valence correlation, together with improved basis sets for third-row atoms. Furthermore, the reduced-cost frozen natural orbital (FNO) model has been introduced and validated for large molecules. Accurate molecular structures can be obtained avoiding complete basis set extrapolation and evaluating core-valence correlation at the MP2 level. Unfortunately, analytical gradients are not available for the FNO version of the model. Therefore, for large molecules, an accurate reduced-cost alternative is offered by evaluation of valence contributions with a double-hybrid functional in conjunction with the same MP2 contribution for core-valence correlation or by means of a one-parameter approximation. The same double-hybrid functional and basis set are employed to evaluate zero-point energies and partition functions. After the validation of the new models for small systems, a panel of molecular bricks of life has been used to analyze their performances for problems of current fundamental or technological interest. The fully black-box implementation of the computational workflow paves the way toward the accurate yet not prohibitively expensive study of medium- to large-sized molecules also by experimentally oriented researchers.

Ab Initio Electron Propagators with an Hermitian, Intermediately Normalized Superoperator Metric Applied to Vertical Electron Affinities

New-generation ab initio electron propagator methods for calculating electron detachment energies of closed-shell molecules and anions have surpassed their predecessors' accuracy and computational efficiency. Derived from an Hermitian, intermediately normalized superoperator metric, these methods contain no adjustable parameters. To assess their versatility, a standard set (NIST-50-EA) of 50 vertical electron affinities of small closed-shell molecules based on NIST reference data has been created. Errors with respect to reference data on 23 large, conjugated organic photovoltaic (OPV23) molecules have also been analyzed. All final states are valence anions that correspond to electron affinities between 0.2 and 4.2 eV. For a given scaling of the arithmetic bottleneck, the new-generation methods obtain the lowest mean absolute errors (MAEs). The best methods with fifth-power arithmetic scaling realize MAEs below 0.1 eV. Composite models comprising cubically and quintically scaling calculations executed with large and small basis sets, respectively, produce OPV23 MAEs near 0.05 eV. The accuracy of quintically scaling methods executed with large basis sets is thereby procured with reduced computational effort. New-generation results obtained with and without the diagonal self-energy approximation in the canonical Hartree-Fock basis have been compared. These results indicate that Dyson orbitals closely resemble canonical Hartree-Fock orbitals multiplied by the square root of a probability factor above 0.85.

Physicochemical Properties of 4-(4-Hydroxyphenyl)-butan-2-one ("Raspberry Ketone") Evaluated Using a Computational Chemistry Approach

Raspberry ketone (RK) is a product of the phenylpropanoid pathway in a variety of plants and is the second most expensive natural flavouring in the world. It is also widely used as a nutritional supplement due to its reported ability to promote lipolysis and fat oxidation in vivo. We have evaluated the thermodynamics of RK using the correlation consistent ccCA-CBS-2 approach which afforded calculation of (inter alia) the enthalpy of formation. To obtain pK a, log D, electrode potential, solubility, and reactivity indices, we used TPSS/def2-TZVP geometries followed by single-point energies obtained at the M06-2X/def2-TZVPP level of theory. We obtained Δf H o = -299.4 ± 0.17 kJ·mol-1; the pK a and logD were found to be 9.95 and 1.84, respectively, consistent with chemometric predictions. Using the enthalpy of fusion obtained from theory, we evaluated the aqueous solubility of RK to be in the region of 2.5 mg·mL-1 which is in agreement with limited literature reports. In terms of reactivity, we obtained a formal electrode potential of 1.29 V (vs SHE) at pH 7.4 and 298.15 K. The HOMO-LUMO energy separation in an aqueous environment was found to be ca. 7.8 eV, suggesting moderate chemical reactivity. Analysis of the frontier molecular orbitals using conceptual density functional theory supported this and revealed a reactivity pattern consistent with the metabolite profile obtained in mammals, namely, a propensity for nucleophilic attack at the carbonyl carbon and electrophilic addition of the benzene ring.

Limiting factors in the accuracy of DFT calculation for redox potentials

In the present study, we have investigated factors affecting the accuracy of computational chemistry calculation of redox potentials, namely the gas-phase ionization energy (IE) and electron affinity (EA), and the continuum solvation effect. In general, double-hybrid density functional theory methods yield IEs and EAs that are on average within ~0.1 eV of our high-level W3X-L benchmark, with the best performing method being DSD-BLYP/ma-def2-QZVPP. For lower-cost methods, the average errors are ~0.2-0.3 eV, with ωB97X-3c being the most accurate (~0.15 eV). For the solvation component, essentially all methods have an average error of ~0.3 eV, which shows the limitation of the continuum solvation model. Curiously, the directly calculated redox potentials show errors of ~0.3 eV for all methods. These errors are notably smaller than what can be expected from error propagation with the two components (IE and EA, and solvation effect). Such a discrepancy can be attributed to the cancellation of errors, with the lowest-cost GFN2-xTB method benefiting the most, and the most accurate ωB97X-3c method benefiting the least. For organometallic species, the redox potentials show large deviations exceeding ~0.5 eV even for DSD-BLYP. The large errors are attributed to those for the gas-phase IEs and EAs, which represents a major barrier to the accurate calculation of redox potentials for such systems.

Quantum Monte Carlo Simulations of the Vibrational Wavefunction of the Aromatic Cyclo[10]carbon Using a Full Dimensional Permutationally Invariant Potential Energy Surface

New experimental measurements [Sun et al., Nature 2023, 623, 972] of the cyclic C10 reveal a cumulenic pentagon-like D5h structure at ∼5 K. However, the long-standing presumption that a large zero-point vibrational energy combined with an extremely flat D5h ↔ D10h ↔ D5h isomerization pathway washes out the pentagonal D5h structure and yields a symmetric D10h decagon remains at odds with the experiment. We resolve this issue with our fitting approach based on a bond-order charge-density matrix expressed in permutationally invariant polynomials. We train the model on τHCTH/cc-pVQZ data morphed to reproduce a relativistic all-electron CCSDT(Q)/CBS D5h-D10h potential energy barrier (benchmarked previously by others). Large scale diffusion Monte Carlo simulations in full dimensionality show that the vibrational ground state of C10 has compositional character of more than 96% D5h, fully reflecting the experimental imaging data. Quantum mechanical variational calculations in 1-D further suggest persistence of the D5h symmetry structure at higher temperatures.

Stepping-Stone CBH: Benchmark and Application of a Multilayered Isodesmic-Based Correction Scheme

We present a generalization of the connectivity-based hierarchy (CBH) of isodesmic-based correction schemes to a multilayered fragmentation platform for overall cost reduction while retaining high accuracy. The newly developed multilayered CBH approach, called stepping-stone CBH (SSCBH), is benchmarked on a diverse set of 959 medium-sized organic molecules. Applying SSCBH corrections to the PBEh-D3 density functional resulted in an average error of 0.76 kcal/mol for the full test set compared to accurate CCSD(T)-quality enthalpies and an even lower error of 0.44 kcal/mol on a subset containing only acyclic molecules. These results rival the traditional CBH-3 approach at a greatly reduced cost, allowing larger fragment corrections to be made at the MP2 level of theory rather than with G4. Our SSCBH approach will enable more widespread applications of CBH methods to a broader range of organic and biomolecular systems.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.

Unbiased Comparison between Theoretical and Experimental Molecular Structures and Properties: Toward an Accurate Reduced-Cost Evaluation of Vibrational Contributions

The tremendous development of hardware and software is constantly increasing the role of quantum chemical (QC) computations in the assignment and interpretation of experimental results. However, an unbiased comparison between theory and experiment requires the proper account of vibrational averaging effects. In particular, high-resolution spectra in the gas phase are now available for molecules containing up to about 50 atoms, which are too large for a brute-force approach with the available QC methods of sufficient accuracy. In the present paper, we introduce hybrid approaches, which allow the accurate evaluation of vibrational averaging effects for molecules of this size beyond the harmonic approximation, with special attention being devoted to rotational constants. After the validation of new tools for relatively small molecules, the β-estradiol hormone and a prototypical molecular motor have been considered to witness the feasibility of accurate computations for large molecules.

COMPAS-2: a dataset of cata-condensed hetero-polycyclic aromatic systems

Polycyclic aromatic systems are highly important to numerous applications, in particular to organic electronics and optoelectronics. High-throughput screening and generative models that can help to identify new molecules to advance these technologies require large amounts of high-quality data, which is expensive to generate. In this report, we present the largest freely available dataset of geometries and properties of cata-condensed poly(hetero)cyclic aromatic molecules calculated to date. Our dataset contains ~500k molecules comprising 11 types of aromatic and antiaromatic building blocks calculated at the GFN1-xTB level and is representative of a highly diverse chemical space. We detail the structure enumeration process and the methods used to provide various electronic properties (including HOMO-LUMO gap, adiabatic ionization potential, and adiabatic electron affinity). Additionally, we benchmark against a ~50k dataset calculated at the CAM-B3LYP-D3BJ/def2-SVP level and develop a fitting scheme to correct the xTB values to higher accuracy. These new datasets represent the second installment in the COMputational database of Polycyclic Aromatic Systems (COMPAS) Project.

Hunting for Complex Organic Molecules in the Interstellar Medium: The Role of Accurate Low-Cost Theoretical Geometries and Rotational Constants

A new approach to computation at affordable cost of accurate geometrical structures and rotational constants for medium-sized molecules in the gas phase is further improved and applied to a large panel of interstellar complex organic molecules. The most distinctive feature of the new model is the effective inclusion of core-valence correlation and vibrational averaging effects in the framework of density functional theory (DFT). In particular, a double-hybrid functional in conjunction with a quadruple-ζ valence/triple-ζ polarization basis set is employed for geometry optimizations, whereas a cheaper hybrid functional in conjunction with a split-valence basis set is used for the evaluation of vibrational corrections. A thorough benchmark based on a wide range of prototypical systems shows that the new scheme approaches the accuracy of state-of-the-art wave function methods with the computational cost of the standard methods (DFT or MP2) routinely employed in the interpretation of microwave spectra. Since the whole computational workflow involves the postprocessing of the output of standard electronic structure codes by a new freely available web utility, the way is paved for the accurate yet not prohibitively expensive study of medium- to large-sized molecules also by nonspecialists.

Theoretical determination of the standard enthalpies of formation of alkyl radicals using the concept of a complete set of homodesmotic reactions

The complete sets of homodesmotic reactions (HDR) for 107 acyclic alkyl free radicals С4-С9 of normal and branched structure were constructed using the graph-theoretic representation and analysis of a tested compound. The absolute enthalpies of the studied compounds and HDR reference structures were calculated using the M062X/cc-pVTZ level of theory. Based on these data, the thermal effects of HDRs were calculated and then applied to determine the standard enthalpies of formation of the studied radicals using the known enthalpies of formation of reference structures. The dissociation energies of BDE C-H and C-CH3 bonds were also calculated. The effect of radical structure on the BDE value is discussed, and a new effect of stabilization of the radical center in the skewed conformation of free radical is established; this effect has not been previously described in the scientific literature.

Simple Composite Approach to Efficiently Estimate Basis Set Limit CCSD(T) Harmonic Frequencies and Reaction Thermochemistry

We introduce a simple strategy that combines the G3(MP2) composite method and explicitly correlated coupled cluster CCSD(T)-F12 method to efficiently estimate complete basis set CCSD(T) molecular geometries and harmonic vibrational frequencies at the cost of a double-ζ basis set calculation. Based on a large test set of 61 neutral, ionic, and open-shell molecules, and additionally 31 molecules in the HFREQ2014 data set, we demonstrate that this composite strategy has an average accuracy of 2 cm-1 or better relative to complete basis set CCSD(T) values. Using this approach, we estimated 696 CCSD(T)/CBS reaction energies of small to medium-sized systems containing up to 6 heavy atoms and confirmed existing approximations that use small basis set density functional theory methods [e.g., M06-2X/6-31+G(d)] to calculate thermal contributions to reaction enthalpies and Gibbs free energies that are accurate to within 0.2 kcal mol-1 on average.

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.

Stereo-electronic factors influencing the stability of hydroperoxyalkyl radicals: transferability of chemical trends across hydrocarbons and ab initio methods

The hydroperoxyalkyl radicals (˙QOOH) are known to play a significant role in combustion and tropospheric processes, yet their direct spectroscopic detection remains challenging. In this study, we investigate molecular stereo-electronic effects influencing the kinetic and thermodynamic stability of a ˙QOOH along its formation path from the precursor, alkylperoxyl radical (ROO˙), and the depletion path resulting in the formation of cyclic ether + ˙OH. We focus on reactive intermediates encountered in the oxidation of acyclic hydrocarbon radicals: ethyl, isopropyl, isobutyl, tert-butyl, neopentyl, and their alicyclic counterparts: cyclohexyl, cyclohexenyl, and cyclohexadienyl. We report reaction energies and barriers calculated with the highly accurate method Weizmann-1 (W1) for the channels: ROO˙ ⇌ ˙QOOH, ROO˙ ⇌ alkene + ˙OOH, ˙QOOH ⇌ alkene + ˙OOH, and ˙QOOH ⇌ cyclic ether + ˙OH. Using W1 results as a reference, we have systematically benchmarked the accuracy of popular density functional theory (DFT), composite thermochemistry methods, and an explicitly correlated coupled-cluster method. We ascertain inductive, resonance, and steric effects on the overall stability of ˙QOOH and computationally investigate the possibility of forming more stable species. With new reactions as test cases, we probe the capacity of various ab initio methods to yield quantitative insights on the elementary steps of combustion.

The influence of substituents in governing the strength of the P-X bonds of substituted halophosphines R1R2P-X (X = F and Cl)

In this study, the gas-phase homolytic P-F and P-Cl bond dissociation energies (BDEs) of a set of thirty fluorophosphine (R1R2P-F) and thirty chlorophosphine-type (R1R2P-Cl) molecules have been obtained using the high-level W2 thermochemical protocol. For the R1R2P-F species, the P-F BDEs (at 298 K) differ by up to 117.0 kJ mol-1, with (H3Si)2P-F having the lowest BDE (439.5 kJ mol-1) and F2P-F having the largest BDE (556.5 kJ mol-1). In the case of the chlorophosphine-type molecules, the difference in BDEs is considerably smaller (i.e., 72.6 kJ mol-1), with (NC)2P-Cl having the lowest P-Cl BDE (299.8 kJ mol-1) and (HO)2P-Cl having the largest (372.4 kJ mol-1). We have further analyzed the effect of substituents in governing the P-F and P-Cl BDEs by considering the effect of substituents in the parent halogenated precursors (using molecule stabilization enthalpies) and the effect of substituents in the product radicals (using radical stabilization enthalpies). Finally, we have also assessed the performance of a wide range of DFT methods for their ability to compute the gas-phase P-F and P-Cl BDEs contained in this dataset. We find that, overall, the double hybrid functional DSD-PBEB95 offers the best performance for both bond types, with mean absolute deviations of just 2.1 (P-F BDEs) and 2.2 (P-Cl BDEs) kJ mol-1.

High-Level Quantum Chemical Prediction of C-F Bond Dissociation Energies of Perfluoroalkyl Substances

In this study, 550 C-F bond dissociation energies (BDEs) of a variety of per- and polyfluoroalkyl substances (PFASs) obtained from high-level DLPNO-CCSD(T)/CBS calculations were used to assess the accuracy of contemporary density functional theory (DFT) and semiempirical methods. DLPNO-CCSD(T)/CBS gas phase C-F BDEs fall between 404.9-550.7 kJ mol-1 and M06-2X and ωB97M-V in conjunction with the aug-cc-pVTZ basis set predicted BDEs closest to the benchmark level with a mean absolute deviation (MAD) of 7.3 and 8.3 kJ mol-1, respectively. It was observed that DFT prediction errors increase with the degree of fluorination and system size. As such, previous model chemistry recommendations based on smaller nonfluorinated systems may not be carried over to modeling the energetics of PFASs and related systems.

DFT Meets Wave-Function Methods for Accurate Structures and Rotational Constants of Histidine, Tryptophan, and Proline

A new computational strategy has been applied to the conformational and spectroscopic properties in the gas phase of amino acids with very distinctive features, ranging from different tautomeric forms (histidine) to ring puckering (proline), and heteroaromatic structures with non-equivalent rings (tryptophan). The integration of modern double-hybrid functionals and wave-function composite methods has allowed us to obtain accurate results for a large panel of conformers with reasonable computer times. The remarkable agreement between computations and microwave experiments allows an unbiased interpretation of the latter in terms of stereoelectronic effects.

6-Endo-dig versus 5-exo-dig: Exploring Radical Cyclization Preference with First-, Second-, and Third-row Linkers using High-level Quantum Chemical Methods

As an expansion upon Baldwin rules, the cyclization reactions of hex-5-yn-1-yl radical systems with different first-, second-, and third-row linkers are explored at the CCSD(T) level via means of the SMD(benzene)-G4(MP2) thermochemical protocol. Unlike C, O, and N linkers, systems with B, Si, P, S, Ge, As, and Se linkers are shown to favor 6-endo-dig cyclization. This offers fundamental insights into the rational synthetic design of cyclic compounds. A thorough analysis of stereoelectronic effects, cyclization barriers, and intrinsic barriers illustrates that structural changes alter the cyclization preference by mainly impacting 5-exo-dig reaction barriers. Based on the high-level computational modeling, we proceed to develop a new tool for cyclization preference prediction from the correlation between cyclization barriers and radical structural parameters (e. g., linker bond length and bond angle). A strong correlation is found between the radical attack trajectory angle and the reaction barrier heights, i. e., cyclization preference. Finally, the influence of stereoelectronic effects on the two radical cyclization pathways is further investigated in stereoisomers of hypervalent silicon system, which provides novel insight into cyclization control.

Accurate Structures and Spectroscopic Parameters of Guanine Tautomers in the Gas Phase by the Pisa Conventional and Explicitly Correlated Composite Schemes (PCS and PCS-F12)

A general strategy for the accurate computation of structural and spectroscopic properties of biomolecule building blocks in the gas phase is proposed and validated for tautomeric equilibria. The main features of the new model are the inclusion of core-valence correlation in geometry optimizations by a double hybrid functional and the systematic use of wave-function composite methods in conjunction with cc-pVnZ-F12 basis sets with separate extrapolation of MP2 and post-MP2 contributions. The resulting Pisa composite scheme employing conventional (PCS) or explicitly correlated (PCS-F12) approaches is applied to the challenging problem of guanine tautomers in the gas phase. The results are in remarkable agreement with the experimental structures, relative stabilities, and spectroscopic signatures of different tautomers. The accuracy of the results obtained at reasonable cost by means of black-box parameter-free approaches paves the way toward systematic investigations of other molecular bricks of life also by non-specialists.

A Systematic Exploration of B-F Bond Dissociation Enthalpies of Fluoroborane-Type Molecules at the CCSD(T)/CBS Level

Fluoroborane-type molecules (R1R2B-F) are of interest in synthetic chemistry, but to date, apart from a handful of small species (such as H2BF, HBF2, and BF3), little is known concerning the effect of substituents in governing the strength of the B-F bonds of such species toward homolytic dissociation in the gas phase. In this study, we have calculated the bond dissociation enthalpies (BDEs) of thirty unique B-F bonds at the CCSD(T)/CBS level using the high-level W1w thermochemical protocol. The B-F bonds in all species considered are very strong, ranging from 545.9 kJ mol-1 in (H2B)2B-F to 729.2 kJ mol-1 HBF2. Nevertheless, these BDEs still vary over a wide range of 183.3 kJ mol-1. The structural properties that affect the BDEs are examined in detail, and the homolytic BDEs are rationalized based on molecule stabilization enthalpies and radical stabilization enthalpies. Since polar B-F bonds may represent a challenging test case for density functional theory (DFT) methods, we proceed to examine the performance of a wide range of DFT methods across the rungs of Jacob's Ladder for their ability to compute B-F BDEs. We find that only a handful of DFT methods can reproduce the CCSD(T)/CBS BDEs with mean absolute deviations (MADs) below the threshold of chemical accuracy (i.e., with average deviations below 4.2 kJ mol-1). The only functionals capable of achieving this feat were (MADs given in parentheses): ωB97M-V (4.0), BMK (3.5), DSD-BLYP (3.8), and DSD-PBEB95 (1.8 kJ mol-1).

Intramolecular Proton-Coupled Hydride Transfers with Relatively Low Activation Barriers

We report that bifunctional molecules containing hydroxyl and carbonyl functional groups can undergo an effective transfer hydrogenation via an intramolecular proton-coupled hydride transfer (PCHT) mechanism. In this reaction mechanism, a hydride transfer between two carbon atoms is coupled with a proton transfer between two oxygen atoms via a cyclic bond rearrangement transition structure. The coupled transfer of the two hydrogens as H^δ+ and H^δ- is supported by atomic polar tensor charges. The activation energy for the PCHT reaction is strongly dependent on the length of the alkyl chain between the hydroxyl and carbonyl functional groups but relatively weakly dependent on the functional groups attached to the hydroxyl and carbonyl carbons. We investigate the PCHT reaction mechanism using the Gaussian-4 thermochemical protocol and obtain high activation energy barriers (ΔH^‡₂₉₈) of 210.5-228.3 kJ mol^-1 for chain lengths of one carbon atom and 160.2-163.9 kJ mol^-1 for chain lengths of two carbon atoms. However, for longer chain lengths containing 3-4 carbon atoms, we obtain ΔH^‡₂₉₈ values as low as 101.9 kJ mol^-1. Importantly, the hydride transfer between two carbon atoms proceeds without the need for a catalyst or hydride transfer activating agent. These results indicate that the intramolecular PCHT reaction provides an effective avenue for uncatalyzed, metal-free hydride transfers at ambient temperatures.

Approaching Coupled Cluster Accuracy with Density Functional Theory Using the Generalized Connectivity-Based Hierarchy

This Perspective reviews connectivity-based hierarchy (CBH), a systematic hierarchy of error-cancellation schemes developed in our group with the goal of achieving chemical accuracy using inexpensive computational techniques ("coupled cluster accuracy with DFT"). The hierarchy is a generalization of Pople's isodesmic bond separation scheme that is based only on the structure and connectivity and is applicable to any organic and biomolecule consisting of covalent bonds. It is formulated as a series of rungs involving increasing levels of error cancellation on progressively larger fragments of the parent molecule. The method and our implementation are discussed briefly. Examples are given for the applications of CBH involving (1) energies of complex organic rearrangement reactions, (2) bond energies of biofuel molecules, (3) redox potentials in solution, (4) pK_a predictions in the aqueous medium, and (5) theoretical thermochemistry combining CBH with machine learning. They clearly show that near-chemical accuracy (1-2 kcal/mol) is achieved for a variety of applications with DFT methods irrespective of the underlying density functional used. They demonstrate conclusively that seemingly disparate results, often seen with different density functionals in many chemical applications, are due to an accumulation of systematic errors in the smaller local molecular fragments that can be easily corrected with higher-level calculations on those small units. This enables the method to achieve the accuracy of the high level of theory (e.g., coupled cluster) while the cost remains that of DFT. The advantages and limitations of the method are discussed along with areas of ongoing developments.

Is DFT Accurate Enough to Calculate Regioselectivity? The Case of 1,3-Dipolar Cycloaddition of Azide to Alkynes and Alkenes

The importance of regioselectivity in 1,3-dipolar cycloadditions (DCs) makes it surprising that no benchmarking study on this problem has appeared. We investigated whether DFT calculations are an accurate tool to predict the regioselectivity of uncatalyzed thermal azide 1,3-DCs. We considered the reaction between HN3 and 12 dipolarophiles, comprising ethynes HC≡C-R and ethenes H2 C=CH-R (R=F, OH, NH2 , Me, CN, CHO), which cover a broad range of electron demand and conjugation ability. We established benchmark data by the W3X protocol [complete-basis-set-extrapolated CCSD(T)-F12 energy with T-(T) and (Q) corrections and MP2-calculated core/valence and relativistic effects] and showed that core/valence effects and high-order excitations are important for accurate regioselectivity. Regioselectivities calculated using an extensive set of density functional approximations (DFAs) were compared with benchmark data. Range-separated and meta-GGA hybrids gave the best results. Good treatment of self-interaction and electron exchange are the key features for accurate regioselectivity. Dispersion correction slightly improves agreement with W3X results. The best DFAs provide the isomeric TS energy difference with an expected error ≈0.7 mh and errors ≈2 mh can occur. The isomer yield provided by the best DFA has an expected error of ±5 %, though errors up to 20 % are not rare. At present, an accuracy of 1-2 % is unfeasible but it seems that we are not far from achieving this goal.

Accurate Structures and Spectroscopic Parameters of Phenylalanine and Tyrosine in the Gas Phase: A Joint Venture of DFT and Composite Wave-Function Methods

A general strategy for the accurate computation of conformational and spectroscopic properties of flexible molecules in the gas phase is applied to two representative proteinogenic amino acids with aromatic side chains, namely, phenylalanine and tyrosine. The main features of all the most stable conformers predicted by this computational strategy closely match those of the species detected in microwave and infrared experiments. Together with their intrinsic interest, the accuracy of the results obtained with reasonable computer times paves the route for accurate investigations of other flexible bricks of life.

Thermochemistry, Tautomerism, and Thermal Stability of 5,7-Dinitrobenzotriazoles

Nitro derivatives of benzotriazoles are safe energetic materials with remarkable thermal stability. In the present study, we report on the kinetics and mechanism of thermal decomposition for 5,7-dinitrobenzotriazole (DBT) and 4-amino-5,7-dinitrobenzotriazole (ADBT). The pressure differential scanning calorimetry was employed to study the decomposition kinetics of DBT experimentally because the measurements under atmospheric pressure are disturbed by competing evaporation. The thermolysis of DBT in the melt is described by a kinetic scheme with two global reactions. The first stage is a strong autocatalytic process that includes the first-order reaction (Ea1I = 173.9 ± 0.9 kJ mol−1, log(A1I/s−1) = 12.82 ± 0.09) and the catalytic reaction of the second order with Ea2I = 136.5 ± 0.8 kJ mol−1, log(A2I/s−1) = 11.04 ± 0.07. The experimental study was complemented by predictive quantum chemical calculations (DLPNO-CCSD(T)). The calculations reveal that the 1H tautomer is the most energetically preferable form for both DBT and ADBT. Theory suggests the same decomposition mechanisms for DBT and ADBT, with the most favorable channels being nitro-nitrite isomerization and C–NO2 bond cleavage. The former channel has lower activation barriers (267 and 276 kJ mol−1 for DBT and ADBT, respectively) and dominates at lower temperatures. At the same time, due to the higher preexponential factor, the radical bond cleavage, with reaction enthalpies of 298 and 320 kJ mol−1, dominates in the experimental temperature range for both DBT and ADBT. In line with the theoretical predictions of C–NO2 bond energies, ADBT is more thermally stable than DBT. We also determined a reliable and mutually consistent set of thermochemical values for DBT and ADBT by combining the theoretically calculated (W1-F12 multilevel procedure) gas-phase enthalpies of formation and experimentally measured sublimation enthalpies.

Benchmark Structures and Conformational Landscapes of Amino Acids in the Gas Phase: A Joint Venture of Machine Learning, Quantum Chemistry, and Rotational Spectroscopy

The accurate characterization of prototypical bricks of life can strongly benefit from the integration of high resolution spectroscopy and quantum mechanical computations. We have selected a number of representative amino acids (glycine, alanine, serine, cysteine, threonine, aspartic acid and asparagine) to validate a new computational setup rooted in quantum-chemical computations of increasing accuracy guided by machine learning tools. Together with low-lying energy minima, the barriers ruling their interconversion are evaluated in order to unravel possible fast relaxation paths. Vibrational and thermal effects are also included in order to estimate relative free energies at the temperature of interest in the experiment. The spectroscopic parameters of all the most stable conformers predicted by this computational strategy, which do not have low-energy relaxation paths available, closely match those of the species detected in microwave experiments. Together with their intrinsic interest, these accurate results represent ideal benchmarks for more approximate methods.

Toward Accurate yet Effective Computations of Rotational Spectroscopy Parameters for Biomolecule Building Blocks

The interplay of high-resolution rotational spectroscopy and quantum-chemical computations plays an invaluable role in the investigation of biomolecule building blocks in the gas phase. However, quantum-chemical methods suffer from unfavorable scaling with the dimension of the system under consideration. While a complete characterization of flexible systems requires an elaborate multi-step strategy, in this work, we demonstrate that the accuracy obtained by quantum-chemical composite approaches in the prediction of rotational spectroscopy parameters can be approached by a model based on density functional theory. Glycine and serine are employed to demonstrate that, despite its limited cost, such a model is able to predict rotational constants with an accuracy of 0.3% or better, thus paving the way toward the accurate characterization of larger flexible building blocks of biomolecules.

Brueckner Doubles variation of W1 theory (W1BD) adapted to pseudopotential: W1BDCEP theory

Composite methods are the combination of ab initio calculations used to achieve high precision in the face of a computational reduction. Weizmann-n theories (n = 1, 2, 3, and 4) stand out for presenting a high precision, and a version of the W1 theory is the W1BD theory that uses ab initio Brueckner Doubles (BD) methods. One way to reduce the computational cost of composite methods and maintain accuracy is to use pseudopotentials in the calculation steps; in this context, W1BDCEP composite method was developed from the respective W1BD all-electron version by considering the implementation of compact effective pseudopotential (CEP). The test set used to evaluate the theory were 8 proton affinities (PA₀), 46 electron affinities (EA₀), 54 ionization energies (IE₀), 80 enthalpies of formation (Δ_fH⁰), and 10 bond dissociation energies (BDE). The mean absolute deviation values (MADs) for W1BD and for the version adapted to the pseudopotential, W1BDCEP, were similar, with values of 0.97 kcal mol^-1 and 1.03 kcal mol^-1, respectively, when the properties PA₀, EA₀, IE₀, and Δ_fH⁰ were evaluated together. Comparing the versions of the theories that employ ab initio Brueckner Doubles calculations with the W1 and W1CEP theories, it is possible to observe that the W1BD and W1BDCEP theories are more accurate than the W1 theory (MAD_W1 = 1.25 kcal mol^-1) and W1CEP (MAD_W1CEP = 1.44 kcal mol^-1), proving the accuracy of using the BD method. Pseudopotential reduces computational time by up to 30% and thus enables more accurate calculations with less computational time.

Benefits of Range-Separated Hybrid and Double-Hybrid Functionals for a Large and Diverse Data Set of Reaction Energies and Barrier Heights

To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, an accurate estimation of barrier heights (forward and reverse) and reaction energies is vital. Because of the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), density functional theory remains the workhorse for such calculations. In this paper, we have assessed the performance of 91 density functionals for modeling the reaction energies and barrier heights on a large and chemically diverse data set (BH9) composed of 449 organic chemistry reactions. We have shown that range-separated hybrid functionals perform better than the global hybrids for BH9 barrier heights and reaction energies. Except for the PBE-based range-separated nonempirical double hybrids, range separation of the exchange term helps improve the performance for barrier heights and reaction energies. The 16-parameter Berkeley double hybrid, ωB97M(2), performs remarkably well for both properties. However, our minimally empirical range-separated double hybrid functionals offer marginally better accuracy than ωB97M(2) for BH9 barrier heights and reaction energies.

Assessment of DLPNO-CCSD(T)-F12 and its use for the formulation of the low-cost and reliable L-W1X composite method

In the present study, we have investigated the performance of RIJCOSX DLPNO-CCSD(T)-F12 methods for a wide range of systems. Calculations with a high-accuracy option ["DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12"] extrapolated to the complete-basis-set limit using the maug-cc-pV[D+d,T+d]Z basis sets provides fairly good agreements with the canonical CCSD(T)/CBS reference for a diverse set of thermochemical and kinetic properties [with mean absolute deviations (MADs) of ~1-2 kJ mol^-1 except for atomization energies]. On the other hand, the low-cost "RIJCOSX DLPNO-CCSD(T)-F12D" option leads to substantial deviations for certain properties, notably atomization energies (MADs of up to tens of kJ mol^-1 ). With the high-accuracy CBS approach, we have formulated the L-W1X method, which further includes a low-cost core-valence plus scalar-relativistic term. It shows generally good accuracy. For improved accuracies in specific cases, we advise replacing maug-cc-pV(n+d)Z with jun-cc-pV(n+d)Z for the calculation of electron affinities, and using well-constructed isodesmic-type reactions to obtain atomization energies. For medium-sized systems, DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 calculations are several times faster than the corresponding canonical computation; the use of the local approximations (RIJCOSX and DLPNO) leads to a better scaling than that for the canonical calculation (from ~6-7 down to ~2-4 for our test systems). Thus, the DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 method, and the L-W1X protocol that based on it, represent a useful means for obtaining accurate thermochemical quantities for larger systems.

Fullerenes Pose a Strain on Hybrid Density Functional Theory

The computational modeling of fullerenes plays a fundamental role in designing low-dimension carbon nanostructures. Nevertheless, the relative energies of fullerenes larger than C20 and C24 have not been comprehensively examined by means of highly accurate ab initio methods, for example, the CCSD(T) method. Here we report such an investigation for a diverse set of 29 C40 isomers. We calculate the energies of the C40 fullerenes using the G4(MP2) composite ab initio method, which approximates the CCSD(T) energy in conjunction with a triple-ζ-quality basis set (CCSD(T)/TZ). The CCSD(T)/TZ isomerization energies span 43.1-763.3 kJ mol-1. We find a linear correlation (R2 = 0.96) between the CCSD(T)/TZ isomerization energies and the fullerene pentagon signatures (P1 index), which reflect the strain associated with fused pentagon-pentagon rings. Using the reference CCSD(T)/TZ isomerization energies, we examine the relationship between the percentage of exact Hartree-Fock (HF) exchange in hybrid density functional theory (DFT) methods and the pentagon-pentagon strain energies. We find that the performance of hybrid DFT methods deteriorates with the pentagon-pentagon strain energy. This deterioration in performance becomes more pronounced with the inclusion of high amounts of HF exchange. For example, for B3LYP (20% HF exchange), the root-mean-square deviation (RMSD) relative to G4(MP2) increases from 8.9 kJ mol-1 for the low-strain isomers (P1 = 11) to 18.0 kJ mol-1 for the high-strain isomers (P1 > 13). However, for BH&HLYP (50% HF exchange) the RMSD increases from 23.0 (P1 = 11) to 113.2 (P1 > 13) kJ mol-1. A similar trend is observed for the M06/M06-2X pair of functionals. Namely, for M06 (27% HF exchange) the RMSD increases from 0.8 (P1 = 11) to 21.0 (P1 > 13) kJ mol-1, whereas for M06-2X (54% HF exchange) the RMSD increases from 16.7 (P1 = 11) to 77.7 (P1 > 13) kJ mol-1. Overall, we find that the strain associated with pentagon adjacency is an inherently challenging problem for hybrid DFT methods involving high amounts of HF exchange and that there is an inverse relationship between the optimal percentage of HF exchange and the pentagon-pentagon strain energy. For example, for BLYP the optimal percentages of HF exchange are 13% (P1 = 11), 10% (P1 = 12), 7.5% (P1 = 13), and 6% (P1 > 13).

Unbiased disentanglement of conformational baths with the help of microwave spectroscopy, quantum chemistry and artificial intelligence: the puzzling case of homocysteine

An integrated experimental-computational strategy for the accurate characterization of the conformational landscape of flexible biomolecule building blocks is proposed. This is based on the combination of rotational spectroscopy with quantum-chemical computations guided by artificial intelligence tools. The first step of the strategy is the conformer search and relative stability evaluation performed by means of an evolutionary algorithm. In this step, last generation semiempirical methods are exploited together with hybrid and double-hybrid density functionals. Next, the barriers ruling the interconversion between the low-lying conformers are evaluated in order to unravel possible fast relaxation paths. The relative stabilities and spectroscopic parameters of the ``surviving' conformers are then refined using state-of-the-art composite schemes. The reliability of the computational procedure is further improved by the inclusion of vibrational and thermal effects. The final step of the strategy is the comparison between experiment and theory without any ad hoc adjustment, which allows an unbiased assignment of the spectroscopic features in terms of different conformers and their spectroscopic parameters. The proposed approach has been tested and validated for homocysteine, a highly flexible non-proteinogenic alpha-amino acid. The synergism of the integrated strategy allowed the characterization of five conformers stabilized by bifurcated N-H-O=C hydrogen bonds, together with an additional conformer involving a more conventional HNH-O hydrogen bond. The stability order estimated from the experimental intensities as well as the number and type of conformers observed in the gas phase are in full agreement with the theoretical predictions. Analogously, a good match has been found for the spectroscopic parameters.

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.

From Molecules with a Planar Tetracoordinate Carbon to an Astronomically Known C5H2 Carbene

Ethynylcyclopropenylidene (2), an isomer of C₅H₂, is a known molecule in the laboratory and has recently been identified in Taurus Molecular Cloud-1 (TMC-1). Using high-level coupled-cluster methods up to the CCSDT(Q)/CBS level of theory, it is shown that two isomers of C₅H₂ with a planar tetracoordinate carbon (ptC) atom, (SP-4)-spiro[2.2]pent-1,4-dien-1,4-diyl (11) and (SP-4)-spiro[2.2]pent-1,4-dien-1,5-diyl (13), serve as the reactive intermediates for the formation of 2. Here, a theoretical connection has been established between molecules containing ptC atoms (11 and 13) and a molecule (2) that is present nearly 430 light years away, thus providing evidence for the existence of ptC species in the interstellar medium. The reaction pathways connecting the transition states and the reactants and products have been confirmed by intrinsic reaction coordinate calculations at the CCSDT(Q)/CBS//B3LYP-D3BJ/cc-pVTZ level. While isomer 11 is non-polar (μ = 0), isomers 2 and 13 are polar, with dipole moment values of 3.52 and 5.17 Debye at the CCSD(T)/cc-pVTZ level. Therefore, 13 is also a suitable candidate for both laboratory and radioastronomical studies.

Tackling an accurate description of molecular reactivity with double-hybrid density functionals

In this Communication, we assess a panel of 18 double-hybrid density functionals for the modeling of the thermochemical and kinetic properties of an extended dataset of 449 organic chemistry reactions belonging to the BH9 database. We show that most of DHs provide a statistically robust performance to model barrier height and reaction energies in reaching the “chemical accuracy.” In particular, we show that nonempirical DHs, such as PBE0-DH and PBE-QIDH, or minimally parameterized alternatives, such as ωB2PLYP and B2K-PLYP, succeed to accurately model both properties in a balanced fashion. We demonstrate, however, that parameterized approaches, such as ωB97X-2 or DSD-like DHs, are more biased to only one of both properties.

High-Level Ab Initio Predictions of Thermochemical Properties of Organosilicon Species: Critical Evaluation of Experimental Data and a Reliable Benchmark Database for Extending Group Additivity Approaches

A high-level composite quantum chemical method, W1X-1, is used herein to calculate the gas-phase standard enthalpy of formation, entropy, and heat capacity of 159 organosilicon compounds. The results set a new benchmark in the field that allows, for the first time, an in-depth assessment of existing experimental data on standard enthalpies of formation, enabling the identification of important trends and possible outliers. The calculated thermochemical data are used to determine Benson group additivity contributions for 60 Benson groups and group pairs involving silicon. These values allow fast and accurate estimation of thermochemical parameters of organosilicon compounds of varying complexity, and the data acquired are used to assess the reliability of experimental work of Voronkov et al. that has been repeatedly criticized by Becerra and Walsh. Recent results from other computational investigations in the field are also carefully discussed through the prism of reported advancements.

Graphene-induced planarization of cyclooctatetraene derivatives

Stable equilibrium compounds containing a planar antiaromatic cyclooctatetraene (COT) ring are promising candidates for organic electronic devices such as organic semiconductor transistors. The planarization of COT by incorporation into rigid planar π-systems, as well as by oxidation or reduction has attracted considerable attention in recent years. Using dispersion-corrected density functional theory calculations, we explore an alternative approach of planarizing COT derivatives by adsorption onto graphene. We show that strong π-π stacking interactions between graphene and COT derivatives induce a planar structure with an antiaromatic central COT ring. In addition to being reversible, this strategy provides a novel approach for planarizing COT without the need for incorporation into a rigid structure, atomic substitution, oxidation, or reduction.

BH9, a New Comprehensive Benchmark Data Set for Barrier Heights and Reaction Energies: Assessment of Density Functional Approximations and Basis Set Incompleteness Potentials

The calculation of accurate reaction energies and barrier heights is essential in computational studies of reaction mechanisms and thermochemistry. To assess methods regarding their ability to predict these two properties, high-quality benchmark sets are required that comprise a reasonably large and diverse set of organic reactions. Due to the time-consuming nature of both locating transition states and computing accurate reference energies for reactions involving large molecules, previous benchmark sets have been limited in scope, the number of reactions considered, and the size of the reactant and product molecules. Recent advances in coupled-cluster theory, in particular local correlation methods like DLPNO-CCSD(T), now allow the calculation of reaction energies and barrier heights for relatively large systems. In this work, we present a comprehensive and diverse benchmark set of barrier heights and reaction energies based on DLPNO-CCSD(T)/CBS called BH9. BH9 comprises 449 chemical reactions belonging to nine types common in organic chemistry and biochemistry. We examine the accuracy of DLPNO-CCSD(T) vis-a-vis canonical CCSD(T) for a subset of BH9 and conclude that, although there is a penalty in using the DLPNO approximation, the reference data are accurate enough to serve as a benchmark for density functional theory (DFT) methods. We then present two applications of the BH9 set. First, we examine the performance of several density functional approximations commonly used in thermochemical and mechanistic studies. Second, we assess our basis set incompleteness potentials regarding their ability to mitigate basis set incompleteness errors. The number of data points, the diversity of the reactions considered, and the relatively large size of the reactant molecules make BH9 the most comprehensive thermochemical benchmark set to date and a useful tool for the development and assessment of computational methods.

Structural and Energetic Properties of Amino Acids and Peptides Benchmarked by Accurate Theoretical and Experimental Data

Structural, energetic, and spectroscopic data derived in this work aim at the setup of an "experimentally validated" database for amino acids and polypeptides conformers. First, the "cheap" composite scheme (ChS, CCSD(T)/(CBS+CV)^MP2) is tested for evaluation of conformational energies of all eight stable conformers of glycine, by comparing to the more accurate CCSD(T)/CBS+CV computations (Phys. Chem. Chem. Phys. 2013, 15, 10094-10111 and J Mol. Model. 2020, 26, 129). The recently proposed jun-ChS (J. Chem. Theory and Comput. 2020, 16, 988-1006), employing the jun-cc-pVnZ basis set family for CCSD(T) computations and CBS extrapolation, yields conformational energies accurate to 0.2 kJ·mol^-1, at reduced computational cost with respect to aug-ChS employing aug-cc-pVnZ basis sets. The jun-ChS composite scheme is further applied to derive conformational energies for three dipeptide analogues Ac-Gly-NH₂, Ac-Ala-NH₂, and Gly-Gly. Finally, dipeptide conformational energies and semiexperimental equilibrium rotational constants along with the CCSD(T)/(CBS+CV)^MP2 structural parameters (J. Phys. Chem. Lett. 2014, 5, 534-540) stand as the reference for benchmarking of selected density functional methodologies. The double-hybrid functionals B2-PLYP-D3(BJ) and DSD-PBEP86, perform best for structural and energetic characterization of all dipeptide analogues. From hybrid functionals CAM-B3LYP-D3(BJ) and ωB97X-D3(BJ) represent promising methods applicable for larger peptide-based systems for which computations with double-hybrid functionals are not feasible.