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

Dactylfungins and Tetralones: Bioactive Metabolites from a Nematode-Associated Laburnicola nematophila

A chemical investigation of Laburnicola nematophila, isolated from cysts of the plant parasitic nematode Heterodera filipjevi, affored three dactylfungin derivatives (1-3) and three tetralone congeners (4-6). Dactylfungin C (1), laburnicolin (4), and laburnicolenone (5) are previously undescribed natural products. Chemical structures of the isolated compounds were determined based on 1D and 2D NMR spectroscopic analyses together with HR-ESI-MS spectrometry and comparison with data reported in the literature. The relative configurations of compounds 1, 2, and 4-6 were determined based on their ROESY data and analysis of their coupling constants (J values). The absolute configurations of 4-6 were determined through the comparison of their measured and calculated TDDFT-ECD spectra. Compounds 1-3 were active against azole-resistant Aspergillus fumigatus.

Ultrafast photochemistry and electron diffraction for cyclobutanone in the S2 state: Surface hopping with time-dependent density functional theory

We simulate the photodynamics of gas-phase cyclobutanone excited to the S2 state using fewest switches surface hopping (FSSH) dynamics powered by time-dependent density functional theory (TDDFT). We predict a total photoproduct yield of 8%, with a C3:C2 product ratio of 0 trajectories to 8 trajectories. One primary S2 → S1 conical intersection is identified involving the compression of an α-carbon-carbon-hydrogen bond angle. Excited state lifetimes computed with respect to electronic state populations were found to be 3.96 ps (S2 → S1) and 498 fs (S1 → S0). We also generate time-resolved difference pair distribution functions (ΔPDFs) from our TDDFT-FSSH dynamics results in order to generate direct comparisons with ultrafast electron diffraction experiment observables. Global and target analysis of time-resolved ΔPDFs produced a distinct set of lifetimes: (i) a 0.548 ps decay and (ii) a 1.69 ps decay, both resembling the S2 minimum, as well as (iii) a long decay that resembles the S1 minimum geometry and the fully separated C2 products. Finally, we contextualize our results by considering the impact of the most likely sources of significant errors.

Ni, Cu, Zn, Pd, Ag and Cd Tetraphenylporphyrin Ab Initio Thermochemistry: Enthalpy of Formation of ZnTPP Revisited

Groups 10-12 metalloporphyrins have been recognized for their numerous properties essential for the development of new sensing materials. In this work, accurate gas-phase enthalpies of formation, ΔfHm0(g,298.15), are predicted for the series of Ni, Cu, Zn, Pd, Ag, and Cd tetraphenylporphyrins (MTPPs) on the basis of the reaction-based Feller-Peterson-Dixon approach and high-level ab initio DLPNO-CCSD(T) calculations. Our recently developed automatic generator of the balanced chemical reactions was employed to reduce the bias of the theoretical ΔfHm0(g,298.15) toward a particular reaction. Theoretical ΔfHm0(g,298.15) for ZnTPP (227.0 ± 3.4 kcal mol-1) does not support the previously reported experimental value of 132 ± 2 kcal mol-1. The origin of the discrepancy probably lies in the experimental solid-state ΔfHm0(ZnTPP, cr,298.15) as it stems from our theoretical evaluations of the ΔfHm0(cr,298.15) values for the entire set of transition metal TPP complexes. The large discrepancy between experiment and theory also holds when different DFT functionals (ωB97M-V, PBE0-D4, and B3LYP-D4) paired with quadruple-ζ quality basis sets are used for the theoretical calculations. Experimental revisiting of the solid-state enthalpy of formation of ZnTPP and analogue measurements for other transition metal TPPs are needed to resolve the observed discrepancy. Based on the predicted enthalpies of formation of MTPPs, the relative energies of the metal-ligand bonding are evaluated and the trends are compared to those for the complexes of the unsubstituted porphyrin with the same set of metals derived in [Can. J. Chem., 2009, 87, 1063]. According to both studies, Pd complexes exhibit the strongest bonding, while the Cd species are the least stable metallocomplexes within the considered series.

Early Steps in the O2 Scavenger Process in the Aqueous Phase: Hydrazine vs DEHA

We investigate the first direct proton abstraction reactions from reducing agents (RAHs) hydrazine and diethyl hydroxylamine (DEHA), toward dioxygen (O2) in the aqueous phase, spanning ambient to high-temperature conditions. Quantum chemistry methods and molecular dynamics simulations are employed in this study. Quantum chemistry methods are used to analyze the quasi-equilibrium between a reactive conformation and a transition state in the [RAH,O2] cluster. On the other hand, molecular dynamics simulations estimate the probability of observing a reactive conformation of the [RAH,O2] cluster in the solution. In this study, we assume that the energy barrier of the quasi-equilibrium is sufficiently high for the RAH/O2 association process to be at equilibrium. Our findings indicate that the first proton abstraction process from a reactive conformation cluster by DEHA is energetically favored compared to hydrazine. Conversely, the association process of hydrazine and O2 in solution is more favorable than that of DEHA. Consequently, the rate constant for the first proton abstraction process is similar for both hydrazine and DEHA, particularly at high temperatures, with activation energies of approximately 21.5 ± 1.5 kcal mol-1 for both compounds. These results align with recent experiments investigating the complete O2 scavenger process in liquid water with hydrazine and DEHA. Therefore, our findings support the assumption that first proton abstraction reactions are the rate-determining steps in O2 scavenger processes in the aqueous phase.

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.

Solv: An Alternative Continuum Model Implementation Based on Fixed Atomic Charges, Scaled Particle Theory, and the Atom-Atom Potential Method

An alternative continuum model implementation is reported. The electrostatic contribution to the solvation Gibbs free energy utilizes the noniterative conductor-like screening model of Vyboishchikov and Voityuk (DOI: 10.1002/jcc.26531) based on the fixed partial atomic charges. The nonelectrostatic solute-solvent dispersion-repulsion energy is calculated through the Caillet-Claverie atom-atom potential method employing the grid-based approach. The nonelectrostatic cavitation energy is computed within the scaled particle theory (SPT) formalism with the solute hard-sphere radius obtained via the Pierotti-Claverie (PC) scheme, from the solute molecular surface (SPT-S) or volume (SPT-V). The solvent hard-sphere radius is derived through the fitting to the experimental total solvation free energies of 2530 neutral species in 92 solvents. Application of the model to reproduce both the absolute and relative (reaction net) solvation free energies indicates that the SPT-V approach based on the CM5 charges is the best performer. The method is suggested for the solvation free energy calculation in the nonaqueous solvents.

Potential Energy Surfaces Sampled in Cremer-Pople Coordinates and Represented by Common Force Field Functionals for Small Cyclic Molecules

The complex conformations of the cyclic moieties impact the physical and chemical properties of molecules. In this work, we chose 22 molecules of four-, five-, and six-membered rings and performed a thorough conformational sampling using Cremer-Pople coordinates. With consideration of symmetries, we obtained a total of 1504 conformational structures for four-membered, 5576 for five-membered, and 13509 for six-membered rings. All well-known and many less well-known conformers for each molecule were identified. We represented the potential energy surfaces (PESs) by fitting the data to common analytical force field (FF) functional forms. We found that the general features of PESs can be described by the essential FF functional forms; however, the accuracy of representation can be improved remarkably by including the torsion-bond and torsion-angle coupling terms. The best fit yields R-squared (R²) values close to 1.0 and mean absolute errors in energy less than 0.3 kcal/mol.

Comparative analysis of the reactivity of anthocyanidins, leucoanthocyanidins, and flavonols using a quantum chemistry approach

Anthocyanidins, leucoanthocyanidins, and flavonols are natural compounds mainly known due to their reported biological activities, such as antiviral, antifungal, anti-inflammatory activities, and antioxidant activity. In the present study, we performed a comparative structural, conformational, electronic, and nuclear magnetic resonance analysis of the reactivity of the chemical structure of primary anthocyanidins, leucoanthocyanidins, and flavonoids. We focused our analysis on the following molecular questions: (i) differences in cyanidin catechols ( +)-catechin, leucocyanidin, and quercetin; (ii) the loss of hydroxyl presents in the R1 radical of leucoanthocyanidin in the functional groups linked to C4 (ring C); and (iii) the electron affinity of the 3-hydroxyl group (R7) in the flavonoids delphinidin, pelargonidin, cyanidin, quercetin, and kaempferol. We show unprecedented results for bond critical point (BCP) of leucopelargonidin and leucodelphirinidin. The BCP formed between hydroxyl hydrogen (R2) and ketone oxygen (R1) of kaempferol has the same degrees of covalence of quercetin. Kaempferol and quercetin exhibited localized electron densities between hydroxyl hydrogen (R2) and ketone oxygen (R1). Global molecular descriptors showed quercetin and leucocyanidin are the most reactive flavonoids in electrophilic reactions. Complementary, anthocyanidins are the most reactive in nucleophilic reactions, while the smallest gap occurs in delphinidin. Local descriptors indicate that anthocyanidins and flavonols are more prone to electrophilic attacks, while in leucoanthocyanidins, the most susceptible to attack are localized in the ring A. The ring C of anthocyanidins is more aromatic than the same found in flavonols and leucoanthocyanidins. METHODS: For the analysis of the molecular properties, we used the DFT to evaluate the formation of the covalent bonds and intermolecular forces. CAM-B3LYP functional with the def2TZV basis set was used for the geometry optimization. A broad analysis of quantum properties was performed using the assessment of the molecular electrostatic potential surface, electron localization function, Fukui functions, descriptors constructed from frontier orbitals, and nucleus independent chemical shift.

Influence of the complete basis set approximation, tight weighted-core, and diffuse functions on the DLPNO-CCSD(T1) atomization energies of neutral H,C,O-compounds

The impact of complete basis set extrapolation schemes (CBS), diffuse functions, and tight weighted-core functions on enthalpies of formation predicted via the DLPNO-CCSD(T1) reduced Feller-Peterson-Dixon approach has been examined for neutral H,C,O-compounds. All tested three-point (TZ/QZ/5Z) extrapolation schemes result in mean unsigned deviation (MUD) below 2 kJ mol^-1 relative to the experiment. The two-point QZ/5Z and TZ/QZ CBS 1 / l max 3 extrapolation schemes are inferior to their inverse power counterpart ( 1 / l max + 1 / 2 4 ) by 1.3 and 4.3 kJ mol^-1 . The CBS extrapolated frozen core atomization energies are insensitive (within 1 kJ mol^-1 ) to augmentation of the basis set with tight weighted core functions. The core-valence correlation effects converge already at triple-ζ, although double-ζ/triple-ζ CBS extrapolation performs better and is recommended. The effect of diffuse function augmentation converges slowly, and cannot be reproduced with double- ζ or triple- ζ calculations as these are plagued with basis set superposition and incompleteness errors.

Physical and numerical aspects of sodium ion solvation free energies via the cluster-continuum model

Sodium cation solvation Gibbs free energies (ΔG_solv(Na⁺)) have been obtained in water, dimethylformamide, dimethyl sulfoxide, ethanol, acetone, acetonitrile, and methanol through the "monomer cycle" cluster-continuum approach where a solvent reference state is described by infinitely separated molecules. The following steps are vital for obtaining reliable ΔG_solv(Na⁺) values: (a) a meticulous conformational search involving dispersion corrected density functional theory (DFT-D) and the continuum solvation model (CSM); (b) gas-phase DFT-D geometry optimization followed by single-point (SP) domain-based local pair natural orbital coupled clusters including single, double, and partly triple excitation (DLPNO-CCSD(T)) calculations in conjunction with the complete basis set extrapolation; (c) advanced statistical thermodynamic treatment of the low harmonic frequencies (<100 cm^-1) to obtain the robust gas-phase Gibbs free energy correction; (d) gas-phase and dielectric continuum SP with non-electrostatic contributions included in the CSM; (e) an evaluation of the relative thermodynamic stability of the Na⁺(S)_n clusters to identify the number of explicit solvent molecules n to be considered. Our refined computational protocol is promising with a Pearson correlation coefficient between the predicted and experimental data, ρ, of 0.82, and the mean signed and mean unsigned errors of 0.3 and 1.4 kcal mol^-1, respectively.

When Gold Is Not Enough: Platinum Standard of Quantum Chemistry with N7 Cost

In this paper, we extend the rank-reduced coupled-cluster formalism to the calculation of non-iterative energy corrections due to quadruple excitations. There are two major components of the proposed formalism. The first is an approximate compression of the quadruple excitation amplitudes using the Tucker format. The second is a modified functional used for the evaluation of the corrections which gives exactly the same results for the exact amplitudes, but is less susceptible to errors resulting from the aforementioned compression. We show, both theoretically and numerically, that the computational cost of the proposed method scales as the seventh power of the system size. Using reference results for a set of small molecules, the method is calibrated to deliver relative accuracy of a few percent in energy corrections. To illustrate the potential of the theory, we calculate the isomerization energy of ortho/meta benzyne (C₆H₄) and the barrier height for the Cope rearrangement in bullvalene (C₁₀H₁₀). The method retains a near-black-box nature of the conventional coupled-cluster formalism and depends on only one additional parameter that controls the accuracy.

"In Vitro" and "In Vivo" Diagnostic Check for the Thermochemistry of Metal-Organic Compounds

Volatile metal β-diketonates are of interest from both practical and theoretical perspectives (manufacturing of film materials, catalysis, and the nature of metal-ligand bonding). Knowledge of their reliable thermochemical properties is essential for effective applications. However, there is an unacceptable scattering of the available data on the enthalpies of formation. In this work, we proposed "in vitro" and "in vivo" diagnostic tools to verify the available enthalpies of formation in both the crystalline and gaseous states for metal tris-β-diketonates. The "in vitro" procedure involved high-level quantum-chemical calculations and was applied to define a consistent data set on the enthalpies of formation for iron(III) β-diketonates. This data set has provided the basis for "in vivo" structure-property-based diagnostics to evaluate the robustness of the thermochemical data for β-diketonate tris-complexes with metals other than iron.

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.

The long road to calibrated prediction uncertainty in computational chemistry

Uncertainty quantification (UQ) in computational chemistry (CC) is still in its infancy. Very few CC methods are designed to provide a confidence level on their predictions, and most users still rely improperly on the mean absolute error as an accuracy metric. The development of reliable UQ methods is essential, notably for CC to be used confidently in industrial processes. A review of the CC-UQ literature shows that there is no common standard procedure to report or validate prediction uncertainty. I consider here analysis tools using concepts (calibration and sharpness) developed in meteorology and machine learning for the validation of probabilistic forecasters. These tools are adapted to CC-UQ and applied to datasets of prediction uncertainties provided by composite methods, Bayesian ensembles methods, and machine learning and a posteriori statistical methods.

Quantification of Geometric Errors Made Simple: Application to Main-Group Molecular Structures

Nearly all electronic structure simulations begin with obtaining approximate geometries, making a systematic quantification of errors in approximate molecular structures of key importance. Recently, the geometric energy offset (GEO) framework based on a single and natural measure for quantifying and analyzing these errors has been proposed ( J. Phys. Chem. Lett. 2020, 11, 99579964). An accurate and far less costly approximation to GEO is utilized here to readily quantify errors in main-group structures and analyze them in a chemically intuitive way. The use of semiexperimental geometries as a reference further simplifies the analysis. The analysis reveals new insights into the geometric performance of methods, their rankings, as well as patterns across different classes of methods and basis sets that arise from the analysis.

Computational Investigation of the Thermochemistry of the CO2 Capture Reaction by Ethylamine, Propylamine, and Butylamine in Aqueous Solution Considering the Full Conformational Space via Boltzmann Statistics

Rubisco is the enzyme responsible for CO₂ fixation in nature, and it is activated by CO₂ addition to the amine group of its lysine 201 side chain. We are designing rubisco-based biomimetic systems for reversible CO₂ capture from ambient air. The oligopeptide biomimetic capture systems are employed in aqueous solution. To provide a solid foundation for the experimental solution-phase studies of the CO₂ capture reaction, we report here the results of computational studies of the thermodynamics of CO₂ capture by small alkylamines in aqueous solution. We studied CO₂ addition to methyl-, ethyl-, propyl-, and butylamine with the consideration of the full conformational space for the amine and the corresponding carbamic acids and with the application of an accurate solvation model for the potential energy surface analyses. The reaction energies of the carbamylation reactions were determined based on just the most stable structures (MSS) and based on the ensemble energies computed with the Boltzmann distribution (BD), and it is found that ΔG_BD ≈ ΔG_MSS. The effect of the proper accounting for the molecular translational entropies in solution with the Wertz approach are much more significant, and the free energy of the capture reactions Δ^WG_BD is more negative by 2.9 kcal/mol. Further accounting for volume effects in solution results in our best estimates for the reaction energies of the carbamylation reactions of Δ^WA_BD = -5.4 kcal/mol. The overall difference is ΔG_BD - Δ^WA_BD = 2.4 kcal/mol for butylamine carbamylation. The full conformational space analyses inform about the conformational isomerizations of carbamic acids, and we determined the relevant rotational profiles and their transition-state structures. Our detailed studies emphasize that, more generally, solution-phase reaction energies should be evaluated with the Helmholtz free energy and can be affected substantially by solution effects on translational entropies.