Minimally Empirical Double-Hybrid Functionals Trained against the GMTKN55 Database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4

Toward Accurate Quantum Mechanical Thermochemistry: (2) Optimal Methods for Enthalpy Calculations from Comprehensive Benchmarks of 284 Model Chemistries

Accurate and efficient computations of the standard enthalpies of formation (ΔHf°) for small organic molecules are crucial for diverse chemical engineering and scientific applications. Building on part 1 of this work [J. Phys. Chem. A 2024, 128, 21, 4335-4352], we systematically benchmark 284 model chemistries for ΔHf° computations. These methods span semiempirical approaches, density functional theory (DFT), wave function theory, and composite schemes. We derive Petersson- and Melius-type bond-additivity corrections (BACs) for each method using a curated database of 421 reference species. We further validate the top-performing methods using an independent test set of 500 species, including ions, radicals, and other challenging cases. Across nearly all methods and species, BACs significantly improve accuracy, especially for neutral singlet species. Composite schemes coupling moderate-level DFT geometries with local coupled-cluster single-point energies strike an excellent balance between cost and accuracy, often approaching chemical accuracy (≤1 kcal/mol). Notably, DLPNO-CCSD(T)-F12d/cc-pVTZ-F12//ωB97X-D/def2-TZVPD with Petersson BAC attains the benchmark-best mean absolute error (MAE) of 0.57 kcal/mol. Switching to DLPNO-CCSD(T)-F12d/cc-pVDZ-F12//GFN2-xTB reduces the computational cost by an order of magnitude, with only a modest increase in MAE (0.96 kcal/mol). Although carefully tuned model chemistries can also benefit charged and open-shell species, the scarcity of robust reference data in these areas highlights the need for broader, high-accuracy thermochemistry datasets. Overall, this benchmark provides practical guidance on selecting optimal model chemistries to efficiently compute accurate ΔHf° under varied computational constraints and molecular complexities, laying a foundation for large-scale, high-throughput thermochemical calculations that will support data-driven discovery and industrial applications.

The Amsterdam Modeling Suite

In this paper, we present the Amsterdam Modeling Suite (AMS), a comprehensive software platform designed to support advanced molecular and materials simulations across a wide range of chemical and physical systems. AMS integrates cutting-edge quantum chemical methods, including Density Functional Theory (DFT) and time-dependent DFT, with molecular mechanics, fluid thermodynamics, machine learning techniques, and more, to enable multi-scale modeling of complex chemical systems. Its design philosophy allows for seamless coupling between components, facilitating simulations that range from small molecules to complex biomolecular and solid-state systems, making it a versatile tool for tackling interdisciplinary challenges, both in industry and in academia. The suite also emphasizes user accessibility, with an intuitive graphical interface, extensive scripting capabilities, and compatibility with high-performance computing environments.

Vibrational second-order perturbation theory based on curvilinear coordinates: Thermochemical applications

This work improves and extends a general and robust workflow for the computation of anharmonic vibrational frequencies to thermodynamic functions, paving the way toward the study of large flexible molecules. The key new feature is the extension of closed-form expressions for both zero-point vibrational energies and partition functions to second-order vibrational perturbation theory based on curvilinear internal coordinates. The use of curvilinear coordinates enables the reduction of couplings between different degrees of freedom, enriching the arsenal of existing vibrational approaches, and can lead to effective, low-dimensional linear-scaling models. The accuracy of the results obtained for some prototypical systems paves the way toward the systematic use of this new implementation in the study of molecules containing a few dozen atoms, as exemplified by the test cases of a molecular motor, a nucleoside, and two hormones.

Reliable Quantum-Chemistry Heats of Formation for an Extensive Set of C-, H-, N-, O-, F-, S-, Cl-, Br-Containing Molecules in the NIST Chemistry Webbook

In the present study, we have computed the heat of formation (HOF) for over 500 C-, H-, N-, O-, F-, S-, Cl-, Br-containing molecules in the NIST Chemistry Webbook with a previously established methodology [from the highest- to lowest-level methods, W1X-2, CCSD(T)-F12b, DSD-PBEP86, and ωB97M-V, with the lower levels calibrated against higher levels for the atomic energies, see: J. Phys. Chem. A 2022, 126, 4981-4990]. We find a reasonable level of agreement between the computed and NIST values for the present set of species. However, the set of F-containing compounds shows considerably larger discrepancies, which can in part be attributed to dubious experimental values, as we have demonstrated in some cases. With our highest-level computed HOFs, we validated the lower-level methods used in our protocol. Specifically, CCSD(T)-F12b yields chemically accurate (±4.2 kJ mol-1) values for all types of molecules, while DSD-PBEP86 and ωB97M-V yield similar levels of accuracy for most systems, with key exceptions being molecules with numerous electron-withdrawing F and NO2 groups. Our results further support the use of the protocol for the computation of HOFs, particularly for systems with few reliable reference values.

Matrix-isolation IR spectra of iodotrifluoroethylene (C2F3I)

The infrared spectra of iodotrifluoroethylene (ITFE) recorded under matrix-isolation (MI) conditions in para-hydrogen, neon and argon were investigated. The experimental spectra were analyzed by comparison with computed anharmonic spectra obtained in the second-order vibrational perturbation theory (VPT2) framework at the MP2 and revDSD-PBEP86-D3BJ levels of theory. In para-hydrogen and neon matrices, the experimentally observable bands in the range of 1800-650 cm-1 could be assigned to vibrational transitions of monomeric ITFE. The spectral resolution even allowed assignments of transitions arising from 13C-isotopologues and the observation of various higher-order resonances in the range up to ∼3550 cm-1. A comprehensive series of MI experiments in argon obtained by varying several experimental parameters revealed a dependence of the spectra on the deposition temperature. The spectra generally showed strong site-splitting effects due to the existence of different local environments around the ITFE molecule. Detailed analysis of the experimental spectra resulted in the identification of bands which are differently affected by matrix annealing. This observation led to the conclusion that ITFE occupies two major matrix sites of different stability. Calculations on ITFE dimers confirmed that spectral changes during annealing are due to the formation of dimers, which are stabilized through π-π interactions.

Correction: The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

Correction for 'The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations' by Thomas Gasevic et al., Phys. Chem. Chem. Phys., 2024, 26, 13884-13908, https://doi.org/10.1039/D3CP06217A.

Vibrational Analysis Based on Cavity-Enhanced Raman Spectroscopy: Cyclohexane

Cyclohexane (CAS: 110-82-7), a colorless organic solvent derived from petroleum, is a valuable reference standard for Raman shift calibration and serves as a model for six-membered ring structures in complex chemical and biological systems. In this study, we measured polarized Raman spectra of gaseous cyclohexane at room temperature using cavity-enhanced Raman spectroscopy (CERS) across the range of 200-3200 cm-1. The observed vibrational wavenumbers, intensities, and depolarization ratios were compared with calculated values, enabling the assignment of several dozen Raman-active bands, including many overtone and combination bands. This work demonstrates the capability of CERS for vibrational analysis of gas-phase polyatomic molecules.

Completing the Spectral Mosaic of Chloromethane by Adding the CHD2Cl Missing Piece Through the Interplay of Rotational/Vibrational Spectroscopy and Quantum Chemical Calculations

Chloromethane (CH3Cl) is a key chlorinated organic compound not only in atmospheric chemistry, but also in the field of molecular astrophysics and a possible biosignature in exoplanetary atmospheres. While the spectroscopic characterization of the main isotopic species has been addressed in great detail, that of its isotopologues remains incomplete. This work aims at filling this gap by focusing on the bideuterated species, CHD2Cl, and exploiting both rotational and vibrational spectroscopy in combination with state-of-the-art quantum-chemical (QC) calculations. First, the rotational spectrum of CHD2Cl has been measured in the millimeter-wave domain, allowing the accurate determination of several spectroscopic constants for four isotopologues, namely 12CHD235Cl, 12CHD237Cl, 13CHD235Cl, and 13CHD237Cl. The newly determined rotational constants have been used to refine the semi-experimental equilibrium structure of chloromethane. Secondly, the vibrational analysis, supported by high-level QC predictions of vibrational energies, has been conducted in the 500-6200 cm-1 infrared (IR) region, enabling the identification of more than 30 bands including fundamental, overtone, and combination transitions. Finally, chloromethane's radiative efficiency has been simulated using the QC IR absorption cross-sections, and the effects of isotopologue distribution on the predicted radiative properties have been investigated. All these findings greatly improve the comprehension of the spectroscopic properties of bideuterated chloromethane isotopologues, and of chloromethane in general, and facilitate future terrestrial and extraterrestrial studies.

Accurate Structures and Spectroscopic Parameters of CN-Substituted Polycyclic Hydrocarbons at DFT Cost

The structures, isomerization energies, and rotational and vibrational spectra of prototypical CN-substituted polycyclic hydrocarbons in the gas phase have been analyzed using a general computational strategy based on Pisa composite schemes (PCS) and second-order vibrational perturbation theory (VPT2). The final results obtained in this way show, in most cases, relative average deviations with respect to experimental rotational constants close to 0.1%, corresponding to errors of around 1 mÅ and 0.1° for bond lengths and valence angles, respectively. At the same time, fundamental IR absorption bands are reproduced with average deviations below 10 cm-1 without any scaling factor. In addition to the intrinsic interest of the studied molecules, this work confirms that spectroscopic studies of large systems can be supported by unsupervised computational tools that couple accuracy with reasonable cost.

Molecular structures with spectroscopic accuracy at DFT cost by the templating synthon approach and the PCS141 database

The computation of accurate geometric parameters at density functional theory cost for large molecules in the gas phase is addressed through a novel strategy that combines quantum chemical models with machine learning techniques. The first key step is the expansion of a database of accurate semi-experimental equilibrium structures with additional molecular geometries optimized by version 2 of the Pisa composite scheme. Then, the templating synthon approach is used to improve the accuracy of structures optimized by a hybrid density functional paired with a double zeta basis set, leveraging chemical similarity to cluster different molecular environments and refine bond lengths and valence angles. A set of prototypical biomolecular building blocks is used to demonstrate that it is possible to achieve spectroscopic accuracy for molecular systems too large to be treated by state-of-the-art composite wavefunction methods. In addition, a freely accessible web-based tool has been developed to facilitate the post-processing of geometries optimized using standard electronic structure codes, thereby providing an accurate and efficient tool for the computational study of medium- to large-sized molecules, also accessible to experiment-oriented researchers.

Prediction of 57Fe Mössbauer Nuclear Quadrupole Splittings with Hybrid and Double-Hybrid Density Functionals

As a crucial parameter in Mössbauer spectroscopy, nuclear quadrupole splitting (NQS) exhibits a strong dependence on quantum chemistry methods, which makes accurate theoretical predictions challenging. Meanwhile, the continuous emergence of new density functionals presents opportunities to advance current NQS research. In this study, we evaluate the performance of eleven hybrid density functionals and twelve double-hybrid density functionals, selected from widely used functionals and newly developed functionals, in predicting the NQS values of the 57Fe nuclide for 32 iron-containing molecules within about 70 atoms. The calculations have incorporated scalar relativistic effects using the exact two-component (X2C) Hamiltonian. In general, the double-hybrid functional PBE-0DH demonstrates superior performance compared to the experimental values, achieving a mean absolute error (MAE) of 0.20 mm/s. Meanwhile, rSCAN38 is the best hybrid functional for our database with an MAE = 0.25 mm/s, and it offers a significant advantage in computational efficiency over PBE-0DH. The +/- sign of NQS has also been considered in our error statistics when it has a clear physical meaning; if neglected, the errors of many functionals decrease, but PBE-0DH and rSCAN38 remain unaffected. Notably, when calculating ferrocene [Fe(C5H5)2], which involves strong static correlations, all hybrid functionals that incorporate more than 10% exact exchange fail, while several double-hybrid functionals continue to deliver reliable results. In addition, we encountered two particularly challenging species characterized by strong static correlations: [Fe(H2O)5NO]2+ and FeO2--porphyrin. Unfortunately, none of the density functionals tested in our study yielded satisfactory results for the two cases since the density functional theory (DFT) is a single-determinant approach, and it is imperative to explore large-scale multi-configurational methods for these species. This research offers valuable guidance for selecting density functionals in Mössbauer NQS calculations and serves as a reference point for the future development of new density functionals.

Near-Basis-Set-Limit Double-Hybrid DFT Energies with Exceptionally Low Computational Costs

The use of density-based basis-set correction (DBBSC) [ J. Phys. Chem. Lett. 2019, 10, 2931] is extended to double-hybrid (DH) functionals. The proposed DBBSC-DH approach significantly reduces the basis-set requirements for accurate calculations, enabling near-basis-set-limit results using affordable one-electron basis sets. The accuracy of this method is comparable to that of the recently proposed DH functionals utilizing explicitly correlated (F12) second-order perturbation theory contribution [ J. Phys. Chem. Lett. 2022, 13, 9332]; however, its computational costs and resource demands are only a fraction of those associated with the DH-F12 scheme. Applications to real-life examples reveal that only a 30% overhead in wall-clock time is observed compared to conventional DH calculations, demonstrating that the DBBSC-DH approach is a compelling alternative to the excellent but relatively costly DH-F12 functionals, particularly for extended molecular systems.

Stabilization of [(N5)2BX]2- and [(N5)2B2X2]2- (X = H, F, Cl, Br) by Conjugation and Hyperconjugation Effects

The isolation of nucleophilic boron bases has led to a paradigm shift in boron chemistry. Previous studies of the bis(carbene) borylene complexes revealed that these compounds possess strong donor abilities, and their reaction inertness is due to the large steric hindrance between boron reagents and reactant. In the present study, we have theoretically studied the [(N5)2BX]2- and [(N5)2B2X2]2- compounds (X = H, F, Cl, Br). Their electronic structures and properties are discussed by using the NBO, LOL, and ELF methods. We found that both π-conjugation and hyperconjugation effects can effectively stabilize the substituted nucleophilic anionic boron compounds [(N5)2BX]2- and [(N5)2B2X2]2-. Substituents, especially X = H, stabilize the boron center through highly delocalized π-bonding, involving the formally "empty" in-plane p orbitals of the boron atom. While the halogen substituents have high electron withdrawal ability, leading to systems being less stable, we suggest the borinium anions [(N5)2BH]2- and [(N5)2B2H2]2- as possible synthetic targets of novel environmentally friendly catalysts.

Predicting Carbonic Anhydrase Binding Affinity: Insights from QM Cluster Models

A systematic series of QM cluster models has been developed to predict the trend in the carbonic anhydrase binding affinity of a structurally diverse dataset of ligands. Reference DLPNO-CCSD(T)/CBS binding energies were generated for a cluster model and used to evaluate the performance of contemporary density functional theory methods, including Grimme's "3c" DFT composite methods (r2SCAN-3c and ωB97X-3c). It is demonstrated that when validated QM methods are used, the predictive power of the cluster models improves systematically with the size of the cluster models. This provided valuable insights into the key interactions that need to be modeled quantum mechanically and could inform how the QM region should be defined in hybrid quantum mechanics/molecular mechanics (QM/MM) models. The use of r2SCAN-3c on the largest cluster model composed of 16 residues appears to be an economical approach to predicting binding trends compared with using more robust DFT methods such as ωB97M-V and provides a significant improvement compared with docking.

Electrostatically tuning radical addition and atom abstraction reactions with distonic radical ions

Although electrostatic catalysis can enhance the kinetics and selectivity of reactions to produce greener synthetic processes, the highly directional nature of electrostatic interactions has limited widespread application. In this study, the influence of oriented electric fields (OEF) on radical addition and atom abstraction reactions are systematically explored with ion-trap mass spectrometry using structurally diverse distonic radical ions that maintain spatially separated charge and radical moieties. When installed on rigid molecular scaffolds, charged functional groups lock the magnitude and orientation of the internal electric field with respect to the radical site, creating an OEF which tunes the reactivity across the set of gas-phase carbon-centred radical reactions. In the first case, OEFs predictably accelerate and decelerate the rate of molecular oxygen addition to substituted phenyl, adamantyl, and cubyl radicals, depending on the polarity of the charged functional group and dipole orientation. In the second case, OEFs modulate competition between chlorine and hydrogen atom abstraction from chloroform based on interactions between charge polarity, dipole orientation, and radical polarizability. Importantly, this means the same charge polarity can induce different changes to reaction selectivity. Quantum chemical calculations of these reactions with DSD-PBEP86-D3(BJ)/aug-cc-pVTZ show correlations between the barrier heights and the experimentally determined reaction kinetics. Field effects are consistent between phenyl and cubyl scaffolds, pointing to through-space rather than through-bond field effects, congruent with computations showing that the same effects can be mimicked by point charges. These results experimentally demonstrate how internal OEFs generated by carefully placed charged functional groups can systematically control radical reactions.

Neighboring-Group Participation by a Less Electron-Donating, Participating C-2-Ester Ensures Higher 1,2-trans Stereoselectivity in Nucleophilic Substitution Reactions of Furanosyl Acetals

Nucleophilic substitution reactions of C-2-acyloxy furanosyl acetals can be highly diastereoselective. We here show that the presence of a less electron-donating p-nitrobenzoyloxy group at C-2 of a furanosyl acetal can be of use to control the 1,2-trans stereoselectivity of acetal substitution reactions with higher stereoselectivity than the analogue with the more electron-donating benzoyloxy group, just as what was observed in the pyranosyl system. Computational results support a reaction manifold involving both open oxocarbenium ions and cis-dioxolenium ions to provide the 1,2-cis and 1,2-trans products. Participation by the less electron-donating C-2-(p-nitrobenzoyloxy) group forms a less stabilized cis-dioxolenium ion that reacts with the incoming nucleophile more readily to provide 1,2-trans products. The relative stability of the furanosyl cis-dioxolenium ion versus the open oxocarbenium ion is much higher than the pyranosyl system as a result of the lower energy penalty for forming the cis-fused [5,5]-bicyclic dioxolenium ion.

Accurate Enthalpies of Formation for Bioactive Compounds from High-Level Ab Initio Calculations with Detailed Conformational Treatment: A Case of Cannabinoids

Our recently developed approach based on the local coupled-cluster with single, double, and perturbative triple excitation [LCCSD(T)] model gives very efficient means to compute the ideal-gas enthalpies of formation. The expanded uncertainty (95% confidence) of the method is about 3 kJ·mol-1 for medium-sized compounds, comparable to typical experimental measurements. Larger compounds of interest often exhibit many conformations that can significantly differ in intramolecular interactions. Although the present capabilities allow processing even a few hundred distinct conformer structures for a given compound, many systems of interest exhibit numbers well in excess of 1000. In this study, we investigate how to reduce the number of expensive LCCSD(T) calculations for large conformer ensembles while controlling the error of the approximation. The best strategy found was to correct the results of the lower-level, surrogate model (density functional theory, DFT) in a systematic manner. It was also found that the error in the conformational contribution introduced by a surrogate model is mainly driven by a systematic (bias) rather than a random component of the DFT energy deviation from the LCCSD(T) target. This distinction is usually overlooked in DFT benchmarking studies. As a result of this work, the enthalpies of formation for 20 cannabinoid and cannabinoid-related compounds were obtained. Comprehensive uncertainty analysis suggests that the expanded uncertainties of the obtained values are below 4 kJ·mol-1.

Cyclo-N9 -: a Novel 5/6 Fused Polynitrogen Anion for High Energy Density Materials

After cyclo-pentazolate anion, a 5/6 fused structure of N9 - is constructed, and four novel nitrogen-rich ionic compounds are assembled on its basis. The results of the quantum calculations revealed an uneven distribution of electrons on cyclo-N9 -, with significant charge density near the N5/N9 atoms and an ADCH charge of -0.425. The relative strength of chemical bonds is assessed through bond order analysis, which is further supplemented by transition state theory and ab initio molecular dynamics, ultimately leading to the identification of the decomposition pathways of cyclo-N9 -. The aromaticity of cyclo-N9 - and its individual sub-rings is cleverly validated through a combination of NICS_ZZ and ICSS methods. Among the eight systems, cyclo-N9 - forms hydrogen bonds with other cations, and IGMH analysis revealed significant LP-π and π-π stacking interactions between [N7H4 +] and cyclo-N9 -, both of which enhance system stability. The theoretical energy densities in all systems are at the forefront in the currently emerging nitrogen-rich compounds. Attributed to its extraordinarily high enthalpy of formation, the detonation performance of [N7H4 +] [N9 -] is particularly excellent. However, [NH3OH+] [N9 -] exhibits better stability and most exciting performance, making it a highly promising candidate with application potential.

Data-Driven Improvement of Local Hybrid Functionals: Neural-Network-Based Local Mixing Functions and Power-Series Correlation Functionals

Local hybrid functionals (LHs) use a real-space position-dependent admixture of exact exchange (EXX), governed by a local mixing function (LMF). The systematic construction of LMFs has been hampered over the years by a lack of exact physical constraints on their valence behavior. Here, we exploit a data-driven approach and train a new type of "n-LMF" as a relatively shallow neural network. The input features are of meta-GGA character, while the W4-17 atomization-energy and BH76 reaction-barrier test sets have been used for training. Simply replacing the widely used "t-LMF" of the LH20t functional by the n-LMF provides the LH24n-B95 functional. Augmented by DFT-D4 dispersion corrections, LH24n-B95-D4 remarkably improves the WTMAD-2 value for the large GMTKN55 test suite of general main-group thermochemistry, kinetics, and noncovalent interactions (NCIs) from 4.55 to 3.49 kcal/mol. As we found the limited flexibility of the B95c correlation functional to disfavor much further improvement on NCIs, we proceeded to replace it by an optimized B97c-type power-series expansion. This gives the LH24n functional. LH24n-D4 gives a WTMAD-2 value of 3.10 kcal/mol, the so far lowest value of a rung 4 functional in self-consistent calculations. The new functionals perform moderately well for organometallic transition-metal energetics while leaving room for further data-driven improvements in that area. Compared to complete neural-network functionals like DM21, the present more tailored approach to train just the LMF in a flexible but well-defined human-designed LH functional retains the possibility of graphical LMF analyses to gain deeper understanding. We find that both the present n-LMF and the recent x-LMF suppress the so-called gauge problem of local hybrids without adding a calibration function as required for other LMFs. LMF plots show that this can be traced back to large LMF values in the small-density region between the interacting atoms in NCIs for n- and x-LMFs and low values for the t-LMF. We also find that the trained n-LMF has relatively large values in covalent bonds without deteriorating binding energies. The current approach enables fast and efficient routine self-consistent calculations using n-LMFs in Turbomole.

Experimental and Theoretical Insights on Gas Trapping of Noble Gases in MFU-4-Type Metal-Organic Frameworks

Isostructural metal-organic frameworks (MOFs), namely MFU-4 and MFU-4-Br, in which the pore apertures are defined by anionic side ligands (Cl- and Br-, respectively), were synthesized and loaded with noble gases. By selecting the type of side ligand, one can fine-tune the pore aperture size, allowing for precise regulation of the entry and release of gas guests. In this study, we conducted experiments to examine gas loading and release using krypton and xenon as model gases, and we complemented our findings with computational modeling. Remarkably, the loaded gas guests remained trapped inside the pores even after being exposed to air under ambient conditions for extended periods, in some cases for up to several weeks. Therefore, we focused on determining the energy barrier preventing gas release using both theoretical and experimental methods. The results were compared in relation to the types of hosts and guests, providing valuable insights into the gas trapping process in MOFs, as well as programmed gas release in air under ambient conditions. Furthermore, the crystal structure of MFU-4-Br was elucidated using the three-dimensional electron diffraction (3DED) technique, and the bulk purity of the sample was subsequently verified through Rietveld refinement.

Structures and Rotational Constants of Monocyclic Monoterpenes at DFT Cost by Pisa Composite Schemes and Vibrational Perturbation Theory

The structures and rotational constants of prototypical monocyclic terpenes and terpenoids have been analyzed by a general computational strategy based on recent Pisa composite schemes (PCS) and vibrational perturbation theory at second order (VPT2). Concerning equilibrium geometries, a one-parameter empirical correction is added to bond lengths obtained by the revDSD-PBEP86 double hybrid functional in conjunction with a slightly modified cc-pVTZ-F12 basis set. The same functional and basis set give accurate harmonic frequencies, whereas the cheaper B3LYP hybrid functional in conjunction with a double-ζ basis set is employed to compute the semidiagonal cubic force constants needed to obtain vibrational corrections to the rotational constants in the framework of the VPT2 model. The final results obtained in this way show in most cases average deviations with respect to the experiment close to 0.1%, which correspond to errors around 1 mÅ and 0.1° for bond lengths and valence angles, respectively. The accuracy of the results has produced reliable estimates for species not analyzed yet experimentally. In addition to the intrinsic interest of the studied molecules, this article confirms that high-resolution spectroscopic studies of quite large systems can now be aided by a very accurate yet robust and user-friendly computational tool.

A General Nonbonded Force Field Based on Accurate Quantum Mechanics Calculations for Elements H-La and Hf-Rn

Noncovalent interactions (NCI) play a central role in numerous physical, chemical, and biological phenomena. An accurate description of NCI is the key to success for any theoretical study in such areas. Although quantum mechanics (QM) methods such as dispersion-corrected density functional theory are sufficiently accurate, their applications are practical only for <300 atoms and <100 ps of simulation time. Thus, empirical force fields (FF) have generally been the only choice for systems with thousands to millions of atoms and for nanoseconds and longer. We want to develop a FF that can be applied to applications of thousands to millions of atoms with an accuracy comparable to QM methods. As the first step, we develop here a new general nonbonded potential (GNB) based on a novel functional form with four adjustable parameters for each element. We report here parameters for elements H-La, Hf-Rn (excluding lanthanides and actinides) by fitting the interaction energy of molecular complexes to QM calculations using the accurate Head-Gordon ωB97M-V density functional. We performed extensive testing of GNB for organic molecules, organometallic molecules, and metal organic-framework (MOF) systems. The mean absolute errors of GNB are 0.37 kcal/mol for the dispersion and mixed groups of the S66 × 8 benchmark set, 0.35 kcal/mol for CO2 adsorption on MOF materials, and 4.53 kcal/mol for the XTMC43 benchmark. GNB outperforms existing FF and in many cases has accuracy comparable to that of QM methods such as PBE-D3. GNB can potentially replace the nonbonded part of existing FFs in a wide range of applications.

The Radiative Efficiency and Global Warming Potential of HCFC-132b

Hydro-chloro-fluoro-carbons (HCFCs) are potent greenhouse gases which strongly absorb the infrared (IR) radiation within the 8-12 μm atmospheric windows. Despite international policies schedule their phasing out by 2020 for developed countries and 2030 globally, HCFC-132b (CH2ClCClF2) has been recently detected with significant atmospheric concentration. In this scenario, detailed climate metrics are of paramount importance for understanding the capacity of anthropogenic pollutants to contribute to global warming. In this work, the radiative efficiency (RE) of HCFC-132b is experimentally measured for the first time and used to determine its global warming potential (GWP) over 20-, 100- and 500-year time horizon. Vibrational- and rotational-spectroscopic properties of this molecule are first characterized by exploiting a synergism between Fourier-transform IR (FTIR) spectroscopy experiments and quantum chemical calculations. Equilibrium geometry, rotational parameters and vibrational properties predicted theoretically beyond the double-harmonic approximation are employed to assist the vibrational assignment of the experimental trace. Finally, FTIR spectra measured over a range of pressures are used to determine the HCFC-132b absorption cross section spectrum from 150 to 3000 cm-1, from which istantaneous and effective REs are derived and, in turn, used for GWP evaluation.

Radical Addition Reactions: Hierarchical Ab Initio Benchmark and DFT Performance Study

We performed a hierarchical ab initio benchmark study of the gas-phase radical addition reactions of X⋅+C2H2 and X⋅+C2H4 (X⋅ = CH3⋅, NH2⋅, OH⋅, SH⋅). The hierarchical series of ab initio methods (HF, MP2, CCSD, CCSD(T)) were paired with a hierarchal series of Dunning basis sets with and without diffuse functions ((aug)-cc-pVDZ, (aug)-cc-pVTZ, (aug)-cc-pVQZ). The HF ground-state wavefunctions were transformed into quasi-restricted orbital (QRO) reference wavefunctions to address spin contamination. Following extrapolation to the CBS limit, the energies from our highest- QRO-CCSD(T)/CBS+ level converged within 0.0-3.4 kcal mol-1 and 0.0-1.0 kcal mol-1 concerning the ab initio method and basis set, respectively. Our QRO-CCSD(T)/CBS+ reference data was used to evaluate the performance of 98 density functional theory (DFT) approximations. The MAE of the best functionals for reaction barriers and energies were: OLYP (1.9 kcal mol-1), BMK (1.0 kcal mol-1), M06-2X (0.9 kcal mol-1), MN12-SX (0.8 kcal mol-1) and CAM-B3LYP (0.8 kcal mol-1). These functionals also accurately reproduce key geometrical parameters of the stationary points within an average 2 % deviation from the reference QRO-CCSD(T)/cc-pVTZ level.

Assessing Computational Methods to Calculate the Binding Energies of Dimers of Five-Membered Heterocyclic Molecules

Computational electronic structure methods, including ab initio and density functional theory (DFT), have been assessed in calculating the binding energies of 14 five-membered heterocyclic dimers. The configurations were generated using classical molecular dynamics before optimization at the MP2/aug-cc-pVTZ. Benchmark binding energies are calculated at the CCSD(T)/CBS level of theory. Among the ab initio methods, the DLPNO-CCSD(T)/CBS method has the best performance, reproducing CCSD(T)/CBS with a mean absolute deviation (MAD) of 0.17 kcal/mol. In addition, a schematic CCSD(T)/CBS approach perfectly reproduces the canonical CCSD(T)/CBS with a mean absolute error of 0.08 kcal/mol. Regarding DFT functionals, it has been found that counterpoise corrections have negligible effects on the accuracy of the functionals. Furthermore, including the D3 empirical dispersion considerably enhances the accuracy of the DFT functionals. As a result, outstanding performance is noted for the double hybrid functional B2K-PLYP, with a mean absolute error of 0.25 kcal/mol. In addition to the B2K-PLYP double hybrid functional, M05-D3, B97D, M05-2X-D3, M05-2X, M06-HF, M08-HX, M11, TPSSh-D3, and RSX-0DH-D3(BJ) have MAD values lower than 0.5 kcal/mol. These functionals are recommended for further investigations of five-membered heterocyclic clusters.

Study of Sterically Crowded Alkanes: Assessment of Non-Empirical Density Functionals Including Double-Hybrid (Cost-Effective) Methods

We theoretically study here the homolytic dissociation reactions of sterically crowded alkanes of increasing size, carrying three different (bulky) substituents such as tert-butyl, adamantyl, and [1.1.1]propellanyl, employing a family of parameter-free functionals ranging from semi-local, to hybrid and double-hybrid models. The study is complemented with the interaction between a pair of HC(CH3)3 molecules at repulsive and attractive regions, as an example of a system composed by a pair of weakly bound sterically crowded alkanes. We also assessed the effect of incorporating reliable dispersion corrections (i. e., D4 or NL) for all the functionals assessed, as well as the use of a tailored basis set (DH-SVPD) for non-covalent interactions, which provides the best trade-off between accuracy and computational cost for a seemingly extended applications to branched or crowded systems. Overall, the PBE-QIDH/DH-SVPD and r2SCAN-QIDH/DH-SVPD methods represent an excellent compromise providing relatively low, and thus very competitive, errors at a fraction of the cost of other quantum-chemical methods in use.

A Benchmark Study of DFT-Computed p-Block Element Lewis Pair Formation Enthalpies Against Experimental Calorimetric Data

The quantification of Lewis acidity is of fundamental and applied importance in chemistry. While the computed fluoride ion affinity (FIA) is the most widely accepted thermodynamic metric, only sparse experimental values exist. Accordingly, a benchmark of methods for computing Lewis pair formation enthalpies, also with a broader set of Lewis bases against experimental data, is missing. Herein, we evaluate different density functionals against a set of 112 experimentally determined Lewis acid/base binding enthalpies and gauge influences such as solvation correction in structure optimization. From that, we can recommend r2SCAN-3c for robust quantification of this omnipresent interaction.

How accurate can Kohn-Sham density functional be for both main-group and transition metal reactions

Achieving chemical accuracy in describing reactions involving both main-group elements and transition metals poses a substantial challenge for density functional approximations (DFAs), primarily due to the significantly different behaviors for electrons moving in the s,p-orbitals or in the d,f-orbitals. MOR41, a representative dataset of transition metal chemistry, has highlighted the PWPB95-D3(BJ) functional, a B2PLYP-type doubly hybrid (bDH) approximation equipped with an empirical dispersion correction, as the leading functional thus far (Dohm et al., J Chem Theory Comput 2018;14: 2596-2608). However, this functional is not among the top bDH methods for main-group chemistry (Goerigk et al., Phys Chem Chem Phys. 2017;19: 32184). Conversely, bDH methods such as DSD-BLYP-D3, proficient in main-group chemistry, often falter for transition metal chemistry. Herein, taking advantage of the home-made Rust-based Electronic-Structure Toolkits, we examine a suite of XYG3-type doubly hybrid (xDH) methods. We confirm that the trade-off in descriptive accuracy between main-group and transition metal systems persists within the realm of perturbation theory (PT2)-based xDH methods. Notably, however, our study ushers in a pivotal advance with the recently proposed renormalized xDH method, R-xDH7-SCC15. This method not only distinguishes itself among the elite methods for main-group chemistry, but also achieves an unprecedented accuracy for the MOR41 dataset, outperforming all other reported DFAs. The efficacy of R-xDH7-SCC15 stems from the successful integration of a renormalized PT2 correlation model (rPT2) and a machine-learning strong-correlation correction (SCC15), marking a significant step forward in the realm of computational chemistry.

Accurate Structure and Spectroscopic Properties of Azulene and Its Derivatives by Means of Pisa Composite Schemes and Vibrational Perturbation Theory to Second Order

The structural and spectroscopic properties in the gas phase of azulene and some of its N-bearing derivatives have been analyzed by a general computational strategy based on the recent Pisa composite schemes (PCSs). First of all, an accurate semiexperimental equilibrium structure has been derived for azulene and employed to validate the geometrical parameters delivered by different quantum chemical methods. Next, different isomerization energies (azulene to naphthalene, 1-aza-azulene to quinoline and to other isomers) have been computed by an explicitly correlated PCS version employing frozen natural orbitals. Accurate geometries have been obtained by a cheaper PCS variant based on a double-hybrid functional improved by one-parameter bond corrections, with the same functional providing also remarkable harmonic frequencies. The corresponding equilibrium rotational constants show average deviations within 0.1% from experimental results when taking into account anharmonic vibrational corrections obtained by a global hybrid functional. Therefore, reliable computational estimates have been produced for the rotational constants of several nitrogen derivatives (isomeric aza-azulenes and guaiazulene), whose non-negligible dipole moments could allow experimental microwave characterizations. An analogous approach delivers infrared spectra in remarkable agreement with their experimental counterparts for naphthalene, quinoline, and azulene, together with reliable predictions for the still-unknown spectrum of 1-aza-azulene. In addition to their intrinsic interest, the results of this paper further confirm that a very accurate yet robust and user-friendly tool is now available for aiding high-resolution spectroscopic studies of quite large systems of current technological and/or biological interest.

Data Quality in the Fitting of Approximate Models: A Computational Chemistry Perspective

Empirical parametrization underpins many scientific methodologies including certain quantum-chemistry protocols [e.g., density functional theory (DFT), machine-learning (ML) models]. In some cases, the fitting requires a large amount of data, necessitating the use of data obtained using low-cost, and thus low-quality, means. Here we examine the effect of using low-quality data on the resulting method in the context of DFT methods. We use multiple G2/97 data sets of different qualities to fit the DFT-type methods. Encouragingly, this fitting can tolerate a relatively large proportion of low-quality fitting data, which may be attributed to the physical foundations of the DFT models and the use of a modest number of parameters. Further examination using "ML-quality" data shows that adding a large amount of low-quality data to a small number of high-quality ones may not offer tangible benefits. On the other hand, when the high-quality data is limited in scope, diversification by a modest amount of low-quality data improves the performance. Quantitatively, for parametrizing DFT (and perhaps also quantum-chemistry ML models), caution should be taken when more than 50% of the fitting set contains questionable data, and that the average error of the full set is more than 20 kJ mol-1. One may also follow the recently proposed transferability principles to ensure diversity in the fitting set.

Assessment of the applicability of DFT methods to [Cp*Rh]-catalyzed hydrogen evolution processes

The present computational study provides a benchmark of density functional theory (DFT) methods in describing hydrogen evolution processes catalyzed by [Cp*Rh]-containing organometallic complexes. A test set was composed of 26 elementary reactions featuring chemical transformations and bonding situations essential for the field, including the emerging concept of non-innocent Cp* behavior. Reference values were obtained from a highly accurate 3/4 complete basis set and 6/7 complete PNO space extrapolated DLPNO-CCSD(T) energies. The performance of lower-level extrapolation procedures was also assessed. We considered 84 density functionals (DF) (including 13 generalized gradient approximations (GGA), nine meta-GGAs, 33 hybrids, and 29 double-hybrids) and three composite methods (HF-3c, PBEh-3c, and r2SCAN-3c), combined with different types of dispersion corrections (D3(0), D3BJ, D4, and VV10). The most accurate approach is the PBE0-DH-D3BJ (MAD of 1.36 kcal mol-1) followed by TPSS0-D3BJ (MAD of 1.60 kcal mol-1). Low-cost r2SCAN-3c composite provides a less accurate but much faster alternative (MAD of 2.39 kcal mol-1). The widely used Minnesota-family M06-L, M06, and M06-2X DFs should be avoided (MADs of 3.70, 3.94, and 4.01 kcal mol-1, respectively).

Contrasting conformational behaviors of molecules XXXI and XXXII in the seventh blind test of crystal structure prediction

Accurate modeling of conformational energies is key to the crystal structure prediction of conformational polymorphs. Focusing on molecules XXXI and XXXII from the seventh blind test of crystal structure prediction, this study employs various electronic structure methods up to the level of domain-local pair natural orbital coupled cluster singles and doubles with perturbative triples [DLPNO-CCSD(T1)] to benchmark the conformational energies and to assess their impact on the crystal energy landscapes. Molecule XXXI proves to be a relatively straightforward case, with the conformational energies from generalized gradient approximation (GGA) functional B86bPBE-XDM changing only modestly when using more advanced density functionals such as PBE0-D4, ωB97M-V, and revDSD-PBEP86-D4, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D), or DLPNO-CCSD(T1). In contrast, the conformational energies of molecule XXXII prove difficult to determine reliably, and variations in the computed conformational energies appreciably impact the crystal energy landscape. Even high-level methods such as revDSD-PBEP86-D4 and SCS-MP2D exhibit significant disagreements with the DLPNO-CCSD(T1) benchmarks for molecule XXXII, highlighting the difficulty of predicting conformational energies for complex, drug-like molecules. The best-converged predicted crystal energy landscape obtained here for molecule XXXII disagrees significantly with what has been inferred about the solid-form landscape experimentally. The identified limitations of the calculations are probably insufficient to account for the discrepancies between theory and experiment on molecule XXXII, and further investigation of the experimental solid-form landscape would be valuable. Finally, assessment of several semi-empirical methods finds r2SCAN-3c to be the most promising, with conformational energy accuracy intermediate between the GGA and hybrid functionals and a low computational cost.

An Acceptor-Substituted N-Heterocyclic ortho-Quinodimethane: Pushing the Boundaries of Polarization in Donor-Acceptor-Substituted Polyenes

We report the synthesis, isolation, and characterization of a stable donor-acceptor substituted ortho-quinodimethane (oQDM). This system with an imidazolidine scaffold as the donor can also be referred to as acceptor-substituted ortho-N-heterocyclic quinodimethane (oNHQ). We have examined the extent of polarization of the conjugated π-system using single-crystal X-ray diffraction, NMR and UV/vis spectroscopy, cyclic voltammetry, and DFT computations. The bond lengths in the phenyl linker do not exhibit the alternation typical of oQDMs. In addition, the 13C and 15N NMR shifts suggest significant charge separation, an interpretation supported by the diatropic ring current determined by NICSZZ(r) computations, which is characteristic of aromatic compounds. DFT calculations show that polarization is an electronic effect that is amplified by steric influences. More strikingly, the oxidation and reduction potentials of the push-pull substituted oQDM are virtually identical to those of authenticated anionic and cationic derivatives. The results therefore indicate that an aromatic zwitterionic structure represents the electronic structure more accurately than a neutral quinoidal Lewis structure, which indicates that the acceptor-substituted oNHQ is a rare example of an organic zwitterion in which the centers of charge are in conjugation. The ambiphilic reactivity of the acceptor-substituted oNHQ, which is evidenced by the dehydrogenation of ammonia borane and the addition of phenylacetylene via heterolytic C-H bond cleavage, further supports its notation as an organic zwitterion and is reminiscent of frustrated Lewis pairs (FLPs). Thus, the acceptor-substituted oNHQ can be considered to be an intramolecular carbogenic FLP in terms of its reactivity.

Ab initio conformational analysis of α/β-D-xylopyranose at pyrolysis conditions

Xylopyranose is the principal monosaccharide unit of hemicellulose, one of the three major biopolymers of lignocellulosic biomass. Understanding its decomposition mechanism is increasingly relevant for thermochemical biorefinery research such as pyrolysis. Significant efforts have been made to study its chemical and structural properties using both computational and experimental methods. However, due to its high structural flexibility and numerous hydroxyl groups, various metastable conformers arise. In this work, we performed a computational exploration of the conformational space of both anomeric forms, α and β, of D-xylopyranose using the semi-empirical GFN2-xTB method in conjunction with metadynamics and density functional theory simulations for structural optimization and vibrational analysis. Xylopyranose conformers free energy and enthalpy variations are analyzed across temperatures typical of fast biomass pyrolysis (298-1068 K), with the Boltzmann population distribution of the most populated conformers determined. This study provides a detailed computational analysis of the conformational space and thermochemistry of xylopyranose. Additionally, 44 and 59 conformers of the α and β anomers were found, for both of which a selection of 10 conformers based on Boltzmann population distribution analysis is performed to reduce the conformational space for ab initio studies of the pyrolysis reaction kinetics.

Calculated ionization energies, orbital eigenvalues (HOMO), and related QSAR descriptors of organic molecules: a set of 61 experimental values enables elimination of systematic errors and provides realistic error estimates

Ionization energies (IEs) of organic compounds come in different forms-adiabatic, vertical, as electrode potentials, or as orbital eigenvalues via Koopmans' theorem. They have been linked to the reactivity towards electrophiles and have been used to quantitatively describe electron transfer processes. The de novo prediction of IEs is only meaningful when an estimate of the prediction's uncertainty is included. Pulsed-field ionization (PFI) experiments have quantified adiabatic IEs with unprecedented precision. In this work, a new set of PFI-derived IEs is compiled from the literature as a benchmark for prediction methods. This set includes many common functional groups, a size range from diatomics to two aromatic rings, and IEs between 7 and 14 eV. The first-principles CCSD(T)/CBS protocol presently used reproduces these values within 0.05 eV. For adiabatic IEs and vertical IEs/orbital eigenvalues predicted using approximate density functional theory (DFT), linear regression models are proposed, so that IEs calculated using different methods can be directly compared on a physical scale. This elimination of systematic errors improves the error statistics and allows the performance of predicted IEs to be evaluated if used in quantitative structure-property or -activity relationships, as the latter implicitly correct a descriptor's bias. Owing to the structural scope of the test set, the minimum and maximum deviations from experiment should correspond to those expected for common organic molecules. Deviations from reference values found for orbital eigenvalues but also for IEs calculated explicitly with HF or semi-empirical MO methods were as large as 0.5 eV to 2.0 eV. Such large errors could also propagate into quantitative structure-property models, as shown in illustrative examples of oxidation rate constants in solution.

Reduced Cost Computation and Exploitation of Accurate Radial Interaction Potentials for Barrier-Less Processes

Barrier-less steps are typical of radical and ionic reactions in the gas-phase, which often take place in extreme environments such as the combustion reactors operating at very high temperatures or the interstellar medium, characterized by ultralow temperatures and pressures. The difficulty of experimental studies in conditions mimicking these environments suggests that computational approaches can provide a valuable support. In this connection, the most advanced treatments of these processes in the framework of transition state theory are able to deliver accurate kinetic parameters provided that the underlying potential energy surface is sufficiently accurate. Since this requires a balanced treatment of static and dynamic correlation (which play different roles in different regions), very sophisticated and expensive quantum chemical approaches are required. One effective solution of this problem is offered by the computation of accurate one-dimensional radial potentials, which are then used to correct the results of a Monte Carlo sampling performed by cheaper quantum chemical approaches. In this paper, we will show that, for a large panel of different barrier-less reaction steps, the radial potential is ruled by the R-4 term and that addition of a further R-6 contribution provides quantitative agreement with the reference points. The consequences of this outcome are not trivial, since the reference potential can be fitted by a very limited number of points possibly with a nonlinear spacing. In the case of reaction steps ruled by long-range transition states, generalized expressions are also given for computing reaction rates in the framework of the phase-space theory. All these improvements pave the way toward the computation of reaction rates for barrier-less reactions involving large molecules.

Carbamic acid and its dimer: A computational study

A recent work by Marks et al. on the formation of carbamic acid in NH  3 -CO  2 interstellar ices pointed out its stability in the gas phase and the concomitant production of its dimer. Prompted by these results and the lack of information on these species, we have performed an accurate structural, energetic and spectroscopic investigation of carbamic acid and its dimer. For the former, the structural and spectroscopic characterization employed composite schemes based on coupled cluster (CC) calculations that account for the extrapolation to the complete basis set limit and core correlation effects. A first important outcome is the definitive confirmation of the nonplanarity of carbamic acid, then followed by an accurate estimate of its rotational and vibrational spectroscopy parameters. As far as the carbamic acid dimer is concerned, the investigation started from the identification of its most stable forms. For them, structure and vibrational properties have been evaluated using density functional theory, while a composite scheme rooted in CC theory has been employed for the energetic characterization. Our results allowed us to provide a better interpretation of the feature observed in the recent experiment mentioned above.

Describing the Disulfide Bond: From the Density Functional Theory and Back through the "Lego Brick" Approach

Selected molecular species containing the disulfide bond, RSSR, have been considered, these ranging from hydrogen disulfide, H2S2 (R = H), to diphenyl disulfide with R = C6H5. The aim of this work is two-fold: (i) to investigate different computational approaches in order to derive accurate equilibrium structures at an affordable cost, (ii) to employ the results from the first goal in order to benchmark cheaper methodologies rooted in the density functional theory. Among the strategies used for the accurate geometrical determinations, the semiexperimental approach has been exploited in combination with a reduced-dimensionality VPT2 model, without however obtaining satisfactory results. Instead, the so-called "Lego brick" approach turned out to be very effective despite the flexibility of the systems investigated. Concerning the second target of this work, the focus was mainly on the S-S bond and the structural parameters related to it. Among those tested, PBE0(-D3BJ), M06-2X(-D3) and DSD-PBEP86-D3BJ have been found to be the best-performing functionals.

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.

Reconciling Accuracy and Feasibility for Barrierless Reaction Steps by the PCS/DDCI/MC-PDFT Protocol: Methane and Ethylene Dissociations as Case Studies

Several enhancements have been introduced into state-of-the-art computational protocols for the treatment of barrierless reaction steps in the framework of variable reaction coordinate variational transition state theory. The first step is the synergistic integration of the Iterative Difference Dedicated Configuration Interaction (I-DDCI) and Pisa Composite Scheme, which defines a reduced cost, yet very accurate, computational workflow. This approach provides a near black box tool for obtaining 1D reference potentials. Then, a general strategy has been devised for tuning the level of theory used in Monte Carlo (MC) sampling, employing Multiconfiguration Pair Density Functional Theory (MC-PDFT) with dynamically adjusted Hartree-Fock exchange. Concurrently, partial geometry optimizations during the MC simulations account for the coupling between the reaction coordinates and conserved modes. The protocol closely approaches full size consistency and yields highly accurate results, with several test computations suggesting rapid convergence of the I-DDCI correction with the basis set dimensions. The capabilities of the new platform are illustrated by two case studies (the hydrogen dissociation from CH4 and C2H4), which highlight its flexibility in handling different carbon hybridizations (sp3 and sp2). The remarkable accuracy of the computed rate constants confirms the robustness of the proposed method. Together with their intrinsic interest, these results pave the way for systematic investigations of complex gas-phase reactions through a reliable, user-friendly tool accessible to specialists and nonspecialists alike.

Enzyme Tunnel Dynamics and Catalytic Mechanism of Norcoclaurine Synthase: Insights from a Combined LiGaMD and DFT Study

This study conducts a systematic investigation into the catalytic mechanism of norcoclaurine synthase (NCS), a key enzyme in the biosynthesis of tetrahydroisoquinolines (THIQs) with therapeutic applications. By integration of LiGaMD and DFT calculations, the reaction pathway of NCS is mapped, providing detailed insights into its catalytic activity and selectivity. Our findings underscore the critical role of E103 in substrate capture and reveal the hitherto unappreciated influence of nonpolar residues M183 and L76 on tunnel dynamics. A prominent discovery is the identification of a high-energy barrier (44.2 kcal/mol) associated with the aromatic electrophilic attack, which pinpoints the rate-limiting step. Moreover, we disclose the existence of dual transition states leading to different products with the energetically favored six-membered ring formation consistent with experimental evidence. These mechanistic revelations not only refine our understanding of NCS but also advocate for a renewed emphasis on enzyme tunnel engineering for optimizing THIQs biosynthesis. The research sets the stage for translating these findings into practical enzyme modifications. Our results highlight the potential of NCS as a biocatalyst to overcome the limitations of current synthetic methodologies, such as low yields and environmental impacts, and provide a theoretical contribution to the efficient, eco-friendly production of THIQs-based pharmaceuticals.

Structural and Electronic Evolution of Ethanolamine upon Microhydration: Insights from Hyperfine Resolved Rotational Spectroscopy

Ethanolamine hydrates containing from one to seven water molecules were identified via rotational spectroscopy with the aid of accurate quantum chemical methods considering anharmonic vibrational corrections. Ethanolamine undergoes significant conformational changes upon hydration to form energetically favorable hydrogen bond networks. The final structures strongly resemble the pure (H2O)3-9 complexes reported before when replacing two water molecules by ethanolamine. The 14N nuclear quadrupole coupling constants of all the ethanolamine hydrates have been determined and show a remarkable correlation with the strength of hydrogen bonds involving the amino group. After addition of the seventh water molecule, both hydrogen atoms of the amino group actively contribute to hydrogen bond formation, reinforcing the network and introducing approximately 21-27 % ionicity towards the formation of protonated amine. These findings highlight the critical role of microhydration in altering the electronic environment of ethanolamine, enhancing our understanding of amine hydration dynamics.

A semi-automated quantum-mechanical workflow for the generation of molecular monolayers and aggregates

Organic electronics (OE) such as organic light-emitting diodes or organic solar cells represent an important and innovative research area to achieve global goals like environmentally friendly energy production. To accelerate OE material discovery, various computational methods are employed. For the initial generation of structures, a molecular cluster approach is employed. Here, we present a semi-automated workflow for the generation of monolayers and aggregates using the GFNn-xTB methods and composite density functional theory (DFT-3c). Furthermore, we present the novel D11A8MERO dye interaction energy benchmark with high-level coupled cluster reference interaction energies for the assessment of efficient quantum chemical and force-field methods. GFN2-xTB performs similar to low-cost DFT, reaching DFT/mGGA accuracy at two orders of magnitude lower computational cost. As an example application, we investigate the influence of the dye aggregate size on the optical and electrical properties and show that at least four molecules in a cluster model are needed for a qualitatively reasonable description.

Predicting pKa Values of Para-Substituted Aniline Radical Cations vs. Stable Anilinium Ions in Aqueous Media

The focus of pKa calculations has primarily been on stable molecules, with limited studies comparing radical cations and stable cations. In this study, we comprehensively investigate models with implicit solvent and explicit water molecules, direct and indirect calculation approaches, as well as methods for calculating free energy, solvation energy, and quasi-harmonic oscillator approximation for para-substituted aniline radical cations (R-PhNH2•+) and anilinium cations (R-PhNH3+) in the aqueous phase. Properly including and positioning explicit H2O molecules in the models is important for reliable pKa predictions. For R-PhNH2•+, precise pKa values were obtained using models with one or two explicit H2O molecules, resulting in a root mean square error (RMSE) of 0.563 and 0.384, respectively, for both the CBS-QB3 and M062X(D3)/ma-def2QZVP methods. Further improvement was achieved by adding H2O near oxygen-containing substituents, leading to the lowest RMSE of 0.310. Predicting pKa values for R-PhNH3+ was more challenging. CBS-QB3 provided an RMSE of 0.349 and the M062X(D3)/ma-def2QZVP method failed to calculate pKa accurately (RMSE > 1). However, by adopting the double-hybrid functional method and adding H2O near the R substituent group, the calculations were significantly improved with an average absolute difference (ΔpKa) of 0.357 between the calculated and experimental pKa values. Our study offers efficient and reliable methods for pKa calculations of R-PhNH2•+ (especially) and R-PhNH3+ based on currently mature quantum chemistry software.

Synergistic Integration of Physical Embedding and Machine Learning Enabling Precise and Reliable Force Field

Machine-learning force fields have achieved significant strides in accurately reproducing the potential energy surface with quantum chemical accuracy. However, this approach still faces several challenges, e.g., extrapolating to uncharted chemical spaces, interpreting long-range electrostatics, and mapping complex macroscopic properties. To address these issues, we advocate for a synergistic integration of physical principles and machine learning techniques within the framework of a physically informed neural network (PINN). This approach involves incorporating physical knowledge into the parameters of the neural network, coupled with an efficient global optimizer, the Tabu-Adam algorithm, proposed in this work to augment optimization under strict physical constraint. We choose the AMOEBA+ force field as the physics-based model for embedding and then train and test it using the diethylene glycol dimethyl ether (DEGDME) data set as a case study. The results reveal a breakthrough in constructing a precise and noise-robust machine learning force field. Utilizing two training sets with hundreds of samples, our model exhibits remarkable generalization and density functional theory (DFT) accuracy in describing molecular interactions and enables a precise prediction of the macroscopic properties such as the diffusion coefficient with minimal cost. This work provides valuable insight into establishing a fundamental framework of the PINN force field.

Aromatic Residues in Proteins: Re-Evaluating the Geometry and Energetics of π-π, Cation-π, and CH-π Interactions

Aromatic residues can participate in various biomolecular interactions, such as π-π, cation-π, and CH-π interactions, which are essential for protein structure and function. Here, we re-evaluate the geometry and energetics of these interactions using quantum mechanical (QM) calculations, focusing on pairwise interactions involving the aromatic amino acids Phe, Tyr, and Trp and the cationic amino acids Arg and Lys. Our findings reveal that π-π interactions, while energetically favorable, are less abundant in structured proteins than commonly assumed and are often overshadowed by previously underappreciated, yet prevalent, CH-π interactions. Cation-π interactions, particularly those involving Arg, show strong binding energies and a specific geometric preference toward stacked conformations, despite the global QM minimum, suggesting that a rather perpendicular T-shape conformation should be more favorable. Our results support a more nuanced understanding of protein stabilization via interactions involving aromatic residues. On the one hand, our results challenge the traditional emphasis on π-π interactions in structured proteins by showing that CH-π and cation-π interactions contribute significantly to their structure. On the other hand, π-π interactions appear to be key stabilizers in solvated regions and thus may be particularly important to the stabilization of intrinsically disordered proteins.

Water-carbon disulfide dimers: observation of a new isomer and ab initio structure theory

The weakly bound dimer water-carbon disulfide is studied by ab initio structure theory and high-resolution infrared spectroscopy. The calculations yield three stable minima in the potential energy surface, all planar. The most stable, isomer 1, was observed previously by microwave spectroscopy. It has C2v symmetry, an S-O bond, and a linear O-S-C-S backbone. Isomer 2, the next most stable, has not been considered previously by theory or experiment. It also has C2v symmetry, but with a side-by-side structure. Isomer 3, which is slightly less stable, is side-by-side with one O-H bond pointing toward an S atom. The first gas phase water-CS2 infrared spectra are reported. For isomer 1, H2O-, HDO-, and D2O-CS2 are observed in the CS2ν1 + ν3 region, H2O-CS2 in the H2O ν2 bend region, and D2O-CS2 in the D2O ν1 and ν3 stretch regions. The latter ν3 spectrum enables an experimental determination of the A rotational parameter, which turns out to be larger than expected. The new isomer 2 is observed by means of a band in the H2O ν2 region, confirming its C2v symmetry and calculated structure.

Toward Reliable Conformational Energies of Amino Acids and Dipeptides─The DipCONFS Benchmark and DipCONL Datasets

Simulating peptides and proteins is becoming increasingly important, leading to a growing need for efficient computational methods. These are typically semiempirical quantum mechanical (SQM) methods, force fields (FFs), or machine-learned interatomic potentials (MLIPs), all of which require a large amount of accurate data for robust training and evaluation. To assess potential reference methods and complement the available data, we introduce two sets, DipCONFL and DipCONFS, which cover large parts of the conformational space of 17 amino acids and their 289 possible dipeptides in aqueous solution. The conformers were selected from the exhaustive PeptideCS dataset by Andris et al. [ J. Phys. Chem. B 2022, 126, 5949-5958]. The structures, originally generated with GFN2-xTB, were reoptimized using the accurate r2SCAN-3c density functional theory (DFT) composite method including the implicit CPCM water solvation model. The DipCONFS benchmark set contains 918 conformers and is one of the largest sets with highly accurate coupled cluster conformational energies so far. It is employed to evaluate various DFT and wave function theory (WFT) methods, especially regarding whether they are accurate enough to be used as reliable reference methods for larger datasets intended for training and testing more approximated SQM, FF, and MLIP methods. The results reveal that the originally provided BP86-D3(BJ)/DGauss-DZVP conformational energies are not sufficiently accurate. Among the DFT methods tested as an alternative reference level, the revDSD-PBEP86-D4 double hybrid performs best with a mean absolute error (MAD) of 0.2 kcal mol-1 compared with the PNO-LCCSD(T)-F12b reference. The very efficient r2SCAN-3c composite method also shows excellent results, with an MAD of 0.3 kcal mol-1, similar to the best-tested hybrid ωB97M-D4. With these findings, we compiled the large DipCONFL set, which includes over 29,000 realistic conformers in solution with reasonably accurate r2SCAN-3c reference conformational energies, gradients, and further properties potentially relevant for training MLIP methods. This set, also in comparison to DipCONFS, is used to assess the performance of various SQM, FF, and MLIP methods robustly and can complement training sets for those.

Toward the identification of cyano-astroCOMs via vibrational features: benzonitrile as a test case

The James Webb Space Telescope (JWST) opened a new era for the identification of molecular systems in the interstellar medium (ISM) by vibrational features. One group of molecules of increasing interest is cyano-derivatives of aromatic organic molecules, which have already been identified in the ISM on the basis of the analysis of rotational signatures, and so, are plausible candidates for the detection by the JWST. Benzonitrile considered in this work represents a suitable example for the validation of a computational strategy, which can be further applied for different, larger, and not-yet observed molecules. For this purpose, anharmonic simulations of infrared (IR) spectra have been compared with recent FTIR experimental studies. The anharmonic computations using the generalized second-order vibrational perturbation theory (GVPT2) in conjunction with a hybrid force field combining the harmonic part of revDSD-PBEP86-D3/jun-cc-pVTZ with anharmonic corrections from B3LYP-D3/SNSD show very good agreement with those in the experiment, with a mean error of 11 c m - 1 for all fundamental transitions overall and only 2 c m - 1 for the C ≡ N stretching fundamental at 4.49 μ m . The inclusion of overtones up to three-quanta transitions also allowed the prediction of spectra in the near-infrared region, which shows distinct features due to C ≡ N overtones at the 2.26 μ m and 1.52 μ m . The remarkable accuracy of the GVPT2 results opens a pathway for the reliable prediction of spectra for a broader range of cyano-astroCOMs.

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.