A general intermolecular force field based on tight-binding quantum chemical calculations

Software Infrastructure for Next-Generation QM/MM-ΔMLP Force Fields

We present software infrastructure for the design and testing of new quantum mechanical/molecular mechanical and machine-learning potential (QM/MM-ΔMLP) force fields for a wide range of applications. The software integrates Amber's molecular dynamics simulation capabilities with fast, approximate quantum models in the xtb package and machine-learning potential corrections in DeePMD-kit. The xtb package implements the recently developed density-functional tight-binding QM models with multipolar electrostatics and density-dependent dispersion (GFN2-xTB), and the interface with Amber enables their use in periodic boundary QM/MM simulations with linear-scaling QM/MM particle-mesh Ewald electrostatics. The accuracy of the semiempirical models is enhanced by including machine-learning correction potentials (ΔMLPs) enabled through an interface with the DeePMD-kit software. The goal of this paper is to present and validate the implementation of this software infrastructure in molecular dynamics and free energy simulations. The utility of the new infrastructure is demonstrated in proof-of-concept example applications. The software elements presented here are open source and freely available. Their interface provides a powerful enabling technology for the design of new QM/MM-ΔMLP models for studying a wide range of problems, including biomolecular reactivity and protein-ligand binding.

Biomimetic nanoplatforms constructed from dialkylaminostyryl hetarene dyes and phospholipids exhibiting selective fluorescent response to specific proteins

The present work explores the specificity of supramolecular assemblies comprising dialkylaminostyrylhetarene dye molecules incorporated into phosphatidylcholine (PC) or phosphatidylserine (PS) aggregates. In PS-based assemblies, the dyes demonstrate a concentration-dependent fluorescent response, distinguishing anionic proteins such as bovine serum albumin (BSA) and pepsin from lysozyme (LYZ) in aqueous solutions. Conversely, no significant response is observed when the dyes are incorporated into the well-organized bilayers of neutral PC. The fluorescent response arises from the binding of dyes to proteins, leading to the detachment of dye molecules from the assemblies, rather than from the binding of proteins to the assemblies, although the latter process is facilitated by electrostatic attraction. Thus, both the poor ordering of PS molecules and the interfacial arrangement of the dyes are prerequisites for the fluorescent response of dye-PS aggregates. The structure of the dyes significantly impacts the spectral features of dye-PS and dye-protein assemblies. An optimal dye structure has been identified for the recognition of BSA, with a limit of detection (LOD) of 10.8 nM.

Amber free energy tools: Interoperable software for free energy simulations using generalized quantum mechanical/molecular mechanical and machine learning potentials

We report the development and testing of new integrated cyberinfrastructure for performing free energy simulations with generalized hybrid quantum mechanical/molecular mechanical (QM/MM) and machine learning potentials (MLPs) in Amber. The Sander molecular dynamics program has been extended to leverage fast, density-functional tight-binding models implemented in the DFTB+ and xTB packages, and an interface to the DeePMD-kit software enables the use of MLPs. The software is integrated through application program interfaces that circumvent the need to perform "system calls" and enable the incorporation of long-range Ewald electrostatics into the external software's self-consistent field procedure. The infrastructure provides access to QM/MM models that may serve as the foundation for QM/MM-ΔMLP potentials, which supplement the semiempirical QM/MM model with a MLP correction trained to reproduce ab initio QM/MM energies and forces. Efficient optimization of minimum free energy pathways is enabled through a new surface-accelerated finite-temperature string method implemented in the FE-ToolKit package. Furthermore, we interfaced Sander with the i-PI software by implementing the socket communication protocol used in the i-PI client-server model. The new interface with i-PI allows for the treatment of nuclear quantum effects with semiempirical QM/MM-ΔMLP models. The modular interoperable software is demonstrated on proton transfer reactions in guanine-thymine mispairs in a B-form deoxyribonucleic acid helix. The current work represents a considerable advance in the development of modular software for performing free energy simulations of chemical reactions that are important in a wide range of applications.

Application of a modern theoretical approach to the study of the interaction of KR-12 peptides derived from human cathelicidins with Cu(II) ions

The human cationic antimicrobial protein (hCAP) corresponding to the overlapping sequences of 151-162 of hCAP named KR-12 peptide is the smallest portion of the only type of human Cathelicidin, which has been shown to be modifiable into a more effective antimicrobial. In this study, an in silico analysis, supported by potentiometric titration and isothermal titration calorimetry techniques, was performed to identify potential Cu(II) binding sites of KR-12. The analysis of the presented data at the given theoretical level (GFN2-xTB/ALPB) revealed which peptide chain fragments are involved in the most favourable KR-12-Cu(II) binding mode. Based on a quantum chemical approach, the most favourable coordination modes of Cu(II) to peptides are proposed together with the discussion of the chemical nature of the interactions. The presented results demonstrated that KR-12 interacts with metal ions mostly via the main chain's oxygen atoms; however, the two types of amino acids that are expected to be vital for the interaction of Cu(II) are D (aspartic acid) and R29 (arginine). It was demonstrated that in order to explain the complexity of the interaction process in peptide-metal ion systems, the use of theoretical methods is sometimes necessary to explain the details of the experimental results and provide an in-depth understanding of these dynamic systems.

Structural flexibility of favipiravir and its structural analogues in solutions: experimental and computational insight

Combined UV-vis and quantum chemical studies of the structural flexibility and tautomerism of 6-R-3-hydroxy-2-pyrazine carboxamides in solutions revealed that their keto-enol transformations are accompanied by the deprotonation of enol tautomers and the formation of the corresponding anionic species. Both the solvent and the 6-R substituent strongly influence the relative abundance of the above forms in solutions. Anions are not formed in 1,2-dichloroethane (DCE), but the probability of deprotonation in neutral water and N,N-dimethylformamide (DMF) increases in the order R = H < F < NO2. Only enol tautomers of all solutes are found in DCE. DMF stabilizes keto forms only moderately and assists much strongly in the deprotonation of all three compounds. Water tends to stabilize both keto tautomers and deprotonated anions: the keto form dominates in the case of R = H (antiviral drug T-1105), the anions are found exclusively for R = NO2, and the aqueous solution of another antiviral drug, favipiravir (R = F), contains both the keto tautomer and the anionic form. The results of quantum chemical free energy calculations are in agreement with the experimental observations.

CREST-A program for the exploration of low-energy molecular chemical space

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Computationally assisted vibrational spectroscopy of nucleic acid bases. 2. Thymine

As in the case of cytosine [Phys. Chem. Chem. Phys. 2023, 25, 24121-24128], Raman and infrared (IR) spectra of aqueous thymine and its N-deuterated derivative, thymine-d2 have been computationally reproduced and interpreted with the use of the recently developed efficient protocol to explicit quantum mechanical modeling of structure and IR spectra of liquids and solutions [J. Phys. Chem. B, 2020, 124, 6664-6670]. A cluster model of a solute surrounded by 30 water molecules is shown to be sufficient to reproduce experimental vibrational frequencies and relative Raman intensities with the use of B3LYP-D3/def2-TZVP or B3LYP-D3/aug-cc-pVDZ simulations. Analogous PBE-D3 computations provided a less good, but still reasonably accurate, modeling of Raman spectra. It is shown that strong changes of frequencies and relative intensities of the Raman bands of thymine, caused by its hydration, can be interpreted mainly as a result of hydrogen bonding with 6 nearest water molecules. Non-negligible improvement of the quality of simulations for larger clusters comprising water molecules that do not have direct contacts with the solute, suggests that spectroscopic effects of hydration should be ascribed to the joined action of solute-solvent and solvent-solvent interactions. Nevertheless, the moderate number of water molecules required for successful simulations of the Raman spectra of aqueous thymine, suggests that the vibrational modes and derivatives of the polarizability of the solute are mainly locally influenced, while the effect of bulk water is rather modest.

Exploration of the Conformational Scenario for α-, β-, and γ-Cyclodextrins in Dry and Wet Conditions, from Monomers to Crystal Structures: A Quantum-Mechanical Study

Cyclodextrins (CDs) constitute a class of cyclic oligosaccharides that are well recognized and largely applied in the drug delivery field, thanks to their biocompatibility, low cost, and the possibility to be derivatized in order to tune and optimize the complexation/release of the specific drug. The conformational flexibility of these systems is one of their key properties and requires a cost-effective methodology to be studied by combining the accuracy of results with the possibility of exploring a large set of conformations. In the present paper, we have explored the conformational potential energy surface of the monomers and dimers of α-, β-, and γ-cyclodextrins (i.e., 6, 7, and 8 monomeric units, respectively) by means of fast but accurate semiempirical methods, which are then refined by state-of-the-art DFT functionals. Moreover, the crystal structure is considered for a more suitable comparison with the IR spectrum experimentally recorded. Calculations are carried out in the gas phase and in water environments, applying both implicit and explicit treatments. We show that the conformation of the studied molecules changes from the gas phase to the water, even if treated implicitly, thus modifying their complexation capability.

Computational analysis of the vibrational spectra and structure of aqueous cytosine

The recently developed efficient protocol for the explicit quantum mechanical modeling of the structure and IR spectra of liquids and solutions [Katsyuba et al., J. Phys. Chem. B, 2020, 124, 6664-6670] is used to describe aqueous solutions of cytosine. The same cluster model of a solute surrounded by the first solvation shell of solvent molecules was shown to be sufficient to reproduce experimental vibrational frequencies and relative IR and Raman intensities. An equally good quality of Raman spectra was provided by B3LYP-D3/def2-TZVP and B3LYP-D3/aug-cc-pVDZ simulations. Computations using the PBE functional were sufficient for modeling of the IR spectra but failed in the simulations of Raman scattering. It is shown that strong changes of frequencies and relative intensities of Raman and IR bands of cytosine, caused by its hydration, cannot be completely assigned to the influence of hydrogen bonds (HBs) with 7 or 8 closest water molecules. They are rather ascribed to the combined effect of solute-solute and solute-solvent HBs with the participation of at least 30 water molecules separating cytosine from the bulk solvent. This suggests that the vibrational modes and derivatives of the polarizability and dipole moment of the solute are mainly locally influenced by its first hydration shell, while the influence of bulk water is rather modest.

Möbius carbon nanobelts interacting with heavy metal nanoclusters

CONTEXT

The interaction between carbon nanostructures and heavy metal clusters is of great interest due to their potential applications as sensors and filters to remove the former from environment. In this work, we investigated the interaction between two types of carbon nanobelts (Möbius-type nanobelt and simple nanobelt) and nickel, cadmium, and lead nanoclusters. Our aim was to determine how both systems interact which would shed light on the potential applications of the carbon nanostructures as pollutant removal and detecting devices.

METHODS

To investigate the interaction between carbon nanostructures and heavy metal nanoclusters, we utilized the semiempirical tight binding framework provided by xTB software with the GFN2-xTB Hamiltonian. We performed calculations to determine the best interaction site, lowest energy geometries, complexes stability (using molecular dynamics at 298K), binding energy, and electronic properties. We also carried out a topological study to investigate the nature and intensity of the bonds formed between the metal nanoclusters and the nanobelts. Our results demonstrate that heavy metal nanoclusters have a favorable binding affinity towards both nanobelts, with the Möbius-type nanobelt having a stronger interaction. Additionally, our calculations reveal that the nickel nanocluster has the lowest binding energy, displaying the greatest charge transfer with the nanobelts, which was nearly twice that of the cadmium and lead nanoclusters. Our combined results lead to the conclusion that the nickel nanoclusters are chemisorbed, whereas cadmium and lead nanoclusters are physisorbed in both nanobelts. These findings have significant implications for the development of sensor and filtering devices based on carbon and heavy metal nanoclusters.

Revisiting Homochiral versus Heterochiral Interactions through a Long Detective Story of a Useful Azobis-Nitrile and Puzzling Racemate

This paper documents and reinvestigates the solid-state and crystal structures of 4,4'-azobis-4-cyanopentanoic acid (ACPA), a water-soluble azobis-nitrile of immense utility as a radical initiator in living polymerizations and a labile mechanophore that can be embedded within long polymer chains to undergo selective scission under mechanical activation. Surprisingly, for such applications, both the commercially available reagent and their derivatives are used as "single initiators" when this azonitrile is actually a mixture of stereoisomers. Although the racemate and meso compounds were identified more than half a century ago and their enantiomers were separated by classical resolution, there have been confusing narratives dealing with their characterization, the existence of a conglomeratic phase, and fractional crystallization. Our results report on the X-ray crystal structures of all stereoisomers for the first time, along with further details on enantiodiscrimination and the always intriguing arguments accounting for the stability of homochiral versus heterochiral crystal aggregates. To this end, metadynamic (MTD) simulations on stereoisomer molecular aggregates were performed to capture the incipient nucleation events at the picosecond time scale. This analysis sheds light on the driving homochiral aggregation of ACPA enantiomers.

Simulating a flexible water model as rigid: Best practices and lessons learned

Two ways to create rigid versions of flexible models are explored. The rigid model can assume the Model's Geometry (MG) as if the molecule is not interacting with any other molecules or the ensemble averaged geometry (EG) under a particular thermodynamic condition. Although the MG model is more straightforward to create, it leads to relatively poor performance. The EG model behaves similarly to the corresponding flexible model (the FL model) and, in some cases, agrees even better with experiments. While the difference between the EG and the FL models is mostly a result of flexibility, the MG and EG models have different dipole moments as a result of an effective induction in the condensed phase. For the three water models studied, the property that shows the most difference is the temperature dependence of density. The MG version of the water model by adaptive force matching for ice and liquid does not possess a temperature of maximum density, which is attributed to a downshift of the putative liquid-liquid phase transition line, leading to the hypothesized second critical point of liquid water to manifest at negative pressure. A new three-phase coexistence method for determining the melting temperature of ice is also presented.

Supramolecular Optimization of Sensory Function of a Hemicurcuminoid through Its Incorporation into Phospholipid and Polymeric Polydiacetylenic Vesicles: Experimental and Computational Insight

This work presents the synthesis of a new representative of hemicurcuminoids with a nonyloxy substituent (HCur) as a fluorescent amphiphilic structural element of vesicular aggregates based on phosphatidylcholine (PC), phosphatidylserine (PS), and 10,12-pentacosadiynoic acid (PCDA). Both X-ray diffraction analysis of the single crystal and ¹H NMR spectra of HCur in organic solvents indicate the predominance of the enol-tautomer of HCur. DFT calculations show the predominance of the enol tautomer HCur in supramolecular assemblies with PC, PS, and PCDA molecules. The results of the molecular modeling show that HCur molecules are surrounded by PC and PS with a rather weak exposure to water molecules, while an exposure of HCur molecules to water is enhanced under its supramolecular assembly with PCDA molecules. This is in good agreement with the higher loading of HCur into PC(PS) vesicles compared to PCDA vesicles converted into polydiacetylene (PDA) ones by photopolymerization. HCur molecules incorporated into HCur-PDA vesicles exhibit greater planarity distortion and hydration effect in comparison with HCur-PC(PS) ones. HCur-PDA is presented as a dual fluorescence-chromatic nanosensor responsive to a change in pH within 7.5-9.5, heavy metal ions and polylysine, and the concentration-dependent fluorescent response is more sensitive than the chromatic one. Thus, the fluorescent response of HCur-PDA allows for the distinguishing between Cd²⁺ and Pb²⁺ ions in the concentration range 0-0.01 mM, while the chromatic response allows for the selective sensing of Pb²⁺ over Cd²⁺ ions at their concentrations above 0.03 mM.

Automated and Efficient Generation of General Molecular Aggregate Structures

Modeling intermolecular interactions of complex non-covalent structures is important in many areas of chemistry. To facilitate the generation of reasonable dimer, oligomer, and general aggregate geometries, we introduce an automated computational interaction site screening (aISS) workflow. This easy-to-use tool combines a genetic algorithm employing the intermolecular force-field xTB-IFF for initial search steps with the general force-field GFN-FF and the semi-empirical GFN2-xTB method for geometry optimizations. Compared with the alternative CREST program, aISS yields similar results but with computer time savings of 1-3 orders of magnitude. This allows for the treatment of systems with thousands of atoms composed of elements up to radon, e.g., metal-organic complexes, or even polyhedra and zeolite cut-outs which were not accessible before. Moreover, aISS can identify reactive sites and provides options like site-directed (user-guided) screening.

Performance of Localized-Orbital Coupled-Cluster Approaches for the Conformational Energies of Longer n-Alkane Chains

We report an update and enhancement of the ACONFL (conformer energies of large alkanes [J. Phys. Chem. A2022,126, 3521-3535]) dataset. For the ACONF12 (n-dodecane) subset, we report basis set limit canonical coupled-cluster with singles, doubles, and perturbative triples [i.e., CCSD(T)] reference data obtained from the MP2-F12/cc-pV{T,Q}Z-F12 extrapolation, [CCSD(F12*)-MP2-F12]/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/aug-cc-pV{D,T}Z calculations. Then, we explored the performance of a variety of single and composite localized-orbital CCSD(T) approximations, ultimately finding an affordable localized natural orbital CCSD(T) [LNO-CCSD(T)]-based post-MP2 correction that agrees to 0.006 kcal/mol mean absolute deviation with the revised canonical reference data. In tandem with canonical MP2-F12 complete basis set extrapolation, this was then used to re-evaluate the ACONF16 and ACONF20 subsets for n-hexadecane and n-icosane, respectively. Combining those with the revised canonical reference data for the dodecane conformers (i.e., ACONF12 subset), a revised ACONFL set was obtained. It was then used to assess the performance of different localized-orbital coupled-cluster approaches, such as pair natural orbital localized CCSD(T) [PNO-LCCSD(T)] as implemented in MOLPRO, DLPNO-CCSD(T₀) and DLPNO-CCSD(T₁) as implemented in ORCA, and LNO-CCSD(T) as implemented in MRCC, at their respective "Normal", "Tight", "vTight", and "vvTight" accuracy settings. For a given accuracy threshold and basis set, DLPNO-CCSD(T₁) and DLPNO-CCSD(T₀) perform comparably. With "VeryTightPNO" cutoffs, explicitly correlated DLPNO-CCSD(T₁)-F12/VDZ-F12 is the best pick among all the DLPNO-based methods tested. To isolate basis set incompleteness from localized-orbital-related truncation errors (domain, LNOs), we have also compared the localized coupled-cluster approaches with canonical DF-CCSD(T)/aug-cc-pVTZ for the ACONF12 set. We found that gradually tightening the cutoffs improves the performance of LNO-CCSD(T), and using a composite scheme such as vTight + 0.50[vTight - Tight] improves things further. For DLPNO-CCSD(T₁), "TightPNO" and "VeryTightPNO" offer a statistically similar accuracy, which gets slightly better when T_CutPNO is extrapolated to the complete PNO space limit. Similar to Brauer et al.'s [Phys. Chem. Chem. Phys.2016,18 (31), 20905-20925] previous report for the S66x8 noncovalent interactions, the dispersion-corrected direct random phase approximation (dRPA)-based double hybrids perform remarkably well for the ACONFL set. While the revised reference data do not affect any conclusions on the less accurate methods, they may upend orderings for more accurate methods with error statistics on the same order as the difference between reference datasets.

Efficient Computation of the Interaction Energies of Very Large Non-covalently Bound Complexes

We present a new benchmark set consisting of 16 large non-covalently bound systems (LNCI16) ranging from 380 up to 1988 atoms and featuring diverse interaction motives. Gas-phase interaction energies are calculated with various composite DFT, semi-empirical quantum mechanical (SQM), and force field (FF) methods and are evaluated using accurate DFT reference values. Of the employed QM methods, PBEh-3c proves to be the most robust for large systems with a relative mean absolute deviation (relMAD) of 8.5% with respect to the reference interaction energies. r2SCAN-3c yields an even smaller relMAD, at least for the subset of complexes for which the calculation could be converged, but is less robust for systems with smaller HOMO–LUMO gaps. The inclusion of Fock-exchange is therefore important for the description of very large non-covalent interaction (NCI) complexes in the gas phase. GFN2-xTB was found to be the best performer of the SQM methods with an excellent result of only 11.1% deviation. From the assessed force fields, GFN-FF and GAFF achieve the best accuracy. Considering their low computational costs, both can be recommended for routine calculations of very large NCI complexes, with GFN-FF being clearly superior in terms of general applicability. Hence, GFN-FF may be routinely applied in supramolecular synthesis planning.

1 Introduction

2 The LNCI16 Benchmark Set

3 Computational Details

4 Generation of Reference Values

5 Results and Discussion

6 Conclusions

Automated Molecular Cluster Growing for Explicit Solvation by Efficient Force Field and Tight Binding Methods

An automated and broadly applicable workflow for the description of solvation effects in an explicit manner is introduced. This method, termed quantum cluster growth (QCG), is based on the semiempirical GFN2-xTB/GFN-FF methods, enabling efficient geometry optimizations and MD simulations. Fast structure generation is provided using the intermolecular force field xTB-IFF. Additionally, the approach uses an efficient implicit solvation model for the electrostatic embedding of the growing clusters. The novel QCG procedure presents a robust cluster generation tool for subsequent application of higher-level (e.g., DFT) methods to study solvation effects on molecular geometries explicitly or to average spectroscopic properties over cluster ensembles. Furthermore, the computation of the solvation free energy with a supermolecular approach can be carried out with QCG. The underlying growing process is physically motivated by computing the leading-order solute-solvent interactions first and can account for conformational and chemical changes due to solvation for low-energy barrier processes. The conformational space is explored with the NCI-MTD algorithm as implemented in the CREST program, using a combination of metadynamics and MD simulations. QCG with GFN2-xTB yields realistic solution geometries and reasonable solvation free energies for various systems without introducing many empirical parameters. Computed IR spectra of some solutes with QCG show a better match to the experimental data compared to well-established implicit solvation models.

What quantum chemical simulations tell us about the infrared spectra, structure and interionic interactions of a bulk ionic liquid

The recently developed efficient protocol to explicit quantum mechanical modeling of the structure and IR spectra of liquids and solutions [Katsyuba et al., J. Phys. Chem. B, 2020, 124, 6664-6670] is applied to ionic liquid 1-ethyl-3-methyl-imidazolium tetrafluoroborate [Emim][BF₄], and its C2-deuterated analog [Emim-d][BF₄]. It is shown that the solvation strongly modifies the frequencies and IR intensities of both cationic and anionic components of the ionic liquids. The main features of the bulk spectra are reproduced by the simulations for cluster ([Emim][BF₄])₈, representing an ion pair solvated by the first solvation shell. The geometry of the cluster closely resembles the solid-state structure of the actual ionic liquid and is characterized by short contacts of all CH moieties of the imidazolium ring with [BF₄]^- anions. Both structural and spectroscopic analyses allow the contacts to be interpreted as hydrogen bonds of approximately equal strength. The enthalpies of these liquid-state H-bonds, estimated with the use of empirical correlations, amount to 1.2-1.5 kcal mol^-1, while the analogous estimates obtained for the gas-phase charged species [Emim][BF₄]₂^- and [Emim]₂[BF₄]⁺ increase to 3.6-3.9 kcal mol^-1.

CARNOT: a Fragment-Based Direct Molecular Dynamics and Virtual-Reality Simulation Package for Reactive Systems

Traditionally, the study of reaction mechanisms of complex reaction systems such as combustion has been performed on an individual basis by optimizations of transition structure and minimum energy path or by reaction dynamics trajectory calculations for one elementary reaction at a time. It is effective, but time-consuming, whereas important and unexpected processes could have been missed. In this article, we present a direct molecular dynamics (DMD) approach and a virtual-reality simulation program, CARNOT, in which plausible chemical reactions are simulated simultaneously at finite temperature and pressure conditions. A key concept of the present ab initio molecular dynamics method is to partition a large, chemically reactive system into molecular fragments that can be adjusted on the fly of a DMD simulation. The theory represents an extension of the explicit polarization method to reactive events, called ReX-Pol. We propose a highest-and-lowest adapted-spin approximation to define the local spins of individual fragments, rather than treating the entire system by a delocalized wave function. Consequently, the present ab initio DMD can be applied to reactive systems consisting of an arbitrarily varying number of closed and open-shell fragments such as free radicals, zwitterions, and separate ions found in combustion and other reactions. A graph-data structure algorithm was incorporated in CARNOT for the analysis of reaction networks, suitable for reaction mechanism reduction. Employing the PW91 density functional theory and the 6-31+G(d) basis set, the capabilities of the CARNOT program were illustrated by a combustion reaction, consisting of 28 650 atoms, and by reaction network analysis that revealed a range of mechanistic and dynamical events. The method may be useful for applications to other types of complex reactions.

Computer-aided simulation of infrared spectra of ethanol conformations in gas, liquid and in CCl4 solution

The recently developed efficient protocol combining implicit and explicit, accurate quantum-mechanical modeling of the condensed state (Katsyuba et al., J. Chem. Phys. 155, 024507 [2021]) is used to describe the IR spectra of liquid ethanol and its solutions in CCl₄ . The relative abundance of the anti and gauche conformers of ethanol is shown to increase from ~40:60 in the gas phase to ~55:45 in the liquid phase. In spite of a moderate impact of media effects on the conformational composition of the liquid, the solvent strongly influences vibrational frequencies, IR intensities, and normal modes of each conformer, producing qualitatively different spectra compared to the gas phase and CCl₄ solution. Further, these solvent effects affecting IR frequencies and intensities depend not only on the conformation of the solvated molecule but also on the solvating species. Nevertheless, vibrational frequencies of anti and gauche conformers of liquid ethanol and its several isotopomers practically coincide with each other. Convenient liquid-state conformational markers in the fingerprint region of IR spectra are revealed for the hydroxyl-deuterated species: CH₃ CH₂ OD, CH₃ CHDOD, CH₃ CD₂ OD, and CD₃ CD₂ OD.

Synthesis and Computationally Assisted Spectroscopic Study of Tautomerism in 3-(Phenyl(2-arylhydrazineylidene)methyl)quinoxalin-2(1H)-ones

The recently developed efficient protocol combining implicit and explicit, accurate quantum mechanical modeling of the condensed state [Katsyuba et al., J. Chem. Phys. 155, 024507 (2021)] is used to describe...

Short-Range Imbalances in the AMBER Lennard-Jones Potential for (Deoxy)Ribose···Nucleobase Lone-Pair···π Contacts in Nucleic Acids

The lone-pair···π (lp···π) (deoxy)ribose···nucleobase stacking is a recurring interaction in Z-DNA and RNAs that is characterized by sub-van der Waals lp···π contacts (<3.0 Å). It is a part of the structural signature of CpG Z-step motifs in Z-DNA and r(UNCG) tetraloops that are known to behave poorly in molecular dynamics (MD) simulations. Although the exact origin of the MD simulation issues remains unclear, a significant part of the problem might be due to an imbalanced description of nonbonded interactions, including the characteristic lp···π stacking. To gain insights into the links between lp···π stacking and MD, we present an in-depth comparison between accurate large-basis-set double-hybrid Kohn-Sham density functional theory calculations DSD-BLYP-D3/ma-def2-QZVPP (DHDF-D3) and data obtained with the nonbonded potential of the AMBER force field (AFF) for NpN Z-steps (N = G, A, C, and U). Among other differences, we found that the AFF overestimates the DHDF-D3 lp···π distances by ∼0.1-0.2 Å, while the deviation between the DHDF-D3 and AFF descriptions sharply increases in the short-range region of the interaction. Based on atom-in-molecule polarizabilities and symmetry-adapted perturbation theory analysis, we inferred that the DHDF-D3 versus AFF differences partly originate in identical nucleobase carbon atom Lennard-Jones (LJ) parameters despite the presence/absence of connected electron-withdrawing groups that lead to different effective volumes or vdW radii. Thus, to precisely model the very short CpG lp···π contact distances, we recommend revision of the nucleobase atom LJ parameters. Additionally, we suggest that the large discrepancy between DHDF-D3 and AFF short-range repulsive part of the interaction energy potential may significantly contribute to the poor performances of MD simulations of nucleic acid systems containing Z-steps. Understanding where, and if possible why, the point-charge-type effective potentials reach their limits is vital for developing next-generation FFs and for addressing specific issues in contemporary MD simulations.

Surprisingly Good Performance of XYG3 Family Functionals Using a Scaled KS-MP3 Correlation

By adding a GLPT3 (third-order Görling-Levy perturbation theory, or KS-MP3) term E₃ to the XYG7 form for a double hybrid, we are able to bring down WTMAD2 (weighted total mean absolute deviation) for the very large and chemically diverse GMTKN55 benchmark to an unprecedented 1.17 kcal/mol, competitive with much costlier composite wave function ab initio approaches. Intriguingly, (a) the introduction of E₃ makes an empirical dispersion correction redundant; (b) generalized gradient approximation (GGA) or meta-GGA semilocal correlation functionals offer no advantage over the local density approximation (LDA) in this framework; (c) if a dispersion correction is retained, then simple Slater exchange leads to no significant loss in accuracy. It is possible to create a six-parameter functional with WTMAD2 = 1.42 that has no post-LDA density functional theory components and no dispersion correction in the final energy.

Revisiting conformations of methyl lactate in water and methanol

The recently developed efficient protocols to implicit [Grimme et al., J. Phys. Chem. A 125, 4039-4054 (2021)] and explicit quantum mechanical modeling of non-rigid molecules in solution [Katsyuba et al., J. Phys. Chem. B 124, 6664-6670 (2020)] are applied to methyl lactate (ML). Building upon this work, a new combination scheme is proposed to incorporate solvation effects for the computation of infrared (IR) absorption spectra. Herein, Boltzmann populations calculated for implicitly solvated single conformers are used to weight the IR spectra of explicitly solvated clusters with a size of typically ten solvent molecules, i.e., accounting for the first solvation shell. It is found that in water and methanol, the most abundant conformers of ML are structurally modified relative to the gas phase, where the major form is ML1, in which the syn conformation of the -OH moiety is stabilized by a OH⋯O=C intramolecular hydrogen bond (HB). In solution, this syn conformation transforms to the gauche form because the intramolecular HB is disrupted by explicit water molecules that form intermolecular HBs with the hydroxyl and carbonyl groups. Similar changes induced by the gas-solution transition are observed for the minor conformers, ML2 and/or ML3, characterized by OH⋯OCH₃ intramolecular HB in the gas phase. The relative abundance of ML1 is shown to decrease from ∼96% in gas to ∼51% in water and ∼92% in methanol. The solvent strongly influences frequencies, IR intensities, and normal modes, resulting in qualitatively different spectra compared to the gas phase. Some liquid-state conformational markers in the fingerprint region of IR spectra are revealed.

Exploring Avenues beyond Revised DSD Functionals: I. Range Separation, with xDSD as a Special Case

We have explored the use of range separation as a possible avenue for further improvement on our revDSD minimally empirical double hybrid functionals. Such ωDSD functionals encompass the XYG3 type of double hybrid (i.e., xDSD) as a special case for ω → 0. As in our previous studies, the large and chemically diverse GMTKN55 benchmark suite was used for evaluation. Especially when using the D4 rather than D3BJ dispersion model, xDSD has a slight performance advantage in WTMAD2. As in previous studies, PBEP86 is the winning combination for the semilocal parts. xDSDn-PBEP86-D4 marginally outperforms the previous "best in class" ωB97M(2) Berkeley double hybrid but without range separation and using fewer than half the number of empirical parameters. Range separation turns out to offer only marginal further improvements on GMTKN55 itself. While ωB97M(2) still yields better performance for small-molecule thermochemistry, this is compensated in WTMAD2 by the superior performance of the new functionals for conformer equilibria. Results for two external test sets with pronounced static correlation effects may indicate that range-separated double hybrids are more resilient to such effects.

Benchmarking London dispersion corrected density functional theory for noncovalent ion-π interactions

The strongly attractive noncovalent interactions of charged atoms or molecules with π-systems are important binding motifs in many chemical and biological systems. These so-called ion-π interactions play a major role in enzymes, molecular recognition, and for the structure of proteins. In this work, a molecular test set termed IONPI19 is compiled for inter- and intramolecular ion-π interactions, which is well balanced between anionic and cationic systems. The IONPI19 set includes interaction energies of significantly larger molecules (up to 133 atoms) than in other ion-π test sets and covers a broad range of binding motifs. Accurate (local) coupled cluster values are provided as reference. Overall, 19 density functional approximations, including seven (meta-)GGAs, eight hybrid functionals, and four double-hybrid functionals combined with three different London dispersion corrections, are benchmarked for interaction energies. DFT results are further compared to wave function based methods such as MP2 and dispersion corrected Hartree-Fock. Also, the performance of semiempirical QM methods such as the GFNn-xTB and PMx family of methods is tested. It is shown that dispersion-uncorrected DFT underestimates ion-π interactions significantly, even though electrostatic interactions dominate the overall binding. Accordingly, the new charge dependent D4 dispersion model is found to be consistently better than the standard D3 correction. Furthermore, the functional performance trend along Jacob's ladder is generally obeyed and the reduction of the self-interaction error leads to an improvement of (double) hybrid functionals over (meta-)GGAs, even though the effect of the SIE is smaller than expected. Overall, the double-hybrids PWPB95-D4/QZ and revDSD-PBEP86-D4/QZ turned out to be the most reliable among all assessed methods for the description of ion-π interactions, which opens up new perspectives for systems where coupled cluster calculations are no longer computationally feasible.

CLIFF: A component-based, machine-learned, intermolecular force field

Computation of intermolecular interactions is a challenge in drug discovery because accurate ab initio techniques are too computationally expensive to be routinely applied to drug-protein models. Classical force fields are more computationally feasible, and force fields designed to match symmetry adapted perturbation theory (SAPT) interaction energies can remain accurate in this context. Unfortunately, the application of such force fields is complicated by the laborious parameterization required for computations on new molecules. Here, we introduce the component-based machine-learned intermolecular force field (CLIFF), which combines accurate, physics-based equations for intermolecular interaction energies with machine-learning models to enable automatic parameterization. The CLIFF uses functional forms corresponding to electrostatic, exchange-repulsion, induction/polarization, and London dispersion components in SAPT. Molecule-independent parameters are fit with respect to SAPT2+(3)δMP2/aug-cc-pVTZ, and molecule-dependent atomic parameters (atomic widths, atomic multipoles, and Hirshfeld ratios) are obtained from machine learning models developed for C, N, O, H, S, F, Cl, and Br. The CLIFF achieves mean absolute errors (MAEs) no worse than 0.70 kcal mol^-1 in both total and component energies across a diverse dimer test set. For the side chain-side chain interaction database derived from protein fragments, the CLIFF produces total interaction energies with an MAE of 0.27 kcal mol^-1 with respect to reference data, outperforming similar and even more expensive methods. In applications to a set of model drug-protein interactions, the CLIFF is able to accurately rank-order ligand binding strengths and achieves less than 10% error with respect to SAPT reference values for most complexes.

New atoms-in-molecules dispersion models for use in ab initio derived force fields

Recently, substantial research efforts have gone into bridging the accuracy-efficiency gap between parameterized force field models and quantum chemical calculations by extracting molecule-specific force fields directly from ab initio data in a robust and automated manner. One of the challenging aspects is deriving localized atomic polarizabilities for pairwise distributed dispersion models. The Tkatchenko-Scheffler model is based upon correcting free-atom C₆ coefficients according to the square of the ratio of the atom-in-molecule volume to the free-atom volume. However, it has recently been shown that a more accurate relationship can be found if static atomic polarizabilities are also taken into account. Using this relationship, we develop two modified Tkatchenko-Scheffler dispersion models and benchmark their performance against SAPT2+3 reference data and other commonly used dispersion models.

Sensory Perception of Non-Deuterated and Deuterated Organic Compounds

The chemical background of olfactory perception has been subject of intensive research, but no available model can fully explain the sense of smell. There are also inconsistent results on the role of the isotopology of molecules. In experiments with human subjects it was found that the isotope effect is weak with acetone and D6 -acetone. In contrast, clear differences were observed in the perception of octanoic acid and D15 -octanoic acid. Furthermore, a trained sniffer dog was initially able to distinguish between these isotopologues of octanoic acid. In chromatographic measurements, the respective deuterated molecule showed weaker interaction with a non-polar liquid phase. Quantum chemical calculations give evidence that deuterated octanoic acid binds more strongly to a model receptor than non-deuterated. In contrast, the binding of the non-deuterated molecule is stronger with acetone. The isotope effect is calculated in the framework of statistical mechanics. It results from a complicated interplay between various thermostatistical contributions to the non-covalent free binding energies and it turns out to be very molecule-specific. The vibrational terms including non-classical zero-point energies play about the same role as rotational/translational contributions and are larger than bond length effects for the differential isotope perception of odor for which general rules cannot be derived.

Reactive Molecular Dynamics at Constant Pressure via Nonreactive Force Fields: Extending the Empirical Valence Bond Method to the Isothermal-Isobaric Ensemble

The Empirical Valence Bond (EVB) method offers a suitable framework to obtain reactive potentials through the coupling of nonreactive force fields. In this formalism, most of the implemented coupling terms are built using functional forms that depend on spatial coordinates, while parameters are fitted against reference data to model the change of chemistry between the participating nonreactive states. In this work, we demonstrate that the use of such coupling terms precludes the computation of the stress tensor for condensed phase systems and prevents the possibility to carry out EVB molecular dynamics in the isothermal-isobaric (NPT) ensemble. Alternatively, we make use of coupling terms that depend on the energy gaps, defined as the energy differences between the participating nonreactive force fields, and derive a general expression for the EVB stress tensor suitable for computation. Implementation of this new methodology is tested for a model of a single reactive malonaldehyde solvated in nonreactive water. Mass densities and probability distributions for the values of the energy gaps computed in the NPT ensemble reveal a negligible role of the reactive potential in the limit of low concentrated solutions, thus corroborating for the first time the validity of approximations based on the canonical NVT ensemble, customarily adopted for EVB simulations. The presented formalism also aims to contribute to future implementations and extensions of the EVB method to research the limit of highly concentrated solutions.

Performance of Electronic Structure Methods for the Description of Hückel-Möbius Interconversions in Extended π-Systems

Expanded porphyrins provide a versatile route to molecular switching devices due to their ability to shift between several π-conjugation topologies encoding distinct properties. DFT remains the workhorse for modeling such extended macrocycles, when taking into account their size and huge conformational flexibility. Nevertheless, the stability of Hückel and Möbius conformers depends on a complex interplay of different factors, such as hydrogen bonding, π···π stacking, steric effects, ring strain, and electron delocalization. As a consequence, the selection of an exchange-correlation functional for describing the energy profile of topological switches is very difficult. For these reasons, we have examined the performance of a variety of wave function methods and density functionals for describing the thermochemistry and kinetics of topology interconversions across a wide range of macrocycles. Especially for hexa- and heptaphyrins, the Möbius structures have a stronger degree of static correlation than the Hückel and twisted-Hückel structures, and as a result the relative energies of singly twisted structures are a challenging test for electronic structure methods. Comparison of limited orbital space full CI calculations with CCSD(T) calculations within the same active spaces shows that post-CCSD(T) correlation contributions to relative energies are very minor. At the same time, relative energies are weakly sensitive to further basis set expansion, as proven by the minor energy differences between the extrapolated MP2/CBS energies estimated from cc-pV{T,Q}Z, diffuse-augmented heavy-aug-cc-pV{T,Q}Z and explicitly correlated MP2-F12/cc-pVDZ-F12 calculations. Hence, our CCSD(T) reference values are reasonably well-converged in both 1-particle and n-particle spaces. While conventional MP2 and MP3 yield very poor results, SCS-MP2 and particularly SOS-MP2 and SCS-MP3 agree to better than 1 kcal mol-1 with the CCSD(T) relative energies. Regarding DFT methods, the range-separated double hybrids, such as ωB97M(2) and B2GP-PLYP, outperform other functionals with RMSDs of 0.6 and 0.8 kcal mol-1, respectively. While the original DSD-PBEP86 double hybrid performs fairly poorly for these extended π-systems, the errors drop down to 1.9 kcal mol-1 for the revised revDOD-PBEP86-NL, which eliminates the same-spin correlation energy. Minnesota meta-GGA functionals with high fractions of exact exchange (M06-2X and M08-HX) also perform reasonably well, outperforming more robust and significantly less empirically parametrized functionals like SCAN0-D3.

Exploring London Dispersion and Solvent Interactions at Alkyl-Alkyl Interfaces Using Azobenzene Switches

Interactions on the molecular level control structure as well as function. Especially interfaces between innocent alkyl groups are hardly studied although they are of great importance in larger systems. Herein, London dispersion in conjunction with solvent interactions between linear alkyl chains was examined with an azobenzene-based experimental setup. Alkyl chains in all meta positions of the azobenzene core were systematically elongated, and the change in rate for the thermally induced Z→E isomerization in n-decane was determined. The stability of the Z-isomer increased with longer chains and reached a maximum for n-butyl groups. Further elongation led to faster isomerization. The origin of the intramolecular interactions was elaborated by various techniques, including 1 H NOESY NMR spectroscopy. The results indicate that there are additional long-range interactions between n-alkyl chains with the opposite phenyl core in the Z-state. These interactions are most likely dominated by attractive London dispersion. This work provides rare insight into the stabilizing contributions of highly flexible groups in an intra- as well as an intermolecular setting.

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

We present a family of minimally empirical double-hybrid DFT functionals parametrized against the very large and diverse GMTKN55 benchmark. The very recently proposed ωB97M(2) empirical double hybrid (with 16 adjustable parameters) has the lowest WTMAD2 (weighted mean absolute deviation over GMTKN55) ever reported at 2.19 kcal/mol. However, refits of the DSD-BLYP and DSD-PBEP86 spin-component-scaled, dispersion-corrected double hybrids can achieve WTMAD2 values as low as 2.33 with the very recent D4 dispersion correction (2.42 kcal/mol with the D3(BJ) dispersion term) using just a handful of adjustable parameters. If we use full DFT correlation in the initial orbital evaluation, the xrevDSD-PBEP86-D4 functional reaches WTMAD2 = 2.23 kcal/mol, statistically indistinguishable from ωB97M(2) but using just four nonarbitrary adjustable parameters (and three semiarbitrary ones). The changes from the original DSD parametrizations are primarily due to noncovalent interaction energies for large systems, which were undersampled in the original parametrization set. With the new parametrization, same-spin correlation can be eliminated at minimal cost in performance, which permits revDOD-PBEP86-D4 and revDOD-PBE-D4 functionals that scale as N⁴ or even N³ with the size of the system. Dependence of WTMAD2 for DSD functionals on the percentage of HF exchange is roughly quadratic; it is sufficiently weak that any reasonable value in the 64% to 72% range can be chosen semiarbitrarily. DSD-SCAN and DOD-SCAN double hybrids involving the SCAN nonempirical meta-GGA as the semilocal component have also been considered and offer a good alternative if one wishes to eliminate either the empirical dispersion correction or the same-spin correlation component. noDispSD-SCAN66 achieves WTMAD2 = 3.0 kcal/mol, compared to 2.7 kcal/mol for DOD-SCAN66-D4. However, the best performance without dispersion corrections (WTMAD2 = 2.8 kcal/mol) is reached by revωB97X-2, a slight reparametrization of the Chai–Head-Gordon range-separated double hybrid. Finally, in the context of double-hybrid functionals, the very recent D4 dispersion correction is clearly superior over D3(BJ).

A generally applicable atomic-charge dependent London dispersion correction

The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models.

GFN2-xTB-An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions

An extended semiempirical tight-binding model is presented, which is primarily designed for the fast calculation of structures and noncovalent interaction energies for molecular systems with roughly 1000 atoms. The essential novelty in this so-called GFN2-xTB method is the inclusion of anisotropic second order density fluctuation effects via short-range damped interactions of cumulative atomic multipole moments. Without noticeable increase in the computational demands, this results in a less empirical and overall more physically sound method, which does not require any classical halogen or hydrogen bonding corrections and which relies solely on global and element-specific parameters (available up to radon, Z = 86). Moreover, the atomic partial charge dependent D4 London dispersion model is incorporated self-consistently, which can be naturally obtained in a tight-binding picture from second order density fluctuations. Fully analytical and numerically precise gradients (nuclear forces) are implemented. The accuracy of the method is benchmarked for a wide variety of systems and compared with other semiempirical methods. Along with excellent performance for the "target" properties, we also find lower errors for "off-target" properties such as barrier heights and molecular dipole moments. High computational efficiency along with the improved physics compared to its precursor GFN-xTB makes this method well-suited to explore the conformational space of molecular systems. Significant improvements are furthermore observed for various benchmark sets, which are prototypical for biomolecular systems in aqueous solution.

New scaling relations to compute atom-in-material polarizabilities and dispersion coefficients: part 1. Theory and accuracy

A new method was developed to compute atom-in-material polarizabilities and dispersion coefficients for diverse material types.

Raising the Bar in Aromatic Donor-Acceptor Interactions with Cyclic Trinuclear Gold(I) Complexes as Strong π-Donors

Aromatic donor-acceptor interactions are of high importance in supramolecular chemistry, materials science and biology. Compared to other noncovalent interactions, such as hydrogen bonding, the binding is often weak. Here we show that strong donor-acceptor interactions between planar aromatics with binding free energies down to -10.1 kcal mol^-1 and association constants of up to 2.34 × 10⁷ L mol^-1 for 1:1 complexes can be realized using cyclic trinuclear complexes of gold(I) with pyridinate, imidazolate, or carbeniate ligands. Data were obtained through NMR and UV/vis absorption spectroscopic studies and supported by quantum chemical calculations for a variety of acceptors. By using a specifically designed bridged naphthalene diimide-based acceptor with only one binding site, we furthermore show that a 1:2 (donor:acceptor) binding model is best suited to quantify the donor and acceptor/complex equilibrium. Scanning electron microscopy on selected donor-acceptor pairs shows crystalline supramolecular assemblies. We anticipate this study to be relevant for the future design of supramolecular systems and chemical sensors and the determination of binding energies between planar donors and acceptors.

Finding the best density functional approximation to describe interaction energies and structures of ionic liquids in molecular dynamics studies

Ionic liquids raise interesting but complicated questions for theoretical investigations due to the fact that a number of different inter-molecular interactions, e.g., hydrogen bonding, long-range Coulomb interactions, and dispersion interactions, need to be described properly. Here, we present a detailed study on the ionic liquids ethylammonium nitrate and 1-ethyl-3-methylimidazolium acetate, in which we compare different dispersion corrected density functional approximations to accurate local coupled cluster data in static calculations on ionic liquid clusters. The efficient new composite method B97-3c is tested and has been implemented in CP2K for future studies. Furthermore, tight-binding based approaches which may be used in large scale simulations are assessed. Subsequently, ab initio as well as classical molecular dynamics simulations are conducted and structural analyses are presented in order to shed light on the different short- and long-range structural patterns depending on the method and the system size considered in the simulation. Our results indicate the presence of strong hydrogen bonds in ionic liquids as well as the aggregation of alkyl side chains due to dispersion interactions.

Steric "attraction": not by dispersion alone

Non-covalent interactions between neutral, sterically hindered organic molecules generally involve a strong stabilizing contribution from dispersion forces that in many systems turns the 'steric repulsion' into a 'steric attraction'. In addition to London dispersion, such systems benefit from electrostatic stabilization, which arises from a short-range effect of charge penetration and gets bigger with increasing steric bulk. In the present work, we quantify this contribution for a diverse set of molecular cores, ranging from unsubstituted benzene and cyclohexane to their derivatives carrying tert-butyl, phenyl, cyclohexyl and adamantyl substituents. While the importance of electrostatic interactions in the dimers of sp²-rich (e.g., π-conjugated) cores is well appreciated, less polarizable assemblies of sp³-rich systems with multiple short-range CH···HC contacts between the bulky cyclohexyl and adamantyl moieties are also significantly influenced by electrostatics. Charge penetration is drastically larger in absolute terms for the sp²-rich cores, but still has a non-negligible effect on the sp³-rich dimers, investigated herein, both in terms of their energetics and equilibrium interaction distances. These results emphasize the importance of this electrostatic effect, which has so far been less recognized in aliphatic systems compared to London dispersion, and are therefore likely to have implications for the development of force fields and methods for crystal structure prediction.

Preface: Special Topic: From Quantum Mechanics to Force Fields

This Special Topic issue entitled "From Quantum Mechanics to Force Fields" is dedicated to the ongoing efforts of the theoretical chemistry community to develop a new generation of accurate force fields based on data from high-level electronic structure calculations and to develop faster electronic structure methods for testing and designing force fields as well as for carrying out simulations. This issue includes a collection of 35 original research articles that illustrate recent theoretical advances in the field. It provides a timely snapshot of recent developments in the generation of approaches to enable more accurate molecular simulations of processes important in chemistry, physics, biophysics, and materials science.

Extension of the D3 dispersion coefficient model

A new model, termed D4, for the efficient computation of molecular dipole-dipole dispersion coefficients is presented. As in the related, well established D3 scheme, these are obtained as a sum of atom-in-molecule dispersion coefficients over atom pairs. Both models make use of dynamic polarizabilities obtained from first-principles time-dependent density functional theory calculations for atoms in different chemical environments employing fractional atomic coordination numbers for interpolation. Different from the D3 model, the coefficients are obtained on-the-fly by numerical Casimir-Polder integration of the dynamic, atomic polarizabilities α(iω). Most importantly, electronic density information is now incorporated via atomic partial charges computed at a semi-empirical quantum mechanical tight-binding level, which is used to scale the polarizabilities. Extended statistical measures show that errors for dispersion coefficients with the proposed D4 method are significantly lower than with D3 and other, computationally more involved schemes. Alongside, accurate isotropic charge and hybridization dependent, atom-in-molecule static polarizabilities are obtained with an unprecedented efficiency. Damping function parameters are provided for three standard density functionals, i.e., TPSS, PBE0, and B3LYP, allowing evaluation of the new DFT-D4 model for common non-covalent interaction energy benchmark sets.