Computational Chemistry: The Fate of Current Methods and Future Challenges

Perspective: multi-configurational methods in bio-inorganic chemistry

Transition metal ions play crucial roles in the structure and function of numerous proteins, contributing to essential biological processes such as catalysis, electron transfer, and oxygen binding. However, accurately modeling the electronic structure and properties of metalloproteins poses significant challenges due to the complex nature of their electronic configurations and strong correlation effects. Multiconfigurational quantum chemistry methods are, in principle, the most appropriate tools for addressing these challenges, offering the capability to capture the inherent multi-reference character and strong electron correlation present in bio-inorganic systems. Yet their computational cost has long hindered wider adoption, making methods such as density functional theory (DFT) the method of choice. However, advancements over the past decade have substantially alleviated this limitation, rendering multiconfigurational quantum chemistry methods more accessible and applicable to a wider range of bio-inorganic systems. In this perspective, we discuss some of these developments and how they have already been used to answer some of the most important questions in bio-inorganic chemistry. We also comment on ongoing developments in the field and how the future of the field may evolve.

Emerging Conformational-Analysis Protocols from the RTCONF55-16K Reaction Thermochemistry Conformational Benchmark Set

RTCONF55-16K is a new, reactive conformational data set based on cost-efficient methods to assess different conformational analysis protocols. Our reference calculations underpinned the accuracy of the CENSO (Grimme et al. J. Phys. Chem. A, 2021, 125, 4039) procedure and resulted in alternative recipes with different cost-accuracy compromises. Our general-purpose and economical protocols (CENSO-light and zero, respectively) were found to be 10-30 times faster than the original algorithm, adding only 0.4-0.7 kcal/mol absolute error to the relative free energy estimates.

Autobench V1.0: Benchmarking Automation for Electronic Structure Calculations

This work reports on new software for automatic conformer energy benchmarking calculations for flexible molecules. The software workflow consists of four parts: conformational search, preoptimization, optimization, and frequency calculations at a higher level and last calculations using several theoretical levels. The software was written to be user-friendly and versatile to be used by nonexperts in computational chemistry. Any theoretical levels available in either Gaussian 16 or ORCA 5 may be applied in the benchmarking study. The workflow will automatically run conformational search calculations and deal with conformers that converge to the same minimum and those that show a negative frequency. At the end of the workflow, the user will have the mean absolute deviations and the most accurate method/DFT functional and basis set in comparison to the benchmark to be applied for the molecular system of interest. Case examples are given at the end of the paper that may help users to get insight into the software's main features.

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.

Long but Strong C-C Single Bonds: Challenges for Theory

Theoretical challenges in describing molecules with anomalously long single C-C bonds are analyzed in terms of the relative contributions of stabilizing and destabilizing intramolecular interactions. Diamondoid dimers that are stable despite the presence of C-C bonds up to 1.7 Å long, as well as other bulky molecules stabilized due to intramolecular noncovalent interactions (London dispersions) are discussed. The unexpected stability of highly crowded molecules, such as diamondoid dimers and tert-butyl-substituted hexaphenylethanes, calls for reconsideration of the "steric effect" traditionally thought to destabilize the molecule. Alternatively, "steric attraction" helps to understand bonding in sterically overloaded molecules, whose structural and energetic analysis requires a proper theoretical description of noncovalent interactions.

Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry

The field of quantum computing has the potential to transform quantum chemistry. The variational quantum eigensolver (VQE) algorithm has allowed quantum computing to be applied to chemical problems in the noisy intermediate-scale quantum (NISQ) era. Applications of VQE have generally focused on predicting absolute energies instead of chemical properties that are relative energy differences and that are most interesting to chemists studying a chemical problem. We address this shortcoming by constructing a molecular benchmark data set in this work containing isomers of C10H16 and carbocationic rearrangements of C10H15+, calculated at a high-level of theory. Using the data set, we compared noiseless VQE simulations to conventionally performed density functional and wavefunction theory-based methods to understand the quality of results. We also investigated the effectiveness of a quantum state tomography-based error mitigation technique in applications of VQE under noise (simulated and real). Our findings reveal that the use of quantum error mitigation is crucial in the NISQ era and advantageous to yield almost noiseless quality results.

Rationale design and synthesis of new apoptotic thiadiazole derivatives targeting VEGFR-2: computational and in vitro studies

This work presents the synthesis and in vitro, and in silico analyses of new thiadiazole derivatives that are designed to mimic the pharmacophoric characteristics of vascular endothelial growth factor receptor-2 (VEGFR-2) inhibitors. A comprehensive evaluation of the inhibitory properties of the synthesized thiadiazole derivatives against the cancer cell lines MCF-7 and HepG2 identified several auspicious candidates. Among them, compound 14 showed remarkably low IC50 values of 0.04 μM and 0.18 μM against MCF-7 and HepG2, respectively. VEGFR-2 inhibitory evaluation of compound 14 revealed a promising IC50 value in the nanomolar range (103 nM). Further examination of the cell cycle revealed that compound 14 has the ability to stop the progression of the cell cycle in MCF-7 cells via G0-G1 phase arrest. Interestingly, compound 14 also demonstrated a noteworthy pro-apoptotic effect in MCF-7 cells, with notable increases in early apoptosis (16.53%) and late apoptosis (29.57%), along with a slight increase in the population of necrotic cells (5.95%). Furthermore, compound 14 showed a significant drop in MCF-7 cells' ability to migrate and heal wounds. Additionally, compound 14 promoted apoptosis by boosting BAX (6-fold) while lowering Bcl-2 (6.2-fold). The binding affinities of the synthesized candidates to their target (VEGFR-2) were confirmed by computational investigations, including molecular docking, principal component analysis of trajectories (PCAT), and molecular dynamics (MD) simulations. Additionally, compound 14's stability and reactivity were investigated using density functional theory (DFT). These thorough results highlight compound 14's potential as a lead contender for additional research in the creation of anticancer drugs that target VEGFR-2. This work establishes a foundation for promising thiadiazole derivatives for future therapeutic developments in anticancer- and angiogenesis-related scientific fields.

Cluster-in-Molecule Local Correlation Method for Dispersion Interactions in Large Systems and Periodic Systems

ConspectusThe noncovalent interactions, including dispersion interactions, control the structures and stabilities of complex chemical systems, including host-guest complexes and the adsorption process of molecules on the solid surfaces. The density functional theory (DFT) with empirical dispersion correction is now the working horse in many areas of applications. Post-Hartree-Fock (post-HF) methods have been well recognized to provide more accurate descriptions in a systematic way. However, traditional post-HF methods are mainly limited to small- or medium-sized systems, and their applications to periodic condensed phase systems are still very limited due to their expensive computational costs.To extend post-HF calculations to large molecules, the cluster-in-molecule (CIM) local correlation approach has been established, allowing highly accurate electron correlation calculations that are routinely available for very large systems. In the CIM approach, the electron correlation energy of a large molecule could be obtained from electron correlation calculations on a series of clusters, each of which contains a subset of occupied and virtual localized molecular orbitals. The CIM method could be massively and efficiently parallelized on general computer clusters. The CIM method has been implemented at various electron correlation levels, including second-order Mo̷ller-Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), CCSD with perturbative triples correction [CCSD(T)], etc. The CIM-MP2 energy gradient algorithm was developed and applied to the geometry optimizations of large systems. The CIM method has also been extended to condensed-phase systems under periodic boundary conditions (PBC-CIM). For periodic systems, the correlation energy per unit cell could be evaluated with correlation energy contributions from a series of clusters that are built with localized Wannier functions.CIM-based electron correlation calculations have been employed to investigate a number of chemical problems in which the dispersion interaction is important. CIM-based post-HF methods including CIM domain-based local pair natural orbital (DLPNO) CCSD(T) are applied to compute the relative or binding energies of biological systems or supramolecular complexes, the reaction barrier in a relatively complex chemical reaction. The CIM-MP2 method is used to obtain the optimized geometry of large systems. CIM-based post-HF calculations have also been used to compute the cohesive energies of molecular crystals and adsorption energies of molecules on the solid surfaces. The CIM and its PBC variant are expected to become a powerful theoretical tool for accurate calculations of the energies and structures for a broad range of large systems and condensed-phase systems with significant dispersion interactions.

Picking the lock of coordination cage catalysis

The design principles of metallo-organic assembly reactions have facilitated access to hundreds of coordination cages of varying size and shape. Many of these assemblies possess a well-defined cavity capable of hosting a guest, pictorially mimicking the action of a substrate binding to the active site of an enzyme. While there are now a growing collection of coordination cages that show highly proficient catalysis, exhibiting both excellent activity and efficient turnover, this number is still small compared to the vast library of metal-organic structures that are known. In this review, we will attempt to unpick and discuss the key features that make an effective coordination cage catalyst, linking structure to activity (and selectivity) using lessons learnt from both experimental and computational analysis of the most notable exemplars. We will also provide an outlook for this area, reasoning why coordination cages have the potential to become the gold-standard in (synthetic) non-covalent catalysis.

Computer-assisted drug discovery of potential natural inhibitors of the SARS-CoV-2 RNA-dependent RNA polymerase through a multi-phase in silico approach

BACKGROUND

The COVID-19 pandemic has led to significant loss of life and economic disruption worldwide. Currently, there are limited effective treatments available for this disease. SARS-CoV-2 RNA-dependent RNA polymerase (SARS-CoV-2 RdRp) has been identified as a potential target for drug development against COVID-19. Natural products have been shown to possess antiviral properties, making them a promising source for developing drugs against SARS-CoV-2.

OBJECTIVES

The objective of this study is to identify the most effective natural inhibitors of SARS-CoV-2 RdRp among a set of 4924 African natural products using a multi-phase in silico approach.

METHODS

The study utilized remdesivir (RTP), the co-crystallized ligand of RdRp, as a starting point to select compounds that have the most similar chemical structures among the examined set of compounds. Molecular fingerprints and structure similarity studies were carried out in the first part of the study. The second part of the study included molecular docking against SARS-CoV-2 RdRp (PDB ID: 7BV2) and Molecular Dynamics (MD) simulations including the calculation of RMSD, RMSF, Rg, SASA, hydrogen bonding, and PLIP. Moreover, the calculations of Molecular mechanics with generalised Born and surface area solvation (MM-GBSA) Lennard-Jones and Columbic electrostatic interaction energies have been conducted. Additionally, in silico ADMET and toxicity studies were performed to examine the drug likeness degrees of the selected compounds.

RESULTS

Eight compounds were identified as the most effective natural inhibitors of SARS-CoV-2 RdRp. These compounds are kaempferol 3-galactoside, kaempferol 3-O-β-D-glucopyranoside, mangiferin methyl ether, luteolin 7-O-β-D-glucopyranoside, quercetin-O-β-D-3-glucopyranoside, 1-methoxy-3-indolylmethyl glucosinolate, naringenin, and asphodelin A 4'-O-β-D-glucopyranoside.

CONCLUSION

The results of this study provide valuable information for the development of natural product-based drugs against COVID-19. However, the elected compounds should be further studied in vitro and in vivo to confirm their efficacy in treating COVID-19.

PyConSolv: A Python Package for Conformer Generation of (Metal-Containing) Systems in Explicit Solvent

We introduce PyConSolv, a freely available Python package that automates the generation of conformers of metal- and nonmetal-containing complexes in explicit solvent, through classical molecular dynamics simulations. Using a streamlined workflow and interfacing with widely used computational chemistry software, PyConSolv is an all-in-one tool for the generation of conformers in any solvent. Input requirements are minimal; only the geometry of the structure and the desired solvent in xyz (XMOL) format are needed. The package can also account for charged systems, by including arbitrary counterions in the simulation. A bonded model parametrization is performed automatically, utilizing AmberTools, ORCA, and Multiwfn software packages. PyConSolv provides a selection of preparametrized solvents and counterions for use in classical molecular dynamics simulations. We show the applicability of our package on a number of (transition-metal-containing) systems. The software is provided open source and free of charge.

Molecular Design of Luminescent Complexes of Eu(III): What Can We Learn from the Ligands

The luminescent metal-organic complexes of rare earth metals are advanced materials with wide application potential in chemistry, biology, and medicine. The luminescence of these materials is due to a rare photophysical phenomenon called antenna effect, in which the excited ligand transmits its energy to the emitting levels of the metal. However, despite the attractive photophysical properties and the intriguing from a fundamental point of view antenna effect, the theoretical molecular design of new luminescent metal-organic complexes of rare earth metals is relatively limited. Our computational study aims to contribute in this direction, and we model the excited state properties of four new phenanthroline-based complexes of Eu(III) using the TD-DFT/TDA approach. The general formula of the complexes is EuL₂A₃, where L is a phenanthroline with -2-CH₃O-C₆H₄, -2-HO-C₆H₄, -C₆H₅ or -O-C₆H₅ substituent at position 2 and A is Cl^- or NO₃^-. The antenna effect in all newly proposed complexes is estimated as viable and is expected to possess luminescent properties. The relationship between the electronic properties of the isolated ligands and the luminescent properties of the complexes is explored in detail. Qualitative and quantitative models are derived to interpret the ligand-to-complex relation, and the results are benchmarked with respect to available experimental data. Based on the derived model and common molecular design criteria for efficient antenna ligands, we choose phenanthroline with -O-C₆H₅ substituent to perform complexation with Eu(III) in the presence of NO₃¯. Experimental results for the newly synthesized Eu(III) complex are reported with a luminescent quantum yield of about 24% in acetonitrile. The study demonstrates the potential of low-cost computational models for discovering metal-organic luminescent materials.

The entropic penalty for associative reactions and their physical treatment during routine computations

A systematic study of the entropic penalty for associative reactions is presented. It is shown that computed solution-phase Gibbs free energies typically overestimate entropic contributions. This entropic penalty for associative reactions in solution, i.e., if the number of particles decreases along the reaction coordinate (sum of stoichiometric numbers ), originates from the insufficient treatment of entropic effects by implicit solvent models. We propose an additive correction scheme to Gibbs free energies that is suitable for routine applications by non-expert users. This correction is based on Garza's formalism for the solution-phase entropy [A. J. Garza, J. Chem. Theory Comput., 2019, 15, 3204.] that is physically sound and embedded into an efficient black-box type algorithm. To critically evaluate the entropic penalty and its proposed treatment, we compiled an experimental benchmark set of 31 Δ_rG and 22 in 15 different solvents. Using a representative best-practice computational protocol (at wave function theory (WFT) based DLPNO-CCSD(T) and density functional theory (DFT) based revDSD-PBEP86-D4 level with an implicit solvent model), we determined a sizeable entropic penalty ranging from 2-11 kcal mol^-1. Using the correction scheme presented herein, the entropic penalty is corrected to the chemical accuracy of ≤1 kcal mol^-1 (WFT and DFT). The same applies to at the WFT level. Barriers at the DFT level are overestimated by 2 kcal mol^-1 (classic) and underestimated by 2 kcal mol^-1 (corrected). This effect is attributed to the finding that barriers computed at the DFT level are systematically 2-3 kcal mol^-1 lower than barriers obtained with WFT.

Eco-Friendly AMPS-Doped Polyaniline/Urethane-Methacrylate Coating as a Corrosion Protection Coating: Electrochemical, Surface, Theoretical, and Thermodynamic Studies

In this study, 2-acrylamido-2-methylpropanesulfonic acid (AMPS)-doped polyaniline (PANI) fibers were used as polymerizable smart anticorrosive agents to prepare eco-friendly UV-curable anticorrosive coatings. For this purpose, AMPS-doped PANI fibers were synthesized through chemical oxidative interfacial polymerization. The size and chemical structure of the prepared conducting fibers were characterized by scanning electron microscopy, ¹H NMR, and Fourier transform infrared (FTIR) analyses. As a binder for the prepared conducting fibers, an eco-friendly fluorinated urethane-methacrylate dispersion was synthesized and fully characterized using FTIR analysis. Subsequently, various amounts of the synthesized fibers were mixed with the fluorinated binder to prepare UV-curable anticorrosive coatings. The physicochemical interactions between the PANI fibers and UV-curable binder were studied thoroughly using differential scanning calorimetry and thermogravimetric analyses and measurement of the gel contents and adhesion strength of the prepared composite coatings. The corrosion resistance performance of the prepared coatings was evaluated using electrochemical impedance spectroscopy analysis, and the obtained results revealed that the presence of 2 wt % of the AMPS-doped PANI fibers significantly enhanced the corrosion resistance of the obtained coating. In addition, the corrosion layers of the coatings were analyzed using X-ray photoelectron spectroscopy, which indicated that the AMPS-doped PANI fibers changed the composition of the corrosion product layer. To expand these attempts, this study also explores the interaction of AMPS-doped PANI fibers with the Fe(100) surface using density functional theory as well as atom in molecule calculations. All of the obtained results proved that the outstanding corrosion protection performance of the prepared composite coatings originated from exceptional chemical interactions between the unsaturated doping agents of the prepared PANI fibers and the UV-cured polymer.

Quantum harmonic free energies for biomolecules and nanomaterials

Obtaining the free energy of large molecules from quantum mechanical energy functions is a long-standing challenge. We describe a method that allows us to estimate, at the quantum mechanical level, the harmonic contributions to the thermodynamics of molecular systems of large size, with modest cost. Using this approach, we compute the vibrational thermodynamics of a series of diamond nanocrystals, and show that the error per atom decreases with system size in the limit of large systems. We further show that we can obtain the vibrational contributions to the binding free energies of prototypical protein-ligand complexes where exact computation is too expensive to be practical. Our work raises the possibility of routine quantum mechanical estimates of thermodynamic quantities in complex systems.

Accelerating the density-functional tight-binding method using graphical processing units

Acceleration of the density-functional tight-binding (DFTB) method on single and multiple graphical processing units (GPUs) was accomplished using the MAGMA linear algebra library. Two major computational bottlenecks of DFTB ground-state calculations were addressed in our implementation: the Hamiltonian matrix diagonalization and the density matrix construction. The code was implemented and benchmarked on two different computer systems: (1) the SUMMIT IBM Power9 supercomputer at the Oak Ridge National Laboratory Leadership Computing Facility with 1-6 NVIDIA Volta V100 GPUs per computer node and (2) an in-house Intel Xeon computer with 1-2 NVIDIA Tesla P100 GPUs. The performance and parallel scalability were measured for three molecular models of 1-, 2-, and 3-dimensional chemical systems, represented by carbon nanotubes, covalent organic frameworks, and water clusters.

SQMBox: Interfacing a semiempirical integral library to modular ab initio electronic structure enables new semiempirical methods

Ab initio and semiempirical electronic structure methods are usually implemented in separate software packages or use entirely different code paths. As a result, it can be time-consuming to transfer an established ab initio electronic structure scheme to a semiempirical Hamiltonian. We present an approach to unify ab initio and semiempirical electronic structure code paths based on a separation of the wavefunction ansatz and the needed matrix representations of operators. With this separation, the Hamiltonian can refer to either an ab initio or semiempirical treatment of the resulting integrals. We built a semiempirical integral library and interfaced it to the GPU-accelerated electronic structure code TeraChem. Equivalency between ab initio and semiempirical tight-binding Hamiltonian terms is assigned according to their dependence on the one-electron density matrix. The new library provides semiempirical equivalents of the Hamiltonian matrix and gradient intermediates, corresponding to those provided by the ab initio integral library. This enables the straightforward combination of semiempirical Hamiltonians with the full pre-existing ground and excited state functionality of the ab initio electronic structure code. We demonstrate the capability of this approach by combining the extended tight-binding method GFN1-xTB with both spin-restricted ensemble-referenced Kohn-Sham and complete active space methods. We also present a highly efficient GPU implementation of the semiempirical Mulliken-approximated Fock exchange. The additional computational cost for this term becomes negligible even on consumer-grade GPUs, enabling Mulliken-approximated exchange in tight-binding methods for essentially no additional cost.

Statistical Equivalence of Quantum Chemical Methods for Energy Distribution in Water Clusters

Methods of quantum chemistry are instrumental in understanding molecular structures and properties. However, the results demonstrate significant variability, which is difficult to predict and rationalize. The fundamental question is whether some molecular systems exhibit properties invariant with respect to the computational method. The idea explored here is that collective properties of statistical ensembles should be more robust than characteristics of individual molecules and their arbitrary sets. This effect is demonstrated for the complete set of hydrogen-bond topologies of the dodecahedral water cluster (H₂ O)₂₀ . Non-Gaussian energy distributions produced by various methods have the same functional form despite strong differences in mean values and standard deviations. The conclusion is tested on methods of different complexity and origin employing a number of criteria. A linear mapping between the energies produced by different methods is discussed. The significance of the results is in establishing a collective equivalence property of quantum chemical methods.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

Engineering lactate-modulating nanomedicines for cancer therapy

Lactate in tumors has long been considered "metabolic junk" derived from the glycolysis of cancer cells and utilized only as a biomarker of malignancy, but is presently believed to be a pivotal regulator of tumor development, maintenance and metastasis. Indeed, tumor lactate can be a "fuel" for energy supply and functions as a signaling molecule, which actively contributes to tumor progression, angiogenesis, immunosuppression, therapeutic resistance, etc., thus providing promising opportunities for cancer treatment. However, the current approaches for regulating lactate homeostasis with available agents are still challenging, which is mainly due to the short half-life, low bioavailability and poor specificity of these agents and their unsatisfactory therapeutic outcomes. In recent years, lactate modulation nanomedicines have emerged as a charming and efficient strategy for fighting cancer, which play important roles in optimizing the delivery of lactate-modulating agents for more precise and effective modulation and treatment. Integrating specific lactate-modulating functions in diverse therapeutic nanomedicines may overcome the intrinsic restrictions of different therapeutic modalities by remodeling the pathological microenvironment for achieving enhanced cancer therapy. In this review, the most recent advances in the engineering of functional nanomedicines that can modulate tumor lactate for cancer therapy are summarized and discussed, and the fundamental mechanisms by which lactate modulation benefits various therapeutics are elucidated. Finally, the challenges and perspectives of this emerging strategy in the anti-tumor field are highlighted.

Machine learning based implicit solvent model for aqueous-solution alanine dipeptide molecular dynamics simulations

Inspired by the recent work from Noé and coworkers on the development of machine learning based implicit solvent model for the simulation of solvated peptides [Chen et al., J. Chem. Phys., 2021, 155, 084101], here we report another investigation of the possibility of using machine learning (ML) techniques to "derive" an implicit solvent model directly from explicit solvent molecular dynamics (MD) simulations. For alanine dipeptide, a machine learning potential (MLP) based on the DeepPot-SE representation of the molecule was trained to capture its interactions with its average solvent environment configuration (ASEC). The predicted forces on the solute deviated only by an RMSD of 0.4 kcal mol-1 Å-1 from the reference values, and the MLP-based free energy surface differed from that obtained from explicit solvent MD simulations by an RMSD of less than 0.9 kcal mol-1. Our MLP training protocol could also accurately reproduce combined quantum mechanical molecular mechanical (QM/MM) forces on the quantum mechanical (QM) solute in ASEC environment, thus enabling the development of accurate ML-based implicit solvent models for ab initio-QM MD simulations. Such ML-based implicit solvent models for QM calculations are cost-effective in both the training stage, where the use of ASEC reduces the number of data points to be labelled, and the inference stage, where the MLP can be evaluated at a relatively small additional cost on top of the QM calculation of the solute.

The FMO2 analysis of the ligand-receptor binding energy: the Biscarbene-Gold(I)/DNA G-Quadruplex case study

In this work, the ab initio fragment molecular orbital (FMO) method was applied to calculate and analyze the binding energy of two biscarbene-Au(I) derivatives, [Au(9-methylcaffein-8-ylidene)₂]⁺ and [Au(1,3-dimethylbenzimidazol-2-ylidene)₂]⁺, to the DNA G-Quadruplex structure. The FMO2 binding energy considers the ligand-receptor complex as well as the isolated forms of energy-minimum state of ligand and receptor, providing a better description of ligand-receptor affinity compared with simple pair interaction energies (PIE). Our results highlight important features of the binding process of biscarbene-Au(I) derivatives to DNA G-Quadruplex, indicating that the total deformation-polarization energy and desolvation penalty of the ligands are the main terms destabilizing the binding. The pair interaction energy decomposition analysis (PIEDA) between ligand and nucleobases suggest that the main interaction terms are electrostatic and charge-transfer energies supporting the hypothesis that Au(I) ion can be involved in π-cation interactions further stabilizing the ligand-receptor complex. Moreover, the presence of polar groups on the carbene ring, as C = O, can improve the charge-transfer interaction with K⁺ ion. These findings can be employed to design new powerful biscarbene-Au(I) DNA-G quadruplex binders as promising anticancer drugs. The procedure described in this work can be applied to investigate any ligand-receptor system and is particularly useful when the binding process is strongly characterized by polarization, charge-transfer and dispersion interactions, properly evaluated by ab initio methods.

Best-Practice DFT Protocols for Basic Molecular Computational Chemistry

Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantum-chemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

QCforever: A Quantum Chemistry Wrapper for Everyone to Use in Black-Box Optimization

To obtain observable physical or molecular properties such as ionization potential and fluorescent wavelength with quantum chemical (QC) computation, multi-step computation manipulated by a human is required. Hence, automating the multi-step computational process and making it a black box that can be handled by anybody are important for effective database construction and fast realistic material design through the framework of black-box optimization where machine learning algorithms are introduced as a predictor. Here, we propose a Python library, QCforever, to automate the computation of some molecular properties and chemical phenomena induced by molecules. This tool just requires a molecule file for providing its observable properties, automating the computation process of molecular properties (for ionization potential, fluorescence, etc.) and output analysis for providing their multi-values for evaluating a molecule. Incorporating the tool in black-box optimization, we can explore molecules that have properties we desired within the limitation of QC computation.

Portable Models for Entropy Effects on Kinetic Selectivity

Differences in entropies of competing transition states can direct kinetic selectivity. Understanding and modeling such entropy differences at the molecular level is complicated by the fact that entropy is statistical in nature; i.e., it depends on multiple vibrational states of transition structures, the existence of multiple dynamically accessible pathways past these transition structures, and contributions from multiple transition structures differing in conformation/configuration. The difficulties associated with modeling each of these contributors are discussed here, along with possible solutions, all with an eye toward the development of portable qualitative models of use to experimentalists aiming to design reactions that make use of entropy to control kinetic selectivity.

Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02-0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2-0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes.

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Ligand and Structure-Based In Silico Determination of the Most Promising SARS-CoV-2 nsp16-nsp10 2'-o-Methyltransferase Complex Inhibitors among 3009 FDA Approved Drugs

As a continuation of our earlier work against SARS-CoV-2, seven FDA-approved drugs were designated as the best SARS-CoV-2 nsp16-nsp10 2'-o-methyltransferase (2'OMTase) inhibitors through 3009 compounds. The in silico inhibitory potential of the examined compounds against SARS-CoV-2 nsp16-nsp10 2'-o-methyltransferase (PDB ID: (6W4H) was conducted through a multi-step screening approach. At the beginning, molecular fingerprints experiment with SAM (S-Adenosylmethionine), the co-crystallized ligand of the targeted enzyme, unveiled the resemblance of 147 drugs. Then, a structural similarity experiment recommended 26 compounds. Therefore, the 26 compounds were docked against 2'OMTase to reveal the potential inhibitory effect of seven promising compounds (Protirelin, (1187), Calcium folinate (1913), Raltegravir (1995), Regadenoson (2176), Ertapenem (2396), Methylergometrine (2532), and Thiamine pyrophosphate hydrochloride (2612)). Out of the docked ligands, Ertapenem (2396) showed an ideal binding mode like that of the co-crystallized ligand (SAM). It occupied all sub-pockets of the active site and bound the crucial amino acids. Accordingly, some MD simulation experiments (RMSD, RMSF, Rg, SASA, and H-bonding) have been conducted for the 2'OMTase-Ertapenem complex over 100 ns. The performed MD experiments verified the correct binding mode of Ertapenem against 2'OMTase exhibiting low energy and optimal dynamics. Finally, MM-PBSA studies indicated that Ertapenem bonded advantageously to the targeted protein with a free energy value of -43 KJ/mol. Furthermore, the binding free energy analysis revealed the essential amino acids of 2'OMTase that served positively to the binding. The achieved results bring hope to find a treatment for COVID-19 via in vitro and in vivo studies for the pointed compounds.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

Single Excitation Energies Obtained from the Ensemble "HOMO-LUMO Gap": Exact Results and Approximations

In calculations based on density functional theory, the "HOMO-LUMO gap" (difference between the highest occupied and lowest unoccupied molecular orbital energies) is often used as a low-cost, ad hoc approximation for the lowest excitation energy. Here we show that a simple correction based on rigorous ensemble density functional theory makes the HOMO-LUMO gap exact in principle and significantly more accurate in practice. The introduced perturbative ensemble density functional theory approach predicts different and useful values for singlet-singlet and singlet-triplet excitations, using semilocal and hybrid approximations. Excitation energies are similar in quality to time-dependent density functional theory, especially at high fractions of exact exchange. The approach therefore offers an easy-to-implement and low-cost route to robust prediction of molecular excitation energies.

Poisoning density functional theory with benchmark sets of difficult systems

Large benchmark sets like GMTKN55 [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184] let us analyse the performance of density functional theory over a diverse range of systems and bonding types. However, assessing over a large and diverse set can miss cases where approaches fail badly, and can give a misleading sense of security. To this end we introduce a series of 'poison' benchmark sets, P30-5, P30-10 and P30-20, comprising systems with up to 5, 10 and 20 atoms, respectively. These sets represent the most difficult-to-model systems in GMTKN55. We expect them to be useful in developing new approximations, identifying weak points in existing ones, and to aid in selecting appropriate DFAs for computational studies involving difficult physics, e.g. catalysis.

CalcUS: An Open-Source Quantum Chemistry Web Platform

Computational chemistry is an increasingly active field due to the improvement of computing resources and theoretical tools. However, its use remains usually limited to technically inclined users due to the technical challenges of preparing, launching, and analyzing calculations. In this context, we have developed CalcUS, an open-source platform to streamline quantum chemistry studies. Its objective is to democratize access to computational chemistry by providing a user-friendly web interface to simplify running and analyzing quantum mechanical calculations. It is freely available, expandable, and customizable. It promotes connectivity to multiple software packages and algorithms, thus providing state-of-the-art techniques to all practitioners. We propose CalcUS as a standalone tool and infrastructure to support other open-source packages.

Reliable prediction of association (free) energies of supramolecular complexes with heavy main group elements – the HS13L benchmark set

We introduce a set of 13 supramolecular complexes featuring diverse non-covalent interactions with heavy main group elements (Zn, As, Se, Te, Br, I), high charges (−2 up to +4), and large systems with up to 266 atoms (HS13L).

Assessing Density Functional Theory for Chemically Relevant Open-Shell Transition Metal Reactions

Due to the principle lack of systematic improvement possibilities of density functional theory, careful assessment of the performance of density functional approximations (DFAs) on well-designed benchmark sets, for example, for reaction energies and barrier heights, is crucial. While main-group chemistry is well covered by several available sets, benchmark data for transition metal chemistry is sparse. This is especially the case for larger, chemically relevant molecules. Addressing this issue, we recently introduced the MOR41 benchmark which covers chemically relevant reactions of closed-shell complexes. In this work, we extend these efforts to single-reference open-shell systems and introduce the "reactions of open-shell single-reference transition metal complexes" (ROST61) benchmark set. ROST61 includes accurate coupled-cluster reference values for 61 reaction energies with a mean reaction energy of -42.8 kcal mol^-1. Complexes with 13-93 atoms covering 20 d-block elements are included, but due to the restriction to single-reference open-shell systems, important elements such as iron or platinum could not be taken into account, or only to a small extent. We assess the performance of 31 DFAs in combination with three London dispersion (LD) correction schemes. Further, DFT-based composite methods, MP2, and a few semiempirical quantum chemical methods are evaluated. Consistent with the results for the MOR41 closed-shell benchmark, we find that the ordering of DFAs according to Jacob's ladder is preserved and that adding an LD correction is crucial, clearly improving almost all tested methods. The recently introduced r²SCAN-3c composite method stands out with a remarkable mean absolute deviation (MAD) of only 2.9 kcal mol^-1, which is surpassed only by hybrid DFAs with low amounts of Fock exchange (e.g., 2.3 kcal mol^-1 for TPSS0-D4/def2-QZVPP) and double-hybrid (DH) DFAs but at a significantly higher computational cost. The lowest MAD of only 1.6 kcal mol^-1 is obtained with the DH DFA PWPB95-D4 in the def2-QZVPP basis set approaching the estimated accuracy of the reference method. Overall, the ROST61 set adds important reference data to a sparsely sampled but practically relevant area of chemistry. At this point, it provides valuable orientation for the application and development of new DFAs and electronic structure methods in general.

Melding of Experiment and Theory Illuminates Mechanisms of Metal-Catalyzed Rearrangements: Computational Approaches and Caveats

This review summarizes approaches and caveats in computational modeling of transition-metal-catalyzed sigmatropic rearrangements involving carbene transfer. We highlight contemporary examples of combined synthetic and theoretical investigations that showcase the synergy achievable by integrating experiment and theory.

1 Introduction

2 Mechanistic Models

3 Theoretical Approaches and Caveats

3.1 Recommended Computational Tools

3.2 Choice of Functional and Basis Set

3.3 Conformations and Ligand-Binding Modes

3.4 Solvation

4 Synergy of Experiment and Theory – Case Studies

4.1 Metal-Bound or Free Ylides?

4.2 Conformations and Ligand-Binding Modes of Paddlewheel Complexes

4.3 No Metal, Just Light

4.4 How To ‘Cope’ with Nonstatistical Dynamic Effects

5 Outlook

[Ni(NHC)2 ] as a Scaffold for Structurally Characterized trans [H-Ni-PR2 ] and trans [R2 P-Ni-PR2 ] Complexes

The addition of PPh2 H, PPhMeH, PPhH2 , P(para-Tol)H2 , PMesH2 and PH3 to the two-coordinate Ni0 N-heterocyclic carbene species [Ni(NHC)2 ] (NHC=IiPr2 , IMe4 , IEt2 Me2 ) affords a series of mononuclear, terminal phosphido nickel complexes. Structural characterisation of nine of these compounds shows that they have unusual trans [H-Ni-PR2 ] or novel trans [R2 P-Ni-PR2 ] geometries. The bis-phosphido complexes are more accessible when smaller NHCs (IMe4 >IEt2 Me2 >IiPr2 ) and phosphines are employed. P-P activation of the diphosphines R2 P-PR2 (R2 =Ph2 , PhMe) provides an alternative route to some of the [Ni(NHC)2 (PR2 )2 ] complexes. DFT calculations capture these trends with P-H bond activation proceeding from unconventional phosphine adducts in which the H substituent bridges the Ni-P bond. P-P bond activation from [Ni(NHC)2 (Ph2 P-PPh2 )] adducts proceeds with computed barriers below 10 kcal mol-1 . The ability of the [Ni(NHC)2 ] moiety to afford isolable terminal phosphido products reflects the stability of the Ni-NHC bond that prevents ligand dissociation and onward reaction.

Data Science Meets Physical Organic Chemistry

ConspectusAt the heart of synthetic chemistry is the holy grail of predictable catalyst design. In particular, researchers involved in reaction development in asymmetric catalysis have pursued a variety of strategies toward this goal. This is driven by both the pragmatic need to achieve high selectivities and the inability to readily identify why a certain catalyst is effective for a given reaction. While empiricism and intuition have dominated the field of asymmetric catalysis since its inception, enantioselectivity offers a mechanistically rich platform to interrogate catalyst-structure response patterns that explain the performance of a particular catalyst or substrate.In the early stages of an asymmetric reaction development campaign, the overarching mechanism of the reaction, catalyst speciation, the turnover limiting step, and many other details are unknown or posited based on related reactions. Considering the unclear details leading to a successful reaction, initial enantioselectivity data are often used to intuitively guide the ultimate direction of optimization. However, if the conditions of the Curtin-Hammett principle are satisfied, then measured enantioselectivity can be directly connected to the ensemble of diastereomeric transition states (TSs) that lead to the enantiomeric products, and the associated free energy difference between competing TSs (ΔΔG⧧ = -RT ln[(S)/(R)], where (S) and (R) represent the concentrations of the enantiomeric products). We, and others, speculated that this important piece of information can be leveraged to guide reaction optimization in a quantitative way.Although traditional linear free energy relationships (LFERs), such as Hammett plots, have been used to illuminate important mechanistic features, we sought to develop data science derived tools to expand the power of LFERs in order to describe complex reactions frequently encountered in modern asymmetric catalysis. Specifically, we investigated whether enantioselectivity data from a reaction can be quantitatively connected to the attributes of reaction components, such as catalyst and substrate structural features, to harness data for asymmetric catalyst design.In this context, we developed a workflow to relate computationally derived features of reaction components to enantioselectivity using data science tools. The mathematical representation of molecules can incorporate many aspects of a transformation, such as molecular features from substrate, product, catalyst, and proposed transition states. Statistical models relating these features to reaction outputs can be used for various tasks, such as performance prediction of untested molecules. Perhaps most importantly, statistical models can guide the generation of mechanistic hypotheses that are embedded within complex patterns of reaction responses. Overall, merging traditional physical organic experiments with statistical modeling techniques creates a feedback loop that enables both evaluation of multiple mechanistic hypotheses and future catalyst design. In this Account, we highlight the evolution and application of this approach in the context of a collaborative program based on chiral phosphoric acid catalysts (CPAs) in asymmetric catalysis.

Integration of theory, simulation, artificial intelligence and virtual reality: a four-pillar approach for reconciling accuracy and interpretability in computational spectroscopy

The established pillars of computational spectroscopy are theory and computer based simulations. Recently, artificial intelligence and virtual reality are becoming the third and fourth pillars of an integrated strategy for the investigation of complex phenomena. The main goal of the present contribution is the description of some new perspectives for computational spectroscopy, in the framework of a strategy in which computational methodologies at the state of the art, high-performance computing, artificial intelligence and virtual reality tools are integrated with the aim of improving research throughput and achieving goals otherwise not possible. Some of the key tools (e.g., continuous molecular perception model and virtual multifrequency spectrometer) and theoretical developments (e.g., non-periodic boundaries, joint variational-perturbative models) are shortly sketched and their application illustrated by means of representative case studies taken from recent work by the authors. Some of the results presented are already well beyond the state of the art in the field of computational spectroscopy, thereby also providing a proof of concept for other research fields.

High-Throughput Non-targeted Chemical Structure Identification Using Gas-Phase Infrared Spectra

The high-throughput identification of unknown metabolites in biological samples remains challenging. Most current non-targeted metabolomics studies rely on mass spectrometry, followed by computational methods that rank thousands of candidate structures based on how closely their predicted mass spectra match the experimental mass spectrum of an unknown. We reasoned that the infrared (IR) spectra could be used in an analogous manner and could add orthologous structure discrimination; however, this has never been evaluated on large data sets. Here, we present results of a high-throughput computational method for predicting IR spectra of candidate compounds obtained from the PubChem database. Predicted spectra were ranked based on their similarity to gas-phase experimental IR spectra of test compounds obtained from the NIST. Our computational workflow (IRdentify) consists of a fast semiempirical quantum mechanical method for initial IR spectra prediction, ranking, and triaging, followed by a final IR spectra prediction and ranking using density functional theory. This approach resulted in the correct identification of 47% of 258 test compounds. On average, there were 2152 candidate structures evaluated for each test compound, giving a total of approximately 555,200 candidate structures evaluated. We discuss several variables that influenced the identification accuracy and then demonstrate the potential application of this approach in three areas: (1) combining IR and mass spectra rankings into a single composite rank score, (2) identifying the precursor and fragment ions using cryogenic ion vibrational spectroscopy, and (3) the incorporation of a trimethylsilyl derivatization step to extend the method compatibility to less-volatile compounds. Overall, our results suggest that matching computational with experimental IR spectra is a potentially powerful orthogonal option for adding significant high-throughput chemical structure discrimination when used with other non-targeted chemical structure identification methods.

Computational Tools to Rationalize and Predict the Self-Assembly Behavior of Supramolecular Gels

Supramolecular gels form a class of soft materials that has been heavily explored by the chemical community in the past 20 years. While a multitude of experimental techniques has demonstrated its usefulness when characterizing these materials, the potential value of computational techniques has received much less attention. This review aims to provide a complete overview of studies that employ computational tools to obtain a better fundamental understanding of the self-assembly behavior of supramolecular gels or to accelerate their development by means of prediction. As such, we hope to stimulate researchers to consider using computational tools when investigating these intriguing materials. In the concluding remarks, we address future challenges faced by the field and formulate our vision on how computational methods could help overcoming them.

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.

Accurate singlet-triplet gaps in biradicals via the spin averaged anti-Hermitian contracted Schrödinger equation

The accurate description of biradical systems, and in particular the resolution of their singlet-triplet gaps, has long posed a major challenge to the development of electronic structure theories. Biradicaloid singlet ground states are often marked by strong correlation and, hence, may not be accurately treated by mainstream, single-reference methods such as density functional theory or coupled cluster theory. The anti-Hermitian contracted Schrödinger equation (ACSE), whose fundamental quantity is the two-electron reduced density matrix rather than the N-electron wave function, has previously been shown to account for both dynamic and strong correlations when seeded with a strongly correlated guess from a complete active space (CAS) calculation. Here, we develop a spin-averaged implementation of the ACSE, allowing it to treat higher multiplicity states from the CAS input without additional state preparation. We apply the spin-averaged ACSE to calculate the singlet-triplet gaps in a set of small main group biradicaloids, as well as the organic four-electron biradicals trimethylenemethane and cyclobutadiene, and naphthalene, benchmarking the results against other state-of-the-art methods reported in the literature.