Low-Cost Quantum Chemical Methods for Noncovalent Interactions

Probing Noncovalent Interactions by Fast Magic-Angle Spinning NMR at 100 kHz and More

Noncovalent interactions are the basis for a large number of chemical and biological molecular-recognition processes, such as those occurring in supramolecular chemistry, catalysis, solid-state reactions in mechanochemistry, protein folding, protein-nucleic acid binding, and biomolecular phase separation processes. In this perspective article, some recent developments in probing noncovalent interactions by proton-detected solid-state Nuclear Magnetic Resonance (NMR) spectroscopy at Magic-Angle Spinning (MAS) frequencies of 100 kHz and more are reviewed. The development of MAS rotors with decreasing outer diameters, combined with the development of superconducting magnets operating at high static magnetic-field strengths up to 28.2 T (1200 MHz proton Larmor frequency) improves resolution and sensitivity in proton-detected solid-state NMR, which is the fundamental requirement for shedding light on noncovalent interactions in solids. The examples reported in this article range from protein-nucleic acid binding in large ATP-fueled motor proteins to a hydrogen-π interaction in a calixarene-lanthanide complex.

Creation of spin switching in graphene oxide-based hybrid film materials with an anionic Fe(III) 5Cl-salicyaldehyde-thiosemicarbazone complex

The present article describes the synthesis of hybrid composite film materials formed during the self-assembly process through non-covalent interactions of graphene oxide (GO) nanosheets with salt 1, represented by an anionic spin-crossover complex [FeIII(5Cl-thsa)2]- (5Cl-thsa - 5-chlorosalicylaldehyde thiosemicarbazone) and the organic tetraethylammonium cation [Et4N]+. The insertion of the salt 1 molecules into the interlayer space of GO nanosheets with the subsequent formation of a hybrid material GO-1 was observed. The film of the hybrid material GO-1 was characterized by scanning electron and confocal laser microscopy, EDX and XPS analysis, IR, Raman and 57Fe Mössbauer spectroscopy, dc magnetic measurements, and powder X-ray diffraction. Comparison of the magnetic properties of salt 1 and a film of the hybrid material GO-1 demonstrated a significant influence of the GO nanosheets matrix on the completeness of spin transition and showed a slight shift of the hysteresis loop by 1 K in the temperature range of 200-230 K. DFT calculations showed an important role of the organic cation [Et4N]+ in the process of adsorption of the spin-crossover anion [FeIII(5Cl-thsa)2]- on the GO nanosheet surface.

Toward Post-Hartree-Fock Accuracy for Protein-Ligand Affinities Using the Molecules-in-Molecules Fragmentation-Based Method

The complexity and size of large molecular systems, such as protein-ligand complexes, pose computational challenges for accurate post-Hartree-Fock calculations. This study delivers a thorough benchmarking of the Molecules-in-Molecules (MIM) method, presenting a clear and accessible strategy for layer/theory selections in post-Hartree-Fock computations on substantial molecular systems, notably protein-ligand complexes. An approach is articulated, enabling augmented computational efficiency by strategically canceling out common subsystem energy terms between complexes and proteins within the supermolecular equation. Employing DLPNO-based post-Hartree-Fock methods in conjunction with the three-layer MIM method (MIM3), this study demonstrates the achievement of protein-ligand binding energies with remarkable accuracy (errors <1 kcal mol-1), while significantly reducing computational costs. Furthermore, noteworthy correlations between theoretically computed interaction energies and their experimental equivalents were observed, with R2 values of approximately 0.90 and 0.78 for CDK2 and BZT-ITK sets, respectively, thus validating the efficacy of the MIM method in calculating binding energies. By highlighting the crucial role of diffuse or small Pople-style basis sets in the middle layer for reducing energy errors, this work provides valuable insights and practical methodologies for interaction energy computations in large molecular complexes and opens avenues for their application across a diverse range of molecular systems.

Encapsulation in Charged Droplets Generates Distorted Host-Guest Complexes

The ability of various hydrogen-bonded resorcinarene-based capsules to bind α,ω-alkylbisDABCOnium (DnD) guests of different lengths was investigated in solution and in the gas-phase. While no host-guest interactions were detected in solution, encapsulation could be achieved in the charged droplets formed during electrospray ionisation (ESI). This included guests, which are far too long in their most stable conformation to fit inside the cavity of the capsules. A combination of three mass spectrometric techniques, namely, collision-induced dissociation, hydrogen/deuterium exchange, and ion-mobility mass spectrometry, together with computational modelling allow us to determine the binding mode of the DnD guests inside the cavity of the capsules. Significant distortions of the guest into horseshoe-like arrangements are required to optimise cation-π interactions with the host, which also adopt distorted geometries with partially open hydrogen-bonding seams when binding longer guests. Such quasi "spring-loaded" capsules can form in the charged droplets during the ESI process as there is no competition between guest encapsulation and ion pair formation with the counterions that preclude encapsulation in solution. The encapsulation complexes are sufficiently stable in the gas-phase - even when strained - because non-covalent interactions significantly strengthen in the absence of solvent.

Structural and dynamic effects of pseudouridine modifications on noncanonical interactions in RNA

Pseudouridine is the most frequently naturally occurring RNA modification, found in all classes of biologically functional RNAs. Compared to uridine, pseudouridine contains an additional hydrogen bond donor group and is therefore widely regarded as a structure stabilizing modification. However, the effects of pseudouridine modifications on the structure and dynamics of RNAs have so far only been investigated in a limited number of different structural contexts. Here, we introduced pseudouridine modifications into the U-turn motif and the adjacent U:U closing base pair of the neomycin-sensing riboswitch (NSR)-an extensively characterized model system for RNA structure, ligand binding, and dynamics. We show that the effects of replacing specific uridines with pseudouridines on RNA dynamics crucially depend on the exact location of the replacement site and can range from destabilizing to locally or even globally stabilizing. By using a combination of NMR spectroscopy, MD simulations and QM calculations, we rationalize the observed effects on a structural and dynamical level. Our results will help to better understand and predict the consequences of pseudouridine modifications on the structure and function of biologically important RNAs.

Second-Shell Residues Contribute to Catalysis by Predominately Preorganizing the Apo State in PafA

Residues beyond the first coordination shell are often observed to make considerable cumulative contributions in enzymes. Due to typically indirect perturbations of multiple physicochemical properties of the active site, however, their individual and specific roles in enzyme catalysis and disease-causing mutations remain difficult to predict and understand at the molecular level. Here we analyze the contributions of several second-shell residues in phosphate-irrepressible alkaline phosphatase of flavobacterium (PafA), a representative system as one of the most efficient enzymes. By adopting a multifaceted approach that integrates quantum-mechanical/molecular-mechanical free energy computations, molecular-mechanical molecular dynamics simulations, and density functional theory cluster model calculations, we probe the rate-limiting phosphoryl transfer step and structural properties of all relevant enzyme states. In combination with available experimental data, our computational results show that mutations of the studied second-shell residues impact catalytic efficiency mainly by perturbation of the apo state and therefore substrate binding, while they do not affect the ground state or alter the nature of phosphoryl transfer transition state significantly. Several second-shell mutations also modulate the active site hydration level, which in turn influences the energetics of phosphoryl transfer. These mechanistic insights also help inform strategies that may improve the efficiency of enzyme design and engineering by going beyond the current focus on the first coordination shell.

Benchmarking two-body contributions to crystal lattice energies and a range-dependent assessment of approximate methods

Using the many-body expansion to predict crystal lattice energies (CLEs), a pleasantly parallel process, allows for flexibility in the choice of theoretical methods. Benchmark-level two-body contributions to CLEs of 23 molecular crystals have been computed using interaction energies of dimers with minimum inter-monomer separations (i.e., closest contact distances) up to 30 Å. In a search for ways to reduce the computational expense of calculating accurate CLEs, we have computed these two-body contributions with 15 different quantum chemical levels of theory and compared these energies to those computed with coupled-cluster in the complete basis set (CBS) limit. Interaction energies of the more distant dimers are easier to compute accurately and several of the methods tested are suitable as replacements for coupled-cluster through perturbative triples for all but the closest dimers. For our dataset, sub-kJ mol^-1 accuracy can be obtained when calculating two-body interaction energies of dimers with separations shorter than 4 Å with coupled-cluster with single, double, and perturbative triple excitations/CBS and dimers with separations longer than 4 Å with MP2.5/aug-cc-pVDZ, among other schemes, reducing the number of dimers to be computed with coupled-cluster by as much as 98%.

Minimal Basis Set Hartree-Fock Corrected with Atom-Centered Potentials for Molecular Crystal Modeling and Crystal Structure Prediction

Crystal structure prediction (CSP), determining the experimentally observable structure of a molecular crystal from the molecular diagram, is an important challenge with technologically relevant applications in materials manufacturing and drug design. For the purpose of screening the randomly generated candidate crystal structures, CSP protocols require energy ranking methods that are fast and can accurately capture the small energy differences between molecular crystals. In addition, a good ranking method should also produce accurate equilibrium geometries, both intramolecular and intermolecular. In this article, we explore the combination of minimal-basis-set Hartree-Fock (HF) with atom-centered potentials (ACPs) as a method for modeling the structure and energetics of molecular crystals. The ACPs are developed for the H, C, N, and O atoms and fitted to a set of reference data at the B86bPBE-XDM level in order to mitigate basis-set incompleteness and missing correlation. In particular, ACPs are developed in combination with two methods: HF-D3/MINIs and HF-3c. The application of ACPs greatly improves the performance of HF-D3/MINIs for lattice energies, crystal energy differences, energy-volume and energy-strain relations, and crystal geometries. In the case of HF-3c, the improvement in the crystal energy differences is much smaller than in HF-D3/MINIs, but lattice energies and particularly crystal geometries are considerably better when ACPs are used. The resulting methods may be useful for CSP but also for quick calculation of molecular crystal lattice energies and geometries.

ULYSSES: An Efficient and Easy to Use Semiempirical Library for C+

We introduce ULYSSES, a user-friendly and robust C++ library for semiempirical quantum chemical calculations. In its current version, ULYSSES is equipped with a large set of different semiempirical models, most of which are based on the Neglect of Diatomic Differential Overlap (NDDO) approximation. Empirical corrections for dispersion and hydrogen bonding are available for most methods, so that higher quality is achieved in the calculation of energies of nonbonded complexes. The library is furthermore equipped with geometry optimization, as well as modules for calculating molecular properties of general interest. Ideal gas thermodynamics is available and allows single structure as well as conformer (multistructure) averaged properties to be calculated. We offer the possibility to use several vibrational partition functions according to the nature of interactions being studied: for covalent systems, the traditional harmonic oscillator approximation is available; for nonbonded complexes, we systematically extended the partition function proposed by Grimme for all thermodynamic functions. The library is also capable of running Born-Oppenheimer molecular dynamics.

Recognition in the Domain of Molecular Chirality: From Noncovalent Interactions to Separation of Enantiomers

It is not a coincidence that both chirality and noncovalent interactions are ubiquitous in nature and synthetic molecular systems. Noncovalent interactivity between chiral molecules underlies enantioselective recognition as a fundamental phenomenon regulating life and human activities. Thus, noncovalent interactions represent the narrative thread of a fascinating story which goes across several disciplines of medical, chemical, physical, biological, and other natural sciences. This review has been conceived with the awareness that a modern attitude toward molecular chirality and its consequences needs to be founded on multidisciplinary approaches to disclose the molecular basis of essential enantioselective phenomena in the domain of chemical, physical, and life sciences. With the primary aim of discussing this topic in an integrated way, a comprehensive pool of rational and systematic multidisciplinary information is provided, which concerns the fundamentals of chirality, a description of noncovalent interactions, and their implications in enantioselective processes occurring in different contexts. A specific focus is devoted to enantioselection in chromatography and electromigration techniques because of their unique feature as "multistep" processes. A second motivation for writing this review is to make a clear statement about the state of the art, the tools we have at our disposal, and what is still missing to fully understand the mechanisms underlying enantioselective recognition.

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.

The PM6-FGC Method: Improved Corrections for Amines and Amides

Recently, we reported a new approach to develop pairwise analytical corrections to improve the description of noncovalent interactions, by approximate methods of electronic structures, such as semiempirical quantum mechanical (SQM) methods. In particular, and as a proof of concept, we used the PM6 Hamiltonian and we named the method PM6-FGC, where the FGC acronym, corresponding to Functional Group Corrections, emphasizes the idea that the corrections work for specific functional groups rather than for individual atom pairs. The analytical corrections were derived from fits to B3LYP-D3/def2-TZVP (reference). PM6 interaction energy differences, evaluated for a reduced set of small bimolecular complexes, were chosen as representatives of saturated hydrocarbons, carboxylic, amine and, tentatively, amide functional groups. For the validation, the method was applied to several complexes of well-known databases, as well as to complexes of diglycine and dialanine, assuming the transferability of amine group corrections to amide groups. The PM6-FGC method showed great potential but revealed significant inaccuracies for the description of some interactions involving the –NH₂ group in amines and amides, caused by the inadequate selection of the model compound used to represent these functional groups (an NH₃ molecule). In this work, methylamine and acetamide are used as representatives of amine and amide groups, respectively. This new selection leads to significant improvements in the calculation of noncovalent interactions in the validation set.

Behavior of counterpoise correction in many-body molecular clusters of organic compounds: Hartree-Fock interaction energy perspective

The counterpoise (CP) correction by Boys and Bernardi has been well accepted as a reliable strategy to account for basis set superposition error (BSSE) in intermolecular complexes. The behavior of the CP correction was thoroughly studied in individual molecules of molecular complexes. This work studies the performance of the CP correction in many‐body clusters including three‐body clusters of organic compounds in the 3B‐69 dataset. Additionally, we used crystal structures of polymorphs of benzene, aspirin, and oxalyl dihydrazide (ODH) to construct a many‐body cluster dataset, abbreviated as the MBC‐36 dataset, consisting of two, four and eight molecules, and 16 molecules in the case of benzene. A series of Dunning's basis sets—cc‐pXZ and aug‐cc‐pXZ (X = D and T)—were used to predict CP‐corrected Hartree–Fock (HF) interaction energies of the 3B‐69 and MBC‐36 datasets. The CP‐corrected interaction energies were found to be basis‐set independent, whereas the non‐CP corrected interaction energies were found not to a follow a smooth exponential fitting as previously found for electronic energies of individual molecules. This observation was attributed to the presence of non‐additive induction forces in some clusters. Two 2 × 2 × 2 supercells of benzene polymorphs were constructed to explore the local nature of BSSE effects. A cut‐off radius of 10 Å was demonstrated to be sufficient to fully recover these effects. Although the behavior of CP correction was found to be non‐conventional in many‐body clusters of organic compounds, the use of a small basis set such as cc‐pVDZ showed excellent performance in the prediction of HF interaction energies.

Reduced-cost supercell approach for computing accurate phonon density of states in organic crystals

Phonon contributions to organic crystal structures and thermochemical properties can be significant, but computing a well-converged phonon density of states with lattice dynamics and periodic density functional theory (DFT) is often computationally expensive due to the need for large supercells. Using semi-empirical methods like density functional tight binding (DFTB) instead of DFT can reduce the computational costs dramatically, albeit with noticeable reductions in accuracy. This work proposes approximating the phonon density of states via a relatively inexpensive DFTB supercell treatment of the phonon dispersion that is then corrected by shifting the individual phonon modes according to the difference between the DFT and DFTB phonon frequencies at the Γ-point. The acoustic modes are then computed at the DFT level from the elastic constants. In several small-molecule crystal test cases, this combined approach reproduces DFT thermochemistry with kJ/mol accuracy and 1-2 orders of magnitude less computational effort. Finally, this approach is applied to computing the free energy differences between the five crystal polymorphs of oxalyl dihydrazide.

A minimalistic hydrolase based on co-assembled cyclic dipeptides

The self-assembly of small peptides into larger aggregates is an important process for the fundamental understanding of abiogenesis. In this article we demonstrate that blends of cyclic dipeptides (2,5-diketopiperazines - DKPs) bearing either histidine or cysteine in combination with a lipophilic amino acid form highly stable aggregates in aqueous solution with esterase-like activity. We demonstrate that the catalytic activity is based on an intermolecular cooperative behavior between histidine and cysteine. A high control of the molecular arrangement of the peptide assemblies was gained by C-H-π interactions between Phe and Leu or Val sidechains, resulting in a significant increase in catalytic activity. These interactions were strongly supported by Hartree-Fock calculations and finally confirmed via1H-NMR HRMAS NOE spectroscopy.

CO2 Capture on Functionalized Calixarenes: A Computational Study

High carbon emissions have shown a strong correlation with rising global temperatures as the world's climate undergoes a dramatic shift. Work to mitigate the potential damage using materials such as metal-organic frameworks (MOFs), covalent organic frameworks (COFs), and polymer membranes (PMs) has proven successful in small-scale approaches; however, research is still being performed to enhance the capabilities of these materials for use at an industrial scale. One strategy for increasing performance is to embed these materials with CO₂-philic molecules, which enhance selective binding over other gases. Calixarenes are promising candidates due to their large chalice shape, which allows for the possibility to bind multiple CO₂ molecules per site. In this study, a dataset including 40 functionalized calixarene structures and one unfunctionalized (bare) calixarene was constructed with an automated, high-throughput structure generation through directed modifications to a molecular scaffold. A conformational search based on molecular mechanics allowed the faster determination of optimal binding energies for a vast array of chemical functional groups with less computational effort. Density functional theory and symmetry-adapted perturbation theory calculations were performed for the exploration of their interactions with CO₂. Our work has identified new organic cages with increased CO₂-philicity. In four cases, CO₂ binding is stronger than 9.0 kcal/mol and very close to the targets set by previous studies. The nature of the noncovalent interactions for these cases is analyzed and discussed. Conclusions from this study can aid synthetic efforts for the next generation of functional materials.

Revisiting the Potential Energy Surface of the Stacked Cytosine Dimer: FNO-CCSD(T) Interaction Energies, SAPT Decompositions, and Benchmarking

Nucleobase stacking interactions are crucial for the stability of nucleic acids. This study investigates base stacking energies of the cytosine homodimer in different configurations, including intermolecular separation plots, detailed twist dependence, and displaced structures. Highly accurate ab initio quantum chemical single point energies using an energy function based on MP2 complete basis set extrapolation ([6 → 7]ZaPa-NR) and a CCSD(T)/cc-pVTZ-F12 high-level correction are presented as new reference data, providing the most accurate stacking energies of nucleobase dimers currently available. Accurate SAPT2+(3)δMP2 energy decomposition is used to obtain detailed insights into the nature of base stacking interactions at varying vertical distances and twist values. The ab initio symmetry adapted perturbation theory (SAPT) energy decomposition suggests that the base stacking originates from an intricate interplay between dispersion attraction, short-range exchange-repulsion, and Coulomb interaction. The interpretation of the SAPT data is a complex issue as key energy terms vary substantially in the region of optimal (low energy) base stacking geometries. Thus, attempts to highlight one leading stabilizing SAPT base stacking term may be misleading and the outcome strongly depends on the used geometries within the range of geometries sampled in nucleic acids upon thermal fluctuations. Modern dispersion-corrected density functional theory (among them DSD-BLYP-D3, ωB97M-V, and ωB97M-D3BJ) is benchmarked and often reaches up to spectroscopic accuracy (below 1 kJ/mol). The classical AMBER force field is benchmarked with multiple different sets of point-charges (e.g. HF, DFT, and MP2-based) and is found to produce reasonable agreement with the benchmark data.

Analysis of Density Functional Tight Binding with Natural Bonding Orbitals

The description of chemical bonding by the density functional tight binding (DFTB) model is analyzed using natural bonding orbitals (NBOs) and compared to results from density functional theory (B3LYP/aug-cc-pVTZ) calculations. Several molecular systems have been chosen to represent fairly diverse bonding scenarios that include standard covalent bonds, hypervalent interactions, multicenter bonds, metal-ligand interactions (with and without the pseudo-Jahn-Teller effect), and through-space donor-acceptor interactions. Overall, the results suggest that DFTB3/3OB provides physically sound descriptions for the different bonding scenarios analyzed here, as reflected by the general agreement between DFTB3 and B3LYP NBO properties, such as the nature of the NBOs, the magnitudes of natural charges and bond orders, and the dominant donor-acceptor interactions. The degree of ligand-to-metal charge transfer and the ionic nature of pentavalent phosphate are overestimated, likely reflecting the minimal-basis nature of DFTB3/3OB. Moreover, certain orbital interactions, such as geminal interactions, are observed to be grossly overestimated by DFTB3 for hypervalent phosphate and several transition metal compounds that involve copper and nickel. The study indicates that results from NBO analysis can be instructive for identifying electronic structure descriptions at the approximate quantum-mechanical level that require improvement and thus for guiding the systematic improvement of these methods.

In silico identification of genetic mutations conferring resistance to acetohydroxyacid synthase inhibitors: A case study of Kochia scoparia

Mutations that confer herbicide resistance are a primary concern for herbicide-based chemical control of invasive plants and are often under-characterized structurally and functionally. As the outcome of selection pressure, resistance mutations usually result from repeated long-term applications of herbicides with the same mode of action and are discovered through extensive field trials. Here we used acetohydroxyacid synthase (AHAS) of Kochia scoparia (KsAHAS) as an example to demonstrate that, given the sequence of a target protein, the impact of genetic mutations on ligand binding could be evaluated and resistance mutations could be identified using a biophysics-based computational approach. Briefly, the 3D structures of wild-type (WT) and mutated KsAHAS-herbicide complexes were constructed by homology modeling, docking and molecular dynamics simulation. The resistance profile of two AHAS-inhibiting herbicides, tribenuron methyl and thifensulfuron methyl, was obtained by estimating their binding affinity with 29 KsAHAS (1 WT and 28 mutated) using 6 molecular mechanical (MM) and 18 hybrid quantum mechanical/molecular mechanical (QM/MM) methods in combination with three structure sampling strategies. By comparing predicted resistance with experimentally determined resistance in the 29 biotypes of K. scoparia field populations, we identified the best method (i.e., MM-PBSA with single structure) out of all tested methods for the herbicide-KsAHAS system, which exhibited the highest accuracy (up to 100%) in discerning mutations conferring resistance or susceptibility to the two AHAS inhibitors. Our results suggest that the in silico approach has the potential to be widely adopted for assessing mutation-endowed herbicide resistance on a case-by-case basis.

PEPCONF, a diverse data set of peptide conformational energies

We present an extensive and diverse database of peptide conformational energies. Our database contains five different classes of model geometries: dipeptides, tripeptides, and disulfide-bridged, bioactive, and cyclic peptides. In total, the database consists of 3775 conformational energy data points and 4530 conformer geometries. All the reference energies have been calculated at the LC-ωPBE-XDM/aug-cc-pVTZ level of theory, which is shown to yield conformational energies with an accuracy in the order of tenths of a kcal/mol when compared to complete-basis-set coupled-cluster reference data. The peptide conformational data set (PEPCONF) is presented as a high-quality reference set for the development and benchmarking of molecular-mechanics and semi-empirical electronic structure methods, which are the most commonly used techniques in the modeling of medium to large proteins.

Understanding non-covalent interactions in larger molecular complexes from first principles

Non-covalent interactions pervade all matter and play a fundamental role in layered materials, biological systems, and large molecular complexes. Despite this, our accumulated understanding of non-covalent interactions to date has been mainly developed in the tens-of-atoms molecular regime. This falls considerably short of the scales at which we would like to understand energy trends, structural properties, and temperature dependencies in materials where non-covalent interactions have an appreciable role. However, as more reference information is obtained beyond moderately sized molecular systems, our understanding is improving and we stand to gain pertinent insights by tackling more complex systems, such as supramolecular complexes, molecular crystals, and other soft materials. In addition, accurate reference information is needed to provide the drive for extending the predictive power of more efficient workhorse methods, such as density functional approximations that also approximate van der Waals dispersion interactions. In this perspective, we discuss the first-principles approaches that have been used to obtain reference interaction energies for beyond modestly sized molecular complexes. The methods include quantum Monte Carlo, symmetry-adapted perturbation theory, non-canonical coupled cluster theory, and approaches based on the random-phase approximation. By considering the approximations that underpin each method, the most accurate theoretical references for supramolecular complexes and molecular crystals to date are ascertained. With these, we also assess a handful of widely used exchange-correlation functionals in density functional theory. The discussion culminates in a framework for putting into perspective the accuracy of high-level wavefunction-based methods and identifying future challenges.

Crystal-energy landscapes of active pharmaceutical ingredients using composite approaches

Composite methods employing dispersion-corrected DFT consistently identify experimentally isolated polymorphs as the lowest-energy crystal structures of common APIs.

Competing Dispersive Interactions: From Small Energy Differences to Large Structural Effects in Methyl Jasmonate and Zingerone

Modern structural studies of biologically relevant molecules require an exhaustive interplay between experiment and theory. In this work, we present two examples where a poor choice of the theoretical method led to a misinterpretation of experimental results. We do that by performing a rotational spectroscopy study on two large and flexible biomolecules: methyl jasmonate and zingerone. The results show the enormous potential of rotational spectroscopy as a benchmark to evaluate the performance of theoretical methods.

Analysis of Phosphoryl-Transfer Enzymes with QM/MM Free Energy Simulations

We discuss the application of quantum mechanics/molecular mechanics (QM/MM) free energy simulations to the analysis of phosphoryl transfers catalyzed by two enzymes: alkaline phosphatase and myosin. We focus on the nature of the transition state and the issue of mechanochemical coupling, respectively, in the two enzymes. The results illustrate unique insights that emerged from the QM/MM simulations, especially concerning the interpretation of experimental data regarding the nature of enzymatic transition states and coupling between global structural transition and catalysis in the active site. We also highlight a number of technical issues worthy of attention when applying QM/MM free energy simulations, and comment on a number of technical and mechanistic issues that require further studies.

Intermolecular interactions in the condensed phase: Evaluation of semi-empirical quantum mechanical methods

To facilitate further development of approximate quantum mechanical methods for condensed phase applications, we present a new benchmark dataset of intermolecular interaction energies in the solution phase for a set of 15 dimers, each containing one charged monomer. The reference interaction energy in solution is computed via a thermodynamic cycle that integrates dimer binding energy in the gas phase at the coupled cluster level and solute-solvent interaction with density functional theory; the estimated uncertainty of such calculated interaction energy is ±1.5 kcal/mol. The dataset is used to benchmark the performance of a set of semi-empirical quantum mechanical (SQM) methods that include DFTB3-D3, DFTB3/CPE-D3, OM2-D3, PM6-D3, PM6-D3H+, and PM7 as well as the HF-3c method. We find that while all tested SQM methods tend to underestimate binding energies in the gas phase with a root-mean-squared error (RMSE) of 2-5 kcal/mol, they overestimate binding energies in the solution phase with an RMSE of 3-4 kcal/mol, with the exception of DFTB3/CPE-D3 and OM2-D3, for which the systematic deviation is less pronounced. In addition, we find that HF-3c systematically overestimates binding energies in both gas and solution phases. As most approximate QM methods are parametrized and evaluated using data measured or calculated in the gas phase, the dataset represents an important first step toward calibrating QM based methods for application in the condensed phase where polarization and exchange repulsion need to be treated in a balanced fashion.

Reliable and Performant Identification of Low-Energy Conformers in the Gas Phase and Water

Prediction of compound properties from structure via quantitative structure-activity relationship and machine-learning approaches is an important computational chemistry task in small-molecule drug research. Though many such properties are dependent on three-dimensional structures or even conformer ensembles, the majority of models are based on descriptors derived from two-dimensional structures. Here we present results from a thorough benchmark study of force field, semiempirical, and density functional methods for the calculation of conformer energies in the gas phase and water solvation as a foundation for the correct identification of relevant low-energy conformers. We find that the tight-binding ansatz GFN-xTB shows the lowest error metrics and highest correlation to the benchmark PBE0-D3(BJ)/def2-TZVP in the gas phase for the computationally fast methods and that in solvent OPLS3 becomes comparable in performance. MMFF94, AM1, and DFTB+ perform worse, whereas the performance-optimized but far more expensive functional PBEh-3c yields energies almost perfectly correlated to the benchmark and should be used whenever affordable. On the basis of our findings, we have implemented a reliable and fast protocol for the identification of low-energy conformers of drug-like molecules in water that can be used for the quantification of strain energy and entropy contributions to target binding as well as for the derivation of conformer-ensemble-dependent molecular descriptors.

Composite and Low-Cost Approaches for Molecular Crystal Structure Prediction

Molecular crystal structure prediction (CSP) requires evaluating differences in lattice energy between candidate crystal structures accurately and efficiently. In this work, we explore and compare several low-cost alternatives to dispersion-corrected density-functional theory (DFT) in the plane-waves/pseudopotential approximation, the most accurate and general approach used for CSP at present. Three types of low-cost methods are considered: DFT with a small basis set of finite-support numerical orbitals (the SIESTA method), dispersion-corrected Gaussian small or minimal-basis-set Hartree-Fock and DFT with additional empirical corrections (HF-3c and PBEh-3c), and self-consistent-charge dispersion-corrected density-functional tight binding (SCC-DFTB3-D3). In addition, we study the performance of composite methods that comprise a geometry optimization using a low-cost approach followed by a single-point calculation using the accurate but comparatively expensive B86bPBE-XDM functional. All methods were tested for their abilities to produce absolute lattice energies, relative lattice energies, and crystal geometries. We show that assessing various methods by their ability to produce absolute lattice energies can be misleading and that relative lattice energies are a much better indicator of performance in CSP. The EE14 set of relative solubilities of homochiral and heterochiral chiral crystals is proposed for relative lattice-energy benchmarking. Our results show that PBE-D2 plus a DZP basis set of numerical orbitals coupled with a final B86bPBE-XDM single-point calculation gives excellent performance at a fraction of the cost of a full B86bPBE-XDM calculation, although the results are sensitive to the particular details of the computational protocol. The B86bPBE-XDM//PBE-D2/DZP method was subsequently tested in a practical CSP application from our recent work on the crystal structure of the enantiopure and racemate forms of 1-aza[6]helicene, a chiral organic semiconductor. Our results show that this multilevel method is able to correctly reproduce the energy ranking of both crystal forms.

Crystal structure prediction of flexible pharmaceutical-like molecules: density functional tight-binding as an intermediate optimisation method and for free energy estimation

Successful methodologies for theoretical crystal structure prediction (CSP) on flexible pharmaceutical-like organic molecules explore the lattice energy surface to find a set of plausible crystal structures. The initial search stages of CSP studies use relatively simple lattice energy approximations as hundreds of thousands of minima have to be considered. These generated crystal structures often have poor molecular geometries, as well as inaccurate lattice energy rankings, and performing reasonably accurate but computationally affordable optimisations of the crystal structures generated in a search would be highly desirable. Here, we seek to explore whether semi-empirical quantum-mechanical methods can perform this task. We employed the dispersion-corrected tight-binding Hamiltonian (DFTB3-D3) to relax all the inter- and intra-molecular degrees of freedom of several thousands of generated crystal structures of five pharmaceutical-like molecules, saving a large amount of computational effort compared to earlier studies. The computational cost scales better with molecular size and flexibility than other CSP methods, suggesting that it could be extended to even larger and more flexible molecules. On average, this optimisation improved the average reproduction of the eight experimental crystal structures (RMSD15) and experimental conformers (RMSD1) by 4% and 23%, respectively. The intermolecular interactions were then further optimised using distributed multipoles, derived from the molecular wave-functions, to accurately describe the electrostatic components of the intermolecular energies. In all cases, the experimental crystal structures are close to the top of the lattice energy ranking. Phonon calculations on some of the lowest energy structures were also performed with DFTB3-D3 methods to calculate the vibrational component of the Helmholtz free energy, providing further insights into the solid-state behaviour of the target molecules. We conclude that DFTB3-D3 is a cost-effective method for optimising flexible molecules, bridging the gap between the approximate methods used in CSP searches for generating crystal structures and more accurate methods required in the final energy ranking.

On the hydrogen activation by frustrated Lewis pairs in the solid state: benchmark studies and theoretical insights

Recently, the concept of small molecule activation by frustrated Lewis pairs (FLPs) has been expanded to the solid state showing a variety of interesting reactivities. Therefore, there is a need to establish a computational protocol to investigate such systems theoretically. In the present study, we selected several FLPs and applied multiple levels of theory, ranging from a semi-empirical tight-binding Hamiltonian to dispersion corrected hybrid density functionals. Their performance is benchmarked for the computation of crystal geometries, thermostatistical contributions, and reaction energies. We show that the computationally efficient HF-3c method gives accurate crystal structures and is numerically stable and sufficiently fast for routine applications. This method also gives reliable values for the thermostatistical contributions to Gibbs free energies. The meta-generalized gradient approximated TPSS-D3 evaluated in a projector augmented plane wave basis set is able to produce sufficiently accurate reaction electronic energies. The established protocol is intended to support experimental studies and to predict new reactions in the emerging field of solid-state FLPs.This article is part of the themed issue 'Frustrated Lewis pair chemistry'.

Computational Studies on the Encapsulation of 1,4-Dihydropyridine Derivatives into CNT(10,10)

Semiempirical and density functional theory (DFT) methods were herein used to study the encapsulation process of 1,4-dihydropyridine (DHP) derivatives into (10,10) armchair carbon nanotube (CNT(10,10)). The encapsulated DHPs do not affect the overall structural and electronic properties of the CNT(10,10). The following binding energy was obtained from DFT-D3 calculations: DHP_Cl2@CNT(10,10) (–62.36 kcal mol–1) < DHP_Ph@CNT(10,10) (–54.71 kcal mol–1) < DHP_OH@CNT(10,10) (–43.92 kcal mol–1) < DHP_NO2@CNT(10,10) (–41.71 kcal mol–1) < DHP_H@CNT(10,10) (–32.74 kcal mol–1). The increase in the dipole moment for all DHPs@CNT(10,10) indicates their partial solubility in water. Our results play a promising role as a guide for future experiments using CNTs as a vehicle to transport DHP derivatives.

A Novel Nanoporous Graphite Based on Graphynes: First-Principles Structure and Carbon Dioxide Preferential Physisorption

Ubiquitous graphene is a stricly 2D material representing an ideal adsorbing platform due to its large specific surface area as well as its mechanical strength and resistance to both thermal and chemical stresses. However, graphene as a bulk material has the tendency to form irreversible agglomerates leading to 3D graphitic structures with a significant decrease of the area available for adsorption and no room for gas intercalation. In this paper, a novel nanoporous graphite formed by graphtriyne sheets is introduced; its 3D structure is theoretically assessed by means of electronic structure and molecular dynamics computations within the DFT level of theory. It is found that the novel layered carbon allotrope is almost as compact as pristine graphite but the inherent porosity of the 2D graphyne sheets and its relative stacking leads to nanochannels that cross the material and whose subnanometer size could allow the diffusion and storage of gas species. A molecular prototype of the nanochannel is used to accurately determine first-principles adsorption energies and enthalpies for CO₂, N₂, H₂O, and H₂ within the pores. The proposed porous graphite presents no significant barrier for gas diffusion and shows a high propensity for CO₂ physisorption with respect to the other relevant components in both pre- and postcombustion gas streams.