A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems

Semiempirical Quantum Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical Applications

Semiempirical (SE) methods can be derived from either Hartree-Fock or density functional theory by applying systematic approximations, leading to efficient computational schemes that are several orders of magnitude faster than ab initio calculations. Such numerical efficiency, in combination with modern computational facilities and linear scaling algorithms, allows application of SE methods to very large molecular systems with extensive conformational sampling. To reliably model the structure, dynamics, and reactivity of biological and other soft matter systems, however, good accuracy for the description of noncovalent interactions is required. In this review, we analyze popular SE approaches in terms of their ability to model noncovalent interactions, especially in the context of describing biomolecules, water solution, and organic materials. We discuss the most significant errors and proposed correction schemes, and we review their performance using standard test sets of molecular systems for quantum chemical methods and several recent applications. The general goal is to highlight both the value and limitations of SE methods and stimulate further developments that allow them to effectively complement ab initio methods in the analysis of complex molecular systems.

Small Atomic Orbital Basis Set First-Principles Quantum Chemical Methods for Large Molecular and Periodic Systems: A Critical Analysis of Error Sources

In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.

Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs

Water in different phases under various external conditions is very important in bio-chemical systems and for material science at surfaces. Density functional theory methods and approximations thereof have to be tested system specifically to benchmark their accuracy regarding computed structures and interaction energies. In this study, we present and test a set of ten ice polymorphs in comparison to experimental data with mass densities ranging from 0.9 to 1.5 g/cm(3) and including explicit corrections for zero-point vibrational and thermal effects. London dispersion inclusive density functionals at the generalized gradient approximation (GGA), meta-GGA, and hybrid level as well as alternative low-cost molecular orbital methods are considered. The widely used functional of Perdew, Burke and Ernzerhof (PBE) systematically overbinds and overall provides inconsistent results. All other tested methods yield reasonable to very good accuracy. BLYP-D3(atm) gives excellent results with mean absolute errors for the lattice energy below 1 kcal/mol (7% relative deviation). The corresponding optimized structures are very accurate with mean absolute relative deviations (MARDs) from the reference unit cell volume below 1%. The impact of Axilrod-Teller-Muto (atm) type three-body dispersion and of non-local Fock exchange is small but on average their inclusion improves the results. While the density functional tight-binding model DFTB3-D3 performs well for low density phases, it does not yield good high density structures. As low-cost alternative for structure related problems, we recommend the recently introduced minimal basis Hartree-Fock method HF-3c with a MARD of about 3%.

High Affinity Macrocycle Threading by a Near-Infrared Croconaine Dye with Flanking Polymer Chains

Croconaine dyes have narrow and intense absorption bands at ∼800 nm, very weak fluorescence, and high photostabilities, which combine to make them very attractive chromophores for absorption-based imaging or laser heating technologies. The physical supramolecular properties of croconaine dyes have rarely been investigated, especially in water. This study focuses on a molecular threading process that encapsulates a croconaine dye inside a tetralactam macrocycle in organic or aqueous solvent. Macrocycle association and rate constant data are reported for a series of croconaine structures with different substituents attached to the ends of the dye. The association constants were highest in water (Ka ∼ 10(9) M(-1)), and the threading rate constants (kon) increased in the solvent order H2O > MeOH > CHCl3. Systematic variation of croconaine substituents located just outside the croconaine/macrocycle complexation interface hardly changed Ka but had a strong influence on kon. A croconaine dye with N-propyl groups at each end of the structure exhibited a desirable mixture of macrocycle threading properties; that is, there was rapid and quantitative croconaine/macrocycle complexation at relatively high concentrations in water, and no dissociation of the preassembled complex when it was diluted into a solution of fetal bovine serum, even after laser-induced photothermal heating of the solution. The combination of favorable near-infrared absorption properties and tunable mechanical stability makes threaded croconaine/macrocycle complexes very attractive as molecular probes or as supramolecular composites for various applications in absorption-based imaging or photothermal therapy.

Gold(I) Vinylidene Complexes as Reactive Intermediates and Their Tendency to π-Backbond

We herein report a computational study of the bonding in gold(I) vinylidene complexes and compare them to their carbene and CO analogues. The relevance of these intermediates is analysed for the intramolecular cyclisation leading to vinyl sulfonates.

π–π stacking between polyaromatic hydrocarbon sheets beyond dispersion interactions

A slipped parallel structure of a stacked graphene flake showing a biconcave curvature.

Paramagnetic spherical nanoparticles by the self-assembly of persistent trityl radicals

The self-association of a water-soluble persistent trityl radical gives rise to paramagnetic nanoparticles: a new class of non-metallic high spin systems.

Novel luminescent β-ketoimine derivative of 2,1,3-benzothiadiazole: synthesis, complexation with Zn(ii) and photophysical properties in comparison with related compounds

2,1,3-Benzothiadiazoles and their Zn complexes show fluorescence in different wavelength regions, one of the complexes reveals white emission.

Demulsification of heavy oil-in-water emulsions by reduced graphene oxide nanosheets

The purpose of this work is to investigate the relationship between the chemical structure of the GO materials and the demulsification performance.

Screened exchange hybrid density functional for accurate and efficient structures and interaction energies

HSE-3c: a computationally efficient and numerically robust screened hybrid functional that can be applied to periodic small gap systems.

Consistent structures and interactions by density functional theory with small atomic orbital basis sets

A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust "high-speed" computational tool in theoretical chemistry and physics.

A simple and efficient dispersion correction to the Hartree-Fock theory (2): Incorporation of a geometrical correction for the basis set superposition error

One of the most challenging problems in computer-aided drug discovery is the accurate prediction of the binding energy between a ligand and a protein. For accurate estimation of net binding energy ΔEbind in the framework of the Hartree-Fock (HF) theory, it is necessary to estimate two additional energy terms; the dispersion interaction energy (Edisp) and the basis set superposition error (BSSE). We previously reported a simple and efficient dispersion correction, Edisp, to the Hartree-Fock theory (HF-Dtq). In the present study, an approximation procedure for estimating BSSE proposed by Kruse and Grimme, a geometrical counterpoise correction (gCP), was incorporated into HF-Dtq (HF-Dtq-gCP). The relative weights of the Edisp (Dtq) and BSSE (gCP) terms were determined to reproduce ΔEbind calculated with CCSD(T)/CBS or /aug-cc-pVTZ (HF-Dtq-gCP (scaled)). The performance of HF-Dtq-gCP (scaled) was compared with that of B3LYP-D3(BJ)-bCP (dispersion corrected B3LYP with the Boys and Bernadi counterpoise correction (bCP)), by taking ΔEbind (CCSD(T)-bCP) of small non-covalent complexes as 'a golden standard'. As a critical test, HF-Dtq-gCP (scaled)/6-31G(d) and B3LYP-D3(BJ)-bCP/6-31G(d) were applied to the complex model for HIV-1 protease and its potent inhibitor, KNI-10033. The present results demonstrate that HF-Dtq-gCP (scaled) is a useful and powerful remedy for accurately and promptly predicting ΔEbind between a ligand and a protein, albeit it is a simple correction procedure.

Quantum chemical benchmark study on 46 RNA backbone families using a dinucleotide unit

We have created a benchmark set of quantum chemical structure-energy data denoted as UpU46, which consists of 46 uracil dinucleotides (UpU), representing all known 46 RNA backbone conformational families. Penalty-function-based restrained optimizations with COSMO TPSS-D3/def2-TZVP ensure a balance between keeping the target conformation and geometry relaxation. The backbone geometries are close to the clustering-means of their respective RNA bioinformatics family classification. High-level wave function methods (DLPNO-CCSD(T) as reference) and a wide-range of dispersion-corrected or inclusive DFT methods (DFT-D3, VV10, LC-BOP-LRD, M06-2X, M11, and more) are used to evaluate the conformational energies. The results are compared to the Amber RNA bsc0χOL3 force field. Most dispersion-corrected DFT methods surpass the Amber force field significantly in accuracy and yield mean absolute deviations (MADs) for relative conformational energies of ∼0.4-0.6 kcal/mol. Double-hybrid density functionals represent the most accurate class of density functionals. Low-cost quantum chemical methods such as PM6-D3H+, HF-3c, DFTB3-D3, as well as small basis set calculations corrected for basis set superposition errors (BSSEs) by the gCP procedure are also tested. Unfortunately, the presently available low-cost methods are struggling to describe the UpU conformational energies with satisfactory accuracy. The UpU46 benchmark is an ideal test for benchmarking and development of fast methods to describe nucleic acids, including force fields.

Enamine/butadienylborane cycloaddition in the frustrated Lewis pair regime

The dienylborane 2a was prepared by regioselective alkyne hydroboration of the conjugated enyne 1a with Piers' borane [HB(C6F5)2]. Its reaction with a series of acetophenone derived enamines 3 resulted in the formation of the strong enamine β-carbon adduct with the borane Lewis acid (4). In contrast B-C adduct formation between the dienylborane 2a and a series of much more bulky cyclohexanone derived enamines (6) is rapidly reversible above ca.-30 °C and then leads to the formation of the [4 + 2]cycloaddition products 8. A DFT study revealed that this reaction is probably taking a stepwise route, proceeding by means of enamine addition to the dienylborane terminus to generate a zwitterionic borata-alkene/iminium ion intermediate that undergoes rapid subsequent ring closure. Heating of the products 8 led to amidoborane elimination from the vicinal amino/borane pair at the product framework to give the respective hexahydronaphthalene product 10. Subsequent treatment with TEMPO (2 equiv.) resulted in selective oxidation of the unsaturated ring to give the respective tetrahydronaphthalene derivative 12.

Noncovalent Binding of Polycyclic Aromatic Hydrocarbons with Genetic Bases Reducing the in Vitro Lateral Transfer of Antibiotic Resistant Genes

In current studies of noncovalent interactions of polycyclic aromatic hydrocarbons (PAHs) with genetic units, the impact of such interactions on gene transfer has not been explored. In this study, we examined the association of some widely occurring PAHs (phenanthrene, pyrene, benzo[g,h,i]perylene, and other congeners) with antibiotic resistant plasmids (pUC19). Small molecular PAHs (e.g., phenanthrene) bind effectively with plasmids to form a loosely clew-like plasmid-PAH complex (16.5-49.5 nm), resulting in reduced transformation of ampicillin resistance gene (Ampr). The in vitro transcription analysis demonstrated that reduced transformation of Ampr in plasmids results from the PAH-inhibited Ampr transcription to RNA. Fluorescence microtitration coupled with Fourier transform infrared spectroscopy (FTIR) and theoretical interaction models showed that adenine in plasmid has a stronger capacity to sequester small Phen and Pyre molecules via a π-π attraction. Changes in Gibbs free energy (ΔG) suggest that the CT-PAH model reliably depicts the plasmid-PAH interaction through a noncovalently physical sorption mechanism. Considering the wide occurrence of PAHs and antibiotic resistant genes (ARGs) in the environment, our findings suggest that small-sized PAHs can well affect the behavior of ARGs via above-described noncovalent interactions.

Monoisomeric phthalocyanine-fullerene dyads with e- and cis-3 addition pattern; synthesis, modeling, photovoltage and solar cell experiments

Synthesis and characterization of two A 2 B 2-type monoisomeric phthalocyanines and phthalocyanine-fullerene (Pc- C 60) dyads, in which fullerene is regioselectively attached to phthalocyanine with two linkers, are described. 1 H NMR spectroscopy results clearly indicate an e addition pattern of the fullerene moiety in trans-dyad 9, and apparently a cis-3 addition pattern in cis-dyad 10. The possible spatial arrangements of 9 and 10 were further examined by molecular modeling. The dyads have polar (– OH ) side chains on the fullerene side of the dyad providing a possibility to produce oriented donor–acceptor (D–A) Langmuir monolayers on aqueous subphase, which can be shifted onto a solid surface. When deposited on a solid electrode material, parallel vertical alignment of the phthalocyanine and fullerene moieties in 100% dyad monolayer was obtained and vertical electron transfer from Pc to C 60 upon photoexcitation was demonstrated. Introduction of the dyads as an oriented interfacial monolayer between the photoactive layer and metal anode improved the power conversion efficiency in inverted organic solar cells.

Theoretical insight into hydrogen adsorption onto graphene: a first-principles B3LYP-D3 study

This work investigates hydrogen adsorption onto graphene flakes as suitable models of graphene within the framework of the B3LYP-D3 method.

Self-assembled trityl radical capsules – implications for dynamic nuclear polarization

The OX63 radical forms supramolecular capsules hosting tetraalkylammonium cations. Extensive self-association is also observed under standard dynamic nuclear polarization conditions.

Mechanistic insight into the aerobic oxidation of benzyl alcohol catalyzed by the CuII–TEMPO catalyst in alkaline water solution

The benzyl alcohol oxidation to benzaldehyde in the alkaline water solution catalyzed by Cu^II/L–TEMPO catalyst is investigated by density functional method. The favorable mechanisms and the role for the water ​have also been predicted.

A QSAR study on the inhibition mechanism of matrix metalloproteinase-12 by arylsulfone analogs based on molecular orbital calculations

The inhibition mechanism of matrix metalloproteinase-12 by arylsulfone analogs is revealed using a comprehensive computational approach including docking simulations, molecular orbital calculations, and QSAR.

Unveiling the non-covalent interactions of molecular homodimers by dispersion-corrected DFT calculations and collision-induced broadening of ro-vibrational transitions: application to (CH2F2)2 and (SO2)2

(CH₂F₂)₂ and (SO₂)₂ are investigated using DFT-D3 computations, and experimental dissociation energies are determined by TDL-IR spectroscopy. DFT-D3 dramatically improves over uncorrected DFT.

Ab initio modelling of the anomeric and exo anomeric effects in 2-methoxytetrahydropyran and 2-methoxythiane corrected for intramolecular BSSE

Oxygen substitution in 2-methoxytetrahydropyran by sulphur in 2-methoxythiane approximately doubles the anomeric effect, which slows down enzymatic processing of 2-methoxythiane.

Low-Cost Quantum Chemical Methods for Noncovalent Interactions

The efficient and reasonably accurate description of noncovalent interactions is important for various areas of chemistry, ranging from supramolecular host-guest complexes and biomolecular applications to the challenging task of crystal structure prediction. While London dispersion inclusive density functional theory (DFT-D) can be applied, faster "low-cost" methods are required for large-scale applications. In this Perspective, we present the state-of-the-art of minimal basis set, semiempirical molecular-orbital-based methods. Various levels of approximations are discussed based either on canonical Hartree-Fock or on semilocal density functionals. The performance for intermolecular interactions is examined on various small to large molecular complexes and organic solids covering many different chemical groups and interaction types. We put the accuracy of low-cost methods into perspective by comparing with first-principle density functional theory results. The mean unsigned deviations of binding energies from reference data are typically 10-30%, which is only two times larger than those of DFT-D. In particular, for neutral or moderately polar systems, many of the tested methods perform very well, while at the same time, computational savings of up to 2 orders of magnitude can be achieved.

Connecting Classical QSAR and LERE Analyses Using Modern Molecular Calculations, LERE-QSAR (VI): Hydrolysis of Substituted Hippuric Acid Phenyl Esters by Trypsin

The reaction mechanism of trypsin was studied by applying DFT and ab initio molecular orbital (MO) calculations to complexes of trypsin with a congeneric series of eight para-substituted hippuric acid phenyl esters, for which a previous quantitative structureactivity relationship (QSAR) study revealed nice linearity of Hammett substitution constant σ(-) with logarithmic values of the MichaelisMenten and catalytic rate constants. Based on the LERE procedure, we performed QSAR analyses on each elementary reaction step during the acylation process. The present calculations showed that the rate-determining step during the acylation process is the transition state (TS) between the enzymesubstrate complex (ES) and tetrahedral intermediate (TET), and that the proton transfer occurs from Ser195 to His57, not between His57 and Asp102. The LERE-QSAR analysis statistically suggested that the variation of overall free-energy changes leading to formation of TS is governed mostly by that of activation energies required to form TS from ES. In spite of a very limited number of congeneric ligands in the current work, it is critically essential to clarify and verify physicochemical meanings of a typical QSAR/Chemoinformatics parameter, Hammett σ(-) based on quantum chemical calculations on the proteinligand kinetics; how Hammett σ(-) behaves in terms of proteinligand interaction energies.

Accurate Modeling of Organic Molecular Crystals by Dispersion-Corrected Density Functional Tight Binding (DFTB)

The ambitious goal of organic crystal structure prediction challenges theoretical methods regarding their accuracy and efficiency. Dispersion-corrected density functional theory (DFT-D) in principle is applicable, but the computational demands, for example, to compute a huge number of polymorphs, are too high. Here, we demonstrate that this task can be carried out by a dispersion-corrected density functional tight binding (DFTB) method. The semiempirical Hamiltonian with the D3 correction can accurately and efficiently model both solid- and gas-phase inter- and intramolecular interactions at a speed up of 2 orders of magnitude compared to DFT-D. The mean absolute deviations for interaction (lattice) energies for various databases are typically 2-3 kcal/mol (10-20%), that is, only about two times larger than those for DFT-D. For zero-point phonon energies, small deviations of <0.5 kcal/mol compared to DFT-D are obtained.

Solid state ¹H spin-lattice relaxation and isolated-molecule and cluster electronic structure calculations in organic molecular solids: the relationship between structure and methyl group and t-butyl group rotation

We report ab initio density functional theory electronic structure calculations of rotational barriers for t-butyl groups and their constituent methyl groups both in the isolated molecules and in central molecules in clusters built from the X-ray structure in four t-butyl aromatic compounds. The X-ray structures have been reported previously. We also report and interpret the temperature dependence of the solid state (1)H nuclear magnetic resonance spin-lattice relaxation rate at 8.50, 22.5, and 53.0 MHz in one of the four compounds. Such experiments for the other three have been reported previously. We compare the computed barriers for methyl group and t-butyl group rotation in a central target molecule in the cluster with the activation energies determined from fitting the (1)H NMR spin-lattice relaxation data. We formulate a dynamical model for the superposition of t-butyl group rotation and the rotation of the t-butyl group's constituent methyl groups. The four compounds are 2,7-di-t-butylpyrene, 1,4-di-t-butylbenzene, 2,6-di-t-butylnaphthalene, and 3-t-butylchrysene. We comment on the unusual ground state orientation of the t-butyl groups in the crystal of the pyrene and we comment on the unusually high rotational barrier of these t-butyl groups.

Blind prediction of binding affinities for charged supramolecular host-guest systems: achievements and shortcomings of DFT-D3

Association free energies ΔGa are calculated for two different types of host-guest systems, the rigid cucurbit[7]uril (CB7) and the basket shaped octa-acid (OA), and a number of charged guest molecules each by quantum chemical methods from first principles in the context of a recent blind test challenge (SAMPL4). For CB7, the overall agreement between theory and experiment is excellent. In comparison with all other submitted calculated relative ΔGa,rel values for this part of the blind test, our results ranked on top. Modeling the binding free energy in the case of the OA host mainly suffers from the problem that the binding situation is undefined with respect to the charge state and due to its intrinsic flexibility the host-guest complex is not represented well by a single configuration, but qualitative features of the binding process such as the proper binding orientation and the order of magnitude of ΔGa are represented in accord with the experimental expectations even though an accurate ranking is not possible.

Critical analysis of the accuracy of models predicting or extracting liquid structure information

This work aims at a critical assessment of properties predicting or extracting information on the density and structure of liquids. State-of-the-art NVT and NpT molecular dynamics (MD) simulations have been performed on five liquids: methanol, chloroform, acetonitrile, tetrahydrofuran, and ethanol. These simulations allow the computation of properties based on first principles, including the equilibrium density and radial distribution functions (RDFs), characterizing the liquid structure. Refinements have been incorporated in the MD simulations by taking into account basis set superposition errors (BSSE). An extended BSSE model for an instantaneous evaluation of the BSSE corrections has been proposed, and their impact on the liquid properties has been assessed. If available, the theoretical RDFs have been compared with the experimentally derived RDFs. For some liquids, significant discrepancies have been observed, and a profound but critical investigation is presented to unravel the origin of these deficiencies. This discussion is focused on tetrahydrofuran where the experiment reveals some prominent peaks completely missing in any MD simulation. Experiments providing information on liquid structure consist mainly of neutron diffraction measurements offering total structure factors as the primary observables. The splitting of these factors in reciprocal space into intra- and intermolecular contributions is extensively discussed, together with their sensitivity in reproducing correct RDFs in coordinate space.