On the origin of the substantial stabilisation of the electron-donor 1,3-dithiole-2-thione-4-carboxyclic acid···I2 and DABCO···I2 complexes

The stabilisation energies of the crystal structures of 1,3-dithiole-2-thione-4-carboxyclic acid···I2 and DABCO···I2 complexes determined by the CCSD(T)/CBS method are very large and exceed 8 and 15 kcal mol(-1), respectively. The DFT-D method (B97-D3/def2-QZVP) strongly overestimates these stabilisation energies, which support the well-known fact that the DFT-D method is not very applicable to the study of charge-transfer complexes. On the other hand, the M06-2X/def2-QZVP method provides surprisingly reliable energies. A DFT-SAPT analysis has shown that a substantial stabilisation of these complexes arises from the charge-transfer energy included in the induction energy and that the respective induction energy is much larger than that of other non-covalently bound complexes. The total stabilisation energies of the complexes mentioned as well as of those where iodine has been replaced by lighter halogens (Br2 and Cl2) or by hetero systems (IF, ICH3, N2) correlate well with the magnitude of the σ-hole (Vs,max value) as well as with the LUMO energy. The nature of the stabilisation of all complexes between both electron donors and X2 (X = I, Br, Cl, N) systems is explained by the magnitude of the σ-hole but surprisingly also by the values of the electric quadrupole moment of these systems. Evidently, the nature of the stabilisation of halogen-bonded complexes between electron donors and systems where the first non-zero electric multipole moment is the quadrupole moment can be explained not only by the recently introduced concept of the σ-hole but also by the classical concept of electric quadrupole moments.

Selective induced polarization through electron transfer in acetone and pyrazole ester derivatives via C–H⋯OC interaction

A set of organic compounds (pyrazole ester derivatives,viz.5-[3-(substituted)-propoxy]-3-methyl-1-phenyl-1H-pyrazole-4-carboxylic acid methyl ester and 5-[2-(substituted)-ethoxy]-3-methyl-1-phenyl-1H-pyrazole-4-carboxylic acid methyl ester) was synthesized and their affinity and stability towards the acetone molecule were tested by NMR.

The nature of bonding and electronic properties of graphene and benzene with iridium adatoms

The strong correlation effects contribute to the opening of the band gap in graphene covered with the Ir adatoms.

Evaluation of composite schemes for CCSDT(Q) calculations of interaction energies of noncovalent complexes

Evaluation of composite schemes for CCSDT(Q) calculations of interaction energies of noncovalent complexes.

Statistical analysis of σ-holes: a novel complementary view on halogen bonding

Halogen σ-hole characteristics are defined and their typical values are provided based on an extensive analysis of more than 2500 molecules from the ZINC database.

Quantum mechanics-based scoring rationalizes the irreversible inactivation of parasitic Schistosoma mansoni cysteine peptidase by vinyl sulfone inhibitors

The quantum mechanics (QM)-based scoring function that we previously developed for the description of noncovalent binding in protein-ligand complexes has been modified and extended to treat covalent binding of inhibitory ligands. The enhancements are (i) the description of the covalent bond breakage and formation using hybrid QM/semiempirical QM (QM/SQM) restrained optimizations and (ii) the addition of the new ΔG(cov)' term to the noncovalent score, describing the "free" energy difference between the covalent and noncovalent complexes. This enhanced QM-based scoring function is applied to a series of 20 vinyl sulfone-based inhibitory compounds inactivating the cysteine peptidase cathepsin B1 of the Schistosoma mansoni parasite (SmCB1). The available X-ray structure of the SmCB1 in complex with a potent vinyl sulfone inhibitor K11017 is used as a template to build the other covalently bound complexes and to model the derived noncovalent complexes. We present the correlation of the covalent score and its constituents with the experimental binding data. Four outliers are identified. They contain bulky R1' substituents structurally divergent from the template, which might induce larger protein rearrangements than could be accurately modeled. In summary, we propose a new computational approach and an optimal protocol for the rapid evaluation and prospective design of covalent inhibitors with a conserved binding mode.

Modulation of aldose reductase inhibition by halogen bond tuning

In this paper, we studied a designed series of aldose reductase (AR) inhibitors. The series was derived from a known AR binder, which had previously been shown to form a halogen bond between its bromine atom and the oxygen atom of the Thr-113 side chain of AR. In the series, the strength of the halogen bond was modulated by two factors, namely bromine-iodine substitution and the fluorination of the aromatic ring in several positions. The role of the single halogen bond in AR-ligand binding was elucidated by advanced binding free energy calculations involving the semiempirical quantum chemical Hamiltonian. The results were complemented with ultrahigh-resolution X-ray crystallography and IC50 measurements. All of the AR inhibitors studied were shown by X-ray crystallography to bind in an identical manner. Further, it was demonstrated that it was possible to decrease the IC50 value by about 1 order of magnitude by tuning the strength of the halogen bond by a monoatomic substitution. The calculations revealed that the protein-ligand interaction energy increased upon the substitution of iodine for bromine or upon the addition of electron-withdrawing fluorine atoms to the ring. However, the effect on the binding affinity was found to be more complex due to the change of the solvation/desolvation properties within the ligand series. The study shows that it is possible to modulate the strength of a halogen bond in a protein-ligand complex as was designed based on the previous studies of low-molecular-weight complexes.

The accuracy of quantum chemical methods for large noncovalent complexes

We evaluate the performance of the most widely used wavefunction, density functional theory, and semiempirical methods for the description of noncovalent interactions in a set of larger, mostly dispersion-stabilized noncovalent complexes (the L7 data set). The methods tested include MP2, MP3, SCS-MP2, SCS(MI)-MP2, MP2.5, MP2.X, MP2C, DFT-D, DFT-D3 (B3-LYP-D3, B-LYP-D3, TPSS-D3, PW6B95-D3, M06-2X-D3) and M06-2X, and semiempirical methods augmented with dispersion and hydrogen bonding corrections: SCC-DFTB-D, PM6-D, PM6-DH2 and PM6-D3H4. The test complexes are the octadecane dimer, the guanine trimer, the circumcoronene…adenine dimer, the coronene dimer, the guanine-cytosine dimer, the circumcoronene…guanine-cytosine dimer, and an amyloid fragment trimer containing phenylalanine residues. The best performing method is MP2.5 with relative root mean square deviation (rRMSD) of 4 %. It can thus be recommended as an alternative to the CCSD(T)/CBS (alternatively QCISD(T)/CBS) benchmark for molecular systems which exceed current computational capacity. The second best non-DFT method is MP2C with rRMSD of 8 %. A method with the most favorable "accuracy/cost" ratio belongs to the DFT family: BLYP-D3, with an rRMSD of 8 %. Semiempirical methods deliver less accurate results (the rRMSD exceeds 25 %). Nevertheless, their absolute errors are close to some much more expensive methods such as M06-2X, MP2 or SCS(MI)-MP2, and thus their price/performance ratio is excellent.

Assessing the accuracy and performance of implicit solvent models for drug molecules: conformational ensemble approaches

The accuracy and performance of implicit solvent methods for solvation free energy calculations were assessed on a set of 20 neutral drug molecules. Molecular dynamics (MD) provided ensembles of conformations in water and water-saturated octanol. The solvation free energies were calculated by popular implicit solvent models based on quantum mechanical (QM) electronic densities (COSMO-RS, MST, SMD) as well as on molecular mechanical (MM) point-charge models (GB, PB). The performance of the implicit models was tested by a comparison with experimental water-octanol transfer free energies (ΔG(ow)) by using single- and multiconformation approaches. MD simulations revealed difficulties in a priori estimation of the flexibility features of the solutes from simple structural descriptors, such as the number of rotatable bonds. An increasing accuracy of the calculated ΔG(ow) was observed in the following order: GB1 ~ PB < GB7 ≪ MST < SMD ~ COSMO-RS with a clear distinction identified between MM- and QM-based models, although for the set excluding three largest molecules, the differences among COSMO-RS, MST, and SMD were negligible. It was shown that the single-conformation approach applied to crystal geometries provides a rather accurate estimate of ΔG(ow) for rigid molecules yet fails completely for the flexible ones. The multiconformation approaches improved the performance, but only when the deformation contribution was ignored. It was revealed that for large-scale calculations on small molecules a recent GB model, GB7, provided a reasonable accuracy/speed ratio. In conclusion, the study contributes to the understanding of solvation free energy calculations for physical and medicinal chemistry applications.

On the importance and origin of aromatic interactions in chemistry and biodisciplines

Aromatic systems contain both σ- and π-electrons, which in turn constitute σ- and π-molecular orbitals (MOs). In discussing the properties of these systems, researchers typically refer to the highest occupied and lowest unoccupied MOs, which are π MOs. The characteristic properties of aromatic systems, such as their low ionization potentials and electron affinities, high polarizabilities and stabilities, and small band gaps (in spectroscopy called the N → V1 space), can easily be explained based on their electronic structure. These one-electron properties point to characteristic features of how aromatic systems interact with each other. Unlike hydrogen bonding systems, which primarily interact through electrostatic forces, complexes containing aromatic systems, especially aromatic stacked pairs, are predominantly stabilized by dispersion attraction. The stabilization energy in the benzene dimer is rather small (~2.5 kcal/mol) but strengthens with heteroatom substitution. The stacked interaction of aromatic nucleic acid bases is greater than 10 kcal/mol, and for the most stable stacked pair, guanine and cytosine, it reaches approximately 17 kcal/mol. Although these values do not equal the planar H-bonded interactions of these bases (~29 kcal/mol), stacking in DNA is more frequent than H-bonding and, unlike H-bonding, is not significantly weakened when passing from the gas phase to a water environment. Consequently, the stacking of aromatic systems represents the leading stabilization energy contribution in biomacromolecules and in related nanosystems. Therefore stacking (dispersion) interactions predominantly determine the double helical structure of DNA, which underlies its storage and transfer of genetic information. Similarly, dispersion is the dominant contributor to attractive interactions involving aromatic amino acids within the hydrophobic core of a protein, which is critical for folding. Therefore, understanding the nature of aromatic interactions, which depend greatly on quantum mechanical (QM) calculations, is of key importance in biomolecular science. This Account shows that accurate binding energies for aromatic complexes should be based on computations made at the (estimated) CCSD(T)/complete basis set limit (CBS) level of theory. This method is the least computationally intensive one that can give accurate stabilization energies for all common classes of noncovalent interactions (aromatic-aromatic, H-bonding, ionic, halogen bonding, charge-transfer, etc.). These results allow for direct comparison of binding energies between different interaction types. Conclusions based on lower-level QM calculations should be considered with care.

Quantification of the interaction forces between metals and graphene by quantum chemical calculations and dynamic force measurements under ambient conditions

The two-dimensional material graphene has numerous potential applications in nano(opto)electronics, which inevitably involve metal graphene interfaces.Theoretical approaches have been employed to examine metal graphene interfaces, but experimental evidence is currently lacking. Here, we combine atomic force microscopy (AFM) based dynamic force measurements and density functional theory calculations to quantify the interaction between metal-coated AFM tips and graphene under ambient conditions. The results show that copper has the strongest affinity to graphene among the studied metals (Cu, Ag, Au, Pt, Si), which has important implications for the construction of a new generation of electronic devices. Observed differences in the nature of the metal-graphene bonding are well reproduced by the calculations, which included nonlocal Hartree-Fock exchange and van der Waals effects.

Benchmark Calculations of Noncovalent Interactions of Halogenated Molecules

We present a set of 40 noncovalent complexes of organic halides, halohydrides, and halogen molecules where the halogens participate in a variety of interaction types. The set, named X40, covers electrostatic interactions, London dispersion, hydrogen bonds, halogen bonding, halogen-π interactions, and stacking of halogenated aromatic molecules. Interaction energies at equilibrium geometries were calculated using a composite CCSD(T)/CBS scheme where the CCSD(T) contribution is calculated using triple-ζ basis sets with diffuse functions on all atoms but hydrogen. For each complex, we also provide 10 points along the dissociation curve calculated at the CCSD(T)/CBS level. We use this accurate reference to assess the accuracy of selected post-HF methods.

Calculations on noncovalent interactions and databases of benchmark interaction energies

Although covalent interactions determine the primary structure of a molecule, the noncovalent interactions are responsible for the tertiary and quaternary structure of a molecule and create the fascinating world of the 3D architectures of biomacromolecules. For example, the double helical structure of DNA is of fundamental importance for the function of DNA: it allows it to store and transfer genetic information. To fulfill this role, the structure is rigid to maintain the double helix with a proper positioning of the complementary base, and floppy to allow for its opening. Very strong covalent interactions cannot fulfill both of these criteria, but noncovalent interactions, which are about 2 orders of magnitude weaker, can. This Account highlights the recent advances in the field of the design of novel wave function theory (WFT) methods applicable to noncovalent complexes ranging in size from less than 100 atoms, for which highly accurate ab initio methods are available, up to extended ones (several thousands atoms), which are the domain of semiempirical QM (SQM) methods. Accurate interaction energies for noncovalent complexes are generated by the coupled-cluster technique, taking single- and double-electron excitations iteratively and triple-electron excitation perturbatively with a complete basis set description (CCSD(T)/CBS). The procedure provides interaction energies with high accuracy (error less than 1 kcal/mol). Because the method is computationally demanding, its application is limited to complexes smaller than 30 atoms. But researchers would also like to use computational methods to determine these interaction energies accurately for larger biological and nanoscale structures. Standard QM methods such as MP2, MP3, CCSD, or DFT fail to describe various types of noncovalent systems (H-bonded, stacked, dispersion-controlled, etc.) with comparable accuracy. Therefore, novel methods are needed that have been parametrized toward noncovalent interactions, and existing benchmark data sets represent an important tool for the development of new methods providing reliable characteristics of noncovalent clusters. Our laboratory developed the first suitable data set of CCSD(T)/CBS interaction energies and geometries of various noncovalent complexes, called S22. Since its publication in 2006, it has frequently been applied in parametrization and/or verification of various wave function and density functional techniques. During the intense use of this data set, several inconsistencies emerged, such as the insufficient accuracy of the CCSD(T) correction term or its unbalanced character, which has triggered the introduction of a new, broader, and more accurate data set called the S66 data set. It contains not only 66 CCSD(T)/CBS interaction energies determined in the equilibrium geometries but also 1056 interaction energies calculated at the same level for nonequilibrium geometries. The S22 and S66 data sets have been used for the verification of various WFT methods, and the lowest RMSE (S66, in kcal/mol) was found for the recently introduced SCS-MI-CCSD/CBS (0.08), MP2.5/CBS (0.16), MP2.X/6-31G* (0.27), and SCS-MI-MP2/CBS (0.38) methods. Because of their computational economy, the MP2.5 and MP2.X/6-31G* methods can be recommended for highly accurate calculations of large complexes with up to 100 atoms. The evaluation of SQM methods was based only on the S22 data set, and because some of these methods have been parametrized toward the same data set, the respective results should be taken with caution. For really extended complexes such as protein-ligand systems, only the SMQ methods are applicable. After adding the corrections to the dispersion energy and H-bonding, several methods exhibit surprisingly low RMSE (even below 0.5 kcal/mol). Among the various SMQ methods, the PM6-DH2 can be recommended because of its computational efficiency and it can be used for optimization (which is not the case for other SQM methods). The PM6-DH2 is the base of our novel scoring function used in in silico drug design.

On Extension of the Current Biomolecular Empirical Force Field for the Description of Halogen Bonds

Until recently, the description of halogen bonding by standard molecular mechanics has been poor, owing to the lack of the so-called σ hole localized at the halogen. This region of positive electrostatic potential located on top of a halogen atom explains the counterintuitive attraction of halogenated compounds interacting with Lewis bases. In molecular mechanics, the σ hole is modeled by a massless point charge attached to the halogen atom and referred to as an explicit σ hole (ESH). Here, we introduce and compare three methods of ESH construction, which differ in the complexity of the input needed. The molecular mechanical dissociation curves of three model complexes containing bromine are compared with accurate CCSD(T)/CBS data. Furthermore, the performance of the Amber force field enhanced by the ESH on geometry characteristics is tested on the casein kinase 2 protein complex with seven brominated inhibitors. It is shown how various schemes depend on the selection of the ESH parameters and to what extent the energies and geometries are reliable. The charge of 0.2e placed 1.5 Å from the bromine atomic center is suggested as a universal model for the ESH.

Evaluation of the performance of post-Hartree-Fock methods in terms of intermolecular distance in noncovalent complexes

Dissociation curves calculated using multiple correlated QM methods for 66 noncovalent complexes (Řezáč et al., J Chem Theory Comput 2011, 7, 2427) have allowed us to interpolate equilibrium intermolecular distances for each studied method. Comparison of these data with CCSD(T)/complete basis set reference geometries provides information on how these methods perform in geometry optimizations. The large set of systems considered here is necessary for reliable statistical evaluation of the results and assessment of the robustness of the studied methods. Our results show that advanced methods such as MP3 and CCSD provide significant improvement over MP2 only when empirical scaling is used. The best results can be achieved with spin component scaled CCSD optimized for noncovalent interactions, with a root mean square error of 0.4% of the equilibrium distance. Scaled MP3, the MP2.5 method, yields comparably good results (error 0.5%) while being substantially cheaper.

The Nature of the Binding of Au, Ag, and Pd to Benzene, Coronene, and Graphene: From Benchmark CCSD(T) Calculations to Plane-Wave DFT Calculations

The adsorption of Ag, Au, and Pd atoms on benzene, coronene, and graphene has been studied using post Hartree-Fock wave function theory (CCSD(T), MP2) and density functional theory (M06-2X, DFT-D3, PBE, vdW-DF) methods. The CCSD(T) benchmark binding energies for benzene-M (M = Pd, Au, Ag) complexes are 19.7, 4.2, and 2.3 kcal/mol, respectively. We found that the nature of binding of the three metals is different: While silver binds predominantly through dispersion interactions, the binding of palladium has a covalent character, and the binding of gold involves a subtle combination of charge transfer and dispersion interactions as well as relativistic effects. We demonstrate that the CCSD(T) benchmark binding energies for benzene-M complexes can be reproduced in plane-wave density functional theory calculations by including a fraction of the exact exchange and a nonempirical van der Waals correction (EE+vdW). Applying the EE+vdW method, we obtained binding energies for the graphene-M (M = Pd, Au, Ag) complexes of 17.4, 5.6, and 4.3 kcal/mol, respectively. The trends in binding energies found for the benzene-M complexes correspond to those in coronene and graphene complexes. DFT methods that use empirical corrections to account for the effects of vdW interactions significantly overestimate binding energies in some of the studied systems.

S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures

With numerous new quantum chemistry methods being developed in recent years and the promise of even more new methods to be developed in the near future, it is clearly critical that highly accurate, well-balanced, reference data for many different atomic and molecular properties be available for the parametrization and validation of these methods. One area of research that is of particular importance in many areas of chemistry, biology, and material science is the study of noncovalent interactions. Because these interactions are often strongly influenced by correlation effects, it is necessary to use computationally expensive high-order wave function methods to describe them accurately. Here, we present a large new database of interaction energies calculated using an accurate CCSD(T)/CBS scheme. Data are presented for 66 molecular complexes, at their reference equilibrium geometries and at 8 points systematically exploring their dissociation curves; in total, the database contains 594 points: 66 at equilibrium geometries, and 528 in dissociation curves. The data set is designed to cover the most common types of noncovalent interactions in biomolecules, while keeping a balanced representation of dispersion and electrostatic contributions. The data set is therefore well suited for testing and development of methods applicable to bioorganic systems. In addition to the benchmark CCSD(T) results, we also provide decompositions of the interaction energies by means of DFT-SAPT calculations. The data set was used to test several correlated QM methods, including those parametrized specifically for noncovalent interactions. Among these, the SCS-MI-CCSD method outperforms all other tested methods, with a root-mean-square error of 0.08 kcal/mol for the S66 data set.

On the role of London dispersion forces in biomolecular structure determination

A DNA dodecamer and the methyladenine···methylthymine (mA···mT) complex in aqueous environment have been studied by means of molecular dynamics simulation, with a modified force field accounting for the hypothetical absence of London dispersion forces. Under these conditions, the mA···mT complex is preserved, while the double-helical DNA oligomer passes via an extended, ladder-like intermediate to a collapsed structure. The results are interpreted in terms of stability and specificity of the structure of studied complexes. While the hydrophobic effect of the solvent accounts for the sufficient stabilization of the complex, the appearance of the native biomolecular conformation is attributed to the London dispersion forces. Thus, the London dispersion seems to provide the native structure of a biomolecular complex with the largest additional stabilization, preferring it among several (or many) possible aggregated structures. The observations are affected by the construction of the modified force field, and this effect is discussed thoroughly. The fundamental issues are the coupling of the components of the Lennard-Jones potential and the way to separate them. Based on the observations, the description of nonbonded interactions with the current biomolecular force fields is discussed. It is proposed that a novel force field composed of physically correct components to describe nonbonded interactions could exhibit more favorable performance in certain up-to-date applications.

Parallelized implementation of the CCSD(T) method in MOLCAS using optimized virtual orbitals space and Cholesky decomposed two-electron integrals

Parallelized implementation of the coupled cluster singles doubles with non-iterative triples in the MOLCAS program suite is described. The code benefits from the Cholesky decomposition of two-electron integrals and the algorithm is particularly designed for calculations using reduced optimized virtual orbital space. Different aspects of parallelization and its efficiency are discussed based on our recent successful calculations for medium sized molecules involving more than 1000 basis functions.

H-Bonding Cooperativity Effects in Amyloids: Quantum Mechanical and Molecular Mechanics Study

The cooperativity effects have been evaluated on three model systems, the formamide, (formylamino)acetamide and amyloidic-layer oligomers with an increasing size of the monomer units (6, 13 and 214 atoms). In the last model, each layer is a dimer of the amino-acid sequence GNNQQNY in one-letter amino-acid abbreviations. The series of oligomers for each model system of up to six monomers have been constructed. For the calculation of the strength of a particular H-bond formed between various sub-oligomers within an oligomer, different wave function, density functional and semi-empirical quantum mechanical methods as well as empirical force fields have been used. Semi-empirical methods are found to be a reasonable compromise between accuracy and computational cost. These methods are able to describe the cooperativity effects with an accuracy almost comparable to that of the ab initio methods. On the contrary, the empirical force-field methods for all of the model systems mostly failed to describe the H-bonding cooperativity effects properly. Based on the results obtained in this work, we recommend using semi-empirical methods. For the systems where this is impossible, we agree to use polarizable force fields with some reservations. Generally, the more flexible the oligomer chain is (the less steric the repulsion or rigid motifs are), the larger the cooperativity that can be achieved. With the increasing number of monomers in a sequence connected via H-bonds, the cooperativity effects appear to be growing, but relatively soon (at 3–4 monomer units) they tend to become saturated.

Photodynamics of the adenine model 4-aminopyrimidine embedded within double strand of DNA

On-the-fly surface hopping nonadiabatic photodynamical simulations using hybrid quantum mechanical/molecular mechanical approach of 4-aminopyrimidine were performed to model the relaxation mechanism of adenine within DNA double strand. The surrounding bases do not affect the overall ring-puckering relaxation mechanisms significantly, however, interesting hydrogen-bond dynamics is observed. First, formation of intra-strand hydrogen bonds is found. It is shown that this effect speeds up the decay process. In addition, the Watson–Crick structure is altered by breaking one of the inter-strand hydrogen bonds also leading to a decrease of the life time.