Jan Řezáč

Halogen bond tunability I: the effects of aromatic fluorine substitution on the strengths of halogen-bonding interactions involving chlorine, bromine, and iodine

AbstractIn the past several years, halogen bonds have been shown to be relevant in crystal engineering and biomedical applications. One of the reasons for the utility of these types of noncovalent interactions in the development of, for example, pharmaceutical ligands is that their strengths and geometric properties are very tunable. That is, substitution of atoms or chemical groups in the vicinity of a halogen can have a very strong effect on the strength of the halogen bond. In this study we investigate halogen-bonding interactions involving aromatically-bound halogens (Cl, Br, and I) and a carbonyl oxygen. The properties of these halogen bonds are modulated by substitution of aromatic hydrogens with fluorines, which are very electronegative. It is found that these types of substitutions have dramatic effects on the strengths of the halogen bonds, leading to interactions that can be up to 100% stronger. Very good correlations are obtained between the interaction energies and the magnitudes of the positive electrostatic potentials (σ-holes) on the halogens. Interestingly, it is seen that the substitution of fluorines in systems containing smaller halogens results in electrostatic potentials resembling those of systems with larger halogens, with correspondingly stronger interaction energies. It is also shown that aromatic fluorine substitutions affect the optimal geometries of the halogen-bonded complexes, often as the result of secondary interactions. FigureSchematic models of halogen bonding complexes studied in this work

Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes.

Because of its construction and parametrization for more than 80 elements, the semiempirical quantum chemical PM6 method is superior to other similar methods. Despite its advantages, however, the PM6 method fails for the description of noncovalent interactions, specifically the dispersion energy and H-bonding. Upon inclusion of correction terms for dispersion and H-bonding, the performance of the method was found to be dramatically improved. The former correction included two parameters in the damping function that were parametrized to reproduce the benchmark interaction energies [CCSD(T)/complete basis set (CBS) limit] of the dispersion-bonded complexes from the S22 data set. The latter correction was parametrized on an extended set of H-bonded stabilization energies determined at the MP2/cc-pVTZ level. The resulting PM6-DH method was tested on the S22 data set, for which chemical accuracy (error < 1 kcal/mol) was achieved, and also on the JSCH2005 set, for which significant improvement over the original PM6 method was also obtained. Implementation of analytical gradients allows very efficient geometry optimization, which, for all complexes, provides better agreement with the benchmark data. Excellent results were also achieved for small peptides, and here again, chemical accuracy was obtained (i.e., the error with respect to CCSD(T)/CBS results was smaller than 1 kcal/mol). The performance of the technique was finally demonstrated on extended complexes, namely, the porphine dimer and various graphene models with DNA bases and base pairs, where the PM6-DH stabilization energies agree very well with available benchmark data obtained with DFT-D, SCS-MP2, and MP2.5 methods. The PM6-DH calculations are very efficient and can be routinely applied for systems of up to 1000 atoms. For nonaromatic systems, the use of a linear scaling version of the SCF procedure based on localized orbitals speeds up the method significantly and allows one to investigate systems with several thousand atoms. The method can thus replace force fields, which face basic problems for the description of quantum effects, in many applications.

A Transferable H-Bonding Correction for Semiempirical Quantum-Chemical Methods

Semiempirical methods could offer a feasible compromise between ab initio and empirical approaches for the calculation of large molecules with biological relevance. A key problem for attempts in this direction is the rather bad performance of current semiempirical methods for noncovalent interactions, especially hydrogen-bonding. On the basis of the recently introduced PM6-DH method, which includes empirical corrections for dispersion (D) and hydrogen-bond (H) interactions, we have developed an improved and transferable H-bonding correction for semiempirical quantum chemical methods. The performance of the improved correction is evaluated for PM6, AM1, OM3, and SCC-DFTB (enhanced by standard empirical dispersion corrections) with several test sets for noncovalent interactions and is shown to reach the quality of current DFT-D approaches for these types of problems.

Advanced Corrections of Hydrogen Bonding and Dispersion for Semiempirical Quantum Mechanical Methods

Semiempirical quantum mechanical methods with corrections for noncovalent interactions, namely dispersion and hydrogen bonds, reach an accuracy comparable to much more expensive methods while being applicable to very large systems (up to 10 000 atoms). These corrections have been successfully applied in computer-assisted drug design, where they significantly improve the correlation with the experimental data. Despite these successes, there are still several unresolved issues that limit the applicability of these methods. We introduce a new generation of both hydrogen-bonding and dispersion corrections that address these problems, make the method more robust, and improve its accuracy. The hydrogen-bonding correction has been completely redesigned and for the first time can be used for geometry optimization and molecular-dynamics simulations without any limitations, as it and its derivatives have a smooth potential energy surface. The form of this correction is simpler than its predecessors, while the accuracy has been improved. For the dispersion correction, we adopt the latest developments in DFT-D, using the D3 formalism by Grimme. The new corrections have been parametrized on a large set of benchmark data including nonequilibrium geometries, the S66x8 data set. As a result, the newly developed D3H4 correction can accurately describe a wider range of interactions. We have parametrized this correction for the PM6, RM1, OM3, PM3, AM1, and SCC-DFTB methods.

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.

Comparative Study of Selected Wave Function and Density Functional Methods for Noncovalent Interaction Energy Calculations Using the Extended S22 Data Set

In this paper, an extension of the S22 data set of Jurecka et al. ( Jurečka , P. ; Šponer , J. ; Černý , J. ; Hobza , P. Phys. Chem. Chem. Phys. 2006 , 8 , 1985. ), the data set of benchmark CCSD(T)/CBS interaction energies of twenty-two noncovalent complexes in equilibrium geometries, is presented. The S22 data set has been extended by including the stretched (one shortened and three elongated) complex geometries of the S22 data set along the main noncovalent interaction coordinate. The goal of this work is to assess the accuracy of the popular wave function methods (MP2-, MP3- and, CCSD-based) and density functional methods (with and without empirical correction for the dispersion energy) for noncovalent complexes based on a statistical evaluation not only in equilibrium, but also in nonequilibrium geometries. The results obtained in this work provide information on whether an accurate and balanced description of the different interaction types and complex geometry distortions can be expected from the tested methods. This information has an important implication in the calculation of large molecular complexes, where the number of distant interacting molecular fragments, often in far from equilibrium geometries, increases rapidly with the system size. The best performing WFT methods were found to be the SCS-CCSD (spin-component scaled CCSD, according to Takatani , T. ; Hohenstein , E. G. ; Sherrill , C. D. J. Chem. Phys. 2008 , 128 , 124111 ), MP2C (dispersion-corrected MP2, according to Hesselmann , A. J. Chem. Phys. 2008 , 128 , 144112 ), and MP2.5 (scaled MP3, according to Pitoňák , M. ; Neogrády , P. ; Černý , J. ; Grimme , S. ; Hobza , P. ChemPhysChem 2009 , 10 , 282. ). Since none of the DFT methods fulfilled the required statistical criteria proposed in this work, they cannot be generally recommended for large-scale calculations. The DFT methods still have the potential to deliver accurate results for large molecules, but most likely on the basis of an error cancellation.

Halogen bond tunability II: the varying roles of electrostatic and dispersion contributions to attraction in halogen bonds

AbstractIn a previous study we investigated the effects of aromatic fluorine substitution on the strengths of the halogen bonds in halobenzene…acetone complexes (halo = chloro, bromo, and iodo). In this work, we have examined the origins of these halogen bonds (excluding the iodo systems), more specifically, the relative contributions of electrostatic and dispersion forces in these interactions and how these contributions change when halogen σ-holes are modified. These studies have been carried out using density functional symmetry adapted perturbation theory (DFT-SAPT) and through analyses of intermolecular correlation energies and molecular electrostatic potentials. It is found that electrostatic and dispersion contributions to attraction in halogen bonds vary from complex to complex, but are generally quite similar in magnitude. Not surprisingly, increasing the size and positive nature of a halogen’s σ-hole dramatically enhances the strength of the electrostatic component of the halogen bonding interaction. Not so obviously, halogens with larger, more positive σ-holes tend to exhibit weaker dispersion interactions, which is attributable to the lower local polarizabilities of the larger σ-holes. FigureIn this work we investigate the roles played by electrostatic and dispersion forces in stabilizing halogen bonding interactions.

Benchmark Calculations of Interaction Energies in Noncovalent Complexes and Their Applications.

Data sets of benchmark interaction energies in noncovalent complexes are an important tool for quantifying the accuracy of computational methods used in this field, as well as for the development of new computational approaches. This review is intended as a guide to conscious use of these data sets. We discuss their construction and accuracy, list the data sets available in the literature, and demonstrate their application to validation and parametrization of quantum-mechanical computational methods. In practical model systems, the benchmark interaction energies are usually obtained using composite CCSD(T)/CBS schemes. To use these results as a benchmark, their accuracy should be estimated first. We analyze the errors of this methodology with respect to both the approximations involved and the basis set size. We list the most prominent data sets covering various aspects of the field, from general ones to sets focusing on specific types of interactions or systems. The benchmark data are then used to validate more efficient computational approaches, including those based on explicitly correlated methods. Special attention is paid to the transition to large systems, where accurate benchmarking is difficult or impossible, and to the importance of nonequilibrium geometries in parametrization of more approximate methods.

Assessment of the Performance of MP2 and MP2 Variants for the Treatment of Noncovalent Interactions

For many years, MP2 served as the principal method for the treatment of noncovalent interactions. Until recently, this was the only technique that could be used to produce reasonably accurate binding energies, with binding energy errors generally below ~35%, at a reasonable computational cost. The past decade has seen the development of many new methods with improved performance for noncovalent interactions, several of which are based on MP2. Here, we assess the performance of MP2, LMP2, MP2-F12, and LMP2-F12, as well as spin component scaled variants (SCS) of these methods, in terms of their abilities to produce accurate interaction energies for binding motifs commonly found in organic and biomolecular systems. Reference data from the newly developed S66 database of interaction energies are used for this assessment, and a further set of 38 complexes is used as a test set for SCS methods developed herein. The strongly basis set-dependent nature of MP2 is confirmed in this study, with the SCS technique greatly reducing this behavior. It is found in this work that the spin component scaling technique can effectively be used to dramatically improve the performance of MP2 and MP2 variants, with overall errors being reduced by factors of about 1.5-2. SCS versions of all MP2 variants tested here are shown to give similarly accurate overall results.

Parameterization of the DFTB3 Method for Br, Ca, Cl, F, I, K, and Na in Organic and Biological Systems

We present an extension to the recent 3OB parametrization of the Density Functional Tight Binding Model DFTB31,2 for biological and organic systems. Parameters for the halogens F, Cl, Br, and I have been developed for use in covalently bound systems and benchmarked on a test set of 106 molecules (the ‘OrgX’ set), using bonding distances, bonding angles, atomization energies, and vibrational frequencies to assess the performance of the parameters. Additional testing has been done with the X40 set of 40 supramolecular systems containing halogens,3 adding a simple correction for the halogen bonds that are strongly overbound in DFTB3. Furthermore, parameters for Ca, K, and Na as counterions in biological systems have been created. To benchmark geometries as well as ligand binding energies a test set ‘BioMe’ of 210 molecules has been created that cover coordination to various functional groups frequently occurring in biological systems. The new DFTB3/3OB parameter set outperforms DFT calculations with a double-ζ basis set in terms of energies and can reproduce DFT geometries, with some minor deviations in bond distances and angles due to the use of a minimal basis set.