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

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 0.2<i>e</i> placed 1.5 Å from the bromine atomic center is suggested as a universal model for the ESH

Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit?

We have quantified the effects of approximations usually made even in accurate CCSD­(T)/CBS calculations of noncovalent interactions, often considered as the “gold standard” of computational chemistry. We have investigated the effect of excitation series truncation, frozen core approximation, and relativistic effects in a set of 24 model complexes. The final CCSD­(T) results at the complete basis set limit with corrections to these approximations are the most accurate estimate of the true interaction energies in noncovalent complexes available. The average error due to these approximations was found to be about 1.5% of the interaction energy

CCSD[T] Describes Noncovalent Interactions Better than the CCSD(T), CCSD(TQ), and CCSDT Methods

The CCSD­(T) method is often called the “gold standard” of computational chemistry, because it is one of the most accurate methods applicable to reasonably large molecules. It is particularly useful for the description of noncovalent interactions where the inclusion of triple excitations is necessary for achieving a satisfactory accuracy. While it is widely used as a benchmark, the accuracy of CCSD­(T) interaction energies has not been reliably quantified yet against more accurate calculations. In this work, we compare the CCSD­[T], CCSD­(T), and CCSD­(TQ) noniterative methods with full CCSDTQ and CCSDT­(Q) calculations. We investigate various types of noncovalent complexes [hydrogen-bonded (water dimer, ammonia dimer, water ··· ammonia), dispersion-bound (methane dimer, methane ··· ammonia), and π–π stacked (ethene dimer)] using various coupled-clusters schemes up to CCSDTQ in 6-31G*(0.25), 6-31G**­(0.25, 0.15), and aug-cc-pVDZ basis sets. We show that CCSDT­(Q) reproduces the CCSDTQ results almost exactly and can thus serve as a benchmark in the cases where CCSDTQ calculations are not feasible. Surprisingly, the CCSD­[T] method provides better agreement with the benchmark values than the other noniterative analogs, CCSD­(T) and CCSD­(TQ), and even than the much more expensive iterative CCSDT scheme. The CCSD­[T] interaction energies differ from the benchmark data by less than 5 cal/mol on average (for all complexes and all basis sets), whereas the error of CCSD­(T) is 9 cal/mol. In larger systems, the difference between these two methods can grow by as much as 0.15 kcal/mol. While this effect can be explained only as an error compensation, the CCSD­[T] method certainly deserves more attention in accurate calculations of noncovalent interactions

Why Is the L‑Shaped Structure of X₂···X₂ (X = F, Cl, Br, I) Complexes More Stable Than Other Structures?

Five different structures (L- and T-shaped (LS, TS), parallel (P), parallel-displaced (PD), and linear (L)) of (X₂)₂ dimers (X = F, Cl, Br, I, N) have been investigated at B97-D3, M06-2X, DFT-SAPT, and CCSD­(T) levels. The <i>Q</i>_zz component of the quadrupole moment of all dihalogens, which coincides with the main rotational axis of the symmetry of the molecule, has been shown to be positive, whereas that of dinitrogen is negative. All of these values correlate well with the most positive value of the electrostatic potential, which, for dihalogens, reflects the magnitude of the σ-hole. The LS structure is the most stable structure for all dihalogen dimers. This trend is the most pronounced in the case of iodine and bromine; for dinitrogen dimer, the LS, TS, and PD structures are comparably stable. The dominant stabilization energy for dihalogen dimers is dispersion energy, followed by Coulomb energy. In the case of dinitrogen dimer, it is only the dispersion energy. At short distances, the Coulomb (polarization) energy for dihalogen dimers is more attractive for the LS structure; at larger distances, the TS structure is more favorable, as dispersion and induction energies are systematically more stable for the TS structure. For all dimers and all distances, the long-range electrostatic energy covering the interactions of multipole moments is the most attractive for the TS structure. In the case of dihalogen dimers, the preference of the LS structure over the others, resulting from the concert action of Coulomb, dispersion, and induction energies, is explained by the presence of a σ-hole. In the case of dinitrogen, comparable stability of LS, TS, and PD structures is obtained, as all are dominantly stabilized by dispersion energy

Accuracy of Several Wave Function and Density Functional Theory Methods for Description of Noncovalent Interaction of Saturated and Unsaturated Hydrocarbon Dimers

The proper description of noncovalent complexes is a notoriously difficult problem, especially for complexes dominated by the dispersion energy. Accurate and reliable results can be obtained using computationally demanding methods such as the coupled clusters with iterative treatment of single and double excitations and perturbative triples correction (CCSD­(T)), close to the complete basis set (CBS) limit. The sizes of the noncovalent complexes of interest, however, often exceed the computational capability of available computer facilities and software. Computationally efficient yet accurate and reliable theoretical methods are highly desired. In this work, we assembled a small test set of noncovalent complexes of un/saturated a/cyclic hydrocarbon (HC) dimers in order to inspect the accuracy and reliability of several routinely used low-order scaling wave function (WFT) and density functional theory (DFT) methods. The test set comprises dispersion dominated complexes of two different monomer types, saturated and unsaturated. The unsaturated systems are relatively well populated in one of the most popular training data sets for noncovalent complexes, the S22 set of Jurečka et al. The opposite is true for saturated systems, for which rather poor performance of “approximate” methods has been observed. From the results shown is this work, it is clear that unsaturated, e.g., π···π stacked, covalent complexes are described more accurately on average. With the exception of a few “balanced methods”, such as MP2C, MP2.5, SCS-/SCS­(MI)-CCSD, or DFT-D₃ with the TPSS and PBE functionals, a simultaneous description of saturated and unsaturated HCs introduces serious errors (i.e., more than 1 kcal/mol)

Extensions of the S66 Data Set: More Accurate Interaction Energies and Angular-Displaced Nonequilibrium Geometries

We present two extensions of the recently published S66 data set [Řezáč, Riley, Hobza; DOI: 10.1021/ct2002946]. Interaction energies for the equilibrium geometry complexes have been recalculated using a triple-ζ basis set for the CCSD(T) term in the CCSD(T)/CBS scheme. This allows for the extrapolation of this term to the complete basis set limit, improving accuracy by almost 1 order of magnitude compared to the scheme previously used for the S66 set. Now, we estimate the largest error in the set to be about 1%. Validation of several methods against the new data indicates the exceptional robustness and accuracy of the SCS-MI-CCSD method. The second extension improves the coverage of nonequilibrium geometries. We introduce a new data set, S66a8, that samples intermolecular angular degrees of freedom in the S66 complexes. For each of the 66 complexes, eight displaced geometries have been constructed, systematically sampling possible rotations of the monomers. Interaction energies in this set are calculated at the CCSD(T)/CBS level consistently with the earlier introduced S66x8 data set that samples the intermolecular distance

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

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

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