Empirical Self-Consistent Correction for the Description of Hydrogen Bonds in DFTB3

The description of hydrogen bonds in the density-functional tight-binding (DFTB) method continues to be a challenging task because the approximations that make the method computationally efficient compromise already the first-order electrostatic contribution to the interaction. So far, the best results have been achieved with fully empirical corrections such as the recently reparametrized DFTB3-D3H4 method. This approach has, however, important limitations that arise from its independence of the actual electronic structure. Here, we present a novel correction denoted as D3H5, which is integrated deeper in the DFTB method, correcting the problem at the place of its origin. It is applied within the self-consistent evaluation of electrostatic interactions, where it empirically models the missing contributions of atomic multipoles and polarization. Despite being very simple and using fewer parameters than D3H4, it is both more accurate and more robust. In data sets of small model systems, it yields errors below 1 kcal/mol, and it performs comparably well in larger systems. Unlike D3H4, it can describe cooperativity in H-bond networks, which makes it more transferable to more complex systems

Accurate DFT-D3 Calculations in a Small Basis Set

Calculations of interaction energies of noncovalent interactions in small basis sets are affected by the basis set superposition error and dispersion-corrected DFT-D methods and are thus usually parametrized only for triple-ζ and larger basis sets. Nevertheless, some smaller basis sets could also perform well. Among many combinations tested, we obtained excellent results with the DZVP-DFT basis and newly parametrized D3 dispersion correction. The accuracy of interaction energies and geometries is close to significantly more expensive calculations

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

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

Empirical D3 Dispersion as a Replacement for ab Initio Dispersion Terms in Density Functional Theory-Based Symmetry-Adapted Perturbation Theory

In density functional theory-based symmetry-adapted perturbation theory (DFT-SAPT) interaction energy calculations, the most demanding step is the calculation of the London dispersion term. For this bottleneck to be avoided and DFT-SAPT to be made applicable to larger systems, the ab initio dispersion terms can be replaced by one calculated empirically at an almost negligible cost (J. Phys. Chem. A 2011; 115, 11321−11330). We present an update of this approach that improves accuracy and makes the method applicable to a wider range of systems. It is based on Grimme’s D3 dispersion correction for DFT, where the damping function is changed to one suitable for the calculation of the complete dispersion energy. The best results have been achieved with the Tang–Toennies damping function. It has been parametrized on the S66×8 data set for which we report density fitting DFT-SAPT/aug-cc-pVTZ interaction energy decomposition. The method has been validated on a diverse set of noncovalent systems including difficult cases such as very compact noncovalent complexes of charge-transfer type. The root-mean-square errors in the complete test set are 0.73 and 0.42 kcal mol^–1 when charge-transfer complexes are excluded. The proposed empirical dispersion terms can also be used outside the DFT-SAPT framework, e.g., for the estimation of the amount of dispersion in a calculation where only the total interaction energy is known

Robust, Basis-Set Independent Method for the Evaluation of Charge-Transfer Energy in Noncovalent Complexes

Separation of the energetic contribution of charge transfer to interaction energy in noncovalent complexes would provide important insight into the mechanisms of the interaction. However, the calculation of charge-transfer energy is not an easy task. It is not a physically well-defined term, and the results might depend on how it is described in practice. Commonly, the charge transfer is defined in terms of molecular orbitals; in this framework, however, the charge transfer vanishes as the basis set size increases toward the complete basis set limit. This can be avoided by defining the charge transfer in terms of the spatial extent of the electron densities of the interacting molecules, but the schemes used so far do not reflect the actual electronic structure of each particular system and thus are not reliable. We propose a spatial partitioning of the system, which is based on a charge transfer-free reference state, namely superimposition of electron densities of the noninteracting fragments. We show that this method, employing constrained DFT for the calculation of the charge-transfer energy, yields reliable results and is robust with respect to the strength of the charge transfer, the basis set size, and the DFT functional used. Because it is based on DFT, the method is applicable to rather large systems

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

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