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.

The reaction energies for 34 typical organic isomerizations including oxygen and nitrogen heteroatoms are investigated with modern quantum chemical methods that have the perspective of also being applicable to large systems. The experimental reaction enthalpies are corrected for vibrational and thermal effects, and the thus derived "experimental" reaction energies are compared to corresponding theoretical data. A series of standard AO basis sets in combination with second-order perturbation theory (MP2, SCS-MP2), conventional density functionals (e.g., PBE, TPSS, B3-LYP, MPW1K, BMK), and new perturbative functionals (B2-PLYP, mPW2-PLYP) are tested. In three cases, obvious errors of the experimental values could be detected, and accurate coupled-cluster [CCSD(T)] reference values have been used instead. It is found that only triple-zeta quality AO basis sets provide results close enough to the basis set limit and that sets like the popular 6-31G(d) should be avoided in accurate work. Augmentation of small basis sets with diffuse functions has a notable effect in B3-LYP calculations that is attributed to intramolecular basis set superposition error and covers basic deficiencies of the functional. The new methods based on perturbation theory (SCS-MP2, X2-PLYP) are found to be clearly superior to many other approaches; that is, they provide mean absolute deviations of less than 1.2 kcal mol-1 and only a few (<10%) outliers. The best performance in the group of conventional functionals is found for the highly parametrized BMK hybrid meta-GGA. Contrary to accepted opinion, hybrid density functionals offer no real advantage over simple GGAs. For reasonably large AO basis sets, results of poor quality are obtained with the popular B3-LYP functional that cannot be recommended for thermochemical applications in organic chemistry. The results of this study are complementary to often used benchmarks based on atomization energies and should guide chemists in their search for accurate and efficient computational thermochemistry methods.

Computational modeling of biological systems is a rapidly evolving field that calls for methods that are able to allow for extensive sampling with systems consisting of thousands of atoms. Semiempirical quantum chemical (SE) methods are a promising tool to aid with this, but the rather bad performance of standard SE methods for noncovalent interactions is clearly a limiting factor. Enhancing SE methods with empirical corrections for dispersion and hydrogen-bonding interactions was found to be a big improvement, but for the hydrogen-bonding corrections the drawback of breaking down in the case of substantial changes to the hydrogen bond, e.g., proton transfer, posed a serious limitation for its general applicability. This work presents a further improved hydrogenbonding correction that can be generally included in parameter fitting procedures, as it does not suffer from the conceptual flaws of previous approaches: hydrogen bonds are now treated as an interaction term between electronegative acceptor and donor atoms, "weighted" by a function of the position of H atoms between them, and multiplied with a damping function to correct the short-and long-range behavior. The performance of the new approach is evaluated for PM6, AM1, OM3, and SCC-DFTB as well as several force-field (FF) methods for a number of standard benchmark sets with hydrogen-bonded systems. The new approach is found to reach the same accuracy as the second-generation hydrogen-bonding correction with less parameters, while it avoids among other issues the conceptual problem with electronic structure changes. SE methods augmented this way reach the accuracy of DFT-D approaches for a large number of cases investigated, while still being about 3 orders of magnitude faster. Moreover, the new correction scheme is transferable also to FF methods that were shown to have serious problems with hydrogen-bonding interactions.

A diversity-oriented approach for the generation of thermochemical benchmark sets is presented. Test sets consisting of randomly generated "artificial molecules" (AMs) are proposed that rely on systematic constraints rather than uncontrolled chemical biases. In this way, the narrow structural space of chemical intuition is opened up and electronically difficult cases can be produced in an unforeseeable manner. For the calculation of chemically meaningful relative energies, AMs are systematically decomposed into small molecules (hydrides and diatomics). Two different example test sets containing eight-atom, single-reference, main group AMs with chemically very diverse and unusual structures are generated. Highly accurate all-electron, estimated CCSD(T)/complete basis set reference energies are also provided. They are used to benchmark the density functionals S-VWN, BP86, B-LYP, B97-D, PBE, TPSS, PBEh, BH-LYP, B3-PW91, B3-LYP, B2-PLYP, B2GP-PLYP, BMK, MPW1B95, M05, M05-2X, PW6B95, M06, M06-L, and M06-2X. In selected cases, an empirical dispersion correction (DFT-D) has been applied. Due to the composition of the sets, it is expected that a good performance indicates "robustness" in many different chemical applications. The results of a statistical analysis of the errors for the entire set with 165 entries (average reaction energy of 117 kcal/mol, dubbed as the MB08-165 set) perfectly fit to the "Jacob's ladder" metaphor for the ordering of density functionals according to their theoretical complexity. The mean absolute deviation (MAD) decreases very strongly from LDA (20 kcal/mol) to GGAs (MAD of about 10 kcal/mol) but then was less pronounced to hybrid-GGAs (MAD of about 6-8 kcal/mol). The best performance (MAD of 4.1-4.2 kcal/mol) is found for the (fifth-rung) double-hybrid functionals B2-PLYP-D and B2GP-PLYP-D, followed by the M06-2X meta-hybrid (MAD of 4.8 kcal/mol). The significance of the proposed approach for thermodynamic benchmarking is discussed and related to the observed performance ranking also regarding wave function based methods.

Semiempirical quantum mechanical (SQM) methods offer a fast approximate treatment of the electronic structure and the properties of large molecules. Careful benchmarks are required to establish their accuracy. Here, we report a validation of standard SQM methods using a subset of the comprehensive GMTKN24 database for general main group thermochemistry, kinetics, and noncovalent interactions, which has recently been introduced to evaluate density functional theory (DFT) methods ( J. Chem. Theory Comput. 2010 , 6 , 107 ). For all SQM methods considered presently, parameters are available for the elements H, C, N, and O, and consequently, we have extracted from the GMTKN24 database all species containing only these four elements (excluding multireference cases). The resulting GMTKN24-hcno database has 370 entries (derived from 593 energies) compared with 715 entries (derived from 1033 energies) in the original GMTKN24 database. The current benchmark covers established standard SQM methods (AM1, PM6), more recent approaches with orthogonalization corrections (OM1, OM2, OM3), and the self-consistent-charge density functional tight binding method (SCC-DFTB). The results are compared against each other and against DFT results using standard functionals. We find that the OMx methods outperform AM1, PM6, and SCC-DFTB by a significant margin, with a substantial gain in accuracy especially for OM2 and OM3. These latter methods are quite accurate even in comparison with DFT, with an overall mean absolute deviation of 6.6 kcal/mol for PBE and 7.9 kcal/mol for OM3. The OMx methods are also remarkably robust with regard to the unusual bonding situations encountered in the "mindless" MB08-165 test set, for which all other SQM methods fail badly.