Accurate Calculation of the Heats of Formation for Large Main Group Compounds with Spin-Component Scaled MP2 Methods

Three MP2-type electron correlation treatments and standard density functional theory (DFT) approaches are used to predict the heats of formation for a wide variety of different molecules. The SCF and MP2 calculations are performed efficiently using the resolution-of-the-identity (RI) approximation such that large basis set (i.e., polarized valence quadruple-ζ quality) treatments become routinely possible for systems with 50−100 atoms. An atom equivalent scheme that corrects the calculated atomic energies is applied to extract the “real” accuracy of the methods for chemically relevant problems. It is found that the spin-component-scaled MP2 method (SCS-MP2, J. Chem. Phys, 2003, 118, 9095) performs best and provides chemical accuracy (MAD of 1.18 kcal/mol) for a G2/97 test set of molecules. The computationally more economical SOS-MP2 variant, which retains only the opposite-spin part of the correlation energy, is slightly less accurate (MAD of 1.36 kcal/mol) than SCS-MP2. Both spin-component-scaled MP2 treatments perform significantly better than standard MP2 (MAD of 1.77 kcal/mol) and DFT-B3LYP (MAD of 2.12 kcal/mol). These conclusions are supported by results obtained for a second test set of complex systems containing 70 molecules, including charged, strained, polyhalogenated, hypervalent, and large unsaturated species (e.g. C60). For this set, DFT-B3LYP performs badly (MAD of 8.6 kcal/mol) with many errors >10−20 kcal/mol while the spin-component-scaled MP2 methods are still very accurate (MAD of 2.8 and 3.7 kcal/mol, respectively). DFT-B3LYP shows an obvious tendency to underestimate molecular stability as the system size increases. Out of six density functionals tested, the hybrid functional PBE0 performs best. All in all, the SCS-MP2 method, together with large AO basis sets, clearly outperforms current DFT approaches and seems to be the most accurate quantum chemical model that routinely can predict the thermodynamic properties of large main group compounds

<i>n</i>-Alkane Isodesmic Reaction Energy Errors in Density Functional Theory Are Due to Electron Correlation Effects

The isodesmic reaction energies of n-alkanes to ethane, which have so far been known to give systematic errors in standard DFT calculations, are successfully reproduced by SCS-MP2 and dispersion-corrected double-hybrid functionals. The failure of conventional DFT is not due to the lack of long-range exchange interactions but results from an inaccurate account of medium-range electron correlation that is attractive for 1,3-interactions (proto-branching). Highly accurate CCSD(T)/CBS data are provided that are recommended in thermochemical benchmarks

“Mindless” DFT Benchmarking

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

Performance of the van der Waals Density Functional VV10 and (hybrid)GGA Variants for Thermochemistry and Noncovalent Interactions

The nonlocal van der Waals density functional VV10 (Vydrov, O. A.; Van Voorhis, T. J. Chem. Phys. 2010, 133, 244103) is tested for the thermochemical properties of 1200+ atoms and molecules in the GMTKN30 database in order to assess its global accuracy. Five GGA and hybrid functionals in unmodified form are augmented by the nonlocal (NL) part of the VV10 functional (one parameter adjusted). The addition of the NL dispersion energy definitely improves the results of all tested functionals. On the basis of little empiricism and basic physical insight, DFT-NL can be recommended as a fully electronic, robust electronic structure method

Double-Hybrid Density Functionals Provide a Balanced Description of Excited ¹L_a and ¹L_b States in Polycyclic Aromatic Hydrocarbons

The time-dependent density functional theory (TD-DFT) double-hybrid methods TD-B2-PLYP and TD-B2GP-PLYP are applied to five linear and 12 nonlinear polycyclic aromatic hydrocarbons. The absolute errors compared to experiment for the two lowest-lying 1La and 1Lb excited states are evaluated and it is also tested whether the energetic order of those states and their energy difference is reproduced correctly. The results are compared to published CC2, global hybrid, and long-range corrected hybrid TD-DFT results. The two double-hybrids outmatch the other methods in terms of absolute and relative accuracy without an empirical adjustment of parameters. Although of different electronic character, both types of states are described on an equal footing by the double-hybrids. Particularly, the B2GP-PLYP functional yields very good results, which is in accordance with previous benchmarks

The Vibronic Structure of Electronic Absorption Spectra of Large Molecules: A Time-Dependent Density Functional Study on the Influence of “Exact” Hartree−Fock Exchange

The functional dependence of excited-state geometries and normal modes calculated with time-dependent density functional theory (TDDFT) is investigated on the basis of vibronic structure calculations of the absorption spectra of large molecules. For a set of molecules covering a wide range of different structures including organic dyes, biological chromophores, and molecules of importance in material science, quantum mechanical simulations of the vibronic structure are performed. In total over 40 singlet−singlet transitions of neutral closed-shell compounds and doublet−doublet transitions of neutral radicals, radical cations, and anions are considered. Calculations with different standard density functionals show that the predicted vibronic structure critically depends on the fraction of the “exact” Hartree−Fock exchange (EEX) included in hybrid functionals. The effect can been traced back to a large influence of EEX on the geometrical displacement upon excitation. On the contrary, the dependence of the results on the choice of the local exchange-correlation functional is found to be rather small. On the basis of detailed comparisons with experimental spectra conclusions are drawn concerning the optimum amount of EEX mixing for a proper description of the excited-state properties. The relationship of the quality of the simulated spectra with the errors for 0−0 transition energies is discussed. For the investigated singlet−singlet π → π* transitions and the first strongly dipole-allowed transitions of PAH radical cations some rules of thumb concerning the optimum portion of EEX are derived. However, in general no universal amount of EEX seems to exist that gives a uniformly good description for all systems and states. Nevertheless an inclusion of about 30−40% of EEX in the functional is found empirically to yield in most cases simulated spectra that compare very well with those from experiment and thus seems to be necessary for an accurate description of the excited-state geometry. Pure density functionals that are computationally more efficient provide less accurate spectra in most cases and their application is recommended solely for comparison purposes to obtain estimates for the reliability of the theoretical predictions

Benchmarking of London Dispersion-Accounting Density Functional Theory Methods on Very Large Molecular Complexes

A new test set (S12L) containing 12 supramolecular noncovalently bound complexes is presented and used to evaluate seven different methods to account for dispersion in DFT (DFT-D3, DFT-D2, DFT-NL, XDM, dDsC, TS-vdW, M06-L) at different basis set levels against experimental, back-corrected reference energies. This allows conclusions about the performance of each method in an explorative research setting on “real-life” problems. Most DFT methods show satisfactory performance but, due to the largeness of the complexes, almost always require an explicit correction for the nonadditive Axilrod–Teller–Muto three-body dispersion interaction to get accurate results. The necessity of using a method capable of accounting for dispersion is clearly demonstrated in that the two-body dispersion contributions are on the order of 20–150% of the total interaction energy. MP2 and some variants thereof are shown to be insufficient for this while a few tested D3-corrected semiempirical MO methods perform reasonably well. Overall, we suggest the use of this benchmark set as a “sanity check” against overfitting to too small molecular cases

Efficient and Accurate Double-Hybrid-Meta-GGA Density FunctionalsEvaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions

We present an extended and improved version of our recently published database for general main group thermochemistry, kinetics, and noncovalent interactions [J. Chem. Theory Comput. 2010, 6, 107], which is dubbed GMTKN30. Furthermore, we suggest and investigate two new double-hybrid-meta-GGA density functionals called PTPSS-D3 and PWPB95-D3. PTPSS-D3 is based on reparameterized TPSS exchange and correlation contributions; PWPB95-D3 contains reparameterized PW exchange and B95 parts. Both functionals contain fixed amounts of 50% Fock-exchange. Furthermore, they include a spin-opposite scaled perturbative contribution and are combined with our latest atom-pairwise London-dispersion correction [J. Chem. Phys. 2010, 132, 154104]. When evaluated with the help of the Laplace transformation algorithm, both methods scale as N4 with system size. The functionals are compared with the double hybrids B2PLYP-D3, B2GPPLYP-D3, DSD-BLYP-D3, and XYG3 for GMTKN30 with a quadruple-ζ basis set. PWPB95-D3 and DSD-BLYP-D3 are the best functionals in our study and turned out to be more robust than B2PLYP-D3 and XYG3. Furthermore, PWPB95-D3 is the least basis set dependent and the best functional at the triple-ζ level. For the example of transition metal carbonyls, it is shown that, mainly due to the lower amount of Fock-exchange, PWPB95-D3 and PTPSS-D3 are better applicable than the other double hybrids. Finally, we discuss in some detail the XYG3 functional [Proc. Nat. Acad. Sci. U.S.A. 2009, 106, 4963], which makes use of B3LYP orbitals and electron densities. We show that it is basically a highly nonlocal variant of B2PLYP and that its partially good performance is mainly due to a larger effective amount of perturbative correlation compared to other double hybrids. We finally recommend the PWPB95-D3 functional in general chemistry applications

Van der Waals Complexes of Polar Aromatic Molecules: Unexpected Structures for Dimers of Azulene

Full geometry optimizations at the dispersion corrected DFT-BLYP/TZV2P level of theory have been performed for dimers of azulene that may serve as a model system for the van der Waals complexes of polar π systems. The structures and binding energies for 11 dimers are investigated in detail. The DFT-D interaction energies have been successfully checked against results from the accurate SCS-MP2/aug-cc-pVTZ approach. Out of the nine investigated stacked complexes, eight have binding energies larger than 7.4 kcal/mol (SCS-MP2) that exceed the value of 7.1 kcal/mol for the best naphthalene dimer. T-shaped arrangements (CH···π) are significantly less stable. Two out of the three best structures have an antiparallel alignment of the monomer dipole moments in the complex, although the best ones with a parallel orientation are only about 0.5 kcal/mol less strongly bound which points to a minor importance of dipole−dipole interactions to binding. Quite surprisingly, the energetically lowest structure (ΔE = −9.2 kcal/mol) corresponds to a situation where the two seven-membered rings are located almost on top of each other (7−7) and the long molecular axes are rotated against each other by 130°. The 7−7 structural motif is found also in other energetically low-lying structures, and the expected 5−7 (two-side) arrangement is less strongly bound by about 2 kcal/mol. This can be explained by the electrostatic potential of azulene that only partially reflects the charge separation according to the common 4n + 2 π electron rule. General rules for predicting stable van der Waals complexes of polar π systems are discussed

Calculation of Electron Ionization Mass Spectra with Semiempirical GFNn-xTB Methods

In this work, we have tested two different extended tight-binding methods in the framework of the quantum chemistry electron ionization mass spectrometry (QCEIMS) program to calculate electron ionization mass spectra. The QCEIMS approach provides reasonable, first-principles computed spectra, which can be directly compared to experiment. Furthermore, it provides detailed insight into the reaction mechanisms of mass spectrometry experiments. It sheds light upon the complicated fragmentation procedures of bond breakage and structural rearrangements that are difficult to derive otherwise. The required accuracy and computational demands for successful reproduction of a mass spectrum in relation to the underlying quantum chemical method are discussed. To validate the new GFN2-xTB approach, we conduct simulations for 15 organic, transition-metal, and main-group inorganic systems. Major fragmentation patterns are analyzed, and the entire calculated spectra are directly compared to experimental data taken from the literature. We discuss the computational costs and the robustness (outliers) of several calculation protocols presented. Overall, the new, theoretically more sophisticated semiempirical method GFN2-xTB performs well and robustly for a wide range of organic, inorganic, and organometallic systems