Double-hybrid Density Functional Theory Procedures Research Articles

Frequency Scale Factors for Some Double-Hybrid Density Functional Theory Procedures: Accurate Thermochemical Components for High-Level Composite Protocols

In the present study, we have obtained geometries and frequency scale factors for a number of double-hybrid density functional theory (DH-DFT) procedures. We have evaluated their performance for obtaining thermochemical quantities [zero-point vibrational energies (ZPVE) and thermal corrections for 298 K enthalpies (ΔH298) and 298 K entropies (S298)] to be used within high-level composite protocols (using the W2X procedure as a probe). We find that, in comparison with the previously prescribed protocol for optimization and frequency calculations (B3-LYP/cc-pVTZ+d), the use of contemporary DH-DFT methods such as DuT-D3 and DSD-type procedures leads to a slight overall improved performance compared with B3-LYP. A major strength of this approach, however, lies in the better robustness of the DH-DFT methods in that the largest deviations are notably smaller than those for B3-LYP. In general, the specific choices of the DH-DFT procedure and the associated basis set do not drastically change the performance. Nonetheless, we find that the DSD-PBE-P86/aug'-cc-pVTZ+d combination has a very slight edge over the others that we have examined, and we recommend its general use for geometry optimization and vibrational frequency calculations, in particular within high-level composite methods such as the higher-level members of the WnX series of protocols. The scale factors determined for DSD-PBE-P86/aug'-cc-pVTZ+d are 0.9830 (ZPVE), 0.9876 (ΔH298), and 0.9923 (S298).

An assessment of theoretical procedures for π-conjugation stabilisation energies in enones

We introduce a representative database of 22 α,β- to β,γ-enecarbonyl isomerisation energies (to be known as the EIE22 data-set). Accurate reaction energies are obtained at the complete basis-set limit CCSD(T) level by means of the high-level W1-F12 thermochemical protocol. The isomerisation reactions involve a migration of one double bond that breaks the conjugated π-system. The considered enecarbonyls involve a range of common functional groups (e.g., Me, NH2, OMe, F, and CN). Apart from π-conjugation effects, the chemical environments are largely conserved on the two sides of the reactions and therefore the EIE22 data-set allows us to assess the performance of a variety of density functional theory (DFT) procedures for the calculation of π-conjugation stabilisation energies in enecarbonyls. We find that, with few exceptions (M05-2X, M06-2X, BMK, and BH&HLYP), all the conventional DFT procedures attain root mean square deviations (RMSDs) between 5.0 and 11.7 kJ mol−1. The range-separated and double-hybrid DFT procedures, on the other hand, show good performance with RMSDs below the ‘chemical accuracy’ threshold. We also examine the performance of composite and standard ab initio procedures. Of these, SCS-MP2 offers the best performance-to-computational cost ratio with an RMSD of 0.8 kJ mol−1.

Assessment of theoretical procedures for a diverse set of isomerization reactions involving double-bond migration in conjugated dienes

We introduce a representative database of 60 accurate diene isomerization energies obtained by means of the high-level, ab initio Wn–F12 thermochemical protocols. The isomerization reactions involve a migration of one double bond that breaks the π-conjugated system. The considered dienes involve a range of hydrocarbon functional groups, including linear, branched, and cyclic moieties. This set of benchmark isomerization energies allows an assessment of the performance of more approximate theoretical procedures for the calculation of π-conjugation stabilization energies in dienes. We evaluate the performance of a large number of density functional theory (DFT) and double-hybrid DFT (DHDFT) procedures. We find that, with few exceptions (most notably BMK-D3 and M05-2X), conventional DFT procedures have difficulty describing reactions of the type: conjugated diene→non-conjugated diene, with root mean square deviations (RMSDs) between 4.5 and 11.7kJmol−1. However, DHDFT procedures show excellent performance with RMSDs well below the ‘chemical accuracy’ threshold.

BDE261: A Comprehensive Set of High-Level Theoretical Bond Dissociation Enthalpies

We have used the high-level W1w protocol to compile a comprehensive collection of 261 bond dissociation enthalpies (BDEs) for bonds connecting hydrogen, first-row and second-row p-block elements. Together they cover 45 bond types, and we term this the BDE261 set. We have used these benchmark values to assess the performance of computationally less demanding theoretical procedures, including density functional theory (DFT), double-hybrid DFT (DHDFT), and high-level composite procedures. We find that the M06-2X (DFT), ROB2-PLYP and DuT-D3 (DHDFT), and G3X(MP2)-RAD and G4(MP2)-6X (composite) procedures yield absolute BDEs with satisfactory to excellent accuracy. Overall, we recommend G4(MP2)-6X as an accurate and relatively cost-effective procedure for the direct computation of BDEs. One important finding is that the deviations for DFT and (especially) DHDFT procedures are often quite systematic. This allows an alternative approach to obtaining accurate absolute BDEs, namely, to evaluate accurate relative BDEs (RBDEs) using a computationally less demanding procedure, and to use these RBDEs in combination with appropriate and accurate reference BDEs to give accurate absolute BDEs. We recommend DuT-D3 for this purpose. For a still less computationally demanding approach, we introduce the deviation from additivity of the RBDE (DARBDE), and demonstrate that the combination of lower-level DARBDEs for larger systems and higher-level (W1w) reference RBDEs and BDEs for small systems can be utilized to obtain improved RBDEs for multiply substituted systems at low cost.

Assessment of Theoretical Procedures for Calculating Barrier Heights for a Diverse Set of Water-Catalyzed Proton-Transfer Reactions

Accurate electronic barrier heights are obtained for a set of nine proton-transfer tautomerization reactions, which are either (i) uncatalyzed, (ii) catalyzed by one water molecule, or (iii) catalyzed by two water molecules. The barrier heights for reactions (i) and (ii) are obtained by means of the high-level ab initio W2.2 thermochemical protocol, while those for reaction (iii) are obtained using the W1 protocol. These three sets of benchmark barrier heights allow an assessment of the performance of more approximate theoretical procedures for the calculation of barrier heights of uncatalyzed and water-catalyzed reactions. We evaluate initially the performance of the composite G4 procedure and variants thereof (e.g., G4(MP2) and G4(MP2)-6X), as well as that of standard ab initio procedures (e.g., MP2, SCS-MP2, and MP4). We find that the performance of the G4(MP2)-type thermochemical procedures deteriorates with the number of water molecules involved in the catalysis. This behavior is linked to deficiencies in the MP2-based basis-set-correction term in the G4(MP2)-type procedures. This is remedied in the MP4-based G4 procedure, which shows good performance for both the uncatalyzed and the water-catalyzed reactions, with mean absolute deviations (MADs) from the benchmark values lying below the threshold of "chemical accuracy" (arbitrarily defined as 1 kcal mol(-1) ≈ 4.2 kJ mol(-1)). We also examine the performance of a large number of density functional theory (DFT) and double-hybrid DFT (DHDFT) procedures. We find that, with few exceptions (most notably PW6-B95 and B97-2), the performance of the DFT procedures that give good results for the uncatalyzed reactions deteriorates with the number of water molecules involved in the catalysis. The DHDFT procedures, on the other hand, show excellent performance for both the uncatalyzed and catalyzed reactions. Specifically, almost all of them afford MADs below the "chemical accuracy" threshold, with ROB2-PLYP and B2K-PLYP showing the best overall performance.

Obtaining Good Performance With Triple-ζ-Type Basis Sets in Double-Hybrid Density Functional Theory Procedures.

A variety of combinations of B-LYP-based double-hybrid density functional theory (DHDFT) procedures and basis sets have been examined. A general observation is that the optimal combination of exchange contributions is in the proximity of 30% Becke 1988 (B88) exchange and 70% Hartree-Fock (HF) exchange, while for the correlation contributions, the use of independently optimized spin-component-scaled Møller-Plesset second-order perturbation theory (SCS-MP2) parameters (MP2OS and MP2SS) is beneficial. The triple-ζ Dunning aug'-cc-pVTZ+d and Pople 6-311+G(3df,2p)+d basis sets are found to be cost-effective for DHDFT methods. As a result, we have formulated the DuT-D3 DHDFT procedure, which employs the aug'-cc-pVTZ+d basis set and includes 30% B88 and 70% HF exchange energies, 59% LYP, 47% MP2OS, and 36% MP2SS correlation energies, and a D3 dispersion correction with the parameters s6 = 0.5, sr,6 = 1.569, and s8 = 0.35. Likewise, the PoT-D3 DHDFT procedure was formulated with the 6-311+G(3df,2p)+d basis set and has 32% B88 and 68% HF exchange energies, 63% LYP, 46% MP2OS, and 27% MP2SS correlation energies, and the D3 parameters s6 = 0.5, sr,6 = 1.569, and s8 = 0.30. Testing using the large E3 set of 740 energies demonstrates the robustness of these methods. Further comparisons show that the performance of these methods, particularly DuT-D3, compares favorably with the previously reported DSD-B-LYP and DSD-B-LYP-D3 methods used in conjunction with quadruple-ζ aug'-pc3+d and aug'-def2-QZVP basis sets but at lower computational expense. The previously reported ωB97X-(LP)/6-311++G(3df,3pd) procedure also performs very well. Our findings highlight the cost-effectiveness of appropriate- and moderate-sized triple-ζ basis sets in the application of DHDFT procedures.

O - H Bond Dissociation Energies

High-level composite, ab initio and density functional theory (DFT) procedures have been employed to study O–H bond dissociation energies (BDEs), as well as radical stabilization energies (RSEs) in the oxygen-centred radicals that are formed in the dissociation of the O–H bonds. Benchmark values are provided by Wn results up to W3.2 and W4.x. We are able to recommend revised BDE values for FO–H (415.6 ± 3 kJ mol–1), MeC(O)O–H (459.8 ± 6 kJ mol–1) and CF3CH2O–H (461.9 ± 6 kJ mol–1) on the basis of high-level calculations. We find that Gn-type procedures are generally reliable and cost-effective, and that some contemporary functionals and double-hybrid DFT procedures also provide adequate O–H BDEs/RSEs. We note that the variations in the O–H BDEs are associated with variations in the stabilities of not only the radicals but also the closed-shell precursor molecules. Most substituents destabilize both species, with σ-electron-withdrawing groups having larger destabilizing effects, while π-electron acceptors are stabilizing. Although there is little correlation between the stabilizing/destabilizing effects of the substituents and the RSEs, we present some general patterns in the RSEs that emerge from the present study.

Consequences of Spin Contamination in Unrestricted Calculations on Open-Shell Species: Effect of Hartree−Fock and Møller−Plesset Contributions in Hybrid and Double-Hybrid Density Functional Theory Approaches

The extent of spin contamination in unrestricted versions of pure, hybrid and double-hybrid density functional theory (DFT) methods, and its consequences, as manifested in the difference between unrestricted and restricted energies (U - R), has been investigated for 22 homolytic bond dissociation reactions. In accordance with previous studies, increasing the amount of Hartree-Fock (HF) exchange in unrestricted hybrid DFT procedures leads to an increase in the extent of spin contamination. However, in unrestricted double-hybrid DFT procedures, which include both a proportion of HF exchange and a perturbative correlation contribution (MP2), the opposing behavior of UHF and UMP2 with respect to spin contamination leads to smaller differences between the energies predicted by unrestricted and restricted variants. For example, for the most spin-contaminated radicals, a 30-100 kJ mol(-1) |U - R| difference at the HF and MP2 levels is reduced to just 0-5 kJ mol(-1) with the double-hybrid functionals. The double-hybrid UDFT procedures can thus benefit from the inclusion of UHF and UMP2 contributions without incurring to the same extent the problems associated with spin contamination.

Bond Dissociation Energies and Radical Stabilization Energies: An Assessment of Contemporary Theoretical Procedures

Various contemporary theoretical procedures have been tested for their accuracy in predicting the bond dissociation energies (BDEs) and the radical stabilization energies (RSEs) for a test set of 22 monosubstituted methyl radicals. The procedures considered include the high-level W1, W1', CBS-QB3, ROCBS-QB3, G3(MP2)-RAD, and G3X(MP2)-RAD methods, unrestricted and restricted versions of the double-hybrid density functional theory (DFT) procedures B2-PLYP and MPW2-PLYP, and unrestricted and restricted versions of the hybrid DFT procedures BMK and MPWB1K, as well as the unrestricted DFT procedures UM05 and UM05-2X. The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the comparatively less expensive DFT procedures. RMPWB1K and both RBMK and UBMK give very promising results for absolute BDEs, while additionally restricted and unrestricted X2-PLYP methods and UM05-2X give excellent RSE values. UM05, UB2-PLYP, UMPW2-PLYP, UM05-2X, and UMPWB1K are among the less well performing methods for BDEs, while UMPWB1K and UM05 perform less well for RSEs. The high-level theoretical results are used to recommend alternative experimental BDEs for propyne, acetaldehyde, and acetic acid.