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In the present study, we have devised the G4(MP2)-XK composite method that covers species with up to fifth-row main-group elements (i.e., up to Rn). This new protocol is based on the previously published G4(MP2)-6X method, which has a general accuracy of ∼5 kJ mol–1 for a diverse range of first- and second-row systems. The main difference between G4(MP2)-6X and G4(MP2)-XK is that the Pople-type basis sets in the former are replaced by Karlsruhe-type basis sets, with adjustments to the standard Karlsruhe basis sets to mimic the ones that they replace. Generally, G4(MP2)-XK is comparable in accuracy to G4(MP2)-6X. It is somewhat computationally more efficient than G4(MP2)-6X for the larger species that we have examined (e.g., a pentaglycine peptide). Importantly, the accuracy of G4(MP2)-XK for heavier elements is similar to that for first- and second-row species, even though it contains parameters that are fitted only to systems of the first two rows. This is indicative of the transferability of G4(MP2)-XK,...

We have used computational quantum chemistry to investigate the thermochemistry of α-hydrogen abstraction from the full set of amino acids normally found in proteins, as well as their peptide forms, by •OH and •SH radicals. These reactions, with their reasonable complexity in the electronic structure (at the α-carbon), are chosen as a consistent set of models for conducting a fairly robust assessment of theoretical procedures. Our benchmarking investigation shows that, in general, the performance for the various classes of theoretical methods improves in the order nonhybrid DFT → hybrid DFT → double-hybrid DFT → composite procedures. More specifically, we find that the DSD-PBE-P86 double-hybrid DFT procedure yields the best agreement with our high-level W1X-2 vibrationless barriers and reaction energies for this particular set of systems. A significant observation is that, when one considers relative instead of absolute values for the vibrationless barriers and reaction energies, even nonhybrid DFT procedures perform fairly well. To exploit this feature in a cost-effective manner, we have examined a number of multilayer schemes for the calculation of reaction energies and barriers for the abstraction reactions. We find that accurate values can be obtained when a "core" of glycine plus the abstracting radical is treated by DSD-PBE-P86, and the substituent effects are evaluated with M06-2X. Inspection of the set of calculated thermochemical data shows that the correlation between the free energy barriers and reaction free energies is strongest when the reactions are either endergonic or nearly thermoneutral.

The relative energies of the YMPJ conformer database of the 20 proteinogenic amino acids, with N- and C-termination, have been re-evaluated using explicitly correlated coupled cluster methods. Lower-cost ab initio methods such as MP2-F12 and CCSD-F12b actually are outperformed by double-hybrid DFT functionals; in particular, the DSD-PBEP86-NL double hybrid performs well enough to serve as a secondary standard. Among range-separated hybrids, ωB97X-V performs well, while B3LYP-D3BJ does surprisingly well among traditional DFT functionals. Treatment of dispersion is important for the DFT functionals; for the YMPJ set, D3BJ generally works as well as the NL nonlocal dispersion functional. Basis set sensitivity for DFT calculations on these conformers is weak enough that def2-TZVP is generally adequate. For conformer corrections to heats of formation, B3LYP-D3BJ and especially DSD-PBEP86-D3BJ or DSD-PBEP86-NL are adequate for all but the most exacting applications. The revised geometries and energetics for the YMPJ database have been made available as Supporting Information and should be useful in the parametrization and validation of molecular mechanics force fields and other low-cost methods. The very recent dRPA75 method yields good performance, without resorting to an empirical dispersion correction, but is still outperformed by DSD-PBEP86-D3BJ and particularly DSD-PBEP86-NL. Core-valence corrections are comparable in importance to improvements beyond CCSD(T*)/cc-pVDZ-F12 in the valence treatment.

The radical anion [Al2O4](-) has been identified as a rare example of a small gas-phase mixed-valence system with partially localized, weakly coupled class II character in the Robin/Day classification. It exhibits a low-lying C2v minimum with one terminal oxyl radical ligand and a high-lying D2h minimum at about 70 kJ/mol relative energy with predominantly bridge-localized-hole character. Two identical C2v minima and the D2h minimum are connected by two C2v-symmetrical transition states, which are only ca. 6-10 kJ/mol above the D2h local minimum. The small size of the system and the absence of environmental effects has for the first time enabled the computation of accurate ab initio benchmark energies, at the CCSDT(Q)/CBS level using W3-F12 theory, for a class-II mixed-valence system. These energies have been used to evaluate wave function-based methods [CCSD(T), CCSD, SCS-MP2, MP2, UHF] and density functionals ranging from semilocal (e.g., BLYP, PBE, M06L, M11L, N12) via global hybrids (B3LYP, PBE0, BLYP35, BMK, M06, M062X, M06HF, PW6B95) and range-separated hybrids (CAM-B3LYP, ωB97, ωB97X-D, LC-BLYP, LC-ωPBE, M11, N12SX), the B2PLYP double hybrid, and some local hybrid functionals. Global hybrids with about 35-43% exact-exchange (EXX) admixture (e.g., BLYP35, BMK), several range hybrids (CAM-B3LYP, ωB97X-D, ω-B97), and a local hybrid provide good to excellent agreement with benchmark energetics. In contrast, too low EXX admixture leads to an incorrect delocalized class III picture, while too large EXX overlocalizes and gives too large energy differences. These results provide support for previous method choices for mixed-valence systems in solution and for the treatment of oxyl defect sites in alumosilicates and SiO2. Vibrational gas-phase spectra at various computational levels have been compared directly to experiment and to CCSD(T)/aug-cc-pV(T+d)Z data.

In the present study, we use composite methods, denoted CM(5)Λ and CM5, with post-CCSD(T) terms up to CCSDTQ(5)Λ and CCSDTQ5, respectively, to evaluate the atomization energies for CrO, CrO2, and CrO3. The heats of formation (ΔHf,298) based on our best estimated atomization energies are 198.3 ± 5 kJ mol(-1) (CrO), -81.3 ± 5 kJ mol(-1) (CrO2), and -286.8 ± 20 kJ mol(-1) (CrO3). Standard G4-type composite methods yield atomization energies that are adequate for CrO, less good for CrO2, and least good for CrO3. CrO3 is highly multireference in character, and therefore, a "black box" approach of using a single-reference RHF wave function is inadequate, even for "high-level" G4-type methods. We find that, for CrO3, there is a very large difference in the G4 atomization energies depending on whether an RHF or a UHF reference is used, which is mainly associated with large differences in the MP4 components. In general, we propose that a large R-versus-U difference is likely to be an indication of potential problems in the theoretical treatment. Going beyond G4 to a more rigorous UCCSD(T)-based composite scheme [termed U-CM(3:[DZ,TZ]) in the present study], we again find a large difference (but significantly smaller than that for G4) between the CrO3 atomization energies based on RHF or UHF references. Intriguingly, the use of Brueckner orbitals as reference orbitals in all components, as in the corresponding Brueckner Doubles (BD) procedure [B-CM(3:[DZ,TZ])], produces results for CrO3 that are independent of whether RHF or UHF orbitals are used as the starting point.

Calculation of accurate water-water interaction energies is of fundamental importance in computational modeling of many biological and chemical phenomena. We have obtained benchmark barrier heights for proton-exchange reactions and complexation energies in water clusters (H2O)n (n = 1-6) by means of the high-level W1-F12 procedure. We find that lower-cost composite procedures (e.g., G4(MP2) and G4(MP2)-6X), as well as MP2 and SCS-MP2, exhibit surprisingly poor performance for the barrier heights of reactions involving multiple proton exchanges. Moreover, the performance significantly deteriorates with increasing size of the clusters. Similar observations apply to complexation energies in water clusters, and to barrier heights for proton exchange in ammonia and hydrogen fluoride clusters. We propose a modified version of G4(MP2)-6X (denoted G4(MP2)-6X+) that includes sp- and d-diffuse functions in the CCSD(T) term, which gives excellent proton-exchange barrier heights at a computational cost only slightly greater than that of standard G4(MP2). G4(MP2)-6X+ also leads to a substantial improvement over G4(MP2) and G4(MP2)-6X for the calculation of electron affinities.