Nitai Sylvetsky

W4-17: A diverse and high-confidence dataset of atomization energies for benchmarking high-level electronic structure methods

Atomization reactions are among the most challenging tests for electronic structure methods. We use the first‐principles Weizmann‐4 (W4) computational thermochemistry protocol to generate the W4‐17 dataset of 200 total atomization energies (TAEs) with 3σ confidence intervals of 1 kJ mol−1. W4‐17 is an extension of the earlier W4‐11 dataset; it includes first‐ and second‐row molecules and radicals with up to eight non‐hydrogen atoms. These cover a broad spectrum of bonding situations and multireference character, and as such are an excellent benchmark for the parameterization and validation of highly accurate ab initio methods (e.g., CCSD(T) composite procedures) and double‐hybrid density functional theory (DHDFT) methods. The W4‐17 dataset contains two subsets (i) a non‐multireference subset of 183 systems characterized by dynamical or moderate nondynamical correlation effects (denoted W4‐17‐nonMR) and (ii) a highly multireference subset of 17 systems (W4‐17‐MR). We use these databases to evaluate the performance of a wide range of CCSD(T) composite procedures (e.g., G4, G4(MP2), G4(MP2)‐6X, ROG4(MP2)‐6X, CBS‐QB3, ROCBS‐QB3, CBS‐APNO, ccCA‐PS3, W1, W2, W1‐F12, W2‐F12, W1X‐1, and W2X) and DHDFT methods (e.g., B2‐PLYP, B2GP‐PLYP, B2K‐PLYP, DSD‐BLYP, DSD‐PBEP86, PWPB95, ωB97X‐2(LP), and ωB97X‐2(TQZ)).

Conventional and Explicitly Correlated ab Initio Benchmark Study on Water Clusters: Revision of the BEGDB and WATER27 Data Sets

Benchmark ab initio energies for BEGDB and WATER27 data sets have been re-examined at the MP2 and CCSD(T) levels with both conventional and explicitly correlated (F12) approaches. The basis set convergence of both conventional and explicitly correlated methods has been investigated in detail, both with and without counterpoise corrections. For the MP2 and CCSD-MP2 contributions, rapid basis set convergence observed with explicitly correlated methods is compared to conventional methods. However, conventional, orbital-based calculations are preferred for the calculation of the (T) term, since it does not benefit from F12. CCSD(F12*) converges somewhat faster with the basis set than CCSD-F12b for the CCSD-MP2 term. The performance of various DFT methods is also evaluated for the BEGDB data set, and results show that Head-Gordons ωB97X-V and ωB97M-V functionals outperform all other DFT functionals. Counterpoise-corrected DSD-PBEP86 and raw DSD-PBEPBE-NL also perform well and are close to MP2 results. In the WATER27 data set, the anionic (deprotonated) water clusters exhibit unacceptably slow basis set convergence with the regular cc-pVnZ-F12 basis sets, which have only diffuse s and p functions. To overcome this, we have constructed modified basis sets, denoted aug-cc-pVnZ-F12 or aVnZ-F12, which have been augmented with diffuse functions on the higher angular momenta. The calculated final dissociation energies of BEGDB and WATER27 data sets are available in the Supporting Information. Our best calculated dissociation energies can be reproduced through n-body expansion, provided one pushes to the basis set and electron correlation limit for the two-body term; for the three-body term, post-MP2 contributions (particularly CCSD-MP2) are important for capturing the three-body dispersion effects. Terms beyond four-body can be adequately captured at the MP2-F12 level.

Surprising performance for vibrational frequencies of the distinguishable clusters with singles and doubles (DCSD) and MP2.5 approximations

We show that the DCSD (distinguishable clusters with all singles and doubles) correlation method permits the calculation of vibrational spectra at near-CCSD(T) quality but at no more than CCSD cost, and with comparatively inexpensive analytical gradients. For systems dominated by a single reference configuration, even MP2.5 is a viable alternative, at MP3 cost. MP2.5 performance for vibrational frequencies is comparable to double hybrids such as DSD-PBEP86-D3BJ, but without resorting to empirical parameters. DCSD is also quite suitable for computing zero-point vibrational energies in computational thermochemistry.

The aug-cc-pVnZ-F12 basis set family: Correlation consistent basis sets for explicitly correlated benchmark calculations on anions and noncovalent complexes

We have developed a new basis set family, denoted as aug-cc-pVnZ-F12 (or aVnZ-F12 for short), for explicitly correlated calculations. The sets included in this family were constructed by supplementing the corresponding cc-pVnZ-F12 sets with additional diffuse functions on the higher angular momenta (i.e., additional d-h functions on non-hydrogen atoms and p-g on hydrogen atoms), optimized for the MP2-F12 energy of the relevant atomic anions. The new basis sets have been benchmarked against electron affinities of the first- and second-row atoms, the W4-17 dataset of total atomization energies, the S66 dataset of noncovalent interactions, the Benchmark Energy and Geometry Data Base water cluster subset, and the WATER23 subset of the GMTKN24 and GMTKN30 benchmark suites. The aVnZ-F12 basis sets displayed excellent performance, not just for electron affinities but also for noncovalent interaction energies of neutral and anionic species. Appropriate CABSs (complementary auxiliary basis sets) were explored for the S66 noncovalent interaction benchmark: between similar-sized basis sets, CABSs were found to be more transferable than generally assumed.

MP2-F12 basis set convergence for the S66 noncovalent interactions benchmark: Transferability of the complementary auxiliary basis set (CABS)

Complementary auxiliary basis sets for F12 explicitly correlated calculations appear to be more transferable between orbital basis sets than has been generally assumed. We also find that aVnZ-F12 basis sets, originally developed with anionic systems in mind, appear to be superior for noncovalent interactions as well, and propose a suitable CABS sequence for them.

Probing the basis set limit for thermochemical contributions of inner-shell correlation: balance of core-core and core-valence contributions*

ABSTRACT The inner-shell correlation contributions to the total atomisation energies of the W4-17 computational thermochemistry benchmark have been determined at the CCSD(T) level near the basis set limit using several families of core correlation basis sets, such as aug-cc-pCVnZ (n = 3–6), aug-cc-pwCVnZ (n = 3–5) and nZaPa-CV (n = 3–5). The three families of basis sets agree very well with each other (0.01 kcal/mol RMS) when extrapolating from the two largest available n: however, there are considerable differences in convergence behaviour for the smaller basis sets. nZaPa-CV is superior for the core-core term and awCVnZ for the core-valence term. While the aug-cc-pwCV(T+d)Z basis set of Yockel and Wilson is superior to aug-cc-pwCVTZ, further extension of this family proved unproductive. The best compromise between accuracy and computational cost, in the context of high-accuracy computational thermochemistry methods, is CCSD(T)/awCV{T,Q}Z, where the {T,Q} notation stands for extrapolation from the awCVTZ and awCVQZ basis set pair. For lower-cost calculations, we recommend a previously proposed combination of CCSD-F12b/cc-pCVTZ-F12 and CCSD(T)/pwCVTZ(no f). While in first-row molecules core-valence correlation on average accounts for over 90% of the inner-shell contribution, in second-row molecules core-core contributions may become important, particularly in systems like P4 and S4 with multiple adjacent second-row atoms. GRAPHICAL ABSTRACT

A simple model for scalar relativistic corrections to molecular total atomisation energies

ABSTRACT Scalar relativistic corrections to atomisation energies of first- and second-row molecules can be rationalised in terms of a simple additive model, linear in changes in atomic s populations. In a sample of 200 first-and second-row molecules, such a model can account for over 98% of the variance (99% for the first-row subset). The remaining error can be halved again by adding a term involving the change in atomic p populations: those coefficients need not be fitted but can be fixed from atomic electron affinity calculations. This model allows a fairly accurate a priori estimate for the importance of scalar relativistic corrections on a reaction energy, at essentially zero computational cost. While this is not a substitute for explicit calculation of Douglas–Kroll–Hess (DKH) or exact two-component (X2C) relativistic corrections, the model offers an interpretative tool for the chemical analysis of scalar relativistic contributions to reaction energies. GRAPHICAL ABSTRACT

The S66 Non-Covalent Interactions Benchmark Reconsidered Using Explicitly Correlated Methods Near the Basis Set Limit*

The S66 benchmark for non-covalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 ‘high-level corrections’ are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66×8 problem set in particular, and for accurate calculations on non-covalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, whereas half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost.