Restricted-Open-Shell G4(MP2)-Type Procedures

Compilation of Ionic Clusters with the Rock Salt Structure: Accurate Benchmark Thermochemical Data, Assessment of Quantum Chemistry Methods, and the Convergence Behavior of Lattice Energies

In the present study, computational quantum chemistry is used to obtain lattice energies (LEs) for a range of ionic clusters with the NaCl structure. Specifically, the compounds include NaF, NaCl, MgO, MgS, KF, CaO, and CaS clusters, (MX)_n, with n = 1, 2, 4, 6, 8, 12, 16, 24, 32, 40, 50, 60, 75, 90, and 108. The highest-level W2 and W1X-2 methods are applied to the small clusters with n = 1 to 8 (the MX35 data set). The assessment with MX35 shows that, for the calculation of geometries and vibrational frequencies, the PBE0-D3(BJ) and PBE-D3(BJ) DFT methods are reasonable, but the calculation of atomization energies is more challenging. This is a result of different systematic deviations for clusters of different species. Thus, species-specific adjustments are applied for larger clusters, which are calculated with the DuT-D3 double-hybrid DFT method, the MN15 DFT method, and the PM7 semi-empirical method. They yield smoothly converging LEs to the bulk values. It is also found that, for the alkali-metal species, the LEs for a single molecule are ∼70% of the bulk values, while for the alkali-earth species, they are ∼80%. This has enabled a straightforward means to the first-principles estimation of LEs for similarly structured ionic compounds.

Assessment of DLPNO-CCSD(T)-F12 and its use for the formulation of the low-cost and reliable L-W1X composite method

In the present study, we have investigated the performance of RIJCOSX DLPNO-CCSD(T)-F12 methods for a wide range of systems. Calculations with a high-accuracy option ["DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12"] extrapolated to the complete-basis-set limit using the maug-cc-pV[D+d,T+d]Z basis sets provides fairly good agreements with the canonical CCSD(T)/CBS reference for a diverse set of thermochemical and kinetic properties [with mean absolute deviations (MADs) of ~1-2 kJ mol^-1 except for atomization energies]. On the other hand, the low-cost "RIJCOSX DLPNO-CCSD(T)-F12D" option leads to substantial deviations for certain properties, notably atomization energies (MADs of up to tens of kJ mol^-1 ). With the high-accuracy CBS approach, we have formulated the L-W1X method, which further includes a low-cost core-valence plus scalar-relativistic term. It shows generally good accuracy. For improved accuracies in specific cases, we advise replacing maug-cc-pV(n+d)Z with jun-cc-pV(n+d)Z for the calculation of electron affinities, and using well-constructed isodesmic-type reactions to obtain atomization energies. For medium-sized systems, DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 calculations are several times faster than the corresponding canonical computation; the use of the local approximations (RIJCOSX and DLPNO) leads to a better scaling than that for the canonical calculation (from ~6-7 down to ~2-4 for our test systems). Thus, the DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 method, and the L-W1X protocol that based on it, represent a useful means for obtaining accurate thermochemical quantities for larger systems.

Three-Dimensional Convolutional Neural Networks Utilizing Molecular Topological Features for Accurate Atomization Energy Predictions

Deep learning methods provide a novel way to establish a correlation between two quantities. In this context, computer vision techniques such as three-dimensional (3D)-convolutional neural networks become a natural choice to associate a molecular property with its structure due to the inherent 3D nature of a molecule. However, traditional 3D input data structures are intrinsically sparse in nature, which tend to induce instabilities during the learning process, which in turn may lead to underfitted results. To address this deficiency, in this project, we propose to use quantum-chemically derived molecular topological features, namely, localized orbital locator and electron localization function, as molecular descriptors, which provide a relatively denser input representation in a 3D space. Such topological features provide a detailed picture of the atomic and electronic configuration and interatomic interactions in the molecule and hence are ideal for predicting properties that are highly dependent on the physical or electronic structure of the molecule. Herein, we demonstrate the efficacy of our proposed model by applying it to the task of predicting atomization energies for the QM9-G4MP2 data set, which contains ∼134k molecules. Furthermore, we incorporated the Δ-machine learning approach into our model, which enabled us to reach beyond benchmark accuracy levels (∼1.0 kJ mol^-1). As a result, we consistently obtain impressive mean absolute errors of the order 0.1 kcal mol^-1 (∼0.42 kJ mol^-1) versus the G4(MP2) theory using relatively modest models, which could potentially be improved further in a systematic manner using additional compute resources.

Accurate Thermochemistry for Main-Group Elements up to Xenon with the Wn-P34 Series of Composite Methods

In the present study, we introduce the accurate Wn-P34 quantum chemistry composite methods with applicability to heavy p-block elements up to xenon. For a set of thermochemical properties for prototypical third- and fourth-row species and for a diverse set of small light-main-group species, they show accuracies of ∼3 kJ mol^-1 or better. Overall, the Wn-P34 methods are comparable in accuracy to Wn, with a widened applicability to heavier elements. We have used Wn-P34 to compile the P34 set of accurate thermochemical values for heavy p-block species, and we have applied this set to assess a wide range of lower-cost methods. The results of our assessment show that the G4(MP2)-XK composite method provides adequate treatments for these species, but several widely used double-hybrid density functional theory (DH-DFT) methods show uncharacteristically large deviations. In contrast, we find it presently surprising that some pure and hybrid DFT methods such as TPSS and SCANh perform quite well. We hope that our findings and new tools would facilitate the application of computational chemistry for heavy elements, of which the properties are yet to be broadly explored.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core-Valence Correlation, and F12 Alternatives

A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput.2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller–Plesset correction and replacing the Weigend–Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrapolation from augmented correlation-consistent core–valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4-type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion’s share of the improvement comes from better capture of valence correlation; the inclusion of core–valence correlation is almost an order of magnitude less important. These robust correlation-consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly, the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component.

Canonical and DLPNO-Based G4(MP2)XK-Inspired Composite Wave Function Methods Parametrized against Large and Chemically Diverse Training Sets: Are They More Accurate and/or Robust than Double-Hybrid DFT?

The large and chemically diverse GMTKN55 benchmark was used as a training set for parametrizing composite wave function thermochemistry protocols akin to G4(MP2)XK theory (Chan, B.; Karton, A.; Raghavachari, K. J. Chem. Theory Comput. 2019, 15, 4478–4484). On account of their availability for elements H through Rn, Karlsruhe def2 basis sets were employed. Even after reparametrization, the GMTKN55 WTMAD2 (weighted mean absolute deviation, type 2) for G4(MP2)-XK is actually inferior to that of the best rung-4 DFT functional, ωB97M-V. By increasing the basis set for the MP2 part to def2-QZVPPD, we were able to substantially improve performance at modest cost (if an RI-MP2 approximation is made), with WTMAD2 for this G4(MP2)-XK-D method now comparable to the better rung-5 functionals (albeit at greater cost). A three-tier approach with a scaled MP3/def2-TZVPP intermediate step, however, leads to a G4(MP3)-D method that is markedly superior to even the best double hybrids ωB97M(2) and revDSD-PBEP86-D4. Evaluating the CCSD(T) component with a triple-ζ, rather than split-valence, basis set yields only a modest further improvement that is incommensurate with the drastic increase in computational cost. G4(MP3)-D and G4(MP2)-XK-D have about 40% better WTMAD2, at similar or lower computational cost, than their counterparts G4 and G4(MP2), respectively: detailed comparison reveals that the difference lies in larger molecules due to basis set incompleteness error. An E2/{T,Q} extrapolation and a CCSD(T)/def2-TZVP step provided the G4-T method of high accuracy and with just three fitted parameters. Using KS orbitals in MP2 leads to the G4(MP3|KS)-D method, which entirely eliminates the CCSD(T) step and has no steps costlier than scaled MP3; this shows a path forward to further improvements in double-hybrid density functional methods. None of our final selections require an empirical HLC correction; this cuts the number of empirical parameters in half and avoids discontinuities on potential energy surfaces. G4-T-DLPNO, a variant in which post-MP2 corrections are evaluated at the DLPNO-CCSD(T) level, achieves nearly the accuracy of G4-T but is applicable to much larger systems.

Assessment of DFT Methods for Transition Metals with the TMC151 Compilation of Data Sets and Comparison with Accuracies for Main-Group Chemistry

In the present study, we have gathered a collection (that we term TMC151) of accurate reference data for transition-metal reactions for the assessment of quantum chemistry methods. It comprises diatomic dissociation energies and reaction energies and barriers for prototypical transition-metal reactions. Our assessment of a diverse range of different types of DFT methods shows that the most accurate functionals include ωB97M-V, ωB97X-V, MN15, and B97M-rV. Notably, they have also been previously validated to be highly robust for main-group chemistry. Nevertheless, even these methods show substantially worse accuracies for transition metals than for main-group chemistry. For less accurate methods, there is not a good correlation between their accuracies for main-group and transition-metal chemistries. Thus, in the development of new DFT, it is important to assess the accuracies for both types of data. In this regard, we have formulated the TMC34 model for efficient assessment of the performance for transition metals, which complements our previously developed MG8 model for main-group chemistry. Together, they provide a cost-effective means for initial assessment of new methodologies.

Extrapolation of high-order correlation energies: the WMS model

We have developed a new composite model chemistry method called WMS (Wuhan-Minnesota scaling method) with three characteristics: (1) a composite scheme to approximate the complete configuration interaction valence energy with the affordability condition of requiring no calculation more expensive than CCSD(T)/jul-cc-pV(T+d)Z, (2) low-cost methods for the inner-shell correlation contribution and scalar relativistic correction, and (3) accuracy comparable to methods with post-CCSD(T) components. The new method is shown to be accurate for the W4-17 database of 200 atomization energies with an average mean unsigned error (averaged with equal weight over strongly correlated and weakly correlated subsets of the data) of 0.45 kcal mol-1, and the performance/cost ratio of these results compares very favorably to previously available methods. We also assess the WMS method against the DBH24-W4 database of diverse barrier heights and the energetics of the reactions of three strongly correlated Criegee intermediates with water. These results demonstrate that higher-order correlation contributions necessary to obtain high accuracy for molecular thermochemistry may be successfully extrapolated from the lower-order components of CCSD(T) calculations, and chemical accuracy can now be obtained for larger and more complex molecules and reactions.

How to computationally calculate thermochemical properties objectively, accurately, and as economically as possible

We have developed the WnX series of quantum chemistry composite protocols for the computation of highly-accurate thermochemical quantities with advanced efficiency and applicability. The W1X-type methods have a general accuracy of ~3–4 kJ mol−1 and they can currently be applied to systems with ~20–30 atoms. Higher-level methods include W2X, W3X and W3X-L, with the most accurate of these being W3X-L. It can be applied to molecules with ~10–20 atoms and is generally accurate to ~1.5 kJ mol−1. The WnX procedures have opened up new possibilities for computational chemists in pursue of accurate thermochemical values in a highly-productive manner.