Automatic Generation of Auxiliary Basis Sets in Spherical Representation Using the Cholesky Decomposition.

Density fitting techniques that use automatically generated auxiliary basis sets generally rely on the formation of basis function products. Recently, Lehtola [ J. Chem. Theory Comput. 2021, 17, 6886-6900] presented a procedure making use of a purely spherical representation by adding auxiliary basis functions coupled to the required angular momentum quantum numbers for the product of spherical harmonics and then removing linear dependencies by means of a Cholesky decomposition. In this work, we extend this idea by making use of the explicit equations for the product of two spherical harmonics in the angular part of the basis function product. Some of the resulting terms are not directly accessible when popular standard integral libraries are used, which could prevent the widespread use of the exact product form. For these terms, we introduce four approximations of increasing sophistication that require integrals involving only standard Gaussian-type orbitals and thus can be computed with standard libraries. We assess the accuracy of the different schemes in the context of the aCD for the reconstruction of the electron repulsion integral matrix and absolute and relative single point energies and in the framework of optimally tuned range-separated hybrid functionals.

Automated Generation of Optimized Auxiliary Basis Sets for Long-Range-Corrected TDDFT Using the Cholesky Decomposition.

Range-separated hybrid functionals making use of a smooth separation of the Coulomb operator in terms of the error function and its complement have proven to be a valuable tool for improving Kohn-Sham density functional theory (DFT) calculations. This holds in particular for obtaining accurate excitation energies from linear-response time-dependent DFT. Evaluating the long-range exchange contributions represents one of the most time-consuming tasks in such calculations. Prefitted auxiliary basis sets can be employed to speed up this step. Here, we present a way to generate auxiliary basis sets optimized to fit the long-range exchange contributions only, contrary to the common optimization strategies on the basis of the full Coulomb operator. For this purpose, we use the atomic Cholesky decomposition technique. The basis sets are generated on-the-fly using the specific range-separation parameter defined in the exchange-correlation functional. We obtain excitation energies and oscillator strengths which are of similar or better accuracy than those obtained with conventional resolution-of-the-identity auxiliary basis sets while drastically reducing the number of auxiliary functions required. This is demonstrated for the QUESTDB#5 benchmark set. In addition, we outline the benefits of this approach in sequences of calculations employing varying range-separation parameters, as is the case in the optimally tuned range-separation strategy. Finally, we illustrate the efficiency of this approach for real-world examples, namely, a chlorophyll tetramer from photosystem II and a carotenoid-porphyrin-C60 triad.

Design of Ru(II)-NHC-Diamine Precatalysts Directed by Ligand Cooperation: Applications and Mechanistic Investigations for Asymmetric Hydrogenation.

A modular synthesis of Ru(II)-NHC-diamine complexes from readily available chiral N-heterocyclic carbenes (NHCs) and chiral diamines is disclosed for the first time. The well-defined Ru(II)-NHC-diamine complexes show unique structure and coordination chemistry including an unusual tridentate coordination effect of 1,2-diphenylethylenediamine. The isolated air- and moisture-stable Ru(II)-NHC-diamine complexes act as versatile precatalysts for the asymmetric hydrogenation of isocoumarines, benzothiophene 1,1-dioxides, and ketones. Moreover, on the basis of the identification of reaction intermediates by stoichiometric reactions and NMR experiments, together with the DFT calculations, a possible catalytic cycle was proposed.