On the Development of Accurate Gaussian Basis Sets for f-Block Elements. Elsevier; 2018. pp. 47-74. [DOI: 10.1016/bs.arcc.2018.06.002]

A DFT perspective on organometallic lanthanide chemistry

Computational studies of the coordination chemistry and bonding of lanthanides have grown in recent decades as the need for understanding the distinct physical, optical, and magnetic properties of these compounds increased. Density functional theory (DFT) methods offer a favorable balance of computational cost and accuracy in lanthanide chemistry and have helped to advance the discovery of novel oxidation states and electronic configurations. This Frontier article examines the scope and limitations of DFT in interpreting structural and spectroscopic data of low-valent lanthanide complexes, elucidating periodic trends, and predicting their properties and reactivity, presented through selected examples.

A route to high-accuracy ab initio description of electronic excited states in high-spin lanthanide-containing species: A case study of GdO

Accurate description of electronic excited states of high-spin molecular species is a yet unsolved problem in modern electronic structure theory. A composite computational scheme developed in the present work contributes to solving this task for a challenging case of lanthanide-containing molecules. In the scheme, the highest-spin states whose wavefunctions are dominated by a single Slater determinant are described at the single-reference (SR) CCSD(T) level, whereas the lower-spin states, being inherently multiconfigurational in their nature, are treated with multireference (MR) methods, MRCI and/or CASPT2. An original technique which scales MR results against SR CCSD(T) ones to improve the accuracy in the former is proposed and examined, taking the example of 12 electronic states of gadolinium monoxide, X9Σ-, Y7Σ-, A'9Δ, A1'7Δ, A9Π, A17Π, B9Σ-, B17Σ-, C9Π, C17Π, D9Σ-, and D17Σ-, up to 35 000 cm-1. A multitude of the corresponding Ω (spin-coupled) states was then studied within the state-interacting approach employing the full Breit-Pauli spin-orbit coupling operator with CASSCF-generated ΛS states as a basis. For all ΛS and Ω states, the Gd-O bond lengths, spectroscopic constants ωe, ωexe, αe, and adiabatic excitation energies are obtained. The theoretical predictions are in good agreement with the experimental data, with deviations in excitation energies not exceeding 350 cm-1 (1 kcal/mol). The spectroscopic properties of the yet unobserved electronic states, A'9Δ, A1'7Δ, C9Π, C17Π, D9Σ-, and D17Σ-, are evaluated for the first time.

Property-optimized Gaussian basis sets for lanthanides

Property-optimized Gaussian basis sets of split-valence, triple-zeta valence, and quadruple-zeta valence quality are developed for the lanthanides Ce-Lu for use with small-core relativistic effective core potentials. They are constructed in a systematic fashion by augmenting def2 orbital basis sets with diffuse basis functions and minimizing negative static isotropic polarizabilities of lanthanide atoms with respect to basis set exponents within the unrestricted Hartree-Fock method. The basis set quality is assessed using a test set of 70 molecules containing the lanthanides in their common oxidation states and f electron occupations. 5d orbital occupation turns out to be the determining factor for the basis set convergence of polarizabilities in lanthanide atoms and the molecular test set. Therefore, two series of property-optimized basis sets are defined. The augmented def2-SVPD, def2-TZVPPD, and def2-QZVPPD basis sets balance the accuracy of polarizabilities across lanthanide oxidation states. The relative errors in atomic and molecular polarizability calculations are ≤8% for augmented split-valence basis sets, ≤ 2.5% for augmented triple-zeta valence basis sets, and ≤1% for augmented quadruple-zeta valence basis sets. In addition, extended def2-TZVPPDD and def2-QZVPPDD are provided for accurate calculations of lanthanide atoms and neutral clusters. The property-optimized basis sets developed in this work are shown to accurately reproduce electronic absorption spectra of a series of LnCp₃ ^'- complexes (Cp' = C₅H₄SiMe₃, Ln = Ce-Nd, Sm) with time-dependent density functional theory.

Gaussian Basis Sets for Crystalline Solids: All-Purpose Basis Set Libraries vs System-Specific Optimizations

It is customary in molecular quantum chemistry to adopt basis set libraries in which the basis sets are classified according to either their size (triple-ζ, quadruple-ζ, ...) and the method/property they are optimal for (correlation-consistent, linear-response, ...) but not according to the chemistry of the system to be studied. In fact the vast majority of molecules is quite homogeneous in terms of density (i.e., atomic distances) and types of bond involved (covalent or dispersive). The situation is not the same for solids, in which the same chemical element can be found having metallic, ionic, covalent, or dispersively bound character in different crystalline forms or compounds, with different packings. This situation calls for a different approach to the choice of basis sets, namely a system-specific optimization of the basis set that requires a practical algorithm that could be used on a routine basis. In this work we develop a basis set optimization method based on an algorithm–similar to the direct inversion in the iterative subspace–that we name BDIIS. The total energy of the system is minimized together with the condition number of the overlap matrix as proposed by VandeVondele et al. [VandeVondele et al. J. Chem. Phys.2007, 227, 114105]. The details of the method are here presented, and its performance in optimizing valence orbitals is shown. As demonstrative systems we consider simple prototypical solids such as diamond, graphene sodium chloride, and LiH, and we show how basis set optimizations have certain advantages also toward the use of large (quadruple-ζ) basis sets in solids, both at the DFT and Hartree–Fock level.