Natural determinant reference functional theory.

The natural determinant reference (NDR) or principal natural determinant is the Slater determinant comprised of the N most strongly occupied natural orbitals of an N-electron state of interest. Unlike the Kohn-Sham (KS) determinant, which yields the exact ground-state density, the NDR only yields the best idempotent approximation to the interacting one-particle reduced density matrix, but it is well-defined in common atom-centered basis sets and is representation-invariant. We show that the under-determination problem of prior attempts to define a ground-state energy functional of the NDR is overcome in a grand-canonical ensemble framework at the zero-temperature limit. The resulting grand potential functional of the NDR ensemble affords the variational determination of the ground state energy, its NDR (ensemble), and select ionization potentials and electron affinities. The NDR functional theory can be viewed as an "exactification" of orbital optimization and empirical generalized KS methods. NDR functionals depending on the noninteracting Hamiltonian do not require troublesome KS-inversion or optimized effective potentials.

Synthesis of Crystallographically Characterizable Bis(cyclopentadienyl) Sc(II) Complexes: (C5H2tBu3)2Sc and {[C5H3(SiMe3)2]2ScI}1.

The synthesis of previously unknown bis(cyclopentadienyl) complexes of the first transition metal, i.e., Sc(II) scandocene complexes, has been investigated using C5H2(tBu)3 (Cpttt), C5Me5 (Cp*), and C5H3(SiMe3)2 (Cp″) ligands. Cpttt2ScI, 1, formed from ScI3 and KCpttt, can be reduced with potassium graphite (KC8) in hexanes to generate dark-red crystals of the first crystallographically characterizable bis(cyclopentadienyl) scandium(II) complex, Cpttt2Sc, 2. Complex 2 has a 170.6° (ring centroid)-Sc-(ring centroid) angle and exhibits an eight-line EPR spectrum characteristic of Sc(II) with Aiso = 82.6 MHz (29.6 G). It sublimes at 200 °C at 10-4 Torr and has a melting point of 268-271 °C. Reductions of Cp*2ScI and Cp″2ScI under analogous conditions in hexanes did not provide new Sc(II) complexes, and reduction of Cp*2ScI in benzene formed the Sc(III) phenyl complex, Cp*2Sc(C6H5), 3, by C-H bond activation. However, in Et2O and toluene, reduction of Cp*2ScI at -78 °C gives a dark-red solution, 4, which displays an eight-line EPR pattern like that of 1, but it did not provide thermally stable crystals. Reduction of Cp″2ScI, in THF or Et2O at -35 °C in the presence of 2.2.2-cryptand, yields the green Sc(II) metallocene iodide complex, [K(crypt)][Cp″2ScI], 5, which was identified by X-ray crystallography and EPR spectroscopy and is thermally unstable. The analogous reaction of Cp*2ScI with KC8 and 18-crown-6 in Et2O gave the ligand redistribution product, [Cp*2Sc(18-crown-6-κ2O,O')][Cp*2ScI2], 6, as the only crystalline product. Density functional theory calculations on the electronic structure of these compounds are reported in addition to a steric analysis using the Guzei method.

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.

TURBOMOLE: Today and Tomorrow.

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Chiral Four-Wave Mixing Signals with Circularly Polarized X-ray Pulses.

Chiral four-wave mixing signals are calculated using the irreducible tensor formalism. Different polarization and crossing angle configurations allow to single out the magnetic dipole and the electric quadrupole interactions. Other configurations can reveal that the chiral interaction occurs at a given step within the nonlinear interaction pathways. Applications are made to the study of valence excitations of S-ibuprofen by chiral stimulated X-ray Raman signals at the carbon K-edge and by chiral visible 2D electronic spectroscopy.