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.

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.

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.

Although there are few reduced dinitrogen complexes of scandium, this metal has revealed a new structural type in reductive dinitrogen chemistry by reduction of bis(pentamethylcyclopentadienyl) scandium halides under N2. Reduction of (Cp* = C5Me5) with potassium graphite (KC8) under dinitrogen generates the dark blue paramagnetic complex , 1. This end-on bridging (N[double bond, length as m-dash]N)2- complex is a diradical with a magnetic moment of 2.8µ B. Upon further reduction of 1 with KC8, the orange diamagnetic trimetallic complex , 2, is obtained. This complex has an unprecedented structure in which two side-on bridging (N[double bond, length as m-dash]N)2- ligands are bound to the central (Cp*Sc)2+ moiety. Complex 2 can also be obtained directly from reduction of or a mixture of and with KC8. The reaction of with KC8 in the presence of 18-crown-6 or 2.2.2-cryptand affords 2 along with small amounts of , 3, which is green at room temperature and purple at low temperature and displays a mixture of side-on and end-on bridging isomers in the crystal structure collected at -180 °C. Density functional theory (DFT) calculations are consistent with a triplet ground state for the end-on complex 1 and singlet ground states for the side-on complexes 2 and 3.

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 TURBOMOLEs 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.