Range Separation Method for Density Functional Theory Based on Two-Electron Infinite-Order Two-Component Hamiltonian.

The range separation method for density functional theory (DFT) was extended to a two-component relativistic theory based on the unitary transformation of one- and two-electron operators and a density operator. In the framework of the spin-free infinite-order two-component Hamiltonian, we implemented several types of two-electron integrals of range-separated two-electron interactions arising from the unitary transformation. Numerical assessments were performed using long-range-corrected (LC)-DFT, which utilizes the range separation of an exchange functional. The present method successfully reproduced the reference values obtained by the four-component LC-DFT calculations when the whole unitary transformations of one-electron, full-range, and range-separated two-electron operators and a density operator were considered. An efficient scheme for the unitary transformation, which is termed the local unitary transformation (LUT), was also applied to the range-separated two-electron term and other operators. The LUT method reduced the computational costs of the LC-DFT calculations significantly without any loss of accuracy.

Experimental and Theoretical Evidence for Relativistic Catalytic Activity in C-H Activation of N-Phenylbenzamide Using a Cationic Iridium Complex.

This study elucidates that relativistic effect plays a key role in catalytic C-H activation using a cationic Ir complex. Experiments show that the cationic Ir(I)-diphosphine catalyst can be used for the deuterium substitution of N-phenylbenzamide, whereas a cationic Rh(I)-diphosphine catalyst is scarcely effective. Density functional theory calculations, including the relativistic effect, demonstrate a large difference in the reaction energy diagrams for the C-H activation of N-phenylbenzamide between the cationic Ir and Rh catalysts. In particular, the relatively low reaction barrier and considerably stabilized product obtained for the Ir catalysts are rationalized by strong Ir-C and Ir-H interactions, which originate from the relativistic self-consistent d-orbital expansion of Ir.

Dynamic hetero-metallic bondings visualized by sequential atom imaging.

Traditionally, chemistry has been developed to obtain thermodynamically stable and isolable compounds such as molecules and solids by chemical reactions. However, recent developments in computational chemistry have placed increased importance on studying the dynamic assembly and disassembly of atoms and molecules formed in situ. This study directly visualizes the formation and dissociation dynamics of labile dimers and trimers at atomic resolution with elemental identification. The video recordings of many homo- and hetero-metallic dimers are carried out by combining scanning transmission electron microscopy (STEM) with elemental identification based on the Z-contrast principle. Even short-lived molecules with low probability of existence such as AuAg, AgCu, and AuAgCu are directly visualized as a result of identifying moving atoms at low electron doses.