Electron Density in Quantum Theory

Electronic structure theory to decipher the chemical bonding in actinide systems

“…In UO 2 2+ , among ELF and QTAIM descriptors, the most affected one by spin-orbit effects is the Laplacian of the density. ∇ 2 ρ(r) is increased by 10% in UO 2 2+ with respect to scalar relativistic calculations, showing a more depleted electron density at the U-O BCPs [166,168]. Anderson et al [169] perform DFT and QTAIM calculations at both the non-relativistic level and using the scalar relativistic ZORA for H 2 O, X(C 5 H 5 ) 2 (X=Fe, Ru, Os), Au 4 and UF 6 compounds.…”

“…In most cases scalar relativistic variants of the Hamiltonian operators as ZORA and DKH are sufficient to obtain a reasonable description of the electron density [166,168]. These effects must be taken into account for a meaningful topological analysis of bonding in actinide compounds.…”

Spin in density‐functional theory

“…As in nonrelativistic theory, an electron density and a current density can be defined in the relativistic many-electron theory such that they fulfill a continuity equation. This results in the definition of the electron density as [57,130] qðrÞ ¼ N Z W y ðr; r 2 ; …; r N Þ Wðr; r 2 ; …; r N Þ d 3 r 2 …d 3 r N (116) and of the current density as where a 1 indicates that the Dirac matrices act on the first electron and the dagger denotes the transposed and complex conjugate spinor. This definition of the current density still holds in the presence of external magnetic fields.…”

“…Hence, as the Dirac a matrices contain the Pauli spin matrices r, we see immediately that the current density j carries the spin information. [130] The relation to the spin density can be made more explicit by invoking a Gordon composition of the current density which separates it into a charge-and a spin-related current. [53,131] For the one-electron case, one can carry out this decomposition by rewriting the Dirac eigenvalue equation as, Equation (130) can now be used to replace w in the first term and w y in the last term.…”

“…For an N-electron system, we start from the definition of the many-electron current density, [130] À 1 2m e c h W y a k 1 b 1Vee W þ ðV ee WÞ y b 1 a k 1 W i :…”