Closed-form expressions for correlated density matrices: Application to dispersive interactions and example of He2

Abstract

Empirically correlated density matrices of N-electron systems are investigated. Exact closed-form expressions are derived for the one-and two-electron reduced density matrices from a general pairwise correlated wave function. Approximate expressions are proposed which reflect dispersive interactions between closed-shell centro-symmetric subsystems. Said expressions clearly illustrate the consequences of second-order correlation effects on the reduced density matrices. Application is made to a simple example: the (He) 2 system. Reduced density matrices are explicitly calculated, correct to second order in correlation, and compared with approximations of independent electrons and independent electron pairs. The models proposed allow for variational calculations of interaction energies and equilibrium distance as well as a clear interpretation of dispersive effects on electron distributions. Both exchange and second order correlation effects are shown to play a critical role on the quality of the results.

Ligand-field transition-induced C–S bond formation from nickelacycles

“…S10 † ). The simulated spectrum obtained with the LC-ωPBE functional 18 ( ω = 0.15) and the 6-311g(d,p) basis set 19 shows that bands 1–5 can be associated with charge transfer transitions from the Ni 3d yz and 3d xz -based molecular orbitals (MOs) to the bpy π*-based MOs (Table S3 † ). This similar Ni-to-bpy CT character of the five bands contrasts with the distinct photoactivities of bands 3–5 relative to bands 1 and 2.…”