Approximate density matrices and wigner distribution functions from density, kinetic energy density, and idempotency constraints

Abstract

The Wigner distribution function and the corresponding density matrix are calculated using a form for the distribution function suggested by maximization of the entropy. Wigner functions and density matrices are determined by imposing conditions of idempotency on the density matrix. Exchange energies and Compton profiles calculated from density matrices obtained by imposing the idempotency constraints are compared with the results of calculations using the Hartree-Fock density matrix and a Gaussian approximation for the density matrix for H and the noble gases He through Xe. Compton profiles from Wigner functions with idempotency constraints show improvements over the Gaussian approximation for the lighter atoms, but do not show significant changes for the heavier atoms. Exchange energies from density matrices with idempotency constraints show improvements over the Gaussian approximation except for the heavier atoms Kr and Xe.

An investigation into the photochemistry of, and the electrochemically induced CO-loss from, [(CO)5MC(OMe)Me](M = Cr or W) using low-temperature matrix isolation, picosecond infrared spectroscopy, cyclic voltammetry, and time-dependent density functional theory

“…The structures of the syn-or anti-isomers of (1) and (4) were optimised to tight convergence at the B3LYP/TZVP level for (1) or B3LYP/Def2TZVP level for (4) [37][38][39][40][41][42][43] Selected bond lengths obtained from these calculations are compared with those obtained from single crystal X-ray diffraction methods in Table S1. † Details of the calculations to derive appropriate cor- (3) and (5) and uncoordinated "free" CO in the matrix and (b) the difference spectrum obtained following irradiation with 395 nm light in a CH 4 /CO matrix (95 : 5) showing primarily the formation of (3).…”

A small molecular electron acceptor based on asymmetric hexacyclic core of thieno[1,2- b ]indaceno[5,6- b ′]thienothiophene for efficient fullerene-free polymer solar cells

“…Quantum chemistry calculations were performed to calculate the molecular energy levels (shown in Fig. 3a) of A201 by using density functional theory (DFT), on the B3LYP/6-31G level [41]. For the A201, the four hexyl side chains were simplified with methyl because of negligible influence of the side chain substituents on the oxidative and reductive properties of the molecules.…”