A measure of the error in wave functions

The quantity ? = (Φ||(H ? E)Φ|) gives a measure of the error in the approximate solution, Φ (with corresponding energy expectation value E), to an eigenfunction of the Hamiltonian operator H of the system under consideration; this quantity vanishes for the exact function ψ. In a percentage scale (with 0% error for the exact function and 100% for a reference, approximate function), the error of Φ may be expressed as 100(?/?_r), where ?_r corresponds to the reference function (e.g., obtained with a minimal basis set). This approach eliminates the need of knowing beforehand the exact solution in order to have an estimate of the error of an approximate solution.     

Preparation and Crystal Structure of Potassium Iron Hydrogen Phosphate,KFe3(HPO4)2(H2PO4)6 · 4 H2O

Single crystals of potassium iron hydrogen phosphate, KFe₃(HPO₄)₂(H₂PO₄)₆ · 4 H₂O, were prepared hydrothermally by heating a mixture of Fe₂O₃, H₃PO₄ and K₂CO₃ with a small amount of water. It crystallizes monoclinic, space group C2/c (N° 15 Int. Tab.) with Z = 4 and a = 1701(2), b = 960.4(5), c = 1750(1) pm, β = 90.88(7)°. The crystal structure was solved by using 1716 unique reflections F₀ > 4σ(F₀) with a final wR2 value of 0.126 (SHELXL-93). The main feature of the crystal structure are layers formed by PO₄-tetrahedra around the FeO₆-octahedra parallel to (001). K⁺ and H₂O molecules connect these layers. Effective Coordination Numbers (ECoN), Mean Fictive Ionic Radii (MEFIR), Charge Distribution (CHARDI) and the Madelung Part of Lattice Energy (MAPLE) are calculated for the title compound. The existence of hydrogen bonds is confirmed by these calculations.     

Physical properties of many-electron atomic systems evaluated from analytical Hartree-Fock functions

The promotion energies, ionization potentials, electron affinities, and orbital electronegativities for the valence states of importance in atoms of the first two rows of the periodic system have been evaluated from analytical Hartree-Fock functions for the corresponding groundstates. The agreement with existing values, determined from experimental data, is very satisfactory.This work has been supported in part by the National Research Council of Canada.