Wavefunctions derived from experiment. IV. Investigation of the crystal environment of ammonia

Abstract

Constrained Hartree–Fock calculations have been performed to obtain wavefunctions that reproduce experimental X‐ray structure‐factor magnitudes for crystalline NH3 to within the limits of experimental error. Different model densities using both a single molecule and clusters of NH3 in the calculation of X‐ray structure‐factor magnitudes have been examined. The effects of the crystalline lattice on the experimental wavefunction of the NH3 unit can be reproducibly recovered. The construction of structure‐factor magnitudes based on normally distributed random perturbations of the experimental values has also been used to gauge the accuracy of integrated atomic properties obtained from the wavefunctions, the point at which the constraint procedure should be terminated, and the approximate error in the experimental values.

Wave functions derived from experiment. V. Investigation of electron densities, electrostatic potentials, and electron localization functions for noncentrosymmetric crystals

“…Equation (9) gives rise to a generalized eigenvalue problem for the coefficients C (see below). Equation (10) ensures that the orbitals are orthonormal so that ⌿ K is normalized; the are Lagrange multipliers associated with this orbital orthonormality constraint.…”

“…First, we wish to extend the formalism we have used for obtaining constrained HartreeFock wave functions for centrosymmetric crystals to noncentrosymmetric crystals (the method has, in fact, already been used without description 9 ), and to extend the method for estimating the errors in properties derived from these constrained wave functions. Details of the new formalism are presented in the following section.…”

Hirshfeld Atom Refinement

“…Given the uncertainties related to the interdependence of electron densities, accurate geometries and ADPs (see x1), Boese's diffraction data and starting geometry have now been used for an iterative HAR (see x3.3) using the same level of theory as in the preceding study by Bytheway et al (2002) 2p)]. This calculation reveals significant changes in the H-atom coordinates and ADPs (Table 1).…”

“…An example concerning the importance of accurate geometries and ADPs Bytheway et al (2002) have published a study on the ammonia molecule. They modified an isolated molecule Hartree-Fock wavefunction and thus the molecular electron density to reproduce observed X-ray structure factors to a 2 value of 1 (starting from an unconstrained value of 10.5) and with the minimum possible electronic energy penalty [so-called X-ray constrained wavefunction (XCW) fitting (Jayatilaka, 1998;Jayatilaka & Grimwood, 2001)].…”

Unconstrained and X-ray constrained extremely localized molecular orbitals: analysis of the reconstructed electron density

“…Since then, many researchers have drawn inspiration from Clinton's original ideas (Clinton & Massa, 1972;Clinton et al, 1973;Frishberg & Massa, 1981;Massa et al, 1985;Tanaka, 1988;Howard et al, 1994;Hibbs et al, 2005;CassamChenaï, 1995;Snyder & Stevens, 1999;Gillet et al, 2001;Gillet, 2007). Within this framework, the most promising method is the X-ray constrained (initially called 'experimental') wavefunction approach developed by Jayatilaka and co-workers (Jayatilaka, 1998;Bytheway, Grimwood, Figgis et al, 2002;Grimwood et al, 2003;Hudá k et al, 2010). This method provides a single Slater determinant which, other than minimizing the corresponding energy, reproduces a set of experimentally collected X-ray structure-factor amplitudes within a predefined precision.…”