Experimental determination of spin-dependent electron density by joint refinement of X-ray and polarized neutron diffraction data

Abstract

New crystallographic tools were developed to access a more precise description of the spin-dependent electron density of magnetic crystals. The method combines experimental information coming from high-resolution X-ray diffraction (XRD) and polarized neutron diffraction (PND) in a unified model. A new algorithm that allows for a simultaneous refinement of the charge- and spin-density parameters against XRD and PND data is described. The resulting software MOLLYNX is based on the well known Hansen-Coppens multipolar model, and makes it possible to differentiate the electron spins. This algorithm is validated and demonstrated with a molecular crystal formed by a bimetallic chain, MnCu(pba)(H(2)O)(3)·2H(2)O, for which XRD and PND data are available. The joint refinement provides a more detailed description of the spin density than the refinement from PND data alone.

First spin-resolved electron distributions in crystals from combined polarized neutron and X-ray diffraction experiments

“…The purpose of this article is to demonstrate that the experimental determination of the electron position probability density has now reached a point where it has become possible to model and separate up and down spin carrier contributions to the distribution. However, this type of result is only possible by combining different types of experiments and interpreting them through a common model (Deutsch et al, 2012). In this paper we report on the first successful experimental reconstruction of a spin-resolved electron density distribution and some insights obtained in this way for a model molecular magnetic crystal.…”

Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree–Fock level of theory

“…Besides DFT/TD-DFT, spin and spin density have an important role in the polarized neutron (PN) scattering theory, both from the theoretical and from the experimental point of view [39,40]. The Fourier transform of PN structure factors are made directly related to the spin density and/or magnetization [39,40,41]. (See in Hirst [42] for a critical analysis of the experimental assessment of spin density with respect to spin magnetization and spin current.)…”

When combined X-ray and polarized neutron diffraction data challenge high-level calculations: spin-resolved electron density of an organic radical

“…Spin-resolved electron distributions are analyzed with the 'spin split multipolar atom model' simultaneously refined against XRD, PND and ND data. More precisely, the electron density distribution is modelled using a generalized Hansen Coppens (HC) model (Hansen & Coppens, 1978) in a joint refinement procedure as developed in the Mollynx program (Deutsch et al, 2012). The total density is expressed as the sum of pseudo-atomic contributions, where the density associated with an atomic centre i is i r ð Þ ¼ ðcoreÞ i r ð Þ þ P "ðvalÞ i "3 i ðvalÞ where P "ðvalÞ , P " ';m , P #ðvalÞ and P # ';m refer to spin up and spin down refined population parameters, respectively, " and # are the refined expansion contraction parameters.…”