Pseudoatom multipole modeling

How extensively parametrized a pseudoatom multipole model is necessary for reproducing crystallographic informations of the electron density in molecules containing first, second-row elements, and first-row transition metals ... 

Pseudoatom multipole modeling reproduces accurately the deformation density within less than 0.05 e A-3 in the bonding and intermolecular regions calculations on theoretical thermally smeared structure factors show that deconvolution between density and thermal parameters is effective. The accuracy obtained from a high-resolution accurate diffraction experiment compares with extended triple- + polarization ab initio SCF calculations. These experiments are tractable for mole-... 

According to the aspherical-atom formalism proposed by Stewart [12], the one-electron density function is represented by an expansion in terms of rigid pseudoatoms, each formed by a core-invariant part and a deformable valence part. Spherical surface harmonics (multipoles) are employed to describe the directional properties of the deformable part. Our model consisted of two monopole (three for the sulfur atom), three dipole, five quadrupole, and seven octopole functions for each non-H atom. The generalised scattering factors (GSF) for the monopoles of these species were computed from the Hartree-Fockatomic functions tabulated by Clementi [14]. 

To take in account the nonspherical shape of the valence electron distribution, the K model has been improved by the addition of multipole parameters [lib]. Then, the pseudoatomic density is written (Molly program),... 

In the most widely applied model [52], the atomic decomposition of the ED is retained, but each nucleus-centered spherical density is supplemented by non-spherical functions. The pseudoatom formalism is a finite nucleus-centered multipole expansion of the molecular (crystalline) ED about each nucleus. A pseudo atom is defined as... 

A temperature dependent X—X+N study (100, 135, 170, and 205 K) on naphthalene [66] addresses the problem of thermal de-convolution, that is, the efficiency of the pseudoatom model to decouple density deformations due to chemical bonding from those due to nuclear motion. The authors analyze the self-consistency of multipole populations, extracted from different temperature XRD data, in terms of statistical distances d ) in the parameter space of the same refinement model ... 

Such observations immediately raise the question how reliable are projections of crystal-field effects onto multipoles The analyses of wavefunction-simulated X-ray data of small model compounds have revealed that the interaction density (8p = p(crystal) — p(isolated molecule)) manifests itself in low-order structure factors, and only to an extent that is comparable with the experimental noise [80]. Nevertheless, the multipole refinement was shown to retrieve this low signal (about 1% in F) successfully. A related study on urea, however, demonstrated that this is not the case if random errors of magnitude comparable with the effect of interaction density are added to the theoretical data [81]. The result also implies that indeterminacies associated with the interpretation of non-centrosymmetric structures can severely limit the pseudoatom model in distinguishing between noise and physical effects [82, 83]. 

A thorough investigation of simulated structure factor data of ammonia provides us with quantitative figures for the accuracy of BCP properties achievable with the pseudoatom projection [72]. The Pbcp> Pbcp> tBCp(H) indices of the static model density obtained by the multipole refinement of HF/6-31IG static structure factors deviate from the correct values (derived... 

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