Atomic occupancy

Stouten, P.F.W., Frdmmel, C., Nakamura, H., Sander, C. An effective solvation term based on atomic occupancies for use in protein simulations. Mol. Simul. 10 (1993) 97-120. 

Different kinds of modulations can be considered the displacive modulation is related to the shift of the atom position from the average structure the occupational (or substitutional) modulation is related to the changes of the atomic occupation probability depending on the position. Generally, in alloys, displacive modulation is small but not negligible (Yamamoto 1996) whereas substitutional modulation often occurs. 

The C60 molecules were found to be executing large amplitude reorientations at room temperature, so that large anisotropic thermal displacement factors of the C60 carbon atoms were found. The thermal displacement parameters for some of the C60 carbon atoms at room temperature are, in fact, so large that the C60 atomic coordinates may well represent only an average over one or more disordered structures involving fractional atomic occupancy. On the other hand, the TDAE N and C atomic coordinates are well-defined already at room temperature. 

Effective Solvation Term Based on Atomic Occupancies for Use in Protein Simulations. 

First approaches to the quantitative understanding of defects in stoichiometric crystals were published in the early years of the last century by Frenkel in Russia and Schottky in Germany. These workers described the statistical thermodynamics of solids in terms of the atomic occupancies of the various crystallographic sites available in the stmcture. Two noninteracting defect types were envisaged. Interstitial defects consisted of atoms that had been displaced from their correct positions into normally unoccupied positions, namely, interstitial sites. Vacancies were positions that should have been occupied but were not. 

For transition metal atoms there are three different atomic occupations which usually lead to states which are energetically low lying. These chemically different states are in general terms denoted d s, d s and Bulk transition metals (and... 

FIGURE 9.8. Use of difference maps to estimate (a) errors in atomic positions and (b) errors in thermal parameters or atomic occupancies. 

The data obtained from an X-ray crystal structure determination are the unit cell dimensions, the space group, the atomic coordinates, the atomic displacement parameters (to be described) and the atomic occupancy factors (which are generally unity). 

Parameters in the structural model, and other experiment-dependent parameters, are allowed to vary until a best-fit of the PDF calculated from the model and the data derived PDF is obtained, using a least-squares approach. The sample dependent parameters thus derived include the unit cell parameters (unit cell lengths and angles), atomic positions in the unit cell expressed in fractional coordinates, anisotropic thermal ellipsoids for each atom and the average atomic occupancy of each site. 

Printed outputs Cartesian Coordinates of Atoms Molecular Orbital Energies and Eigenfunctions Mulliken Population Analysis Atom Occupancies and Charges Vibrational Frequencies and Intensities Raman Active, yes/no Zero Point Energy Enthalpy Entropy Gibbs Free Energy, Cy. 

Coupled perturbation procedure Potential energy surface of side chain determined first with nearby side chains truncated to alanine then model is energy minimized with all atoms present Copy template dihedrals by maximal atomic occupancy, search by 10° for rest + many checks... 

To explain these quantities, consider the general case of a discrete atom distribution with N different unit cell position vectors /7 = Xja + yjb + zf for the same fluorescent atom, plus an added random distribution of the same atoms. The ordered fraction C is the fraction of the atoms in the distribution that are coherently located or are crystallographically registered with the substrate crystal lattice. If the atoms occupation fractions for the ordered positions are Cj, C2, Cv, respectively, the ordered fraction is... 

Fig. 3.49 Calculated phase diagram of the binary system Sn/Zn (a) and its Gibbs energy (b) at p = 1 bar and T = 180 °C for the liquid and the elemental structure types with random atomic occupation.

The oxidation state +4 appears to be missing in group 5a, which contains the elements N, P, As, Sb, and Bi. The solids BaSbOj and BaBi03 do exist, but it turns out from the BiO distances that there are alternant sites with Sb /Sb and BP+/BP+, respectively. The reason is found if we consider the atomic occupancies of the ions. The Sb " ions are stripped of electrons down to the Kr core and the BP+ ions down to a Xe core. The Sb " and BP+ ions contain in addition a 5s pair and a 6s pair, respectively, that is, a filled subshell. A 5s and 6s subshell with a single electron in the valence shell is not feasible, since this electron demands almost the same space as two electrons. It is better to add another electron in the same subsheU for the same price. ... 

H2 transport through dense metal membranes proceeds by a series of elementary steps known collectively as solution-diffusion. In the first step, molecular H2 adsorbs on the upstream side of the membrane and dissociates on its catalytically active surface to form H atoms. The H atoms then dissolve into the bulk metallic lattice and diffuse to the downstream side of the membrane, where they combine to re-form molecular H2 and desorb. Because other s)mgas components do not display significant diffusivity in dense metals, H2 can be separated from the mixture with near-perfect selectivity. While beyond the scope of this discussion, it is worth noting that the rates of each of these elementary steps are complex functions of temperature, pressure, membrane composition, and H-atom occupancy. For a detailed discussion, we refer the reader to [5] and references therein. 

Orbital or EFG Spherical atom occupancy Experimental occupancy... 

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