Pseudo-atom

Figure 7-14. All-atom and united-atom representation of the amino acid isoleucine. In this example, 13 atoms, which are able to form explicit non-bonding interactions, are reduced to only four pseudo-atoms,...

Some force fields use the so-called united atom approach where (for example) a methyl group is treated as a single pseudo-atom. They arose historically in order to save computer resource when dealing with large systems such as amino-acid chains. 

The least-squares Molly program based on the Hansen-Coppens model [10] was used to determine atomic coordinates, thermal parameters and multipolar density coefficients in scolecite. In the Hansen-Coppens model, the electron density of unit cell is considered as the superposition of the pseudo-atomic densities. The pseudoatom electron density is given by... 

At each stage of the refinement of a new set of parameters, the hat matrix diagonal elements were calculated in order to detect the influential observations following the criterium of Velleman and Welsh [8,9]. The inspection of the residues of such reflections revealed those which are aberrant but progressively, these aberrations disappeared when the pseudo-atoms model was used (introduction of multipoler coefficients). This fact confirms that the determination of the phases in acentric structures is improved by sophisticated models like the multipole density model. 

When combining QM with MM methods, the partitioning of the system will often intersect a chemical bond. This bond is usually chosen to be a carbon-carbon single bond (whenever possible) and three major coupling methods have been developed, which are referred to as the link-atom [54] , pseudo-atom/bond [55] and hybrid-orbital [56] approach, respectively. In the link atom approach the open valency at the border is capped by a hydrogen atom, and most DFTB QM/MM implementations are based on this simple scheme [49, 50] or related variations [57], Recently,... 

Theoretical considerations leading to a density functional theory (DFT) formulation of the reaction field (RF) approach to solvent effects are discussed. The first model is based upon isolelectronic processes that take place at the nucleus of the host system. The energy variations are derived from the nuclear transition state (ZTS) model. The solvation energy is expressed in terms of the electrostatic potential at the nucleus of a pseudo atom having a fractional nuclear charge. This procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy, since all integrations involved are performed over [O.ooJ The quality of the approximations made are discussed within the frame of the Kohn-Sham formulation of density functional theory. 

The MM2 force field3 is probably the most extensively parameterized and intensively used force field to date. It reproduces a variety of molecular properties such as geometry, dipole moments, conformational energies, barriers to rotation and heats of formation. Of particular importance for calculations of amines is that MM2 treats lone pairs on sp3 nitrogens (and oxygens) as pseudo atoms with a special atom type and parameters. A closely related force field, MM2 7, was derived from MM2 by Osawa and Jaime. MM2 uses the same potential functions as MM2, but employs a different set of parameters in an attempt to better reproduce barriers to rotation about single C—C bonds. 

CTP, see Cluster with terminal pseudo-atoms Cu. Pd -TSM, propylene gas-phase oxidation over, 39 320-322 Cubane, isomerization of, 24 148 Cubooctahedron, small supported particle model, 36 80-81... 

Where p (r) is the electron density of each pseudo atom, Pcore(r) and pvai ( r) are the core and spherical densities of the valence electron shells, Pvai and Pim (multipoles) describe the electron shell occupations, k and k denote the spherical deformation and y (r/r) is a geometrical function. The parameters K, k , Pvai and Pim are refined during adjustment of the experimental and models structure amplitudes. 

There are two approaches to map crystal charge density from the measured structure factors by inverse Fourier transform or by the multipole method [32]. Direct Fourier transform of experimental structure factors was not useful due to the missing reflections in the collected data set, so a multipole refinement is a better approach to map charge density from the measured structure factors. In the multipole method, the crystal charge density is expanded as a sum of non-spherical pseudo-atomic densities. These consist of a spherical-atom (or ion) charge density obtained from multi-configuration Dirac-Fock (MCDF) calculations [33] with variable orbital occupation factors to allow for charge transfer, and a small non-spherical part in which local symmetry-adapted spherical harmonic functions were used. 

PA pseudo-atom index to the lower left atomic number... 

However, if the atoms are not related by symmetry, the normal rules break down. The homoionic N-N bond in the hydrazinium ion is an electron pair bond, but one in which N1 contributes 1.25 and N2 0.75 electrons. How can we apply the bond valence model in such cases where no solution to the network equations is possible One approach is to isolate the non-bipartite portion of the graph into a complex pseudo-atom. Thus in the hydrazinium ion the homoionic bond and its two terminating N atoms are treated as a single pseudo-anion which forms six bonds with a valence sum equal to the formal charge of —4. 

A fairly simple pseudo-atomic method has been developed (286) for calculating the ligand field splittings in the linear molecules Me2Cd and Me2Zn. The paper also contains a useful list of references to previous work in this area. 

Applying the pseudo-atom convention to the iron complex in Figure 8, the iodine atom is priority 1, the t1S-C5H3R2 ligand is priority number 2, the phosphorus atom is priority number 3, and carbon is priority number 4.15 When the iron is viewed from the side opposite the priority number 4, the sequence is 1,2,3 in the anticlockwise or 5 direction. The highest priority carbon in the cyclopentadienyl ligand, indicated by an asterisk, is designated with the R chirality symbol by application of the extended CIP sequence rule. 

The assignment of descriptors and configuration is sometimes arbitrary, at best, when based on model structures and pseudo-atom coordination numbers. A more explicit stereochemical notation is achieved by using this notation, which states within the stereodescriptor the model structure on which the notation is based. In this notation the pseudo-square pyramidal structure is [5PF-5-14-C(i )]. This structure can be expected to result in geometric isomers when one of the... 

In the case of BPA-PC [51], the chosen microstructures had cube-edge lengths of 18.44 A and a degree of polymerisation of 35 (Mw = 4532). There are 485 atoms or atom groups in each cube (methyl groups are represented as spherical pseudo-atoms). The force field [46] has fixed bond lengths and fixed... 

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