Nonhydrogenic atoms

Atoms other than H have characteristics essentially similar to those of the H atom in an electric field, but there are important differences due to the presence of the finite sized ionic core. In zero field the presence of the core simply depresses 

The most important implication of not being a good quantum number is that blue and red states are coupled by their slight overlap at the core. In the region below the classical ionization limit blue and red states of adjacent n do not cross as they do in H, but exhibit avoided crossings as a result of their being coupled. Above the classical ionization limit blue states, which would be perfectly stable in H, are coupled to degenerate red states, which are unbound, and ionization occurs rapidly compared to radiative decay. It is really an autoionization process in which the blue state is coupled to the red continuum state at the ionic core. 

Fabre et a/.28 used a projection operator technique to describe the Stark shifts at fields below where low states of large quantum defects join the manifold. A less formal explanation is as follows. If, for example, the s and p states are excluded, as in Fig. 6.13 below 800 V/cm, effectively only the nearly degenerate (22 states are coupled by the electric field. The only differences among the m = 0,1, and 2 manifolds occur in the angular parts of the matrix element, i.e.1 

Only in a few low states is the m dependence significant, and as a result the m = 0,1, and 2 energy levels are almost degenerate. However, due to the low i states, the m = 0 levels are displaced more than the m = 1 levels, which are displaced insignificantly more than the m = 2 levels. 

The method used by Zimmerman et al.21 to measure the Li avoided crossing shown in Fig. 6.14 requires that the resolution of the laser be finer than the size of 

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They compared the PME method with equivalent simulations based on a 9 A residue-based cutoflF and found that for PME the averaged RMS deviations of the nonhydrogen atoms from the X-ray structure were considerably smaller than in the non-PME case. Also, the atomic fluctuations calculated from the PME dynamics simulation were in close agreement with those derived from the crystallographic temperature factors. In the case of DNA, which is highly charged, the application of PME electrostatics leads to more stable dynamics trajectories with geometries closer to experimental data [30]. A theoretical and numerical comparison of various particle mesh routines has been published by Desemo and Holm [31]. 

For the purposes of the following discussion small molecules are considered to have fewer than 200 nonhydrogen atoms. Macromolecules, primarily proteins, polynucleic acids, and vimses, can have many thousands of atoms. 

Information on the electronic configuration of each nonhydrogen atom is incorporated in the second order atomic index (S ) of the atom. 

Aldehydes up to a chain length of four nonhydrogen atoms are tolerated as acceptors. 2-Hydroxyaldehydes are relatively good acceptors, and the D-isomers are preferred over the t-isomers [180]. Reactions that lead to thermodynamically unfavorable structures may proceed with low stereoselectivity at the reaction center [181]. Recently, a single-point mutant aldolase was found 2.5 times more effective than the wild type in accepting unphosphorylated glyceraldehyde [182,183]. 

The CASE approach is quite different. CASE decomposes a molecule into all possible fragments from two to ten heavy (nonhydrogen) atoms. With a statistical technique, these are then classified into biophores (allied to toxicity) and biophobes (not allied to toxicity). These are then combined into an equation ... 

The geometry of nitromethane (1) is characterized by the equivalence of the two NO bonds, the single bond character of the CN bond, the coplanarity of the four nonhydrogen atoms, and a value of the zONO angle larger than 120°. The geometry of aci-nitromethane (4) is characterized by the nonequivalence of two NO bonds, the double bond character of the... 

Thus, in each molecule, there are two sets of E-state values one for all nonhydrogen atoms and the second for the hydrogen atoms. The HS values are zero for atoms without hydrogens. 

Percentage of structures with an RM S deviation of the nonhydrogen atoms less than 0.3 A. 

Quasielastic (Rayleigh) scattering of the 46.5 keV Mossbauer radiation was used to examine the liquid dynamics of glycerol [245, 246] and the harmonic vibrations of the nonhydrogen atoms in polycrystalline myoglobin [247] as a function of temperature. The y-quanta emitted by the Mossbauer source are... 

Figure 4. A perspective drawing of C.jH NjSi.B, with nonhydrogen atoms represented by thermal vibration ellipsoids drawn to encompass 50% of their electron density hydrogen atoms are represented by arbitrarily small spheres which are in no way representative of their true thermal motion.

Figure 2. ORTEP drawing of the nonhydrogen atoms of one of the two crystal-lographically independent Th[(CHS)5C5]2[p-CO(CH2C(CHs)s)CO]Cl molecules in the unit cell of 5. The stereochemistry of the second molecule differs from this one primarily in the orientation of the t-butyl groups. All atoms are represented by thermal-vibration ellipsoids drawn to encompass 50% of the electron density...

Intramolecular distances in theophylline monohydrate involving nonhydrogen atoms [20]... 

DN2Sy Triplet index from distance matrix, square of graph order ( of nonhydrogen atoms), and distance sum operation y — 1-5... 

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