Core atom

Figure 2 40. To illustrate the isomorphism problem, phenylalanine is simplified to a core without representing the substituents. Then every core atom is numbered arbitrarily (first line). On this basis, the substituents of the molecule can be permuted without changing the constitution (second line). Each permutation can be represented through a permutation group (third line). Thus the first line of the mapping characterizes the numbering of the atoms before changing the numbering, and the second line characterizes the numbering afterwards. In the initial structure (/) the two lines are identical. Then, for example, the substituent number 6 takes the place of substituent number 4 in the second permutation (P2), when compared with the reference molecule.

Split-Valence Basis Sets. In split-valence basis sets, inner or core atomic orbitals ar e represented by one basis function and valence atomic orbitals are represented by two. The carbon atom in methane is represented by one Is inner orbital and 2(2s, 2pj., 2py, 2pj) = 8 valence orbitals. Each hydrogen atom is represented by 2 valence orbitals hence, the number of orbitals is... 

Step 1, Second Symbol. A bond is being broken between C and H. The symbol is D. In any process, the subscript is E if a core atom is forming a bond to an electrophile (Ag) or breaking a bond to an electrofuge (De). Since C is a core atom, the symbol here is De- Alternatively, the symbol could be Dh- The rules allow Ah or Dh to replace Ae or De if the electrophile or electrofuge is H. Because a core atom is involved in this primitive change the H in the subscript is capitalized. 

Step 2. Only one bond is broken in this step and no bonds are formed. (The movement of a pair of unshared electrons into the C-C bond, forming a double bond, is not designated by any symbol. In this system, bond multiplicity changes are understood without being specified.) Thus the symbol is D. The broken bond is between a core atom (C) and a nucleofuge (Cl), so the designation is D. ... 

Nano-sized Au particles (>1.5 nm) obtained by evaporation of metallic gold on Mylar [431] exhibit differences in 6 and A q for surface and core atoms when the particle sizes are less than 6 nm. 

Any residual doubt about the actual 7r-stabilization of such carbanions, that is, the question concerning the importance of resonance structure 52a, has been decisively banished by an XRD analysis of the lithium bis(12-crown-4) salt of dimesityl(methyl)borane (54).56 Noteworthy are the slightly elongated mesityl C—B bonds at 1.617 A (over those in Mes2BMe at 1.586 A) and the pronouncedly shorter methylene C—B bond at 1.444 A. Moreover, the C2BCH2 core atoms lie essentially in a plane. All these data support the view of 54 as a borataethene, just as structure 52a would imply. 

To ensure a smooth and continuous change of the environment set during the optimization, the initial coordinates for the environment atoms are set to be the same for all the replicas along the path. Thus, the initially guessed replicas differ only in the coordinates of the core atoms. In other words, the initial environment for all the points on the path is the same and is taken to be the environment from one of the end points. 

Binuclear Technetium Cluster Compounds with the d4-d4 Electronic Configuration of the Core Atoms... 

Another way for silicon to form cages is to establish a core-shell structure, in which the Si core atoms are arranged like carbon atoms in C60. The protruding bonds, which point out of the inner cage, are connected to a shell structure comprised of Si atoms arranged in distorted sp3 bonding (23). However, such structures have eluded the experimenters and could not be synthesized, so far. 

Both macrocycles display a slight saddle distortion with mean deviation from the least-squares plane of the 24 core atoms of 0.07 A for molecule 147 A and 0.09 A for molecule 147 B. The asymmetry of the periphery is apparent in the macrocyclic core of both molecules in that each is elongated... 

Unfortunately, these aza-ethers showed limited solubility in the polar solvents that are typically preferred in nonaqueous electrolytes, and the electrochemical stability window of the LiCl-based electrolytes is not sufficient at the 4.0 V operation range required by the current state-of-the-art cathode materials. They were also found to be unstable with LiPFe. Hence, the significance of these aza-ether compounds in practical applications is rather limited, although their synthesis successfully proved that the concept of the anion receptor is achievable by means of substituting an appropriate core atom with strong electron-withdrawing moieties. 

Among the three subcategories, boronate compounds seemed to be the most efficient in coordinating with anions and enhancing lithium ion stability, although the number of electron-withdrawing substituents in boronate is only two. The authors thus inferred that the ability of these anion receptors to capture an anion depends not only on the electron-deficiency of the core atom but perhaps also on the steric hindrance presented by these substituents on the core. With only two substituents, the core of the boronates is obviously more exposed and therefore more easily accessible for an anion. The higher ion conductivity achieved by boronate additive therefore comes from the better balance between the electron-deficiency and steric openness of this compound as... 

Of course, more complex carbon groups can be attached at any of the 3 bonds to nitrogen. Notice that the nitrogen atom is truly the core atom in an amine, in contrast to the functional groups in alcohols, aldehydes, and carboxylic acids, in each of which the functional group must be at the end of the molecule. 

Secondly, the unbonded surface Au atoms are much more numerous than the core atoms. Lack of experimental observation of a shoulder on the low b.e. side of the AU4/7/2 peak therefore argues for an assignment of the first component in the Au4/ peak to the surface Au atoms. Accordingly, as may be seen in Table 2, in the presently proposed fitting, the lowest b.e. component of the peak is assigned to the unbonded gold surface atoms. 

Thirdly, there is no possible way to fit the peak component due to the 13 core atoms by locating this component on the high b.e. side of the AU4/7/2 peak (See the procedure in ref. [76]), because of the shape of the peak. The highest b.e. component must be assigned to a component representing a relatively small number of Au atoms, i.e. those coordinated by chlorine. 

Fourthly, as a consequence of the previous point, the Aujj cluster reveals a very different core than lower nuclearity gold molecular clusters such as [AugLg] and AU11L7X3, which all possess largely positively charged cores [76,153]. In Aujs the core atoms have a relatively low b.e., showing a low oxidation state. 

A split-valence basis set represents core atomic orbitals by one set of functions and valence atomic orbitals by two sets of functions. Hydrogen is provided by two s-type functions, and main-group elements are provided two sets of valence s and p-type functions. 

It is difficult to assess the conversion of the hydroxyl groups on the core since the percentage contribution from core atoms diminish rapidly when the samples are analyzed, with e.g. NMR. However, when bis-MPA was esterified in absence of core moiety the resulting polymer was very dilficult to dissolve in any solvent. This serves as indirect evidence of the importance of the core moiety. 

In a similar manner, the reaction of 6.28 with CuCl in CH2CI2-CH3CN produces the spherical complex [ Cp Ta(CO)2(t " -P4) 6 CuCl g] (6.31). The tantalum complex 6.31 is comprised of 32 core atoms forming four-membered P4 rings and six-membered P4CU2 rings in an extended cubic arrangement with... 

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