Sequencing of atoms

It should be noted that it does not matter which atom is picked out of a group of atoms which cannot be assigned a unique number in the first place because these atoms are in fact constitutionally equivalent. 

In this aspect our new indexing routine differs from our previous approach ). Our new procedure does not have the drawbacks of other methods ) known, like instability of the calculations, oscillatory behaviour, nonconvergence and indeterminancy. 

The BE-matrix, together with its associated vectors (atoms, stereochemical parity bits) contains all structural information about a molecule. In a variety of applications, such information has to be stored and 

ACS Symposium Series American Chemical Society Washington, DC, 1977. 

The information that is contained in the BE-matrix and its associated atom vector is compressed to the minimum number of bytes which is necessary for the expected range of values for each of these items. 

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Figure C2.16.2. The sequence of atoms in tlie two poly types of SiC, zincblende and wurtzite, along tlie c-direction. The zincblende lattice has perfect tetraliedral angles.

Large systems contain ring atoms enough to allow more than one way of bonding between a given sequence of atoms, and a wealth of valence isomerizations becomes possible. Already for seven ring members, two types of bicyclic isomer are observed, namely the [4.1.0] and the [3.2.0] systems, each with positional ring isomers if more than one heteroatom is present. 

To sum-up, we can to some extent recover the order of filling by calculating the ground state configurations of a sequence of atoms but nobody has yet deduced the n + rule from the principles of quantum mechanics.13... 

Pyrophillite, talc, muscovite, and biotite have the following sequence of atom-planes along the pseudo-hexagonal axes ... 

Peptoids are an archetypal and relatively conservative example of a peptidomimetic oligomer (Tab. 1.1). In fact, the sequence of atoms along the peptoid backbone is identical to that of peptides. However, peptoids differ from peptides in the marmer of side chain appendage. Specifically, the side chains of peptoid oligo-... 

A repeat unit is the sequence of atoms that is repeated to build a polymer chain. This definition, although very simple, distinguishes between X-Y and X-XY-Y units. For instance, the repeat units of polyamide 6 and polyamide 6610 are ... 

In order to apply this rule we had to transform the original three-dimensional structural formula in two stages (Fig. 5). In the first, the ligand model, the sequences of atoms constituting the ligands of an element of stereoisomerism... 

In the reactions described in Section III,C, a three-atom fragment in the heterocycle is replaced by the same atoms of the reagent and with the same sequence of atoms. This type of reaction has been referred to as an inter-molecular transfragment reaction (67JA6911) and therefore can be clearly distinguished from molecular rearrangements, such as the Dimroth reactions (68MI1 see also Chapter IV) and photochemical transposition reactions. 

Intermolecular N-C-C transfragment replacement occurs less widely than the N-C-N replacement. A synthesis of alkyl(aryl)pyrimidines has been published that was based on the replacement of the N-C-C fragment of the pyrimidine ring by an identical sequence of atoms derived from a ketone in the presence of ammonia [94H(38)249]. Heating a solution of 3-methyl-5-nitropyrimidin-4(3//)-one (120) in acetonitrile with cyclohexanone and ammonia gas in a sealed tube at 100°C for 3 hours gave tetrahy-... 

Sequence of atoms in the constitutional unit(s) of a macromolecule, an oligomer molecule, a block, or a chain, which defines the essential topological representation. 

We have already stated that the sequence of atomic symbols in an empirical or molecular formula is arbitrary, but that in the absence of any other requirements a... 

Dipolar cycloaddition is one of the most important methods in assembling five-membered ring heterocycles. For the 1,4-(oxa/thia)-2-azole system, nitrile oxides, and nitrile sulfides have the correct sequence of atoms for the 47t 1,3-dipolar component and the 2n component can be a either a C=0 or a C=S heterodipolarophile (Scheme 41). Nitrile oxides, usually generated in situ from the corresponding hydroximoyl chlorides and a base, add to various types of (3=0 bond affording 1,4,2-dioxazole derivatives. 

In l-bromo-3-chlorocyclobutane there are cis and trans isomers, but no enantiomers C and C are not chiral, because a plane perpendicular to the ring bisects them and their four substituents. The sequence of atoms is identical going around the ring clockwise or counterclockwise from C to C. ... 

Most 1,2-rearrangements are provoked by the presence of a disjoint sequence of atoms. In other words, the molecule is not in the best electronic order. For example, epoxides, glycols and p-amino alcohols contain two d-a segments which are linked... 

SAMPLE SOLUTION (a) The hydroxyl-bearing carbon in 2-cydopentenol is a chirality center. There is no chirality center in 3-cydopentenol, because the sequence of atoms 1 2 3 4 5 is equivalent regardless of whether one proceeds clockwise or counterclockwise. 

First, the simple high-molecular-weight polymer with the same sequence of atoms in the chain as in the glycerol TA was prepared in the following way 49) ... 

Primary structure the chemical sequence of atoms in a molecule. 

Studies of isoelectronic sequences of atomic systems (that is, a number of elements with gradually increasing atomic number and degree of ionisation such that they all possess the same number of electrons) are, as mentioned above, very fruitful in theoretical, semiempirical and experimental investigations of atomic spectra. They reveal important regularities and pecularities in the behaviour and physical characteristics of many-electron atoms and ions, help to identify and classify their energy levels within an optimal coupling scheme, find values of semiempirical parameters, etc. 

Structural isomerism is when the molecules differ in the sequence of atomic attachments in the skeleton of the molecule. The compounds in Example 1 are structural isomers. The IUPAC names clearly state the difference between compounds with the same molecular formula, but different structures. 

One says that the microstate of a macromolecule is determined, if a sequence of atoms, the distances between atoms, valence angles, the potentials of interactions and so on are determined. The statistical theory of long chains developed in considerable detail in monographs (Birshtein and Ptitsyn 1966 Flory 1969) defines the equilibrium quantities that characterise a macromolecule in a whole as functions of the macromolecular microparameters. 

Calix[4]arene provides a suitable semi-rigid concave scaffold for the construction of dimeric capsules. Both the upper and lower rim can be decorated with a wide variety of functional groups, in particular the urea moiety is known to provide a good combination of hydrogen bond donor and acceptor character implemented in the same functional group and this sequence of atoms have been extensively employed in the constructions of calix[4]arene dimeric molecular capsules (Fig. 9). Characteristic of these dimers is the presence of a cyclic seam of hydrogen bonds that seal the capsule and provides an internal molecular cavity that easily accommodates molecules as big as benzene. 

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