Spatial configurations, symmetry

Atactic. A characteristic of the spatial configuration of atoms or groups in a polymer chain. Atactic indicates a random distribution- of those atoms or groups, i.e., no symmetry to the spatial configuration. This characteristic is important, for example, in determining the properties of polypropylene. 

After the resolution of 1-2-chloro-ammino-diethylenediamino-cobaltie chloride many analogous resolutions of optically active compounds of octahedral symmetry were carried out, and active isomers of substances containing central cobalt, chromium, platinum, rhodium, iron atoms are known. The asymmetry is not confined to ammines alone, but is found in salts of complex type for example, potassium tri-oxalato-chromium, [Cr(Ca04)3]K3, exists in two optically active forms. These forms were separated by Werner2 by means of the base strychnine. More than forty series of compounds possessing octahedral symmetry have been proved to exist in optically active forms, so that the spatial configuration for co-ordination number six is firmly established. 

Spin-coupled VB calculations were carried out using a total of 26 orbitals six occupied, six a virtual and 14 n virtual orbitals. The final wavefunctions consisted of 500 structures of the type described in Eq. (17) formed from 286 distinct spatial configurations of S symmetry. These consist of the spin-coupled reference function and (1 -I- 2 -I- 3 -I- 4)-fold excitations. No excitations from the (ffj, ffj) core were included. About half of these structures (single plus double replacements) contribute to the ground state, the remainder improves the description of the excited states. 

Because the Schrodinger equation cannot be solved exactly for polyelectron atoms, it has become the practice to approximate the electron configuration by assigning electrons to hydrogen-like orbitals, which are designated by the same labels as for hydrogen and have the same spatial characteristics (symmetry, nodes, etc.). 

Whichever kind of interaction prevails, the molecular or ionic units must tend to set themselves into arrays which possess a minimum of potential energy. Hence the existence of the crystaUine state and its characteristics of symmetry. Symmetrical orderings naturally allow potential energies lower than the unsymmetrical arrangements which would result from their distortion. To represent a possible spatial configuration of ions or molecules the system need not possess a potential energy which is an absolute minimum. Several relative minima may be separated from one another and from the absolute minimum by intervening maxima. 

Thus several spatial configurations which correspond to relatively but not absolutely stable minima may have to be taken into consideration. Each has certain elements of symmetry, but some have more than others. Hence the existence of polymorphic modifications. 

Fig. 1 Depiction of the SOCI Hamiltonian matrix for the RuO " MRS calculation. This plot indicates the number of nonzero doublegroup configuration interaction terms (height) versus the specified configuration pair (base). The total number of spatial configuration is 607,965, and the total double-group symmetry-adapted function is 6,078,210. The four J symmetries (1, 3, 5, 7) that mix for this problem are evident in the block nature of the block nature...

FIGURE 12.15 (a) Movre-Pichler potentials for a pair of molecules as a function of their separation r. The potentials E(gi(r)) for the four ground states (dashed lines) and the potentials (X(r)) for the first 24 excited states (solid lines). The symmetries 1T of the corresponding excited manifolds are indicated, as are the asymptotic manifolds Ni,Ji Nj,Jj). (b) Implementation of spin model Shown is the spatial configuration of 12 polar molecules trapped by... 

Molecular symmetry is used to describe the spatial configuration of a single molecular structure, inasmuch as it describes the geo-... 

Seetion treats the spatial, angular momentum, and spin symmetries of the many-eleetron wavefunetions that are formed as anti symmetrized produets of atomie or moleeular orbitals. Proper eoupling of angular momenta (orbital and spin) is eovered here, and atomie and moleeular term symbols are treated. The need to inelude Configuration Interaetion to aehieve qualitatively eorreet deseriptions of eertain speeies eleetronie struetures is treated here. The role of the resultant Configuration Correlation Diagrams in the Woodward-Hoffmann theory of ehemieal reaetivity is also developed. 

The UHF option allows only the lowest state of a given multiplicity to be requested. Thus, for example, you could explore the lowest Triplet excited state of benzene with the UHF option, but could not ask for calculations on an excited singlet state. This is because the UHF option in HyperChem does not allow arbitrary orbital occupations (possibly leading to an excited single determinant of different spatial symmetry than the lowest determinant of the same multiplicity), nor does it perform a Configuration Interaction (Cl) calculation that allows a multitude of states to be described. 

Spatial function Spin function Symmetry Configuration... 

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