Restriction atom states

Restricting atom states Restrict the number of occurrences of atom states by an interval. 

A very high stereoselectivity was observed in the reduction of 4-tert-butylcyclohexanone to the m-alcohol (> 95%), which is the industrially relevant product. The observed high selectivity to the thermodynamically unfavorable cis-alcohol was explained by a restricted transition-state for the formation of the trans-alcohol within the pores of the zeolites (Scheme 5). This reaction was found not only to be catalysed by Al-Beta, van der Waal et al. reported the catalytic activity of aluminum-free zeolite titanium beta (Ti-Beta) in the same reaction.74 Again, a very high selectivity to the cis-alcohol was observed indicating similar steric restrictions on the mechanism. Kinetically restricted product distributions were also reported for the 2-,3- and 4-methylcyclohexanone the cis, trans- and ds-isomers being the major products, respectively. In this case the tetrahedrally coordinated Ti-atom was assumed to behave as the Lewis acid metal center. Recent quantum-chemical calculations on zeolite TS-1 and Ti-Beta confirm the higher Lewis acidic nature of the latter one.75... 

Selection rules reflect the restrictions on state changes available to an atom or molecule. Any transition in violation of a selection rule is said to be forbidden, but as we shall see, some transitions are more forbidden than others (to paraphrase George OrwelH<>). We shall not pursue the theoretical bases of the rules in any detail but merely outline simple tests for their application. 

Heterogeneous catalysts which are active for the catalysis of the MPVO reactions include amorphous metal oxides and zeolites. Their activity is related to their surface basicity or Lewis acidity. Zeolites are only recently being developed as catalysts in the MPVO reactions. Their potential is related to the possibility of shape-selectivity as illustrated by an example showing absolute stereoselectivity as a result of restricted transition-state selectivity. In case of alkali or alkaline earth exchanged zeolites with a high aluminium content (X-type) the catalytic activity is most likely related to basic properties. For zeolite BEA (Si/Al=12), however, the dynamic character of those aluminium atoms which are only partially connected to the framework appear to play a role in the catalytic activity. Similarly, the Lewis acid character of the titanium atoms in aluminium free [Ti]-BEA explains its activity in the MPVO reactions. 

Even this double-resonance spectroscopy has already been applied to the study of atomic transitions before lasers were available. In these pre-laser experiments incoherent atomic resonance lamps served as pump sources and a radio frequency field provided probe transitions between Zeeman levels of optically excited atomic states [509]. However, with tunable lasers as pump sources, these techniques are no longer restricted to some special favorable cases, and the achievable signal-to-noise ratio of the double-resonance signals may be increased by several orders of magnitude [510]. 

Restricting the double bond equivalent, DBE Prescribe an interval for DBE, based on the prescribed admissible atom states. 

This is a straightforward description of the process implemented in all MO calculations. To complete the picture, Lennard-Jones identifies some electrons, those in atomic states, as restricted to a single nucleus while others, those in molecular ... 

Here the crystallographic indices in the subscripts refer to the hybrid molecular orbital directions. Because the Schrbdinger Equation governing electron motion is linear, any combination of wave functions that solve it will also be a solution. In other words, choosing the hybrid orbitals or the atomic orbitals as a starting point for the calculation must yield identical results. The most flexible and general approaeh is not to be restricted to specific hybrid orbitals but rather to consider all possible orbital-by-orbital interactions of the fundamental atomic states. These states apply to a given atom in any environment. Thus, their use is valid for any material in which the atom occurs. As an example of a specific interaction, one can ask how does the Px orbital on one atom interact with the orbital on another atom. 

As the number of atoms in the asyimnetric unit increases, the solution of a structure by any of these phase-independent methods becomes more difficult, and by 1950 a PhD thesis could be based on a single crystal structure. At about that time, however, several groups observed that the fact that the electron density must be non-negative everywhere could be exploited to place restrictions on possible phases. The first use of this fact was by D Marker and J S Kasper [24], but their relations were special cases of more general relations introduced by J Karle and H Hauptman [25]. Denoting by A. the set of indices h., k., /., the Karle-Hauptman condition states that all matrices of the fonu... 

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