Admissible atom state

If we leave the ground state, more valence states are possible for the seime element. Mathematically speaking, we associate a set of admissible atom states to... 

The set of admissible atom states Zx for element X depends on the underlying chemistry chosen in a particular situation. The hiercuchic classification of chemistries described in [61] can be expressed in terms of allowed atom states ... 

Table 1.3. Some admissible atom states for the elements in ,...

More explicitly, a molecule graph is an unlabeled graph where the nodes are colored by an element symbol, together with an admissible atom state. For example, the molecule of cyanic acid is modeled by the following unlabeled, colored graph ... 

Definition (Chemical reaction, reactant and product graph) Assume n > 0, a set of chemical elements and 2, = UxeE x> 3nd a set of admissible atom states of the elements in . Then ... 

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

The atom states admissible in RC are given in Table 1.3 in the rows containing a x in column RC. in RC it is in particular possible to associate a unique valence with each element X e , the standard valence vx-... 

Although the implementation of the methods so fer may seem obvious, efficiency has not yet been mentioned. The distribution of elements and atom states of ambiguous molecules could be calculated easily using a list of all the admissible sequences of elements and atom states (E(i), Z(i)). However, this would turn out to be highly inefficient as soon as ( ) = emd Z(i) = Zg need to be represented. This problem was solved by introducing em abstract basis class atom type with the function... 

Constraints (4.9a,b) determine a convex domain of the 4-dimensional Euclidean space [6], within which all points with integer coordinates correspond to admissible valence states of the octet chemistry their total number is equal to 136. A geometrical interpretation of the valence states of atoms is shown in the following figure. 

In our work [7] we have presented a list of all admissible valence states of the elements with atomic numbers from 1 to 31 (except for He I Ne and Ar)t and for Br and 1. 

The graph a) A= C, or for another one-atom synthon family> may serve as a guide for a global critical estimation of admissible valence state conversions of the given atom. Scheme 5.3 contains carbanions C-, -C=, and Cm accompanied by the corresponding sets of synthon precursors. 

Steady state and non steady state kinetic measurements suggest that methane carbon dioxide reforming proceeds in sequential steps combining dissociation and surface reaction of methane and CO2 During admission of pulses of methane on the supported Pt catalysts and on the oxide supports, methane decomposes into hydrogen and surface carbon The amount of CH, converted per pulse decreases drastically after the third pulse (this corresponds to about 2-3 molecules of CH< converted per Pt atom) indicating that the reaction stops when Pt is covered with (reactive) carbon CO2 is also concluded to dissociate under reaction conditions generating CO and adsorbed... 

We also mentioned stereospecificity of metal-catalyzed reactions inside zeolite cavities. In acid catalysis by zeolites it is well known that shape selectivity can be imposed by (1) selective admission of reactants fitting into zeolite pores, (2) selective release of products able to diffuse through zeolite channels, while larger molecules are retained, and (3) transition state selectivity, favoring, e.g., a monomolecular transition state over a bimolecular state in a narrow cavity. New tools that have conceptually been added to this arsenal include the collimation of molecules diffusing through well-defined pores, which then hit an active site preferentially via one particular atom or group. 

When we combine the spatial and spin wavefunctions, the overall wavefunction must be antisymmetric with respect to exchange of electrons. It is therefore only admissible to combine a syrrunetric spatial part with an antisymmetric spin part, or an antisymmetric spatial part with a symmetric spin part. The following functional forms are therefore permissible functional forms for the wavefunctions of the ground and first few excited states of the helium atom ... 

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