Configurations, isoenergetic

Fig. 2. The twelve isoenergetic configurations and non-rigid operations corresponding to the internal rotation in methyl boron difluoride.

In Fig. 2, the twelve possible isoenergetic configurations that can be obtained by permutations and permutations-inversions of the hydrogen and fluorine atoms, are presented. In this figure, the identical particles, the protons... 

In fact, it is easily seen that there are four isoenergetic configurations, as illustrated in Figure 7. 

Figure 7. The four isoenergetic configurations of non-planar pyrocatechin in stereographic projection.

These six isoenergetic configurations are not necessarily the energetically lowest ones. However, they may be assumed to be for our purposes, and if the energy barrier height between the minima are sufficiently low then inter-conversion movements can occur. The Hamiltonian operator corresponding to such a movement may be transcribed if we take into account ... 

In fact, it is easily seen that there exist 20 isoenergetic configurations, and 20 interconversion operations connecting them. The Altmann s isodynamic group could be written then in terms of 20 double rotation operations according to [46] ... 

To find the different number of isoenergetic configurations of our system (number of the different ways of forming or distributing the hydrogen bonds in the system) we have to do the following ... 

Keywords Exponential-type orbitals Generalized Sturmians Hyperspherical harmonics Interelectron repulsion integrals Isoenergetic configurations Momentum space Quantum theory Sturmians... 

It can be shown that a set of isoenergetic configurations of the form shown in equation (6) obeys the potential-weighted orthonormality relation... 

In equation (3), the constants j8 are especially chosen in such a way as to make all of the eigenfunctions correspond to the same energy, E, regardless of their quantum numbers v [1,5,11-35]. The isoenergetic configurations can be used to build up solutions to the actual Schrddinger equation... 

In this notation, fi j) stands for the one-electron spin-orbital Xn,i,m,m, as a function of the space and spin coordinates of electron j. We now let S be the matrix of overlap integrals between the isoenergetic configurations... 

Table 2. Percentage of isoenergetic configurations and mean Fe - 0 istan-... 

BERTRAN - Really you have made an excellent suggestion, because the probability to find isoenergetic configurations from the macroscopic equilibrium distribution of the reactants is very low, in such a way that in some cases it is practically impossible to get them with the present calculation facilities. If... 

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