Periodic orbits period-energy diagram

Figure 14. Period-energy diagram of the fundamental periodic orbits 0, I, and 2 in Hgl2 with the bifurcations of the transition region marked by dashed lines.

To construct an orbital energy diagram for a diatomic molecule in which the two nuclei are different, we must remember that orbitals with the same symmetry repel each other. As shown earlier, this re-. pulsion is dependent on the energy difference between the molecular orbitals and on the size of the interaction. For diatomic molecules in which the two nuclei are not far from each other in the periodic table, the diagram will be approximately as shown in Figure 2-19. 

Figure 9-5 shows molecular orbital energy level diagrams for homonuclear diatomic molecules of elements in the first and second periods. Each diagram is an extension of the... 

Figure 9-5 Energy level diagrams for first- and second-period homonuclear diatomic molecules and ions (not drawn to scale). The sohd lines represent the relative energies of the indicated atomic and molecular orbitals, (a) The diagram for H2, Hc2, Li2, Bc2, B2, C2, and N2 molecules and their ions, (b) The diagram for O2, F2 and Nc2 molecules and their...

Fig. 9.2. A schematic molecular orbital energy diagram which, together with the Aufbau principle leads to the prediction of the correct electron configuration of all the diatomic homonuclear species of second-period elements from Li2 to Nc2.

A Molecular orbital energy diagrams for second-period diatomic molecules show that the energy ordering of the 772 and a-2p molecular orbitals can vary. 

Draw an energy diagram for the molecular orbitals of period 2 diatomic molecules. Show the difference in ordering for B2, C2, and N2 compared to O2, F2, and Ne2-... 

The electron configuration or orbital diagram of an atom of an element can be deduced from its position in the periodic table. Beyond that, position in the table can be used to predict (Section 6.8) the relative sizes of atoms and ions (atomic radius, ionic radius) and the relative tendencies of atoms to give up or acquire electrons (ionization energy, electronegativity). 

Now we can see the development of the entire periodic table. The special stabilities of the inert gases are fixed by the large energy gaps in the energy level diagram, Figure 15-11. The number of orbitals in a cluster, multiplied by two because of our double occupancy assumption, fixes the number of electrons needed to reach the inert gas electron population. The numbers at the... 

FIGURE 3.32 The molecular orbital energy-level diagram for the homonuclear diatomic molecules on the right-hand side of Period 2, specifically 02 and F2. 

Let us first briefly review the construction of molecular orbitals in simple diatomic molecules, AB, using the linear combination of atomic orbitals (LCAO) scheme. The end product for the first long row of the periodic table is the well-known diagram in Fig. 6-1. We focus on two broad principles that are exploited in the construction of this diagram one has to do with symmetry and overlap, the other concerns energies. 

C08-0031. Construct an orbital energy level diagram for all orbitals with < 8 and / < 4. Use the periodic table to help determine the correct order of the energy levels. 

The data show that bond energies for these three diatomic molecules increase moving across the second row of the periodic table. We must construct molecular orbital diagrams for the three molecules and use the results to interpret the trend. 

In addition to the homonudear molecules, the elements of the second period form numerous important and interesting heteronudear species, both neutral molecules and diatomic ions. The molecular orbital diagrams for several of these species are shown in Figure 3.9. Keep in mind that the energies of the molecular orbitals having the same designations are not equal for these species. The diagrams are only qualitatively correct. 

Figure 9. Supercritical antipitchfork bifurcation scenario for symmetric XYX molecules on the left, bifurcation diagram in the plane of energy versus position in the center, typical phase portraits in some Poincare section in the different regimes on the right, the fundamental periodic orbits in position space.

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