Degenerate orbitals atomic

Each shell contains one s atomic orbital. The second and higher shells—in addition to their 5 orbital—each contain three degenerate p atomic orbitals. Degenerate orbitals are orbitals that have the same energy. The third and higher shells—in... 

Figure 7.14 Molecular orbital energy level diagram for first-row homonuclear diatomic molecules. The 2p, 2py, 2p atomic orbitals are degenerate in an atom and have been separated for convenience. (In O2 and F2 the order of

The number of electrons in an atom affects the properties of the atom. The hydrogen atom, with one electron, has no electron-electron repulsions therefore, all the orbitals of a given shell in the hydrogen atom are degenerate. For instance, the 2s-orbital and all three 2p-orbitaIs have the same energy. In many-electron atoms, however, the results of spectroscopic experiments and calculations show... 

Fig. 1 A schematic illustration of the in-phase and out-of-phase combinations of the atomic orbitals into the bonding and antibonding molecular orbitals, respectively. The dissociation limit of a H molecule corresponds to a pure diradical with degenerate singlet and triplet states...

B The H-atom orbitals 3s, 3p and 3d are degenerate. Therefore, the 9 quantum number combinations are ... 

Fig. 2.6-3. Schematic representation of one of the P4 HOMOs of symmetry constructed from four radially arranged 3p atomic orbitals. The degenerate HOMO is similar and, therefore, omitted.

Figure 1.15 Is, 2p, and 3d degenerate atomic orbitals (ADs) and corresponding wave functions (cf. eq. 1.125). Upper left spherical coordinate system. Adapted from Harvey and Porter (1976).

As R —> oo, the CSF energies (i H T>j) are more difficult to "intuit" because the O and o orbitals become degenerate (in the homonuclear case) or nearly so. To pursue this point and arrive at an energy ordering for the CSFs that is appropriate to the R — °° region, it is useful to express each of the above CSFs in terms of the atomic orbitals sx and sy that comprise o and o. To do so, the LCAO-MO expressions for o and o, ... 

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