Energy levels orbital

Figure Cl.2.5. Illustration of the pn orbital energy levels in [ ]fullerene, [TOJfullerene and monofunctionalized pvrrolidinol601fullerene 1261.

The splitting of the d orbital energy levels when ligands are bonded to a central transition atom or ion has already been mentioned (p. 60). Consider the two ions [Co(NH3)g] and [Co(NH3)g] we have just discussed. The splitting of the d orbital energy levels for these two ions is shown in Figure 13.2. 

I he Koothaan equations just described are strictly the equations fora closed-shell Restricted Hartrce-Fock fRHK) description only, as illustrated by the orbital energy level diagram shown earlier. To be more specific ... 

One of molecular orbital theories early successes came m 1931 when Erich Huckel dis covered an interesting pattern m the tt orbital energy levels of benzene cyclobutadiene and cyclooctatetraene By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar geometries Huckel found that whether a hydrocarbon of this type was aromatic depended on its number of tt electrons He set forth what we now call Huckel s rule... 

In addition to total energy and gradient, HyperChem can use quantum mechanical methods to calculate several other properties. The properties include the dipole moment, total electron density, total spin density, electrostatic potential, heats of formation, orbital energy levels, vibrational normal modes and frequencies, infrared spectrum intensities, and ultraviolet-visible spectrum frequencies and intensities. The HyperChem log file includes energy, gradient, and dipole values, while HIN files store atomic charge values. 

Once you have calculated an ab initio or a semi-empirical wave function via a single point calculation, geometry optimization, molecular dynamics or vibrations, you can plot the electrostatic potential surrounding the molecule, the total electronic density, the spin density, one or more molecular orbitals /i, and the electron densities of individual orbitals You can examine orbital energies and select orbitals for plotting from an orbital energy level diagram. 

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

Figure 14.1 Schematic molecular-orbital energy level diagram for the molecule O2 in its ground state,. The intemuclear vector is along the z-axis.

Figure 6.1 Orbital energy-level diagram for a typical organic molecule...

Figure 6.14a shows the sp and d bands of a transition metal (e.g. Pt), i.e. the density of states (DOS) as a function of electron energy E. It also shows the outer orbital energy levels of a gaseous CO molecule. Orbitals 4a, l7t and 5cr are occupied, as indicated by the arrows, orbital 27c is empty. The geometry of these molecular orbitals is shown in Figure 6.14b. 

FIGURE 3.31 Atypical molecular orbital energy-level diagram for the homonuclear diatomic molecules Li2 through N2. Each box represents one molecular orbital and can accommodate up to two electrons. 

Step 2 Use matching valence-shell atomic orbitals to build bonding and antibonding molecular orbitals and draw the resulting molecular orbital energy-level diagram (Figs. 3.31 and 3.32). 

FIGURE 3.33 A typical d molecular orbital energy-level diagram for a heteronuclear diatomic molecule AB the relative contributions of the atomic orbitals to the molecular orbitals are represented by the relative sizes of the spheres and the horizontal position of the boxes. In this case, A is the more electronegative of the two elements. 

The molecular orbital energy-level diagrams of heteronuclear diatomic molecules are much harder to predict qualitatitvely and we have to calculate each one explicitly because the atomic orbitals contribute differently to each one. Figure 3.35 shows the calculated scheme typically found for CO and NO. We can use this diagram to state the electron configuration by using the same procedure as for homonuclear diatomic molecules. 

Sei f-Test 3.1 IB Write the configuration of the ground state of the cyanide ion, CN, assuming that its molecular orbital energy-level diagram is the same as that for CO. 

FIGURE 3.37 The molecular orbital energy-level diagram for methane and the occupation of the orbitals by the eight valence electrons of the atoms. 

FIGURE 3.39 The molecular orbital energy-level diagram for the ir-orbitals of benzene. In the ground state of the molecule, only the net bonding orbitals are occupied. 

FIGURE 3.40 The molecular orbital energy-level diagram for SFf, and the occupation of the orbitals by the 12 valence electrons of the atoms. Note that no antibonding orbitals are occupied and that there is a net bonding interaction even though no d-orbitals are involved. 

Construct and interpret a molecular orbital energy-level diagram for a homonuclear diatomic species (Sections 3.9 and 3.10). 

Draw simple molecular orbital energy-level diagrams to indicate how the bonding in the saline hydrides, such as NaH or KH, differs from that between hydrogen and a light p-block element such as carbon or nitrogen. 

Draw an orbital energy-level diagram (like those in Figs. 

Suggest the form that the orbital energy-level diagram would take for a square planar complex with the ligands in the xy plane, and discuss how the building-up principle applies. Hint The d -orbital has more electron density in the xy plane than the dzx- or d -orbitals but less than the dXJ,-orbital. 

In a nickel-containing enzyme various groups of atoms in the enzyme form a complex with the metal, which was found to be in the +2 oxidation state and to have no unpaired electrons. What is the most probable geometry of the Ni2+ complex (a) octahedral (b) tetrahedral (c) square planar (see Exercise 16.96) Justify your answer by drawing the orbital energy-level diagram of the ion. 

Three-membered ring Scheme 4 Orbital energy levels... 

The i-orbital array of three and four-membered rings is of the Hiickel conjugation. (Scheme 2). The splitting patterns of the orbital energy levels (Scheme 3) show that the total number of valence electrons for the closed-shell structures is 4Af + 2 for the three- N= 0) and four-membered rings (N= 0, 1). 

Scheme 5 Orbital energy levels of the regular octahedron...

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