Molecular-Orbital Energy Levels

2-4 MOLECULAR-ORBITAL ENERGY LEVELS The approximate wave functions for the and a molecular orbitals are  

Equations (2-1) and (2-2) are simply the analytical expressions for the molecular orbitals shown in Figs. 2-5 and 2-7, respectively. The values of the constants and N in Eqs. (2-1) and (2-2) are fixed by the normalization condition, 

The integral involving both l.r and 1 6 is called the overlap integral and is denoted by the letter S  

In our approximate scheme we shall neglect the overlap integral in determining the normalization constant Therefore, arbitrarily-picking the positive sign in Eq. (2-8), we have 

The energies of these molecular orbitals are obtained from the Schrodinger equation, 

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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 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. 

For each of the following, draw a molecular orbital energy level diagram and give the bond order. Tell whether the species would be more or less stable after gaining an electron, (a) 02+ (b) CN (c) S2 (d) NO (e) Be2+. 

Draw the molecular orbital energy level diagram for SO. What properties do you predict for this molecule ... 

FIGU RE 16.11 The molecular orbital energy level diagrams for 02 and N2. 

Fig. 13 Qualitative molecular orbital energy level diagram of the dimer d orbitals with the 14 electrons showing the electronic configuration 525 27i47i 4o2 (singlet) and the first excited state 828 2it4it 4a1CT 1 (triplet)...

Choose the correct molecular orbital energy level diagram. 

Figure 15. Canonical molecular orbital energy levels for [Rh(PH3)2(formamide)]+, showing the filled and unfilled orbitals with the woner symmetry to interact with C C jc and it-orbitals, seen on the right. Scale markings are in eV. All calculations were done at the B3LYP/LANL2DZ level.

Sketch a molecular orbital energy-level diagram. Use the same diagram to save time, unless it becomes too messy. 

Figure 4.1 re-Molecular orbital energy levels of (a) C4H4, (b) CgHg and (c) CgHs... 

Fig. 3.14 The occupancy of the molecular orbital energy levels across the first row diatomic molecules. (After Cotton and Wilkinson (1980).)...

Figure 6. Molecular orbital energy level diagram for [ Mo( and related complexes. The half-arrows designate...

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