Molecular Orbitals from

Figure 7.12 Formation of two molecular orbitals from two identical atomic orbitals...

Figure 7.13 Formation of molecular orbitals from Is, 2s, and 2p atomic orbitals...

Fig. 11.13. Coefficients and relative energies of dienophile and diene molecular orbitals. [From K.. N. Houk, J. Am. Chem. Soc. 95 4092 (1973).]...

The double zeta basis sets, such as the Dunning-Huzinaga basis set (D95), form all molecular orbitals from linear combinations of two sizes of functions for each atomic orbital. Similarly, triple split valence basis sets, like 6-3IIG, use three sizes of contracted functions for each orbital-type. 

We will find an excitation which goes from a totally symmetric representation into a different one as a shortcut for determining the symmetry of each excited state. For benzene s point group, this totally symmetric representation is Ajg. We ll use the wavefunction coefficients section of the excited state output, along with the listing of the molecular orbitals from the population analysis ... 

In the present work a theory for the facile construction of complex molecular orbitals from bond and group orbitals is presented and complemented by accurate drawings of the valence molecular orbitals for over one hundred molecules representing a wide range of connectivities and functional groupings. Direct applications to phenomena in organic chemistry are also discussed. 

Many of the figures given in Section II are actually simplified plots of the molecular orbitals. From any MO calculation, these are given by a set of coefficients, c,7, in the linear combination of AOs Xj (LCAO) ... 

In the molecular orbital description of homonuclear diatomic molecules, we first build all possible molecular orbitals from the available valence-shell atomic orbitals. Then we accommodate the valence electrons in molecular orbitals by using the same procedure we used in the building-up principle for atoms (Section 1.13). That is,... 

The ground-state electron configurations of diatomic molecules are deduced by forming molecular orbitals from all the valence-sbell atomic orbitals of the two atoms and adding the valence electrons to the molecular orbitals in order of increasing energy, in accord ivith the building-up principle. 

Butadiene has two n bonds. The interaction between the two n bonds is one of the simplest models to derive molecular orbitals from bond orbitals. A n bond in butadiene is similar to that in ethylene. The n bond is represented by the bonding and antibonding orbitals. The interactions occur between the n bonds in butadiene. The bond interactions are represented by the bond orbital interactions. 

The selection rules appropriate for a shake-up transition are of the monopole type2, 76. The intensity of a shake-up peak depends on the overlap integral between the lower state molecular orbital from which the electron is excited (in the neutral molecule) and the upper state molecular orbital to which the electron is excited (in the core-ionized molecule). Consequently one expects transitions of the type au au, ag " ag> 7T nu, and irg - ng with g u and u - g transitions forbidden. 

The trigonal bond orbitals in the ten valence electron system as well as the two sets of trigonal lone pair orbitals in the 14 valence electron system are superpositions of it orbitals and o orbitals. The formation of such trigonally symmetric molecular orbitals from a-type and w-type molecular orbitals is entirely analogous in character to the formation of the three (sp2) hybrid atomic orbitals from one (s) and two ip) atomic orbitals which was discussed in the preceding section. This can be visualized by looking at the diatomic molecule... 

Figure 2.28 Relative energies of benzene and cyclooctatetraene molecular orbitals from Frost circles...

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