Symmetric molecular systems

Introduction to Group Theory for Non-Rigid Moiecuies 6.2. Centro-Symmetric Molecular Systems... 

In a symmetrical octahedral system such as SFg, each polar S—F bond has a counterpart pointing in the opposite direction. The bond polarities cancel in pairs, leaving this molecule without a dipole moment. Example examines molecular variations on octahedral geometry. 

To explain the formation of non-crosslinked polymers from the diallyl quaternary ammonium system, Butler and Angelo proposed a chain growth mechanism which involved a series of intra- and inter-molecular propagation steps (15). This type of polymerization was subsequently shown to occur in a wide variety of symmetrical diene systems which cyclize to form five or six-membered ring structures. This mode of propagation of a non-conjugated diene with subsequent ring formation was later called cyclopolymerization. 

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... 

In our non-BO calculations performed so far, we have considered atomic systems with only -electrons and molecular systems with only a-electrons. The atomic non-BO calculations are much less complicated than the molecular calculations. After separation of the center-of-mass motion from the Hamiltonian and placing the atom nucleus in the center of the coordinate system, the internal Hamiltonian describes the motion of light pseudoelectrons in the central field on a positive charge (the charge of the nucleus) located in the origin of the internal coordinate system. Thus the basis functions in this case have to be able to accurately describe only the electronic correlation effect and the spherically symmetric distribution of the electrons around the central positive charge. 

An electronic transition takes place through the interaction of the electric held of incident electromagnetic radiation with a component of the dipole moment of the absorbing atomic or molecular system. Such transitions usually involving light in the visible region of the spectrum can occur only between states that differ in parity that is, one state must have a symmetric (g) wave function and the other an antisymmetric (n) wave function. 

It is generally found that if one increases the flexibility of a single-determinantal wavefunction by allowing each space orbital to assume an independent form (rather than insisting on double occupation by an and a (1 electron for those orbitals which would otherwise be so occupied as dictated by the electronic configuration) that the asymptotic difficulties of the wavefunction are removed. Thus, the unrestricted Hartree-Fock method usually predicts the correct dissociation products of a molecular system.140 The symmetrical (C2 ,) insertion of Of3P) into Ha yields the 33i state of the HaO system. The electronic configuration of this state expressed in terms of the unrestricted set of orbitals is... 

For a symmetrical atomic or molecular system, these considerations place a severe restriction on the possible eigenfunctions of the system. All possible eigenfunctions must form bases for some irreducible representation of the group of symmetry operations. The form of the possible eigenfunctions is also determined to a large extent since they must transform in a quite definite way under the operations of the group. 

---