Atomic orbitals representation

The simplest possible atomic orbital representation is termed a minimal basis set. This comprises only those functions required to accommodate all of the electrons of the atom, while still maintaining its overall spherical symmetry. In practice, this involves a single (Is) function for hydrogen and helium, a set of five functions (Is, 2s, 2px, 2py, 2pz) for lithium to neon and a set of nine functions (Is, 2s, 2px,... 

Problem 15.5 (a) Draw (i) an atomic orbital representation of the carbonyl group and (ii) resonance structures, (b) What is the major difference between the C==0 and C==C groups M... 

The simple carbocation intermediate of Equation 10-1 does not account for formation of the antarafacial-addition product. The results with SN1 reactions (Section 8-6) and the atomic-orbital representation (see Section 6-4E) predict that the bonds to the positively charged carbon atom of a carbocation should lie in a plane. Therefore, in the second step of addition of bromine to cyclo-alkenes, bromide ion could attack either side of the planar positive carbon to give a mixture of cis- and trans-1,2-dibromocyclohexanes. Nonetheless, antarafacial addition occurs exclusively ... 

Figure 14-2 Atomic-orbital representation of the transition state for Sn2 displacement of 3-chloropropene (allyl chloride) with iodide ion. The halide orbitals are represented here as spherical for simplicity. The purpose of this figure is to show the -n bonding, which can stabilize the transition state.

It was long ago suggested that the low extinction coefficient absorption band of ketones and aldehydes occurring in the 280-360 m i region of the ultraviolet corresponds to an excitation process in which a nonbonding (hence n ) electron is promoted to the antibonding t (i.e., ir ) orbital. This constitutes the n ir process and is conveniently depicted in three dimensions using an atomic orbital representation ... 

Canonical transformations from the tight-binding (atomic orbitals) representation to the eigenstate (molecular orbitals) representation play an important role, and we consider it in detail. Assume, that we find two unitary matrices SR and SR, such that the Hamiltonians of the left part Hi and of the right part Hi can be diagonalized by the canonical transformations... 

Consider then the Hamiltonian matrix in this atomic orbital representation. We denote... 

The chemical shifts (2.4 ppm) of acetylenic hydrogens (RCHC-H) are considerably more toward higher magnetic fields than those of alkene hydrogens (4.6 to 6.9 ppm). Show how this shielding effect might be explained in terms of the atomic orbital representation of acetylenes. 

This chapter deals with the discussion and interpretation of approximate molecular electronic structure methods in terms of propagator concepts. Only situations with fixed nuclear frameworks are considered, and the discussion is limited to the description of states that are close in energy to the normal state of the system. We adopt the view that the main features of the electronic structure of such states can be developed in terms of atomic orbital representations of operators and that only valence shell orbitals need be considered. 

MOLECULAR ORBITAL and valence bond calculations of the IT—electron energies of unsaturated molecules customarily start with models in which appropriate atomic orbitals are assigned to each nucleus to provide a framework for -notions of the binding electrons. Atomic orbital representations of organic molecules are now very commonly used in the teaching of elementary organic chemistry, although there often seems to be confusion between atomic orbital and molecular orbital representations. 

Knowledge of how to set up an atomic orbital model for an organic molecule is crucial to the LCAO calculations described in these notes. Any reader who is familiar with atomic orbital representations can omit study of Chapter 1— or else only work the problems at the end of the chapter. 

Hie molecular orbitals of cyclopentadienyl (atomic orbital representation)... 

---