Ethylene, LCAO model

Draw the LCAO model of ethylene in the bonding and antibonding orbitals. Distinguish the ground state of ethylene from its excited state. Distinguish from ir 7T. 

The key to get a diabatic electronic state is a strict constraint i.e. keep local symmetry elements invariant. For ethylene, let us start from the cis con-former case. The nuclear geometry of the attractor must be on the (y,z)-plane according to Fig.l. The reaction coordinate must be the dis-rotatory displacement. Due to the nature of the LCAO-MO model in quantum computing chemistry, the closed shell filling of the HOMO must change into a closed shell of the LUMO beyond 0=n/4. The symmetry of the diabatic wave function is hence respected. Mutatis mutandis, the trans conformer wave function before n/4 corresponds to a double filling of the LUMO beyond the n/4 point on fills the HOMO twice. At n/4 there is the diradical singlet and triplet base wavefunctions. 

The Linear Combination of Atomic Orbitals (LCAO) approximation is fundamental to many of our current models of chemistry. Both the vast majority of the calculational programs that we use, be they ab initioy density functional, semiempirical molecular orbital, or even some sophisticated force-fields, and our qualitative understanding of chemistry are based on the concept that the orbitals of a given molecule can be built from the orbitals of the constituent atoms. We feel comfortable with the Ji-HOMO (Highest Occupied Molecular Orbital) of ethylene depicted as a combination of two carbon p-orbitals, as shown in Fig. 2.1, although this is not a very accurate description of the electron density of this Molecular Orbital (MO). The use of the Jt-Atomic Orbitals (AOs), however, makes it easier to understand both the characteristics of the MO itself and the transformations that it can undergo during reactions. 

Early theoretical work by Dedieu and coworkers focused on individual elementary transition metal (TM) reactions for the hydrogenation of ethylene using a model of Wilkinson s catalyst [RhCl(PPH3)3] [3-6]. They used LCAO-MO-SCF calculations to perform an orbital analysis of the oxidative addition step, determine intermediate stability, and analyze the olefin insertion step. Using SCF calculations and orbital correlation diagrams for the valence orbitals of the reactants and products, they analyzed the feasibility and geometry of the oxidative addition shown in (1). 

In the case of ethylene the a framework is formed by the carbon sp -orbitals and the rr-bond is formed by the sideways overlap of the remaining two p-orbitals. The two 7r-orbitals have the same symmetry as the ir 2p and 7T 2p orbitals of a homonuclear diatomic molecule (Fig. 1.6), and the sequence of energy levels of these two orbitals is the same (Fig. 1.7). We need to know how such information may be deduced for ethylene and larger conjugated hydrocarbons. In most cases the information required does not provide a searching test of a molecular orbital approximation. Indeed for 7r-orbitals the information can usually be provided by the simple Huckel (1931) molecular orbital method (HMO) which uses the linear combination of atomic orbitals (LCAO), or even by the free electron model (FEM). These methods and the results they give are outlined in the remainder of this chapter. 

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