Atomic Orbitals and Their Interactions

HyperChem uses the Linear Combination of Atomic Orbitals-Molecular Orbital (LCAO-MO) approximation for all ofitsnl) initio semi-empirical methods. If /j represents a molecular orbital and 

This equation is important in interpreting the results of calculations. In ab initio and semi-empirical calculations, atomic orbitals are functions of the x, y, and z coordinates of the electron that closely resemble the valence orbitals of the isolated atoms. 

These atomic orbitals, called Slater Type Orbitals (STOs), are a simplification of exact solutions of the Schrodinger equation for the hydrogen atom (or any one-electron atom, such as Li ). Hyper-Chem uses Slater atomic orbitals to construct semi-empirical molecular orbitals. The complete set of Slater atomic orbitals is called the basis set. Core orbitals are assumed to be chemically inactive and are not treated explicitly. Core orbitals and the atomic nucleus form the atomic core. 

Because the calculation of multi-center integrals that are inevitable for ab initio method is very difficult and time-consuming, Hyper-Chem uses Gaussian Type Orbital (GTO) for ab initio methods. In truly reflecting a atomic orbital, STO may be better than GTO, so HyperChem uses several GTOs to construct a STO. The number of GTOs depends on the basis sets. For example, in the minimum STO-3G basis set HyperChem uses three GTOs to construct a STO. 

All molecular orbitals are combinations of the same set of atomic orbitals they differ only by their LCAO expansion coefficients. HyperChem computes these coefficients, Cp , and the molecular orbital energies by requiring that the ground-state electronic energy be at a minimum. That is, any change in the computed coefficients can only increase the energy. 

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In this chapter the necessary theory to understand these two approaches is outlined. Orbital symmetry is introduced by consideration of atomic orbitals and their interaction to form molecular orbitals. The construction of correlation diagrams is illustrated for the formation of molecular orbitals of diatomic molecules. 

Bonding can be treated as interactions of all individual atomic orbitals with all others as represented by the eigenvalues of the matrix of Equation 5.13. The matrix elements are affected by the electron wave vectors, the location of atoms contributing orbitals, and the energy of atomic orbitals and their interactions. 

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