Linear Combination of Atomic Orbitals Approximation

The coefficients indicate the contribution of each atomic orbital to the molecular orbital. This method of representing the molecular orbital wave function in terms of combinations of atomic orbital wave functions is known as the linear combination of atomic orbitals approximation (LCAO). The combination of atomic orbitals chosen is called the basis set. 

LCAO Approximation. Linear Combination of Atomic Orbitals approximation. Expresses the Molecular Orbitals by linear combinations of atom-centered functions (Atomic Orbitals). 

Molecular-orbital theory treats molecule formation from the separated atoms as arising from the interaction of the separate atomic orbitals to form new orbitals (molecular orbitals) which embrace the complete framework of the molecule. The ground state of the molecule is then one in which the electrons are assigned to the orbitals of lowest energy and are subject to the Pauli exclusion principle. Excited states are obtained by promoting an electron from a filled molecular orbital to an orbital which is normally empty in the ground state. The form of the molecular orbitals depends upon our model of molecule formation, but we shall describe (and use in detail in Sec. IV) only the most common, viz., the linear combination of atomic orbitals approximation. 

Short of the ab initio calculations, there are several semi-empirical approaches to the calculation and interpretation of electric quadrupole coupling constants. These were developed originally by Townes and Dailey [47, 48] and are well documented in the book by Gordy and Cook [49], They are based on the linear combination of atomic orbitals approximation for molecular orbitals, mentioned earlier in equation (7.266) and described in more detail in chapter 6 ... 

De-localized Bonds Molecular Orbital Theory and the Linear Combination of Atomic Orbitals Approximation... 

We are often seduced by our models, even to the extent that we indulge in heated discussions about controversies that can only arise within a given simphfied model. Examples are the involvement of dorbitals in bonding to sulfur [58] (only meaningful within the LCAO (Linear Combination of Atomic Orbitals) approximation), diradical versus zwitterionic intermediates [59] (only meaningful in the context of single Lewis structures) and many others. 

The resulting operators are products of algebraic functions (square root expressions) of p and are usually not evaluated analytically in the framework of a basis set in the LCAO (linear combination of atomic orbitals) approximation. Rather, a matrix technique employing the approximate resolution of the identity is used to evaluate the operators. ... 

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