Molecular orbital approach tetrahedral bonding

A model of carbon bonding established to account for the tetrava-lent nature of carbon involves two steps, in which the atoms are first raised to excited states (valence states), and are then permitted to interact in these states to form the molecule. In the case of carbon, one of the 2s orbitals is thus "promoted" to a p orbital to make available four unpaired electrons. The result is the "hybridization" of an s orbital with three p orbitals to form four equivalent and tetrahedrally oriented sp orbitals. To devise molecular orbitals, one takes a linear combination of atomic orbitals. Following the valence bond theory, the atoms are in their excited state when hybridized, and then come together to form a molecule. In the molecular orbital approach, when the proper coefficients for the wave functions of the linear combination of atomic orbitals are chosen—i.e., those coefficients which will minimize the energy of the resultant molecule—the results will be the same as when hybrid orbitals are employed. Thus, both approaches lead to a minimization of energy and to stable bond formation. 

We apply an approach based on the local site symmetry that has been used in classic texts on molecular orbital theory [11,12], and subsequently addressed in a more formal way for TM bonding in octahedral and tetrahedral arrangements, as for example in Ti02, and in cubic titanate and manganite perovskites by F.A. Cotton [13]. 

Another approach to the problem of molecular stability in terms of the valence bond picture was introduced by Linnett [8] (also see reference [3]). According to Linnett s model, valence electrons occupy tetrahedrally oriented spatial configurations. Six possible resonance structures can be drawn for this model, as shown below for the NJ, CNO", and NCO ions. (A full line indicates a pair of electrons of opposite spin in the same spatial orbital a dotted line indicates a pair of electrons of opposite spin in different spatial orbitals, and o andx represent single electrons of different spin.)... 

It is traditional for quantmn theory of molecular systems (molecular quantum chemistry) to describe the properties of a many-atom system on the grounds of interatomic interactions applying the hnear combination of atomic orbitals (LCAO) approximation in the electronic-structure calculations. The basis of the theory of the electronic structure of solids is the periodicity of the crystalline potential and Bloch-type one-electron states, in the majority of cases approximated by a linear combination of plane waves (LCPW). In a quantmn chemistry of solids the LCAO approach is extended to periodic systems and modified in such a way that the periodicity of the potential is correctly taken into account, but the language traditional for chemistry is used when the interatomic interaction is analyzed to explain the properties of the crystalhne sohds. At first, the quantum chemistry of solids was considered simply as the energy-band theory [2] or the theory of the chemical bond in tetrahedral semiconductors [3]. From the beginning of the 1970s the use of powerful computer codes has become a common practice in molecular quantum chemistry to predict many properties of molecules in the first-principles LCAO calculations. In the condensed-matter studies the accurate description of the system at an atomic scale was much less advanced [4]. 

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