MATHEMATICAL NATURE OF HYBRID ATOMIC ORBITALS In Part 1, does this concept of HAO from the 1930s have mathematical and logical bases? In Part 2, what are the practical problems with this concept as a pedagogical model and how can we overcome these challenges? In this article, we present modern calculations about hybrid atomic orbitals, we provide irrefutable evidence, based on Schrödinger’s time-independent equation for the hydrogen atom, that HAO lack justification, and we list six logical errors and a further critique of the hybridization model. We divide our critique into two parts the present analysis arose from our endeavor to answer these two relevant scientific questions. The use and reliability of hybrid atomic orbitals (which we abbreviate as HAO) has since become challenged. By 1935, Van Vleck had reviewed the ‘quantum theory of valence’ to include most concepts of hybridization that are common in contemporary chemistry. Furthermore, in 1934, Penney provided the first illustration of the hybrid orbital structure of ethane and ethene ‘Penney’s model’ is sometimes used to describe ‘ideal’ 109.5º angles for ethane and the 120º angles provided by sp 2 hybrids in ethene. Penney extended this system to ethyne using bond energies to justify the sp hybridization with 180º bond angles. For a carbon atom, there are thus three principal hybrid combinations - commonly denoted sp, sp 2 and sp 3 one or other combination is invoked to describe a linear, trigonal planar or tetrahedral geometry, respectively, of a central atom. To achieve orbitals with an appropriate directionality, mixtures of atomic orbitals on the same atom are formed through hybridization. before being accepted by the entire scientific community. The term ‘hybrid atomic orbitals’ and the related process ‘hybridization’ were introduced by Mulliken 5 5 Mulliken, R. In 1932, Hultgren included ‘ s-p-d quantization’ to describe equivalent bonds for elements in the long periods of the periodic chart. How do we achieve such a bond angle when the s and p atomic orbitals are not mutually oriented at this angle? The quantization approach was to invoke a tetrahedral geometry of carbon in CH 4 involving combinations of s and p orbitals orbitals with directionality would presumably provide stronger bonds.
For example, methane has H-C-H bond angle ~109.5º. Pauling refers to this process in methane as ‘ s-p quantization’. originated independently the concept of taking linear combinations of 2s and 2p wave functions to build four new orthogonal wave functions, or valences.
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