0. Glyph Basics l. GVB Orbitals
0. Glyph Basics

The glyphs arise initially from very basic atomic orbitals for elements in the s- and p-blocks of the periodic table. s orbitals are spherical and can be represented by a circle in 2D or a a sphere rendered in 3D (I use POV-Ray to generate 3D images). Here are the glyphs that can be used to represent 1s systems in both 2D and 3D forms:

As the figure indicates, orbital occupations are denoted differently in the 2D and 3D versions of the glyphs. 2D glyphs use dots to indicate occupation, while 3D glyphs use color. p orbitals consist of lobes with positive and negative amplitude that align with the three cartesian axes. Here is the glyph that can be used to represent nnp systems in both 2D and 3D, along with the oxygen atom as an example:

The orientation shown above is arbitrary. It would be suitable for creating a coupling diagram for water with two in-plane covalent bonds to hydrogen atoms. But for other cases a different orientation might be more suitable. Here are three equivalent glyphs for the oxygen atom:

Three additional glyphs arise when ns and np orbitals hybridize strongly when recoupling occurs. The glyphs correspond to the linear, planar, and tetrahedral bonding motifs that are common in carbon-containing compounds but are also present in other compounds such as BH3 and some nitrogen-containing compounds and transition states. §4 covers organic compounds modeled with these glyphs. Here are the three sp hybridized glyphs occupied for carbon, along with their nominal bond angles:

§7 is dedicated to coupling diagrams that use 3D glyphs. I mostly lecture on a blackboard or whiteboard, where I am limited to 2D coupling glyphs and coupling diagrams. I include both forms, however, in the pdf versions of my lectures notes.

A sixth glyph is present on the far right of the graphic shown at the bottom of each page of this sampler. It arises when pd hydridization occurs when p2 recoupling occurs in certain compounds of sulfur and chlorine or their excited states.

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1. Using GVB Orbitals in Physical Chemistry Courses
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