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III. The Geometry of Orbitals


Volume III of the “How Atoms Form Molecules” series

How electrons sculpt the shapes of the s, p, d, and f orbitals

Electrons do not float randomly.

They settle into patterns shaped by direction, boundaries, energy, and symmetry.

Those patterns define where electrons are most likely to be found.

In this volume, we show how electrons shape these three-dimensional regions of probability.

These regions—these patterns—are the orbitals.

Interested in early access?
I’m inviting a small group of beta-readers to read the serialized early release of Volume III: The Geometry of Orbitals.

The first installment includes Chapters 1–4. You can choose either PDF or EPUB. New installments will be sent as they become available.

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p orbital geometry

p orbital geometry

What You’ll Learn

  • First, we look at how QM describes orbitals as solutions to the Schrödinger equation, using minimal jargon and visuals.
  • Then, we identify the geometric constraints that shape those solutions.
  • Finally, we build the s, p, d, and f orbitals using both perspectives.
  • The goal is not to replace QM.
  • It is to make its structure visible.

Quantum mechanics describes these patterns through equations and energy constraints.
Geometry helps make the same patterns visible as spatial structure.

In this volume, we show that both lead to the same patterns: the s, p, d, and f orbitals.

This volume prepares the ground for Volume IV, where Geometric rules are used to explain orbital filling rules in the Periodic table of Elements.

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