"What shape is this?"
Kana pointed at a diagram in the textbook.
"p orbital," Rei answered. "A region where electrons have high probability of existing."
"Probability?"
"In quantum mechanics, electron position can only be expressed as probability."
Milia showed another diagram. s orbital is spherical, p orbital is dumbbell-shaped.
"Beautiful," Kana murmured.
"There's symmetry," Rei confirmed. "Nature favors symmetry."
"Why this shape?"
"Solutions to the Schrödinger equation," Rei explained. "The shape of the wave function determines orbital shape."
"Wave? Are electrons waves?"
"Both particles and waves," Milia added.
"Which one?" Kana was confused.
"Both. They have both particle and wave properties," Rei explained.
"When measured, particle. When not measured, wave."
"Strange..."
Milia drew hydrogen atom energy levels.
"1s, 2s, 2p, 3s, 3p, 3d..."
"What do the numbers and letters mean?" Kana asked.
"Number is principal quantum number n, represents energy level. Letter is angular momentum quantum number l, represents orbital shape."
"s=0, p=1, d=2, f=3," Rei supplemented.
"Why that order?"
"Historical naming. Sharp, principal, diffuse, fundamental."
Kana took notes. "But is this related to biochemistry?"
"Very much so," Rei emphasized. "Chemical bonds are overlaps of electron orbitals."
Milia drew a molecular orbital diagram.
"Water molecule H₂O. Oxygen's sp³ hybrid orbital overlaps with hydrogen's 1s orbital."
"Hybrid orbital?"
"Different orbitals mix to create new orbitals," Rei explained.
"In carbon sp³ hybridization, one s orbital and three p orbitals mix to create four equivalent sp³ orbitals."
"Tetrahedral arrangement," Milia added.
"That's why methane CH₄ is tetrahedral," Kana understood.
"Exactly. Molecular shape is determined by electron orbitals."
Rei continued. "For double bonds, sp² hybridization."
"One s orbital and two p orbitals mix. The remaining one p orbital becomes a π bond."
"π bond?"
"A bond where orbitals overlap from the side. Weaker than σ bonds, but more reactive."
Milia drew a diagram. The structure of ethylene C₂H₄.
"Becomes planar structure," Rei explained.
"sp³ is tetrahedral, sp² is planar, sp is linear," Kana summarized.
"Perfect," Rei acknowledged.
"But quantum chemistry calculations seem difficult," Kana said anxiously.
"Indeed. Exact calculation of multi-electron systems is impossible," Rei admitted.
"We use approximation methods. Hückel method, molecular orbital method, density functional theory."
Milia supplemented. "Calculate with computers."
"Even large molecules like proteins?" Kana asked.
"With simplified methods. Complete quantum chemical calculations are difficult even for small molecules."
Rei continued. "But understanding electron configuration is important."
"For example?"
"Enzyme active sites. Electron configuration around metal ions determines reactivity."
Milia showed an example. "Heme iron. d orbital electrons interact with oxygen."
"Function is determined by electron configuration," Kana understood.
"Conjugated systems are also important," Rei added.
"Alternating single and double bonds. Electrons become delocalized."
"Pigment molecules, like chlorophyll. The broader the conjugated system, the longer the absorption wavelength."
Kana said excitedly, "Electron orbitals also determine color!"
"Light absorption is electron excitation," Milia confirmed.
"Electrons move from lower to higher energy levels."
Rei said finally. "The beautiful symmetry of electron orbitals. It's a manifestation of nature's fundamental laws."
"Invisible, but existing," Kana murmured.
Milia smiled. "Beauty lies in symmetry."
Outside the window, a rainbow appeared. Light refracts in water droplets, separating by wavelength. Those colors are determined by atomic electron orbitals. The quantum world and our world are connected.
"We've covered the basics of biochemistry now," Rei reflected.
"There's still much to learn," Milia added.
Kana nodded. "But I've come to like biochemistry."
"That's the most important thing," Rei smiled.
The three began preparing for the next experiment. The journey of biochemistry continues.