"Where are electrons?"
Kana rotated the molecular model.
Rei answered. "Everywhere, nowhere."
"That's not an answer."
"In quantum mechanics, electrons are also waves. We can only speak of position probabilistically."
Milia drew a diagram. "Wave function. Gives probability amplitude for electron existence at each point in space."
Kana was confused. "Probability amplitude?"
"Like wave height. Square it to get probability density."
Rei continued. "Atomic orbitals are the shape of this wave function. s orbital, p orbital..."
"The round one and dumbbell-shaped one?"
"Yes. But in molecules, the story changes."
Milia showed a wave animation on the tablet. "When two atoms approach, waves overlap."
"Overlap?"
"Interfere. Constructively or destructively."
Rei explained. "Linear combination of wave functions. Molecular orbitals form."
Kana asked. "What does constructive mean?"
"When they overlap in-phase, amplitude increases. Bonding orbital."
Milia pointed to the diagram. "Electron density increases between nuclei."
"That's a bond?"
"Yes. Electrons link both nuclei."
Rei continued. "Conversely, out-of-phase overlap cancels out. Antibonding orbital."
"Cancel out?"
"A node forms between nuclei. Electron density is zero."
Kana thought. "So they don't bond?"
"Rather, they repel. Energy increases."
Milia drew an energy diagram. "Bonding orbitals have low energy. Antibonding is high."
"Which do electrons enter?"
"Starting from lowest. Following Pauli exclusion principle."
Rei organized. "Hydrogen molecule. Two 1s orbitals overlap."
"What happens?"
"Bonding orbital σ and antibonding orbital σ* form. Two electrons enter σ."
Milia supplemented. "So H₂ is stable. Bonding energy exceeds dissociation energy."
Kana asked for another example. "What about oxygen?"
"More complex. 2s, 2p orbitals are involved."
Rei drew a diagram. "p orbitals have two types of overlap. σ and π."
"π?"
"Sideways overlap. Weaker than head-on σ overlap."
Milia explained. "Oxygen molecule is O=O. One σ bond and two π bonds."
"Not a triple bond?"
"Double bond. In molecular orbital theory, electrons sometimes enter antibonding orbitals too."
Kana was confused. "In antibonding too?"
"Yes. That's why oxygen is paramagnetic. Has unpaired electrons."
Rei added. "Property that valence bond theory can't explain. Victory of molecular orbital theory."
Milia played the wave animation. "The moment they overlap, new orbitals are born."
Kana gazed intently. "Beautiful..."
"Aesthetics of the quantum world," Rei said quietly.
"But," Kana raised a question. "Why waves? Aren't electrons particles?"
"They have both wave and particle nature. De Broglie matter waves."
Milia wrote the formula. "λ = h/p. Smaller momentum, longer wavelength."
"Electrons are light, so wave properties are prominent," Rei continued.
Kana began to understand. "So interference occurs."
"The essence of chemical bonds is wave overlap," Milia summarized.
Rei nodded. "Covalent bonds are quantum phenomena."
Kana stared at the model. "Molecules are wave art."
Milia smiled. "The moment atoms meet, waves dance."
"And new molecules are born," Rei concluded.
The three fell silent. Quantum waves create chemistry, create life.