Computational Materials Science

The Journey of Materials

The study and design of materials form the backbone of modern technology. An incredible journey of research, meticulous attention to detail, and hard work has transformed technology into what we have today. However, many of these discoveries originate from intriguing and unexpected sources.

🔄 Density Functional Theory

First-principle methods enable us to simulate electronic behavior, optical response by looping the Hamiltonian of the many-body system through the charge density.

The iterative process solves the Kohn-Sham equations and updates the charge density until self-consistency is achieved.

Initial Charge Density ρ(r)

       ↓
Compute Effective Potential Veff(r)
Veff(r) = Ven(r) + ∫ ρ(r') / |r - r'| dr' + Vxc[ρ(r)]

       ↓
Solve Kohn-Sham Equations
[-ħ²/2me ∇² + Veff(r)] ψi(r) = εi ψi(r)

       ↓
Compute New Charge Density
ρ(r) = Σ |ψi(r)|²

       ↓
Calculate Total Energy
Etot[ρ(r)] = T[ρ(r)] + ∫ Vext(r) ρ(r) dr + Ehartree[ρ(r)] + Exc[ρ(r)]

       ↓
Check Convergence

Converged?
  /       \
 No        Yes
 ↓           ↓
Loop      Output Data:
          ρ₀(r), Energy Levels, Forces, etc.

🧠 Machine Learning in Materials Discovery

Even more recently, Machine Learning techniques have transformed the landscape of materials search by predicting many prototype materials capable of optimizing and launching a new way to find new materials.

Exploring Quantum Materials at SUNY New Paltz.

Computational Materials Science

The Journey of Materials

💻 Data-Driven Methods

🔄 Density Functional Theory

🧠 Machine Learning in Materials Discovery

💡 Discoveries in Unexpected Places

Saccharin: Bad Lab Practices

Stainless Steel: Rusty Experiments

Teflon: Frozen Gases Surprise

Vulcanized Rubber: Spilled Sulfur