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Core Concepts

This page explains the theoretical foundation and key principles behind ASCICat.

The Multi-Objective Challenge

Traditional catalyst screening focuses on a single objective: activity. The classic volcano plot identifies catalysts with optimal binding energies. However, real-world catalyst selection must balance:

  1. Activity - Can it catalyze the reaction efficiently?
  2. Stability - Will it survive under operating conditions?
  3. Cost - Is it economically viable at scale?

The Fundamental Trade-off

A catalyst might be highly active (like platinum) but prohibitively expensive. Another might be cheap (like iron) but unstable. ASCICat provides a systematic framework to navigate these trade-offs.

The Sabatier Principle

The foundation of activity scoring is the Sabatier principle (1911):

An optimal catalyst binds reaction intermediates neither too strongly nor too weakly.

Activity
   ↑
   |        /\
   |       /  \
   |      /    \
   |     /      \
   |____/________\____→ Binding Energy
        weak   optimal   strong

Mathematical formulation:

\[S_a(\Delta E) = \max\left(0, 1 - \frac{|\Delta E - \Delta E_{opt}|}{\sigma_a}\right)\]

Where:

  • \(\Delta E\) = Adsorption energy (from DFT calculations)
  • \(\Delta E_{opt}\) = Sabatier-optimal energy (reaction-specific)
  • \(\sigma_a\) = Activity tolerance (typically 0.15 eV)

Surface Energy and Stability

Catalyst stability correlates with surface energy (\(\gamma\)):

  • Low \(\gamma\) → Strong metal-metal bonds → Resistant to dissolution
  • High \(\gamma\) → Weaker bonding → Prone to reconstruction

Inverse linear normalization:

\[S_s(\gamma) = \frac{\gamma_{max} - \gamma}{\gamma_{max} - \gamma_{min}}\]

This ensures:

  • Lowest surface energy → \(S_s = 1\) (most stable)
  • Highest surface energy → \(S_s = 0\) (least stable)

Economic Considerations

Material costs span 5+ orders of magnitude:

Material Cost ($/kg) Log₁₀(Cost)
Iron ~2 0.3
Copper ~10 1.0
Silver ~900 2.95
Gold ~60,000 4.78
Platinum ~30,000 4.48
Iridium ~150,000 5.18

Logarithmic normalization handles this range:

\[S_c(C) = \frac{\log C_{max} - \log C}{\log C_{max} - \log C_{min}}\]

Why Logarithmic?

Linear scaling would make all precious metals indistinguishable (all near zero). Logarithmic scaling preserves discrimination across the full cost spectrum.

The ASCI Integration

The Activity-Stability-Cost Index combines all three scores:

\[\phi_{ASCI} = w_a \cdot S_a + w_s \cdot S_s + w_c \cdot S_c\]

Properties

  1. Bounded: \(\phi_{ASCI} \in [0, 1]\)
  2. Interpretable: Higher = better
  3. Customizable: Weights reflect priorities
  4. Transparent: Each component is traceable

Weight Constraint

\[w_a + w_s + w_c = 1\]

This ensures:

  • Scores are directly comparable
  • Maximum possible ASCI is 1.0
  • Weights represent true relative importance

Why Not Just Use Pareto?

Pareto frontier analysis identifies non-dominated solutions - catalysts where no other catalyst is better on all objectives. However:

Pareto Analysis ASCI
Produces a set of solutions Produces a ranked list
No preference required Explicit preferences (weights)
Hard to compare across studies Reproducible comparison
Requires subjective final selection Deterministic ranking

Complementary Approaches

ASCICat works alongside Pareto analysis. Top ASCI-ranked catalysts are predominantly Pareto-optimal, validating both methodologies.

Scoring Methods

Linear Scoring (Default)

Score = max(0, 1 - |deviation| / tolerance)

Advantages:

  • Computationally efficient
  • Easy to interpret
  • Consistent with volcano plots

Gaussian Scoring (Alternative)

Score = exp(-(deviation)² / (2 × tolerance²))

Advantages:

  • Smoother discrimination
  • Never reaches exactly zero
  • Sharper peak at optimum

Data-Driven Normalization

For stability and cost scores, ASCICat uses data-driven normalization:

\[S = \frac{x_{max} - x}{x_{max} - x_{min}}\]

Where \(x_{max}\) and \(x_{min}\) are computed from your dataset.

Important

This means scores are relative to your specific dataset, not absolute. The same catalyst might have different scores in different datasets.

Key Assumptions

ASCICat makes these assumptions:

  1. DFT accuracy - Calculated binding energies are reliable proxies for experimental values
  2. Surface energy correlation - Lower surface energy indicates better stability
  3. Material cost proxy - Bulk material costs reflect catalyst fabrication costs
  4. Linear combination - Trade-offs can be captured by weighted sums
  5. Score independence - Activity, stability, and cost can be scored separately

Limitations

Be aware of these limitations:

  • Kinetic barriers - ASCI focuses on thermodynamics, not kinetics
  • Support effects - Metal-support interactions not captured
  • Electrolyte effects - pH, ion concentration not considered
  • Mass transport - Only intrinsic properties considered
  • Deactivation mechanisms - Specific degradation pathways not modeled

Further Reading