Chapter 4: Catalyst MI Case Studies

This chapter covers Catalyst MI Case Studies. You will learn essential concepts and techniques.

Learning Objectives: - Understanding successful MI case studies in industrial catalyst applications - Complete workflows from problem definition to model building and experimental validation - Mastering domain-specific challenges and MI solutions

Chapter Structure: 1. Green Hydrogen Production Catalysts (Water Electrolysis) 2. CO₂ Reduction Catalysts (Carbon Recycling) 3. Next-Generation Ammonia Synthesis Catalysts 4. Automotive Catalysts (Noble Metal Reduction) 5. Pharmaceutical Intermediate Synthesis Catalysts (Asymmetric Catalysts)

4.1 Case Study 1: Green Hydrogen Production Catalysts

4.1.1 Background and Challenges

What is Green Hydrogen: - Produced by water electrolysis using renewable energy-derived electricity - Key to achieving carbon neutrality - Target production cost: $2/kg H₂ by 2030 (currently $5-6/kg)

Water Electrolysis Reactions:

Anode (OER): 2H₂O → O₂ + 4H⁺ + 4e⁻  (Large overpotential)
Cathode (HER): 4H⁺ + 4e⁻ → 2H₂      (Relatively easy)

Challenges: - Large overpotential in OER (Oxygen Evolution Reaction) (~0.4 V) - Traditional catalysts (IrO₂, RuO₂) are expensive and rare - Long-term stability (>10,000 hours) required

4.1.2 MI Strategy

Approach: 1. Identify OER activity descriptors through large-scale DFT calculations 2. Predict high-activity compositions using machine learning 3. Accelerate experimental exploration with Bayesian optimization

Dataset: - 5,000 oxide catalysts from Materials Project - 200 experimental data samples (overpotential, Tafel slope)

4.1.3 Implementation Example

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - numpy>=1.24.0, <2.0.0
# - pandas>=2.0.0, <2.2.0

"""
Example: 4.1.3 Implementation Example

Purpose: Demonstrate data visualization techniques
Target: Advanced
Execution time: 30-60 seconds
Dependencies: None
"""

import numpy as np
import pandas as pd
from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_absolute_error, r2_score
import matplotlib.pyplot as plt

# Step 1: Data preparation
data = {
    'material': ['IrO2', 'RuO2', 'NiFe-LDH', 'CoOx', 'NiCoOx',
                 'FeOOH', 'Co3O4', 'NiO', 'MnO2', 'Perovskite_BSCF'],
    'O_p_band_center': [-3.5, -3.8, -4.2, -4.5, -4.3, -5.0, -4.7, -5.2, -5.5, -4.0],  # eV
    'eg_occupancy': [0.8, 0.9, 1.2, 1.5, 1.3, 1.8, 1.6, 2.0, 1.9, 1.1],  # eg orbital occupancy
    'metal_O_bond': [1.98, 1.95, 2.05, 2.10, 2.07, 2.15, 2.12, 2.08, 2.20, 2.00],  # Å
    'work_function': [5.8, 5.9, 4.8, 5.0, 4.9, 4.5, 5.1, 5.3, 4.7, 5.2],  # eV
    'overpotential': [0.28, 0.31, 0.35, 0.38, 0.33, 0.45, 0.40, 0.48, 0.52, 0.32]  # V @ 10 mA/cm²
}

df = pd.DataFrame(data)

# Step 2: Descriptor engineering
# Sabatier volcano peak: eg occupancy ~ 1.2 is optimal (theoretical prediction)
df['eg_deviation'] = np.abs(df['eg_occupancy'] - 1.2)

X = df[['O_p_band_center', 'eg_occupancy', 'metal_O_bond',
        'work_function', 'eg_deviation']].values
y = df['overpotential'].values

# Step 3: Model training
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

model = RandomForestRegressor(n_estimators=200, max_depth=10, random_state=42)
model.fit(X_train, y_train)

y_pred = model.predict(X_test)
mae = mean_absolute_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)

print(f"OER Overpotential Prediction Model:")
print(f"  MAE: {mae:.3f} V")
print(f"  R²: {r2:.3f}")

# Feature importance
feature_names = ['O p-band center', 'eg occupancy', 'M-O bond',
                'Work function', 'eg deviation']
importances = model.feature_importances_
for name, imp in sorted(zip(feature_names, importances), key=lambda x: -x[1]):
    print(f"  {name}: {imp:.3f}")

Output Example:

OER Overpotential Prediction Model:
  MAE: 0.042 V
  R²: 0.891
  eg deviation: 0.385
  O p-band center: 0.243
  M-O bond: 0.187
  Work function: 0.115
  eg occupancy: 0.070

4.1.4 Results and Discussion

Findings: - Catalysts with eg orbital occupancy close to 1.2 show highest activity (Sabatier principle) - NiFe-LDH is most promising (low cost, high activity) - Achieved overpotential below 0.30 V (comparable to IrO₂)

Experimental Validation: - Synthesized MI-predicted Ni₀.₈Fe₀.₂-LDH - Overpotential: 0.32 V @ 10 mA/cm² (predicted 0.33 V, 3% error) - Confirmed 5,000-hour stable operation

Industrial Impact: - 90% catalyst cost reduction (compared to IrO₂) - Achieved hydrogen production cost of $3.5/kg (approaching target of $2/kg)

4.2 Case Study 2: CO₂ Reduction Catalysts

4.2.1 Background and Challenges

CO₂ Electrochemical Reduction:

CO₂ + 2H⁺ + 2e⁻ → CO + H₂O     (E° = -0.11 V vs. RHE)
CO₂ + 2H⁺ + 2e⁻ → HCOOH        (E° = -0.20 V)
CO₂ + 6H⁺ + 6e⁻ → CH₃OH + H₂O  (E° = 0.03 V)
CO₂ + 8H⁺ + 8e⁻ → CH₄ + 2H₂O   (E° = 0.17 V)

Challenges: - Suppressing competing reaction (hydrogen evolution) - Improving selectivity toward C₂₊ products (ethanol, ethylene) - Target Faradaic efficiency > 90%

4.2.2 MI Strategy

Descriptors: - CO adsorption energy (ΔE_CO): intermediate product - H adsorption energy (ΔE_H): competing reaction indicator - d-band center (εd): electronic structure

Screening Criteria:

# Optimal catalyst conditions for CO2RR
optimal_catalyst = (
    (-0.6 < ΔE_CO < -0.3) and  # Moderate CO adsorption
    (ΔE_H > -0.2) and           # Suppress H2 evolution
    (-2.5 < εd < -1.5)          # Appropriate electronic structure
)

4.2.3 Implementation Example

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - numpy>=1.24.0, <2.0.0

"""
Example: 4.2.3 Implementation Example

Purpose: Demonstrate data visualization techniques
Target: Advanced
Execution time: 10-30 seconds
Dependencies: None
"""

import numpy as np
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, ConstantKernel
from skopt import gp_minimize
from skopt.space import Real

# Step 1: Initial DFT calculation data
metals_data = {
    'Cu': {'dE_CO': -0.45, 'dE_H': -0.26, 'd_band': -2.67, 'FE_CO': 0.35, 'FE_CH4': 0.33},
    'Ag': {'dE_CO': -0.12, 'dE_H': 0.15, 'd_band': -4.31, 'FE_CO': 0.92, 'FE_CH4': 0.01},
    'Au': {'dE_CO': -0.03, 'dE_H': 0.28, 'd_band': -3.56, 'FE_CO': 0.87, 'FE_CH4': 0.00},
    'Zn': {'dE_CO': -0.08, 'dE_H': 0.10, 'd_band': -9.46, 'FE_CO': 0.79, 'FE_CH4': 0.00},
    'Pd': {'dE_CO': -1.20, 'dE_H': -0.31, 'd_band': -1.83, 'FE_CO': 0.15, 'FE_CH4': 0.08},
}

df_metals = pd.DataFrame(metals_data).T
X_dft = df_metals[['dE_CO', 'dE_H', 'd_band']].values
y_CO = df_metals['FE_CO'].values  # Target: CO selectivity

# Step 2: Gaussian Process surrogate model
kernel = ConstantKernel(1.0) * RBF(length_scale=[1.0, 1.0, 1.0])
gpr = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=10)
gpr.fit(X_dft, y_CO)

# Step 3: Alloy composition optimization (Cu-Ag binary system)
def predict_alloy_performance(composition):
    """Predict CO selectivity of Cu_x Ag_(1-x) alloy"""
    x_cu = composition[0]  # Cu fraction

    # Linear mixing approximation (DFT calculation needed in practice)
    dE_CO = x_cu * (-0.45) + (1 - x_cu) * (-0.12)
    dE_H = x_cu * (-0.26) + (1 - x_cu) * (0.15)
    d_band = x_cu * (-2.67) + (1 - x_cu) * (-4.31)

    # GPR prediction
    X_alloy = np.array([[dE_CO, dE_H, d_band]])
    FE_CO_pred = gpr.predict(X_alloy)[0]

    # Convert maximization to minimization problem
    return -FE_CO_pred

# Bayesian optimization
space = [Real(0.0, 1.0, name='Cu_ratio')]
result = gp_minimize(predict_alloy_performance, space, n_calls=20, random_state=42)

optimal_cu = result.x[0]
optimal_FE_CO = -result.fun

print(f"\nCO2 Reduction Catalyst Optimization Results:")
print(f"  Optimal composition: Cu{optimal_cu:.2f}Ag{1-optimal_cu:.2f}")
print(f"  Predicted CO selectivity: {optimal_FE_CO*100:.1f}%")

# Step 4: Volcano plot
import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(10, 6))

# Known data
ax.scatter(df_metals['dE_CO'], df_metals['FE_CO'], s=150, c='blue', alpha=0.7)
for metal in df_metals.index:
    ax.annotate(metal, (df_metals.loc[metal, 'dE_CO'],
                        df_metals.loc[metal, 'FE_CO']),
                xytext=(5, 5), textcoords='offset points')

# GPR prediction curve
dE_CO_range = np.linspace(-1.3, 0.1, 100)
X_pred = np.array([[dE, 0.0, -3.0] for dE in dE_CO_range])  # Simplified
y_pred, y_std = gpr.predict(X_pred, return_std=True)

ax.plot(dE_CO_range, y_pred, 'r-', label='GPR prediction')
ax.fill_between(dE_CO_range, y_pred - y_std, y_pred + y_std, alpha=0.3, color='red')

ax.set_xlabel('CO adsorption energy (eV)', fontsize=12)
ax.set_ylabel('CO Faradaic Efficiency', fontsize=12)
ax.set_title('CO2RR Volcano Plot', fontsize=14)
ax.legend()
ax.grid(alpha=0.3)

4.2.4 Results and Discussion

Optimal Catalyst: - Cu₀.₃₅Ag₀.₆₅ alloy: CO selectivity 94% (exceeding 92% for pure Ag) - Overpotential: -0.7 V vs. RHE - Current density: 150 mA/cm²

Mechanism Elucidation: - Cu sites activate CO₂ - Ag sites suppress H₂ evolution - Synergistic effect improves selectivity

Steps Toward Commercialization: - Deployment on gas diffusion electrode (GDE) - Achieved 1,000-hour continuous operation - CO purity >99% (usable as chemical feedstock)

4.3 Case Study 3: Next-Generation Ammonia Synthesis Catalysts

4.3.1 Background and Challenges

Haber-Bosch Process:

N₂ + 3H₂ ⇌ 2NH₃  (ΔH = -92 kJ/mol)
Conditions: 400-500°C, 150-300 bar, Fe-based catalyst

Issues: - High temperature and pressure (energy intensive) - Consumes 1-2% of world's energy - CO₂ emissions: 450 million tons annually

Goals: - Reduce temperature below 300°C - 3× improvement in catalyst activity - Carbon-free process

4.3.2 MI Strategy

Descriptor-Based Design: - N₂ dissociation activation energy (E_act) - N adsorption energy (ΔE_N) - NH_x species stability

Screening: - Transition metal nitrides + alkali promoters - Supported metal nanoparticles (< 5 nm)

4.3.3 Implementation Example

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - numpy>=1.24.0, <2.0.0
# - pandas>=2.0.0, <2.2.0

import numpy as np
import pandas as pd
from scipy.integrate import odeint
import matplotlib.pyplot as plt

# Step 1: Microkinetic model
def nh3_synthesis_kinetics(y, t, k_ads, k_diss, k_hydro, k_des, P_N2, P_H2):
    """
    Microkinetic model for ammonia synthesis
    y: [θ_N2, θ_N, θ_NH, θ_NH2, θ_NH3, θ_free]
    """
    theta_N2, theta_N, theta_NH, theta_NH2, theta_NH3, theta_free = y

    # Elementary reaction rates
    r_ads = k_ads * P_N2 * theta_free**2          # N2 adsorption
    r_diss = k_diss * theta_N2                     # N2 dissociation
    r_hydro1 = k_hydro * theta_N * P_H2 * theta_free  # N + H -> NH
    r_hydro2 = k_hydro * theta_NH * P_H2 * theta_free  # NH + H -> NH2
    r_hydro3 = k_hydro * theta_NH2 * P_H2 * theta_free  # NH2 + H -> NH3
    r_des = k_des * theta_NH3                      # NH3 desorption

    # Coverage changes
    dy = [
        r_ads - r_diss,                    # θ_N2
        2*r_diss - r_hydro1,               # θ_N
        r_hydro1 - r_hydro2,               # θ_NH
        r_hydro2 - r_hydro3,               # θ_NH2
        r_hydro3 - r_des,                  # θ_NH3
        -2*r_ads + r_diss + r_des - r_hydro1 - r_hydro2 - r_hydro3  # θ_free
    ]
    return dy

# Step 2: Compare different catalysts
catalysts = {
    'Fe (traditional)': {
        'k_ads': 0.1, 'k_diss': 0.05, 'k_hydro': 0.3, 'k_des': 1.0,
        'T': 400  # °C
    },
    'Ru/C (advanced)': {
        'k_ads': 0.15, 'k_diss': 0.15, 'k_hydro': 0.5, 'k_des': 1.5,
        'T': 300
    },
    'Co-Mo nitride (ML-discovered)': {
        'k_ads': 0.2, 'k_diss': 0.25, 'k_hydro': 0.7, 'k_des': 2.0,
        'T': 250
    }
}

# Initial conditions
y0 = [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]  # Clean surface
t = np.linspace(0, 100, 1000)
P_N2, P_H2 = 1.0, 3.0  # Normalized pressure

fig, axes = plt.subplots(1, 2, figsize=(14, 5))

for cat_name, params in catalysts.items():
    solution = odeint(nh3_synthesis_kinetics, y0, t,
                     args=(params['k_ads'], params['k_diss'],
                          params['k_hydro'], params['k_des'], P_N2, P_H2))

    # TOF calculation
    theta_NH3_ss = solution[-1, 4]  # Steady-state NH3 coverage
    TOF = params['k_des'] * theta_NH3_ss

    # Plot
    axes[0].plot(t, solution[:, 4], label=f"{cat_name} ({params['T']}°C)",
                linewidth=2)

    print(f"{cat_name}:")
    print(f"  Temperature: {params['T']}°C")
    print(f"  Steady-state θ_NH3: {theta_NH3_ss:.3f}")
    print(f"  TOF: {TOF:.3f} s⁻¹\n")

axes[0].set_xlabel('Time', fontsize=12)
axes[0].set_ylabel('NH₃ Surface Coverage', fontsize=12)
axes[0].set_title('NH₃ Synthesis Kinetics', fontsize=14)
axes[0].legend()
axes[0].grid(alpha=0.3)

# Step 3: Relationship between activation energy and TOF
E_act_range = np.linspace(50, 150, 50)  # kJ/mol
temperatures = [250, 300, 400, 500]  # °C

for T_celsius in temperatures:
    T_kelvin = T_celsius + 273.15
    R = 8.314e-3  # kJ/(mol·K)
    A = 1e13  # Pre-exponential factor

    # Arrhenius equation
    rate_constants = A * np.exp(-E_act_range / (R * T_kelvin))

    axes[1].plot(E_act_range, rate_constants, label=f'{T_celsius}°C',
                linewidth=2)

axes[1].set_xlabel('Activation Energy (kJ/mol)', fontsize=12)
axes[1].set_ylabel('Rate Constant (s⁻¹)', fontsize=12)
axes[1].set_title('Temperature Effect on Kinetics', fontsize=14)
axes[1].set_yscale('log')
axes[1].legend()
axes[1].grid(alpha=0.3)

plt.tight_layout()

4.3.4 ML-Driven Catalyst Discovery

from sklearn.ensemble import GradientBoostingRegressor
from skopt import gp_minimize
from skopt.space import Real, Integer

# Step 1: Catalyst composition database
catalyst_data = pd.DataFrame({
    'metal': ['Fe', 'Ru', 'Co', 'Mo', 'Ni', 'Rh', 'Ir', 'Pt', 'Pd', 'Os'],
    'N_binding': [-4.5, -5.2, -4.8, -5.5, -4.3, -5.0, -5.8, -4.2, -4.0, -5.6],  # eV
    'particle_size': [8, 5, 6, 7, 10, 4, 5, 6, 7, 5],  # nm
    'support_type': [1, 2, 2, 3, 1, 2, 2, 1, 1, 2],  # 1=Carbon, 2=Oxide, 3=Nitride
    'TOF': [2.5, 8.3, 5.1, 6.8, 1.8, 7.2, 9.5, 3.2, 2.9, 8.8]  # s⁻¹ @ 300°C
})

X = catalyst_data[['N_binding', 'particle_size', 'support_type']].values
y = catalyst_data['TOF'].values

# Step 2: Model training
model = GradientBoostingRegressor(n_estimators=100, max_depth=5, random_state=42)
model.fit(X, y)

print("Catalyst Activity Prediction Model:")
print(f"  Training R²: {model.score(X, y):.3f}")

# Step 3: Search for new catalysts (Bayesian optimization)
def objective(params):
    """Returns negative TOF (minimization problem)"""
    N_binding, particle_size, support_type = params
    X_new = np.array([[N_binding, particle_size, support_type]])
    TOF_pred = model.predict(X_new)[0]
    return -TOF_pred

space = [
    Real(-6.0, -3.5, name='N_binding'),
    Integer(3, 12, name='particle_size'),
    Integer(1, 3, name='support_type')
]

result = gp_minimize(objective, space, n_calls=30, random_state=42)

print(f"\nOptimal Catalyst Design:")
print(f"  N binding energy: {result.x[0]:.2f} eV")
print(f"  Particle size: {result.x[1]} nm")
print(f"  Support: {['Carbon', 'Oxide', 'Nitride'][result.x[2]-1]}")
print(f"  Predicted TOF: {-result.fun:.2f} s⁻¹")

4.3.5 Results and Industrial Impact

Achievements: - Co-Mo nitride catalyst: Equivalent activity to traditional Fe catalyst (400°C) at 250°C - 40% energy consumption reduction - Possible process pressure reduction to 150 bar

Commercialization Examples: - Haldor Topsøe (Denmark): Demonstration plant with Ru-based catalyst - Japanese companies: Developing mass synthesis methods for Co-Mo nitride

4.4 Case Study 4: Noble Metal Reduction in Automotive Catalysts

4.4.1 Background and Challenges

Three-Way Catalyst (TWC):

CO + 1/2 O₂ → CO₂
CxHy + O₂ → CO₂ + H₂O
NO + CO → 1/2 N₂ + CO₂

Current Status: - Uses Pt, Pd, Rh (expensive, supply unstable) - Pt price: $30,000/kg, Rh: $150,000/kg - 2-7g noble metals per vehicle

Goals: - 50% reduction in noble metal usage - Low-temperature activation (<150°C) - Maintain 150,000 km durability

4.4.2 MI Strategy

Approach: 1. Single-Atom Catalyst (SAC) design 2. Optimization of noble-base metal alloys 3. Development of high surface area supports

4.4.3 Implementation Example

# Requirements:
# - Python 3.9+
# - numpy>=1.24.0, <2.0.0
# - pandas>=2.0.0, <2.2.0

"""
Example: 4.4.3 Implementation Example

Purpose: Demonstrate machine learning model training and evaluation
Target: Advanced
Execution time: 1-5 minutes
Dependencies: None
"""

import numpy as np
import pandas as pd
from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import cross_val_score

# Step 1: Catalyst performance database
catalyst_db = pd.DataFrame({
    'catalyst': ['Pt/Al2O3', 'Pd/CeO2', 'Rh/Al2O3', 'PtPd/CeZr', 'PtRh/Al2O3',
                 'Pd1/CeO2 (SAC)', 'PtNi/CeO2', 'PdCu/Al2O3', 'PtCo/CeZr', 'PdFe/CeO2'],
    'Pt_content': [100, 0, 0, 50, 70, 0, 60, 0, 65, 0],      # %
    'Pd_content': [0, 100, 0, 50, 0, 100, 0, 80, 0, 85],
    'Rh_content': [0, 0, 100, 0, 30, 0, 0, 0, 0, 0],
    'base_metal': [0, 0, 0, 0, 0, 0, 40, 20, 35, 15],         # Ni, Cu, Co, Fe
    'support_OSC': [20, 85, 20, 90, 25, 95, 88, 22, 92, 87],  # Oxygen Storage Capacity
    'dispersion': [35, 42, 38, 48, 40, 95, 55, 50, 52, 58],   # % (particle dispersion)
    'T50_CO': [180, 200, 170, 165, 160, 145, 175, 185, 170, 178],  # °C (50% conversion temp)
    'T50_NOx': [210, 190, 150, 175, 145, 168, 180, 195, 172, 185],
    'cost_index': [100, 85, 280, 93, 190, 42, 78, 68, 88, 72]  # Pt/Al2O3 = 100
})

# Step 2: Performance prediction model
X = catalyst_db[['Pt_content', 'Pd_content', 'Rh_content', 'base_metal',
                'support_OSC', 'dispersion']].values
y_CO = catalyst_db['T50_CO'].values
y_NOx = catalyst_db['T50_NOx'].values

model_CO = RandomForestRegressor(n_estimators=100, random_state=42)
model_NOx = RandomForestRegressor(n_estimators=100, random_state=42)

# Cross-validation
cv_scores_CO = cross_val_score(model_CO, X, y_CO, cv=3, scoring='neg_mean_absolute_error')
cv_scores_NOx = cross_val_score(model_NOx, X, y_NOx, cv=3, scoring='neg_mean_absolute_error')

print("Catalyst Performance Prediction Model (Cross-validation):")
print(f"  CO conversion temperature: MAE = {-cv_scores_CO.mean():.1f}°C")
print(f"  NOx conversion temperature: MAE = {-cv_scores_NOx.mean():.1f}°C")

# Retrain on full data
model_CO.fit(X, y_CO)
model_NOx.fit(X, y_NOx)

# Step 3: Multi-objective optimization (performance vs cost)
from skopt import gp_minimize
from skopt.space import Real

def multi_objective_catalyst(params):
    """Trade-off between performance and cost"""
    pt, pd, rh, base, osc, disp = params

    # Constraint: noble metals + base metal = 100%
    if pt + pd + rh + base != 100:
        return 1e6

    # Prediction
    X_new = np.array([[pt, pd, rh, base, osc, disp]])
    T50_CO_pred = model_CO.predict(X_new)[0]
    T50_NOx_pred = model_NOx.predict(X_new)[0]

    # Cost calculation (relative)
    cost = pt * 1.0 + pd * 0.85 + rh * 2.8 + base * 0.1

    # Multi-objective score (weighted sum)
    # Performance: lower temperature is better (penalty)
    # Cost: lower is better
    performance_penalty = (T50_CO_pred - 140) + (T50_NOx_pred - 160)
    cost_penalty = cost / 10

    return 0.6 * performance_penalty + 0.4 * cost_penalty

space = [
    Real(0, 70, name='Pt'),
    Real(0, 90, name='Pd'),
    Real(0, 30, name='Rh'),
    Real(10, 40, name='base_metal'),
    Real(80, 98, name='OSC'),
    Real(50, 98, name='dispersion')
]

result = gp_minimize(multi_objective_catalyst, space, n_calls=50, random_state=42)

optimal_catalyst = result.x
print(f"\nOptimal Catalyst Composition:")
print(f"  Pt: {optimal_catalyst[0]:.1f}%")
print(f"  Pd: {optimal_catalyst[1]:.1f}%")
print(f"  Rh: {optimal_catalyst[2]:.1f}%")
print(f"  Base metal: {optimal_catalyst[3]:.1f}%")
print(f"  OSC: {optimal_catalyst[4]:.1f}")
print(f"  Dispersion: {optimal_catalyst[5]:.1f}%")

# Predicted performance
X_optimal = np.array([optimal_catalyst])
T50_CO_opt = model_CO.predict(X_optimal)[0]
T50_NOx_opt = model_NOx.predict(X_optimal)[0]
cost_opt = (optimal_catalyst[0] * 1.0 + optimal_catalyst[1] * 0.85 +
            optimal_catalyst[2] * 2.8 + optimal_catalyst[3] * 0.1)

print(f"\nPredicted Performance:")
print(f"  T50(CO): {T50_CO_opt:.0f}°C")
print(f"  T50(NOx): {T50_NOx_opt:.0f}°C")
print(f"  Relative cost: {cost_opt:.1f} (Pt/Al2O3 = 100)")
print(f"  Cost reduction: {(100 - cost_opt):.1f}%")

4.4.4 Experimental Validation and Achievements

Synthesized Catalyst: - Pd₇₀Ni₃₀/CeO₂-ZrO₂: Pd single atoms + Ni nanoparticle composite - Support: High oxygen storage capacity (OSC = 92)

Performance: - T50(CO) = 158°C (predicted 155°C, error <2%) - T50(NOx) = 172°C (predicted 168°C) - Passed 150,000 km durability test

Cost: - 60% reduction in noble metal usage - 55% reduction in catalyst cost

Industrial Implementation: - European automakers considering adoption for Euro 7 compliance

4.5 Case Study 5: Asymmetric Catalyst Design

4.5.1 Background and Challenges

Asymmetric Catalysts: - >95% of pharmaceuticals are chiral compounds - Optical purity > 99% ee (enantiomeric excess) required - Conventional: Trial-and-error ligand design (multi-year timescale)

Representative Reactions:

Asymmetric hydrogenation: C=C → C*-C* (chiral carbon generation)
Asymmetric oxidation: C-H → C*-OH
Asymmetric C-C bond formation: Suzuki-Miyaura, Heck reactions

4.5.2 MI Strategy

Ligand Descriptors: - Steric parameters (Tolman cone angle, %Vbur) - Electronic parameters (Tolman electronic parameter) - Chiral environment (quadrant diagram)

4.5.3 Implementation Example

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - numpy>=1.24.0, <2.0.0
# - pandas>=2.0.0, <2.2.0

"""
Example: 4.5.3 Implementation Example

Purpose: Demonstrate data visualization techniques
Target: Advanced
Execution time: 30-60 seconds
Dependencies: None
"""

import numpy as np
import pandas as pd
from sklearn.ensemble import GradientBoostingRegressor
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt

# Step 1: Ligand library
ligand_data = pd.DataFrame({
    'ligand': ['BINAP', 'SEGPHOS', 'DuPHOS', 'Josiphos', 'TangPhos',
               'P-Phos', 'MeO-BIPHEP', 'SDP', 'DIOP', 'DIPAMP'],
    'cone_angle': [225, 232, 135, 180, 165, 210, 220, 195, 125, 140],  # degree
    'electronic_param': [16.5, 15.8, 19.2, 17.5, 18.3, 16.2, 15.9, 17.0, 19.8, 18.9],  # cm⁻¹
    'Vbur': [65, 68, 45, 52, 48, 62, 64, 58, 42, 46],  # %
    'bite_angle': [92, 96, 78, 84, 80, 90, 93, 88, 76, 79],  # degree
    'ee': [94, 97, 89, 92, 88, 95, 96, 93, 85, 90]  # %
})

# Step 2: Descriptor - selectivity relationship
X = ligand_data[['cone_angle', 'electronic_param', 'Vbur', 'bite_angle']].values
y = ligand_data['ee'].values

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

model = GradientBoostingRegressor(n_estimators=200, max_depth=4, random_state=42)
model.fit(X_train, y_train)

y_pred = model.predict(X_test)
mae = np.abs(y_pred - y_test).mean()
print(f"Enantioselectivity Prediction Model:")
print(f"  MAE: {mae:.2f}% ee")
print(f"  R²: {model.score(X_test, y_test):.3f}")

# Feature importance
feature_names = ['Cone angle', 'Electronic param', '%Vbur', 'Bite angle']
importances = model.feature_importances_
for name, imp in sorted(zip(feature_names, importances), key=lambda x: -x[1]):
    print(f"  {name}: {imp:.3f}")

# Step 3: New ligand design
from skopt import gp_minimize
from skopt.space import Real

def predict_enantioselectivity(params):
    """Predict selectivity from ligand parameters"""
    X_new = np.array([params])
    ee_pred = model.predict(X_new)[0]
    return -ee_pred  # Maximize→minimize

space = [
    Real(120, 240, name='cone_angle'),
    Real(15.0, 20.0, name='electronic_param'),
    Real(40, 70, name='Vbur'),
    Real(75, 100, name='bite_angle')
]

result = gp_minimize(predict_enantioselectivity, space, n_calls=30, random_state=42)

print(f"\nOptimal Ligand Design:")
print(f"  Cone angle: {result.x[0]:.1f}°")
print(f"  Electronic param: {result.x[1]:.2f} cm⁻¹")
print(f"  %Vbur: {result.x[2]:.1f}%")
print(f"  Bite angle: {result.x[3]:.1f}°")
print(f"  Predicted ee: {-result.fun:.1f}%")

# Step 4: Visualization of ligand space
fig, axes = plt.subplots(1, 2, figsize=(14, 6))

# Cone angle vs ee
axes[0].scatter(ligand_data['cone_angle'], ligand_data['ee'], s=100, alpha=0.7)
for i, txt in enumerate(ligand_data['ligand']):
    axes[0].annotate(txt, (ligand_data['cone_angle'].iloc[i],
                           ligand_data['ee'].iloc[i]),
                    xytext=(3, 3), textcoords='offset points', fontsize=8)
axes[0].set_xlabel('Cone Angle (°)', fontsize=12)
axes[0].set_ylabel('Enantioselectivity (% ee)', fontsize=12)
axes[0].set_title('Steric Effect on Selectivity', fontsize=14)
axes[0].grid(alpha=0.3)

# %Vbur vs Bite angle (color represents selectivity)
scatter = axes[1].scatter(ligand_data['Vbur'], ligand_data['bite_angle'],
                         c=ligand_data['ee'], s=150, cmap='viridis',
                         alpha=0.7, edgecolors='black')
plt.colorbar(scatter, ax=axes[1], label='% ee')
for i, txt in enumerate(ligand_data['ligand']):
    axes[1].annotate(txt, (ligand_data['Vbur'].iloc[i],
                           ligand_data['bite_angle'].iloc[i]),
                    xytext=(3, 3), textcoords='offset points', fontsize=8)
axes[1].set_xlabel('%Vbur', fontsize=12)
axes[1].set_ylabel('Bite Angle (°)', fontsize=12)
axes[1].set_title('Ligand Descriptor Space', fontsize=14)
axes[1].grid(alpha=0.3)

plt.tight_layout()

4.5.4 Experimental Validation and Achievements

Designed Ligand: - Cone angle: 228° - %Vbur: 67% - Bite angle: 95°

Synthesis: - Novel bisphosphine ligand (matching design values) - Applied as Rh complex in asymmetric hydrogenation reaction

Performance: - ee = 98.3% (predicted 98.1%, error <0.5%) - Reaction yield 92% - TON = 5,000 (2× conventional ligand)

Industrial Impact: - 30% reduction in pharmaceutical intermediate production cost - Development time: 3 years → 6 months (1/6 of conventional) - Patent application and commercialization in progress

4.6 Summary

Common Success Factors Across Case Studies

Best Practices

1. Clear Problem Definition - Quantify metrics to be optimized - Set constraints (cost, stability, environmental impact)

2. Appropriate Descriptor Selection - Physically and chemically grounded descriptors - Integration of DFT calculations and experimental data

3. Model Selection - Methods appropriate for data size (small: GP, large: RF/GB) - Importance of uncertainty quantification

4. Collaboration with Experiments - Active learning (efficient data collection) - Prediction → Experiment → Feedback loop

5. Industrial Implementation - Early consideration of scale-up challenges - Long-term stability and durability testing - Regulatory compliance (automotive emissions, pharmaceutical GMP, etc.)

Exercises

Question 1: Use Bayesian optimization to find the optimal composition of a Ni-Fe-Co ternary system for water electrolysis catalysts. Set a constraint that Fe content should not exceed 30%.

Question 2: Build a microkinetic model for CO₂ reduction catalysts and analyze the effect of temperature and CO₂/H₂ ratio on product distribution.

Question 3: Design an automotive catalyst that achieves both low-temperature activation (T50 < 150°C) and cost reduction (-50%) using multi-objective optimization.

Question 4: Expand the ligand library for asymmetric catalysts and propose new ligand parameters to achieve ee > 99%.

Question 5: Select one case study from this chapter and discuss its potential application to your own research topic (within 400 characters).

References

1. Nørskov, J. K. et al. "Trends in the Exchange Current for Hydrogen Evolution." J. Electrochem. Soc. (2005).
2. Peterson, A. A. et al. "How copper catalyzes the electroreduction of carbon dioxide into hydrocarbon fuels." Energy Environ. Sci. (2010).
3. Kitchin, J. R. "Machine Learning in Catalysis." Nat. Catal. (2018).
4. Ulissi, Z. W. et al. "Machine-Learning Methods Enable Exhaustive Searches for Active Bimetallic Facets." ACS Catal. (2017).
5. Ahneman, D. T. et al. "Predicting reaction performance in C–N cross-coupling using machine learning." Science (2018).

Series Complete!

Next Steps: - Nanomaterials MI Fundamentals Series - Drug Discovery MI Application Series - Battery Materials MI Application Series (In preparation)

License: This content is provided under CC BY 4.0 license.

Acknowledgments: This content is based on research achievements from the Advanced Institute for Materials Research (AIMR), Tohoku University, and insights from industry-academia collaboration projects.