Sjoerd de Haan, DataDrivenLab · July 2025 · ML for materials and measurement

Modeling Gold Nanosphere UV/Vis with SCUFF-EM and GMSH

Electromagnetic Modeling of Gold Nanospheres

Today I’m exploring computational electromagnetic simulation of gold nanoparticles to predict their UV/Vis absorption spectra. This connects to my previous work on gold nanorod optical profiles - but instead of using existing quantum simulation data, I’m trying to model the physics directly.

The Setup: 20nm Gold Sphere in Water

Gold nanoparticles exhibit strong surface plasmon resonance (SPR) that creates characteristic absorption peaks in the UV/Vis spectrum. For a 20nm diameter gold sphere in water, we expect:

• Peak wavelength: ~520-530 nm (green light absorption → red appearance)
• LSPR bandwidth: Depends on particle size and shape
• Water environment: Refractive index n ≈ 1.33

Tools: SCUFF-EM + GMSH

SCUFF-EM (Surface CUrrent/Field Formulation - ElectroMagnetics):

• Boundary element method for electromagnetic scattering
• Works with surface meshes (perfect for nanoparticles)
• Can compute extinction, scattering, absorption spectra

GMSH:

• Mesh generation for complex 3D geometries
• Integrates well with SCUFF-EM workflow

Geometry Definition

The sphere geometry is defined in sphere.geo:

// Sphere.geo - Creates a sphere of radius 10 nm (20 nm diameter)
SetFactory("OpenCASCADE");

// Create a sphere centered at origin (radius in nanometers)
Sphere(1) = {0, 0, 0, 10e-9};

// Set mesh characteristic length 
Characteristic Length{:} = 1e-10;

// Define physical surface (for SCUFF-EM)
Physical Surface("sphere_surface") = {1};

Key considerations:

• Surface-only geometry: SCUFF-EM works with boundaries, not volumes
• Nanometer scale: 10nm radius = 20nm diameter
• Mesh resolution: 0.1nm elements for smooth curvature

Expected Physics

For a 20nm gold sphere in water, the dominant physics is:

1. Mie scattering: Exact analytical solution exists for spheres
2. Localized Surface Plasmon Resonance (LSPR): Collective electron oscillation
3. Size effects: Small particles → broader resonances
4. Environment: Water shifts resonance vs vacuum

The resonance frequency depends on: $$\omega_{\text{LSPR}} \propto \sqrt{\frac{n_{\text{bulk}}}{n_{\text{medium}}^2 + 2n_{\text{bulk}}}}$$

Where $n_{\text{bulk}}$ is the bulk gold permittivity and $n_{\text{medium}}$ is water’s refractive index.

Complete Workflow Implementation

Based on the detailed blueprint, I’ve created a complete SCUFF-EM simulation workflow:

Files

1. nanosphere_water.scuffgeo - SCUFF-EM geometry file defining:
   • Gold nanoparticle with Drude model optical properties
   • Water environment with Sellmeier dispersion
   • Alternative materials (silver, TiO2) commented out
2. generate_frequencies.py - Python script to generate angular frequencies:
   • UV/Vis range: 200-800 nm in 10 nm steps
   • Converts wavelengths to SCUFF-EM angular frequency format
   • Creates omega_UVVis.dat input file
3. run_uvvis.sh - Bash script for complete simulation:
   • Generates frequencies and mesh automatically
   • Runs scuff-scatter with appropriate parameters
   • Calculates extinction, absorption, and scattering
4. process_uvvis.py - Results analysis script:
   • Extracts cross sections from SCUFF-EM output
   • Plots extinction, absorption, scattering spectra
   • Calculates efficiency factors and identifies plasmon peak
   • Saves data and publication-quality figures

Usage

# Run complete simulation
./run_uvvis.sh

# Process results and create plots
./process_uvvis.py

Expected Output

For a 10nm radius gold sphere in water:

• Plasmon peak: ~520-530 nm (LSPR resonance)
• Extinction dominated by absorption (small particle regime)
• Efficiency factors: Q_ext ≈ 1-3 at resonance
• Output files: uvvis_spectrum.png, uvvis_data.txt

Physics Validation

The simulation includes:

• Drude model for gold with realistic plasma frequency and damping
• Water dispersion via Sellmeier equation
• Proper normalization for cross sections in dispersive media
• Size effects captured by full electromagnetic calculation

This provides a direct computational path from nanoparticle geometry to UV/Vis spectrum, complementing the experimental data analysis from the previous nanorod work.