plasmonX: Nanoplasmonic Simulation Software

• plasmonX is an advanced open-source software package that integrates atomistic (ωFQ/ωFQFμ) and continuum (BEM) models to simulate plasmonic responses in complex nanostructures.
• It supports a wide range of materials including metals, graphene, and nanoalloys, providing accurate quantum-aware and classical representations for diverse geometries.
• The platform bridges nanoscale effects with scalable simulations, enabling precise spectral predictions, hot spot mapping, and design optimization in nanoplasmonic research.

plasmonX refers to a recently released open-source software package specifically developed for simulating the plasmonic response of complex nanostructures across a wide range of materials and geometries. It integrates atomistic and continuum models, supporting metallic, graphene-based, and multi-metal nanostructures with optimized algorithms for both quantum-aware (fluctuating charge/dipole) and classical (BEM) representations. The platform addresses the challenges of scale, nonlocal response, and accurate field-property mapping central to nanoplasmonics (Giovannini et al., 14 Oct 2025).

1. Simulation Models and Theoretical Framework

plasmonX implements two principal families of models for the simulation of nanoplasmonic systems: atomistic fluctuating charge/dipole models and implicit continuum boundary-element methods.

• ωFQ (Frequency-Dependent Fluctuating Charges): Assigns to each atom a complex, frequency-dependent charge, $q(\omega)$, with intraband conduction captured via a Drude-like response and quantum tunneling incorporated through a Fermi-like damping function $f(r_{ij})$ decaying exponentially with interatomic distance. The collective charge response is calculated by solving the following linear system:

$$[\bar{K} \cdot T^{(qq)} - z_q(\omega) I_N] q(\omega) = -\bar{K} \cdot V(\omega)$$

where $\bar{K}$ encodes geometrical interatomic interactions, $T^{(qq)}$ is a smeared Coulomb matrix, and $z_q(\omega)$ is a complex, frequency-dependent Drude parameter.

• ωFQFμ (Fluctuating Charge and Dipole): Extends ωFQ by coupling atomic charges $q(\omega)$ and dipoles $\mu(\omega)$, crucial for metals with significant interband transitions (e.g., Au, Ag). The full atomistic response is obtained by solving the block matrix system:

$$\begin{bmatrix} \bar{K} & 0 \ 0 & I_{3N} \end{bmatrix} \begin{bmatrix} T^{(qq)} & T^{(q\mu)} \ T^{(\mu q)} & T^{(\mu\mu)} \end{bmatrix} \begin{bmatrix} q(\omega) \ \mu(\omega) \end{bmatrix} - \begin{bmatrix} z_q(\omega)I_N & 0 \ 0 & z_\mu(\omega)I_{3N} \end{bmatrix} \begin{bmatrix} q(\omega) \ \mu(\omega) \end{bmatrix} = \begin{bmatrix} \bar{K} & 0 \ 0 & I_{3N} \end{bmatrix} \begin{bmatrix} -V(\omega) \ -E(\omega) \end{bmatrix}$$

The term $z_\mu(\omega)$ captures the interband polarizability, $z_\mu(\omega) = -1/\alpha^{IB}(\omega)$.

Both models inherently account for nonlocal and quantum effects (notably for ωFQ via the Fermi-like damping), rendering them suitable for sub-nanometer systems and heterostructures.

2. Supported Nanostructures and Geometrical Flexibility

plasmonX is structured to simulate a diverse range of nanoplasmonic systems:

• Materials: Simple metals (free-electron-like), $d$-metals (Ag, Au), graphene-based structures (through effective 2D mass and electron density models), and nanoalloys/multimetallic assemblies.
• Nanostructure Geometries: Spheres, rods, cones, pyramids, icosahedra, complex tips, and arbitrary assemblies are accessible via the GEOM interface.
• Scale: Atomistic models operate efficiently up to thousands of atoms (with quantum tunneling), while continuum implicit representations via the Boundary Element Method (BEM) enable the simulation of systems with up to millions of atoms.

3. Continuum Methods: BEM-DPCM and BEM-IEF-PCM

For larger or topologically complex systems, plasmonX offers robust continuum solvers:

Model	Description	Key Equation / Implementation
BEM-DPCM	Surface is tessellated; solves for surface charge σ(ω) considering dielectric constants	$$\left[2\pi \frac{\varepsilon_2(\omega)+\varepsilon_1(\omega)}{\varepsilon_2(\omega)-\varepsilon_1(\omega)} A + F\right]\sigma(\omega) = -E_n(\omega)$$
BEM-IEF-PCM	Integral-equation formalism incorporates both potential and its derivative	$$\left[2\pi \frac{\varepsilon_2(\omega)+\varepsilon_1(\omega)}{\varepsilon_2(\omega)-\varepsilon_1(\omega)} I + F\right] S A^{-1} \sigma(\omega) = -[2\pi I + F] V(\omega)$$

$A$ is the area matrix, $F$ is from surface derivatives of the Green function, $S$ is a geometry-dependent matrix. These BEM implementations share tessellation and output standards with advanced quantum chemistry codes.

4. Post-Processing and Analysis

plasmonX includes a comprehensive post-processing suite designed for in-depth field and charge analysis:

• Output Files: Cartesian (XYZ/PQR) for induced states, volumetric CUBE files for charge densities.
• Field and Charge Maps: Two-dimensional cross-sectional maps (e.g., $xy$ plane) to visualize spatial field enhancements (“hot spots”).
• Custom Cuts: User-specified planes for CSV-based data extraction, supporting advanced data analysis and visualization.
• Applications: Evaluation of electric field enhancements in TERS/SERS substrates, mapping hot-spot formation in dimer or tip structures, and direct comparison to experimental near-field or optical cross section data.

5. Optical Cross Sections and Physical Observables

Key physical observables simulated by plasmonX include:

• Absorption Cross Section:

$$\sigma^{abs}(\omega) = \frac{4\pi\omega}{3c} \text{Tr}\{\text{Im}[\alpha(\omega)]\}$$

• Scattering Cross Section:

$$\sigma^{sca}(\omega) = \frac{8\pi\omega^4}{3c^4} |\alpha(\omega)|^2$$

$\alpha(\omega)$ is the polarizability tensor, and these observables can be directly compared with experimental and Vegard’s law trends, e.g., for plasmon peak shifts in Ag–Au alloys.

6. Applications and Impact in Nanoplasmonics

plasmonX serves as a unified computational platform for several research avenues:

• Nanoplasmonic Spectroscopy: Accurate spectral prediction of plasmonic resonances, including composition and geometry-driven peak shifts in alloys and heterostructures.
• Sensor and Hot Spot Design: Optimization of field localization for SERS, TERS, and nanoantenna applications via field/charge visualization.
• Multiscale Modeling: Integration of quantum-mechanical and classical approaches accommodates both quantum tunneling at short scales and scalability to device-relevant dimensions.
• Nanoengineered Devices: Enables the design and predictive modeling of advanced nanophotonic elements, arrays, and metasurfaces with tailored optical responses.

A plausible implication is that plasmonX bridges the methodological gap between atomistic quantum-informed models, which are essential for tunneling/nonlocal effects, and continuum classical models, which are critical for scalability and device design.

7. Implementation and Extensibility

plasmonX is structured as a modular, open-source codebase. It offers:

• Efficient sparse and dense linear algebra solvers for large system sizes.
• Modular routines for geometry generation, solution, and analysis.
• A post-processing workflow designed to interface with both visualization tools and downstream theoretical/experimental analyses.

Given its support for atomistic–continuum hybrid descriptions and general applicability to metals, graphene, and alloys, it provides a flexible platform for the broader nanoplasmonics and nanophotonics communities (Giovannini et al., 14 Oct 2025).