A Topology-Preserving Python Framework for Reliable Initialization of Star and Cyclic Polymer Architectures in Molecular Dynamics (LAMMPS) Simulations

Technical Summary: A Topology-Preserving Python Framework for Reliable Initialization of Star and Cyclic Polymer Architectures

Problem Statement
Accurate initialization of polymer architectures is a critical, yet frequently underappreciated, determinant of reliability in molecular dynamics (MD) simulations of soft matter. While modern simulation engines (e.g., LAMMPS, GROMACS) can handle millions of particles, the workflow is often bottlenecked not by integration performance, but by the structural integrity of initial configurations. Traditional initialization methods, such as naive random-walk generators or stochastic packing algorithms, frequently introduce artificial stresses, topological inconsistencies (e.g., incomplete ring closure), and severe steric overlaps. These artifacts propagate through simulation trajectories, manifesting as extreme pressure spikes, unstable neighbor list builds, constraint violation cascades, and prolonged nonphysical relaxation transients. This is particularly acute for complex architectures like star and cyclic polymers, where global topological constraints (e.g., exact loop closure) and local steric constraints (e.g., arm separation) are difficult to satisfy simultaneously without extensive post-hoc energy minimization.

Methodology
The authors present a self-contained, topology-preserving Python framework designed to generate star and cyclic polymer architectures with deterministic bond connectivity and exact geometric constraints. The core methodology treats polymer initialization as a constrained graph-embedding problem rather than a stochastic packing exercise.

• Algorithmic Design: The framework operates using only standard Python modules (math, random), ensuring portability and minimizing dependency overhead. It represents polymers as connectivity graphs $G=(V, E)$ and embeds them into 3D Euclidean space.
• Star Polymer Construction: Star polymers are constructed deterministically by anchoring multiple arms to a central core. Arms are generated along reference direction vectors with uniform angular spacing ($\Delta\theta = 2\pi/f$), which are then mapped to 3D space via random rotation matrices to ensure isotropic orientation. Bond lengths are fixed during construction, and angular symmetry is preserved to prevent immediate steric congestion.
• Cyclic Polymer Construction: Cyclic polymers are generated via analytic geometric embedding. The ring radius is derived analytically from regular polygon geometry ($R = b / 2\sin(\pi/N)$), and bead coordinates are constructed to ensure exact loop closure with zero geometric strain. The ring is embedded in a randomly oriented plane to eliminate planar bias.
• Overlap Detection and Placement: To enforce excluded volume, the framework employs spatial hashing. The simulation domain is discretized into cubic cells, restricting overlap checks to local neighborhoods. This reduces the computational complexity of neighbor searching from $O(N^2)$ to near-linear $O(N)$.
• Placement Strategy: Molecular centers are sampled stochastically within the simulation box. Candidate configurations are accepted only if all beads satisfy a minimum separation threshold relative to previously placed particles. If a molecule fails to place after a maximum number of attempts, a "fallback" procedure inserts the molecule stochastically without overlap constraints (though the paper notes this occurs in fewer than 1% of cases under tested conditions).
• Output: The generator produces LAMMPS-compatible data files (atom style full) containing atoms, bonds, angles, and simulation box dimensions, with deterministic indexing to ensure reproducibility.

Key Contributions

1. Deterministic Topological Integrity: Unlike existing tools that often rely on stochastic growth or post-hoc relaxation, this framework enforces bond-length constraints, exact ring closure, and angular consistency during coordinate generation. This eliminates the need for extensive soft-potential relaxation phases to repair geometric inconsistencies.
2. Computational Scalability: By utilizing spatial hashing for overlap detection and adjacency lists for topology construction, the algorithm achieves $O(N)$ scaling with respect to the number of beads, making it suitable for large-scale systems ($10^4$–$10^6$ beads).
3. Native LAMMPS Compatibility: The framework outputs simulation-ready data files directly, avoiding the indexing errors and topology corruption risks associated with intermediate format conversions.
4. Mechanical Stability: The generated structures are mechanically stable at initialization, satisfying bond-length and excluded-volume criteria before any dynamical evolution occurs.

Results and Benchmarking
Benchmark comparisons against naive random placement schemes demonstrate significant improvements:

• Reduced Instabilities: Spatial hashing reduced the incidence of bead overlaps by more than 90% compared to naive placement.
• Suppressed Artifacts: Systems generated by the framework exhibited no FENE bond stretch errors or broken bonds during initialization. In contrast, naive systems frequently showed severe local overlaps, leading to large energy spikes and simulation termination in some cases.
• Faster Equilibration: Topology-preserving systems stabilized within a few thousand timesteps, whereas naive systems often required relaxation times exceeding an order of magnitude.
• Reproducibility: Structural observables, such as the radius of gyration ($R_g$) and diffusion coefficients, showed high reproducibility across independent random seeds, with variance below approximately 3%.

Significance and Claims
The paper posits that initialization should be reclassified from a stochastic preprocessing step to a "controlled physical boundary condition." By embedding topological constraints and geometric consistency directly into the coordinate-generation algorithm, the framework ensures that subsequent MD trajectories probe intrinsic polymer physics (e.g., conformational entropy, interfacial adsorption) rather than transient artifacts inherited from flawed initialization.

The authors claim this work addresses a foundational gap in polymer simulation workflows: the generation of geometrically consistent initial configurations for complex architectures. While the framework is demonstrated using the Kremer–Grest bead-spring model, the authors assert its principles are engine-agnostic and applicable to other simulation engines. The method is presented not as a replacement for general-purpose polymer builders focused on chemical realism, but as a complementary, lightweight tool specifically optimized for the deterministic construction of coarse-grained star and cyclic architectures, thereby enhancing the robustness, efficiency, and reproducibility of large-scale polymer simulations.