Genarris 3.0: Efficient Screening of Molecular Crystals

• Genarris 3.0 is a Python-based platform for automated generation, screening, and clustering of molecular crystal structures, emphasizing efficient energy evaluation and diverse configuration sampling.
• The platform employs a fast Harris approximation and a novel relative coordinate descriptor with machine learning to rapidly rank and cluster candidate structures with reduced computational cost.
• Modular workflows in Genarris 3.0 enable tailored approaches for crystal structure prediction, dataset curation, and optimization algorithm initialization in computational chemistry and materials science.

Genarris 3.0 is a Python-based platform for the automated generation, screening, and clustering of molecular crystal structures, with an emphasis on rigid or semi-rigid molecules. Distinguished by its integration of a fast energy prescreening step using the Harris approximation, machine learning–driven clustering via a novel relative coordinate descriptor (RCD), and modular workflows for tailored structure set construction, Genarris 3.0 enables efficient exploration of the molecular crystal energy landscape. It is widely used for crystal structure prediction (CSP), dataset curation, and to provide diverse, physically sensible initial populations for metaheuristic algorithms in computational chemistry and materials science.

1. Random Molecular Crystal Structure Generation

Genarris 3.0 initiates its workflow by generating large pools of random molecular crystal candidates under stringent physical and crystallographic constraints, including:

• Unit Cell Parameter Sampling: Lattice vectors, angles, and unit cell volumes are sampled stochastically. These volumes are estimated using machine learning models trained on experimental solid-state structures, ensuring physically plausible packing.
• Molecular Placement: Molecules are positioned in the asymmetric unit with randomized orientations, subject to the enforcement of minimum intermolecular distances (typically scaled van der Waals radii).
• Space Group Selection: Sampling occurs over crystallographic space groups, including both general and special Wyckoff positions, which is especially critical for symmetric molecules.
• Hierarchical Structure Screening: Unphysical structures are eliminated through a hierarchical three-stage screening: (1) intra-cell Euclidean checks, (2) periodic image approximation, and (3) rigorous minimum image conventions using algorithms such as Fincke–Pohst sphere decoding for non-orthogonal cells.

This protocol ensures the raw structure pool is both physically meaningful and sufficiently broad to cover the relevant configuration space.

2. Harris Approximation for Efficient Energy Ranking

A central methodological advance is Genarris 3.0’s use of the Harris approximation (HA) for rapid energy evaluation:

• Theory: HA constructs the total crystal electron density $\rho_{\rm Harris}(r)$ by superposing precomputed single-molecule densities, each rotated and translated appropriately within the unit cell:

$$\rho_{\rm Harris}(r) \approx \sum_{\alpha} \rho_{\alpha} \left( R_{\alpha}^{-1}[r - t_{\alpha}] \right)$$

where $\rho_\alpha$ is the density of molecule $\alpha$, $R_\alpha$ its rotation, and $t_\alpha$ its translation.

• Energy Calculation: The Harris density is evaluated with dispersion-inclusive DFT functionals (e.g., PBE+TS) to provide a non-self-consistent estimate of the total energy.
• Validation: The HA is validated for both dimer binding curves and bulk structure pools, demonstrating reliable structure ranking capability without the computational burden of full self-consistent DFT cycles.

By leveraging HA, Genarris 3.0 enables the screening of thousands of candidate structures with drastically reduced computational cost, establishing a scalable framework for CSP and molecular materials discovery.

3. Machine Learning: Relative Coordinate Descriptor and Affinity Propagation Clustering

Genarris 3.0 introduces a machine learning pipeline based on the relative coordinate descriptor (RCD):

• Descriptor Definition: For each structure, the RCD encodes the set of nearest-neighbor relationships as

$R = \{ (P_1, Q_1), \ldots, (P_N, Q_N) \}$

where $P_i$ represents the relative position and $Q_i$ the relative orientation (e.g., quaternion) of neighbor $i$ to a reference molecule.

• Distance Metric: The structural difference is quantified by an $N \times N$ matrix, typically formulated as

$$D_{i,j} = \frac{|P_i - P_j|^4 + k \cdot |Q_i - Q_j|^4}{3}$$

with an adjustable weight $k$, summing the smallest $M$ elements to obtain a “RCD difference.”

• Clustering Algorithm: Affinity Propagation (AP) is employed to partition the pool into clusters corresponding to unique packing motifs. AP does not require pre-specified cluster numbers, allowing robust identification of structurally distinct regions of configuration space and elimination of near-duplicate structures.
• Significance: This process underpins the construction of final structure sets that are both representative and non-redundant, optimizing computational resources for downstream quantum chemical calculations.

4. Modular Workflows: Diverse, Energy, and Rigorous

Genarris 3.0 provides three modular workflows tailored for different CSP objectives:

Workflow	Selection Principle	Typical Use
Diverse	Uniform configuration sampling	GA/ML initial pools
Energy	Low-energy structure focus	Locating energy minima
Rigorous	Exhaustive, iterative refinement	In-house CSP, polymorph recovery

• Diverse Workflow: Initial HA energy evaluation followed by two rounds of RCD-based AP clustering (each reducing the pool to $\approx$10% of prior size), selecting the lowest-energy exemplar per cluster. Designed for maximal diversity, recommended for initializing genetic algorithms and other exploration techniques.
• Energy Workflow: Begins with coarse clustering (1% of raw pool), proceeds by selecting the 10 lowest-HA-energy structures per cluster for full DFT single-point energy refinement. Following a broad (10% size) AP clustering and selection, emphasizes collection of low-energy candidates but can introduce redundancy due to motif-energy correlations.
• Rigorous Workflow: Targets exhaustive landscape sampling: after a full HA or lower-level DFT evaluation of all raw structures, iteratively applies RCD clustering (targeting a silhouette score $\approx 0.5$) to select low-energy exemplars, followed by partial relaxations and further reduction over multiple iterations ($\rightarrow$1% of initial pool). Recovers known polymorphs and serves as a CSP engine.

These workflows allow users to balance between diversity, energetic favorability, and computational effort, according to their scientific objectives.

5. Test Cases and Performance

The practical utility of Genarris 3.0 was demonstrated on three test cases (Targets II, XIII, XXII) drawn from previous CSP blind tests:

• Raw Pool Sizes: Approximately 5,000–10,000 candidate structures generated for each target, depending on molecular flexibility.
• Workflow Outcomes:
  • The Rigorous workflow successfully recovered the experimental structure for all three targets, validating the platform’s potential as a first-principles CSP tool.
  • The Diverse workflow achieved a set characterized by uniform sampling and both low energies and varied packing motifs.
  • Using the output of the Diverse workflow as an initial population in the GAtor genetic algorithm improved convergence rates to representative low-energy structures, compared to Energy or purely Random initial pools.

This empirical evidence underscores Genarris 3.0’s versatility across structure prediction, diversity maximization, and rapid screening.

6. Applications and Research Integration

Genarris 3.0’s modular design lends itself to a broad array of use cases in research and industry:

• Crystal Structure Prediction (CSP): Serves as both a rapid generator of plausible candidates and as a full in-house CSP pipeline via the Rigorous workflow, facilitating polymorph discovery.
• Optimization Algorithm Initialization: Delivers diverse and physically meaningful pools of structures for genetic algorithms, swarm optimization, Monte Carlo, and Bayesian approaches.
• Machine Learning Dataset Curation: Provides curated, representative structure pools for training and validation of ML models targeting energetic, structural, or functional properties.
• Materials Discovery Pipelines: Supports rapid exploration of molecular crystals in pharmaceuticals, organic electronics, and materials chemistry, especially where polymorphism and property tunability are paramount.

A plausible implication is that its separation of structure generation, energy ranking, and clustering is adaptable to future extensions—for example, treatment of flexible molecules or integration of more advanced non-linear ML models. This suggests ongoing potential for Genarris as a core component of autonomous materials discovery platforms.

7. Developmental Context and Future Directions

Genarris 3.0 builds upon Genarris 2.0’s core advances, including MPI-based parallelization, machine-learned unit cell volume estimation, Wyckoff position algorithms, refined hydrogen bond contact thresholds, and hierarchical screening. Anticipated and suggested directions for further development, as highlighted in Genarris 2.0 and implicated by the 3.0 architecture, include:

• Parallelization Enhancements: Optimization of dynamic load balancing and adaptive scheduling for high-performance computing.
• Descriptor and ML Pipeline Expansion: Adoption of more sophisticated, potentially non-linear descriptors for both volumetric and energetic modeling.
• Flexible Molecule Support: Extension to handle conformationally complex molecules, expanding the accessible chemical space.
• Refined Hydrogen Bond Modeling: Incorporation of directional and angular criteria in contact screening, beyond simple distance settings.
• Robust Handling of Near-Symmetry: Automated identification of quasi-special Wyckoff site occupancy to accommodate nearly-symmetric molecules.

These developmental trajectories signal ongoing refinement of Genarris for more comprehensive, efficient, and accurate molecular crystal structure exploration.