The escalating concentration of greenhouse gases, particularly CO₂, necessitates advancements in carbon capture and storage technologies. Current methods like liquid amine-based solvents are energy-intensive. Membrane-based technologies offer a cost-effective alternative, relying on weak noncovalent interactions. Understanding how material structure impacts gas selectivity is crucial. Functional groups that selectively interact with CO₂ (CO₂-philic groups, usually Lewis bases) improve membrane performance. Electronic structure theory calculations quantify these interactions, but the vast number of potential CO₂-philic groups makes exhaustive ab initio studies impractical. High-throughput computational screening, aided by machine learning (ML), can accelerate the discovery of new functional materials. ML algorithms efficiently learn complex structure-property relationships, but their effectiveness depends heavily on the molecular representation used to feed structural data to the algorithm. Existing representations like Coulomb matrices (CM), Bag-of-Bonds (BoB), FCHL, and SOAP have limitations, including varying vector sizes depending on molecular size and a lack of explicit chemical information integration. This study introduces a novel molecular representation based on persistent homology, aiming to overcome these limitations.

Several molecular representations have been proposed for use in machine learning applications in chemistry. Coulomb matrices (CM) represent molecules as atom-by-atom matrices containing approximate potential energies. Bag-of-Bonds (BoB) represents each atomic pair in vectors based on elemental pairs. FCHL uses Gaussian distribution functions, while Smooth Overlap of Atomic Positions (SOAP) calculates the local density of atoms, but incurs high computational cost. These methods, while useful, often struggle with scalability and the incorporation of chemical information into the representation.

This research introduces a new molecular representation scheme based on persistent homology, a branch of computational topology. This approach encodes 3D structural data into 2D persistence images (PIs). The process starts by computing homological features (connected components and holes) that capture interatomic distances and topological features (rings, functional groups). These features are summarized in a persistence diagram (PD). The PD is then vectorized into a persistence image (PI) using a Gaussian kernel. To address potential inconsistencies arising from identical treatment of all atoms, particularly in molecules with the same geometry but different atom types, atomistic information (electronegativity differences) is incorporated into the variance of the Gaussian kernels. This chemically-driven PI differentiates molecules with similar geometries but different atomic compositions. The PI representation offers a similar-size vectorization regardless of molecular size, which is advantageous for ML applications. The performance of the PI representation is evaluated by comparing it against CM, BoB, FCHL, and SOAP for predicting CO₂ and N₂ interaction energies. A subset of 100 organic molecules with DFT-calculated interaction energies is used for model training and validation. Different machine learning algorithms (random forest, Gaussian process regression, kernel ridge regression) are tested. An active learning approach is employed to screen the GDB-9 database (133,885 molecules), iteratively expanding the training set based on predicted CO₂ interaction strength. DFT calculations are used to verify the predictions of the top candidates.

The chemically-driven persistence images (PIs) generally outperform other molecular representations (CM, BoB, FCHL, SOAP) in predicting CO₂ interaction energies, demonstrating high accuracy and low computational cost. The PI representation overcomes size limitations, maintaining a constant vector size regardless of molecular complexity. The active learning strategy effectively screens the GDB-9 database, revealing 44 molecules with CO₂ interaction energies exceeding -6.5 kcal/mol. The identified molecules often involve cooperative effects between N-containing heterocycles and amino or hydroxo groups, enhancing CO₂ interaction strength. The PI-based screening is significantly faster than SOAP-based screening (approximately 40 times faster). The 4,5-diamino-1H-imidazol-2-ol molecule is identified as having a particularly strong CO₂ affinity. The study highlights the effectiveness of incorporating chemical information into the persistent homology-based representation to improve the accuracy and efficiency of ML models for predicting molecular interactions.

The superior performance of the chemically-driven PI representation demonstrates the importance of incorporating chemical domain knowledge into topological data analysis for molecular property prediction. The method effectively captures both topological and chemical information, leading to more accurate and reliable predictions compared to other representations. The successful application to the large GDB-9 database highlights the scalability and efficiency of the approach. The identification of novel CO₂-philic moieties contributes to the development of improved carbon capture technologies. The active learning strategy is crucial for efficient exploration of the vast chemical space, focusing computational resources on the most promising candidates.

This study successfully introduces a novel chemically-driven persistence image (PI) molecular representation for predicting gas interaction energies. PIs outperform existing methods in accuracy and computational efficiency, particularly for large datasets. The active learning approach enabled the identification of promising CO₂-philic molecules from the GDB-9 database. Future work will expand the applicability of this method to other chemical problems, including catalysis and lanthanide/actinide separations.

The accuracy of the predictions relies on the accuracy of the DFT calculations used to generate the training data. The active learning approach, while efficient, might miss some promising molecules if the initial training set is not sufficiently representative. The generalizability of the PI representation to other types of molecular systems and properties requires further investigation.