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Extension of Graph Convolution Network for Sigma-Profile Prediction to Silicon-Containing Compounds

This study proposes an integrated machine-learning framework that extends a Group Contribution-based Graph Convolution Network to predict sigma-profiles for silicon-containing compounds, enabling accurate and computationally efficient thermodynamic property predictions via the COSMO-SAC model without requiring quantum-chemical calculations.

Original authors: Ji Eun Rhee, Beom Chan Ryu, Sun Yoo Hwang, Seung Yeop Baek, Seon Min Kim, Ha Young Kim, Jeong Won Kang

Published 2026-09-21

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CC BY 4.0

Original authors: Ji Eun Rhee, Beom Chan Ryu, Sun Yoo Hwang, Seung Yeop Baek, Seon Min Kim, Ha Young Kim, Jeong Won Kang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast world of chemical engineering, predicting how different substances will behave when mixed is a fundamental challenge. Imagine trying to design a new lubricant, a refrigerant, or a coating for electronic devices without knowing how the ingredients will interact under heat or pressure. For decades, scientists have relied on complex computer simulations based on quantum mechanics to map out these interactions. These simulations calculate the electrical charge distribution on the surface of every molecule, creating a unique fingerprint that dictates how the molecule will bond with its neighbors. While accurate, this process is incredibly slow and expensive, requiring powerful supercomputers and specialized expertise. It is like trying to measure the exact weight of every grain of sand on a beach to understand the beach's shape; the data is perfect, but the effort is often too great for rapid discovery.

To speed things up, researchers have turned to machine learning, teaching computers to recognize patterns in molecular structures so they can predict these fingerprints without running the heavy simulations every time. However, a significant gap remained in this approach. Most existing models were trained on common organic compounds made of carbon, hydrogen, and oxygen. They struggled when faced with silicon-containing compounds, a class of materials essential for everything from sealants and lubricants to the very chips inside our computers. Because silicon behaves differently than carbon, the old models could not accurately predict how these materials would act in mixtures, leaving engineers to guess or rely on scarce experimental data.

A team of researchers from Korea University and SK Inc. AX has now bridged this gap by expanding the reach of these predictive tools. They developed a new framework that combines a specialized type of artificial intelligence with a refined thermodynamic model to accurately forecast the behavior of silicon-based chemicals. Instead of running the slow, heavy quantum calculations for every new molecule, their system looks at the molecular structure—specifically the arrangement of functional groups—and instantly generates the necessary surface charge map. This map, known as a sigma-profile, acts as a blueprint for how the molecule will interact with others.

The researchers began by building a massive new training database. They took an existing collection of over 3,500 organic compounds and added 546 newly generated silicon-containing compounds, bringing the total to 4,102 distinct molecules. To create the training data for these new silicon compounds, they first performed the rigorous quantum calculations to establish the correct "ground truth." They then taught their machine learning model, which uses a graph-based neural network, to recognize the specific patterns of silicon-centered groups, such as silicon atoms bonded to hydrogen or oxygen. This allowed the model to learn the unique chemical language of silicon, which had been missing from previous datasets.

Once trained, the model was tested on its ability to predict the vapor-liquid equilibrium of various mixtures. This is a critical measurement that tells engineers at what temperature and pressure a liquid will turn into a gas, or how two liquids will separate. The researchers compared the model's predictions against real-world experimental data for binary systems involving silicon compounds. The results were highly accurate. The model predicted the pressure of the system with an average error of just 4.56 percent and the composition of the vapor with an error of only 0.02 in mole fraction. These numbers indicate that the machine learning approach can reproduce the behavior of complex silicon mixtures with a level of precision that rivals the much slower, traditional quantum methods.

A key part of this success was the adoption of an updated thermodynamic model that explicitly accounts for carboxylic acid interactions, ensuring that even molecules with specific acidic groups were handled correctly. The entire process works without generating molecular structure files or performing quantum calculations for the target molecules. Instead, it takes a simple text string representing the molecule's structure and outputs the necessary thermodynamic properties in a fraction of the time. This achievement provides a practical, efficient tool for the chemical industry, allowing for the rapid screening and design of new silicon-based materials for electronics, refrigeration, and industrial coatings, all without the computational bottleneck that previously slowed down discovery.

Technical Summary: Extension of Graph Convolution Network for Sigma-Profile Prediction to Silicon-Containing Compounds

Problem Statement
Silicon-containing compounds are critical to various industrial sectors, including electronics, lubricants, and refrigerants, yet their thermodynamic properties remain difficult to predict accurately. Experimental data for these compounds is scarce, and traditional quantum-chemical calculations (specifically Density Functional Theory-based COSMO calculations) required for accurate thermodynamic modeling are computationally expensive and time-consuming. While machine learning (ML) approaches have been developed to predict sigma-profiles for organic compounds, existing datasets and models largely exclude silicon-containing species, creating a significant gap in the ability to rapidly screen and model these industrially relevant materials.

Methodology
The authors propose an integrated machine-learning framework designed to predict thermodynamic properties directly from molecular structures without performing quantum-chemical calculations. The methodology consists of three primary components:

Dataset Expansion: The training database was significantly expanded to include 546 newly generated silicon-containing compounds, bringing the total dataset size to 4,102 compounds. These new sigma-profiles were generated using DFT-based COSMO calculations to serve as ground truth for training.
Model Architecture (GC-GCN): The study utilizes a Group Contribution-based Graph Convolution Network (GC-GCN). In this architecture, molecules are represented as graphs where functional groups serve as nodes and chemical connectivity defines edges. To accommodate silicon chemistry, nine additional silicon-centered functional groups were introduced, increasing the total functional group count to 57. The model employs five independent GC-GCN networks to predict the cavity volume ( $V$ ) and four distinct sigma-profile components: non-hydrogen-bonding ( $p_{nhb}$ ), hydroxyl-group hydrogen-bonding ( $p_{OH}$ ), other hydrogen-bonding ( $p_{OT}$ ), and carboxylic-acid hydrogen-bonding ( $p_{COOH}$ ).
Thermodynamic Framework: The predicted sigma-profiles are fed into an extended version of the COSMO-SAC model, specifically the COSMO-SAC-COOH variant. This variant explicitly accounts for carboxylic acid interactions. The framework calculates activity coefficients, which are then combined with pure-component saturation pressures (via Antoine or Wagner equations) to perform Vapor–Liquid Equilibrium (VLE) calculations using modified Raoult's law.

Key Contributions

Chemical Space Extension: The primary contribution is the successful extension of the GC-GCN framework to silicon-containing compounds, addressing a previous limitation where such compounds were underrepresented in ML-based COSMO datasets.
Model Integration: The study integrates the COSMO-SAC-COOH model with the ML-predicted descriptors, allowing for the explicit treatment of carboxylic acid interactions alongside silicon chemistry.
Efficiency: The framework eliminates the need for DFT calculations or the generation of molecular structure files for new silicon-containing compounds, offering a computationally efficient alternative for property prediction.

Results
The performance of the proposed framework was evaluated against experimental data and DFT-based benchmarks:

Sigma-Profile Prediction: The predicted sigma-profiles showed good agreement with DFT-based COSMO descriptors.
VLE Prediction: The model successfully reproduced vapor–liquid equilibrium behavior across systems with diverse phase-equilibrium characteristics.
Error Metrics: When compared to experimental data, the framework yielded an average squared error in pressure (RRMSE $_P$ ) of 4.56% and a root mean square error in vapor-phase mole fraction (RMSE $_y$ ) of 0.02.

Significance and Claims
The authors claim that this work provides a practical and computationally efficient tool for predicting thermodynamic and phase-equilibrium properties for a broad range of compounds, specifically including silicon-containing systems. By enabling reliable predictions directly from molecular structures without quantum-chemical calculations, the framework facilitates large-scale molecular screening for industrial applications where experimental data is limited. The study demonstrates that expanding the training database to include specific chemical families (like silicon compounds) and adopting specialized thermodynamic models (like COSMO-SAC-COOH) allows ML frameworks to maintain high accuracy while significantly reducing computational costs.

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