---
title: "Neural Message Passing for Quantum Chemistry — Gilmer 2017"
description: "Predicting quantum-mechanical properties of molecules with density functional theory (DFT) is accurate but slow."
authors: ["Justin Gilmer", "Samuel S. Schoenholz", "Patrick F. Riley", "Oriol Vinyals", "George E. Dahl"]
year: 2017
venue: "arXiv:1704.01212"
source: "https://arxiv.org/abs/1704.01212"
doi: "10.48550/arxiv.1704.01212"
arxiv: "1704.01212"
licence: "arXiv — non-exclusive licence to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/gilmer-2017-neural-message-passing-quantum-chemistry/"
---
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# Neural Message Passing for Quantum Chemistry

**Authors:** Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, [Oriol Vinyals](https://md.research.elamur.ai/free/en/authors/oriol-vinyals/), George E. Dahl · **Year:** 2017 · **Venue:** arXiv:1704.01212 · **Licence:** [arXiv — non-exclusive licence to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/1704.01212) · [PDF](https://arxiv.org/pdf/1704.01212) · [DOI 10.48550/arxiv.1704.01212](https://doi.org/10.48550/arxiv.1704.01212) · [arXiv 1704.01212](https://arxiv.org/abs/1704.01212) · [OpenAlex](https://openalex.org/W2606780347)

**Citations:** 3440 citations (openalex-snapshot · 2026-10-14) · [259](#cited-by) in our library, of the 140673 papers whose bibliographies we read

## Summary
Predicting quantum-mechanical properties of molecules with density functional theory (DFT) is accurate but slow. Gilmer et al. ask whether neural networks that read molecular graphs directly, without hand-crafted descriptors, can replace such calculations. They show that at least eight earlier graph models are special cases of one scheme, Message Passing Neural Networks (MPNNs). In an MPNN, node states are refined over several rounds using messages from neighbouring atoms, and a permutation-invariant readout then turns those states into a molecule-level prediction. Within this framework they test new variants, including an edge-network message function, a set2set readout, virtual edges, a master node and a multi-tower design that keeps cost down for wide node representations. On the QM9 benchmark (about 130k small organic molecules, 13 DFT-computed regression targets), their best model beats all baselines on every target and matches DFT within chemical accuracy on 11 of them. The work made MPNNs a standard reference point for molecular machine learning. The authors argue that future benchmarks should use larger molecules or more accurate labels.

## Key points
- **Data:** QM9 contains 13 properties per molecule plus 3D geometry, so the authors could test models both with and without spatial input. Trained networks run roughly 300,000× faster than the DFT calculation they approximate.
- **Best model:** The enn-s2s model (edge network plus set2set) reaches an average error ratio of 0.68 relative to chemical accuracy, and a 5-model ensemble reaches 0.52. The strongest earlier baselines scored about 1.35 (HDAD) and 1.36 (GG-NN).
- **Graph-only input:** Without spatial information, adding long-range mechanisms to GG-NN lowers the average error ratio from 3.47 to 2.90 with virtual edges, 2.62 with a master node and 2.57 with set2set. The set2set version hits chemical accuracy on 5 of 13 targets.
- **Towers variant:** Splitting node states into 8 towers improves scalability and slightly improves accuracy, with error ratio falling from 1.53 to 1.37 under per-target training.
- **Message functions:** Under joint training, the edge network outperforms the pair-message function (1.53 vs 3.98). Tying weights across time steps while increasing the hidden size worked better than untied weights.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

Fields: [Other](https://md.research.elamur.ai/free/en/shelves/other/)

## Cited by

Cited by

259 papers of our library cite it (of the 140673 whose bibliographies we read); 11 of them have a page here, 248 not yet.

- [Graph Convolutional Encoders for Syntax-aware Neural Machine Translation](https://md.research.elamur.ai/free/en/papers/bastings-2017-graph-convolutional-encoders-syntax-aware/)
- [Relational inductive biases, deep learning, and graph networks](https://md.research.elamur.ai/free/en/papers/battaglia-2018-relational-inductive-biases-deep-learning/)
- [Scalable Multi-Hop Relational Reasoning for Knowledge-Aware Question Answering](https://md.research.elamur.ai/free/en/papers/feng-2020-scalable-multi-hop-relational-reasoning/)
- [Fast Graph Representation Learning with PyTorch Geometric](https://md.research.elamur.ai/free/en/papers/fey-2019-fast-graph-representation-learning-pytorch/)
- [DialogueGCN: A Graph Convolutional Neural Network for Emotion Recognition in Conversation](https://md.research.elamur.ai/free/en/papers/ghosal-2019-dialoguegcn-graph-convolutional-neural-network/)
- [Encoding Sentences with Graph Convolutional Networks for Semantic Role Labeling](https://md.research.elamur.ai/free/en/papers/marcheggiani-2017-encoding-sentences-graph-convolutional-networks/)
- [Heterogeneous Graph Neural Networks for Extractive Document Summarization](https://md.research.elamur.ai/free/en/papers/wang-2020-heterogeneous-graph-neural-networks-extractive/)
- [A Comprehensive Survey on Graph Neural Networks](https://md.research.elamur.ai/free/en/papers/wu-2019-comprehensive-survey-graph-neural-networks/)
- [How Powerful are Graph Neural Networks?](https://md.research.elamur.ai/free/en/papers/xu-2018-powerful-graph-neural-networks/)
- [Distinguish Confusing Law Articles for Legal Judgment Prediction](https://md.research.elamur.ai/free/en/papers/xu-2020-distinguish-confusing-law-articles-legal/)
- [基于学习-推理的约束求解方法研究进展](https://md.research.elamur.ai/free/en/papers/zou-2023-methods-constraint-solving/)

## Cite

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{gilmer2017neural,
  title = {{Neural Message Passing for Quantum Chemistry}},
  author = {Gilmer, Justin and Schoenholz, Samuel S. and Riley, Patrick F. and Vinyals, Oriol and Dahl, George E.},
  year = {2017},
  doi = {10.48550/arxiv.1704.01212},
  eprint = {1704.01212},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1704.01212}
}
```

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