Summary: Researchers have developed a brain-inspired artificial intelligence technique that uses neural networks to model advanced quantum states of molecules, which is critical for technologies such as solar panels and photocatalysts.
This new approach significantly improves accuracy and enables better prediction of molecular behavior during energy transfer. By better understanding molecular excited states, this research could revolutionize the development of materials prototypes and chemical synthesis.
Important facts:
- Neural networks modeled excited molecular states with unprecedented accuracy.
- For complex molecules, five times higher accuracy was achieved compared to previous methods.
- This could lead to the creation of computer-simulated chemical and material prototypes.
Source: Imperial College London
New research using neural networks a form of brain‑inspired artificial intelligence offers a promising solution to the long‑standing challenge of accurately modeling molecular states.
Research shows how technology can help solve fundamental equations in complex molecular systems.
This could lead to practical applications in the future, allowing researchers to develop prototypes of new materials and synthesize chemicals using computer simulations before producing them in the laboratory.
The research, led by scientists from Imperial College London and Google DeepMind, was published today in Science.
Excited molecules
The team investigated how molecules enter and exit excited states. When molecules and materials are stimulated with high energy, such as light or high temperature, their electrons can temporarily move into a new configuration, called an excited state.
The exact amount of energy absorbed or released as molecules change state forms a unique “fingerprint” for each molecule or material. These energy signatures influence the performance of technologies such as solar panels, LED lighting, semiconductors, and photocatalysts, and are equally vital in light‑driven biological processes like photosynthesis and vision.
However, this fingerprint is particularly difficult to model because excited electrons are quantum mechanical in nature. This means that their positions within molecules are never certain and can only be expressed as probabilities.
Dr David Pau, lead researcher at Google DeepMind and Imperial College Physics Department, said: “Representing the state of a quantum system is extremely difficult. You have to assign a probability to every possible arrangement of electron positions.”
The space of all possible configurations is enormous: if it were represented as a grid with 100 points in each dimension, the number of possible electron configurations of a silicon atom would exceed the number of atoms in the universe. This is where we believe deep neural networks can be useful.
Neural networks
The researchers developed a new mathematical approach and applied it to a neural network called a FermiNet (fermionic neural network). This was the first example of using deep learning to calculate the energy of atoms and molecules from scratch with enough accuracy to be useful.
The team tested their approach on several examples and got promising results. For a small but complex molecule called a carbon dimer, they obtained a mean absolute error (MEE) of 4 meV (millielectronvolts, a small unit of energy), which is five times closer than the experimental results from previous benchmark methods, which yielded 20 meV.
Dr. Pau explained, “We applied our method to some of the most challenging problems in computational chemistry cases where two electrons are excited at the same time and achieved results within about 0.1 eV of the most complex and demanding calculations performed to date.”
“Today we are making our latest work available as open source, and we hope that the research community will use our methods to explore unexpected interactions between matter and light.”
Abstract
Accurate calculation of quantum excited states using neural networks
Introduction
To understand the physics of the interaction between matter and light, accurate modeling of the excited electronic states of quantum systems is required. This underlies the behavior of photocatalysts, fluorescent dyes, quantum dots, light-emitting diodes (LEDs), lasers, solar cells, and more.
Current quantum chemical methods for excited states can be significantly less accurate than for ground states, sometimes by a factor of one, or require specific prior knowledge about certain states. Neural networks combined with variational Monte Carlo (VMC) have achieved remarkable accuracy for ground state wave functions in diverse systems, such as spin models, molecules, and solid-state systems.
Although Variational Monte Carlo (VMC) has been applied to the study of excited states, earlier approaches have significant limitations that make integration with neural networks challenging or even unfeasible. In addition, these methods often rely on numerous free parameters that require careful tuning to achieve accurate results.
RATIONALE
We combine the flexibility of neural network analysis with a mathematical approach, allowing us to transform the problem of determining the excited states of a system into the problem of determining the ground state of an extended system. This can be solved using the standard VMC method.
The linear independence of excited states is automatically enforced by the practical form of proximity. The energy and other observations of each excited state are obtained by skewing the matrix of Hamiltonian expectation values from the individual state estimates, which can be summed up at no additional cost.
Importantly, this approach does not require free parameters for the optimization or penalty terms to implement orthogonalization. We evaluated the accuracy of our approach with two distinct neural network architectures: FermiNet and Psiformer.
Results
We demonstrate our approach in reference systems ranging from a single atom to molecules the size of benzene. We demonstrate the accuracy of NES-VMC on first-row atoms (with very similar experimental results) and on a range of small molecules, obtaining highly accurate oscillator energies and intensities that are comparable to the best current theoretical estimates.
We calculated the potential energy curves for the lowest excited states of the carbon dimer, identifying each state across bond lengths by analyzing its symmetry and curvature. The vertical excitation energies obtained with NES‑VMC matched those from high‑precision semistochastic heat bath configuration interaction (SHCI) with chemical accuracy at all bond lengths. Adiabatic excitation energies stayed within 4 meV of experimental values on average — a fourfold improvement over SHCI. For ethylene, NES‑VMC accurately captured the conical intersection of the bent molecule and aligned closely with the highly accurate results of multi‑reference configuration interaction (MR‑CI). We extended the analysis to five complex systems with low‑intensity dual excitations, including several benzene‑scale molecules.
Across all systems, vertical excitation energies showed strong agreement between methods. Psiformer achieved acceptable chemical accuracy in every state, including butadiene, where the ordering of certain states has been debated for decades. For tetrazine and cyclopentadienone — systems where state‑of‑the‑art calculations from only a few years ago were highly inaccurate — NES‑VMC results were largely consistent with recent advanced Diffusion Monte Carlo (DMC) and third‑order perturbation theory (CASPT3) calculations across the full active space. In benzene, NES‑VMC combined with Psiformer delivered significantly better agreement with the best theoretical estimates than other approaches, including neural network methods using penalty techniques. These results confirm the mathematical soundness of our approach and demonstrate that neural networks can accurately represent molecular excited states within current computational limits.
CONCLUSION
NES‑VMC is a parameter‑free, mathematically rigorous variational principle for excited states. When combined with neural network analysis, it delivers exceptional accuracy across a broad range of benchmark problems. The development of such a precise VMC framework for excited states in quantum systems opens new possibilities and greatly extends the scope of neural network wave functions.
While this work focuses on electronic excitations in molecular systems using neural network methods, the NES‑VMC approach is applicable to any quantum Hamiltonian and any computational framework. This versatility enables highly accurate studies that can deepen our understanding of phenomena such as vibronic couplings, optical band gaps, nuclear physics, and other complex challenges in quantum science.
