**summary: **Researchers have developed a brain-inspired AI technique that uses neural networks to model the difficult quantum states of molecules, which is crucial for technologies such as solar panels and photocatalysts.

This new approach greatly improves accuracy, enabling better prediction of molecular behaviors during energy transitions. By enhancing our understanding of excited molecular states, this research could revolutionize materials prototyping and chemical synthesis.

**Key facts:**

- Neural networks have modeled molecular excited states with unprecedented accuracy.
- Five times greater accuracy than previous methods for complex molecules was achieved.
- It can lead to computer simulation of materials and chemical models.

**source: **Imperial College London

**New research using neural networks, a form of brain-inspired artificial intelligence, suggests a solution to the difficult challenge of modeling the states of molecules.**

The research shows how this technique can help solve fundamental equations in complex molecular systems.

This could lead to practical uses in the future, helping researchers create prototypes of new materials and chemical combinations using computer simulations before attempting to manufacture them in the laboratory.

Led by scientists from Imperial College London and Google DeepMind, the study is published today in *sciences*.

**excited molecules**

The team studied the problem of understanding how molecules transition into and out of “excited states.” When molecules and materials are excited by a large amount of energy, such as exposure to light or high temperatures, the electrons in them can move into a temporary new configuration, known as an excited state.

The precise amount of energy absorbed and released as molecules transition between states creates a unique fingerprint for different molecules and materials. This affects the performance of technologies ranging from solar panels and LEDs to semiconductors and photocatalysts. It also plays a crucial role in biological processes involving light, including photosynthesis and vision.

However, it is very difficult to create a model for this fingerprint because the excited electrons are quantum in nature, which means that their positions within molecules are never certain, and can only be expressed as probabilities.

Lead researcher Dr David Faw from Google DeepMind and the Department of Physics at Imperial College said: “Representing the state of a quantum system is very difficult. You have to assign a probability to every possible configuration of electron positions.

“The space of all possible configurations is enormous – if you tried to represent it as a grid with 100 points along each dimension, the number of possible electronic configurations for a silicon atom would be greater than the number of atoms in the universe. This is exactly where we thought deep neural networks could help.”

**Neural networks**

The researchers developed a new mathematical approach and used it with a neural network called FermiNet, which was the first example where deep learning was used to calculate the energy of atoms and molecules from fundamental principles that were accurate enough to be useful.

The team tested their approach on a range of examples, and the results were promising. In a small but complex molecule called dicarbonyl, they were able to achieve a mean absolute error of 4 MeV (millielectronvolts — a small measure of energy), which is about five times the experimental results of previous standard methods of 20 MeV.

“We tested our method on some of the most challenging systems in computational chemistry, where two electrons are excited at once, and found that we were about 0.1 electron volts away from the most complex and demanding calculations ever performed,” said Dr. Faw.

“Today, we are making our latest work open source, and we hope the research community will build on our methods to explore the unexpected ways in which matter interacts with light.”

## About AI Research News

**author: **Hayley Downing**source: **Imperial College London**communication: **Hayley Downing – Imperial College London**image: **Image taken from Neuroscience News

**Original research: **Access is closed.

“Accurate computation of quantum excited states using neural networksBy David Faw et al. *sciences*

**a summary**

**Accurate computation of quantum excited states using neural networks**

### introduction

Understanding the physics of how matter interacts with light requires accurate modeling of the excited electronic states of quantum systems. This forms the basis for the behavior of photocatalysts, fluorescent dyes, quantum dots, light-emitting diodes (LEDs), lasers, solar cells, and much more.

Current quantum chemistry methods for excited states can be much less accurate than those for ground states, sometimes qualitatively inaccurate, or may require prior knowledge of which states to target. Neural networks combined with variational Monte Carlo (VMC) have achieved remarkable accuracy for ground state wave functions for a range of systems, including spin models, molecules, and condensed matter systems.

Although VMC has been used to study excited states, previous methods have limitations that make them difficult or impossible to use with neural networks and often have many free parameters that require tuning to achieve good results.

### Rationale

We combine the flexibility of neural network solutions with mathematical insight that allows us to transform the problem of finding excited states of a system into the problem of finding the ground state of an extended system, which can then be addressed using standard VMC. We call this approach Natural Excited States VMC (NES-VMC).

The linear independence of the excited states is automatically imposed by the state functional form. The energy and other capacities of each excited state are obtained by transforming the Hamiltonian expectation matrix taken on the individual state, which can be assembled at no additional cost.

Crucially, this approach does not involve any free parameters to tune and does not require penalty terms to enforce vertical alignment. We tested the accuracy of this approach using two different neural network architectures – FermiNet and Psiformer.

### results

We have demonstrated our approach on reference systems ranging from single atoms to benzene-sized molecules. We have demonstrated the accuracy of NES-VMC on first-row atoms, closely matching experimental results, and on a range of small molecules, obtaining very precise energies and oscillator strengths comparable to the best existing theoretical estimates.

We calculated the potential energy curves for the lower excited states in the dicarbonate and identified the states across bond lengths by analyzing their symmetries and rotations. The NES-VMC vertical excitation energies matched those obtained using the high-resolution pseudo-random thermal bath configuration (SHCI) method with chemical accuracy for all bond lengths, while the adiabatic excitations were within 4 meV of experimental values on average—a fourfold improvement over SHCI.

In the case of ethylene, NES-VMC correctly described the conical intersection of the twisted molecule and was in excellent agreement with high-resolution multiple-reference configuration reaction (MR-CI) results. We also considered five challenging systems with low-altitude double excitations, including multiple benzene-sized molecules.

In all systems where there was good agreement between methods on vertical excitation energies, the Psiformer was within chemical accuracy across cases, including butadiene, where the ordering of particular states had been in dispute for many decades. In tetrazine and cyclopentadienone, where modern calculations made only a few years ago were known to be inaccurate, the NES-VMC results closely matched modern sophisticated diffusion Monte Carlo calculations and complete active space third-order perturbation theory (CASPT3).

Finally, we consider the benzene molecule, where the combination of NES-VMC and the Psiformer method was in better agreement with the best theoretical estimates than other methods, including neural network analysis methods using penalty methods. This validates our approach mathematically and shows that neural networks can accurately represent excited states of molecules at the current limit of computational methods.

### conclusion

NES-VMC is a parameter-free and mathematically sound variational principle for excited states. Its combination with neural network solutions allows for remarkable accuracy across a wide range of benchmark problems. The development of a precise VMC approach for excited states of quantum systems opens up many possibilities and greatly expands the range of applications of neural network wave functions.

Although we have only considered electronic excitations of molecular systems and neural network solutions, NES-VMC is applicable to any quantum Hamiltonian and any solution, enabling rigorous computational studies that could improve our understanding of vibrational couplings, optical band gaps, nuclear physics, and other challenging problems.

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