AIが量子化学の難題に挑む(AI tackles one of the most difficult challenges in quantum chemistry)

2024-08-22 インペリアル・カレッジ・ロンドン(ICL)

＜関連情報＞

• https://www.imperial.ac.uk/news/255673/ai-tackles-most-difficult-challenges-quantum/
• https://www.science.org/doi/10.1126/science.adn0137

ニューラルネットワークによる量子励起状態の正確な計算 Accurate computation of quantum excited states with neural networks

David Pfau, Simon Axelrod, Halvard Sutterud, Ingrid von Glehn, and James S. Spencer
Science  Published:23 Aug 2024
DOI:https://doi.org/10.1126/science.adn0137

Natural excited states.
Combining neural networks with a mathematical insight enables accurate calculations of challenging excited states of molecules.

Editor’s summary

Excited states are important in many areas of physics and chemistry; however, scalable, accurate, and robust calculations of excited-state properties from first principles remain a critical theoretical challenge. Recent advances in computing the ground-state properties of molecular systems driven by deep learning demonstrate that this technique has the potential to address this problem. Pfau et al. present a parameter-free mathematical principle for computing excited states using deep neural networks by directly generalizing variational quantum Monte Carlo to ground states. The proposed method achieves accurate excited-state calculations on a number of atoms and molecules, far outperforms existing methods for computing excited-state properties with deep learning (especially on larger systems), and can be applied to various quantum systems. —Yury Suleymanov

Abstract

We present an algorithm to estimate the excited states of a quantum system by variational Monte Carlo, which has no free parameters and requires no orthogonalization of the states, instead transforming the problem into that of finding the ground state of an expanded system. Arbitrary observables can be calculated, including off-diagonal expectations, such as the transition dipole moment. The method works particularly well with neural network ansätze, and by combining this method with the FermiNet and Psiformer ansätze, we can accurately recover excitation energies and oscillator strengths on a range of molecules. We achieve accurate vertical excitation energies on benzene-scale molecules, including challenging double excitations. Beyond the examples presented in this work, we expect that this technique will be of interest for atomic, nuclear, and condensed matter physics.

Abstract

INTRODUCTION
Understanding the physics of how matter interacts with light requires accurate modeling of electronic excited states of quantum systems. This underpins the behavior of photocatalysts, fluorescent dyes, quantum dots, light-emitting diodes (LEDs), lasers, solar cells, and more. Existing quantum chemistry methods for excited states can be much more inaccurate than those for ground states, sometimes qualitatively so, or can require prior knowledge targeted to specific states. 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, prior approaches have limitations that make it difficult or impossible to use them with neural networks and often have many free parameters that require tuning to achieve good results.

RATIONALE
We combine the flexibility of neural network ansätze with a mathematical insight that allows us to convert the problem of finding excited states of a system to one of finding the ground state of an expanded system, which can then be tackled with standard VMC. We call this approach natural excited states VMC (NES-VMC). Linear independence of the excited states is automatically imposed through the functional form of the ansatz. The energy and other observables of each excited state are obtained from diagonalizing the matrix of Hamiltonian expectation values taken over the single-state ansätze, which can be accumulated with no additional cost. Crucially, this approach has no free parameters to tune and needs no penalty terms to enforce orthogonalization. We examined the accuracy of this approach with two different neural network architectures—the FermiNet and Psiformer.

RESULTS
We demonstrated our approach on benchmark systems ranging from individual atoms up to molecules the size of benzene. We validated the accuracy of NES-VMC on first-row atoms, closely matching experimental results, and on a range of small molecules, obtaining highly accurate energies and oscillator strengths comparable to existing best theoretical estimates. We computed the potential energy curves of the lowest excited states of the carbon dimer and identified the states across bond lengths by analyzing their symmetries and spins. The NES-VMC vertical excitation energies matched those obtained using the highly accurate semistochastic heat-bath configuration interaction (SHCI) method to within chemical accuracy for all bond lengths, whereas 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 highly accurate multireference configuration interaction (MR-CI) results. We also considered five challenging systems with low-lying double excitations, including multiple benzene-scale molecules. On all systems where there is good agreement between methods on the vertical excitation energies, the Psiformer was within chemical accuracy across states, including butadiene, where even the ordering of certain states has been disputed for many decades. On tetrazine and cyclopentadienone, where state-of-the-art calculations from just a few years ago were known to be inaccurate, NES-VMC results closely matched recent sophisticated diffusion Monte Carlo (DMC) and complete-active-space third-order perturbation theory (CASPT3) calculations. Finally, we considered the benzene molecule, where NES-VMC combined with the Psiformer ansatz is in substantially better agreement with theoretical best estimates compared with other methods, including neural network ansätze using penalty methods. This both validates the mathematical correctness of our approach and shows that neural networks can accurately represent excited states of molecules right at the current limit of computational approaches.

CONCLUSION
NES-VMC is a parameter-free and mathematically sound variational principle for excited states. Combining it with neural network ansätze enables marked accuracy across a wide range of benchmark problems. The development of an accurate VMC approach to excited states of quantum systems opens many possibilities and substantially expands the scope of applications of neural network wave functions. Although we considered only electronic excitations of molecular systems and neural network ansätze, NES-VMC is applicable to any quantum Hamiltonian and any ansatz, enabling accurate computational studies that could improve our understanding of vibronic couplings, optical bandgaps, nuclear physics, and other challenging problems.