# Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State

Source: [Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State](<https://www.sota2.com/research/paper/69b8e01b0636e5bf4afbeb40>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-29T05:00:05.519Z

Authors: Nicholas Gao, Till Grutschus, Frank No\\'e, Stephan G\\"unnemann

Published: 2026-03-15T17:51:16.000Z

## Abstract

Neural-network wave functions in Variational Monte Carlo (VMC) have achieved great success in accurately representing both ground and excited states. However, achieving sufficient numerical accuracy in state overlaps requires increasing the number of Monte Carlo samples, and consequently the computational cost, with the number of states. We present a nearly constant sample-size approach, Multi-State Importance Sampling (MSIS), that leverages samples from all states to estimate pairwise overlap. To efficiently evaluate all states for all samples, we introduce Excited Pfaffians. Inspired by Hartree-Fock, this architecture represents many states within a single neural network. Excited Pfaffians also serve as generalized wave functions, allowing a single model to represent multi-state potential energy surfaces. On the carbon dimer, we match the $O(N\_s^4)$-scaling natural excited states while training $\>200\\times$ faster and modeling 50% more states. Our favorable scaling enables us to be the first to use neural networks to find all distinct energy levels of the beryllium atom. Finally, we demonstrate that a single wave function can represent excited states across various molecules.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Atomic and excitation energy prediction on Beryllium NIST ASD](<https://www.sota2.com/research/sota/atomic-and-excitation-energy-prediction-on-beryllium-nist-asd.md>): Atomic and excitation energy prediction; Beryllium NIST ASD; Absolute Energy (Ha): -14.37377.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.14515>)

[PDF](<https://arxiv.org/pdf/2603.14515.pdf>)