发表机构
North Carolina State University; Oak Ridge National Laboratory（北卡罗来纳州立大学; 橡树岭国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究评估基于Psiformer的神经网络变分蒙特卡洛方法在预测过渡金属氢化物键解离能上的表现，引入外推方案减小误差，证明其对主族和早期过渡金属氢化物具有竞争力，并将晚期过渡金属氢化物作为未来基准。
AI 中文摘要
过渡金属氢化物（TM-H）键解离能（BDEs）的准确预测仍具挑战性，原因在于强电子关联、相对论效应和核量子贡献。本文评估了基于Psiformer ansatz的神经网络变分蒙特卡洛（NN-VMC）方法在复杂度递增的系统（LiH、OH、TiH和NiH）上的表现，并将其与CCSDT(Q)/CBS以及现有理论和实验数据进行比较。在整个研究过程中，NN-VMC和从头计算均采用共同的ccECP哈密顿量，以实现可行且一致的比较。为减少有限训练误差，我们引入了互补的零方差和无限步外推方案。对于LiH和OH体系，NN-VMC得到的总能量与CBS外推的从头计算结果相差在亚毫哈特里以内，BDE差异保持在2σ以内。对于Ti和TiH，训练结束时的变分NN-VMC能量已与CCSD(T)/CBS一致，而训练后的外推系统地缩小了与CCSDT(Q)/CBS结果的差距。相比之下，NiH对波函数表达能力提出了严格测试，增加NN波函数ansatz中行列式的数量可提高恢复的关联能。NiH BDE的比较表明，尽管现有理论预测分为明显的高和低BDE两组，但可用实验数据的广泛分散性阻碍了对最准确理论方法的明确评估。这项工作表明，采用ccECP哈密顿量的NN-VMC为定量预测主族和早期过渡金属氢化物能量提供了有竞争力的框架，同时将晚期过渡金属氢化物确定为未来神经网络波函数和电子结构理论发展的重要基准。
英文摘要
Accurate prediction of transition-metal hydride (TM-H) bond dissociation energies (BDEs) remains challenging because of strong electron correlation, relativistic effects, and nuclear quantum contributions. Here, we assess the performance of neural-network variational Monte Carlo (NN-VMC) based on the Psiformer ansatz for systems with increasing complexity (LiH, OH, TiH and NiH), and compare it against CCSDT(Q)/CBS as well as available theoretical and experimental data. Throughout this study, both NN-VMC and ab initio calculations employ a common ccECP Hamiltonian to enable tractable and consistent comparisons. To reduce finite-training errors, we introduce complementary zero-variance and infinite-step extrapolation schemes. For LiH and OH systems, NN-VMC yields total energies that differ within sub-milli Hartree compared to CBS extrapolated ab initio results and the BDE differences remain under 2$σ$. In case of Ti and TiH, the variational NN-VMC energies at the end of training are already consistent with CCSD(T)/CBS, while post-training extrapolation systematically closes the gap towards the CCSDT(Q)/CBS results. In contrast, NiH provides a stringent test of wavefunction expressivity, where increasing the number of determinants in NN-wavefunction ansatz improves the recovered correlation energy. The comparison of NiH BDE reveals that, while the existing theoretical predictions cluster into distinct high and low BDE groups, the broad scatter in available experimental data prevents a definitive assessment of the most accurate theoretical approach. This work demonstrates that NN-VMC with ccECPs Hamiltonian provides a competitive framework for quantitative prediction of main-group and early TM-H energetics, while identifying late TM-H as an important benchmark for future developments in neural-network wavefunctions and electronic structure theory.
