Toward Predictive Hydride Bond Energetics with Neural-Network Wavefunctions

Abstract

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.