Nodal error behind discrepancies between coupled cluster and diffusion Monte Carlo in hydrogen-bonded systems

TL;DR

This study identifies the fixed-node error in diffusion Monte Carlo as the main cause of discrepancies with coupled cluster results in hydrogen-bonded systems, emphasizing CC's reliability as a benchmark.

Contribution

It systematically isolates the fixed-node error as the primary source of differences, guiding future improvements in quantum chemical methods for hydrogen-bonded systems.

Findings

Fixed-node error dominates DMC discrepancies

CC errors are less significant in these systems

CC remains a reliable benchmark for hydrogen-bonded interactions

Abstract

The small magnitude and long-range character of non-covalent interactions pose a significant challenge for computational quantum chemical and electronic-structure methods alike. State-of-the-art coupled cluster (CC) theory and benchmark-grade diffusion Monte Carlo (DMC) are ideally positioned to tackle these problems, but concerning differences between both methods have been reported in numerous studies of the interaction energy of non-covalently bound dimers. Given that the basic theoretical frameworks underpinning both methods are exact in principle, the error must arise from one or several of the approximations required to make the calculations computationally tractable. Here, we carry out a rigorous and systematic examination of the effect of each of these approximations using the acetic acid dimer and water-peptide systems as convenient testing grounds. Thanks to the use of stringently optimized backflow wave functions we are able to find that the significant discrepancies are dominated by the fixed-node error incurred by the Slater-Jastrow DMC result, while errors in the CC calculations do not significantly alter the result. This finding, likely applicable to other hydrogen-bonded systems, helps establish that CC should be regarded as the benchmark for these systems, and can potentially guide the search for pragmatic solutions to the fixed-node problem in the future.