# On Achieving High Accuracy in Quantum Chemical Calculations of 3d Transition Metal Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules

## TL;DR

This study demonstrates that phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) achieves superior accuracy in calculating bond dissociation energies of 3d transition metal diatomics compared to DFT and CCSD(T), showing promise as a benchmark method.

## Contribution

The paper provides the first comprehensive comparison of ph-AFQMC with DFT and CCSD(T) for 3d transition metal diatomics, highlighting its higher accuracy and consistency.

## Key findings

- ph-AFQMC has a mean absolute error of 1.4 kcal/mol, outperforming DFT and CCSD(T).
- ph-AFQMC shows robust agreement with experimental data across 41 molecules.
- Other methods exhibit larger errors, with some exceeding 17 kcal/mol.

## Abstract

The bond dissociation energies of a set of 44 3d transition metal-containing diatomics are computed with phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing a correlated sampling technique. We investigate molecules with H, N, O, F, Cl, and S ligands, including those in the 3dMLBE20 database first compiled by Truhlar and co-workers with calculated and experimental values that have since been revised by various groups. In order to make a direct comparison of the accuracy of our ph-AFQMC calculations with previously published results from 10 DFT functionals, CCSD(T), and icMR-CCSD(T), we establish an objective selection protocol which utilizes the most recent experimental results except for a few cases with well-specified discrepancies. With the remaining set of 41 molecules, we find that ph-AFQMC gives robust agreement with experiment superior to that of all other methods, with a mean absolute error (MAE) of 1.4(4) kcal/mol and maximum error of 3(3) kcal/mol (parenthesis account for reported experimental uncertainties and the statistical errors of our ph-AFQMC calculations). In comparison, CCSD(T) and B97, the best performing DFT functional considered here, have MAEs of 2.8 and 3.7 kcal/mol, respectively, and maximum errors in excess of 17 kcal/mol for both methods. While a larger and more diverse data set would be required to demonstrate that ph-AFQMC is truly a benchmark method for transition metal systems, our results indicate that the method has tremendous potential, exhibiting unprecedented consistency and accuracy compared to other approximate quantum chemical approaches.