Three decades of quantum science: how quantum chemistry transformed thermochemical database generation for benchmarking DFT and machine learning

In celebration of the United Nations’ declaration of 2025 as the International Year of Quantum Science and Technology, marking 100 years since the development of quantum mechanics, this review highlights how accurate quantum mechanical calculations have transformed gas-phase thermochemistry. In particular, the developments of high-level composite ab initio methods over the past 30 years enable the calculations of thermochemical properties with confident chemical accuracy (i.e. with 95% confidence intervals ≤1 kcal mol⁻¹) for molecules with up to 12 non-hydrogen atoms. Lower-level composite ab initio methods can be applied to molecules containing up to ~50 nonhydrogen atoms; however, they cannot achieve confident chemical accuracy in terms of 95% confidence intervals. Over the past three decades, hundreds of composite ab initio methods have been developed, covering different theoretical frameworks, levels of accuracy and computational costs. To guide users in selecting an appropriate composite ab initio method for a given system size and level of accuracy, we present a general approach for categorising the accuracy of these methods. This approach places composite ab initio methods on four rungs of Jacob’s Ladder. Lower rungs offer less accuracy but are applicable to larger systems, and higher rungs offer greater accuracy but are applicable to smaller systems. Each consecutive rung of this ladder represents an improvement in the treatment of the one-particle space, n-particle space, or both, leading toward the exact solution of the relativistic Schrödinger equation. The Jacob’s Ladder of composite ab initio methods can be considered as an extension to the Jacob’s Ladder of density functional theory (DFT), which leads from ‘Hartree Hell’ to the ‘Heaven’ of double-hybrid DFT methods.