Propagators in Quantum Chemistry

Anna Diaz Farias, Shalith Chamantha, Jonathan M. Waldrop +3 more

Quantum chemistry relies on numerical approximations. Establishing the correctness and limits of these approximations traditionally requires laborious benchmarking. We introduce a more direct approach, quantum chemistry uncertainty propagation (QCUP), and apply it to a full iterative self-consistent field (SCF) calculation. QCUP-SCF estimates uncertainty from floating-point arithmetic, primitive-Gaussian screening, and incomplete SCF convergence, and propagates it to the final energy and density. Across all systems tested, predictions are typically within 1 kcal/mol compared to analytic error bars and within an order of magnitude of the true error ─ enough to establish significant figures and support runtime decision making. We also show how thresholded-affine forms improve on interval bounds by exploiting guaranteed error cancellation. This is, to our knowledge, the first end-to-end forward uncertainty quantification demonstration for an iterative ab initio method, and the first applied to both energy and wave function.

Albino Hernández-Galeana, J. M. Rivera-Rebolledo, José Luis López-Bonilla +1 more

Hinne Hettema

Matthew K. Matlock, Na Le Dang, S. Joshua Swamidass

quantum mechanics calculations with learned estimators. This raises questions about the representability of complex quantum chemical systems with neural networks. Can local-variable models efficiently approximate nonlocal quantum chemical features? Here, we find that convolutional architectures, those that only aggregate information locally, cannot efficiently represent aromaticity and conjugation in large systems. They cannot represent long-range nonlocality known to be important in quantum chemistry. This study uses aromatic and conjugated systems computed from molecule graphs, though reproducing quantum simulations is the ultimate goal. This task, by definition, is both computable and known to be important to chemistry. The failure of convolutional architectures on this focused task calls into question their use in modeling quantum mechanics. To remedy this heretofore unrecognized deficiency, we introduce a new architecture that propagates information back and forth in waves of nonlinear computation. This architecture is still a local-variable model, and it is both computationally and representationally efficient, processing molecules in sublinear time with far fewer parameters than convolutional networks. Wave-like propagation models aromatic and conjugated systems with high accuracy, and even models the impact of small structural changes on large molecules. This new architecture demonstrates that some nonlocal features of quantum chemistry can be efficiently represented in local variable models.

Ángel S. Sanz

Perhaps because of the popularity that trajectory-based methodologies have always had in Chemistry and the important role they have played, Bohmian mechanics has been increasingly accepted within this community, particularly in those areas of the theoretical chemistry based on quantum mechanics, e.g., quantum chemistry, chemical physics, or physical chemistry. From a historical perspective, this evolution is remarkably interesting, particularly when the scarce applications of Madelung's former hydrodynamical formulation, dating back to the late 1960s and the 1970s, are compared with the many different applications available at present. As also happens with classical methodologies, Bohmian trajectories are essentially used to described and analyze the evolution of chemical systems, to design and implement new computational propagation techniques, or a combination of both. In the first case, Bohmian trajectories have the advantage that they avoid invoking typical quantum-classical correspondence to interpret the corresponding phenomenon or process, while in the second case quantum-mechanical effects appear by themselves, without the necessity to include artificially quantization conditions. Rather than providing an exhaustive revision and analysis of all these applications (excellent monographs on the issue are available in the literature for the interested reader, which can be consulted in the bibliography here supplied), this Chapter has been prepared in a way that it may serve the reader to acquire a general view (or impression) on how Bohmian mechanics has permeated the different traditional levels or pathways to approach molecular systems in Chemistry: electronic structure, molecular dynamics and statistical mechanics. This is done with the aid of some illustrative examples -- theoretical developments in some cases and numerical simulations in other cases.

Ken–ichi Fukui, Bernard Pullman