Regularized Alternatives to Conventional Density Fitting: Tikhonov Regularization with Discrete Picard Condition
Year: 2026
Type: preprint
Abstract: Density fitting (DF) reduces the computational cost of correlated electronic-structure methods but can become unstable when the fitting metric contains small eigenvalues or near-linear dependencies. We introduce a set of protocols based on Tikhonov regularization (TR) combined with the Discrete Picard Condition (DPC) to adaptively determine an effective truncation of the auxiliary space in DF-MP2. Truncation indices are selected using either a two-line L-curve fit or local sharp-corner protocols. The TR-DPC approaches are evaluated against conventional DF-MP2 and Cholesky decomposition (CD) across the S22 benchmark set and an AlkB hydrogen-atom-transfer reaction. The three-point sharp-corner methods provide the best overall accuracy among the TR-DPC protocols, while the two-line method is less accurate but more robust for reduced or poorly matched auxiliary spaces. CD provides the closest agreement with conventional DF-MP2; however, for the systems examined here, it generates more Cholesky vectors than the number of functions in the corresponding DF auxiliary basis and is accompanied by greater computational cost. TR-DPC provides a useful alternative by reducing the effective auxiliary representation while maintaining small, often sub-kcal mol⁻¹, errors, providing a balance between accuracy, representation size, and computational cost.
Source: ChemRxiv
Authors: Jose P. Madriaga, G. Andrés Cisneros
Institution: The University of Texas at Dallas
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213559634