Regularized Alternatives to Conventional Density Fitting: Tikhonov Regularization with Discrete Picard Condition
- 1Department of Chemistry and Biochemistry
- 2The University of Texas at Dallas
- 3Department of Physics
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.
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BibTeX
@misc{madriaga2026regularized,
title = {{Regularized Alternatives to Conventional Density Fitting: Tikhonov Regularization with Discrete Picard Condition}},
author = {Jose P. Madriaga and G. Andrés Cisneros},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15007787/v2},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007787/v2},
note = {CC BY},
}
RIS
TY - UNPB
TI - Regularized Alternatives to Conventional Density Fitting: Tikhonov Regularization with Discrete Picard Condition
AU - Jose P. Madriaga
AU - G. Andrés Cisneros
PY - 2026
DA - 2026/09/17
PB - ChemRxiv
DO - 10.26434/chemrxiv.15007787/v2
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007787/v2
AB - 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.
ER -