Formulation of an Efficient 𝒪 (M 4)-Scaling Explicitly Correlated MP2-F12 Correction by Combining Numerical Quadrature with Density Fitting and CABS-RI
Lars Urban, Henryk Laqua, Travis H. Thompson, Christian Ochsenfeld
TL;DR
This paper introduces a new computational method that reduces the cost of quantum chemistry calculations by achieving O(M⁴) scaling.
Contribution
A novel hybrid method combining numerical quadrature, density fitting, and CABS-RI to achieve efficient MP2-F12 calculations.
Findings
The new method achieves O(M⁴) scaling for MP2-F12 corrections.
Mean errors for noncovalent interactions are below 0.01 kcal/mol with modest grid sizes.
Speedups of one order of magnitude are achieved for expensive computational steps.
Abstract
We present a novel approach that combines numerical quadrature with density fitting and CABS-RI for the evaluation of exchange-type intermediates in RI-MP2-F12 theory, rigorously reducing the formal and practical scaling of the total correction from O(M5) to O(M4) . Our new hybrid NQ/DF/CABS-RI ansatz is based directly on our previously developed NQ/CABS-RI method for the efficient evaluation of 6c3e integrals [Urban, L.; Laqua, H; Thompson, T. H.; Ochsenfeld, C. J. Chem. Theory Comput. 2024, 20, 3706–3718] and extends this approach to the optimized computation of products of 4c2e integrals. In this framework, the main exchange-type intermediates V , X , and B are reformulated, resulting in more compact expressions, increased shared computations, and fewer CABS-RI insertions. We introduce efficient algorithms that cover all exchange-type contributions, including advantageous…
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Chemical Physics Studies · Mathematical functions and polynomials