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Auxiliary basis sets for density-fitted correlated wavefunction calculations: weighted core-valence and ECP basis

Christof Hättig1, Gunnar Schmitz, Jörg Kossmann

  • 1Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany. christof.haettig@rub.de

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Summary

Optimized auxiliary basis sets for density-fitting in electronic structure calculations significantly reduce errors for post-d elements. These sets accelerate calculations while maintaining high accuracy for Møller-Plesset perturbation theory (MP2).

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Accurate electronic structure calculations are crucial for understanding molecular properties.
  • The resolution-of-the-identity (RI) or density-fitting (DF) approximation accelerates calculations by approximating two-electron integrals.
  • Efficient RI/DF methods are needed for large systems and heavier elements.

Purpose of the Study:

  • To develop and optimize auxiliary basis sets for RI/DF approximation in second-order Møller-Plesset perturbation theory (MP2).
  • To ensure density-fitting errors are negligible compared to one-electron basis set errors for post-d elements.
  • To improve the efficiency and accuracy of electronic structure calculations for elements Ga-Kr, In-Xe, and Tl-Rn.

Main Methods:

  • Optimization of auxiliary basis sets for RI/DF approximation.
  • Calculation of correlation energy at the MP2 level for a test set of 80 molecules.
  • Estimation of basis set limit of correlation energy.
  • Evaluation of density-fitting and one-electron basis set errors.

Main Results:

  • Optimized auxiliary basis sets were developed for post-d elements (Ga-Kr, In-Xe, Tl-Rn).
  • Density-fitting errors were found to be negligible compared to one-electron basis set errors.
  • Auxiliary basis sets are 2-6 times larger than one-electron basis sets.
  • MP2 calculations showed speed-ups of 10-1000 times in integral evaluation.
  • Density-fitting errors in correlation energy are at least 100 times smaller than one-electron basis set errors (1-100 μH per atom).

Conclusions:

  • The developed auxiliary basis sets enable highly accurate and efficient RI/DF-MP2 calculations.
  • These optimized sets significantly reduce computational cost for electronic structure calculations involving heavier elements.
  • The findings pave the way for more extensive studies of systems containing post-d elements.