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A Schwarz inequality for complex basis function methods in non-Hermitian quantum chemistry.

Travis H Thompson1, Christian Ochsenfeld1, Thomas-C Jagau1

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Researchers developed a new Schwarz bound for non-Hermitian quantum-chemical calculations. This method efficiently screens complex-scaled two-electron integrals, reducing computational scaling for molecular metastable states.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Non-Hermitian methods treat molecular metastable states using L^2-integrable wave functions with complex energies.
  • Efficient upper bounds for electron-repulsion integrals in complex-scaled methods were previously unavailable due to non-Hermiticity complications.

Purpose of the Study:

  • Introduce a generalization of the Schwarz bound for non-Hermitian quantum-chemical calculations.
  • Enable efficient integral screening procedures by estimating sparsity in complex-scaled two-electron integral tensors.

Main Methods:

  • Generalization of the Schwarz bound for complex-scaled basis functions.
  • Incorporation of a screening algorithm based on the new Schwarz bound into existing integral code.
  • Application in non-Hermitian Hartree-Fock calculations.

Main Results:

  • The new bound rigorously and inexpensively estimates sparsity in the complex-scaled two-electron integral tensor.
  • The screening algorithm effectively reduces computational cost.
  • Demonstrated effectiveness in calculations of static field ionization for a molecular complex.

Conclusions:

  • The developed Schwarz bound is crucial for efficient computational scaling in non-Hermitian quantum chemistry.
  • This advancement facilitates the study of molecular metastable states.
  • The screening procedure is validated through practical computational examples.