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

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.