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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

Numerically stable optimized effective potential method with balanced Gaussian basis sets.

Andreas Hesselmann¹, Andreas W Götz, Fabio Della Sala

¹Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstrasse 3, D-91058 Erlangen, Germany.

The Journal of Chemical Physics

|August 11, 2007

Summary

A new numerically stable optimized effective potential (OEP) method using Gaussian basis sets is introduced. This approach ensures accurate calculations for exact exchange Kohn-Sham methods and enables novel density functional development.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Theoretical Physics

Background:

Developing numerically stable optimized effective potential (OEP) methods with Gaussian basis sets has been a long-standing challenge.
Previous OEP calculations often lacked numerical stability and may have produced inaccurate total energies.

Purpose of the Study:

To present a numerically stable and analytical approach for optimized effective potential (OEP) methods using Gaussian basis sets.
To enable the development and application of novel orbital-dependent exchange-correlation functionals.

Main Methods:

Introduced an exact exchange OEP method with a construction and balancing scheme for auxiliary and orbital Gaussian basis sets.
Developed a purely analytical method that scales efficiently and does not require numerical grids.
Ensured proper representation of the exact exchange Kohn-Sham method.

Main Results:

The presented method is numerically stable and straightforward to implement.
The approach scales comparably to Hartree-Fock and B3LYP methods.
Demonstrated the crucial role of the Kohn-Sham orbital spectrum's continuum part for stability.

Conclusions:

The developed OEP approach overcomes previous limitations in numerical stability for Gaussian basis sets.
Adequate convergence of orbital basis sets with respect to auxiliary basis sets is mandatory for accurate OEP calculations.
This work paves the way for advanced orbital-dependent density functional development.