Completeness of a kinetically balanced Gaussian basis.

Area of Science:

• Quantum Chemistry
• Atomic Physics
• Computational Chemistry

Background:

• Relativistic effects are crucial for accurate descriptions of heavy atoms and ions.
• Gaussian basis sets are widely used in quantum chemistry for approximating wave functions.
• Kinetically balanced basis sets are employed to mitigate errors in relativistic calculations.

Purpose of the Study:

• To investigate the convergence properties of relativistic wave functions for H-like ions.
• To analyze the accuracy of approximations using kinetically balanced even-tempered Gaussian basis sets.
• To determine the dependence of approximation errors on basis set size.

Main Methods:

• Expansion of the exact relativistic wave function in a kinetically balanced even-tempered Gaussian basis.
• Analysis of the error in overlap integrals for both large and small components of the wave function.
• Comparison of the error dependence on basis set size (n) for relativistic and nonrelativistic energy calculations.

Main Results:

• The error in the overlap integral exhibits a dependence of approximately n^(3/2+nu) exp[-pi*sqrt(3/2+nu)*n].
• The error in the energy shows a similar dependence on basis set size (n).
• Relativistic energy errors decay only slightly slower than their nonrelativistic counterparts.

Conclusions:

• Kinetically balanced even-tempered Gaussian basis sets provide a reliable method for approximating relativistic wave functions.
• The convergence rate of the approximation error is well-defined and depends on the basis set size.
• This approach offers a computationally feasible way to obtain accurate relativistic energies for H-like ions.