Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians

Area of Science:

• Computational Chemistry
• Quantum Chemistry

Background:

• Drachmann's regularization is crucial for relativistic corrections in molecular systems.
• Analytic matrix elements for 1/rix1/rjy operators with explicitly correlated Gaussians (fECGs) were previously unknown, hindering calculations.

Purpose of the Study:

• To implement Drachmann's regularization for floating explicitly correlated Gaussians (fECGs).
• To overcome the challenge of unknown analytic matrix elements for specific operators in molecular systems.

Main Methods:

• Approximating one 1/r factor in 1/rix1/rjy operators with a linear combination of Gaussians.
• Developing a numerical approach for calculable integrals with fECGs.

Main Results:

• The numerical approach provides precise and robust calculations for various molecular systems and configurations.
• Enables automated evaluation of high-precision relativistic corrections over potential energy surfaces.
• Facilitates matrix representation of the electronic Hamiltonian's square for energy and time-dependent computations.

Conclusions:

• The developed method allows for accurate relativistic corrections in molecular systems using fECGs.
• Opens new avenues for high-precision quantum chemistry calculations, including energy lower-bound and time-dependent studies.