Deformed explicitly correlated Gaussians.

Area of Science:

• Quantum Chemistry
• Atomic and Molecular Physics
• Cavity Quantum Electrodynamics (QED)

Background:

• Solving light-matter coupled systems requires accurate basis functions.
• Nonspherical potentials present challenges for standard computational methods.
• Cavity QED systems involve complex interactions that demand precise theoretical tools.

Purpose of the Study:

• Introduce and evaluate Deformed Explicitly Correlated Gaussian (DECG) basis functions.
• Demonstrate the analytical tractability of DECG matrix elements.
• Showcase the application of DECGs for systems with nonspherical potentials.

Main Methods:

• Analytical calculation of matrix elements for DECG basis functions.
• Approximation of Coulomb matrix elements using Gaussian expansion.
• Application to the dipole self-interaction term in the Pauli-Fierz Hamiltonian.

Main Results:

• All DECG matrix elements are analytically calculable, except the Coulomb term.
• The Coulomb term can be accurately approximated by a Gaussian expansion.
• DECGs provide accurate solutions for light-matter coupled systems with nonspherical potentials.

Conclusions:

• DECG basis functions are a powerful tool for quantum chemistry and cavity QED.
• Their ability to handle nonspherical potentials is crucial for accurate simulations.
• These functions are necessary for precisely solving complex light-matter interactions.