Lower Bounds for Nonrelativistic Atomic Energies

Area of Science:

• Quantum Chemistry
• Atomic Physics
• Computational Physics

Background:

• Accurate calculation of ground-state energies is crucial in quantum chemistry.
• Existing lower bound methods often lack the required precision for complex atomic systems.
• Explicitly correlated basis sets offer highly accurate upper bounds.

Purpose of the Study:

• To further develop and apply a novel lower bound theory for Coulombic problems.
• To achieve highly accurate ground-state energy calculations for two- and three-electron atoms.
• To assess the viability of the refined method for quantum chemistry applications.

Main Methods:

• Implementation of a developed lower bound theory using explicitly correlated many-particle basis sets of Gaussian type.
• Application to calculate ground-state energies of Helium, Li+, H-, and Lithium atoms.
• Further development of explicitly correlated Gaussians for variance computation and necessary modifications.

Main Results:

• Computed lower bounds achieved submilli-Hartree precision (parts per million relative).
• The method yielded the best lower bounds ever obtained for the Lithium atom.
• The obtained lower bounds are orders of magnitude tighter than those from other lower bound methods.

Conclusions:

• The refined lower bound theory is a viable method for quantum chemistry applications.
• The computed bounds, while not yet matching upper bounds, demonstrate significant improvement.
• Wave function optimization is critical for both solving the lower bound problem and validating the theory.