Distribution of r·p in atomic systems.

Area of Science:

• Quantum Chemistry
• Atomic Physics
• Computational Chemistry

Background:

• Understanding electron behavior in atoms is fundamental to chemistry and physics.
• Existing spectroscopic techniques like X-ray crystallography and Compton spectroscopy provide complementary, but incomplete, information about electron states.
• The momentum distribution (posmom density) offers unique insights into electron dynamics.

Purpose of the Study:

• To derive formulas for calculating the probability distribution of electron momentum (posmom) in atoms.
• To investigate the posmom density for electrons in the ground states of the 36 lightest atoms (H-Kr).
• To develop an empirical model for the contribution of individual atomic orbitals to the total posmom density.

Main Methods:

• Formulas were developed for computing the posmom probability distribution.
• Electronic wave functions were expanded using a single-particle Gaussian basis set.
• The posmom density, S(s), was studied for the ground states of atoms from H to Kr.
• An empirical model was constructed to represent the contribution of each atomic orbital to S(s).

Main Results:

• Formulas for calculating atomic posmom distributions were successfully presented.
• The posmom density, S(s), was analyzed for the ground states of 36 light atoms.
• An empirical model was established to quantify the contribution of atomic orbitals to the posmom density.

Conclusions:

• The posmom density offers a novel perspective on electron trajectories within atoms.
• This work provides a theoretical foundation and predictions for future experimental validation.
• The findings complement existing spectroscopic methods, enhancing our understanding of quantum mechanical electron behavior.