Exploring the role of mean-field potentials and short-range wave function behavior in the adiabatic connection

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Investigating Hamiltonians with long-range interactions is crucial for accurate electronic structure calculations.
• Previous work focused on constant one-particle potentials, necessitating further study on potential optimization.

Purpose of the Study:

• To explore Hamiltonian construction with long-range interactions and corrections.
• To examine the impact of optimizing the one-particle potential on adiabatic connections.
• To analyze energy errors and densities in a two-electron system (harmonium).

Main Methods:

• Utilizing a parameter-dependent potential for computational efficiency.
• Analyzing energy errors and densities in a two-electron system (harmonium).
• Employing various confinement potentials and interaction parameters.

Main Results:

• Mean-field potentials improve the expectation value of the physical Hamiltonian but not necessarily system energy within chemical accuracy.
• Density variations in adiabatic connections challenge the assumption that mean fields always improve results.
• Mean fields do not significantly outperform bare potentials when energy errors are within chemical accuracy.

Conclusions:

• Corrections based on short-range wave function behavior are highly effective.
• The distinction between using mean-field or bare potentials diminishes due to effective short-range corrections.
• Potential optimization's impact on adiabatic connections requires careful consideration in quantum system studies.