Local effective potential theory: nonuniqueness of potential and wave function.

Area of Science:

• Quantum chemistry
• Computational physics
• Density functional theory

Background:

• Local effective potential energy theories like Hohenberg-Kohn-Sham density functional theory (HKS-DFT) map electronic systems to noninteracting models.
• These models yield total energy and ionization potentials, crucial for understanding electronic structure.

Purpose of the Study:

• To investigate the nonuniqueness of local effective potential energy functions in mapping ground and excited states.
• To explore the nonuniqueness of model system wave functions when mapping to an excited state.

Main Methods:

• Utilizing quantal density functional theory (Q-DFT) to analyze the nonuniqueness of potential energy functions.
• Constructing model systems with configurations distinct from the interacting system.
• Examining the exactly solvable Hooke's atom for concrete examples.

Main Results:

• An infinite number of local potential energy functions can generate both ground and excited state densities.
• The differences between these potentials are solely in their correlation-kinetic contributions.
• Nonuniqueness of the model system wave function exists when mapping to an excited state.

Conclusions:

• The nonuniqueness of potentials for excited states confirms that ground-state HKS-DFT theorems cannot be generalized.
• Correlation-kinetic effects are responsible for the lack of unique theorems for excited states.
• Different wave functions can yield the same density, highlighting the nonuniqueness in excited state mappings.