A variance-based optimization for determining ground and excited N-electron wave functions within the doubly occupied...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Accurate determination of N-electron system wave functions is crucial for understanding molecular properties and electronic spectra.
• Traditional methods for solving the Schrödinger equation can be computationally intensive, especially for larger systems.
• Configuration interaction (CI) methods offer a systematic way to improve wave function accuracy.

Purpose of the Study:

• To explore the application of simulated annealing (SA) for optimizing wave functions within the doubly occupied configuration interaction (CI) framework.
• To investigate the ability of SA to determine both ground and excited electronic states by minimizing energy variance.
• To compare the performance of SA-based methods with traditional energy minimization approaches and full CI.

Main Methods:

• Utilized the simulated annealing technique to minimize the energy variance of a Hamiltonian for N-electron systems.
• Employed the doubly occupied configuration interaction (CI) framework.
• Performed calculations using both restricted and unrestricted treatments.
• Compared results with traditional energy minimization and full configuration interaction (FCI) methods.

Main Results:

• Simulated annealing successfully determined wave functions for ground and excited states by minimizing energy variance.
• The method demonstrated comparable performance to traditional energy minimization techniques.
• Analysis of energy, spin, and wave function characteristics provided insights into the efficacy of SA-based approaches.
• SA offers a viable alternative for electronic structure calculations, particularly for determining excited states.

Conclusions:

• Simulated annealing is an effective technique for optimizing N-electron wave functions within the doubly occupied CI framework.
• Minimizing energy variance provides a robust route to identifying both ground and excited electronic states.
• The SA approach presents a promising computational tool for electronic structure research, complementing existing methodologies.