Higher-order Rayleigh-quotient gradient effect on electron correlations.

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Accurate calculation of electron correlation in many-electron systems remains a challenge due to the lack of exact solutions to the Schrödinger equation.
• Standard methods often struggle to fully capture the complex interactions and correlations between electrons.

Purpose of the Study:

• To develop and present a novel method for calculating correlation-induced changes in many-electron systems.
• To improve the accuracy and efficiency of quantum mechanical calculations by addressing limitations of standard residuals.

Main Methods:

• Implementation of a higher-order residual method within the Rayleigh quotient minimization framework.
• Iterative search for lowest eigenpairs in a subspace including the wave function, its gradient, and the higher-order residual.
• Correction of correlation energy components using the higher-order residual.

Main Results:

• Significant improvements in calculation performance, including reduced iterations, faster convergence, and decreased elapsed time.
• Enhanced accuracy in satisfying the correlation virial theorem.
• Demonstrated improvement in electron binding energy and electron localization.

Conclusions:

• The higher-order residual method offers a substantial advancement over standard approaches for studying electron correlation.
• This method leads to more accurate predictions of electron distribution, binding energies, and interelectron interactions.
• The findings pave the way for more precise quantum chemical calculations of complex systems.