Hylleraas' variational method with orthogonality restrictions.

Area of Science:

• Computational physics
• Quantum chemistry
• Theoretical chemistry

Background:

• Minimizing Hylleraas' functional often involves complex orthogonality restrictions.
• Existing methods for constrained optimization can be computationally intensive.

Purpose of the Study:

• To develop a novel computational technique for minimizing Hylleraas' functional with orthogonality constraints.
• To reduce a constrained problem to an unconstrained one with minimal computational cost.

Main Methods:

• Application of the Asymptotic Projection (AP) method, previously used for Rayleigh's quotient.
• Construction of a modified Hylleraas' functional that automatically satisfies constraints.
• Derivation of equivalence between the original and modified Hamilton operators.

Main Results:

• The AP method provides a unified approach for handling orthogonality restrictions in both Rayleigh's quotient and Hylleraas' functional.
• Demonstration of the method's effectiveness using the electronic parallel polarizability of H2+.
• Analysis of basis set selection for polarizability computations.

Conclusions:

• The proposed computational technique efficiently simplifies constrained minimization problems.
• The AP method offers a versatile and unified framework for various quantum mechanical calculations.
• The study provides valuable insights for accurate polarizability calculations.