Quasirelativistic theory. II. Theory at matrix level.

Area of Science:

• Quantum Chemistry
• Relativistic Quantum Mechanics

Background:

• The Dirac operator is fundamental in relativistic quantum mechanics, describing electron behavior.
• Existing quasirelativistic methods often involve approximations or expansion parameters.
• Accurate treatment of electronic eigenstates is crucial for molecular property calculations.

Purpose of the Study:

• To develop a transformation from the Dirac operator to a quasirelativistic Hamiltonian.
• To derive an exact identity for the transformation matrix X.
• To investigate efficient iterative schemes for constructing X and analyze existing methods.

Main Methods:

• Matrix representation of the Dirac operator in a kinetically balanced basis.
• Derivation of an exact identity for the transformation matrix X.
• Development and numerical comparison of noniterative and iterative (linear and quadratic convergence) schemes for constructing X.

Main Results:

• The transformation yields a quasirelativistic Hamiltonian with the same electronic eigenstates as the Dirac matrix.
• An exact identity for matrix X is derived.
• Three distinct iterative schemes demonstrate convergence within 3-4 iterations, even in unfavorable cases.
• The theory is presented for both non-Hermitian and Hermitian quasirelativistic Hamiltonians.

Conclusions:

• The developed transformation provides an accurate quasirelativistic Hamiltonian for electronic structure calculations.
• The derived iterative schemes offer efficient and robust methods for constructing the transformation matrix.
• This work critically analyzes and contextualizes existing quasirelativistic matrix-level approaches within a unified theoretical framework.