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Idempotency-conserving iteration scheme for the one-electron density matrix.

Dóra Kohalmi¹, Agnes Szabados, Péter R Surján

¹Eötvös University, Department of Theoretical Chemistry, H-1518 Budapest 112, P.O.B. 32, Hungary.

Physical Review Letters

|August 11, 2005

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A new iterative formula for the first-order density matrix (P) in noninteracting N-electron systems ensures trace and idempotency preservation. This method converges to the exact solution, simplifying electronic structure calculations.

Area of Science:

Quantum chemistry
Computational physics
Materials science

Background:

Calculating the first-order density matrix (P) is crucial for electronic structure theory.
Existing methods may require computationally expensive purification steps.
Maintaining properties like trace and idempotency during iteration is challenging.

Purpose of the Study:

To present a novel iterative formula for the first-order density matrix (P).
To ensure the preservation of P's trace and idempotency throughout the iterative process.
To develop an efficient method for electronic structure calculations.

Main Methods:

An iterative formula is developed for the first-order density matrix (P).
The formula inherently preserves the trace and idempotency of P.

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Hermiticity is restored upon convergence of the iteration.

An O(N) procedure is used to obtain the energy for sparse P.

Main Results:

The iterative formula successfully preserves trace and idempotency without purification.
Converged P accurately corresponds to the exact solution, with restored hermiticity.
The O(N) energy calculation is efficient, especially for sparse density matrices.
Illustrative calculations demonstrate the method's validity at tight-binding and Hartree-Fock levels.

Conclusions:

The presented iterative method offers an efficient and accurate approach for electronic structure calculations.
It eliminates the need for density matrix purification steps.
The method is suitable for various computational chemistry and physics applications.