Grassmann extrapolation via direct inversion in the iterative subspace

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Accurate density matrix extrapolation is crucial for efficient electronic structure calculations.
• Existing methods face challenges in preserving geometric structure and physical constraints.
• Direct extrapolation methods often require parameter tuning or lack robustness.

Purpose of the Study:

• To develop a novel, robust, and efficient method for density matrix extrapolation in electronic structure calculations.
• To combine the Grassmann manifold framework with direct inversion in the iterative subspace (DIIS) for enhanced accuracy.
• To overcome limitations of existing extrapolation techniques, such as parameter dependence and numerical instability.

Main Methods:

• Introduced the Grassmann extrapolation with direct inversion in the iterative subspace (G-Ext-DIIS) method.
• Utilized Coulomb, overlap, and core Hamiltonian matrix descriptors for extrapolation.
• Evaluated G-Ext-DIIS on alanine dipeptide and its zwitterionic form using various basis sets (6-311++G(d,p), aug-cc-pVTZ).

Main Results:

• G-Ext-DIIS achieved sub-millihartree accuracy using overlap or core Hamiltonian descriptors.
• The method demonstrated superior accuracy, variational consistency, and reliability compared to direct extrapolation and Löwdin extrapolation.
• G-Ext-DIIS showed robustness and computational efficiency, independent of descriptor dimensionality, system size, and basis set.

Conclusions:

• G-Ext-DIIS provides a robust, efficient, and transferable framework for constructing accurate density matrices.
• The method eliminates the need for regularization parameter tuning, unlike Tikhonov-regularized G-Ext.
• G-Ext-DIIS shows significant potential for applications in geometry optimization and ab initio molecular dynamics simulations.