Accelerating geometry optimization via Grassmann-DIIS extrapolation

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Electronic Structure Theory

Background:

• Self-consistent field (SCF) calculations are computationally intensive, forming a bottleneck in quantum chemistry.
• Efficient geometry optimization is crucial for accurate molecular simulations.

Purpose of the Study:

• To develop an improved method for generating initial density matrices in SCF calculations.
• To accelerate geometry optimization by reducing the number of SCF iterations.

Main Methods:

• Developed a Grassmann extrapolation framework combined with direct inversion in the iterative subspace (G-Ext-DIIS).
• Exploited the geometric structure of density matrices on the nonlinear Grassmann manifold.
• Preserved fundamental physical constraints of the density matrix during extrapolation.

Main Results:

• G-Ext-DIIS consistently reduced the total number of SCF iterations during geometry optimization.
• Achieved significant reductions (20-30%) in SCF iterations for flexible cluster systems.
• Demonstrated negligible computational overhead compared to a single SCF iteration.

Conclusions:

• G-Ext-DIIS is an efficient, transferable, and inexpensive strategy for accelerating geometry optimization.
• The method shows promise as a default SCF initialization scheme for quantum chemistry software.
• Reduced computational cost enhances large-scale quantum chemical simulations.