Acceleration of self-consistent-field convergence by combining conventional diagonalization and a...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Self-consistent-field (SCF) calculations are fundamental in quantum chemistry.
• Calculating the density matrix is a critical step in SCF procedures.
• Existing methods for density matrix calculation have limitations in convergence speed and robustness.

Purpose of the Study:

• To develop a new computational scheme for obtaining the density matrix in SCF calculations.
• To combine the strengths of conventional matrix diagonalization and diagonalization-free algorithms.
• To improve the efficiency and robustness of SCF calculations.

Main Methods:

• A hybrid scheme combining conventional matrix diagonalization and a diagonalization-free algorithm was developed.
• The new scheme obtains the density matrix for the next SCF iteration from the current Fock matrix.
• The method was implemented in one- and two-component SCF procedures within the TURBOMOLE program system.

Main Results:

• The combined scheme leverages the rapid convergence of the diagonalization-free algorithm near self-consistency.
• It also utilizes the robust convergence of conventional matrix diagonalization for density matrices further from self-consistency.
• Typically, the number of iterations is reduced by approximately 10%, with larger savings in slowly converging cases.

Conclusions:

• The new hybrid scheme offers an efficient and robust approach for density matrix calculations in SCF procedures.
• This method effectively reduces the number of iterations required for convergence.
• The implementation in TURBOMOLE demonstrates practical applicability and potential for significant computational savings in quantum chemistry.