An improved DIIS method using a versatile residual matrix to accelerate SCF starting from a crude guess.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Self-consistent field (SCF) calculations are fundamental in quantum chemistry for determining molecular electronic structure.
• Pulay's Direct Inversion in Iterative Subspace (CDIIS) is an effective SCF acceleration technique, but its performance depends on a good initial guess.
• Minimizing the commutator of Fock and density matrices is the standard error metric in CDIIS.

Purpose of the Study:

• To introduce and evaluate a novel SCF acceleration technique, Residual Direct Inversion in Iterative Subspace (RDIIS).
• To compare the performance of RDIIS against established methods like CDIIS and Second-Order SCF (SOSCF).
• To demonstrate RDIIS's robustness and efficiency, particularly with challenging initial guesses.

Main Methods:

• Development of RDIIS, utilizing the energy functional's gradient (residual) as the error matrix.
• Implementation of RDIIS within the GAMESS computational chemistry package.
• Comparative analysis of RDIIS, CDIIS, and SOSCF using various molecules and crude initial guesses.

Main Results:

• RDIIS demonstrates stable and efficient acceleration of SCF convergence.
• The RDIIS method shows considerable independence from the subspace size.
• Linear coefficients in RDIIS concentrate proportionally on Fock matrices near the current iteration, enhancing stability.

Conclusions:

• RDIIS presents a viable and effective alternative for accelerating SCF calculations.
• The method's robustness with poor initial guesses and its stability make it a valuable tool in computational chemistry.
• RDIIS offers improved convergence properties compared to traditional methods, especially in challenging computational scenarios.