Diagonalization-free self-consistent field approach with localized molecular orbitals

• Published in: Theoretical chemistry accounts 2021-11, Vol.140 (11), Article 152
• Main Authors: Villalobos-Castro, J., Köster, A. M.
• Format: Article
• Language: English
• Subjects: 20th deMon Developers Workshop; Algorithms; Alkanes; Atomic/Molecular Structure and Spectra; Chemistry; Chemistry and Materials Science; Convergence; Density functional theory; Graphene; Inorganic Chemistry; Mathematical analysis; Molecular orbitals; Organic Chemistry; Physical Chemistry; Regular Article; Self consistent fields; Theoretical and Computational Chemistry
• ISSN: 1432-881X; 1432-2234
• DOI: 10.1007/s00214-021-02850-w

A pseudo-diagonalization (PD) algorithm based on the annihilation of the occupied-virtual Kohn-Sham matrix elements is developed in the framework of auxiliary density functional theory (ADFT). The working equations are presented, and their parallel implementation in deMon2k is discussed. To avoid any matrix diagonalization in the PD ADFT self-consistent field (SCF) calculations, the pseudo-diagonalization of the Kohn-Sham matrix is accompanied by the iterative density fitting with the MINRES approach. In order to explore the sparsity of the ADFT Kohn-Sham matrix, localized molecular orbitals (LMOs) are used. Our analysis of the PD ADFT SCF shows that the LMOs remain localized throughout the SCF. Surprisingly, we found this behavior not only for naturally localizable systems such as alkane chains and water clusters but also for less localizable systems such as fullerenes and hydrogen saturated graphene sheets. Despite the very different extensions of the converged molecular orbitals in PD and Roothaan-Hall ADFT SCF calculations, both methods yield, within the given SCF tolerance, nearly identical converged SCF energies.