The linear scaling semiempirical localSCF method and the variational finite LMO approximation

Artur Panczakiewicz, Victor M. Anisimov

Research output: Chapter in Book/Report/Conference proceedingChapter


When dealing with large biological systems speed determines the utility of the computational method. Therefore in order to bring quantum-mechanical (QM) methods to computational studies of biomolecules it is necessary to significantly reduce their resource requirement. In this light semiempirical QM methods are particularly encouraging because of their modest computational cost combined with potentially high accuracy. However, even semiempirical methods are frequently found to be too demanding for typical biological applications which require extensive conformational sampling. Significant speed up is obtained in the linear scaling LocalSCF method which is based on the variational finite localized molecular orbital (VFL) approximation. The VFL provides an approximate variational solution to the Hartree-Fock-Roothaan equation by seeking the density matrix and energy of the system in the basis of compact molecular orbitals using constrained atomic orbital expansion (CMO). Gradual release of the expansion constraints leads to determination of the theoretically most localized solution under small non-orthogonality of CMOs. Validation tests confirm good agreement of the LocalSCF method with matrix diagonalization results on partial atomic charges, dipole moment, conformational energies, and geometry gradients while the method exhibits low computer memory and CPU time requirements. We observe stable dynamics when using the LocalSCF method.

Original languageEnglish (US)
Title of host publicationChallenges and Advances in Computational Chemistry and Physics
Number of pages29
StatePublished - 2011
Externally publishedYes

Publication series

NameChallenges and Advances in Computational Chemistry and Physics
ISSN (Print)2542-4491
ISSN (Electronic)2542-4483


  • CMO
  • Linear scaling
  • LMO
  • NDDO method
  • Normalization condition
  • Orthogonality condition
  • QM MD
  • SCF method
  • VFL approximation

ASJC Scopus subject areas

  • Computer Science Applications
  • Chemistry (miscellaneous)
  • Physics and Astronomy (miscellaneous)


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