Linear-Scaling Techniques in Computational Chemistry and Physics

Volume 13 of the series Challenges and Advances in Computational Chemistry and Physics pp 409-437


The Linear Scaling Semiempirical LocalSCF Method and the Variational Finite LMO Approximation

  • Artur PanczakiewiczAffiliated withFQS Poland
  • , Victor M. AnisimovAffiliated withFQS Poland Email author 

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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.


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