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

  • Artur Panczakiewicz
  • Victor M. AnisimovEmail author
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 13)


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 



Austin model 1


Atomic orbital


Becke 3-term correlation, Lee-Yang-Parr exchange functional


Coupled cluster


Configuration interaction


Constrained expansion molecular orbital


Central processing unit


Density functional theory;


Hartree-Fock method using Pople 6-31G* basis set


Heat of formation


Localized molecular orbital


Local self consistent field


Molecular dynamics


Molecular orbital


Second-order Moller-Plesset perturbation theory


Neglect of diatomic differential overlap


Constant number of particles, pressure, and temperature


Constant number of particles, volume, and energy


Constant number of particles, volume and temperature


Periodic boundary condition


Parametric method 3


Parametric method 5


Quantum mechanics


Random access memory


Spherical boundary potential


Self-consistent field


Variational finite localized molecular orbital approximation


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.FQS PolandKrakowPoland

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