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

Chapter
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 13)

Abstract

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.

Keywords

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

Abbreviations

AM1

Austin model 1

AO

Atomic orbital

B3LYP

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

CC

Coupled cluster

CI

Configuration interaction

CMO

Constrained expansion molecular orbital

CPU

Central processing unit

DFT

Density functional theory;

HF/6-31G*

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

HOF

Heat of formation

LMO

Localized molecular orbital

LocalSCF

Local self consistent field

MD

Molecular dynamics

MO

Molecular orbital

MP2

Second-order Moller-Plesset perturbation theory

NDDO

Neglect of diatomic differential overlap

NPT

Constant number of particles, pressure, and temperature

NVE

Constant number of particles, volume, and energy

NVT

Constant number of particles, volume and temperature

PBC

Periodic boundary condition

PM3

Parametric method 3

PM5

Parametric method 5

QM

Quantum mechanics

RAM

Random access memory

SBP

Spherical boundary potential

SCF

Self-consistent field

VFL

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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