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