Linear-scaling method

The localized nature of the atomic basis set makes it possible to implement a linear-scaling TB algoritluu, i.e. a TB method that scales linearly with the number of electrons simulated [17]. (For more infonnation on linear scaling methods, see section B3.2.3.3.)... 

Gain G 2000 Large-scale electronic structure calculations using linear scaling methods Status Solidi B 217 231... 

The problem with most quantum mechanical methods is that they scale badly. This means that, for instance, a calculation for twice as large a molecule does not require twice as much computer time and resources (this would be linear scaling), but rather 2" times as much, where n varies between about 3 for DFT calculations to 4 for Hartree-Fock and very large numbers for ab-initio techniques with explicit treatment of electron correlation. Thus, the size of the molecules that we can treat with conventional methods is limited. Linear scaling methods have been developed for ab-initio, DFT and semi-empirical methods, but only the latter are currently able to treat complete enzymes. There are two different approaches available. 

Apart from the question of linear scaling methods, we may employ the so-constructed orbitals for studying weakly interacting complexes. Of course, usual functionals do not include the important dispersion terms, but such an approach remains effective to study induction in large assemblies of molecules and, as we will see, for extracting monomer properties and interaction-induced changes of these. 

Ochsenfeld C, Kussmann J, Lambrecht DS (2007) Linear-scaling methods in quantum chemistry. In Lipkowitz KB, Cundari TR (ed) Rev Comp Chem 23(1), VCH, New York... 

Keywords Ribozyme catalysis, multiscale simulation, linear-scaling method, QM/MM, DFT... 

Vol. 23, K. B. Lipkowitz and T. R. Cundari, Eds., Wiley, New York, 2006. Linear Scaling Methods in Quantum Chemistry. 

LARGER SYSTEM SIZES WITH LINEAR SCALING METHODS 229... 

The scaling shown in Eq. (10.10) has motivated strenuous efforts to develop alternative calculation methods with better scaling. This work has focused on so-called linear scaling methods, for which the time needed for a single energy calculation scales as... 

Also, various spectroscopic quantities can be calculated in order to test experimental assumptions Once a structure of a supramolecular assembly has been assumed, optimized or propagated in time, properties like vibrational frequencies, infrared, Raman [93], or Resonance Raman [159] intensities, NMR or EPR parameters can be calculated with first-principles methods to be compared with the experimentally measured spectra in order to confirm or reject the structural basis assumed in the interpretation of the experimental spectra. It is impossible to review the work and achievements of theoretical chemistry in this respect. Therefore, we concentrate on selected examples in the following. The interested reader is referred to the book by Kaupp, Biihl and Malkin [160] for the calculation of NMR and ESR parameters and to Refs. [161, 162] for more general discussions of molecular property calculations. NMR parameters are molecular properties probed at atomic nuclei and thus ideal for linear-scaling or empirical approaches. An efficient linear-scaling method for supramolecular systems has been presented recently [163]. 

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