Linear scaling exchange

C. Ochsenfeld, Chem. Phys. Lett., 327, 216 (2000), Linear Scaling Exchange Gradients for... 

Goh, S. K., Gallant, R. T., St-Amant, A., 1998, Towards Linear Scaling for the Fits of the Exchange-Correlation Terms in the LCGTO-DF Method via a Divide-and-Conquer Approach , Int. J. Quant. Chem., 69, 405. 

Challacombe, M., E. Schwegler, and J. Almlof. 1995. Linear scaling computations of the Hartree-Fock exchange matrix. J. Chem. Phys. 105, 2726. 

The present review has been very selective, stressing the rationale behind density-functional methods above their applications and excluding many important topics (both theoretical and computational). The interested reader may refer to anyone of the many books [91-93] or review articles [94-101] on density-functional theory for more details. Of special importance is the extension of density-functional theory to time-dependent external potentials [102-105], as this enables the dynamical behavior of molecules, including electronic excitation, to be addressed in the context of DFT [106-108]. As they are particularly relevant to the present discussion, we cite several articles related to the formal foundations of density-functional theory [85,100,109-111], linear-scaling methods [63,112-116], exchange-correlation energy functionals [25, 117-122], and qualitative tools for describing chemical reactions [123-126,126-132]. 

This chapter has sought to stimulate the exchange of effective strategies used to describe many-body effects and electrostatics within the context of a linear-scaling quantum force field. In particular, we ve provided the mathematical details required to implement the multipolar densities used in the mDC model and highlighted the importance of using multipoles in our method with some illustrative examples. 

The coordinate scaling of the exchange energy should be linear, i.e. multiplying the electron coordinates with a constant factor should result in a similar linear scaling of the exchange energy. ... 

Keywords Ab initio molecular dynamics simulations Always stable predictor-corrector algorithm Associated liquids Basis set Bom-Oppenheimer molecular dynamics simulations Car-Parrinello molecular dynamics simulations Catalysis Collective variable Discrete variable representation Dispersion Effective core potential Enhanced sampling Fictitious mass First-principles molecular dynamics simulations Free energy surface Hartree-Fock exchange Ionic liquids Linear scaling Metadynamics Nudged elastic band Numerically tabulated atom-centered orbitals Plane waves Pseudopotential Rare event Relativistic electronic structure Retention potential Self consistent field SHAKE algorithm ... 

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