a mia enhanced linear scaling approach to the computation of the exchange-凯发官网入口

a mia enhanced linear scaling approach to the computationof the exchange-correlation terms in dft/ldab. rousseau a , c. van alsenoy a, * , a. peeters a , f. boga ´r b , g. paragi ba department of chemistry, university of antwerp, universiteitsplein 1, antwerpen b-2610, belgiumb protein chemistry research group, hungarian academy of sciences, university of szeged, do´m te ´r 8, szeged h-6720, hungaryabstractthe multiplicative integral approximation is applied in the linear scaling local density approximation density functionaltheory.our method is a modified version ofthe algorithmof stratmann et al.[chem. phys. lett. 257 (1996)213].wesuggest analternative shell pair based selection scheme for the identification of non-negligible terms in the expression of charge densityand exchange-correlation contribution of kohn–sham matrix together with an iterative update procedure for these quantities.these modifications enable us to implement the multiplicative integral approach, which further reduces the computationalcost. the linear scaling behaviour as well as the cpu time reduction is demonstrated on a test system containing up to 350 watermolecules.q 2004 elsevier b.v. all rights reserved.keywords: density functional theory/local density approximation; exchange-correlation; linear scaling1. introductionalthough the kohn–sham formulation of densityfunctional theory (dft) opened new perspectives inthe theoretical treatment of spatially extendedsystems, the computations for large clusters andbiological macromolecules remained unfeasible. thisproblem induced an intensive development ofcomputer algorithms and resulted in several methodsthat require a computational effort proportional to thesystem size (linear scaling methods). instead ofsummarizing them, we refer here only to two recentreview articles written by goedecker [2] and wu andjayanthi [3].besides the treatment of coulomb interactionsand diagonalization of the kohn–sham matrix,the numerical integration needed for the calculationof the exchange part of the kohn–sham matrix is themost time-consuming part of a dft calculation.stratmann et al. [1] suggested in 1996 a grid pointdriven linear scaling method which selects the basisfunctions (significant basis functions) giving non-negligible contribution to the numerical integrationduring the exchange build-up procedure. mostrecently, challacombe [4] suggested a new hierarch-ical cubature for the numerical integration of theexchange-correlation matrix. he uses an entirelycartesian grid and a k-dimensional binary searchtree data structure that fits well to the large variabilityof electron density both in range and in magnitude.the multiplicative integral approach (mia) wasoriginally developed for the linear scaling hartree–fock treatment of large molecules [7] and wassuccessfully applied in many cases [8]. in this paper,0166-1280/$ - see front matter q 2004 elsevier b.v. all rights reserved.doi:10.1016/j.theochem.2003.08.011journal of molecular structure (theochem) 666–667 (2003) 41–50www.elsevier.com/locate/theochem* corresponding author.