A systematic way for the cost reduction of density fitting methods
Abstract
We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of threecenter twoelectron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of the computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of threecenter Coulomb integrals is a bottleneck.
 Authors:
 MTABME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H1521 Budapest (Hungary)
 Publication Date:
 OSTI Identifier:
 22415410
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 24; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; COULOMB FIELD; DENSITY; EFFICIENCY; ELECTRONS; FUNCTIONS; GAIN; INTEGRALS; ITERATIVE METHODS; RANDOM PHASE APPROXIMATION; REDUCTION
Citation Formats
Kállay, Mihály, Email: kallay@mail.bme.hu. A systematic way for the cost reduction of density fitting methods. United States: N. p., 2014.
Web. doi:10.1063/1.4905005.
Kállay, Mihály, Email: kallay@mail.bme.hu. A systematic way for the cost reduction of density fitting methods. United States. doi:10.1063/1.4905005.
Kállay, Mihály, Email: kallay@mail.bme.hu. 2014.
"A systematic way for the cost reduction of density fitting methods". United States.
doi:10.1063/1.4905005.
@article{osti_22415410,
title = {A systematic way for the cost reduction of density fitting methods},
author = {Kállay, Mihály, Email: kallay@mail.bme.hu},
abstractNote = {We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of threecenter twoelectron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of the computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of threecenter Coulomb integrals is a bottleneck.},
doi = {10.1063/1.4905005},
journal = {Journal of Chemical Physics},
number = 24,
volume = 141,
place = {United States},
year = 2014,
month =
}

A local density fitting scheme is considered in which atomic orbital (AO) products are approximated using only auxiliary AOs located on one of the nuclei in that product. The possibility of variational collapse to an unphysical “attractive electron” state that can affect such density fitting [P. Merlot, T. Kjærgaard, T. Helgaker, R. Lindh, F. Aquilante, S. Reine, and T. B. Pedersen, J. Comput. Chem. 34, 1486 (2013)] is alleviated by including atomwise semidiagonal integrals exactly. Our approach leads to a significant decrease in the computational cost of density fitting for Hartree–Fock theory while still producing results with errors 2–5 timesmore »

Interpolating moving leastsquares methods for fitting potential energy surfaces : computing highdensity potential energy surface data from lowdensity ab initio data points.
A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolatingmovingleastsquares (IMLS)based method is developed using lowdensity ab initio Hessian values to compute highdensity PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modifiedShepardbased methods. Second,more » 
Automated ligand fitting by corefragment fitting and extensioninto density
A procedure for fitting of ligands to electron density mapsby first fitting a core fragment of the ligand to density and thenextending the remainder of the ligand into density is presented. Theapproach was tested by fitting 9327 ligands over a wide range ofresolutions ( most are in the range 0.84.8 angstrom) from the ProteinData Bank (PDB) into (Fo  Fc) exp(i phi(c)) difference densitycalculated using entries from the PDB without these ligands. Theprocedure was able to place 58 percent of these 9327 ligands within 2angstrom (r.m. s.d.) of the coordinates of the atoms in the original PDBentry for that ligand.more » 
Automated ligand fitting by corefragment fitting and extension into density
An automated ligandfitting procedure has been developed and tested on 9327 ligands and (F{sub o} − F{sub c})exp(iϕ{sub c}) difference density from macromolecular structures in the Protein Data Bank. A procedure for fitting of ligands to electrondensity maps by first fitting a core fragment of the ligand to density and then extending the remainder of the ligand into density is presented. The approach was tested by fitting 9327 ligands over a wide range of resolutions (most are in the range 0.84.8 Å) from the Protein Data Bank (PDB) into (F{sub o} − F{sub c})exp(iϕ{sub c}) difference density calculated using entriesmore »