
@article{PhysRevA.85.033403,
author = {Vence, Nicholas and Harrison, Robert and Krsti\'{c}, Predrag},
doi = {10.1103/PhysRevA.85.033403},
file = {:sandbox/vama/docs/madness/Attosencond electron dynamics MRA Vence PRA 2012.pdf:pdf},
issn = {1050-2947},
journal = {Physical Review A},
month = mar,
number = {3},
pages = {033403},
title = {{Attosecond electron dynamics: A multiresolution approach}},
url = {http://link.aps.org/doi/10.1103/PhysRevA.85.033403},
volume = {85},
year = {2012}
}
@article{Sekino2008,
abstract = {We describe the evaluation of response properties using multiresolution multiwavelet (MRMW) basis sets. The algorithm uses direct projection of the perturbed density operator onto the zeroth order density operator on the real space spanned by the MRMW basis set and is applied for evaluating the polarizability of small molecules using Hartree-Fock and Kohn-Sham density functional theory. The computed polarizabilities can be considered to be converged to effectively complete space within the requested precision. The efficiency of the method against the ordinary Gaussian basis computation is discussed.},
author = {Sekino, Hideo and Maeda, Yasuyuki and Yanai, Takeshi and Harrison, Robert J},
doi = {10.1063/1.2955730},
file = {:sandbox/vama/artis/teoria-docs-quimica/M-A-D-N-E-S-S/basis set limit LR madness JCP 2008.pdf:pdf},
issn = {1089-7690},
journal = {The Journal of chemical physics},
month = jul,
number = {3},
pages = {034111},
pmid = {18647020},
title = {{Basis set limit Hartree-Fock and density functional theory response property evaluation by multiresolution multiwavelet basis.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18647020},
volume = {129},
year = {2008}
}
@article{Sekino2012,
author = {Sekino, Hideo and Yokoi, Yukina and Harrison, Robert J},
doi = {10.1088/1742-6596/352/1/012014},
file = {:sandbox/vama/docs/madness/A new implementation of dynamic polarizabiliti evaliation using MRMW Sekino 2012.pdf:pdf},
issn = {1742-6596},
journal = {Journal of Physics: Conference Series},
month = mar,
pages = {012014},
title = {{A new implementation of dynamic polarizability evaluation using a multi-resolution multi-wavelet basis set}},
url = {http://stacks.iop.org/1742-6596/352/i=1/a=012014?key=crossref.2c930e5d52c303caafa925cbdfb6350e},
volume = {352},
year = {2012}
}
@article{Kato2012,
author = {Kato, Tetsuya and Yokoi, Yukina and Sekino, Hideo},
doi = {10.1002/qua.24148},
file = {:sandbox/vama/docs/madness/polarizability/Basis set limit Computation Dynamic Polarizability ar Near-Resonance Region IJQC Kato 2012.pdf:pdf},
issn = {00207608},
journal = {International Journal of Quantum Chemistry},
month = feb,
number = {3},
pages = {286--289},
title = {{Basis set limit computation of dynamic polarizability at near-resonance region}},
url = {http://doi.wiley.com/10.1002/qua.24148},
volume = {113},
year = {2013}
}

@article{Yanai*2005,
author = {Yanai , Takeshi and Harrison , Robert J. and Handy, Nicholas C.},
doi = {10.1080/00268970412331319236},
file = {:homes/vama/docs/madness/yanai\_molphys\_tddft.pdf:pdf},
issn = {0026-8976},
journal = {Molecular Physics},
month = jan,
number = {2-3},
pages = {413--424},
title = {{Multiresolution quantum chemistry in multiwavelet bases: time-dependent density functional theory with asymptotically corrected potentials in local density and generalized gradient approximations}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00268970412331319236},
volume = {103},
year = {2005}
}
@article{Fosso-Tande2013,
author = {Fosso-Tande, Jacob and Harrison, Robert J},
doi = {10.1016/j.cplett.2013.01.065},
file = {:sandbox/vama/docs/madness/Implicit solvation models in a multiresolution multiwavelet basis CPL Tande 2013.pdf:pdf},
issn = {0009-2614},
journal = {Chemical Physics Letters},
month = mar,
pages = {179--184},
title = {{Implicit solvation models in a multiresolution multiwavelet basis}},
url = {http://dx.doi.org/10.1016/j.cplett.2013.01.065 http://linkinghub.elsevier.com/retrieve/pii/S000926141300170X},
volume = {561-562},
year = {2013}
}
@incollection{Harrison:2003:ICCS:Madness,
abstract = {Multiresolution analysis in multiwavelet bases is being investigated as an alternative computational framework for molecular electronic structure calculations. The features that make it attractive include an orthonormal basis, fast algorithms with guaranteed precision and sparse representations of many operators (e.g., Green functions). In this paper, we discuss the multiresolution formulation of quantum chemistry including application to density functional theory and developments that make practical computation in three and higher dimensions.},
annote = {10.1007/3-540-44864-0\_11},
author = {Harrison, Robert and Fann, George and Yanai, Takeshi and Beylkin, Gregory},
booktitle = {Computational Science - \{ICCS\} 2003},
doi = {10.1007/3-540-44864-0\_11},
editor = {Sloot, Peter and Abramson, David and Bogdanov, Alexander and Gorbachev, Yuriy and Dongarra, Jack and Zomaya, Albert},
file = {:homes/vama/docs/madness/wavelets/ebook Multiresolution Quantum Chemistry in Multiwavelet Bases LNCS 2003 Harrison.pdf:pdf},
isbn = {978-3-540-40197-1},
pages = {707},
publisher = {Springer Berlin / Heidelberg},
series = {Lecture Notes in Computer Science},
title = {{Multiresolution Quantum Chemistry in Multiwavelet Bases}},
url = {http://dx.doi.org/10.1007/3-540-44864-0\_11},
volume = {2660},
year = {2003}
}


@article{Fann2007,
author = {Fann, George I and Harrison, Robert J and Beylkin, Gregory and Jia, J and Hartman-Baker, R and Shelton, W A and Sugiki, S},
doi = {10.1088/1742-6596/78/1/012018},
file = {:sandbox/vama/docs/madness/MADNESS applied to DFT in Chemistry and nuclear physics SciDAC Fann.pdf:pdf},
issn = {1742-6588},
journal = {Journal of Physics: Conference Series},
month = jul,
pages = {012018},
title = {{MADNESS applied to density functional theory in chemistry and nuclear physics}},
url = {http://stacks.iop.org/1742-6596/78/i=1/a=012018?key=crossref.8db57058ca0d6fd4613e6932ec80df4c},
volume = {78},
year = {2007}
}
@article{Fann2009,
abstract = {We describe a fast real-analysis based O(N) algorithm based on multiresolution analysis and low separation rank approximation of functions and operators for solving the Schr\"{o}dinger and Lippman-Schwinger equations in 3-D with spin-orbit potential to high precision for bound states. Each of the operators and wavefunctions has its own structure of refinement to achieve and guarantee the desired finite precision. To our knowledge, this is the first time such adaptive methods have been used in computational physics, even in 1-D. Accurate solutions for each of the wavefunctions are obtained for a sample test problem. Spin orbit potentials commonly occur in the simulations of semiconductors, quantum chemistry, molecular electronics and nuclear physics. We compare our results with those obtained by direct diagonalization using the Hermite basis and the spline basis with an example from nuclear structure theory.},
author = {Fann, G I and Pei, J and Harrison, R J and Jia, J and Hill, J and Ou, M and Nazarewicz, W and Shelton, W A and Schunck, N},
file = {:sandbox/vama/artis/teoria-docs-quimica/M-A-D-N-E-S-S/FAST MRA for DFT in nuclear physics JCC Fann 2009.pdf:pdf},
journal = {Journal of Physics: Conference Series},
number = {1},
pages = {12080},
title = {{Fast multiresolution methods for density functional theory in nuclear physics}},
url = {http://stacks.iop.org/1742-6596/180/i=1/a=012080},
volume = {180},
year = {2009}
}

@inproceedings{harrison2011periodic,
  title={Periodic Density Functional Theory Solver using Multiresolution Analysis with MADNESS},
  author={Harrison, Robert and Thornton, William},
  booktitle={APS Meeting Abstracts},
  volume={1},
  pages={24005},
  year={2011}
}
@article{pei2012coordinate,
  title={{Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Super fluid Fermi Systems in Large Boxes}},
  author={Pei, JC and Fann, George I and Harrison, Robert J and Nazarewicz, W and Hill, J and Galindo, D and Jia, Jun},
  journal = {Journal of Physics: Conference Series},
  volume={402},
  year={2012},
  organization={IOP Publishing}
}

@article{pei-stoitsov-fann:2008,
  title={{Deformed coordinate-space Hartree-Fock-Bogoliubov approach to weakly bound nuclei and large deformations}},
  author={Pei, JC and Stoitsov, MV and Fann, GI and Nazarewicz, W and Schunck, N and Xu, FR},
  journal={Physical Review C},
  volume={78},
  number={6},
  pages={064306},
  year={2008},
  publisher={APS}
}

@article{valeev:2012:jcp,
abstract = {We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. Because of the exponential storage complexity of the spectral-element representation with the number of dimensions, a brute-force computation of two-electron (six-dimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12-type terms in the wave function to regularize the Coulomb electron-electron singularities of the Hamiltonian. All operations necessary to solve the Schr\"{o}dinger equation were expressed so that the reconstruction of the full-rank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the first-order M\o ller-Plesset wave function of a helium atom. The computed second-order M\o ller-Plesset energy is precise to \~{}2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.},
author = {Bischoff, Florian a and Harrison, Robert J and Valeev, Edward F},
doi = {10.1063/1.4747538},
issn = {1089-7690},
journal = {The Journal of chemical physics},
month = sep,
number = {10},
pages = {104103},
pmid = {22979846},
title = {{Computing many-body wave functions with guaranteed precision: the first-order M\o ller-Plesset wave function for the ground state of helium atom.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22979846},
volume = {137},
year = {2012}
}


@article{hill2013gaussian,
  title={Gaussian basis sets for molecular applications},
  author={Hill, J Grant},
  journal={International Journal of Quantum Chemistry},
  volume={113},
  number={1},
  pages={21--34},
  year={2013},
  publisher={Wiley Online Library}
}
@article{peterson2007gaussian,
  title={Gaussian basis sets exhibiting systematic convergence to the complete basis set limit},
  author={Peterson, Kirk A},
  journal={Annual Reports in Computational Chemistry},
  volume={3},
  pages={195--206},
  year={2007},
  publisher={Elsevier}
}

@article{Kobus2013,
author = {Kobus, Jacek},
doi = {10.1016/j.cpc.2012.09.033},
file = {:sandbox/vama/docs/madness/chap-ref/A finite difference Hartree-Fock program for atoms and diatomic molecules CPC Kobus 2013.pdf:pdf},
issn = {00104655},
journal = {Computer Physics Communications},
keywords = {atomic and diatomic systems,fock method,restricted open-shell hartree,schr\"{o}dinger equation of one-electron},
month = mar,
number = {3},
pages = {799--811},
publisher = {Elsevier B.V.},
title = {{A finite difference Hartree-Fock program for atoms and diatomic molecules}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0010465512003311},
volume = {184},
year = {2013}
}

@article{Hu2014,
author = {Hu, Shi-Lin and Zhao, Zeng-Xiu and Shi, Ting-Yun},
doi = {10.1002/qua.24582},
file = {:sandbox/vama/docs/madness/chap-ref/B-spline one center method for molecular Hartree-Fock Calculations IJQC Hu 2014.pdf:pdf},
issn = {00207608},
journal = {International Journal of Quantum Chemistry},
month = apr,
number = {7},
pages = {441--448},
title = {{B-spline one-center method for molecular Hartree-Fock calculations}},
url = {http://doi.wiley.com/10.1002/qua.24582},
volume = {114},
year = {2014}
}

@article{PAHL2002,
author = {Pahl, Felix A. and Handy, Nicholas C},
doi = {10.1080/00268970210133206},
file = {:sandbox/vama/docs/madness/chap-ref/Plane waves and radial polynomials a new mixed basis  MPR Pahl 2002.pdf:pdf},
issn = {0026-8976},
journal = {Molecular Physics},
month = oct,
number = {20},
pages = {3199--3224},
title = {{Plane waves and radial polynomials: a new mixed basis}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00268970210133206},
volume = {100},
year = {2002}
}

@article{Mitin2000,
author = {Mitin, Alexander V.},
doi = {10.1103/PhysRevA.62.010501},
file = {:sandbox/vama/docs/madness/chap-ref/Exact solution of the Hartree-Fock equation for the H2 molecule in the LCAO PRA Mitin 2000.pdf:pdf},
issn = {1050-2947},
journal = {Physical Review A},
month = jun,
number = {1},
pages = {010501},
title = {{Exact solution of the Hartree-Fock equation for the H\_\{2\} molecule in the linear-combination-of-atomic-orbitals approximation}},
url = {http://link.aps.org/doi/10.1103/PhysRevA.62.010501},
volume = {62},
year = {2000}
}

@inbook{Fridman76,
 author = {D. Friedman},
 year = {1976},
 title = {{CONS} should not evaluate its arguments},
 booktitle = {Automata, Languages and Programming},
 pages = {257-284},
 publisher = {Edinburgh University Press, Edinburgh}
}
@inbook{Fridman761,

 year = {1976},
 title = {{CONS} should not evaluate its arguments},
 editor = {S. Michaelson and R. Milner},
 booktitle = {Automata, Languages and Programming},
 page = {257-284},
 publisher = {Edinburgh University Press, Edinburgh}
}

@misc{Valeev,
  title   = {{TiledArray}},
  author  = {{Valeev, Edward F, et al.}},
  note    = {https://github.com/ValeevGroup/tiledarray},
  url     = {https://github.com/ValeevGroup/tiledarray},
  address = {Virginia Tech, {VT}},
  year    = {2014},
}

@article{bischoff2011low,
  title={Low-order tensor approximations for electronic wave functions: Hartree--Fock method with guaranteed precision},
  author={Bischoff, Florian A and Valeev, Edward F},
  journal={The Journal of Chemical Physics},
  volume={134},
  pages={104104},
  year={2011}
}

@article{bischoff2012computing,
  title={Computing many-body wave functions with guaranteed precision: The first-order M{\o}ller-Plesset wave function for the ground state of helium atom},
  author={Bischoff, Florian A and Harrison, Robert J and Valeev, Edward F},
  journal={The Journal of Chemical Physics},
  volume={137},
  pages={104103},
  year={2012}
}

@article{Baker77,
  author = {H. Baker},
  year = {1977},
  title = {The Incremental Garbage Collection of Processes},
  journal = {Proceedings of the Symposium on Artificial Intelligence Programming Languages, {SIGPLAN} Notices},
  volume = {12}
}

@book{koch2001chemist,
  title = {A chemist's guide to density functional theory},
  author = {Koch, Wolfram and Holthausen, Max C},
  volume = {2},
  year = {2001},
  publisher = {Wiley-Vch Weinheim}
}

@misc{MADNESS-web,
  title   = {{Multiresolution ADaptive NumErical Scientific Simulation (MADNESS)}},
  author  = {{Robert J. Harrison, et al.}},
  note    = {https://github.com/m-a-d-n-e-s-s/madness},
  url     = {https://github.com/m-a-d-n-e-s-s/madness},
  address = {Stony Brook, {NY}},
  year    = {2014},
}

@article{kalos1962monte,
  title={Monte Carlo calculations of the ground state of three-and four-body nuclei},
  author={Kalos, MH},
  journal={Physical Review},
  volume={128},
  number={4},
  pages={1791},
  year={1962},
  publisher={APS}
}


@misc{MADNESS1,
  author  = {{Robert J. Harrison, et al.}},
  title   = {{Multiresolution ADaptive NumErical Scientific Simulation (MADNESS)}},
  note    = {http://code.google.com/p/m-a-d-n-e-s-s/},
  url     = {http://code.google.com/p/m-a-d-n-e-s-s/},
  address = {Oak Ridge, {TN}},
  year    = {2010},
}

@misc{Eigen3,
  title   = {{Eigen3}},
  note    = {http://eigen.tuxfamily.org},
  url     = {http://eigen.tuxfamily.org}
}
@misc{Elemental,
  title   = {{Elemental}},
  note    = {https://code.google.com/p/elemental/},
  url     = {https://code.google.com/p/elemental/}
}

@misc{mtxm-notes,
  author  = {Robert J. Harrison},
  title   = {Fast matrix-transpose matrix products on x86 architectures for small square and long rectangular matrices},
  address = {Oak Ridge, {TN}},
  howpublished = {},
  year    = {2007},
}

@misc{harrison-madness-overview,
  author = {David E. Bernholdt and Wael R. Elwasif and Robert J. Harrison and Aniruddha G. Shet},
  title = {The what, why, and how of {MADNESS}},
  howpublished = {\url{http://m-a-d-n-e-s-s.googlecode.com/files/MADNESS%20summary-v3.pdf}},
  year = {2011}
}

@inproceedings{Thornton:2009:CUG:MADNESS,
    author = {W. Scott Thornton and Nicholas Vence and Robert Harrison},
    title = {Introducing the {MADNESS} numerical framework for petascale computing},
    booktitle = {{CUG} 2009, the {Cray} User Group meeting},
    pages = {1 --5},
    year = {2009}
}
@article{Vence2012,
author = {Vence, Nicholas and Harrison, Robert and Krsti\'{c}, Predrag},
doi = {10.1103/PhysRevA.85.033403},
file = {:sandbox/vama/docs/madness/Attosencond electron dynamics MRA Vence PRA 2012.pdf:pdf},
issn = {1050-2947},
journal = {Physical Review A},
month = mar,
number = {3},
pages = {033403},
title = {{Attosecond electron dynamics: A multiresolution approach}},
url = {http://link.aps.org/doi/10.1103/PhysRevA.85.033403},
volume = {85},
year = {2012}
}

@article{Reuter:2012:CPC:madness-irregular-pdes1,
  author = {Matthew G. Reuter and Judith C. Hill and Robert J. Harrison},
  title = {Solving {PDE}s in irregular geometries with multiresolution methods {I}: Embedded {D}irichlet boundary conditions},
  journal = {Computer Physics Communications},
  volume = {183},
  number = {1},
  pages = {1 - 7},
  year = {2012},
  note = {},
  issn = {0010-4655},
  doi = {10.1016/j.cpc.2011.07.001},
  url = {http://www.sciencedirect.com/science/article/pii/S0010465511002396},
  keywords = {Multiresolution analysis},
  keywords = {Domain embedding techniques},
  keywords = {Electrostatics}
}

@article{Fann:2007:JoPCS:Madness-DFT,
  author={G. I. Fann and R. J. Harrison and G. Beylkin and J. Jia and R. Hartman-Baker and W. A. Shelton and S. Sugiki},
  title={{MADNESS} applied to density functional theory in chemistry and nuclear physics},
  journal={Journal of Physics: Conference Series},
  volume={78},
  number={1},
  pages={012018},
  url={http://stacks.iop.org/1742-6596/78/i=1/a=012018},
  year={2007},
  abstract={We describe some recent mathematical results in constructing computational methods that lead to the development of fast and accurate multiresolution numerical methods for solving quantum chemistry and nuclear physics problems based on Density Functional Theory (DFT). Usi
ng low separation rank representations of functions and operators in conjunction with representations in multiwavelet bases, we developed a multiscale solution method for integral and differential equations and integral transforms. The Poisson equation, the Schrodinger equation, and
 the projector on the divergence free functions provide important examples with a wide range of applications in computational chemistry, nuclear physics, computational electromagnetic and fluid dynamics. We have implemented this approach along with adaptive representations of operat
ors and functions in the multiwavelet basis and low separation rank (LSR) approximation of operators and functions. These methods have been realized and implemented in a software package called Multiresolution Adaptive Numerical Evaluation for Scientific Simulation (MADNESS).}
}

@article{Harrison:2005:JoPCS:Madness-chemistry,
  author={Robert J. Harrison and George I. Fann and Zhengting Gan and Takeshi Yanai and Shinichiro Sugiki and Ariana Beste and Gregory Beylkin},
  title={Multiresolution computational chemistry},
  journal={Journal of Physics: Conference Series},
  volume={16},
  number={1},
  pages={243},
  url={http://stacks.iop.org/1742-6596/16/i=1/a=032},
  year={2005},
  abstract={Multiresolution techniques in multiwavelet bases, made practical in three and higher dimensions by separated representations, have enabled significant advances in the accuracy and manner of computation of molecular electronic structure. The mathematical and numerical tec
hniques are described in the article by Fann. This paper summarizes the major accomplishments in computational chemistry which represent the first substantial application of most of these new ideas in three and higher dimensions. These include basis set limit computation with linear
 scaling for Hartree-Fock and Density Functional Theory with a wide variety of functionals including hybrid and asymptotically corrected forms. Current capabilities include energies, analytic derivatives, and excitation energies from linear response theory. Direct solution in 6-D of
 the two-particle wave equation has also been demonstrated. These methods are written using MADNESS which provides a high level of composition using functions and operators with guarantees of speed and precision.}
}

@article{Fann:2009:JoPCS:Madness-nuclear,
  author={G. I. Fann and J. Pei and R. J. Harrison and J. Jia and J. Hill and M. Ou and W. Nazarewicz and W. A. Shelton and N. Schunck},
  title={Fast multiresolution methods for density functional theory in nuclear physics},
  journal={Journal of Physics: Conference Series},
  volume={180},
  number={1},
  pages={012080},
  url={http://stacks.iop.org/1742-6596/180/i=1/a=012080},
  year={2009},
  abstract={We describe a fast real-analysis based O(N) algorithm based on multiresolution analysis and low separation rank approximation of functions and operators for solving the Schr��dinger and Lippman-Schwinger equations in 3-D with spin-orbit potential to high precision for boun
d states. Each of the operators and wavefunctions has its own structure of refinement to achieve and guarantee the desired finite precision. To our knowledge, this is the first time such adaptive methods have been used in computational physics, even in 1-D. Accurate solutions for each of the wavefunctions are obtained for a sample test problem. Spin orbit potentials commonly occur in the simulations of semiconductors, quantum chemistry, molecular electronics and nuclear physics. We compare our results with those obtained by direct diagonalization using the Her
mite basis and the spline basis with an example from nuclear structure theory.}
}

@article{Fann:2009:JoPCS:Madness-lowrank,
  author={G. I. Fann and R. J. Harrison and G. Beylkin},
  title={{MRA} and low-separation rank approximation with applications to quantum electronics structures computations},
  journal={Journal of Physics: Conference Series},
  volume={16},
  number={1},
  pages={461},
  url={http://stacks.iop.org/1742-6596/16/i=1/a=062},
  year={2005},
  abstract={We describe some recent mathematical results in constructing computational methods that lead to the development of fast and accurate multiresolution numerical methods for solving problems in computational chemistry (the so-called multiresolution quantum chemistry). Using
 low separation rank representations of functions and operators and representations in multiwavelet bases, we developed a multiscale solution method for integral and differential equations and integral transforms. The Poisson equation and the Schrodinger equation, the projector on t
he divergence free functions, provide important examples with a wide range of applications in computational chemistry, computational electromagnetic and fluid dynamics. We have implemented these ideas that include adaptive representations of operators and functions in the multiwavel
et basis and low separation rank approximation of operators and functions. These methods have been implemented into a software package called Multiresolution Adaptive Numerical Evaluation for Scientific Simulation (MADNESS).}
}

@article{Alpert:2002:JCoP:multiwavelet,
  title = {Adaptive Solution of Partial Differential Equations in Multiwavelet Bases},
  journal = {Journal of Computational Physics},
  volume = {182},
  number = {1},
  pages = {149 - 190},
  year = {2002},
  note = {},
  issn = {0021-9991},
  doi = {10.1006/jcph.2002.7160},
  url = {http://www.sciencedirect.com/science/article/pii/S0021999102971603},
  author = {B. Alpert and G. Beylkin and D. Gines and L. Vozovoi},
  abstract = {We construct multiresolution representations of derivative and exponential operators with linear boundary conditions in multiwavelet bases and use them to develop a simple, adaptive scheme for the solution of nonlinear, time-dependent partial differential equations. Th
e emphasis on hierarchical representations of functions on intervals helps to address issues of both high-order approximation and efficient application of integral operators, and the lack of regularity of multiwavelets does not preclude their use in representing differential operato
rs. Comparisons with finite difference, finite element, and spectral element methods are presented, as are numerical examples with the heat equation and Burgers' equation.},
}

@article{Beylkin:2011:ACHA:multiresolution,
  title = {Multiresolution representation of operators with boundary conditions on simple domains},
  journal = {Applied and Computational Harmonic Analysis},
  volume = {},
  number = {0},
  pages = { - },
  year = {2011},
  note = {},
  issn = {1063-5203},
  doi = {10.1016/j.acha.2011.10.001},
  url = {http://www.sciencedirect.com/science/article/pii/S1063520311001072},
  author = {Gregory Beylkin and George Fann and Robert J. Harrison and Christopher Kurcz and Lucas Monzon},
  keywords = {Multiresolution},
  keywords = {Non-standard form},
  keywords = {Projector on divergence free functions},
  keywords = {Poisson Green's function},
  keywords = {Non-oscillatory Helmholtz Green's function},
  keywords = {Hilbert transform},
  keywords = {Periodic boundary conditions},
  keywords = {Separated representations},
  abstract = {We develop a multiresolution representation of a class of integral operators satisfying boundary conditions on simple domains in order to construct fast algorithms for their application. We also elucidate some delicate theoretical issues related to the construction of 
periodic Green's functions for Poisson's equation.  By applying the method of images to the non-standard form of the free space operator, we obtain lattice sums that converge absolutely on all scales, except possibly on the coarsest scale. On the coarsest scale the lattice sums may 
be only conditionally convergent and, thus, allow for some freedom in their definition. We use the limit of square partial sums as a definition of the limit and obtain a systematic, simple approach to the construction (in any dimension) of periodized operators with sparse non-standa
rd forms.  We illustrate the results on several examples in dimensions one and three: the Hilbert transform, the projector on divergence free functions, the non-oscillatory Helmholtz Green's function and the Poisson operator. Remarkably, the limit of square partial sums yields a per
iodic Poisson Green's function which is not a convolution.  Using a short sum of decaying Gaussians to approximate periodic Green's functions, we arrive at fast algorithms for their application. We further show that the results obtained for operators with periodic boundary condition
s extend to operators with Dirichlet, Neumann, or mixed boundary conditions.},
}

@article{Beylkin:2007:ACHA:singular,
  title = {Multiresolution separated representations of singular and weakly singular operators},
  journal = {Applied and Computational Harmonic Analysis},
  volume = {23},
  number = {2},
  pages = {235 - 253},
  year = {2007},
  issn = {1063-5203},
  doi = {10.1016/j.acha.2007.01.001},
  url = {http://www.sciencedirect.com/science/article/pii/S1063520307000048},
  author = {Gregory Beylkin and Robert Cramer and George Fann and Robert J. Harrison},
  keywords = {Separated representation},
  keywords = {Poisson kernel},
  keywords = {Projector on the divergence free functions},
  keywords = {Multiwavelet bases},
  keywords = {Integral operators},
  abstract = {For a finite but arbitrary precision, we construct efficient low separation rank representations for the Poisson kernel and for the projector on the divergence free functions in the dimension d = 3 . Our construction requires computing only one-dimensional integrals. W
e use scaling functions of multiwavelet bases, thus making these representations available for a variety of multiresolution algorithms. Besides having many applications, these two operators serve as examples of weakly singular and singular operators for which our approach is applica
ble. Our approach provides a practical implementation of separated representations of a class of weakly singular and singular operators in dimensions d $\ge$ 2.},
}

@incollection{Harrison2003ICCSMadness,
   author = {Harrison, Robert and Fann, George and Yanai, Takeshi and Beylkin, Gregory},
   affiliation = {Oak Ridge National Laboratory P.O. Box 2008 MS6367 Oak Ridge TN 37831-6367},
   title = {Multiresolution Quantum Chemistry in Multiwavelet Bases},
   booktitle = {Computational Science - {ICCS} 2003},
   series = {Lecture Notes in Computer Science},
   editor = {Sloot, Peter and Abramson, David and Bogdanov, Alexander and Gorbachev, Yuriy and Dongarra, Jack and Zomaya, Albert},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-540-40197-1},
   keyword = {Computer Science},
   pages = {707-707},
   volume = {2660},
   url = {http://dx.doi.org/10.1007/3-540-44864-0_11},
   note = {10.1007/3-540-44864-0_11},
   year = {2003}
}
@incollection{harrison2003multiresolution,
  title={Multiresolution quantum chemistry in multiwavelet bases},
  author={Harrison, Robert J and Fann, George I and Yanai, Takeshi and Beylkin, Gregory},
  booktitle={Computational Science���ICCS 2003},
  pages={103--110},
  year={2003},
  publisher={Springer}
}

@ARTICLE{Fann:2004:IBM:singular,
  author={Fann, G. and Beylkin, G. and Harrison, R. J. and Jordan, K. E.},
  journal={{IBM} Journal of Research and Development},
  title={Singular operators in multiwavelet bases},
  year={2004},
  month={march},
  volume={48},
  number={2},
  pages={161 -171},
  abstract={We review some recent results on multiwavelet methods for solving integral and partial differential equations and present an efficient representation of operators using discontinuous multiwavelet bases, including the case for singular integral operators. Numerical calcul
us using these representations produces fast O(N) methods for multiscale solution of integral equations when combined with low separation rank methods. Using this formulation, we compute the Hilbert transform and solve the Poisson and Schr #x00F6;dinger equations. For a fixed order 
of multiwavelets and for arbitrary but finite-precision computations, the computational complexity is O(N). The computational structures are similar to fast multipole methods but are more generic in yielding fast O(N) algorithm development.},
  keywords={},
  doi={10.1147/rd.482.0161},
  ISSN={0018-8646},
}

@article{Harrison:2004:JChP:MRQC-basic,
  author = {Robert J. Harrison and George I. Fann and Takeshi Yanai and Zhengting Gan and Gregory Beylkin},
  title = {Multiresolution quantum chemistry: Basic theory and initial applications},
  publisher = {AIP},
  year = {2004},
  journal = {The Journal of Chemical Physics},
  volume = {121},
  number = {23},
  pages = {11587-11598},
  keywords = {density functional theory; atomic structure; molecular electronic states; Helmholtz equations; Poisson equation; Green's function methods; quantum chemistry; water; organic compounds; beryllium; magnesium; calcium; strontium; helium neutral atoms},
  url = {http://link.aip.org/link/?JCP/121/11587/1},
  doi = {10.1063/1.1791051}
}

@article{Yanai:2004:JChP:MRQC-HFX,
  author = {Takeshi Yanai and George I. Fann and Zhenting Gan and Robert J. Harrison and Gregory Beylkin},
  title = {Multiresolution quantum chemistry in multiwavelet bases: {H}artree--{F}ock exchange},
  publisher = {AIP},
  year = {2004},
  journal = {The Journal of Chemical Physics},
  volume = {121},
  number = {14},
  pages = {6680-6688},
  keywords = {quantum chemistry; SCF calculations; HF calculations; molecular electronic states; orbital calculations; water; molecular clusters; integral equations; numerical analysis; chemistry computing; wavelet transforms},
  url = {http://link.aip.org/link/?JCP/121/6680/1},
  doi = {10.1063/1.1790931}
}

@article{Yanai:2004:JChP:MRQC-derivatives,
  author = {Takeshi Yanai and George I. Fann and Zhengting Gan and Robert J. Harrison and Gregory Beylkin},
  title = {Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for {H}artree--{F}ock and density functional theory},
  publisher = {AIP},
  year = {2004},
  journal = {The Journal of Chemical Physics},
  volume = {121},
  number = {7},
  pages = {2866-2876},
  keywords = {nitrogen; water; HF calculations; density functional theory; quantum chemistry; quantum theory; molecular configurations},
  url = {http://link.aip.org/link/?JCP/121/2866/1},
  doi = {10.1063/1.1768161}
}

@INPROCEEDINGS{Stock:2011:IPDPS:SIMD,
  author={Stock, K. and Henretty, T. and Murugandi, I. and Sadayappan, P. and Harrison, R.},
  booktitle={International Parallel Distributed Processing Symposium ({IPDPS})},
  title={Model-Driven {SIMD} Code Generation for a Multi-resolution Tensor Kernel},
  year={2011},
  month={may},
  volume={},
  number={},
  pages={1058-1067},
  abstract={In this paper, we describe a model-driven compile-time code generator that transforms a class of tensor contraction expressions into highly optimized short-vector SIMD code. We use as a case study a multi-resolution tensor kernel from the MADNESS quantum chemistry applic
ation. Performance of a C-based implementation is low, and because the dimensions of the tensors are small, performance using vendor optimized BLAS libraries is also sub optimal. We develop a model-driven code generator that determines the optimal loop permutation and placement of v
ector load/store, transpose, and splat operations in the generated code, enabling portable performance on short-vector SIMD architectures. Experimental results on an SSE-based platform demonstrate the efficiency of the vector-code synthesizer.},
  keywords={C-based implementation;MADNESS quantum chemistry application;model-driven SIMD code generation;model-driven code generator;model-driven compile-time code generator;multiresolution tensor kernel;optimal loop permutation;short-vector SIMD architecture;short-vector SIMD cod
e;splat operation;tensor contraction expression;vector-code synthesizer;parallel processing;tensors;},
  doi={10.1109/IPDPS.2011.101},
  ISSN={1530-2075},
}


@article{nielsen2000multi,
  title={Multi-threading: A new dimension to massively parallel scientific computation},
  author={Nielsen, Ida and Janssen, Curtis L},
  journal={Computer physics communications},
  volume={128},
  number={1},
  pages={238--244},
  year={2000},
  publisher={Elsevier}
}
@book{goedecker1997wavelets,
  title={Wavelets and their application for the solution of partial differential equations in physics},
  author={Goedecker, Stefan},
  year={1997},
  publisher={Universit{\'e}, B{\^a}timent des sciences physiques, MD Reymond}
}
@article{Johnson2001,
author = {Johnson, Bruce R and Mackey, Jeffrey L and Kinsey, James L},
doi = {10.1006/jcph.2001.6701},
file = {:sandbox/vama/docs/madness/wavelets/Solution of Cartesian and curvilinear Quantum eq Multiwavelets Johnson 2000.pdf:pdf},
issn = {00219991},
journal = {Journal of Computational Physics},
keywords = {curvilinear,eigenvalue,interval,multiwavelets,quantum},
month = apr,
number = {2},
pages = {356--383},
title = {{Solution of Cartesian and Curvilinear Quantum Equations via Multiwavelets on the Interval}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999101967014},
volume = {168},
year = {2001}
}
@article{meyer1991ondelettes,
  title={Ondelettes sur l'intervalle.},
  author={Meyer, Yves},
  journal={Revista Matematica Iberoamericana},
  volume={7},
  number={2},
  pages={115--133},
  year={1991},
  publisher={European Mathematical Society}
}
@book{meyer1992ondelettes,
  title={Ondelettes et algorithmes concurrents},
  author={Meyer, Yves},
  volume={1435},
  year={1992},
  publisher={Editions Hermann}
}
@book{meyer1992ondelettes,
  title={Ondelettes et algorithmes},
  author={Meyer, Yves},
  year={1990},
  publisher={Editions Hermann}
}

@article{Daubechies1988,
author = {Daubechies, Ingrid},
doi = {10.1002/cpa.3160410705},
file = {:sandbox/vama/docs/madness/wavelets/Orthonormal bases of compactly supported wavelets CPC Daubechies 1988.pdf:pdf},
issn = {00103640},
journal = {Communications on Pure and Applied Mathematics},
month = oct,
number = {7},
pages = {909--996},
title = {{Orthonormal bases of compactly supported wavelets}},
url = {http://doi.wiley.com/10.1002/cpa.3160410705},
volume = {41},
year = {1988}
}

@article{Beste2006,
abstract = {Chemists are mainly interested in energy differences. In contrast, most quantum chemical methods yield the total energy which is a large number compared to the difference and has therefore to be computed to a higher relative precision than would be necessary for the difference alone. Hence, it is desirable to compute energy differences directly, thereby avoiding the precision problem. Whenever it is possible to find a parameter which transforms smoothly from an initial to a final state, the energy difference can be obtained by integrating the energy derivative with respect to that parameter (cf. thermodynamic integration or adiabatic connection methods). If the dependence on the parameter is predominantly linear, accurate results can be obtained by single-point integration. In density functional theory and Hartree-Fock, we applied the formalism to ionization potentials, excitation energies, and chemical bond breaking. Example calculations for ionization potentials and excitation energies showed that accurate results could be obtained with a linear estimate. For breaking bonds, we introduce a nongeometrical parameter which gradually turns the interaction between two fragments of a molecule on. The interaction changes the potentials used to determine the orbitals as well as the constraint on the orbitals to be orthogonal.},
author = {Beste, A and Harrison, R J and Yanai, T},
doi = {10.1063/1.2244559},
file = {:sandbox/vama/docs/anatole/chemicalcomp/papers/Direct computation of general chemical energy diff JCP Beste 2011.pdf:pdf},
issn = {0021-9606},
journal = {The Journal of chemical physics},
month = aug,
number = {7},
pages = {074101},
pmid = {16942316},
title = {{Direct computation of general chemical energy differences: Application to ionization potentials, excitation, and bond energies.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16942316},
volume = {125},
year = {2006}
}

@article{Goedecker1996,
author = {Goedecker, S and Teter, M and Hutter, J},
doi = {10.1103/PhysRevB.54.1703},
file = {:sandbox/vama/docs/anatole/DCAPCP/Separable dual-space Gaussian Pseudopotentials PRB Goedecker 1996.pdf:pdf},
issn = {0163-1829},
journal = {Physical Review B},
month = jul,
number = {3},
pages = {1703--1710},
title = {{Separable dual-space Gaussian pseudopotentials}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.54.1703},
volume = {54},
year = {1996}
}
@article{Hartwigsen1998,
author = {Hartwigsen, C and Goedecker, S and Hutter, J},
doi = {10.1103/PhysRevB.58.3641},
file = {:sandbox/vama/docs/bigdft/psp/HGH-PhysRevB.58.3641.pdf:pdf;:sandbox/vama/docs/anatole/DCAPCP/Relativistic separable dual-space Gaussian pseudopotentials from H to Rn Hartwigsen 1998.pdf:pdf},
issn = {0163-1829},
journal = {Physical Review B},
month = aug,
number = {7},
pages = {3641--3662},
title = {{Relativistic separable dual-space Gaussian pseudopotentials from H to Rn}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.58.3641},
volume = {58},
year = {1998}
}

@article{zalesny2011linear,
  title={Linear-Scaling Techniques in Computational Chemistry and Physics: Methods and Applications},
  author={Zalesny, Robert and Papadopoulos, Manthos G and Mezey, Paul G and Leszczynski, Jerzy},
  journal={Challenges and Advances in Computational Chemistry and Physics (13)},
  year={2011},
  publisher={Dordrecht: Springer Science+ Business Media BV}
}
@article{Goedecker1999,
author = {Goedecker, Stefan},
doi = {10.1103/RevModPhys.71.1085},
file = {:sandbox/vama/docs/bigdft/Linear Scaling electronic structure methods RevModPhys Goedecker.pdf:pdf},
issn = {0034-6861},
journal = {Reviews of Modern Physics},
month = jul,
number = {4},
pages = {1085--1123},
title = {{Linear scaling electronic structure methods}},
url = {http://link.aps.org/doi/10.1103/RevModPhys.71.1085},
volume = {71},
year = {1999}
}
@article{Goedecker:Ivanov:1999,
author = {Goedecker, S and Ivanov, OV},
doi = {10.1103/PhysRevB.59.7270},
file = {:sandbox/vama/docs/madness/wavelets/Frequency localization properties of the density matrix and its resulting hypersparsity in a wavelet  PRB Goedecker 1999.pdf:pdf},
issn = {0163-1829},
journal = {Physical Review B},
month = mar,
number = {11},
pages = {7270--7273},
title = {{Frequency localization properties of the density matrix and its resulting hypersparsity in a wavelet representation}},
url = {http://link.aps.org/doi/10.1103/PhysRevB.59.7270 http://prb.aps.org/abstract/PRB/v59/i11/p7270\_1},
volume = {59},
year = {1999}
}
@article{murakami1992three,
author = {Murakami, H and Sonnad, V and Clementi, E},
doi = {10.1002/qua.560420418},
issn = {0020-7608},
journal = {International Journal of Quantum Chemistry},
month = may,
number = {4},
pages = {785--817},
publisher = {Wiley Online Library},
title = {{A three-dimensional finite element approach towards molecular SCF computations}},
url = {http://doi.wiley.com/10.1002/qua.560420418},
volume = {42},
year = {1992}
}
@article{Bylaska2009,
author = {Bylaska, Eric J. and Holst, Michael and Weare, John H.},
doi = {10.1021/ct800350j},
file = {:sandbox/vama/artis/teoria-docs-quimica/Finite Element Method/Adaptive FEM for solving exact KS-DFT JCTC 2009 Bylaska.pdf:pdf},
issn = {1549-9618},
journal = {Journal of Chemical Theory and Computation},
month = apr,
number = {4},
pages = {937--948},
title = {{Adaptive Finite Element Method for Solving the Exact Kohn-Sham Equation of Density Functional Theory}},
url = {http://pubs.acs.org/doi/abs/10.1021/ct800350j},
volume = {5},
year = {2009}
}

@article{Stock2012,
author = {Stock, Kevin and Pouchet, Louis-No\"{e}l and Sadayappan, P.},
doi = {10.1145/2086696.2086729},
file = {:sandbox/vama/docs/madness/Using Machine Learning to Imporve Automatic Vectorization - Kevin Stock.pdf:pdf},
issn = {15443566},
journal = {ACM Transactions on Architecture and Code Optimization},
month = jan,
number = {4},
pages = {1--23},
title = {{Using machine learning to improve automatic vectorization}},
url = {http://dl.acm.org/citation.cfm?doid=2086696.2086729},
volume = {8},
year = {2012}
}
@article{Yanai2004,
abstract = {An efficient and accurate analytic gradient method is presented for Hartree-Fock and density functional calculations using multiresolution analysis in multiwavelet bases. The derivative is efficiently computed as an inner product between compressed forms of the density and the differentiated nuclear potential through the Hellmann-Feynman theorem. A smoothed nuclear potential is directly differentiated, and the smoothing parameter required for a given accuracy is empirically determined from calculations on six homonuclear diatomic molecules. The derivatives of N2 molecule are shown using multiresolution calculation for various accuracies with comparison to correlation consistent Gaussian-type basis sets. The optimized geometries of several molecules are presented using Hartree-Fock and density functional theory. A highly precise Hartree-Fock optimization for the H2O molecule produced six digits for the geometric parameters.},
author = {Yanai, Takeshi and Fann, George I and Gan, Zhengting and Harrison, Robert J and Beylkin, Gregory},
doi = {10.1063/1.1768161},
file = {:home/alvaro/mas/artis/teoria-docs-quimica/M-A-D-N-E-S-S/analytic derivatives for HF and LDA madness JCP Yanai 2004.pdf:pdf},
issn = {0021-9606},
journal = {The Journal of chemical physics},
month = aug,
number = {7},
pages = {2866--76},
pmid = {15291596},
title = {{Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree-Fock and density functional theory.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15291596},
volume = {121},
year = {2004}
}
@article{Rappoport2010,
abstract = {With recent advances in electronic structure methods, first-principles calculations of electronic response properties, such as linear and nonlinear polarizabilities, have become possible for molecules with more than 100 atoms. Basis set incompleteness is typically the main source of error in such calculations since traditional diffuse augmented basis sets are too costly to use or suffer from near linear dependence. To address this problem, we construct the first comprehensive set of property-optimized augmented basis sets for elements H-Rn except lanthanides. The new basis sets build on the Karlsruhe segmented contracted basis sets of split-valence to quadruple-zeta valence quality and add a small number of moderately diffuse basis functions. The exponents are determined variationally by maximization of atomic Hartree-Fock polarizabilities using analytical derivative methods. The performance of the resulting basis sets is assessed using a set of 313 molecular static Hartree-Fock polarizabilities. The mean absolute basis set errors are 3.6\%, 1.1\%, and 0.3\% for property-optimized basis sets of split-valence, triple-zeta, and quadruple-zeta valence quality, respectively. Density functional and second-order M\o ller-Plesset polarizabilities show similar basis set convergence. We demonstrate the efficiency of our basis sets by computing static polarizabilities of icosahedral fullerenes up to C(720) using hybrid density functional theory.},
author = {Rappoport, Dmitrij and Furche, Filipp},
doi = {10.1063/1.3484283},
file = {:home/alvaro/docs/madness/chap-ref/gaussianbasisref/Property-optimized Gaussian basis sets for molecular response calculations Rappoport JCP 2010.pdf:pdf},
issn = {1089-7690},
journal = {The Journal of chemical physics},
month = oct,
number = {13},
pages = {134105},
pmid = {20942521},
title = {{Property-optimized gaussian basis sets for molecular response calculations.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20942521},
volume = {133},
year = {2010}
}
@article{Poulson2013,
author = {Poulson, Jack and Marker, Bryan and van de Geijn, Robert A. and Hammond, Jeff R. and Romero, Nichols A. and Geijn, Robert A V A N D E and Hammond, Jeff R. and Romero, Nichols A.},
doi = {10.1145/2427023.2427030},
file = {:sandbox/vama/docs/jhammond/elemental/Elemental-TOMS-revised.pdf:pdf;:sandbox/vama/docs/software/Elemental-rev2.pdf:pdf},
issn = {00983500},
journal = {ACM Transactions on Mathematical Software},
month = feb,
number = {2},
pages = {1--24},
title = {{Elemental: A new framework for distributed memory dense matrix computations}},
url = {http://dl.acm.org/citation.cfm?doid=2427023.2427030},
volume = {39},
year = {2013}
}

@MISC{eigenweb,
  author = {Ga\"{e}l Guennebaud and Beno\^{i}t Jacob and others},
  title = {Eigen v3},
  howpublished = {http://eigen.tuxfamily.org},
  year = {2010}
 }

@article{Andrade2007,
abstract = {The authors present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency-dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, they implemented it in a real-space (basis-set-free) code and applied it to benchmark molecules, namely, CO, H2O, and para-nitroaniline. Their results are in agreement with experimental and previous theoretical studies and fully validate their approach.},
author = {Andrade, Xavier and Botti, Silvana and Marques, Miguel a L and Rubio, Angel},
doi = {10.1063/1.2733666},
file = {:sandbox/vama/artis/dynamic properties/Polarizability/TDDFT dynamyc polarizablities Octopus JCP 2007.PDF:PDF},
issn = {0021-9606},
journal = {The Journal of chemical physics},
month = may,
number = {18},
pages = {184106},
pmid = {17508791},
title = {{Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17508791},
volume = {126},
year = {2007}
}
@article{Senatore1987,
author = {Senatore, G. and Subbaswamy, K.},
doi = {10.1103/PhysRevA.35.2440},
file = {:sandbox/vama/artis/dynamic properties/Polarizability/Nonlinear response of closed shell atoms in the DFT PRA Senatore 1987.pdf:pdf},
issn = {0556-2791},
journal = {Physical Review A},
month = mar,
number = {6},
pages = {2440--2447},
title = {{Nonlinear response of closed-shell atoms in the density-functional formalism}},
url = {http://link.aps.org/doi/10.1103/PhysRevA.35.2440},
volume = {35},
year = {1987}
}
@article{alpert1993class,
  title={A class of bases in L\^{}2 for the sparse representation of integral operators},
  author={Alpert, Bradley K},
  journal={SIAM journal on Mathematical Analysis},
  volume={24},
  number={1},
  pages={246--262},
  year={1993},
  publisher={SIAM}
}
@article{PSP:2037060,
author = {McWeeny,R.},
title = {Note on the iterative method in nuclear problems},
journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
volume = {45},
issue = {02},
month = {4},
year = {1949},
issn = {1469-8064},
pages = {315--317},
numpages = {3},
doi = {10.1017/S0305004100024889}
}
@ARTICLE{1950RSPSA.200..542B,
   author = {{Boys}, S.~F.},
    title = "{Electronic Wave Functions. I. A General Method of Calculation for the Stationary States of Any Molecular System}",
  journal = {Royal Society of London Proceedings Series A},
     year = 1950,
    month = feb,
   volume = 200,
    pages = {542-554},
      doi = {10.1098/rspa.1950.0036},
   adsurl = {http://adsabs.harvard.edu/abs/1950RSPSA.200..542B},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{Taylor2013,
author = {Frediani, Luca and Fossgaard, Eirik and Fl\aa, Tor and Ruud, Kenneth},
doi = {10.1080/00268976.2013.810793},
file = {:sandbox/vama/docs/madness/Fully adaptive algorithms for multivariable integral equations using  NS and wavelets MP Frediani 2013.pdf:pdf},
issn = {0026-8976},
journal = {Molecular Physics},
month = jul,
number = {9-11},
pages = {1143--1160},
title = {{Fully adaptive algorithms for multivariate integral equations using the non-standard form and multiwavelets with applications to the Poisson and bound-state Helmholtz kernels in three dimensions}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00268976.2013.810793},
volume = {111},
year = {2013}
}

@article{Weijo2009,
abstract = {The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF-PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N(1.5) scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used.},
author = {Weijo, Ville and Randrianarivony, Maharavo and Harbrecht, Helmut and Frediani, Luca},
doi = {10.1002/jcc.21431},
file = {:sandbox/vama/docs/madness/Solvent PCM wavelet Frediani 2009.pdf:pdf},
issn = {1096-987X},
journal = {Journal of computational chemistry},
keywords = {algorithms,galerkin methods,interpolation,linear complexity,solvent effect,sparse operators,wavelets},
month = may,
number = {7},
pages = {1469--77},
pmid = {19834886},
title = {{Wavelet formulation of the polarizable continuum model.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19834886},
volume = {31},
year = {2010}
}


@article{Jorgensen2012JCP,
   author = "HÃžyvik, Ida-Marie and Jansik, Branislav and JÃžrgensen, Poul",
   title = "Orbital localization using fourth central moment minimization",
   journal = "The Journal of Chemical Physics",
   year = "2012",
   volume = "137",
   number = "22", 
   eid = 224114,
   pages = "-",
   url = "http://scitation.aip.org/content/aip/journal/jcp/137/22/10.1063/1.4769866",
   doi = "http://dx.doi.org/10.1063/1.4769866" 
}
@article{Bischoff2012,
abstract = {We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. Because of the exponential storage complexity of the spectral-element representation with the number of dimensions, a brute-force computation of two-electron (six-dimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12-type terms in the wave function to regularize the Coulomb electron-electron singularities of the Hamiltonian. All operations necessary to solve the Schr\"{o}dinger equation were expressed so that the reconstruction of the full-rank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the first-order M\o ller-Plesset wave function of a helium atom. The computed second-order M\o ller-Plesset energy is precise to \~{}2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.},
author = {Bischoff, Florian A and Harrison, Robert J and Valeev, Edward F},
doi = {10.1063/1.4747538},
file = {:sandbox/vama/docs/madness/MP2 He in Madness JCP Bischoff 2012.pdf:pdf},
issn = {1089-7690},
journal = {The Journal of chemical physics},
month = sep,
number = {10},
pages = {104103},
pmid = {22979846},
title = {{Computing many-body wave functions with guaranteed precision: the first-order M\o ller-Plesset wave function for the ground state of helium atom.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22979846},
volume = {137},
year = {2012}
}

@article{Marques2012,
author = {a.L. Marques, Miguel and Oliveira, Micael J.T. and Burnus, Tobias},
doi = {10.1016/j.cpc.2012.05.007},
file = {:sandbox/vama/docs/software/Libxc a library CPC Marques 2012.pdf:pdf},
issn = {00104655},
journal = {Computer Physics Communications},
keywords = {density functional theory},
month = oct,
number = {10},
pages = {2272--2281},
publisher = {Elsevier B.V.},
title = {{Libxc: A library of exchange and correlation functionals for density functional theory}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0010465512001750},
volume = {183},
year = {2012}
}
@article{Ekstrom2010,
author = {Ekström, Ulf and Visscher, Lucas and Bast, Radovan and Thorvaldsen, Andreas J. and Ruud, Kenneth and Ekstro, Ulf and Visscher, Lucas and Bast, Radovan and Thorvaldsen, Andreas J.},
doi = {10.1021/ct100117s},
file = {:sandbox/vama/artis/teoria-docs-quimica/grimme/Arbitrary-order DFT automatic diff JCTC 2010 Ekstrom.pdf:pdf},
issn = {1549-9618},
journal = {Journal of Chemical Theory and Computation},
month = jul,
number = {7},
pages = {1971--1980},
title = {{Arbitrary-Order Density Functional Response Theory from Automatic Differentiation}},
url = {http://pubs.acs.org/doi/abs/10.1021/ct100117s},
volume = {6},
year = {2010}
}
@book{dftrepo,
author = { van Dam, Huub and Sherwood, Paul  },
address = {Daresbury, Cheshire, WA4 4AD United Kingdom},
year = {2001},
publisher = {Quantum Chemistry Group, CCLRC Daresbury Laboratory},
title = {{Density Functional Repository}},
url = {ftp://ftp.dl.ac.uk/qcg/dft\_library/contents.html}
}
@incollection{pulay2011plane,
  title={Plane-Wave Based Low-Scaling Electronic Structure Methods for Molecules},
  author={Pulay, Peter},
  booktitle={Linear-Scaling Techniques in Computational Chemistry and Physics},
  pages={1--16},
  year={2011},
  publisher={Springer}
}
@article{Kutzelnigg1985,
author = {Kutzelnigg, Werner},
doi = {10.1007/BF00527669},
issn = {0040-5744},
journal = {Theoretica Chimica Acta},
month = dec,
number = {6},
pages = {445--469},
title = {{r 12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l}},
url = {http://link.springer.com/10.1007/BF00527669},
volume = {68},
year = {1985}
}
