text:
249}
}

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  Title                    = {Cumulant expansion of the reduced density matrices},
  Author                   = {Kutzelnigg, Werner and Mukherjee, Debashis},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1999},
  Number                   = {6},
  Pages                    = {2800-2809},
  Volume                   = {110},

  Doi                      = {http://dx.doi.org/10.1063/1.478189},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/110/6/10.1063/1.478189}
}

@Article{lowdin,
  Title                    = {Quantum Theory of Many-Particle Systems. {I}. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction},
  Author                   = {L\"owdin, Per-Olov},
  Journal                  = {Physical Review},
  Year                     = {1955},

  Month                    = {Mar},
  Pages                    = {1474--1489},
  Volume                   = {97},

  Doi                      = {10.1103/PhysRev.97.1474},
  Issue                    = {6},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRev.97.1474},
  Publisher                = {American Physical Society}
}

@Article{PhysRev.97.1509,
  Title                    = {Quantum Theory of Many-Particle Systems. {III}. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects},
  Author                   = {L\"owdin, Per-Olov},
  Journal                  = {Physical Review},
  Year                     = {1955},

  Month                    = {Mar},
  Pages                    = {1509--1520},
  Volume                   = {97},

  Doi                      = {10.1103/PhysRev.97.1509},
  Issue                    = {6},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRev.97.1509}
}

@Article{lowdinortho,
  Title                    = {On the Non-Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals},
  Author                   = {L\"owdin, Per-Olov},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1950},
  Number                   = {3},
  Pages                    = {365-375},
  Volume                   = {18},

  Doi                      = {10.1063/1.1747632},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/18/3/10.1063/1.1747632}
}

@InBook{rendl_laurent,
  Title                    = {Handbook on Discrete Optimization},
  Author                   = {Laurent, M. and Rendl, F.},
  Chapter                  = {Semidefinite Programming and Integer Programming},
  Editor                   = {Aardal, K. and Nemhauser, G. and Weismantel, R.},
  Pages                    = {393--514},
  Publisher                = {Elsevier},
  Year                     = {2005}
}

@Article{b3lyp2,
  Title                    = {Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density},
  Author                   = {Lee, Chengteh and Yang, Weitao and Parr, Robert G.},
  Journal                  = {Physical Review B},
  Year                     = {1988},

  Month                    = {Jan},
  Pages                    = {785--789},
  Volume                   = {37},

  Doi                      = {10.1103/PhysRevB.37.785},
  Issue                    = {2},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevB.37.785},
  Numpages                 = {0},
  Publisher                = {American Physical Society}
}

@InCollection{ccsdt-book,
  Title                    = {Achieving Chemical Accuracy with Coupled-Cluster Theory},
  Author                   = {Lee, TimothyJ. and Scuseria, GustavoE.},
  Booktitle                = {Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy},
  Publisher                = {Springer Netherlands},
  Year                     = {1995},
  Editor                   = {Langhoff, StephenR.},
  Pages                    = {47-108},
  Series                   = {Understanding Chemical Reactivity},
  Volume                   = {13},

  Doi                      = {10.1007/978-94-011-0193-6_2},
  ISBN                     = {978-94-010-4087-7},
  Language                 = {English},
  Url                      = {http://dx.doi.org/10.1007/978-94-011-0193-6_2}
}

@Article{doi:10.1137/S0895479895281484,
  Title                    = {Deflation Techniques for an Implicitly Restarted Arnoldi Iteration},
  Author                   = {R. B. Lehoucq and D. C. Sorensen},
  Journal                  = {{SIAM} Journal on Matrix Analysis and Applications},
  Year                     = {1996},
  Number                   = {4},
  Pages                    = {789-821},
  Volume                   = {17},

  Doi                      = {10.1137/S0895479895281484},
  Url                      = {http://dx.doi.org/10.1137/S0895479895281484}
}

@Article{deltadftcodes,
  Title                    = {The Kohn-Sham equation of state for elemental solids: a solved problem},
  Author                   = {Lejaeghere, Kurt and Bihlmayer, Gustav and Björkman, Torbjörn and Blaha, Peter and Blügel, Stefan and Blum, Volker and Caliste, Damien and Castelli, Ivano E. and Clark, Stewart J. and Corso, Andrea Dal and Gironcoli, Stefano de and Deutsch, Thierry and Marco, Igor Di and Draxl, Claudia and Dułak, Marcin and Eriksson, Olle and Garrity, Kevin F. and Genovese, Luigi and Giannozzi, Paolo and Giantomassi, Matteo and Goedecker, Stefan and Gonze, Xavier and Grånäs, Oscar and Gulans, Andris and Gygi, François and Hamann, D. R. and Hasnip, Phil J. and Holzwarth, N. A. W. and Iusan, Diana and Jochym, Dominik B. and Jollet, François and Jones, Daniel and Kresse, Georg and Koepernik, Klaus and Küçükbenli, Emine and Kvashnin, Yaroslav O. and Locht, Inka L. M. and Lubeck, Sven and Marsman, Martijn and Marzari, Nicola and Mortensen, Jens Jørgen and Ozaki, Taisuke and Paulatto, Lorenzo and Pickard, Chris J. and Poelmans, Ward and Probert, Matt I. J. and Refson, Keith and Richter, Manuel and Rignanese, Gian-Marco and Saha, Santanu and Scheffler, Matthias and Schlipf, Martin and Schwarz, Karlheinz and Tavazza, Francesca and Thunström, Patrik and Tkatchenko, Alexandre and Torrent, Marc and Vanderbilt, David and Setten, Michiel J. van and Van Speybroeck, Veronique and Wills, John M. and Yates, Jonathan R. and Zhang, Guo-Xu and Cottenier, Stefaan},
  Journal                  = {Science},
  Year                     = {2015},
  Note                     = {submitted},

  Owner                    = {ward},
  Timestamp                = {23.06.2015}
}

@Article{mcscflengsfield,
  Title                    = {General second order {MCSCF} theory: A density matrix directed algorithm},
  Author                   = {Lengsfield, Byron H.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1980},
  Number                   = {1},
  Pages                    = {382-390},
  Volume                   = {73},

  Doi                      = {10.1063/1.439885},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/73/1/10.1063/1.439885}
}

@Article{:/content/aip/journal/jcp/75/1/10.1063/1.441840,
  Title                    = {A second order MCSCF method for large {CI} expansions},
  Author                   = {Lengsfield, Byron H. and Liu, Bowen},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1981},
  Number                   = {1},
  Pages                    = {478-480},
  Volume                   = {75},

  Doi                      = {10.1063/1.441840},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/75/1/10.1063/1.441840}
}

@Article{:/content/aip/journal/jcp/78/9/10.1063/1.445451,
  Title                    = {The valence-bond self-consistent field method ({VB-SCF}): Theory and test calculations},
  Author                   = {van Lenthe, J. H. and Balint-Kurti, G. G.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1983},
  Number                   = {9},
  Pages                    = {5699-5713},
  Volume                   = {78},

  Doi                      = {http://dx.doi.org/10.1063/1.445451}
}

@Article{doi:10.1021/ja02261a002,
  Title                    = {The atom and the molecule},
  Author                   = {Lewis, Gilbert N.},
  Journal                  = {Journal of the American Chemical Society},
  Year                     = {1916},
  Number                   = {4},
  Pages                    = {762-785},
  Volume                   = {38},

  Doi                      = {10.1021/ja02261a002}
}

@Article{n2ref1,
  Title                    = {Reduced multireference coupled cluster method: Ro-vibrational spectra of {N}$_2$},
  Author                   = {Li, Xiangzhu and Paldus, Josef},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2000},
  Number                   = {22},
  Pages                    = {9966-9977},
  Volume                   = {113},

  Doi                      = {10.1063/1.1323260},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/113/22/10.1063/1.1323260}
}

@Article{liebwu_2,
  Title                    = {The one-dimensional Hubbard model: a reminiscence},
  Author                   = {Elliott H. Lieb and F.Y. Wu},
  Journal                  = {Physica A: Statistical Mechanics and its Applications},
  Year                     = {2003},
  Number                   = {1-2},
  Pages                    = {1 - 27},
  Volume                   = {321},

  Doi                      = {10.1016/S0378-4371(02)01785-5},
  ISSN                     = {0378-4371},
  Keywords                 = {Hubbard model},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0378437102017855}
}

@Article{liebwu,
  Title                    = {Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension},
  Author                   = {Lieb, Elliott H. and Wu, F. Y.},
  Journal                  = {Physical Review Letters},
  Year                     = {1968},

  Month                    = {Jun},
  Pages                    = {1445--1448},
  Volume                   = {20},

  Doi                      = {10.1103/PhysRevLett.20.1445},
  Issue                    = {25},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevLett.20.1445},
  Publisher                = {American Physical Society}
}

@Article{C3CP53301H,
  Title                    = {Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals},
  Author                   = {Limacher, Peter A. and Ayers, Paul W. and Johnson, Paul A. and De Baerdemacker, Stijn and Neck, Dimitri Van and Bultinck, Patrick},
  Journal                  = {Physical Chemistry Chemical Physics},
  Year                     = {2014},
  Pages                    = {5061-5065},
  Volume                   = {16},

  Doi                      = {10.1039/C3CP53301H},
  Issue                    = {11},
  Myurl                    = {http://dx.doi.org/10.1039/C3CP53301H},
  Publisher                = {The Royal Society of Chemistry}
}

@Article{69Limacher_2013,
  Title                    = {A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals},
  Author                   = {Limacher, P. A. and Ayers, P. W. and Johnson, P. A. and De Baerdemacker, S. and Van Neck, D. and Bultinck, P.},
  Journal                  = {Journal of Chemical Theory and Computation},
  Year                     = {2013},
  Number                   = {3},
  Pages                    = {1394-1401},
  Volume                   = {9},

  Date-added               = {2014-01-15 16:56:01 +0000},
  Date-modified            = {2014-01-15 16:56:01 +0000},
  Doi                      = {10.1021/ct300902c},
  ISSN                     = {1549-9618},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article},
  Url                      = {<Go to ISI>://WOS:000316168700010}
}

@Article{peter_doci_orbital_dep,
  Title                    = {The influence of orbital rotation on the energy of closed-shell wavefunctions},
  Author                   = {Limacher, Peter A. and Kim, Taewon D. and Ayers, Paul W. and Johnson, Paul A. and De Baerdemacker, Stijn and Van Neck, Dimitri and Bultinck, Patrick},
  Journal                  = {Molecular Physics},
  Year                     = {2014},
  Number                   = {5-6},
  Pages                    = {853-862},
  Volume                   = {112},

  Doi                      = {10.1080/00268976.2013.874600},
  Myurl                    = {http://dx.doi.org/10.1080/00268976.2013.874600}
}

@Article{PhysRevLett.98.110503,
  Title                    = {Quantum Computational Complexity of the $N$-Representability Problem: QMA Complete},
  Author                   = {Liu, Yi-Kai and Christandl, Matthias and Verstraete, F.},
  Journal                  = {Physical Review Letters},
  Year                     = {2007},

  Month                    = {Mar},
  Pages                    = {110503},
  Volume                   = {98},

  Doi                      = {10.1103/PhysRevLett.98.110503},
  Issue                    = {11},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevLett.98.110503},
  Numpages                 = {4},
  Publisher                = {American Physical Society}
}

@Article{qma,
  Title                    = {Quantum Computational Complexity of the \mbox{$N$}-Representability Problem: \mbox{QMA} Complete},
  Author                   = {Liu, Yi-Kai and Christandl, Matthias and Verstraete, F.},
  Journal                  = {Physical Review Letters},
  Year                     = {2007},

  Month                    = {Mar},
  Pages                    = {110503},
  Volume                   = {98},

  Doi                      = {10.1103/PhysRevLett.98.110503},
  Issue                    = {11},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevLett.98.110503},
  Numpages                 = {4},
  Publisher                = {American Physical Society}
}

@Article{luttinger,
  Title                    = {An Exactly Soluble Model of a Many-Fermion System},
  Author                   = {J. M. Luttinger},
  Journal                  = {Journal of Mathematical Physics},
  Year                     = {1963},
  Number                   = {9},
  Pages                    = {1154-1162},
  Volume                   = {4},

  Doi                      = {10.1063/1.1704046},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JMP/4/1154/1}
}

@Article{RevModPhys.35.496,
  Title                    = {Discussion on The Hartree-Fock Approximation},
  Author                   = {Lykos, P. and Pratt, G. W.},
  Journal                  = {Reviews of Modern Physics},
  Year                     = {1963},

  Month                    = {Jul},
  Pages                    = {496--501},
  Volume                   = {35},

  Doi                      = {10.1103/RevModPhys.35.496},
  Issue                    = {3},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/RevModPhys.35.496}
}

@Article{Malbouisson2012,
  Title                    = {Optimization of Geometry at Hartree-Fock level Using the Generalized Simulated Annealing},
  Author                   = {Malbouisson, Luiz Augusto Carvalho and Sobrinho, Antonio Moreira de Cerqueira and Nascimento, Marco Antônio Chear and Andrade, Miceal Dias de},
  Journal                  = {Applied Mathematics},
  Year                     = {2012},
  Number                   = {10},
  Pages                    = {1526–1531},
  Volume                   = {03},

  Doi                      = {10.4236/am.2012.330212},
  ISSN                     = {2152-7393},
  Owner                    = {ward},
  Publisher                = {Scientific Research Publishing, Inc,},
  Timestamp                = {14.06.2015},
  Url                      = {http://dx.doi.org/10.4236/am.2012.330212}
}

@Article{malick,
  Title                    = {Regularization Methods for Semidefinite Programming},
  Author                   = {Jerome Malick and Janez Povh and Franz Rendl and Angelika Wiegele},
  Journal                  = {SIAM Journal on Optimization},
  Year                     = {2009},
  Number                   = {1},
  Pages                    = {336-356},
  Volume                   = {20},

  Publisher                = {SIAM}
}

@Article{malick_regularization_2009,
  Title                    = {Regularization {Methods} for {Semidefinite} {Programming}},
  Author                   = {Malick, Jerome and Povh, Janez and Rendl, Franz and Wiegele, Angelika},
  Journal                  = {SIAM Journal on Optimization},
  Year                     = {2009},
  Pages                    = {336},
  Volume                   = {20},

  Doi                      = {10.1137/070704575},
  ISSN                     = {10526234},
  Myurl                    = {http://link.aip.org/link/SJOPE8/v20/i1/p336/s1&Agg=doi},
  Urldate                  = {2011-09-29}
}

@Article{mattis,
  Title                    = {Exact Solution of a Many-Fermion System and Its Associated Boson Field},
  Author                   = {{Mattis}, D.~C. and {Lieb}, E.~H.},
  Journal                  = {Journal of Mathematical Physics},
  Year                     = {1965},

  Month                    = feb,
  Pages                    = {304-312},
  Volume                   = {6},

  Adsnote                  = {Provided by the SAO/NASA Astrophysics Data System},
  Adsurl                   = {http://adsabs.harvard.edu/abs/1965JMP.....6..304M},
  Doi                      = {10.1063/1.1704281}
}

@InCollection{Mayer1980189,
  Title                    = {The Spin-Projected Extended Hartree-Fock Method},
  Author                   = {István Mayer},
  Booktitle                = {The Spin-Projected Extended Hartree-Fock Method},
  Publisher                = {Academic Press},
  Year                     = {1980},
  Editor                   = {Per-Olov Löwdin},
  Pages                    = {189 - 262},
  Series                   = {Advances in Quantum Chemistry },
  Volume                   = {12},

  Doi                      = {10.1016/S0065-3276(08)60317-2},
  ISSN                     = {0065-3276},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0065327608603172}
}

@Article{Mayer_2002,
  Title                    = {On Löwdin’s method of symmetric orthogonalization},
  Author                   = {Mayer, I.},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {2002},
  Number                   = {1},
  Pages                    = {63–65},
  Volume                   = {90},

  Doi                      = {10.1002/qua.981},
  ISSN                     = {1097-461X},
  Owner                    = {ward},
  Publisher                = {Wiley-Blackwell},
  Timestamp                = {12.06.2015},
  Url                      = {http://dx.doi.org/10.1002/qua.981}
}

@Article{mayer,
  Title                    = {Electron Correlation},
  Author                   = {J.E. Mayer},
  Journal                  = {Physical Review},
  Year                     = {1955},
  Pages                    = {6},
  Volume                   = {100}
}

@Book{mazz_book,
  Title                    = {\mbox{R}educed-\mbox{D}ensity-\mbox{M}atrix \mbox{M}echanics: \mbox{W}ith \mbox{A}plication to \mbox{M}any-\mbox{E}lectron \mbox{A}toms and \mbox{M}olecules},
  Author                   = {Mazziotti, D. A.},
  Editor                   = {Mazziotti, D. A.},
  Publisher                = {Wiley: New York},
  Year                     = {2007},
  Volume                   = {134},

  Pages                    = {93}
}

@Article{maz_review,
  Title                    = {Two-Electron Reduced Density Matrix as the Basic Variable in Many-Electron Quantum Chemistry and Physics},
  Author                   = {Mazziotti, David A.},
  Journal                  = {Chemical Reviews},
  Year                     = {2012},
  Note                     = {PMID: 21863900},
  Number                   = {1},
  Pages                    = {244-262},
  Volume                   = {112},

  Doi                      = {10.1021/cr2000493},
  Url                      = {http://dx.doi.org/10.1021/cr2000493}
}

@Article{Mazziotti2012,
  Title                    = {Structure of Fermionic Density Matrices: Complete {N}-Representability Conditions},
  Author                   = {Mazziotti, David A.},
  Journal                  = {Physical Review Letters},
  Year                     = {2012},

  Month                    = {Jun},
  Number                   = {26},
  Volume                   = {108},

  Doi                      = {10.1103/physrevlett.108.263002},
  ISSN                     = {1079-7114},
  Owner                    = {ward},
  Publisher                = {American Physical Society (APS)},
  Timestamp                = {01.06.2015}
}

@Article{PhysRevA.85.062507,
  Title                    = {Significant conditions for the two-electron reduced density matrix from the constructive solution of $N$ representability},
  Author                   = {Mazziotti, David A.},
  Journal                  = {Physical Review A},
  Year                     = {2012},

  Month                    = {Jun},
  Pages                    = {062507},
  Volume                   = {85},

  Doi                      = {10.1103/PhysRevA.85.062507},
  Issue                    = {6},
  Numpages                 = {11},
  Publisher                = {American Physical Society}
}

@Article{maz_bp,
  Title                    = {Large-Scale Semidefinite Programming for Many-Electron Quantum Mechanics},
  Author                   = {Mazziotti, David A.},
  Journal                  = {Physical Review Letters},
  Year                     = {2011},

  Month                    = {Feb},
  Pages                    = {083001},
  Volume                   = {106},

  Publisher                = {American Physical Society}
}

@Article{mazziotti_large-scale_2011,
  Title                    = {Large-{Scale} {Semidefinite} {Programming} for {Many}-{Electron} {Quantum} {Mechanics}},
  Author                   = {Mazziotti, David A.},
  Journal                  = {Physical Review Letters},
  Year                     = {2011},

  Month                    = feb,
  Number                   = {8},
  Pages                    = {083001},
  Volume                   = {106},

  Abstract                 = {The energy of a many-electron quantum system can be approximated by a constrained optimization of the two-electron reduced density matrix (2-RDM) that is solvable in polynomial time by semidefinite programming (SDP). Here we develop a SDP method for computing strongly correlated 2-RDMs that is 10–20 times faster than previous methods [D. A. Mazziotti, Phys. Rev. Lett. 93 213001 (2004)]. We illustrate with (i) the dissociation of N2 and (ii) the metal-to-insulator transition of H50. For H50 the SDP problem has 9.4×106 variables. This advance also expands the feasibility of large-scale applications in quantum information, control, statistics, and economics.},
  Doi                      = {10.1103/PhysRevLett.106.083001},
  File                     = {APS Full Text PDF:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/2DPJBR95/Mazziotti - 2011 - Large-Scale Semidefinite Programming for Many-Elec.pdf:application/pdf;APS Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/R2H8C88V/e083001.html:text/html},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevLett.106.083001},
  Urldate                  = {2011-09-29}
}

@Article{maz_alg_3,
  Author                   = {Mazziotti, D. A.},
  Journal                  = {Math. Model. and Num. Anal.},
  Year                     = {2007},
  Pages                    = {249},
  Volume                   = {41}
}

@InBook{mazz-cse,
  Title                    = {Contracted Schrödinger Equation},
  Author                   = {Mazziotti, David A.},
  Pages                    = {165--203},
  Publisher                = {John Wiley \& Sons, Inc.},
  Year                     = {2007},

  Booktitle                = {Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules},
  Doi                      = {10.1002/9780470106600.ch8},
  ISBN                     = {9780470106600},
  Keywords                 = {contracted Schrödinger equation, 2-RDM purification, CSE solving algorithm},
  Url                      = {http://dx.doi.org/10.1002/9780470106600.ch8}
}

@Article{maz_T2_prime,
  Title                    = {Variational reduced-density-matrix method using three-particle $N$-representability conditions with application to many-electron molecules},
  Author                   = {Mazziotti, David A.},
  Journal                  = {Physical Review A},
  Year                     = {2006},

  Month                    = {Sep},
  Pages                    = {032501},
  Volume                   = {74},

  Doi                      = {10.1103/PhysRevA.74.032501},
  Issue                    = {3},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevA.74.032501},
  Publisher                = {American Physical Society}
}

@Article{PhysRevA.74.032501,
  Title                    = {Variational reduced-density-matrix method using three-particle $N$-representability conditions with application to many-electron molecules},
  Author                   = {Mazziotti, David A.},
  Journal                  = {Physical Review A},
  Year                     = {2006},

  Month                    = {Sep},
  Pages                    = {032501},
  Volume                   = {74},

  Doi                      = {10.1103/PhysRevA.74.032501},
  Issue                    = {3},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevA.74.032501},
  Numpages                 = {9},
  Publisher                = {American Physical Society}
}

@Article{mazz_T_con,
  Title                    = {Variational two-electron reduced density matrix theory for many-electron atoms and molecules: Implementation of the spin- and symmetry-adapted \mbox{T}2 condition to non-equilibrium geometries.},
  Author                   = {Mazziotti, D. A.},
  Journal                  = {Physical Review A},
  Year                     = {2005},
  Pages                    = {032510},
  Volume                   = {72}
}

@Article{maz_alg_2,
  Title                    = {First-order semidefinite programming for the direct determination of two-electron reduced density matrices with application to many-electron atoms and molecules},
  Author                   = {Mazziotti, David A.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2004},
  Number                   = {22},
  Pages                    = {10957-10966},
  Volume                   = {121},

  Doi                      = {http://dx.doi.org/10.1063/1.1810134}
}

@Article{maz_prl,
  Title                    = {Realization of Quantum Chemistry without Wave Functions through First-Order Semidefinite Programming},
  Author                   = {David A. Mazziotti},
  Journal                  = {Physical Review Letters},
  Year                     = {2004},
  Pages                    = {213001},
  Volume                   = {93}
}

@Article{mazziotti,
  Title                    = {Variational Minimization of atomic and molecular ground-state energies via the two-particle density matrix},
  Author                   = {David A. Mazziotti},
  Journal                  = {Physical Review A},
  Year                     = {2002},
  Pages                    = {062511},
  Volume                   = {65}
}

@Article{Mazziotti1998419,
  Title                    = {Approximate solution for electron correlation through the use of Schwinger probes },
  Author                   = {David A Mazziotti},
  Journal                  = {Chemical Physics Letters },
  Year                     = {1998},
  Number                   = {5–6},
  Pages                    = {419 - 427},
  Volume                   = {289},

  Doi                      = {10.1016/S0009-2614(98)00470-9},
  ISSN                     = {0009-2614},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0009261498004709}
}

@Article{maz_gen_T_1,
  Title                    = {Uncertainty relations and reduced density matrices: Mapping many-body quantum mechanics onto four particles},
  Author                   = {Mazziotti, David A. and Erdahl, Robert M.},
  Journal                  = {Physical Review A},
  Year                     = {2001},

  Month                    = {Mar},
  Pages                    = {042113},
  Volume                   = {63},

  Doi                      = {10.1103/PhysRevA.63.042113},
  Issue                    = {4},
  Numpages                 = {9},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRevA.63.042113}
}

@Article{davidson_2,
  Title                    = {Linear Inequalities for Density Matrices. {II}},
  Author                   = {McRae, Walter B. and Davidson, Ernest R.},
  Journal                  = {Journal of Mathematical Physics},
  Year                     = {1972},
  Number                   = {10},
  Pages                    = {1527-1538},
  Volume                   = {13},

  Doi                      = {10.1063/1.1665874},
  Url                      = {http://scitation.aip.org/content/aip/journal/jmp/13/10/10.1063/1.1665874}
}

@Article{mcweeny-agp,
  Title                    = {The Density Matrix in Many-Electron Quantum Mechanics. {III}. Generalized Product Functions for Beryllium and Four-Electron Ions},
  Author                   = {McWeeny, R. and Sutcliffe, B. T.},
  Journal                  = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences},
  Year                     = {1963},
  Number                   = {1352},
  Pages                    = {103--116},
  Volume                   = {273},

  Abstract                 = {The theory of generalized product functions is extended to non-orthogonal group functions in the case of two groups. Calculations on beryllium and on some four-electron ions are based on such group functions, and are compared with similar calculations using orthogonal group functions. It is shown that, in the case of the systems examined, the strong orthogonality restriction is not severe.},
  Doi                      = {10.1098/rspa.1963.0077},
  ISSN                     = {0080-4630},
  Publisher                = {The Royal Society}
}

@Article{mihailovic,
  Title                    = {The variational approach to the density matrix for light nuclei},
  Author                   = {M.V. Mihailovic and M. Rosina},
  Journal                  = {Nuclear Physics A},
  Year                     = {1974},
  Pages                    = {221},
  Volume                   = {237}
}

@Article{mishra,
  Title                    = {Algebra for fermions with a new exclusion principle},
  Author                   = {Mishra, A and Rajasekaran, G},
  Journal                  = {Pramana},
  Year                     = {1991},
  Pages                    = {537-555},
  Volume                   = {36},

  Affiliation              = {Central Electrochemical Research Institute 623 006 Karaikudi India},
  ISSN                     = {0304-4289},
  Issue                    = {5},
  Keyword                  = {Physics and Astronomy},
  Myurl                    = {http://dx.doi.org/10.1007/BF02894926},
  Publisher                = {Springer India, in co-publication with Indian Academy of Sciences}
}

@Article{Moret1998,
  Title                    = {Stochastic molecular optimization using generalized simulated annealing},
  Author                   = {Moret, M. A. and Pascutti, P. G. and Bisch, P. M. and Mundim, K. C.},
  Journal                  = {Journal of Computational Chemistry},
  Year                     = {1998},

  Month                    = {Apr},
  Number                   = {6},
  Pages                    = {647–657},
  Volume                   = {19},

  Doi                      = {10.1002/(sici)1096-987x(19980430)19:6<647::aid-jcc6>3.0.co;2-r},
  ISSN                     = {1096-987X},
  Owner                    = {ward},
  Publisher                = {Wiley-Blackwell},
  Timestamp                = {14.06.2015},
  Url                      = {http://dx.doi.org/10.1002/(SICI)1096-987X(19980430)19:6<647::AID-JCC6>3.0.CO;2-R}
}

@Article{Moret2002,
  Title                    = {New Stochastic Strategy to Analyze Helix Folding},
  Author                   = {Moret, M.A. and Bisch, P.M. and Mundim, K.C. and Pascutti, P.G.},
  Journal                  = {Biophysical Journal},
  Year                     = {2002},

  Month                    = {Mar},
  Number                   = {3},
  Pages                    = {1123–1132},
  Volume                   = {82},

  Doi                      = {10.1016/s0006-3495(02)75471-4},
  ISSN                     = {0006-3495},
  Owner                    = {ward},
  Publisher                = {Elsevier BV},
  Timestamp                = {14.06.2015},
  Url                      = {http://dx.doi.org/10.1016/S0006-3495(02)75471-4}
}

@Article{mori,
  Title                    = {Many-electron self-interaction error in approximate density functionals},
  Author                   = {Paula Mori-Sanchez and Aron J. Cohen and Weitao Yang},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2006},
  Number                   = {20},
  Pages                    = {201102},
  Volume                   = {125},

  Doi                      = {10.1063/1.2403848},
  Eid                      = {201102},
  Keywords                 = {density functional theory; reaction kinetics theory; thermochemistry},
  Numpages                 = {4},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JCP/125/201102/1}
}

@Article{Mori-Sanchez2009,
  Title                    = {Failure of the random phase approximation correlation energy},
  Author                   = {Paula Mori-Sánchez and Aron J. Cohen and Weitao Yang},
  Year                     = {2009},

  Month                    = mar,

  Abstract                 = {The random phase approximation (RPA) to the correlation energy is extended to fractional occupations and its performance examined for exact conditions on fractional charges and fractional spins. RPA satisfies the constancy condition for fractional spins that leads to correct bond dissociation and no static correlation error for H$_2$ but massively fails for fractional charges, with an enormous delocalization error even for a one-electron system such as H$_2^+$. Other methods such as range-separated RPA can reduce this delocalization error but only at the cost of increasing the static correlation error. None of the RPA methods seem to have the discontinuous nature required to satisfy both exact conditions and the full unified condition, emphasizing the need to go further than just smooth functionals of the orbitals.},
  Comments                 = {4 pages, 7 figures},
  Eprint                   = {0903.4403},
  Oai2identifier           = {0903.4403},
  Owner                    = {ward},
  Timestamp                = {09.06.2015}
}

@Article{morisa,
  Author                   = {P. Mori-Sanchez and A. J. Cohen and W. T. Yang},
  Journal                  = {Physical Review Letters},
  Year                     = {2008},
  Pages                    = {146401},
  Volume                   = {100}
}

@Article{morrell,
  Title                    = {Calculation of ionization potentials from density matrices and natural functions, and the long-range behavior of natural orbitals and electron density},
  Author                   = {Marilyn M. Morrell and Robert G. Parr and Mel Levy},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1975},
  Number                   = {2},
  Pages                    = {549-554},
  Volume                   = {62},

  Doi                      = {10.1063/1.430509},
  Keywords                 = {ATOMS; IONIZATION POTENTIALS; DENSITY MATRIX; ELECTRON DENSITY},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JCP/62/549/1}
}

@Article{mulliken,
  Title                    = {Electronic Population Analysis on \mbox{LCAO-MO} Molecular Wave Functions. I},
  Author                   = {R. S. Mulliken},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1955},
  Number                   = {10},
  Pages                    = {1833-1840},
  Volume                   = {23},

  Doi                      = {10.1063/1.1740588},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JCP/23/1833/1}
}

@Article{Mulliken1955,
  Title                    = {Electronic Population Analysis on {LCAO-MO} Molecular Wave Functions. {I}},
  Author                   = {Mulliken, R. S.},
  Journal                  = {The Journal of Chemical Physics},
  Year                     = {1955},
  Number                   = {10},
  Pages                    = {1833},
  Volume                   = {23},

  Doi                      = {10.1063/1.1740588},
  ISSN                     = {0021-9606},
  Owner                    = {ward},
  Publisher                = {AIP Publishing},
  Timestamp                = {16.06.2015},
  Url                      = {http://dx.doi.org/10.1063/1.1740588}
}

@Article{geo-sa-opt,
  Title                    = {Geometry optimization and conformational analysis through generalized simulated annealing},
  Author                   = {Mundim, Kleber C. and Tsallis, Constantino},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {1996},
  Number                   = {4},
  Pages                    = {373--381},
  Volume                   = {58},

  Doi                      = {10.1002/(SICI)1097-461X(1996)58:4<373::AID-QUA6>3.0.CO;2-V},
  ISSN                     = {1097-461X},
  Publisher                = {John Wiley \& Sons, Inc.},
  Url                      = {http://dx.doi.org/10.1002/(SICI)1097-461X(1996)58:4<373::AID-QUA6>3.0.CO;2-V}
}

@Book{murnaghan1962unitary,
  Title                    = {The unitary and rotation groups},
  Author                   = {Murnaghan, F.D.},
  Publisher                = {Spartan Books},
  Year                     = {1962},
  Series                   = {Lectures on applied mathematics},

  Lccn                     = {62019096},
  Url                      = {https://books.google.com/books?id=R1E3AAAAIAAJ}
}

@Misc{nagy,
  Title                    = {Real Analysis},

  Author                   = {Gabriel Nagy},

  Url                      = {http://www.math.ksu.edu/\verb|~|nagy/real-an/}
}

@Article{dispersion,
  Title                    = {Simple Hamiltonians which exhibit drastic failures by variational determination of the two-particle reduced density matrix with some well known \mbox{$N$}-representability conditions},
  Author                   = {Nakata, M. and Braams, B.J. and Fukuda, M. and Percus, J.K. and Yamashita, M. and Zhao, Z.J.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2006},

  Month                    = {december},
  Pages                    = {244109},
  Volume                   = {125}
}

@Article{nakata_last,
  Title                    = {Variational calculation of second-order reduced density matrices by strong \mbox{N}-representability conditions and an accurate semidefinite programming solver},
  Author                   = {Maho Nakata and Bastiaan J. Braams and Katsuki Fujisawa and Mituhiro Fukuda and Jerome K. Percus and Makoto Yamashita and Zhengji Zhao},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2008},
  Pages                    = {164113},
  Volume                   = {128}
}

@Article{nakata_first,
  Title                    = {Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm},
  Author                   = {Nakata, Maho and Nakatsuji, Hiroshi and Ehara, Masahiro and Fukuda, Mitsuhiro and Nakata, Kazuhide and Fujisawa, Katsuki},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2001},
  Number                   = {19},
  Pages                    = {8282},
  Volume                   = {114},

  Doi                      = {10.1063/1.1360199},
  ISSN                     = {0021-9606},
  Owner                    = {ward},
  Publisher                = {AIP Publishing},
  Timestamp                = {21.06.2015},
  Url                      = {http://dx.doi.org/10.1063/1.1360199}
}

@Article{doi:10.1021/ct100396y,
  Title                    = {Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?},
  Author                   = {Neese, Frank and Valeev, Edward F.},
  Journal                  = {Journal of Chemical Theory and Computation},
  Year                     = {2011},
  Number                   = {1},
  Pages                    = {33-43},
  Volume                   = {7},

  Doi                      = {10.1021/ct100396y},
  Myurl                    = {http://dx.doi.org/10.1021/ct100396y}
}

@Article{PhysRev.109.1632,
  Title                    = {Brueckner's Theory and the Method of Superposition of Configurations},
  Author                   = {Nesbet, R. K.},
  Journal                  = {Physical Review},
  Year                     = {1958},

  Month                    = {Mar},
  Pages                    = {1632--1638},
  Volume                   = {109},

  Doi                      = {10.1103/PhysRev.109.1632},
  Issue                    = {5},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRev.109.1632}
}

@Book{nesterov,
  Title                    = {Interior Point Polynomial Algorithms in Convex Programming},
  Author                   = {Nesterov, Y.E. and Nemirovski, A.},
  Publisher                = {SIAM, Philadelphia},
  Year                     = {1994},
  Series                   = {Studies in Applied and Numerical Mathematics},
  Volume                   = {13}
}

@Article{self_concord,
  Title                    = {Self-concordant functions and polynomial time methods in convex programming},
  Author                   = {Nesterov, Y.E. and Nemirovski, A.},
  Journal                  = {Tech. report for USSR Acad. Sci. Centr. Econ. \& Math. Inst., Moscow},
  Year                     = {1990},

  Month                    = {april}
}

@Article{nest_todd,
  Title                    = {Self-Scaled Barriers and Interior-Point Methods for Convex Programming},
  Author                   = {Nesterov, Yu. E. and Todd, M. J.},
  Journal                  = {Mathematics of Operations Research},
  Year                     = {1997},
  Number                   = {1},
  Pages                    = {1--42},
  Volume                   = {22},

  ISSN                     = {0364765X},
  Url                      = {http://www.jstor.org/stable/3690138}
}

@Book{von_neumann,
  Title                    = {Mathematische Grundlagen der Quantenmechanik},
  Author                   = {Neumann, Johann von},
  Publisher                = {Springer-Verlag, Berlin},
  Year                     = {1932}
}

@Article{PhysRevLett.106.110501,
  Title                    = {Quantum Codes Give Counterexamples to the Unique Preimage Conjecture of the $N$-Representability Problem},
  Author                   = {Ocko, Samuel A. and Chen, Xie and Zeng, Bei and Yoshida, Beni and Ji, Zhengfeng and Ruskai, Mary Beth and Chuang, Isaac L.},
  Journal                  = {Physical Review Letters},
  Year                     = {2011},

  Month                    = {Mar},
  Pages                    = {110501},
  Volume                   = {106},

  Doi                      = {10.1103/PhysRevLett.106.110501},
  Issue                    = {11},
  Numpages                 = {4},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRevLett.106.110501}
}

@Article{ogata,
  Title                    = {Bethe-ansatz wave function, momentum distribution, and spin correlation in the one-dimensional strongly correlated Hubbard model},
  Author                   = {Ogata, Masao and Shiba, Hiroyuki},
  Journal                  = {Physical Review B},
  Year                     = {1990},

  Month                    = {Feb},
  Pages                    = {2326--2338},
  Volume                   = {41},

  Doi                      = {10.1103/PhysRevB.41.2326},
  Issue                    = {4},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevB.41.2326},
  Publisher                = {American Physical Society}
}

@InBook{eltit,
  Title                    = {Optimization and Characterization of a Multiconfigurational Self-Consistent Field (MCSCF) State},
  Author                   = {Olsen, Jeppe and Yeager, Danny L. and Jørgensen, Poul},
  Pages                    = {1--176},
  Publisher                = {John Wiley \& Sons, Inc.},
  Year                     = {2007},

  Booktitle                = {Advances in Chemical Physics},
  Doi                      = {10.1002/9780470142783.ch1},
  ISBN                     = {9780470142783},
  Keywords                 = {MCSCF optimization, Newton-Raphson iterative function, Newton-Raphson approach, Newton-Raphson perturbative approach, Hessian approaches},
  Myurl                    = {http://dx.doi.org/10.1002/9780470142783.ch1}
}

@Article{paldus_application_1993,
  Title                    = {Application of {Hilbert}-space coupled-cluster theory to simple $\left(\mathrm{H}_2\right)_2$ model systems: {Planar} models},
  Author                   = {Paldus, J. and Piecuch, P. and Pylypow, L. and Jeziorski, B.},
  Journal                  = {Physical Review A},
  Year                     = {1993},

  Month                    = apr,
  Number                   = {4},
  Pages                    = {2738--2782},
  Volume                   = {47},

  Abstract                 = {The recently developed explicit formalism of orthogonally-spin-adapted, Hilbert-space (or state-universal), multireference (MR), coupled-cluster (CC) theory, exploiting the model space spanned by two closed-shell-type reference configurations, is applied to a simple four-electron model system consisting of two interacting hydrogen molecules. Four planar minimum-basis-set H4 models are examined, each characterized by a single parameter that fully determines its geometry, assuming the trapezoidal (H4 model), rectangular (P4 model), linear (D4 model), and square (S4 model) nuclear configuration. Varying this geometry-determining parameter, in each case we obtain different cross sections of the H4 potential-energy hypersurface, involving the dissociation of one, two, or all four H-H ‘‘bonds.’’ Comparing the resulting CC energies with exact values that are easily obtained for this model using the full configuration-interaction method, we can assess the performance of various MRCC Hilbert-space approaches at both the linear and nonlinear levels of approximation, while a continuous transition is being made between the degenerate and nondegenerate regimes. This enables us to elucidate the sources and the type of singular behavior in both linear and nonlinear versions of MRCC theory, to examine the role played by various intruder states, the existence and types of multiple solutions and their ability to describe various excited states, and, by performing a cluster analysis of the exact solutions, to assess the quality of the MRCC wave functions as well as the energies.},
  Doi                      = {10.1103/PhysRevA.47.2738},
  File                     = {APS Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/5DPCH8MF/PhysRevA.47.html:text/html},
  Shorttitle               = {Application of {Hilbert}-space coupled-cluster theory to simple (\$\{{\textbackslash}mathrm\{{H}\}\}\_\{2\}\$\$\{)\}\_\{2\}\$ model systems},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRevA.47.2738},
  Urldate                  = {2015-06-11}
}

@Article{palev,
  Title                    = {A Note on the Statistics of Hardcore Fermions},
  Author                   = {{Palev}, T.~D.},
  Journal                  = {ArXiv e-prints},
  Year                     = {2007},

  Month                    = dec,

  Archiveprefix            = {arXiv},
  Eprint                   = {cond-mat.str-el/0712.2736}
}

@Book{parr_density-functional_1994,
  Title                    = {Density-{Functional} {Theory} of {Atoms} and {Molecules}},
  Author                   = {Parr, Robert G. and Weitao, Yang},
  Publisher                = {Oxford University Press},
  Year                     = {1994},

  Address                  = {New York, NY},
  Month                    = may,

  Abstract                 = {This book is a rigorous, unified account of the fundamental principles of the density-functional theory of the electronic structure of matter and its applications to atoms and molecules. Containing a detailed discussion of the chemical potential and its derivatives, it provides an understanding of the concepts of electronegativity, hardness and softness, and chemical reactivity. Both the Hohenberg-Kohn-Sham and the Levy-Lieb derivations of the basic theorems are presented, and extensive references to the literature are included. Two introductory chapters and several appendices provide all the background material necessary beyond a knowledge of elementary quantum theory. The book is intended for physicists, chemists, and advanced students in chemistry.},
  ISBN                     = {9780195092769},
  Language                 = {English}
}

@Book{9780192670175,
  Title                    = {Quantum Theory of Solids},
  Author                   = {R. E. Peierls},
  Publisher                = {Clarendon Press},
  Year                     = {1996},

  ISBN                     = {0192670174},
  Url                      = {http://www.amazon.com/Quantum-Theory-International-Monographs-Physics/dp/0192670174}
}

@Article{frac_N_1,
  Title                    = {Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy},
  Author                   = {Perdew, John P. and Parr, Robert G. and Levy, Mel and Balduz, Jose L.},
  Journal                  = {Physical Review Letters},
  Year                     = {1982},

  Month                    = {Dec},
  Pages                    = {1691--1694},
  Volume                   = {49},

  Doi                      = {10.1103/PhysRevLett.49.1691},
  Issue                    = {23},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevLett.49.1691},
  Publisher                = {American Physical Society}
}

@Article{PhysRevLett.49.1691,
  Title                    = {Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy},
  Author                   = {Perdew, John P. and Parr, Robert G. and Levy, Mel and Balduz, Jose L.},
  Journal                  = {Physical Review Letters},
  Year                     = {1982},

  Month                    = {Dec},
  Pages                    = {1691--1694},
  Volume                   = {49},

  Doi                      = {10.1103/PhysRevLett.49.1691},
  Issue                    = {23},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRevLett.49.1691}
}

@Article{perdew,
  Title                    = {Exchange and correlation in open systems of fluctuating electron number},
  Author                   = {Perdew, John P. and Ruzsinszky, Adrienn and Csonka, G\'abor I. and Vydrov, Oleg A. and Scuseria, Gustavo E. and Staroverov, Viktor N. and Tao, Jianmin},
  Journal                  = {Physical Review A},
  Year                     = {2007},

  Month                    = {Oct},
  Pages                    = {040501},
  Volume                   = {76},

  Doi                      = {10.1103/PhysRevA.76.040501},
  Issue                    = {4},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevA.76.040501},
  Numpages                 = {4},
  Publisher                = {American Physical Society}
}

@Article{s-represen,
  Title                    = {Traces of spin-adapted reduced density matrices},
  Author                   = {Pérez-Romero, E. and Tel, L. M. and Valdemoro, C.},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {1997},
  Number                   = {1},
  Pages                    = {55--61},
  Volume                   = {61},

  Doi                      = {10.1002/(SICI)1097-461X(1997)61:1<55::AID-QUA6>3.0.CO;2-3},
  ISSN                     = {1097-461X},
  Myurl                    = {http://dx.doi.org/10.1002/(SICI)1097-461X(1997)61:1<55::AID-QUA6>3.0.CO;2-3},
  Publisher                = {John Wiley \& Sons, Inc.}
}

@Article{piecuch_stateselective_1994,
  Title                    = {State-selective multireference coupled-cluster theory employing the single-reference formalism: {Implementation} and application to the {H}$_8$ model system},
  Author                   = {Piecuch, Piotr and Adamowicz, Ludwik},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1994},

  Month                    = apr,
  Number                   = {8},
  Pages                    = {5792--5809},
  Volume                   = {100},

  Doi                      = {10.1063/1.467143},
  ISSN                     = {0021-9606, 1089-7690},
  Keywords                 = {Charge coupled devices, Cluster analysis, Configuration interaction, Special unitary groups, Wave functions},
  Shorttitle               = {State-selective multireference coupled‐cluster theory employing the single-reference formalism},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/100/8/10.1063/1.467143},
  Urldate                  = {2015-06-12}
}

@Article{Pisinger20061380,
  Title                    = {Upper bounds and exact algorithms for {p}-dispersion problems},
  Author                   = {David Pisinger},
  Journal                  = {Computers \& Operations Research},
  Year                     = {2006},
  Number                   = {5},
  Pages                    = {1380 - 1398},
  Volume                   = {33},

  Doi                      = {http://dx.doi.org/10.1016/j.cor.2004.09.033},
  ISSN                     = {0305-0548},
  Keywords                 = {Locational analysis},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0305054804002552}
}

@Misc{full-doci-code,
  Title                    = {{FullDOCI} solver},

  Author                   = {Ward Poelmans},
  HowPublished             = {\url{https://github.com/wpoely86/DOCI-Exact}},
  Note                     = {(accessed May 3, 2015)},
  Year                     = {2015},

  Owner                    = {ward},
  Timestamp                = {19.03.2015}
}

@Misc{v2dm-doci-code,
  Title                    = {{v2DM-DOCI} solver},

  Author                   = {Ward Poelmans},
  HowPublished             = {\url{https://github.com/wpoely86/doci_sdp-atom}},
  Note                     = {(accessed May 3, 2015)},
  Year                     = {2015},

  Doi                      = {10.5281/zenodo.17326},
  Owner                    = {ward},
  Timestamp                = {19.03.2015}
}

@Article{ward-doci,
  Title                    = {Variational optimization of the second order density matrix corresponding to a seniority-zero configuration interaction wave function},
  Author                   = {Poelmans, Ward and Van Raemdonck, Mario and Verstichel, Brecht and De Baerdemacker, Stijn and Torre, Alicia and Lain, Luis and Massaccesi, Gustavo E. and Alcoba, Diego Ricardo and Bultinck, Patrick and Van Neck, Dimitri},
  Journal                  = {Journal of Chemical Theory and Computation},
  Year                     = {2015},
  Number                   = {9},
  Pages                    = {4064-4076},
  Volume                   = {11},

  Doi                      = {10.1021/acs.jctc.5b00378},
  Owner                    = {ward},
  Timestamp                = {19.06.2015},
  Url                      = {http://dx.doi.org/10.1021/acs.jctc.5b00378}
}

@Article{povh_boundary_2006,
  Title                    = {A {Boundary} {Point} {Method} to {Solve} {Semidefinite} {Programs}},
  Author                   = {Povh, J. and Rendl, F. and Wiegele, A.},
  Journal                  = {Computing},
  Year                     = {2006},

  Month                    = nov,
  Pages                    = {277--286},
  Volume                   = {78},

  Doi                      = {10.1007/s00607-006-0182-2},
  File                     = {SpringerLink - Computing, Volume 78, Number 3:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/3ZPAJGB3/e11xj78r565jv395.html:text/html},
  ISSN                     = {0010-485X, 1436-5057},
  Url                      = {http://www.springerlink.com.libaccess.lib.mcmaster.ca/content/e11xj78r565jv395/},
  Urldate                  = {2011-09-29}
}

@Article{rendl,
  Title                    = {A Boundary Point Method to Solve Semidefinite Programs},
  Author                   = {Povh, J. and Rendl, F. and Wiegele, A.},
  Journal                  = {Computing},
  Year                     = {2006},
  Pages                    = {277-286},
  Volume                   = {78},

  Publisher                = {Springer Wien}
}

@Book{press2007numerical,
  Title                    = {Numerical recipes : the art of scientific computing},
  Author                   = {Press, William},
  Publisher                = {Cambridge University Press},
  Year                     = {2007},

  Address                  = {Cambridge, UK New York},

  ISBN                     = {978-0-521-88068-8},
  Url                      = {http://www.amazon.com/NUMERICAL-RECIPES-WILLIAM-H-PRESS/dp/B0073KCO5O}
}

@Article{jacobirots,
  Title                    = {Efficient use of Jacobi rotations for orbital optimization and localization},
  Author                   = {Raffenetti, RichardC. and Ruedenberg, Klaus and Janssen, CurtisL. and Schaefer, HenryF.},
  Journal                  = {Theoretica chimica acta},
  Year                     = {1993},
  Number                   = {1-2},
  Pages                    = {149-165},
  Volume                   = {86},

  Doi                      = {10.1007/BF01113521},
  ISSN                     = {0040-5744},
  Keywords                 = {Jacobi rotations; Four-index transformation; Orbital optimization; Orbital localization},
  Language                 = {English},
  Myurl                    = {http://dx.doi.org/10.1007/BF01113521},
  Publisher                = {Springer-Verlag}
}

@Article{QUA:QUA560040725,
  Title                    = {Parametrization of an orthogonal matrix in terms of generalized eulerian angles},
  Author                   = {Raffenetti, Richard C. and Ruedenberg, Klaus},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {1969},
  Number                   = {S3B},
  Pages                    = {625--634},
  Volume                   = {4},

  Doi                      = {10.1002/qua.560040725},
  ISSN                     = {1097-461X},
  Publisher                = {John Wiley \& Sons, Inc.},
  Url                      = {http://dx.doi.org/10.1002/qua.560040725}
}

@Article{ccsdt,
  Title                    = {A fifth-order perturbation comparison of electron correlation theories },
  Author                   = {Krishnan Raghavachari and Gary W. Trucks and John A. Pople and Martin Head-Gordon},
  Journal                  = {Chemical Physics Letters },
  Year                     = {1989},
  Number                   = {6},
  Pages                    = {479 - 483},
  Volume                   = {157},

  Doi                      = {10.1016/S0009-2614(89)87395-6},
  ISSN                     = {0009-2614},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0009261489873956}
}

@Article{rashid_quadratically_2013,
  Title                    = {A quadratically convergent {VBSCF} method},
  Author                   = {Rashid, Zahid and Lenthe, Joop H. van},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2013},

  Month                    = feb,
  Number                   = {5},
  Pages                    = {054105},
  Volume                   = {138},

  Abstract                 = {A quadratically convergent valence bond self-consistent field method is described where the simultaneous optimisation of orbitals and the coefficients of the configurations (VB structures) is based on a Newton-Raphson scheme. The applicability of the method is demonstrated in actual calculations. The convergence and efficiency are compared with the Super-CI method. A necessary condition to achieve convergence in the Newton-Raphson method is that the Hessian is positive definite. When this is not the case, a combination of the Super-CI and Newton-Raphson methods is shown to be an optimal choice instead of shifting the eigenvalues of the Hessian to make it positive definite. In the combined method, the first few iterations are performed with the Super-CI method and then the Newton-Raphson scheme is switched on based on an internal indicator. This approach is found computationally a more economical choice than using either the Newton-Raphson or Super-CI method alone to perform a full optimisation of the nonorthogonal orbitals.},
  Doi                      = {10.1063/1.4788765},
  File                     = {Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/9ACAQPTE/1.html:text/html},
  ISSN                     = {0021-9606, 1089-7690},
  Keywords                 = {Brillouin scattering, Newton Raphson method, Optimization, Valence bond methods, Wave functions},
  Owner                    = {ward},
  Timestamp                = {14.04.2015},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/138/5/10.1063/1.4788765},
  Urldate                  = {2015-04-14}
}

@Article{doi:10.1287/opre.42.2.299,
  Title                    = {Heuristic and Special Case Algorithms for Dispersion Problems},
  Author                   = {S. S. Ravi and D. J. Rosenkrantz and G. K. Tayi},
  Journal                  = {Operations Research},
  Year                     = {1994},
  Number                   = {2},
  Pages                    = {299-310},
  Volume                   = {42},

  Doi                      = {10.1287/opre.42.2.299}
}

@Article{richardson2,
  Title                    = {Numberical study of the 8-32-particle eigenstates of the pairing hamiltonian},
  Author                   = {Richardson, R. W.},
  Journal                  = {Physical Review},
  Year                     = {1966},
  Pages                    = {949},
  Volume                   = {141}
}

@Article{richardson3,
  Title                    = {A restricted class of exact eigenstates of the pairing-force Hamiltonian},
  Author                   = {Richardson, R. W.},
  Journal                  = {Physics Letters},
  Year                     = {1963},
  Number                   = {6},
  Pages                    = {277 - 279},
  Volume                   = {3},

  Doi                      = {10.1016/0031-9163(63)90259-2},
  ISSN                     = {0031-9163},
  Url                      = {http://www.sciencedirect.com/science/article/pii/0031916363902592}
}

@Article{richardson,
  Title                    = {Exact eigenstates of the pairing-force Hamiltonian},
  Author                   = {Richardson, R. W. and Sherman, N.},
  Journal                  = {Nuclear Physics},
  Year                     = {1964},
  Pages                    = {221--238},
  Volume                   = {52},

  Doi                      = {10.1016/0029-5582(64)90687-X}
}

@Book{ring_nuclear_2005,
  Title                    = {The {Nuclear} {Many}-{Body} {Problem}},
  Author                   = {Ring, Peter and Schuck, Peter},
  Publisher                = {Springer},
  Year                     = {2005},
  Month                    = may,

  Abstract                 = {From the reviews:"Its scope and complexity are suitable for easy reading by beginning students of nuclear theory. With a crisp and concise style, the authors quickly develop the shell-model approach to the nuclear many-body problem and subsequently devote more than a third of the text to Hartree-Fock and related models…" Physics Today},
  ISBN                     = {9783540212065},
  Language                 = {English},
  Owner                    = {ward},
  Timestamp                = {14.04.2015}
}

@Article{rombouts,
  Title                    = {Solving the Richardson equations for fermions},
  Author                   = {Rombouts, S. and Van Neck, D. and Dukelsky, J.},
  Journal                  = {Physical Review C},
  Year                     = {2004},

  Month                    = {Jun},
  Pages                    = {061303},
  Volume                   = {69},

  Doi                      = {10.1103/PhysRevC.69.061303},
  Issue                    = {6},
  Numpages                 = {5},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRevC.69.061303}
}

@Article{PhysRevB.55.2164,
  Title                    = {Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group},
  Author                   = {Rommer, Stefan and \"Ostlund, Stellan},
  Journal                  = {Physical Review B},
  Year                     = {1997},

  Month                    = {Jan},
  Pages                    = {2164--2181},
  Volume                   = {55},

  Doi                      = {10.1103/PhysRevB.55.2164},
  Issue                    = {4},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRevB.55.2164}
}

@Article{raeyraey,
  Title                    = {Density matrix averaged atomic natural orbital ({ANO}) basis sets for correlated molecular wave functions},
  Author                   = {Björn O. Roos and Roland Lindh and Per-Åke Malmqvist and Valera Veryazov and Per-Olof Widmark},
  Journal                  = {Theoretica chimica acta},
  Year                     = {1990},
  Number                   = {5},
  Pages                    = {291-306},
  Volume                   = {77},

  Doi                      = {10.1007/BF01120130},
  ISSN                     = {0040-5744},
  Keywords                 = {Atomic natural orbitals; Basis sets; General contraction},
  Myurl                    = {http://dx.doi.org/10.1007/BF01120130},
  Publisher                = {Springer-Verlag}
}

@Article{Roos1980157,
  Title                    = {A complete active space \{SCF\} method (CASSCF) using a density matrix formulated super-CI approach },
  Author                   = {Björn O. Roos and Peter R. Taylor and Per E.M. Siegbahn},
  Journal                  = {Chemical Physics },
  Year                     = {1980},
  Number                   = {2},
  Pages                    = {157 - 173},
  Volume                   = {48},

  Doi                      = {10.1016/0301-0104(80)80045-0},
  ISSN                     = {0301-0104},
  Url                      = {http://www.sciencedirect.com/science/article/pii/0301010480800450}
}

@Article{rosina,
  Title                    = {The variational calculation of reduced density matrices },
  Author                   = {M. Rosina and C. Garrod},
  Journal                  = {Journal of Computational Physics },
  Year                     = {1975},
  Number                   = {3},
  Pages                    = {300 - 310},
  Volume                   = {18},

  Doi                      = {http://dx.doi.org/10.1016/0021-9991(75)90004-2},
  ISSN                     = {0021-9991},
  Url                      = {http://www.sciencedirect.com/science/article/pii/0021999175900042}
}

@Article{QUA:QUA560160511,
  Title                    = {{MCSCF} optimization through combined use of natural orbitals and the brillouin–levy–berthier theorem},
  Author                   = {Ruedenberg, K. and Cheung, L. M. and Elbert, S. T.},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {1979},
  Number                   = {5},
  Pages                    = {1069--1101},
  Volume                   = {16},

  Doi                      = {10.1002/qua.560160511},
  ISSN                     = {1097-461X},
  Myurl                    = {http://dx.doi.org/10.1002/qua.560160511},
  Publisher                = {John Wiley \& Sons, Inc.}
}

@Article{ruzs,
  Title                    = {Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for \mbox{$\mathrm{H_2^+}$}, \mbox{$\mathrm{He_2^+}$}, \mbox{$\mathrm{LiH^+}$}, and \mbox{$\mathrm{Ne_2^+}$}},
  Author                   = {Adrienn Ruzsinszky and John P. Perdew and Gabor I. Csonka and Oleg A. Vydrov and Gustavo E. Scuseria},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2007},
  Number                   = {10},
  Pages                    = {104102},
  Volume                   = {126},

  Doi                      = {10.1063/1.2566637},
  Eid                      = {104102},
  Keywords                 = {hydrogen ions; helium ions; lithium compounds; neon; positive ions; density functional theory; binding energy; dissociation energies; HF calculations},
  Numpages                 = {8},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JCP/126/104102/1}
}

@Book{0719033861,
  Title                    = {Numerical Methods for Large Nonsymmetric Eigenvalue Problems (Algorithms \& Architectures for Advanced Scientific Computing)},
  Author                   = {Youcef Saad},
  Publisher                = {Manchester University Press},
  Year                     = {1995},

  ISBN                     = {0719033861},
  Url                      = {http://www.amazon.com/Nonsymmetric-Eigenvalue-Algorithms-Architectures-Scientific/dp/0719033861}
}

@Article{sasaki,
  Title                    = {Eigenvalues of Fermion Density Matrices},
  Author                   = {Sasaki, Fukashi},
  Journal                  = {Physical Review},
  Year                     = {1965},

  Month                    = {Jun},
  Pages                    = {B1338--B1342},
  Volume                   = {138},

  Doi                      = {10.1103/PhysRev.138.B1338},
  Issue                    = {5B},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRev.138.B1338},
  Publisher                = {American Physical Society}
}

@Book{savin,
  Title                    = {Recent Developments and Applications of Modern Density Functional Theory},
  Author                   = {A. Savin and J. M. Seminario},
  Publisher                = {Elsevier, New York},
  Year                     = {1996}
}

@Book{schaefer2013methods,
  Title                    = {Methods of Electronic Structure Theory},
  Author                   = {Schaefer, H.F.},
  Publisher                = {Springer US},
  Year                     = {2013},
  Series                   = {Modern Theoretical Chemistry},

  ISBN                     = {9781475708875},
  Url                      = {https://books.google.be/books?id=vXzSBwAAQBAJ}
}

@Book{schaefer_methods_1977,
  Title                    = {Methods of {Electronic} {Structure} {Theory}},
  Author                   = {Schaefer, Henry F.},
  Publisher                = {Springer},
  Year                     = {1977},
  Edition                  = {First Edition edition},
  Month                    = sep,

  Abstract                 = {These two volumes deal with the quantum theory of the electronic structure of molecules. Implicit in the term ab initio is the notion that approximate solutions of Schrödinger's equation are sought "from the beginning," i. e. , without recourse to experimental data. From a more pragmatic viewpoint, the distin guishing feature of ab initio theory is usually the fact that no approximations are involved in the evaluation of the required molecular integrals. Consistent with current activity in the field, the first of these two volumes contains chapters dealing with methods per se, while the second concerns the application of these methods to problems of chemical interest. In asense, the motivation for these volumes has been the spectacular recent success of ab initio theory in resolving important chemical questions. However, these applications have only become possible through the less visible but equally important efforts of those develop ing new theoretical and computational methods and models. Henry F Schaefer Vll Contents Contents of Volume 4 XIX Chapter 1. Gaussian Basis Sets for Molecular Calculations Thom. H. Dunning, Ir. and P. Ieffrey Hay 1. Introduction . . . . . . . . . . . . . . . . 1 1. 1. Slater Functions and the Hydrogen Moleeule 1 1. 2. Gaussian Functions and the Hydrogen Atom 3 2. Hartree-Fock Calculations on the First Row Atoms 5 2. 1. Valence States of the First Row Atoms 6 7 2. 2. Rydberg States of the First Row Atoms 9 2. 3.},
  ISBN                     = {9780306335037},
  Language                 = {English}
}

@Article{schilling_quantum_2014,
  Title                    = {The {Quantum} {Marginal} {Problem}},
  Author                   = {Schilling, Christian},
  Journal                  = {arXiv:1404.1085 [math-ph, physics:quant-ph]},
  Year                     = {2014},

  Month                    = apr,
  Note                     = {arXiv: 1404.1085},

  Abstract                 = {The question of whether given density operators for subsystems of a multipartite quantum system are compatible to one common total density operator is known as the quantum marginal problem. We briefly review the solution of a subclass of such problems found just recently. In particular, this provides the solution of the \$1\$-body \$N\$-representability problem. Its solution, the so-called generalized Pauli constraints, restrict the set of mathematically possible fermionic occupation numbers significantly, and strengthens Pauli's exclusion principle. Moreover, we review the study of a concrete physical model of interacting fermions confined to a harmonic trap. There, we found occupation numbers close, but not exactly on the boundary of the allowed region. This new effect of quasipinning is physically relevant since it corresponds to a simplified structure of the corresponding \$N\$-fermion quantum state.},
  Keywords                 = {Mathematical Physics, Quantum Physics},
  Url                      = {http://arxiv.org/abs/1404.1085},
  Urldate                  = {2015-05-08}
}

@Article{doi:10.1146/annurev.physchem.49.1.233,
  Title                    = {The construction and interpretation of {MCSCF} wavefunctions},
  Author                   = {Schmidt, Michael W. and Gordon, Mark S.},
  Journal                  = {Annual Review of Physical Chemistry},
  Year                     = {1998},
  Number                   = {1},
  Pages                    = {233-266},
  Volume                   = {49},

  Doi                      = {10.1146/annurev.physchem.49.1.233}
}

@Article{schollwock,
  Title                    = {The density-matrix renormalization group in the age of matrix product states},
  Author                   = {Schollw\"ock, Ulrich},
  Journal                  = {Annals of Physics},
  Year                     = {2011},
  Number                   = {1},
  Pages                    = {96 - 192},
  Volume                   = {326},

  Doi                      = {10.1016/j.aop.2010.09.012},
  ISSN                     = {0003-4916},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0003491610001752}
}

@Article{dmrg2,
  Title                    = {The density-matrix renormalization group in the age of matrix product states },
  Author                   = {Ulrich Schollwöck},
  Journal                  = {Annals of Physics },
  Year                     = {2011},
  Note                     = {January 2011 Special Issue },
  Number                   = {1},
  Pages                    = {96 - 192},
  Volume                   = {326},

  Doi                      = {http://dx.doi.org/10.1016/j.aop.2010.09.012},
  ISSN                     = {0003-4916},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0003491610001752}
}

@Article{schuch_computational_2009,
  Title                    = {Computational complexity of interacting electrons and fundamental limitations of density functional theory},
  Author                   = {Schuch, Norbert and Verstraete, Frank},
  Journal                  = {Nature Physics},
  Year                     = {2009},

  Month                    = oct,
  Number                   = {10},
  Pages                    = {732--735},
  Volume                   = {5},

  Doi                      = {10.1038/nphys1370},
  ISSN                     = {1745-2473},
  Url                      = {http://www.nature.com/nphys/journal/v5/n10/full/nphys1370.html},
  Urldate                  = {2015-05-08}
}

@Book{shaik2007chemist,
  Title                    = {A Chemist's Guide to Valence Bond Theory},
  Author                   = {Shaik, S.S. and Hiberty, P.C.},
  Publisher                = {Wiley},
  Year                     = {2007},

  ISBN                     = {9780470192580},
  Lccn                     = {2007040432},
  Url                      = {https://books.google.be/books?id=yM7Od\_dSxTQC}
}

@Article{shenvi,
  Title                    = {Active-Space $N$-Representability Constraints for Variational Two-Particle Reduced Density Matrix Calculations},
  Author                   = {Shenvi, Neil and Izmaylov, Artur F.},
  Journal                  = {Physical Review Letters},
  Year                     = {2010},

  Month                    = {Nov},
  Pages                    = {213003},
  Volume                   = {105},

  Publisher                = {American Physical Society}
}

@Article{doi:10.1021/bk-2007-0958.ch005,
  Title                    = {Bond Breaking in Quantum Chemistry: A Comparison of Single- and Multi-Reference Methods},
  Author                   = {Sherrill, C. David and Dutta, Antara and Abrams, Micah L. and Sears, John S.},
  Journal                  = {ACS Symposium Series},
  Year                     = {2007},

  Month                    = {Mar},
  Pages                    = {75–88},

  Doi                      = {10.1021/bk-2007-0958.ch005},
  ISBN                     = {http://id.crossref.org/isbn/0-8412-2076-X},
  ISSN                     = {1947-5918},
  Owner                    = {ward},
  Publisher                = {American Chemical Society (ACS)},
  Timestamp                = {25.06.2015},
  Url                      = {http://dx.doi.org/10.1021/bk-2007-0958.ch005}
}

@Misc{jrs,
  Title                    = {An Introduction to the Conjugate Gradient Method Without the Agonizing Pain},

  Author                   = {Jonathan Richard Shewchuk},
  Month                    = {august},
  Year                     = {1994},

  Url                      = {http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf}
}

@Article{Shor1999,
  Title                    = {Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer},
  Author                   = {Shor, Peter W.},
  Journal                  = {SIAM Review},
  Year                     = {1999},

  Month                    = {Jan},
  Number                   = {2},
  Pages                    = {303–332},
  Volume                   = {41},

  Doi                      = {10.1137/s0036144598347011},
  ISSN                     = {1095-7200},
  Owner                    = {ward},
  Publisher                = {Society for Industrial \& Applied Mathematics (SIAM)},
  Timestamp                = {21.06.2015},
  Url                      = {http://dx.doi.org/10.1137/S0036144598347011}
}

@Article{siegbahn_comparison_1980,
  Title                    = {A {Comparison} of the {Super}-{CI} and the {Newton}-{Raphson} {Scheme} in the {Complete} {Active} {Space} {SCF} {Method}},
  Author                   = {Siegbahn, Per and Heiberg, Anders and Roos, Björn and Levy, Bernard},
  Journal                  = {Physica Scripta},
  Year                     = {1980},

  Month                    = jan,
  Number                   = {3-4},
  Pages                    = {323},
  Volume                   = {21},

  Abstract                 = {A density matrix formulation is presented of the super-C I and Newton-Raphson methods in complete active space SCF (CASSCF) calculations. The CASSCF method is a special form of the MC-SCF method, where the C I wave function is assumed to be complete in a subset of the orbital space (the active space), leaving the remaining orbitals doubly occupied in all configurations. Explicit formulas are given for all matrix elements in the super-C I method and the first and second derivatives in the Newton-Raphson formulation. The similarities between the two methods are pointed out and the differences in the detailed formulations are discussed. Especially interesting is the fact, that while the second derivatives can be expressed in terms of first and second order density matrices, the matrix elements between the super-C I states involve also the third order density matrix in some cases.},
  Doi                      = {10.1088/0031-8949/21/3-4/014},
  File                     = {Full Text PDF:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/S3WATD68/Siegbahn et al. - 1980 - A Comparison of the Super-CI and the Newton-Raphso.pdf:application/pdf;Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/G6HIIX22/014.html:text/html},
  ISSN                     = {1402-4896},
  Owner                    = {ward},
  Timestamp                = {14.04.2015},
  Url                      = {http://iopscience.iop.org/1402-4896/21/3-4/014},
  Urldate                  = {2015-04-14}
}

@Article{:/content/aip/journal/jcp/43/10/10.1063/1.1701504,
  Title                    = {{$N$}-Representability Problem for Fermion Density Matrices. {I}. The Second-Order Density Matrix with {$N=3$}},
  Author                   = {Smith, Darwin W.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1965},
  Number                   = {10},
  Pages                    = {S258-S264},
  Volume                   = {43},

  Doi                      = {10.1063/1.1701504},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/43/10/10.1063/1.1701504}
}

@Article{smith,
  Title                    = {Extension of Koopmans' theorem. {I}. Derivation},
  Author                   = {Darwin W. Smith and Orville W. Day},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1975},
  Number                   = {1},
  Pages                    = {113-114},
  Volume                   = {62},

  Doi                      = {10.1063/1.430253},
  Keywords                 = {ATOMS; IONIZATION POTENTIAL; WAVEFUNCTIONS; HARTREEFOCK METHOD; ELECTRON CORRELATION; ELECTRONIC STRUCTURE},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JCP/62/113/1}
}

@Book{mpi2,
  Title                    = {MPI: The Complete Reference},
  Author                   = {Marc Snir and Steve W. Otto and Steven Huss-Lederman and David W. Walker and Jack Dongarra},
  Publisher                = {The MIT Press},
  Year                     = {1998},
  Edition                  = {2nd},
  Volume                   = {1},

  ISBN                     = {0262692155},
  Url                      = {http://www.amazon.com/MPI-Complete-Reference-Vol-Edition/dp/0262692155}
}

@Article{sorella,
  Title                    = {Non–Fermi-Liquid Exponents of the One-Dimensional Hubbard Model},
  Author                   = {S. Sorella and A. Parola and M. Parrinello and E. Tosatti},
  Journal                  = {EPL (Europhysics Letters)},
  Year                     = {1990},
  Number                   = {8},
  Pages                    = {721},
  Volume                   = {12},

  Url                      = {http://stacks.iop.org/0295-5075/12/i=8/a=009}
}

@Article{doi:10.1137/0613025,
  Title                    = {Implicit Application of Polynomial Filters in a k-Step Arnoldi Method},
  Author                   = {D. C. Sorensen},
  Journal                  = {{SIAM} Journal on Matrix Analysis and Applications},
  Year                     = {1992},
  Number                   = {1},
  Pages                    = {357-385},
  Volume                   = {13},

  Doi                      = {10.1137/0613025},
  Url                      = {http://dx.doi.org/10.1137/0613025}
}

@Book{sra2012optimization,
  Title                    = {Optimization for machine learning},
  Author                   = {Sra, Suvrit},
  Publisher                = {MIT Press},
  Year                     = {2012},

  Address                  = {Cambridge, Mass},

  ISBN                     = {9780262016469}
}

@Article{stein_seniority_2014,
  Title                    = {Seniority zero pair coupled cluster doubles theory},
  Author                   = {Stein, Tamar and Henderson, Thomas M. and Scuseria, Gustavo E.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2014},

  Month                    = jun,
  Number                   = {21},
  Pages                    = {214113},
  Volume                   = {140},

  Abstract                 = {Coupled cluster theory with single and double excitations accurately describes weak electron correlation but is known to fail in cases of strong static correlation. Fascinatingly, however, pair coupled cluster doubles (p-CCD), a simplified version of the theory limited to pair excitations that preserve the seniority of the reference determinant (i.e., the number of unpaired electrons), has mean field computational cost and is an excellent approximation to the full configuration interaction (FCI) of the paired space provided that the orbital basis defining the pairing scheme is adequately optimized. In previous work, we have shown that optimization of the pairing scheme in the seniority zero FCI leads to a very accurate description of static correlation. The same conclusion extends to p-CCD if the orbitals are optimized to make the p-CCD energy stationary. We here demonstrate these results with numerous examples. We also explore the contributions of different seniority sectors to the coupled cluster doubles (CCD) correlation energy using different orbital bases. We consider both Hartree-Fock and Brueckner orbitals, and the role of orbital localization. We show how one can pair the orbitals so that the role of the Brueckner orbitals at the CCD level is retained at the p-CCD level. Moreover, we explore ways of extending CCD to accurately describe strongly correlated systems.},
  Doi                      = {10.1063/1.4880819},
  File                     = {Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/5MXRC234/1.html:text/html},
  ISSN                     = {0021-9606, 1089-7690},
  Keywords                 = {Charge coupled devices, Coupled cluster, Electron correlation calculations, Hubbard model, Wave functions},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/140/21/10.1063/1.4880819},
  Urldate                  = {2015-04-14}
}

@InBook{symbrokhf,
  Title                    = {Symmetry breaking in the independent particle model},
  Author                   = {Stuber, J. L. and Paldus, J.},
  Chapter                  = {4},
  Editor                   = {Erkki J. Brändas and Eugene S. Kryachko},
  Pages                    = {67--139},
  Publisher                = {Kluwer Academic},
  Year                     = {2003},

  Address                  = {Dordrecht, The Nederlands},
  Series                   = {Fundamental World of Quantum Chemistry, A Tribute Volume to the Memory of Per-Olov Löwdin},
  Volume                   = {1},

  Owner                    = {ward},
  Timestamp                = {21.05.2015}
}

@Article{Sturm1999,
  Title                    = {Using {SeDuMi} 1.02, A Matlab toolbox for optimization over symmetric cones},
  Author                   = {Sturm, Jos F.},
  Journal                  = {Optimization Methods and Software},
  Year                     = {1999},

  Month                    = {Jan},
  Number                   = {1-4},
  Pages                    = {625–653},
  Volume                   = {11},

  Doi                      = {10.1080/10556789908805766},
  ISSN                     = {1029-4937},
  Owner                    = {ward},
  Publisher                = {Informa UK Limited},
  Timestamp                = {18.06.2015},
  Url                      = {http://dx.doi.org/10.1080/10556789908805766}
}

@Book{sturm,
  Title                    = {Primal-dual interior point approach to semidefinite programming},
  Author                   = {Sturm, J. F.},
  Publisher                = {Amsterdam Thesis publishers},
  Year                     = {1997},
  Series                   = {Tinbergen institute research series},

  Pages                    = {156}
}

@InCollection{surjan-geminals,
  Title                    = {An Introduction to the Theory of Geminals},
  Author                   = {Surján, PéterR.},
  Booktitle                = {Correlation and Localization},
  Publisher                = {Springer Berlin Heidelberg},
  Year                     = {1999},
  Editor                   = {Surján, PéterR. and Bartlett, R.J. and Bogár, F. and Cooper, D.L. and Kirtman, B. and Klopper, W. and Kutzelnigg, W. and March, N.H. and Mezey, P.G. and Müller, H. and Noga, J. and Paldus, J. and Pipek, J. and Raimondi, M. and Røeggen, I. and Sun, J.Q. and Surján, P.R. and Valdemoro, C. and Vogtner, S.},
  Pages                    = {63-88},
  Series                   = {Topics in Current Chemistry},
  Volume                   = {203},

  Doi                      = {10.1007/3-540-48972-X_4},
  ISBN                     = {978-3-540-65754-5},
  Keywords                 = {Geminals Localization Arai theorem Brillouin theorem},
  Language                 = {English},
  Url                      = {http://dx.doi.org/10.1007/3-540-48972-X_4}
}

@Book{szabo_modern_1996,
  Title                    = {Modern {Quantum} {Chemistry}: {Introduction} to {Advanced} {Electronic} {Structure} {Theory}},
  Author                   = {Szabo, Attila and Ostlund, Neil S.},
  Publisher                = {Dover Publications},
  Year                     = {1996},

  Abstract                 = {The aim of this graduate-level textbook is to present and explain, at other than a superficial level, modem ab initio approaches to the calculation of the electronic structure and properties of molecules. The first three chapters contain introductory material culminating in a thorough discussion of the Hartree-Fock approximation.The remaining four chapters describe a variety of more sophisticated approaches, which improve upon this approximation.Among the highlights of the seven chapters are (1) a review of the mathematics (mostly matrix algebra) required for the rest of the book, (2) an introduction to the basic techniques, ideas, and notations of quantum chemistry, (3) a thorough discussion of the Hartree-Fock approximation, (4) a treatment of configuration interaction (Cl) and approaches incorporating electron correlation, (5) a description of the independent electron pair approximation and a variety of more sophisticated approaches that incorporate coupling between pairs, (6) a consideration of the perturbative approach to the calculation of the correlation energy of many-electron systems and (7) a brief introduction to the use of the one-particle many-body Green's function in quantum chemistry.Over 150 exercises, designed to help the reader acquire a working knowledge of the material, are embedded in the text. The book is largely self-contained and requires no prerequisite other than a solid undergraduate physical chemistry course; however, some exposure to quantum chemistry will enhance the student's appreciation of the material. Clear and well-written, this text is ideal for the second semester of a two-semester course in quantum chemistry, or for a special topics course.},
  ISBN                     = {9780486691862},
  Language                 = {English},
  Shorttitle               = {Modern {Quantum} {Chemistry}}
}

@Article{szalay_multiconfiguration_2012,
  Title                    = {Multiconfiguration {Self}-{Consistent} {Field} and {Multireference} {Configuration} {Interaction} {Methods} and {Applications}},
  Author                   = {Szalay, Péter G. and Müller, Thomas and Gidofalvi, Gergely and Lischka, Hans and Shepard, Ron},
  Journal                  = {Chemical Reviews},
  Year                     = {2012},

  Month                    = jan,
  Number                   = {1},
  Pages                    = {108--181},
  Volume                   = {112},

  Doi                      = {10.1021/cr200137a},
  File                     = {ACS Full Text Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/ER6NWFQJ/cr200137a.html:text/html},
  ISSN                     = {0009-2665},
  Myurl                    = {http://dx.doi.org/10.1021/cr200137a},
  Urldate                  = {2015-04-14}
}

@Book{talmi1993simple,
  Title                    = {Simple models of complex nuclei : the shell model and interacting boson model},
  Author                   = {Talmi, Igal},
  Publisher                = {Harwood Academic Publishers},
  Year                     = {1993},

  Address                  = {Chur, Switzerland Langhorne, Pa., U.S.A},

  ISBN                     = {9783718605514}
}

@Article{dunning,
  Title                    = {Gaussian basis sets for use in correlated molecular calculations. {I}. The atoms boron through neon and hydrogen},
  Author                   = {Thom H. Dunning, Jr.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1989},
  Number                   = {2},
  Pages                    = {1007-1023},
  Volume                   = {90},

  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JCP/90/1007/1}
}

@Article{lio_trip,
  Title                    = {Lithium monoxide anion: A ground-state triplet with the strongest base to date},
  Author                   = { Zhixin Tian and Bun Chan and Sullivan, Michael B. and Leo Radom and Kass, Steven R.},
  Journal                  = {Proceedings of the National Academy of Sciences of the United States of America},
  Year                     = {2008},
  Pages                    = {7647-7651},
  Volume                   = {105}
}

@Article{tomonaga,
  Title                    = {Remarks on Bloch's Method of Sound Waves applied to Many-Fermion Problems},
  Author                   = {{Tomonaga}, S.},
  Journal                  = {Progress of Theoretical Physics},
  Year                     = {1950},

  Month                    = jul,
  Pages                    = {544-569},
  Volume                   = {5},

  Adsnote                  = {Provided by the SAO/NASA Astrophysics Data System},
  Adsurl                   = {http://adsabs.harvard.edu/abs/1950PThPh...5..544T}
}

@Book{tomonaga_story_1998,
  Title                    = {The {Story} of {Spin}},
  Author                   = {Tomonaga, Sin-itiro},
  Publisher                = {University Of Chicago Press},
  Year                     = {1998},

  Address                  = {Chicago},
  Edition                  = {1 edition},
  Month                    = aug,

  Abstract                 = {All atomic particles have a particular "spin," analogous to the earth's rotation on its axis. The quantum mechanical reality underlying spin is complex and still poorly understood. Sin-itiro Tomonaga's The Story of Spin remains the most complete and accessible treatment of spin, and is now available in English translation. Tomonaga tells the tale of the pioneers of physics and their difficult journey toward an understanding of the nature of spin and its relationship to statistics. His clear unfolding of the tale of spin is invaluable to students of physics, chemistry, and astronomy, and his description of the historical development of spin will interest historians and philosophers of science."This piece of the history of physics will provide excellent and exciting reading. . . . It also provides the personal touch of an expert in the field that is so often lacking in the physics literature. I recommend it very highly."—Fritz Rohrlich, Physics TodaySin-itiro Tomonaga was awarded the Nobel Prize for Physics in 1965.},
  ISBN                     = {9780226807942},
  Language                 = {English},
  Translator               = {Oka, Takeshi}
}

@Article{tredgold,
  Title                    = {Density Matrix and the Many-Body problem},
  Author                   = {R. H. Tredgold},
  Journal                  = {Physical Review},
  Year                     = {1957},
  Pages                    = {5},
  Volume                   = {105}
}

@Article{Turing01011938,
  Title                    = {On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction},
  Author                   = {Turing, A. M.},
  Journal                  = {Proceedings of the London Mathematical Society},
  Year                     = {1938},
  Number                   = {1},
  Pages                    = {544-546},
  Volume                   = {s2-43},

  Doi                      = {10.1112/plms/s2-43.6.544},
  Url                      = {http://plms.oxfordjournals.org/content/s2-43/1/544.short}
}

@Article{Turing01011937,
  Title                    = {On Computable Numbers, with an Application to the Entscheidungsproblem},
  Author                   = {Turing, A. M.},
  Journal                  = {Proceedings of the London Mathematical Society},
  Year                     = {1937},
  Number                   = {1},
  Pages                    = {230-265},
  Volume                   = {s2-42},

  Doi                      = {10.1112/plms/s2-42.1.230},
  Url                      = {http://plms.oxfordjournals.org/content/s2-42/1/230.short}
}

@Article{psi4,
  Title                    = {Psi4: an open-source ab initio electronic structure program},
  Author                   = {Turney, Justin M. and Simmonett, Andrew C. and Parrish, Robert M. and Hohenstein, Edward G. and Evangelista, Francesco A. and Fermann, Justin T. and Mintz, Benjamin J. and Burns, Lori A. and Wilke, Jeremiah J. and Abrams, Micah L. and Russ, Nicholas J. and Leininger, Matthew L. and Janssen, Curtis L. and Seidl, Edward T. and Allen, Wesley D. and Schaefer, Henry F. and King, Rollin A. and Valeev, Edward F. and Sherrill, C. David and Crawford, T. Daniel},
  Journal                  = {Wiley Interdisciplinary Reviews: Computational Molecular Science},
  Year                     = {2012},
  Number                   = {4},
  Pages                    = {556--565},
  Volume                   = {2},

  Doi                      = {10.1002/wcms.93},
  ISSN                     = {1759-0884},
  Myurl                    = {http://dx.doi.org/10.1002/wcms.93},
  Publisher                = {John Wiley \& Sons, Inc.}
}

@Article{DBLP:journals/corr/cs-CC-0409051,
  Title                    = {Quantum Complexity Classes},
  Author                   = {Tereza Tusarova},
  Journal                  = {CoRR},
  Year                     = {2004},
  Volume                   = {cs.CC/0409051},

  Bibsource                = {dblp computer science bibliography, http://dblp.org},
  Biburl                   = {http://dblp.uni-trier.de/rec/bib/journals/corr/cs-CC-0409051},
  Timestamp                = {Mon, 05 Dec 2011 18:05:28 +0100},
  Url                      = {http://arxiv.org/abs/cs.CC/0409051}
}

@InBook{valdemoro-cse,
  Title                    = {Theory and Methodology of The Contracted Schrödinger Equation},
  Author                   = {Valdemoro, C.},
  Pages                    = {119--164},
  Publisher                = {John Wiley \& Sons, Inc.},
  Year                     = {2007},

  Booktitle                = {Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules},
  Doi                      = {10.1002/9780470106600.ch7},
  ISBN                     = {9780470106600},
  Keywords                 = {contracted Schrödinger equation, reduced density matrix construction algorithm, 2-RDM and 2-CSE iterative process convergence},
  Url                      = {http://dx.doi.org/10.1002/9780470106600.ch7}
}

@Article{helen_1,
  Title                    = {Incorrect diatomic dissociation in variational reduced density matrix theory arises from the flawed description of fractionally charged atoms},
  Author                   = {Van Aggelen, Helen and Bultinck, Patrick and Verstichel, Brecht and Van Neck, Dimitri and Ayers, Paul W.},
  Journal                  = {Physical Chemistry Chemical Physics},
  Year                     = {2009},
  Pages                    = {5558-5560},
  Volume                   = {11},

  Doi                      = {10.1039/B907624G},
  Issue                    = {27},
  Myurl                    = {http://dx.doi.org/10.1039/B907624G},
  Publisher                = {The Royal Society of Chemistry}
}

@Article{VanHouteghem2014,
  Title                    = {Critical Analysis of the Accuracy of Models Predicting or Extracting Liquid Structure Information},
  Author                   = {Van Houteghem, Marc and Ghysels, An and Verstraelen, Toon and Poelmans, Ward and Waroquier, Michel and Van Speybroeck, Veronique},
  Journal                  = {The Journal of Physical Chemistry B},
  Year                     = {2014},

  Month                    = {Mar},
  Number                   = {9},
  Pages                    = {2451–2470},
  Volume                   = {118},

  Doi                      = {10.1021/jp411737s},
  ISSN                     = {1520-5207},
  Owner                    = {ward},
  Publisher                = {American Chemical Society (ACS)},
  Timestamp                = {23.06.2015},
  Url                      = {http://dx.doi.org/10.1021/jp411737s}
}

@Article{dimi,
  Title                    = {Necessary conditions for the \mbox{N}-representability of the second-order reduced density matrix: Upper bounds on the \mbox{P} and \mbox{Q} matrices.},
  Author                   = {Van Neck, Dimitri and Ayers, Paul W.},
  Journal                  = {Physical Review A},
  Year                     = {2007},
  Pages                    = {032502},
  Volume                   = {75}
}

@Article{mario-doci,

   author = "Van Raemdonck, Mario and Alcoba, Diego R. and Poelmans, Ward and De Baerdemacker, Stijn and Torre, Alicia and Lain, Luis and Massaccesi, Gustavo E. and Van Neck, Dimitri and Bultinck, Patrick",
   title = "Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions",
   journal = "The Journal of Chemical Physics",
   year = "2015",
   volume = "143",
   number = "10",
   eid = 104106,
   doi = "10.1063/1.4930260",

  Owner                    = {ward},
  Timestamp                = {03.06.2015}
}

@Article{84Van-Raemdonck_2013,
  Title                    = {Perturbations on the superconducting state of metallic nanoparticles: influence of geometry and impurities},
  Author                   = {Van Raemdonck, M. and De Baerdemacker, S. and Van Neck, D.},
  Journal                  = {European Physical Journal D},
  Year                     = {2013},
  Number                   = {1},
  Pages                    = {14},
  Volume                   = {67},

  Date-added               = {2014-01-15 16:56:01 +0000},
  Date-modified            = {2014-01-15 16:56:01 +0000},
  Doi                      = {10.1140/epjd/e2012-30543-0},
  ISSN                     = {1434-6060},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article},
  Url                      = {<Go to ISI>://WOS:000315353900014}
}

@Article{vandenberghe,
  Title                    = {Semidefinite Programming},
  Author                   = {Vandenberghe, Lieven and Boyd, Stephen},
  Journal                  = {SIAM Review},
  Year                     = {1996},
  Number                   = {1},
  Pages                    = {49--95},
  Volume                   = {38},

  ISSN                     = {00361445},
  Publisher                = {Society for Industrial and Applied Mathematics},
  Url                      = {http://www.jstor.org/stable/2132974}
}

@Article{:/content/aip/journal/jcp/140/12/10.1063/1.4868242,
  Title                    = {Global solutions of restricted open-shell Hartree-Fock theory from semidefinite programming with applications to strongly correlated quantum systems},
  Author                   = {Veeraraghavan, Srikant and Mazziotti, David A.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2014},
  Number                   = {12},
  Pages                    = {-},
  Volume                   = {140},

  Doi                      = {10.1063/1.4868242},
  Eid                      = {124106},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/140/12/10.1063/1.4868242}
}

@Article{PhysRevA.89.010502,
  Title                    = {Global solutions of Hartree-Fock theory and their consequences for strongly correlated quantum systems},
  Author                   = {Veeraraghavan, Srikant and Mazziotti, David A.},
  Journal                  = {Physical Review A},
  Year                     = {2014},

  Month                    = {Jan},
  Pages                    = {010502},
  Volume                   = {89},

  Doi                      = {10.1103/PhysRevA.89.010502},
  Issue                    = {1},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevA.89.010502},
  Numpages                 = {5},
  Publisher                = {American Physical Society}
}

@PhdThesis{brechtphd,
  Title                    = {Variational determination of the two-particle density matrix as a quantum many-body technique},
  Author                   = {Verstichel, Brecht},
  School                   = {Ghent University},
  Year                     = {2012},

  Pages                    = {VI, 198},
  Publisher                = {Ghent University. Faculty of Sciences},
  Url                      = {http://arxiv.org/abs/1203.5659}
}

@Article{218Verstichel_2012,
  Title                    = {Variational Two-Particle Density Matrix Calculation for the Hubbard Model Below Half Filling Using Spin-Adapted Lifting Conditions},
  Author                   = {Verstichel, B. and van Aggelen, H. and Poelmans, W. and Van Neck, D.},
  Journal                  = {Physical Review Letters},
  Year                     = {2012},
  Number                   = {21},
  Pages                    = {213001},
  Volume                   = {108},

  Date-added               = {2014-01-15 16:56:01 +0000},
  Date-modified            = {2014-01-15 16:56:01 +0000},
  Doi                      = {10.1103/PhysRevLett.108.213001},
  ISSN                     = {0031-9007},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article}
}

@Article{99Verstichel_2013,
  Title                    = {Extensive {v2DM} study of the one-dimensional Hubbard model for large lattice sizes: Exploiting translational invariance and parity},
  Author                   = {Verstichel, B. and van Aggelen, H. and Poelmans, W. and Wouters, S. and Van Neck, D.},
  Journal                  = {Computational and Theoretical Chemistry},
  Year                     = {2013},
  Pages                    = {12-21},
  Volume                   = {1003},

  Date-added               = {2014-01-15 16:56:01 +0000},
  Date-modified            = {2014-01-15 16:56:01 +0000},
  Doi                      = {10.1016/j.comptc.2012.09.014},
  ISSN                     = {2210-271X},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article}
}

@Article{cpc_proc,
  Title                    = {Variational density matrix optimization using semidefinite programming},
  Author                   = {Verstichel, Brecht and van Aggelen, Helen and Van Neck, Dimitri and Ayers, Paul W. and Bultinck, Patrick},
  Journal                  = {Computer Physics Communications},
  Year                     = {2011},

  Month                    = {SEP},
  Number                   = {9, SI},
  Pages                    = {2025-2028},
  Volume                   = {182},

  Doi                      = {10.1016/j.cpc.2010.12.034},
  ISSN                     = {0010-4655},
  Journal-iso              = {Comput. Phys. Commun.}
}

@Article{qsep,
  Title                    = {Subsystem constraints in variational second order density matrix optimization: Curing the dissociative behavior},
  Author                   = {Verstichel, Brecht and van Aggelen, Helen and Van Neck, Dimitri and Ayers, Paul W. and Bultinck, Patrick},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2010},
  Number                   = {11},
  Pages                    = {114113},
  Volume                   = {132},

  Doi                      = {10.1063/1.3354911},
  Eid                      = {114113},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/132/11/10.1063/1.3354911}
}

@Article{atomic,
  Title                    = {Variational determination of the second-order density matrix for the isoelectronic series of beryllium, neon, and silicon},
  Author                   = {Verstichel, Brecht and van Aggelen, Helen and Van Neck, Dimitri and Ayers, Paul W. and Bultinck, Patrick},
  Journal                  = {Physical Review A},
  Year                     = {2009},

  Month                    = {Sep},
  Pages                    = {032508},
  Volume                   = {80},

  Doi                      = {10.1103/PhysRevA.80.032508},
  Issue                    = {3},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevA.80.032508},
  Numpages                 = {14},
  Publisher                = {American Physical Society}
}

@Article{primal_dual,
  Title                    = {A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix},
  Author                   = {Verstichel, Brecht and van Aggelen, Helen and Van Neck, Dimitri and Bultinck, Patrick and De Baerdemacker, Stijn},
  Journal                  = {Computer Physics Communications},
  Year                     = {2011},

  Month                    = {june},
  Number                   = {6},
  Pages                    = {1235-1244},
  Volume                   = {182},

  Doi                      = {10.1016/j.cpc.2011.

license: MIT

license_type: permissive

branch_name: refs/heads/master

gha_license_id: MIT

extension: bib