text:
% This file was created with JabRef 2.10.
% Encoding: UTF8

@PhdThesis{phdhelen,
  Title                    = {Variational optimization of second order density matrices for electronic structure calculation},
  Author                   = {van Aggelen, Helen},
  School                   = {Ghent University},
  Year                     = {2011},

  Abstract                 = {The exponential growth of the dimension of the exact wavefunction with the size of a chemical system makes it impossible to compute chemical properties of large chemical systems exactly. A myriad of ab initio methods that use simpler mathematical objects to describe the system has thrived on this realization, among which the variational second order density matrix method. The aim of my thesis has been to evaluate the use of this method for chemistry and to identify the major theoretical and computational challenges that need to be overcome to make it successful for chemical applications.
The major theoretical challenges originate from the need for the second order density matrix to be N-representable: it must be derivable from an ensemble of N-electron states. Our calculations have pointed out major drawbacks of commonly used necessary N-representability conditions, such as incorrect dissociation into fractionally charged products and size-inconsistency. We have derived subspace energy constraints that fix these problems, albeit in an ad-hoc manner. Additionally, we have found that standard constraints on spin properties cause serious problems, such as false multiplet splitting and size-inconsistency. The subspace constraints relieve these problems as well, though only in the dissociation limit.
The major computational challenges originate from the method{\textquoteright}s formulation as a vast semidefinite optimization problem. We have implemented and compared several algorithms that exploit the specific structure of the problem. Even so, their slow speed remains prohibitive. Both the second order methods and the zeroth order boundary point method that we tried performed quite similar, which suggests that the underlying problem responsible for their slow convergence, ill-conditioning due to the singularity of the optimal matrix, manifests itself in all these algorithms even though it is most explicit in the barrier method.
Significant progress in these theoretical and computational aspects is needed to make the variational second order density matrix method competitive to comparable wavefunction based methods.},
  Keyword                  = {size-consistency,S-representability,N-representability,variational optimization,second order density matrices},
  Language                 = {English},
  Pages                    = {XIII, 192 + annexes},
  Publisher                = {Ghent University. Faculty of Sciences}
}

@Article{12Aggelen_2013,
  Title                    = {Extended random phase approximation method for atomic excitation energies from correlated and variationally optimized second-order density matrices},
  Author                   = {van Aggelen, H. and Verstichel, B. and Acke, G. and Degroote, M. and Bultinck, P. and Ayers, P. W. and Van Neck, D.},
  Journal                  = {Computational and Theoretical Chemistry},
  Year                     = {2013},
  Pages                    = {50-54},
  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.2012.09.036},
  ISSN                     = {2210-271X},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article},
  Url                      = {<Go to ISI>://WOS:000314074200010}
}

@Article{helen_3,
  Title                    = {Variational second order density matrix study of \mbox{$\mathrm{F_3^-}$}: Importance of subspace constraints for size-consistency},
  Author                   = {Helen van Aggelen and Brecht Verstichel and Patrick Bultinck and Dimitri Van Neck and Paul W. Ayers and David L. Cooper},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2011},
  Number                   = {5},
  Pages                    = {054115},
  Volume                   = {134},

  Doi                      = {10.1063/1.3532409},
  Eid                      = {054115},
  Keywords                 = {density functional theory; dissociation energies; fluorine; negative ions; potential energy surfaces},
  Numpages                 = {8},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JCP/134/054115/1}
}

@Article{128Aggelen_2012,
  Title                    = {Considerations on describing non-singlet spin states in variational second order density matrix methods},
  Author                   = {van Aggelen, H. and Verstichel, B. and Bultinck, P. and Van Neck, D. and Ayers, P. W.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2012},
  Number                   = {1},
  Pages                    = {014110},
  Volume                   = {136},

  Date-added               = {2014-01-15 16:56:01 +0000},
  Date-modified            = {2014-01-15 16:56:01 +0000},
  Doi                      = {10.1063/1.3672087},
  ISSN                     = {0021-9606},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article},
  Url                      = {<Go to ISI>://WOS:000298967200010}
}

@Article{helen_2,
  Title                    = {Chemical verification of variational second-order density matrix based potential energy surfaces for the N2 isoelectronic series},
  Author                   = {van Aggelen, Helen and Verstichel, Brecht and Bultinck, Patrick and Van Neck, Dimitri and Ayers, Paul W. and Cooper, David L.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2010},
  Number                   = {11},
  Pages                    = {114112},
  Volume                   = {132},

  Doi                      = {10.1063/1.3354910},
  Eid                      = {114112},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/132/11/10.1063/1.3354910}
}

@Article{primeisp,
  Title                    = {{PRIMES} Is in {P}},
  Author                   = {Agrawal, Manindra and Kayal, Neeraj and Saxena, Nitin},
  Journal                  = {Annals of Mathematics},
  Year                     = {2004},
  Number                   = {2},
  Pages                    = {pp. 781-793},
  Volume                   = {160},

  Abstract                 = {We present an unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite.},
  Copyright                = {Copyright © 2004 Annals of Mathematics},
  ISSN                     = {0003486X},
  Jstor_articletype        = {research-article},
  Jstor_formatteddate      = {Sep., 2004},
  Language                 = {English},
  Publisher                = {Annals of Mathematics},
  Series                   = {Second Series},
  Url                      = {http://www.jstor.org/stable/3597229}
}

@Article{diego3,
  Title                    = {Configuration interaction wave functions: A seniority number approach},
  Author                   = {Alcoba, Diego R. and Torre, Alicia and Lain, Luis and Massaccesi, Gustavo E. and Oña, Ofelia B.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2014},
  Number                   = {23},
  Pages                    = {234103},
  Volume                   = {140},

  Doi                      = {10.1063/1.4882881},
  Eid                      = {234103},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/140/23/10.1063/1.4882881}
}

@Article{diego1,
  Title                    = {Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions},
  Author                   = {Alcoba, Diego R. and Torre, Alicia and Lain, Luis and Massaccesi, Gustavo E. and Oña, Ofelia B.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2013},
  Number                   = {8},
  Pages                    = {084103},
  Volume                   = {139},

  Doi                      = {10.1063/1.4818755},
  Eid                      = {084103},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/139/8/10.1063/1.4818755}
}

@Article{alcoba_hybrid_2014,
  Title                    = {A hybrid configuration interaction treatment based on seniority number and excitation schemes},
  Author                   = {Alcoba, Diego R. and Torre, Alicia and Lain, Luis and Oña, Ofelia B. and Capuzzi, Pablo and Raemdonck, Mario Van and Bultinck, Patrick and Neck, Dimitri Van},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2014},

  Month                    = dec,
  Number                   = {24},
  Pages                    = {244118},
  Volume                   = {141},

  Abstract                 = {We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method.},
  Doi                      = {10.1063/1.4904755},
  File                     = {Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/WUPRQDBH/1.html:text/html},
  ISSN                     = {0021-9606, 1089-7690},
  Keywords                 = {Basis sets, Configuration interaction, Determinants, Rotational correlation time, Wave functions},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/141/24/10.1063/1.4904755},
  Urldate                  = {2015-04-14}
}

@Article{diego2,
  Title                    = {A hybrid configuration interaction treatment based on seniority number and excitation schemes},
  Author                   = {Alcoba, Diego R. and Torre, Alicia and Lain, Luis and Oña, Ofelia B. and Capuzzi, Pablo and Van Raemdonck, Mario and Bultinck, Patrick and Van Neck, Dimitri},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2014},
  Number                   = {24},
  Pages                    = {244118},
  Volume                   = {141},

  Doi                      = {10.1063/1.4904755},
  Eid                      = {244118},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/141/24/10.1063/1.4904755}
}

@Article{QUA:QUA20487,
  Title                    = {Spin structure and properties of the correlation matrices corresponding to pure spin states: Controlling the S-representability of these matrices},
  Author                   = {Alcoba, D. R. and Valdemoro, C.},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {2005},
  Number                   = {5},
  Pages                    = {629--644},
  Volume                   = {102},

  Doi                      = {10.1002/qua.20487},
  ISSN                     = {1097-461X},
  Keywords                 = {reduced density matrix, correlation matrix, N-representability problem, S-representability problem},
  Myurl                    = {http://dx.doi.org/10.1002/qua.20487},
  Publisher                = {Wiley Subscription Services, Inc., A Wiley Company}
}

@Article{PhysRevA.77.042508,
  Title                    = {Controlling the $N$- and $S$-representability of the second-order reduced density matrix: The doublet-state case},
  Author                   = {Alcoba, D. R. and Valdemoro, C. and Tel, L. M. and P\'erez-Romero, E.},
  Journal                  = {Physical Review A},
  Year                     = {2008},

  Month                    = {Apr},
  Pages                    = {042508},
  Volume                   = {77},

  Doi                      = {10.1103/PhysRevA.77.042508},
  Issue                    = {4},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevA.77.042508},
  Numpages                 = {12},
  Publisher                = {American Physical Society}
}

@Article{Alizadeh1995,
  Title                    = {Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization},
  Author                   = {Alizadeh, Farid},
  Journal                  = {SIAM Journal on Optimization},
  Year                     = {1995},

  Month                    = {Feb},
  Number                   = {1},
  Pages                    = {13–51},
  Volume                   = {5},

  Doi                      = {10.1137/0805002},
  ISSN                     = {1095-7189},
  Owner                    = {ward},
  Publisher                = {Society for Industrial \& Applied Mathematics (SIAM)},
  Timestamp                = {18.06.2015},
  Url                      = {http://dx.doi.org/10.1137/0805002}
}

@Article{anderson,
  Title                    = {The Resonating Valence Bond State in La2CuO4 and Superconductivity},
  Author                   = {Anderson, P. W.},
  Journal                  = {Science},
  Year                     = {1987},
  Number                   = {4793},
  Pages                    = {1196-1198},
  Volume                   = {235}
}

@Article{multiplesolcas,
  Title                    = {Multiple complete active space self-consistent field solutions},
  Author                   = {ANGELI, CELESTINO and CALZADO, CARMEN J. and CIMIRAGLIA, RENZO and EVANGELISTI, STEFANO and MAYNA, DANIEL},
  Journal                  = {Molecular Physics},
  Year                     = {2003},
  Number                   = {13},
  Pages                    = {1937-1944},
  Volume                   = {101},

  Doi                      = {10.1080/0026897031000109293},
  Myurl                    = {http://www.tandfonline.com/doi/abs/10.1080/0026897031000109293}
}

@Article{Ayers20131,
  Title                    = {Forward for Special Issue },
  Author                   = {Paul Ayers and Ajit Thakkar},
  Journal                  = {Computational and Theoretical Chemistry },
  Year                     = {2013},
  Note                     = {Reduced Density Matrices: A Simpler Approach to Many-Electron Problems? },
  Number                   = {0},
  Pages                    = {1 - },
  Volume                   = {1003},

  Doi                      = {10.1016/j.comptc.2012.09.032},
  ISSN                     = {2210-271X},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S2210271X12004987}
}

@Article{payers,
  Title                    = {Using classical many-body structure to determine electronic structure: An approach using $k$-electron distribution functions},
  Author                   = {Ayers, Paul W.},
  Journal                  = {Physical Review A},
  Year                     = {2006},

  Month                    = {Oct},
  Pages                    = {042502},
  Volume                   = {74},

  Doi                      = {10.1103/PhysRevA.74.042502},
  Issue                    = {4},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevA.74.042502},
  Numpages                 = {12},
  Publisher                = {American Physical Society}
}

@Article{aydav,
  Author                   = {P. W. Ayers and E. R. Davidson},
  Journal                  = {Advances in Chemical Physics},
  Year                     = {2007},
  Pages                    = {443},
  Volume                   = {134}
}

@Article{Bach2013,
  Title                    = {Representability Conditions by Grassmann Integration},
  Author                   = {Volker Bach and Hans Konrad Knörr and Edmund Menge},
  Journal                  = {arXiv},
  Year                     = {2013},

  Month                    = jul,

  Abstract                 = {Representability conditions on the one- and two-particle density matrix for fermion systems are formulated by means of Grassmann integrals. A positivity condition for a certain kind of Grassmann integral is established which, in turn, induces the well-known G-, P- and Q-Conditions of quantum chemistry by an appropriate choice of the integrand. Similarly, the T1- and T2-Conditions are derived. Furthermore, quasifree Grassmann states are introduced and it is shown that every so-called generalized one-particle density matrix which is bounded between 0 and 1 corresponds to a unique quasifree Grassmann state.},
  Eprint                   = {1307.0465},
  Oai2identifier           = {1307.0465},
  Owner                    = {ward},
  Timestamp                = {25.05.2015}
}

@Article{stijn,
  Title                    = {The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing},
  Author                   = {Stijn De Baerdemacker},
  Journal                  = {Journal of Physics: Conference Series},
  Year                     = {2011},
  Number                   = {1},
  Pages                    = {012020},
  Volume                   = {284},

  Eprint                   = {nucl-th/1011.3691v1},
  Url                      = {http://stacks.iop.org/1742-6596/284/i=1/a=012020}
}

@Article{BCS,
  Title                    = {Theory of superconductivity},
  Author                   = {Bardeen, J. and Cooper, L. N. and Schrieffer, J. R.},
  Journal                  = {Physical Review},
  Year                     = {1957},
  Pages                    = {1175},
  Volume                   = {108}
}

@Article{bartlett_coupled-cluster_2007,
  Title                    = {Coupled-cluster theory in quantum chemistry},
  Author                   = {Bartlett, Rodney J. and Musiał, Monika},
  Journal                  = {Reviews of Modern Physics},
  Year                     = {2007},

  Month                    = feb,
  Number                   = {1},
  Pages                    = {291--352},
  Volume                   = {79},

  Abstract                 = {Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physi
cs, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are
explained and illustrated with informative numerical results.},
  Doi                      = {10.1103/RevModPhys.79.291},
  File                     = {APS Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/PT4VNB86/RevModPhys.79.html:text/html},
  Myurl                    = {http://link.aps.org/doi/10.1103/RevModPhys.79.291},
  Urldate                  = {2015-04-14}
}

@Article{b3lyp1,
  Title                    = {A new mixing of Hartree–Fock and local density-functional theories},
  Author                   = {Becke, Axel D.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1993},
  Number                   = {2},
  Pages                    = {1372-1377},
  Volume                   = {98},

  Doi                      = {10.1063/1.464304},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/98/2/10.1063/1.464304}
}

@Article{Bentler1980,
  Title                    = {Inequalities among lower bounds to reliability: With applications to test construction and factor analysis},
  Author                   = {Bentler, P. M. and Woodward, J. Arthur},
  Journal                  = {Psychometrika},
  Year                     = {1980},

  Month                    = {Jun},
  Number                   = {2},
  Pages                    = {249–267},
  Volume                   = {45},

  Doi                      = {10.1007/bf02294079},
  ISSN                     = {1860-0980},
  Owner                    = {ward},
  Publisher                = {Springer Science + Business Media},
  Timestamp                = {18.06.2015},
  Url                      = {http://dx.doi.org/10.1007/BF02294079}
}

@Book{constrained-lagrange,
  Title                    = {Constrained Optimization and Lagrange Multiplier Methods},
  Author                   = {Dimitri P. Bertsekas},
  Publisher                = {Athena Scientific},
  Year                     = {1996},

  ISBN                     = {1886529043},
  Url                      = {http://www.amazon.com/Constrained-Optimization-Lagrange-Multiplier-computation/dp/1886529043}
}

@Article{bethe,
  Title                    = {Zur Theorie der Metalle},
  Author                   = {Bethe, H.},
  Journal                  = {Zeitschrift f\"ur Physik A Hadrons and Nuclei},
  Year                     = {1931},
  Pages                    = {205-226},
  Volume                   = {71},

  Affiliation              = {Rom},
  ISSN                     = {0939-7922},
  Issue                    = {3},
  Keyword                  = {Physics and Astronomy},
  Myurl                    = {http://dx.doi.org/10.1007/BF01341708},
  Publisher                = {Springer Berlin / Heidelberg}
}

@Article{Blatt01031960,
  Title                    = {Electron Pairs in the Theory of Superconductivity},
  Author                   = {Blatt, John M.},
  Journal                  = {Progress of Theoretical Physics},
  Year                     = {1960},
  Number                   = {3},
  Pages                    = {447-450},
  Volume                   = {23},

  Abstract                 = {The detailed mathematical correspondence between the Bogoliubov theory and the quasi-chemical equilibrium theory is established by means of identities. The Bogoliubov-BCS Ansatz is a special case of the quasi-chemical equilibrium Ansatz, corresponding to prefect Bose-Einstein condensation of the electron pairs.},
  Doi                      = {10.1143/PTP.23.447},
  Url                      = {http://ptp.oxfordjournals.org/content/23/3/447.abstract}
}

@Article{boguslawski_efficient_2014,
  Title                    = {Efficient description of strongly correlated electrons with mean-field cost},
  Author                   = {Boguslawski, Katharina and Tecmer, Paweł and Ayers, Paul W. and Bultinck, Patrick and De Baerdemacker, Stijn and Van Neck, Dimitri},
  Journal                  = {Physical Review B},
  Year                     = {2014},

  Month                    = may,
  Number                   = {20},
  Pages                    = {201106},
  Volume                   = {89},

  Abstract                 = {We present an efficient approach to the electron correlation problem that is well suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. The performance of our approach is illustrated for one-dimensional Hubbard rings with different numbers of sites, and for the nonrelativistic quantum-chemical Hamiltonian exploring the symmetric dissociation of the H50 hydrogen chain.},
  Doi                      = {10.1103/PhysRevB.89.201106},
  File                     = {APS Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/TNPN2BI6/PhysRevB.89.html:text/html},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevB.89.201106},
  Urldate                  = {2015-04-14}
}

@Article{doi:10.1021/ct500759q,
  Title                    = {Nonvariational Orbital Optimization Techniques for the AP1roG Wave Function},
  Author                   = {Boguslawski, Katharina and Tecmer, Paweł and Bultinck, Patrick and De Baerdemacker, Stijn and Van Neck, Dimitri and Ayers, Paul W.},
  Journal                  = {Journal of Chemical Theory and Computation},
  Year                     = {2014},
  Number                   = {11},
  Pages                    = {4873-4882},
  Volume                   = {10},

  Doi                      = {10.1021/ct500759q},
  Url                      = {
 http://dx.doi.org/10.1021/ct500759q

}
}

@Article{boguslawski_projected_2014,
  Title                    = {Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal},
  Author                   = {Boguslawski, Katharina and Tecmer, Paweł and Limacher, Peter A. and Johnson, Paul A. and Ayers, Paul W. and Bultinck, Patrick and Baerdemacker, Stijn De and Neck, Dimitri Van},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2014},

  Month                    = jun,
  Number                   = {21},
  Pages                    = {214114},
  Volume                   = {140},

  Abstract                 = {We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys.135, 044119 (2011)]. A numerical analysis is performed for the C2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.},
  Doi                      = {10.1063/1.4880820},
  File                     = {Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/KC6IM5HQ/1.html:text/html},
  ISSN                     = {0021-9606, 1089-7690},
  Keywords                 = {Configuration interaction, Dissociation, Electron correlation calculations, Lagrangian mechanics, Wave functions},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/140/21/10.1063/1.4880820},
  Urldate                  = {2015-04-14}
}

@Article{Bondi1964,
  Title                    = {van der Waals Volumes and Radii},
  Author                   = {Bondi, A.},
  Journal                  = {Journal of Physical Chemistry},
  Year                     = {1964},

  Month                    = {Mar},
  Number                   = {3},
  Pages                    = {441–451},
  Volume                   = {68},

  Doi                      = {10.1021/j100785a001},
  ISSN                     = {1541-5740},
  Owner                    = {ward},
  Publisher                = {American Chemical Society (ACS)},
  Timestamp                = {16.06.2015},
  Url                      = {http://dx.doi.org/10.1021/j100785a001}
}

@Article{Borchers1999,
  Title                    = {{CSD}P, A {C} library for semidefinite programming},
  Author                   = {Borchers, Brian},
  Journal                  = {Optimization Methods and Software},
  Year                     = {1999},

  Month                    = {Jan},
  Number                   = {1-4},
  Pages                    = {613–623},
  Volume                   = {11},

  Doi                      = {10.1080/10556789908805765},
  ISSN                     = {1029-4937},
  Owner                    = {ward},
  Publisher                = {Informa UK Limited},
  Timestamp                = {18.06.2015},
  Url                      = {http://dx.doi.org/10.1080/10556789908805765}
}

@Book{Boyd1994,
  Title                    = {Linear Matrix Inequalities in System and Control Theory},
  Author                   = {Boyd, S. and El Ghaoui, L. and Feron, E. and Balakrishnan, V.},
  Publisher                = {Society for Industrial and Applied Mathematics},
  Year                     = {1994},

  Doi                      = {10.1137/1.9781611970777},
  ISBN                     = {978-0-89871-485-2},
  Url                      = {http://epubs.siam.org/doi/abs/10.1137/1.9781611970777}
}

@Book{boyd,
  Title                    = {Convex Optimization},
  Author                   = {Boyd, Stephen and Vandenberghe, Lieven},
  Publisher                = {Cambridge University Press},
  Year                     = {2006},

  ISBN                     = {0521833787}
}

@Book{brandas2013fundamental,
  Title                    = {Fundamental World of Quantum Chemistry: A Tribute to the Memory of Per-Olov L{\"o}wdin},
  Author                   = {Br{\"a}ndas, E.J. and Kryachko, E.S.},
  Publisher                = {Springer Netherlands},
  Year                     = {2013},
  Number                   = {v. 3},

  ISBN                     = {9789401704489},
  Url                      = {https://books.google.be/books?id=ZUHsCAAAQBAJ}
}

@InBook{braams_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                   = {Braams, B. J. and Percus, J. K. and Zhao, Z.},
  Editor                   = {Mazziotti, D. A.},
  Pages                    = {93},
  Publisher                = {Wiley: New York},
  Year                     = {2007},
  Volume                   = {134}
}

@Book{bransden_quantum_2000,
  Title                    = {Quantum {Mechanics}},
  Author                   = {Bransden, B. H. and Joachain, C. J.},
  Publisher                = {Addison-Wesley},
  Year                     = {2000},

  Address                  = {Harlow, England ; New York},
  Edition                  = {2 edition},
  Month                    = feb,

  Abstract                 = {This book gives a modern, comprehensive introduction to the principles of quantum mechanics, to the main approximation methods and to the application of quantum theory to a wide variety of systems. The needs of students having an average mathematical ability are kept very much in mind, with the avoidance of complex mathematical arguments and any undue compression of material},
  ISBN                     = {9780582356917},
  Language                 = {English}
}

@Book{angmom,
  Title                    = {Angular momentum},
  Author                   = {Brink, D. M. and Satchler, G. R.},
  Publisher                = {Oxford university press},
  Year                     = {1993}
}

@Article{PhysRev.103.1008,
  Title                    = {Nuclear Saturation and Two-Body Forces: Self-Consistent Solutions and the Effects of the Exclusion Principle},
  Author                   = {Brueckner, K. A. and Wada, W.},
  Journal                  = {Physical Review},
  Year                     = {1956},

  Month                    = {Aug},
  Pages                    = {1008--1016},
  Volume                   = {103},

  Doi                      = {10.1103/PhysRev.103.1008},
  Issue                    = {4},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRev.103.1008}
}

@Article{bulik_can_2015,
  Title                    = {Can single-reference coupled cluster theory describe static correlation?},
  Author                   = {Bulik, Ireneusz W. and Henderson, Thomas M. and Scuseria, Gustavo E.},
  Journal                  = {arXiv:1505.01894 [physics]},
  Year                     = {2015},

  Month                    = may,
  Note                     = {arXiv: 1505.01894},

  Abstract                 = {While restricted single-reference coupled cluster theory truncated to singles and doubles (CCSD) provides very accurate results for weakly correlated systems, it usually fails in the presence of static or strong correlation. This failure is generally attributed to the qualitative breakdown of the reference, and can accordingly be corrected by using a multi-determinant reference, including higher-body cluster operators in the ansatz, or allowing symmetry breaking in the reference. None of these solutions are ideal; multi-reference coupled cluster is not black box, including higher-body cluster operators is computationally demanding, and allowing symmetry breaking leads to the loss of good quantum numbers. It has long been recognized that quasidegeneracies can instead be treated by modifying the coupled cluster ansatz. The recently introduced pair coupled cluster doubles (pCCD) approach is one such example which avoids catastrophic failures and accurately models strong correlations in a symmetry-adapted framework. Here we generalize pCCD to a singlet-paired coupled cluster model (CCD0) intermediate between coupled cluster doubles and pCCD, yielding a method that possesses the invariances of the former and much of the stability of the latter. Moreover, CCD0 retains the full structure of coupled cluster theory, including a fermionic wave function, antisymmetric cluster amplitudes, and well-defined response equations and density matrices.},
  File                     = {arXiv\:1505.01894 PDF:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/Q4NEMZ23/Bulik et al. - 2015 - Can single-reference coupled cluster theory descri.pdf:application/pdf;arXiv.org Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/ZQI2KWKR/1505.html:text/html},
  Keywords                 = {Physics - Chemical Physics},
  Url                      = {http://arxiv.org/abs/1505.01894},
  Urldate                  = {2015-05-20}
}

@Article{632Bultinck_2013,
  Title                    = {Bond Fukui Indices: Comparison of Frozen Molecular Orbital and Finite Differences through Mulliken Populations},
  Author                   = {Bultinck, P. and Van Damme, S. and Cedillo, A.},
  Journal                  = {Journal of Computational Chemistry},
  Year                     = {2013},
  Number                   = {28},
  Pages                    = {2421-2429},
  Volume                   = {34},

  Date-added               = {2014-01-15 17:11:46 +0000},
  Date-modified            = {2014-01-15 17:11:46 +0000},
  Doi                      = {10.1002/jcc.23405},
  ISSN                     = {0192-8651},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article},
  Url                      = {<Go to ISI>://WOS:000324919200003}
}

@Article{158Bultinck_2012,
  Title                    = {Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods},
  Author                   = {Bultinck, P. and Van Neck, D. and Acke, G. and Ayers, P. W.},
  Journal                  = {Physical Chemistry Chemical Physics},
  Year                     = {2012},
  Number                   = {7},
  Pages                    = {2408-2416},
  Volume                   = {14},

  Date-added               = {2014-01-15 16:56:01 +0000},
  Date-modified            = {2014-01-15 16:56:01 +0000},
  Doi                      = {10.1039/c2cp22543c},
  ISSN                     = {1463-9076},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article},
  Url                      = {<Go to ISI>://WOS:000299505400036}
}

@Article{scuseria_seniority,
  Title                    = {Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy},
  Author                   = {Bytautas, Laimutis and Henderson, Thomas M. and Jiménez-Hoyos, Carlos A. and Ellis, Jason K. and Scuseria, Gustavo E.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2011},
  Number                   = {4},
  Pages                    = {044119},
  Volume                   = {135},

  Doi                      = {10.1063/1.3613706},
  Eid                      = {044119},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/135/4/10.1063/1.3613706}
}

@Article{cances,
  Title                    = {The electronic ground-state energy problem: A new reduced density matrix approach},
  Author                   = {Canc\`es, E. and Stoltz, G. and Lewin, M.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2006},
  Pages                    = {064101},
  Volume                   = {125}
}

@Article{bultinck,
  Title                    = {A General Procedure to Obtain Quantum Mechanical Charge and Bond Order Molecular Parameters},
  Author                   = {Carbó-Dorca, Ramon and Bultinck, Patrick},
  Journal                  = {Journal of Mathematical Chemistry},
  Year                     = {2004},
  Pages                    = {201-210},
  Volume                   = {36},

  ISSN                     = {0259-9791},
  Issue                    = {3},
  Keyword                  = {Chemistry and Materials Science},
  Myurl                    = {http://dx.doi.org/10.1023/B:JOMC.0000044219.02356.be},
  Publisher                = {Springer Netherlands}
}

@Article{PhysRev.105.102,
  Title                    = {Orthogonalization Procedures and the Localization of Wannier Functions},
  Author                   = {Carlson, B. C. and Keller, Joseph M.},
  Journal                  = {Physical Review},
  Year                     = {1957},

  Month                    = {Jan},
  Pages                    = {102--103},
  Volume                   = {105},

  Doi                      = {10.1103/PhysRev.105.102},
  Issue                    = {1},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRev.105.102}
}

@Book{9780821836798,
  Title                    = {The Millennium Prize Problems},
  Author                   = {James Carlson},
  Editor                   = {Arthur Jaffe and Andrew Wiles},
  Publisher                = {American Mathematical Society},
  Year                     = {2006},

  ISBN                     = {082183679X},
  Url                      = {http://www.amazon.com/Millennium-Problems-Arthur-editors-Carlson/dp/082183679X}
}

@Article{simanneal2,
  Title                    = {Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm},
  Author                   = {Černý, V.},
  Journal                  = {Journal of Optimization Theory and Applications},
  Year                     = {1985},
  Number                   = {1},
  Pages                    = {41-51},
  Volume                   = {45},

  Doi                      = {10.1007/BF00940812},
  ISSN                     = {0022-3239},
  Keywords                 = {Traveling salesman problem; Monte Carlo optimization; importance sampling},
  Language                 = {English},
  Publisher                = {Kluwer Academic Publishers-Plenum Publishers},
  Url                      = {http://dx.doi.org/10.1007/BF00940812}
}

@Article{chakravorty,
  Title                    = {Ground-state correlation energies for atomic ions with 3 to 18 electrons},
  Author                   = {Subhas J. Chakravorty and Steven R. Gwaltney and Ernest R. Davidson and Farid A. Parpia and Froese Fischer, Charlotte},
  Journal                  = {Physical Review A},
  Year                     = {1993},
  Pages                    = {5},
  Volume                   = {47}
}

@Article{:/content/aip/journal/jcp/116/11/10.1063/1.1449459,
  Title                    = {Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group},
  Author                   = {Chan, Garnet Kin-Lic and Head-Gordon, Martin},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2002},
  Number                   = {11},
  Pages                    = {4462-4476},
  Volume                   = {116},

  Doi                      = {10.1063/1.1449459},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/116/11/10.1063/1.1449459}
}

@Article{n2ref3,
  Title                    = {State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve},
  Author                   = {Chan, Garnet Kin-Lic and Kállay, Mihály and Gauss, Jürgen},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2004},
  Number                   = {13},
  Pages                    = {6110-6116},
  Volume                   = {121},

  Doi                      = {10.1063/1.1783212},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/121/13/10.1063/1.1783212}
}

@InCollection{chan,
  Title                    = {Chapter 7 The Density Matrix Renormalization Group in Quantum Chemistry},
  Author                   = {Garnet Kin-Lic Chan and Dominika Zgid},
  Publisher                = {Elsevier},
  Year                     = {2009},
  Editor                   = {Ralph A. Wheeler},
  Pages                    = {149 - 162},
  Series                   = {Annual Reports in Computational Chemistry},
  Volume                   = {5}
}

@Article{Cleveland1976,
  Title                    = {Obtaining a Heisenberg Hamiltonian from the Hubbard model},
  Author                   = {Cleveland, Charles L.},
  Journal                  = {American Journal of Physics},
  Year                     = {1976},
  Number                   = {1},
  Pages                    = {44},
  Volume                   = {44},

  __markedentry            = {[ward:6]},
  Doi                      = {10.1119/1.10537},
  ISSN                     = {0002-9505},
  Owner                    = {ward},
  Publisher                = {American Association of Physics Teachers (AAPT)},
  Timestamp                = {09.09.2015},
  Url                      = {http://dx.doi.org/10.1119/1.10537}
}

@Article{Cohen,
  Title                    = {Insights into Current Limitations of Density Functional Theory},
  Author                   = {Cohen, A. J. and Mori-Sanchez, P. and Yang, W.},
  Journal                  = {Science},
  Year                     = {2008},

  Month                    = {Aug},
  Number                   = {5890},
  Pages                    = {792–794},
  Volume                   = {321},

  Doi                      = {10.1126/science.1158722},
  ISSN                     = {1095-9203},
  Owner                    = {ward},
  Publisher                = {American Association for the Advancement of Science (AAAS)},
  Timestamp                = {16.06.2015},
  Url                      = {http://dx.doi.org/10.1126/science.1158722}
}

@Article{ajcoh,
  Author                   = {A. J. Cohen and P. Mori-Sanchez and W. T. Yang},
  Journal                  = {Journal of Chemical Theory and Computation},
  Year                     = {2009},
  Pages                    = {786},
  Volume                   = {5}
}

@Book{rdm_book,
  Title                    = {Many-electron densities and reduced density matrices},
  Author                   = {Coleman, A. J.},
  Editor                   = {Cioslowski, J.},
  Publisher                = {Kluwer Academic/Plenum Publishers},
  Year                     = {2000},
  Series                   = {mathematical and computational chemistry}
}

@Article{coleman-agp,
  Title                    = {Structure of Fermion Density Matrices. {II}. Antisymmetrized Geminal Powers},
  Author                   = {Coleman, A. J.},
  Journal                  = {Journal of Mathematical Physics},
  Year                     = {1965},
  Number                   = {9},
  Pages                    = {1425-1431},
  Volume                   = {6},

  Doi                      = {http://dx.doi.org/10.1063/1.1704794},
  Url                      = {http://scitation.aip.org/content/aip/journal/jmp/6/9/10.1063/1.1704794}
}

@Article{coleman,
  Title                    = {Structure of Fermion Density Matrices},
  Author                   = {Coleman, A. J.},
  Journal                  = {Reviews of Modern Physics},
  Year                     = {1963},

  Month                    = {Jul},
  Pages                    = {668--686},
  Volume                   = {35},

  Doi                      = {10.1103/RevModPhys.35.668},
  Issue                    = {3},
  Myurl                    = {http://link.aps.org/doi/10.1103/RevModPhys.35.668},
  Publisher                = {American Physical Society}
}

@Book{coleman_book,
  Title                    = {Reduced Density Matrices: Coulson's Challange},
  Author                   = {Coleman, A. J. and Yukalov, V. I.},
  Publisher                = {Springer-Verlag, New York},
  Year                     = {2000}
}

@Article{PhysRevA.47.971,
  Title                    = {Approximating \textit{q}-order reduced density matrices in terms of the lower-order ones. {I}. General relations},
  Author                   = {Colmenero, F. and P\'erez del Valle, C. and Valdemoro, C.},
  Journal                  = {Physical Review A},
  Year                     = {1993},

  Month                    = {Feb},
  Pages                    = {971--978},
  Volume                   = {47},

  Doi                      = {10.1103/PhysRevA.47.971},
  Issue                    = {2},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRevA.47.971}
}

@Article{PhysRevA.47.979,
  Title                    = {Approximating \textit{q}-order reduced density matrices in terms of the lower-order ones. {II}. Applications},
  Author                   = {Colmenero, F. and Valdemoro, C.},
  Journal                  = {Physical Review A},
  Year                     = {1993},

  Month                    = {Feb},
  Pages                    = {979--985},
  Volume                   = {47},

  Doi                      = {10.1103/PhysRevA.47.979},
  Issue                    = {2},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRevA.47.979}
}

@Book{cornwell,
  Title                    = {Group Theory in Physics: An introduction},
  Author                   = {Cornwell, J.F.},
  Publisher                = {Academic Press, San Diego},
  Year                     = {1997}
}

@Book{cornwell_group_1997,
  Title                    = {Group {Theory} in {Physics}, {Volume} 1: {An} {Introduction}},
  Author                   = {Cornwell, John F.},
  Publisher                = {Academic Press},
  Year                     = {1997},

  Address                  = {San Diego},
  Edition                  = {Abridged edition},
  Month                    = aug,

  Abstract                 = {This book, an abridgment of Volumes I and II of the highly respected Group Theory in Physics, presents a carefully constructed introduction to group theory and its applications in physics. The book provides anintroduction to and description of the most important basic ideas and the role that they play in physical problems. The clearly written text contains many pertinent examples that illustrate the topics, even for those with no background in group theory. This work presents important mathematical developments to theoretical physicists in a form that is easy to comprehend and appreciate. Finite groups, Lie groups, Lie algebras, semi-simple Lie algebras, crystallographic point groups and crystallographic space groups, electronic energy bands in solids, atomic physics, symmetry schemes for fundamental particles, and quantum mechanics are all covered in this compact new edition. Key Features* Covers both group theory and the theory of Lie algebras* Includes studies of solid state physics, atomic physics, and fundamental particle physics* Contains a comprehensive index* Provides extensive examples},
  ISBN                     = {9780121898007},
  Language                 = {English},
  Shorttitle               = {Group {Theory} in {Physics}, {Volume} 1}
}

@Book{cornwell_group_1984,
  Title                    = {Group {Theory} in {Physics}, {Volume} 2},
  Author                   = {Cornwell, John F.},
  Publisher                = {Academic Press},
  Year                     = {1984},

  Address                  = {London ; Orlando},
  Month                    = feb,

  Abstract                 = {Techniques of physics find wide application in biology, medicine, engineering and technology generally. This series is devoted to techniques which have found and are finding application. The aim is to clarify the principles of each technique, to emphasize and illustrate the applications and to draw attention to new fields of possible employment.},
  ISBN                     = {9780121898021},
  Language                 = {English}
}

@Article{RevModPhys.32.170,
  Title                    = {Present State of Molecular Structure Calculations},
  Author                   = {Coulson, C. A.},
  Journal                  = {Reviews of Modern Physics},
  Year                     = {1960},

  Month                    = {Apr},
  Pages                    = {170--177},
  Volume                   = {32},

  Doi                      = {10.1103/RevModPhys.32.170},
  Issue                    = {2},
  Myurl                    = {http://link.aps.org/doi/10.1103/RevModPhys.32.170},
  Numpages                 = {0},
  Publisher                = {American Physical Society}
}

@Article{n2ref2,
  Title                    = {Generalized Molecular Orbital Theory {II}},
  Author                   = {Couty, Marc and Hall, Michael B.},
  Journal                  = {Journal of Physical Chemistry A},
  Year                     = {1997},
  Number                   = {37},
  Pages                    = {6936-6944},
  Volume                   = {101},

  Doi                      = {10.1021/jp963953l},
  Myurl                    = {http://dx.doi.org/10.1021/jp963953l}
}

@InCollection{crawford_introduction_2000,
  Title                    = {An {Introduction} to {Coupled} {Cluster} {Theory} for {Computational} {Chemists}},
  Author                   = {Crawford, T. Daniel and Schaefer, Henry F.},
  Booktitle                = {Reviews in {Computational} {Chemistry}},
  Publisher                = {John Wiley \& Sons, Inc.},
  Year                     = {2000},
  Editor                   = {Lipkowitz, Kenny B. and Boyd, Donald B.},
  Pages                    = {33--136},

  Copyright                = {Copyright © 2000 by Wiley-VCH, Inc.},
  File                     = {Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/6K8BZBN6/summary.html:text/html},
  ISBN                     = {9780470125915},
  Myurl                    = {http://onlinelibrary.wiley.com/doi/10.1002/9780470125915.ch2/summary},
  Urldate                  = {2015-04-14}
}

@InCollection{cullum_minimization_1975,
  Title                    = {The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices},
  Author                   = {Cullum, Jane and Donath, W. E. and Wolfe, P.},
  Booktitle                = {Nondifferentiable {Optimization}},
  Publisher                = {Springer Berlin Heidelberg},
  Year                     = {1975},
  Editor                   = {Balinski, M. L. and Wolfe, Philip and Cottle, R. W. and Dixon, L. C. W. and Korte, B. and Todd, M. J. and Allgower, E. L. and Cunningham, W. H. and Dennis, J. E. and Eaves, B. C. and Fletcher, R. and Goldfarb, D. and Hiriart-Urruty, J.- B. and Iri, M. and Jeroslow, R. G. and Johnson, D. S. and Lemarechal, C. and Lovasz, L. and McLinden, L. and Powell, M. J. D. and Pulleyblank, W. R. and Rinnooy Kan, A. H. G. and Ritter, K. and Sargent, R. W. H. and Shanno, D. F. and Trotter, L. E. and Tuy, H. and Wets, R. J. B. and Beale, E. M. L. and Dantzig, G. B. and Kantorovich, L. V. and Koopmans, T. C. and Tucker, A. W. and Wolfe, P.},
  Pages                    = {35--55},
  Series                   = {Mathematical {Programming} {Studies}},
  Volume                   = {3},

  Abstract                 = {Properties of the sum of the q algebraically largest eigenvalues of any real symmetric matrix as a function of the diagonal entries of the matrix are derived. Such a sum is convex but not necessarily everywhere differentiable. A convergent procedure is presented for determining a minimizing point of any such sum subject to the condition that the trace of the matrix is held constant. An implementation of this procedure is described and numerical results are included. Minimization problems of this kind arose in graph partitioning studies [8]. Use of existing procedures for minimizing required either a strategy for selecting, at each stage, a direction of search from the subdifferential and an appropriate step along the direction chosen [10,13] or computationally feasible characterizations of certain enlargements of subdifferentials [1,6] neither of which could be easily determined for the given problem. The arguments use results from eigenelement analysis and from optimization theory.},
  File                     = {SpringerLink Full Text PDF:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/UCRGQMKC/Cullum et al. - 1975 - The minimization of certain nondifferentiable sums.pdf:application/pdf;SpringerLink Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/TR74CVZJ/Cullum et al. - 1975 - The minimization of certain nondifferentiable sums.html:text/html},
  ISBN                     = {978-3-642-00764-4},
  Keywords                 = {Mathematics and Statistics},
  Url                      = {http://www.springerlink.com.libaccess.lib.mcmaster.ca/content/w4w17112t074u841/abstract/},
  Urldate                  = {2012-04-18}
}

@Article{davidson_3,
  Title                    = {Linear inequalities for density matrices: \mbox{III}},
  Author                   = {Davidson, Ernest R.},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {2003},
  Number                   = {1},
  Pages                    = {1--4},
  Volume                   = {91},

  Doi                      = {10.1002/qua.10340},
  ISSN                     = {1097-461X},
  Keywords                 = {\mbox{$N$}-representability, density matrices, linear inequalities},
  Myurl                    = {http://dx.doi.org/10.1002/qua.10340},
  Publisher                = {Wiley Subscription Services, Inc., A Wiley Company}
}

@Article{:/content/aip/journal/jcp/62/2/10.1063/1.430484,
  Title                    = {Use of double cosets in constructing integrals over symmetry orbitals},
  Author                   = {Davidson, Ernest R.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1975},
  Number                   = {2},
  Pages                    = {400-403},
  Volume                   = {62},

  Doi                      = {http://dx.doi.org/10.1063/1.430484},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/62/2/10.1063/1.430484}
}

@Article{davidson_1,
  Title                    = {Linear Inequalities for Density Matrices},
  Author                   = {Davidson, Ernest R.},
  Journal                  = {Journal of Mathematical Physics},
  Year                     = {1969},
  Number                   = {4},
  Pages                    = {725-734},
  Volume                   = {10},

  Doi                      = {10.1063/1.1664899},
  Url                      = {http://scitation.aip.org/content/aip/journal/jmp/10/4/10.1063/1.1664899}
}

@Article{davidson,
  Title                    = {Ground-state correlation energies for two- to ten-electron atomic ions},
  Author                   = {Ernest R. Davidson and Stanley A. Hagstrom and Subhas J. Chakravorty and Meiser Umar, Verena and Froese Fischer, Charlotte},
  Journal                  = {Physical Review A},
  Year                     = {1991},
  Pages                    = {11},
  Volume                   = {44}
}

@Article{day,
  Title                    = {Extension of Koopmans' theorem. {II}. Accurate ionization energies from correlated wavefunctions for closed-shell atoms},
  Author                   = {Orville W. Day and Darwin W. Smith and Robert C. Morrison},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1975},
  Number                   = {1},
  Pages                    = {115-119},
  Volume                   = {62},

  Doi                      = {10.1063/1.430254},
  Keywords                 = {LITHIUM IONS; BERYLLIUM; BORON IONS; CARBON IONS; NITROGEN IONS; OXYGEN IONS; IONIZATION POTENTIAL; HARTREEFOCK METHOD; CONFIGURATION INTERACTION; SELFCONSISTENT FIELD},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JCP/62/115/1}
}

@Article{DeAndrade2008,
  Title                    = {Atomic basis sets optimization using the generalized simulated annealing approach: New basis sets for the first row elements},
  Author                   = {De Andrade, M. D. and Nascimento, M. A. C. and Mundim, K. C. and Sobrinho, A. M. C. and Malbouisson, L. A. C.},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {2008},
  Number                   = {13},
  Pages                    = {2486–2498},
  Volume                   = {108},

  Doi                      = {10.1002/qua.21666},
  ISSN                     = {1097-461X},
  Owner                    = {ward},
  Publisher                = {Wiley-Blackwell},
  Timestamp                = {14.06.2015},
  Url                      = {http://dx.doi.org/10.1002/qua.21666}
}

@Article{DiasDeAndrade2006,
  Title                    = {{GSA} algorithm applied to electronic structure {II}: {UHF}-{GSA} method},
  Author                   = {Dias De Andrade, Micael and Nascimento, Marco and Mundim, Kleber and Malbouisson, Luiz},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {2006},
  Number                   = {13},
  Pages                    = {2700–2705},
  Volume                   = {106},

  Doi                      = {10.1002/qua.21080},
  ISSN                     = {1097-461X},
  Owner                    = {ward},
  Publisher                = {Wiley-Blackwell},
  Timestamp                = {14.06.2015},
  Url                      = {http://dx.doi.org/10.1002/qua.21080}
}

@Book{bijbel,
  Title                    = {Many-Body Theory Exposed!},
  Author                   = {Willem H. Dickhoff and Van Neck, Dimitri},
  Publisher                = {World Scientific},
  Year                     = {2008},

  Url                      = {http://www.worldscientific.com/worldscibooks/10.1142/5804}
}

@Article{dirac_dm,
  Title                    = {Note on Exchange Phenomena in the Thomas Atom},
  Author                   = {Dirac, P.A.M.},
  Journal                  = {Mathematical Proceedings of the Cambridge Philosophical Society},
  Year                     = {1930},
  Number                   = {03},
  Pages                    = {376-385},
  Volume                   = {26}
}

@Article{dirac,
  Title                    = {Quantum Mechanics of Many-Electron Systems},
  Author                   = {Dirac, P. A. M.},
  Journal                  = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences},
  Year                     = {1929},
  Number                   = {792},
  Pages                    = {714--733},
  Volume                   = {123},

  Doi                      = {10.1098/rspa.1929.0094},
  ISSN                     = {0950-1207},
  Publisher                = {The Royal Society}
}

@Book{dh,
  Title                    = {Methods of \mbox{E}lectronic \mbox{S}tructure \mbox{T}heory},
  Author                   = {Dunning, T.H. Jr. and Hay, P.J.},
  Editor                   = {H.F. Schaefer III},
  Publisher                = {Plenum Press},
  Year                     = {1977},
  Volume                   = {2}
}

@Article{RevModPhys.35.457,
  Title                    = {Localized Atomic and Molecular Orbitals},
  Author                   = {Edmiston, Clyde and Ruedenberg, Klaus},
  Journal                  = {Reviews of Modern Physics},
  Year                     = {1963},

  Month                    = {Jul},
  Pages                    = {457--464},
  Volume                   = {35},

  Doi                      = {10.1103/RevModPhys.35.457},
  Issue                    = {3},
  Numpages                 = {0},
  Publisher                = {American Physical Society},
  Url                      = {http://link.aps.org/doi/10.1103/RevModPhys.35.457}
}

@Book{edmonds_angular_1957,
  Title                    = {Angular {Momentum} in {Quantum} {Mechanics}},
  Author                   = {Edmonds, A. R.},
  Publisher                = {Princeton University Press},
  Year                     = {1957},

  Address                  = {Princeton, N.J},
  Edition                  = {Revised edition},
  Month                    = sep,

  Abstract                 = {This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics. Beginning with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the author goes on to discuss the Clebsch-Gordan coefficients for a two-component system. After developing the necessary mathematics, specifically spherical tensors and tensor operators, the author then investigates the 3-j, 6-j, and 9-j symbols. Throughout, the author provides practical applications to atomic, molecular, and nuclear physics. These include partial-wave expansions, the emission and absorption of particles, the proton and electron quadrupole moment, matrix element calculation in practice, and the properties of the symmetrical top molecule.},
  ISBN                     = {9780691079127},
  Language                 = {English}
}

@Book{elliott_symmetry_1985,
  Title                    = {Symmetry in {Physics}: {Further} {Applications} {Volume} 2},
  Author                   = {Elliott, James Philip and Dawber, P. G.},
  Publisher                = {Oxford University Press},
  Year                     = {1985},

  Address                  = {New York},
  Month                    = may,

  Abstract                 = {Preface
In volume 1 the fundamental role of symmetry was developed and applied to a wide range of problems in classical and quantum physics. In this volume we move on to some more difficult applications and to a more general study of the symmetric and unitary groups, particular cases of which were met in volume 1. These topics would probably only arise at postgraduate level, but would none the less be of interest to the more inquisitive undergraduate.
Preface to Volume 2, Paragraph One},
  ISBN                     = {9780195204568},
  Language                 = {English},
  Shorttitle               = {Symmetry in {Physics}}
}

@Book{elliott_symmetry_1985-1,
  Title                    = {Symmetry in {Physics}: {Principles} and {Simple} {Applications} {Volume} 1},
  Author                   = {Elliott, James Philip and Dawber, P. G.},
  Publisher                = {Oxford University Press},
  Year                     = {1985},

  Address                  = {New York},
  Month                    = may,

  Abstract                 = {Originally published in 1979, this successful text is now available in a convenient paperback edition. Volume 1 develops the fundamental role of symmetry and applies it to to wide range of problems in classical and quantum physics. Volume 2 moves on to some more difficult applications and to a more general study of the symmetric and unitary groups. The text includes worked examples and a selection of problems with solutions.},
  ISBN                     = {9780195204551},
  Language                 = {English},
  Shorttitle               = {Symmetry in {Physics}}
}

@Article{erdahl,
  Title                    = {Representability},
  Author                   = {Erdahl, R. M.},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {1978},

  Month                    = {june},
  Number                   = {6},
  Pages                    = {697--718},
  Volume                   = {13},

  Doi                      = {10.1002/qua.560130603},
  ISSN                     = {1097-461X},
  Myurl                    = {http://dx.doi.org/10.1002/qua.560130603}
}

@Book{1D_hub,
  Title                    = {The One-Dimensional Hubbard Model},
  Author                   = {Essler, Fabian H.L. and Frahm, Holger and G\"ohmann, Frank and Kl\"umper, Andreas and Korepin, Vladimir E.},
  Publisher                = {Cambridge University Press},
  Year                     = {2005}
}

@Book{1dhubbook,
  Title                    = {The One-Dimensional Hubbard Model},
  Author                   = {Fabian H. L. Essler and Holger Frahm and Frank Göhmann and Andreas Klümper and Vladimir E. Korepin},
  Publisher                = {Cambridge University Press},
  Year                     = {2010},

  ISBN                     = {0521143942},
}

@Article{essler,
  Title                    = {Complete solution of the one-dimensional Hubbard model},
  Author                   = {Essler, Fabian H. L. and Korepin, Vladimir E. and Schoutens, Kareljan},
  Journal                  = {Physical Review Letters},
  Year                     = {1991},

  Month                    = {Dec},
  Pages                    = {3848--3851},
  Volume                   = {67},

  Doi                      = {10.1103/PhysRevLett.67.3848},
  Issue                    = {27},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevLett.67.3848},
  Publisher                = {American Physical Society}
}

@Article{fan_intriguing_2006,
  Title                    = {Intriguing accuracies of the exponential wave function expansions exploiting finite two-body correlation operators in calculations for many-electron systems},
  Author                   = {Fan, Peng-Dong and Piecuch, Piotr},
  Journal                  = {Journal of Molecular Structure: THEOCHEM},
  Year                     = {2006},

  Month                    = aug,
  Number                   = {1–3},
  Pages                    = {3--16},
  Volume                   = {768},

  Doi                      = {10.1016/j.theochem.2006.04.050},
  ISSN                     = {0166-1280},
  Keywords                 = {Exact many-electron wave functions, Excited states, Generalized coupled-cluster methods, Multi-determinantal reference states, Nooijen's conjecture, Two-body correlation operators, Variational calculations},
  Series                   = {Coupled-cluster {Methods}: {Theory} and {Applications}. {A} {Collection} of {Invited} {Papers} in {Honor} of {Debashis} {Mukherjee} on the {Occasion} of his 60th {Birthday}},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0166128006002685},
  Urldate                  = {2015-06-12}
}

@Article{faribault,
  Title                    = {Gaudin models solver based on the correspondence between Bethe ansatz and ordinary differential equations},
  Author                   = {Faribault, Alexandre and El Araby, Omar and Str\"ater, Christoph and Gritsev, Vladimir},
  Journal                  = {Physical Review B},
  Year                     = {2011},

  Month                    = {Jun},
  Pages                    = {235124},
  Volume                   = {83},

  Doi                      = {10.1103/PhysRevB.83.235124},
  Issue                    = {23},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevB.83.235124},
  Numpages                 = {8},
  Publisher                = {American Physical Society}
}

@Book{fetter_walecka,
  Title                    = {Quantum theory of many-particle systems},
  Author                   = {Fetter, L. A. and Walecka, J. D.},
  Publisher                = {McGraw-Hill book company},
  Year                     = {1971}
}

@Article{finley_applications_1995,
  Title                    = {Applications of multireference perturbation theory to potential energy surfaces by optimal partitioning of {H}: {Intruder} states avoidance and convergence enhancement},
  Author                   = {Finley, James P. and Chaudhuri, Rajat K. and Freed, Karl F.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1995},

  Month                    = sep,
  Number                   = {12},
  Pages                    = {4990--5010},
  Volume                   = {103},

  Abstract                 = {The minimum basis set hydrogen rectangular system (HRS), consisting of four hydrogen atoms arranged in a rectangle, is examined using a variety of partitionings of the Hamiltonian H for high order single and double reference perturbation computations. The potential energy surface is mapped out over a range of geometries in which the length L of one side of the rectangle is varied. Several criteria are derived governing the necessary conditions for perturbative convergence of two‐state systems, and these criteria are useful in explaining the behavior of the HRS for the range of geometries and partitioning methods investigated. The divergence caused by intruder states, observed by Zarrabian and Paldus [Int. J Quantum Chem. 38, 761 (1990)] for the nondegenerate, double reference space perturbation expansions at L=3.0 a.u. with traditional partitioning methods, is shown to correspond to avoided crossings with negative real values of the perturbation parameter—backdoor intruder states. These intruder state induced divergences result from too small zeroth order energy differences between the high lying reference space state and an orthogonal space intruder state whose identity depends on the partitioning method. Forcing the valence orbitals to be degenerate enlarges these zeroth order energy differences and, thus, yields a convergent perturbative expansion for L=3.0 a.u. The convergent or divergent behavior of all the partitioning method computations and the locations of their avoided crossings are accurately predicted by using two‐state models composed of the high lying reference space state and the intruder state. A partitioning method is introduced in which the zeroth order state energies are selected to optimize the convergence in low orders of the perturbation expansion. This optimization method yields perturbative convergence which is both rapid and free of intruder state for geometries between L=2.0 and 3.0 a.u. The divergent behavior for various partitioning methods at L=5.0 a.u., also observed by Zarrabian and Paldus, is caused by one or more orthogonal space states and the high lying reference space state that are strongly coupled and have close expectation values of H. The two‐state model illustrates why no partitioning choice with a double reference space can yield a satisfactory rate of perturbative convergence for L=5.0. Therefore, the entire potential energy surface is treated using more than one reference space: a double reference space for L≤3.0 a.u. and a single reference space for L≳3.0 a.u. The entire potential surface of interest, which is generated with the optimized partitioning method and the two different reference spaces, is very accurate by third order, with eigenvalues for all geometries considered differing from the FCI by no more than 1 kcal/mol.},
  Doi                      = {10.1063/1.470586},
  File                     = {Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/WHWJVAVG/1.html:text/html},
  ISSN                     = {0021-9606, 1089-7690},
  Keywords                 = {Eigenvalues, Optimization, Perturbation methods, Perturbation theory, Potential energy surfaces},
  Shorttitle               = {Applications of multireference perturbation theory to potential energy surfaces by optimal partitioning of {H}},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/103/12/10.1063/1.470586},
  Urldate                  = {2015-06-11}
}

@Article{QUA:QUA560200502,
  Title                    = {Unrestricted Hartree-Fock theory and its applications to molecules and chemical reactions},
  Author                   = {Fukutome, Hideo},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {1981},
  Number                   = {5},
  Pages                    = {955--1065},
  Volume                   = {20},

  Doi                      = {10.1002/qua.560200502},
  ISSN                     = {1097-461X},
  Publisher                = {John Wiley \& Sons, Inc.},
  Url                      = {http://dx.doi.org/10.1002/qua.560200502}
}

@Article{fusco,
  Title                    = {A density matrix variational calculation for atomic Be},
  Author                   = {Garrod, Claude and Fusco, Mario A.},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {1976},
  Number                   = {3},
  Pages                    = {495--510},
  Volume                   = {10},

  Doi                      = {10.1002/qua.560100311},
  ISSN                     = {1097-461X},
  Myurl                    = {http://dx.doi.org/10.1002/qua.560100311}
}

@Article{garrod_mih_ros,
  Title                    = {The variational approach to the two - body density matrix},
  Author                   = {C. Garrod and M. V. Mihailovic and M. Rosina},
  Journal                  = {Journal of Mathematical Physics},
  Year                     = {1975},
  Number                   = {4},
  Pages                    = {868-874},
  Volume                   = {16},

  Doi                      = {10.1063/1.522634},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JMP/16/868/1}
}

@Article{garrod,
  Title                    = {Reduction of the \mbox{$N$}-particle Variational Problem},
  Author                   = {C. Garrod and J. K. Percus},
  Journal                  = {Journal of Mathematics and Physics},
  Year                     = {1964},

  Month                    = {june},
  Pages                    = {1756--1776},
  Volume                   = {5},

  Issue                    = {12}
}

@Article{gaudin,
  Title                    = {Diagonalisation d'une classe d'hamiltoniens de spin},
  Author                   = {Gaudin, M.},
  Journal                  = {Journal de Physique France},
  Year                     = {1976},
  Number                   = {10},
  Pages                    = {1087-1098},
  Volume                   = {37},

  Doi                      = {10.1051/jphys:0197600370100108700},
  Url                      = {http://dx.doi.org/10.1051/jphys:0197600370100108700}
}

@Article{maz_as_2,
  Title                    = {Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian},
  Author                   = {Gidofalvi, Gergely and Mazziotti, David A.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2008},
  Number                   = {13},
  Pages                    = {-},
  Volume                   = {129},

  Doi                      = {10.1063/1.2983652},
  Eid                      = {134108},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/129/13/10.1063/1.2983652}
}

@Article{:/content/aip/journal/jcp/126/2/10.1063/1.2423008,
  Title                    = {Molecular properties from variational reduced-density-matrix theory with three-particle N-representability conditions},
  Author                   = {Gidofalvi, Gergely and Mazziotti, David A.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2007},
  Number                   = {2},
  Pages                    = {-},
  Volume                   = {126},

  Doi                      = {http://dx.doi.org/10.1063/1.2423008},
  Eid                      = {024105},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/126/2/10.1063/1.2423008}
}

@Article{Gido_T_con,
  Title                    = {Molecular properties from variational reduced-density-matrix theory with three-particle N-representability conditions},
  Author                   = {Gergely Gidofalvi and David A. Mazziotti},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2007},
  Number                   = {2},
  Pages                    = {024105},
  Volume                   = {126},

  Doi                      = {10.1063/1.2423008},
  Eid                      = {024105},
  Numpages                 = {7},
  Publisher                = {AIP},
  Url                      = {http://link.aip.org/link/?JCP/126/024105/1}
}

@Article{maz_as_1,
  Title                    = {Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method},
  Author                   = {Gidofalvi, Gergely and Mazziotti, David A.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2007},
  Number                   = {24},
  Pages                    = {-},
  Volume                   = {127},

  Doi                      = {10.1063/1.2817602},
  Eid                      = {244105},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/127/24/10.1063/1.2817602}
}

@Article{maz_gen_T_3,
  Author                   = {Gidofalvi, G. and Mazziotti, D. A.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2007},
  Pages                    = {024105},
  Volume                   = {126}
}

@Article{maz_spin,
  Title                    = {Spin and symmetry adaptation of the variational two-electron reduced-density-matrix method},
  Author                   = {Gergely Gidofalvi and David A. Mazziotti},
  Journal                  = {Physical Review A},
  Year                     = {2005},
  Pages                    = {052505},
  Volume                   = {72}
}

@Article{maz_ham,
  Title                    = {Variational reduced-density-matrix theory: strenght of Hamiltonian-dependent positivity condtions},
  Author                   = {Gergely Gidofalvi and David A. Mazziotti},
  Journal                  = {Chemical Physics Letters},
  Year                     = {2004},
  Pages                    = {434-439},
  Volume                   = {398}
}

@Article{:/content/aip/journal/jcp/48/1/10.1063/1.1667943,
  Title                    = {Improved Quantum Theory of Many-Electron Systems. {III}. The GF Method},
  Author                   = {Goddard, William A.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1968},
  Number                   = {1},
  Pages                    = {450-461},
  Volume                   = {48},

  Doi                      = {10.1063/1.1667943},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/48/1/10.1063/1.1667943}
}

@Book{golub,
  Title                    = {Matrix Computations},
  Author                   = {Gene H. Golub and Van Loan, Charles F.},
  Publisher                = {The Johns Hopkins University Press, Baltimore},
  Year                     = {1989}
}

@Article{greenman,
  Author                   = {Greenman, L. and Mazziotti, D. A.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2009},
  Pages                    = {184101},
  Volume                   = {130}
}

@Book{mpi1,
  Title                    = {Using {MPI}: Portable Parallel Programming with the Message Passing Interface},
  Author                   = {William Gropp and Ewing Lusk and Anthony Skjellum},
  Publisher                = {The MIT Press},
  Year                     = {1999},
  Edition                  = {2nd},

  ISBN                     = {0262571323},
  Url                      = {http://www.amazon.com/Using-MPI-Programming-Engineering-Computation/dp/0262571323}
}

@Article{Gross10121996,
  Title                    = {The role of symmetry in fundamental physics},
  Author                   = {Gross, David J.},
  Journal                  = {Proceedings of the National Academy of Sciences},
  Year                     = {1996},
  Number                   = {25},
  Pages                    = {14256-14259},
  Volume                   = {93},

  Url                      = {http://www.pnas.org/content/93/25/14256.abstract}
}

@InProceedings{Grover-algo,
  Title                    = {A Fast Quantum Mechanical Algorithm for Database Search},
  Author                   = {Grover, Lov K.},
  Booktitle                = {Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing},
  Year                     = {1996},

  Address                  = {New York, NY, USA},
  Pages                    = {212--219},
  Publisher                = {ACM},
  Series                   = {STOC '96},

  Acmid                    = {237866},
  Doi                      = {10.1145/237814.237866},
  ISBN                     = {0-89791-785-5},
  Location                 = {Philadelphia, Pennsylvania, USA},
  Numpages                 = {8},
  Url                      = {http://doi.acm.org/10.1145/237814.237866}
}

@Article{gutz_2,
  Title                    = {Correlation of Electrons in a Narrow $s$ Band},
  Author                   = {Gutzwiller, Martin C.},
  Journal                  = {Physical Review},
  Year                     = {1965},

  Month                    = {Mar},
  Pages                    = {A1726--A1735},
  Volume                   = {137},

  Publisher                = {American Physical Society}
}

@Article{gutzwiller_effect_1964,
  Title                    = {Effect of {Correlation} on the {Ferromagnetism} of {Transition} {Metals}},
  Author                   = {Gutzwiller, Martin C.},
  Journal                  = {Physical Review},
  Year                     = {1964},

  Month                    = may,
  Number                   = {4A},
  Pages                    = {A923},
  Volume                   = {134},

  Abstract                 = {The wave function for the electrons is investigated when a set of narrow bands (valence states) has its energies within a wide band (conduction states). The valence states are linear combinations of localized states which are attached to each lattice site. The intra-atomic Coulomb and exchange integrals for the localized states are much larger than the bandwidths of the valence states. Some of the narrow bands are neither completely empty nor completely filled. The wave function is therefore expected to be correlated, because it is disadvantageous for the electrons to crowd into the same lattice site, or take up some configuration contrary to Hund's rule. This correlation is important in trasition metals, where it is considered to be the cause of ferromagnetism. The correlated wave function is obtained by applying to the uncorrelated antisymmetrized product of Bloch functions an operator which provides each configuration of localized valence states with an appropriate amplitude and phase factor. The procedure is worked out in detail for the case of few particles (electrons or holes) in the narrow bands with the help of a diagram analysis. The localized orbits of different lattice sites do not have to be orthogonal to on another, and the computational rules are actually simplified thereby. The example of a twofold degenerate band such as the upper part of the 3d band in Ni is treated, and the conditions for the occurrence of ferromagnetism are stated in the case of few 3d holes per lattice site.},
  Doi                      = {10.1103/PhysRev.134.A923},
  File                     = {APS Full Text PDF:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/39HB4K73/Gutzwiller - 1964 - Effect of Correlation on the Ferromagnetism of Tra.pdf:application/pdf;APS Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/GC38MA3D/pA923_1.html:text/html},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRev.134.A923},
  Urldate                  = {2011-09-29}
}

@Article{gutz_1,
  Title                    = {Effect of Correlation on the Ferromagnetism of Transition Metals},
  Author                   = {Gutzwiller, Martin C.},
  Journal                  = {Physical Review Letters},
  Year                     = {1963},

  Month                    = {Mar},
  Pages                    = {159--162},
  Volume                   = {10},

  Publisher                = {American Physical Society}
}

@Article{gutzwiller_effect_1963,
  Title                    = {Effect of {Correlation} on the {Ferromagnetism} of {Transition} {Metals}},
  Author                   = {Gutzwiller, Martin C.},
  Journal                  = {Physical Review Letters},
  Year                     = {1963},

  Month                    = mar,
  Number                   = {5},
  Pages                    = {159},
  Volume                   = {10},

  Doi                      = {10.1103/PhysRevLett.10.159},
  File                     = {APS Full Text PDF:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/KKE56CIZ/Gutzwiller - 1963 - Effect of Correlation on the Ferromagnetism of Tra.pdf:application/pdf;APS Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/ZHTAU6DX/p159_1.html:text/html},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRevLett.10.159},
  Urldate                  = {2011-09-29}
}

@Article{hachmann_multireference_2006,
  Title                    = {Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group},
  Author                   = {Hachmann, Johannes and Cardoen, Wim and Chan, Garnet Kin-Lic},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2006},

  Month                    = oct,
  Number                   = {14},
  Pages                    = {144101},
  Volume                   = {125},

  Doi                      = {10.1063/1.2345196},
  ISSN                     = {0021-9606, 1089-7690},
  Keywords                 = {Chemical bonds, Dissociation, Electron correlation calculations, Renormalization, Wave functions},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/125/14/10.1063/1.2345196},
  Urldate                  = {2015-06-12}
}

@Book{hamermesh,
  Title                    = {Group Theory and its Application to physical problems},
  Author                   = {Hamermesh, Morton},
  Publisher                = {Dover Publications},
  Year                     = {1962}
}

@Article{maz_hub,
  Title                    = {Variational reduced-density-matrix calculation of the one-dimensional Hubbard model},
  Author                   = {Hammond, Jeff R. and Mazziotti, David A.},
  Journal                  = {Physical Review A},
  Year                     = {2006},
  Pages                    = {062505},
  Volume                   = {73}
}

@Article{hammond,
  Title                    = {Variational two-electron reduced-density-matrix theory: Partial 3-positivity conditions for \mbox{N}-representability},
  Author                   = {J. R. Hammond and D. A. Mazziotti},
  Journal                  = {Physical Review A},
  Year                     = {2005},
  Pages                    = {062503},
  Volume                   = {71}
}

@Article{PSP:1733252,
  Title                    = {The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part {I}. Theory and Methods},
  Author                   = {Hartree,D. R.},
  Journal                  = {Mathematical Proceedings of the Cambridge Philosophical Society},
  Year                     = {1928},

  Month                    = {1},
  Pages                    = {89--110},
  Volume                   = {24},

  Doi                      = {10.1017/S0305004100011919},
  ISSN                     = {1469-8064},
  Issue                    = {01},
  Numpages                 = {22},
  Url                      = {http://journals.cambridge.org/article_S0305004100011919}
}

@Article{sto-3g,
  Title                    = {Self-Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals},
  Author                   = {Hehre, W. J. and Stewart, R. F. and Pople, J. A.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {1969},
  Number                   = {6},
  Pages                    = {2657-2664},
  Volume                   = {51},

  Doi                      = {10.1063/1.1672392},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/51/6/10.1063/1.1672392}
}

@Book{helgaker2007molecular,
  Title                    = {Molecular Electronic-Structure Theory},
  Author                   = {Helgaker, T. and Jorgensen, P. and Olsen, J.},
  Publisher                = {Wiley},
  Year                     = {2014},

  Doi                      = {10.1002/9781119019572},
  ISBN                     = {9780470017593},
  Url                      = {http://onlinelibrary.wiley.com/book/10.1002/9781119019572}
}

@Article{henderson_pair_2015,
  Title                    = {Pair extended coupled cluster doubles},
  Author                   = {Henderson, Thomas M. and Bulik, Ireneusz W. and Scuseria, Gustavo E.},
  Journal                  = {arXiv:1503.04878 [physics]},
  Year                     = {2015},

  Month                    = mar,
  Note                     = {arXiv: 1503.04878},

  Abstract                 = {The accurate and efficient description of strongly correlated systems remains an important challenge for computational methods. Doubly occupied configuration interaction (DOCI), in which all electrons are paired and no correlations which break these pairs are permitted, can in many cases provide an accurate account of strong correlations, albeit at combinatorial computational cost. Recently, there has been significant interest in a method we refer to as pair coupled cluster doubles (pCCD), a variant of coupled cluster doubles in which the electrons are paired. This is simply because pCCD provides energies nearly identical to those of DOCI, but at mean-field computational cost (disregarding the cost of the two-electron integral transformation). Here, we introduce the more complete pair extended coupled cluster doubles (pECCD) approach which, like pCCD, has mean-field cost and reproduces DOCI energetically. We show that unlike pCCD, pECCD also reproduces the DOCI wave function with high accuracy. Moreoever, pECCD yields sensible albeit inexact results even for attractive interactions where pCCD breaks down.},
  File                     = {arXiv\:1503.04878 PDF:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/M2IHV7MB/Henderson et al. - 2015 - Pair extended coupled cluster doubles.pdf:application/pdf;arXiv.org Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/IVAZN8NQ/1503.html:text/html},
  Keywords                 = {Physics - Chemical Physics},
  Url                      = {http://arxiv.org/abs/1503.04878},
  Urldate                  = {2015-05-20}
}

@Article{pccd2,
  Title                    = {Seniority-based coupled cluster theory},
  Author                   = {Henderson, Thomas M. and Bulik, Ireneusz W. and Stein, Tamar and Scuseria, Gustavo E.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2014},
  Number                   = {24},
  Pages                    = {244104},
  Volume                   = {141},

  Doi                      = {10.1063/1.4904384},
  Eid                      = {244104},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/141/24/10.1063/1.4904384}
}

@Book{jmol2,
  Title                    = {How to Use Jmol to Study and Present Molecular Structures},
  Author                   = {Angel Herrez},
  Publisher                = {Lulu.com},
  Year                     = {2008},
  Volume                   = {I},

  ISBN                     = {1847992595},
  Url                      = {http://www.amazon.com/Jmol-Study-Present-Molecular-Structures/dp/1847992595}
}

@Article{:/content/aip/journal/jmp/13/4/10.1063/1.1666011,
  Title                    = {Generalization of Euler Angles to {N}-Dimensional Orthogonal Matrices},
  Author                   = {Hoffman, David K. and Raffenetti, Richard C. and Ruedenberg, Klaus},
  Journal                  = {Journal of Mathematical Physics},
  Year                     = {1972},
  Number                   = {4},
  Pages                    = {528-533},
  Volume                   = {13},

  Doi                      = {http://dx.doi.org/10.1063/1.1666011},
  Url                      = {http://scitation.aip.org/content/aip/journal/jmp/13/4/10.1063/1.1666011}
}

@InCollection{classical_marg,
  Title                    = {The general marginal problem},
  Author                   = {Hoffmann-Jørgensen, J.},
  Booktitle                = {Functional Analysis II},
  Publisher                = {Springer Berlin / Heidelberg},
  Year                     = {1987},
  Editor                   = {Butkovic, Davor and Kurepa, Svetozar and Kraljevic, Hrvoje},
  Note                     = {10.1007/BFb0072443},
  Pages                    = {77-367},
  Series                   = {Lecture Notes in Mathematics},
  Volume                   = {1242},

  ISBN                     = {978-3-540-17833-0},
  Keyword                  = {Mathematics and Statistics},
  Myurl                    = {http://dx.doi.org/10.1007/BFb0072443}
}

@InCollection{raey,
  Title                    = {The general marginal problem},
  Author                   = {Hoffmann-Jørgensen, J.},
  Booktitle                = {Functional Analysis II},
  Publisher                = {Springer Berlin Heidelberg},
  Year                     = {1987},
  Editor                   = {Butković, Davor and Kurepa, Svetozar and Kraljević, Hrvoje},
  Pages                    = {77-367},
  Series                   = {Lecture Notes in Mathematics},
  Volume                   = {1242},

  Doi                      = {10.1007/BFb0072443},
  ISBN                     = {978-3-540-17833-0},
  Language                 = {English},
  Myurl                    = {http://dx.doi.org/10.1007/BFb0072443}
}

@Article{PhysRev.136.B864,
  Title                    = {Inhomogeneous Electron Gas},
  Author                   = {Hohenberg, P. and Kohn, W.},
  Journal                  = {Physical Review},
  Year                     = {1964},

  Month                    = {Nov},
  Pages                    = {B864--B871},
  Volume                   = {136},

  Doi                      = {10.1103/PhysRev.136.B864},
  Issue                    = {3B},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRev.136.B864},
  Numpages                 = {0},
  Publisher                = {American Physical Society}
}

@Book{horn1994topics,
  Title                    = {Topics in Matrix Analysis},
  Author                   = {Horn, R.A. and Johnson, C.R.},
  Publisher                = {Cambridge University Press},
  Year                     = {1994},

  ISBN                     = {9780521467131},
  Lccn                     = {86023310},
  Url                      = {https://books.google.be/books?id=LeuNXB2bl5EC}
}

@Article{hubac_multireference_2005,
  Title                    = {Multireference {Brillouin}-{Wigner} coupled cluster ({MR}-{BWCC}) theory applied to the {H}$_8$ model: {Comparison} with {CCSD}({T}) theory},
  Author                   = {Hubač, I. and Mach, P. and Wilson, S.},
  Journal                  = {International Journal of Quantum Chemistry},
  Year                     = {2005},

  Month                    = sep,
  Number                   = {4},
  Pages                    = {387--396},
  Volume                   = {104},

  Copyright                = {Copyright © 2005 Wiley Periodicals, Inc.},
  Doi                      = {10.1002/qua.20632},
  ISSN                     = {1097-461X},
  Keywords                 = {Brillouin–Wigner theory, CCSD(T), coupled cluster theory, electron correlation},
  Shorttitle               = {Multireference {Brillouin}–{Wigner} coupled cluster ({MR}-{BWCC}) theory applied to the {H}8 model},
  Url                      = {http://onlinelibrary.wiley.com/doi/10.1002/qua.20632/abstract},
  Urldate                  = {2015-06-12}
}

@Article{hubbard,
  Title                    = {Electron Correlations in Narrow Energy Bands},
  Author                   = {Hubbard, J.},
  Journal                  = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences},
  Year                     = {1963},
  Number                   = {1365},
  Pages                    = {238},
  Volume                   = {276}
}

@Article{hurley-lennard-jones-pople,
  Title                    = {The Molecular Orbital Theory of Chemical Valency. {XVI}. A Theory of Paired-Electrons in Polyatomic Molecules},
  Author                   = {Hurley, A. C. and Lennard-Jones, John and Pople, J. A.},
  Journal                  = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences},
  Year                     = {1953},
  Number                   = {1143},
  Pages                    = {446--455},
  Volume                   = {220},

  Abstract                 = {A further step is made in the development of the orbital theory of molecular structure, the object being to allow for the tendency of two electrons in the same space orbital to keep apart because of the repulsive field between them. The description of a molecule is generalized in such a way as to bracket together electrons in pairs, the simple theory of molecular orbitals being used as a starting point for a wider treatment. If two orbitals are used for each electron pair (paired electron orbitals), it is shown that the theory contains as special cases both previous results of the present series of papers and also the valence-bond wave function which is shown to be an alternative particular approximation to the general function.},
  Doi                      = {10.1098/rspa.1953.0198},
  ISSN                     = {0080-4630},
  Publisher                = {The Royal Society}
}

@Article{husimi,
  Title                    = {Some formal properties of the density matrix},
  Author                   = {K. Husimi},
  Journal                  = {Proceedings of the Physico-Mathematical Society of Japan},
  Year                     = {1940},
  Pages                    = {264},
  Volume                   = {22}
}

@Article{JCC:JCC10291,
  Title                    = {A {MCSCF} method for ground and excited states based on full optimizations of successive Jacobi rotations},
  Author                   = {Ivanic, Joseph and Ruedenberg, Klaus},
  Journal                  = {Journal of Computational Chemistry},
  Year                     = {2003},
  Number                   = {10},
  Pages                    = {1250--1262},
  Volume                   = {24},

  Doi                      = {10.1002/jcc.10291},
  ISSN                     = {1096-987X},
  Keywords                 = {electronic structure theory, variation principle orbital optimization, Jacobi-rotation based minimization, multi-configuration self-consistent field method (MCSCF)},
  Publisher                = {Wiley Subscription Services, Inc., A Wiley Company},
  Url                      = {http://dx.doi.org/10.1002/jcc.10291}
}

@Article{doi:10.1021/ct200345a,
  Title                    = {Generalized Hartree–Fock Description of Molecular Dissociation},
  Author                   = {Jiménez-Hoyos, Carlos A. and Henderson, Thomas M. and Scuseria, Gustavo E.},
  Journal                  = {Journal of Chemical Theory and Computation},
  Year                     = {2011},
  Number                   = {9},
  Pages                    = {2667-2674},
  Volume                   = {7},

  Doi                      = {10.1021/ct200345a},
  Owner                    = {ward},
  Timestamp                = {09.06.2015},
  Url                      = {http://dx.doi.org/10.1021/ct200345a}
}

@Article{phf-scuseria,
  Title                    = {Projected Hartree–Fock theory},
  Author                   = {Jiménez-Hoyos, Carlos A. and Henderson, Thomas M. and Tsuchimochi, Takashi and Scuseria, Gustavo E.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2012},
  Number                   = {16},
  Pages                    = {-},
  Volume                   = {136},

  Doi                      = {10.1063/1.4705280},
  Eid                      = {164109},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/136/16/10.1063/1.4705280}
}

@Article{41Johnson_2013,
  Title                    = {A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals},
  Author                   = {Johnson, P. A. and Ayers, P. W. and Limacher, P. A. and De Baerdemacker, S. and Van Neck, D. and Bultinck, P.},
  Journal                  = {Computational and Theoretical Chemistry},
  Year                     = {2013},
  Pages                    = {101-113},
  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.2012.09.030},
  ISSN                     = {2210-271X},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article},
  Url                      = {<Go to ISI>://WOS:000314074200017}
}

@Article{55Johnson_2013a,
  Title                    = {The sharp-G N-representability condition},
  Author                   = {Johnson, P. A. and Ayers, P. W. and Verstichel, B. and Van Neck, D. and van Aggelen, H.},
  Journal                  = {Computational and Theoretical Chemistry},
  Year                     = {2013},
  Pages                    = {32-36},
  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.2012.09.029},
  ISSN                     = {2210-271X},
  Owner                    = {ward},
  Timestamp                = {10.03.2015},
  Type                     = {Journal Article},
  Url                      = {<Go to ISI>://WOS:000314074200007}
}

@Article{kamarchik,
  Author                   = {Kamarchik, E. and Mazziotti, D. A.},
  Journal                  = {Physical Review Letters},
  Year                     = {2007},
  Pages                    = {243002},
  Volume                   = {99}
}

@MastersThesis{karush,
  Title                    = {Minima of Functions of Several Variables with Inequalities as Side Constraints},
  Author                   = {Karush, W.},
  School                   = {Dept. of Mathematics, Univ. of Chicago, Chicago, Illinois},
  Year                     = {1939},

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

@Article{ccmanby,
  Title                    = {Communication: The distinguishable cluster approximation},
  Author                   = {Kats, Daniel and Manby, Frederick R.},
  Journal                  = {Journal of Chemical Physics},
  Year                     = {2013},
  Number                   = {2},
  Pages                    = {021102},
  Volume                   = {139},

  Doi                      = {10.1063/1.4813481},
  Eid                      = {021102},
  Url                      = {http://scitation.aip.org/content/aip/journal/jcp/139/2/10.1063/1.4813481}
}

@Article{cuttingplane1960,
  Title                    = {The Cutting-Plane Method for Solving Convex Programs},
  Author                   = {Kelley, J. E., Jr.},
  Journal                  = {Journal of the Society for Industrial and Applied Mathematics},
  Year                     = {1960},
  Number                   = {4},
  Pages                    = {pp. 703-712},
  Volume                   = {8},

  Copyright                = {Copyright © 1960 Society for Industrial and Applied Mathematics},
  ISSN                     = {03684245},
  Jstor_articletype        = {research-article},
  Jstor_formatteddate      = {Dec., 1960},
  Language                 = {english},
  Publisher                = {Society for Industrial and Applied Mathematics},
  Url                      = {http://www.jstor.org/stable/2099058}
}

@Article{doi:10.1137/S0097539704445226,
  Title                    = {The Complexity of the Local Hamiltonian Problem},
  Author                   = {Julia Kempe and Alexei Kitaev and Oded Regev},
  Journal                  = {SIAM Journal on Computing},
  Year                     = {2006},
  Number                   = {5},
  Pages                    = {1070-1097},
  Volume                   = {35},

  Doi                      = {10.1137/S0097539704445226},
  Myurl                    = {http://dx.doi.org/10.1137/S0097539704445226 }
}

@Article{Kirkpatrick13051983,
  Title                    = {Optimization by Simulated Annealing},
  Author                   = {Kirkpatrick, S. and Gelatt, C. D. and Vecchi, M. P.},
  Journal                  = {Science},
  Year                     = {1983},
  Number                   = {4598},
  Pages                    = {671-680},
  Volume                   = {220},

  Abstract                 = {There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.},
  Doi                      = {10.1126/science.220.4598.671},
  Url                      = {http://www.sciencemag.org/content/220/4598/671.abstract}
}

@Article{kishore,
  Title                    = {On the solutions of the infinite U Hubbard model through orthofermions},
  Author                   = {Kishore, R. and Mishra, A.K.},
  Journal                  = {Physics Letters A},
  Year                     = {2007},
  Number                   = {3},
  Pages                    = {226 - 229},
  Volume                   = {369},

  Doi                      = {10.1016/j.physleta.2007.04.080},
  ISSN                     = {0375-9601},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0375960107006536}
}

@Book{Kitaev:2002:CQC:863284,
  Title                    = {Classical and Quantum Computation},
  Author                   = {Kitaev, A. Yu. and Shen, A. H. and Vyalyi, M. N.},
  Publisher                = {American Mathematical Society},
  Year                     = {2002},

  Address                  = {Boston, MA, USA},

  ISBN                     = {0821832298}
}

@Misc{lagrangemult,
  Title                    = {Lagrange Multipliers without Permanent Scarring},

  Author                   = {Dan Klein},
  Year                     = {2002},

  Owner                    = {ward},
  Timestamp                = {05.06.2015},
  Url                      = {http://nlp.cs.berkeley.edu/tutorials/lagrange-multipliers.pdf}
}

@Article{klyachko_quantum_2004,
  Title                    = {Quantum marginal problem and representations of the symmetric group},
  Author                   = {Klyachko, Alexander},
  Journal                  = {arXiv:quant-ph/0409113},
  Year                     = {2004},

  Month                    = sep,
  Note                     = {arXiv: quant-ph/0409113},

  Abstract                 = {We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive tables of marginal inequalities, including arrays up to 4 qubits. In the second part of the paper we pursue another approach based on reduction of the problem to representation theory of the symmetric group.},
  File                     = {arXiv.org Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/3JK29SCE/0409113.html:text/html;arXiv\:quant-ph/0409113 PDF:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/7UF7TP9Z/Klyachko - 2004 - Quantum marginal problem and representations of th.pdf:application/pdf},
  Keywords                 = {Quantum Physics},
  Url                      = {http://arxiv.org/abs/quant-ph/0409113},
  Urldate                  = {2015-05-08}
}

@Article{1742-6596-36-1-014,
  Title                    = {Quantum marginal problem and N-representability},
  Author                   = {Alexander A Klyachko},
  Journal                  = {Journal of Physics: Conference Series},
  Year                     = {2006},
  Number                   = {1},
  Pages                    = {72},
  Volume                   = {36},

  Abstract                 = {A fermionic version of the quantum marginal problem was known from the early sixties as N-representability problem . In 1995 it was mentioned by the National Research Council of the USA as one of ten most prominent research challenges in quantum chemistry. In spite of this recognition the progress was very slow, until a couple of years ago the problem came into focus again, now in the framework of quantum information theory. In the paper I give a survey of the recent development.},
  Url                      = {http://stacks.iop.org/1742-6596/36/i=1/a=014}
}

@Article{PhysRev.140.A1133,
  Title                    = {Self-Consistent Equations Including Exchange and Correlation Effects},
  Author                   = {Kohn, W. and Sham, L. J.},
  Journal                  = {Physical Review},
  Year                     = {1965},

  Month                    = {Nov},
  Pages                    = {A1133--A1138},
  Volume                   = {140},

  Doi                      = {10.1103/PhysRev.140.A1133},
  Issue                    = {4A},
  Myurl                    = {http://link.aps.org/doi/10.1103/PhysRev.140.A1133},
  Numpages                 = {0},
  Publisher                = {American Physical Society}
}

@Article{kowalski_full_1998,
  Title                    = {Full solution to the coupled-cluster equations: the {H}$_4$ model},
  Author                   = {Kowalski, K and Jankowski, K},
  Journal                  = {Chemical Physics Letters},
  Year                     = {1998},

  Month                    = jun,
  Number                   = {1–3},
  Pages                    = {180--188},
  Volume                   = {290},

  Abstract                 = {A version of the homotopy (continuation) methods is successfully applied to calculating the full set of geometrically isolated solutions to a set of nonlinear equations determining the cluster amplitudes in coupled-cluster (CC) methods. The set of equations considered is obtained when applying the CC method, including two-body amplitudes (CCD), to the H4 model. The complete sets of solutions for the spinorbital and spin-symmetry adapted variants of the CCD equations consist of 20 and 12 solutions, respectively. At least 5 solutions are physically meaningful. In addition to standard and nonstandard solutions of the desired symmetry, broken-symmetry solutions are also documented. A preliminary analysis of the significance of the latter solutions is presented.},
  Doi                      = {10.1016/S0009-2614(98)00464-3},
  File                     = {ScienceDirect Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/6WE5QQF7/S0009261498004643.html:text/html},
  ISSN                     = {0009-2614},
  Shorttitle               = {Full solution to the coupled-cluster equations},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0009261498004643},
  Urldate                  = {2015-06-11}
}

@Article{kowalski_towards_1998,
  Title                    = {Towards {Complete} {Solutions} to {Systems} of {Nonlinear} {Equations} of {Many}-{Electron} {Theories}},
  Author                   = {Kowalski, Karol and Jankowski, Karol},
  Journal                  = {Physical Review Letters},
  Year                     = {1998},

  Month                    = aug,
  Number                   = {6},
  Pages                    = {1195--1198},
  Volume                   = {81},

  Abstract                 = {Employing the homotopy method we have obtained the complete set of real solutions to the equations of the restricted Hartree-Fock method as well as the full set of solutions to the equations of the coupled-cluster-with-doubles method for the H4 and P4 models broadly applied in various many-electron studies. These are the first global results obtained so far for any formulations of the Hartree-Fock and coupled-cluster methods when applied to realistic models.},
  Doi                      = {10.1103/PhysRevLett.81.1195},
  File                     = {APS Snapshot:/home/ward/.mozilla/firefox/u1pwfk5g.default/zotero/storage/UI3RCVZA/PhysRevLett.81.html:text/html},
  Url                      = {http://link.aps.org/doi/10.1103/PhysRevLett.81.1195},
  Urldate                  = {2015-06-11}
}

@Article{Krein1940,
  Title                    = {On extreme points of regular convex sets},
  Author                   = {Krein, M. and Milman, D.},
  Journal                  = {Studia Mathematica},
  Year                     = {1940},
  Number                   = {1},
  Pages                    = {133-138},
  Volume                   = {9},

  Publisher                = {Institute of Mathematics Polish Academy of Sciences},
  Url                      = {http://eudml.org/doc/219061}
}

@Article{krivnov,
  Title                    = {Some properties of the Hubbard model with infinite repulsion},
  Author                   = {Krivnov, V.Ya. and Ovchinnikov, A.A. and Cheranovskii, V.O.},
  Journal                  = {Teoreticheskaya i Matematicheskaya Fizika},
  Year                     = {1990},

  Month                    = {Feb},
  Pages                    = {216--223},
  Volume                   = {82},

  Issue                    = {2}
}

@Article{1962JPSJ...17.1100K,
  Title                    = {Generalized Cumulant Expansion Method},
  Author                   = {{Kubo}, R.},
  Journal                  = {Journal of the Physical Society of Japan},
  Year                     = {1962},

  Month                    = jul,
  Pages                    = {1100},
  Volume                   = {17},

  Adsnote                  = {Provided by the SAO/NASA Astrophysics Data System},
  Adsurl                   = {http://adsabs.harvard.edu/abs/1962JPSJ...17.1100K}
}

@InProceedings{kuhn1951,
  Title                    = {Nonlinear Programming},
  Author                   = {Kuhn, H. W. and Tucker, A. W.},
  Booktitle                = {Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability},
  Year                     = {1951},

  Address                  = {Berkeley, Calif.},
  Pages                    = {481--492},
  Publisher                = {University of California Press},

  Url                      = {http://projecteuclid.org/euclid.bsmsp/1200500

gha_language: TeX