@Article{Kutzelnigg85,
  author = 	"W. Kutzelnigg",
  title = 	"$r_{12}$-dependent terms in the wave function as closed
		  sums of partial wave amplitudes for large $l$",
  journal = 	"Theor. Chim. Acta",
  volume = 	68,
  pages = 	445,
  year = 	1985,
  comments = {

An excellent paper in which the idea of $linear$ $r_{12}$-methods was
formulated (to my knowledge) for the first time.
Several $r_{12}$-dependent ansatzes were proposed. 
It is shown that for single-reference problems only the reference wavefunction
have to be multiplied by the $g_{12}$-factor to achive VERY fast
convergence. Two cases were examined : MP2 and full CI on the ground
state of He. CI procedure converged much faster than MP2. 
Applicability to larger systems (with more than 2 electrons) is
discussed. The ways to avoid ``difficult'' integrals are outlined.

  }
}

@Article{Kutzelnigg91,
  author = 	"W. Kutzelnigg and W. Klopper",
  title = 	"Wave functions with terms linear in the
		  interelectronic coordinates to take care of the
		  correlation cusp. {I}. {General} theory.",
  journal = 	"J. Chem. Phys.",
  volume = 	94,
  pages = 	1985,
  year = 	1991,
  comments = {

No notes yet.

  }
}

@Book{KnuthACP,
  author =       "D.~E.~Knuth",
  title =        "{The Art of Computer Programming}",
  publisher =    "Addison-Wesley",
  year =         1997,
  edition =      "Third",
  address =      "Reading, MA"
}

@Article{Klopper92,
  author =       "W. Klopper and {R. R\"{o}hse}",                              
  title =        "Computation of some new two-electron {Gaussian} integrals.",
  journal =      "Theor. Chim. Acta",
  year =         1992,
  volume =       83,   

		  pages =        441,
}

@Misc{Libint1,
  author =       "J.~T.~Fermann and E.~F.~Valeev",
  title =        "{Libint: Machine-generated library for efficient evaluation of molecular integrals over Gaussians}",
  howpublished = "",
  note =         "Freely available at {\tt http://libint.valeyev.net/} or one of the authors.",
  year =         2003
  }
}

@Article{Valeev00:r12ints,
  author =       "E. F. Valeev and H. F. Schaefer",
  title  =       "Evaluation of two-electron integrals for explicit
		  $r_{12}$ theories",
  journal =      "J. Chem. Phys.",
  year =         2000,
  volume =       113,
  pages =        3990
}

@Article{Head-Gordon88,
  author =       "M. Head-Gordon and J. A. Pople",
  journal =      "J. Chem. Phys.",
  title =        "A method for 2-electron {Gaussian} integral and integral derivative evaluation using recurrence relations.",
  year =         1988,
  volume =       89,
  pages =        5777,
  comments = {
HGP improved Obara-Saika recursion relations by introducing VRR(work
for uncontracted classes only) and HRR (work for contracted classes).
  }
}

@Article{Obara86,
  author =       "S. Obara and A. Saika",
  title =        "Efficient recursive computations of molecular
		  integrals over {Cartesian Gaussian} functions.",
  journal =      "J. Chem. Phys.",
  year =         1986,
  volume =       84,
  pages =        3963
}

@Article{Obara88,
  author =       "S. Obara and A. Saika",
  title =        "General recurrence formulas for molecular
          integrals over Cartesian Gaussian functions.",
  journal =      "J. Chem. Phys.",
  year =         1988,
  volume =       89,
  pages =        1540
}

@Article{Hamilton91,
  author =       "T. P. Hamilton and H. F. Schaefer",
  title =        "New variations in two-electron integral evaluation in
		  the context of direct SCF procedures.",
  journal =      {Chem. Phys.},
  year =         1991,
  volume =       150,
  pages =        163
}

@Article{Lindh91,
  author =       "R. Lindh and U. Ryu and B. Liu",
  title =        "THE REDUCED MULTIPLICATION SCHEME OF THE RYS QUADRATURE AND NEW RECURRENCE RELATIONS FOR AUXILIARY FUNCTION BASED 2-ELECTRON INTEGRAL EVALUATION",
  journal =      {J. Chem. Phys.},
  year =         1991,
  volume =       95,
  pages =        5889,
  comments = {
Abstract: The reduced multiplication scheme of the Rys quadrature is presented. The method is based on new ways in which the Rys quadrature can be developed if it is implemented together with the transfer equation applied to the contracted integrals. In parallel to the new scheme of the Rys quadrature improvements are suggested to the auxiliary function based algorithms. The two new methods have very favorable theoretical floating point operation (FLOP) counts as compared to other methods. It is noted that the only significant difference in performance of the two new methods is due to the vectorizability of the presented algorithms. In order to exhibit this, both methods were implemented in the integral program SEWARD. Timings are presented for comparisons with other implementations. Finally, it is demonstrated how the transfer equation in connection with the use of spherical harmonic Gaussians offers a very attractive path to compute the two-electron integrals of such basis functions. It is demonstrated both theoretically and with actual performance that the use of spherical harmonic Gaussians offers a clear advantage over the traditional evaluation of the two-electron integrals in the Cartesian Gaussian basis.
  }
}

@Article{Gill91,
  author =       "P. M. W. Gill and J. A. Pople",
  title =        "The PRISM algorithm for 2-electron integrals.",
  journal =      "Int. J. Quantum Chem.",
  year =         1991,
  volume =       "40",
  pages =        753
}

@PhdThesis{Fermann96:PhD,
  author = 	 "J. T. Fermann",
  title = 	 "Efficient implementation of vertical recursion
		  relations for the generation of electron repulsion intgerals.",
  school = 	 "University of Georgia",
  year = 	 1996
}

@Article{Persson96,
  author =       "B. J. Persson and P. R. Taylor",
  title =        "Accurate quantum-chemical calculation: The use of
          Gaussian-type geminal functions in the treatment of
          electron correlation.",
  journal =      "J. Chem. Phys.",           
  year =         1996,
  volume =       105,
  pages =        5915
}

@article{Ahlrichs:2006,
author = {R.~Ahlrichs},
title = {{A simple algebraic derivation of the Obara-Saika scheme for general two-electron interaction potentials}},
journal = {Phys. Chem. Chem. Phys.},
year = {2006},
volume = {8},
number = {26},
pages = {3072}
}
