Free Access
Issue 
ESAIM: M2AN
Volume 41, Number 2, MarchApril 2007
Special issue on Molecular Modelling



Page(s)  249  259  
DOI  https://doi.org/10.1051/m2an:2007021  
Published online  16 June 2007 
 D.R. Alcoba, F.J. Casquero, L.M. Tel, E. PerezRomero and C. Valdemoro, Convergence enhancement in the iterative solution of the secondorder contracted Schrödinger equation. Int. J. Quantum Chem. 102 (2005) 620–628. [CrossRef]
 M.D. Benayoun, A.Y. Lu and D.A. Mazziotti, Invariance of the cumulant expansion under 1particle unitary transformations in reduced density matrix theory. Chem. Phys. Lett. 387 (2004) 485–489. [CrossRef]
 D.P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York (1982).
 S. Burer and C. Choi, Computational enhancements in lowrank semidefinite programming. Optim. Methods Soft. 21 (2006) 493–512. [CrossRef]
 S. Burer and R.D.C. Monteiro, Nonlinear programming algorithm for solving semidefinite programs via lowrank factorization. Math. Program. Ser. B 95 (2003) 329–357. [CrossRef]
 S. Burer and R.D.C. Monteiro, Local minima and convergence in lowrank semidefinite programming. Math. Program. Ser. A 103 (2005) 427–444. [CrossRef]
 L. Cohen and C. Frishberg, Hierarchy equations for reduced density matrices, Phys. Rev. A 13 (1976) 927–930.
 A.J. Coleman, Structure of fermion density matrices. Rev. Mod. Phys. 35 (1963) 668. [CrossRef]
 A.J. Coleman and V.I. Yukalov, Reduced Density Matrices: Coulson's Challenge. SpringerVerlag, New York (2000).
 F. Colmenero and C. Valdemoro, Approximating qorder reduced densitymatrices in terms of the lowerorder ones. 2. Applications. Phys. Rev. A 47 (1993) 979–985. [CrossRef] [PubMed]
 F. Colmenero and C. Valdemoro, Selfconsistent approximate solution of the 2ndorder contracted Schrödinger equation. Int. J. Quantum Chem. 51 (1994) 369–388. [CrossRef]
 A.R. Conn, I.M. Gould and P.L. Toint, TrustRegion Methods. SIAM: Philadelphia (2000).
 C.A. Coulson, Present state of molecular structure calculations. Rev. Mod. Phys. 32 (1960) 170–177. [CrossRef] [MathSciNet]
 R.M. Erdahl, Representability. Int. J. Quantum Chem. 13 (1978) 697–718. [CrossRef]
 R.M. Erdahl, Two algorithms for the lower bound method of reduced density matrix theory. Reports Math. Phys. 15 (1979) 147–162. [CrossRef]
 R.M. Erdahl and B. Jin, The lower bound method for reduced density matrices. J. Mol. Struc. (Theochem) 527 (2000) 207–220. [CrossRef]
 R. Fletcher, Practical Methods of Optimization. John Wiley and Sons, New York (1987).
 M. Fukuda, B.J. Braams, M. Nakata, M.L. Overton, J.K. Percus, M. Yamashita and Z. Zhao, Largescale semidefinite programs in electronic structure calculation. Math. Program., Ser. B 109 (2007) 553.
 C. Garrod and J. Percus, Reduction of Nparticle variational problem. J. Math. Phys. 5 (1964) 1756–1776. [CrossRef]
 G. Gidofalvi and D.A. Mazziotti, Boson correlation energies via variational minimization with the twoparticle reduced density matrix: Exact Nrepresentability conditions for harmonic interactions. Phys. Rev. A 69 (2004) 042511. [CrossRef]
 G. Gidofalvi and D.A. Mazziotti, Application of variational reduceddensitymatrix theory to organic molecules. J. Chem. Phys. 122 (2005) 094107. [CrossRef] [PubMed]
 G. Gidofalvi and D.A. Mazziotti, Application of variational reduceddensitymatrix theory to the potential energy surfaces of the nitrogen and carbon dimers. J. Chem. Phys. 122 (2005) 194104. [CrossRef] [PubMed]
 G. Gidofalvi and D.A. Mazziotti, Spin and symmetryadapted twoelectron reduceddensitymatrix theory. Phys. Rev. A 72 (2005) 052505. [CrossRef]
 G. Gidofalvi and D.A. Mazziotti, Potential energy surface of carbon monoxide in the presence and absence of an electric field using the twoelectron reduceddensitymatrix method. J. Phys. Chem. A 110 (2006) 5481–5486. [CrossRef] [PubMed]
 G. Gidofalvi and D.A. Mazziotti, Computation of quantum phase transitions by reduceddensitymatrix mechanics. Phys. Rev. A 74 (2006) 012501. [CrossRef]
 J.R. Hammond and D.A. Mazziotti, Variational twoelectron reduceddensitymatrix theory: Partial 3positivity conditions for Nrepresentability. Phys. Rev. A 71 (2005) 062503. [CrossRef]
 J.R. Hammond and D.A. Mazziotti, Variational reduceddensitymatrix calculations on radicals: a new approach to openshell ab initio quantum chemistry. Phys. Rev. A 73 (2006) 012509. [CrossRef]
 J.R. Hammond and D.A. Mazziotti, Variational reduceddensitymatrix calculation of the onedimensional Hubbard model. Phys. Rev. A 73 (2006) 062505. [CrossRef]
 J.E. Harriman, Geometry of density matrices. II. Reduced density matrices and Nrepresentability. Phys. Rev. A 17 (1978) 1257–1268. [CrossRef]
 T. Juhász and D.A. Mazziotti, Perturbation theory corrections to the twoparticle reduced density matrix variational method. J. Chem. Phys. 121 (2004) 1201–1205. [CrossRef] [PubMed]
 W. Kutzelnigg and D. Mukherjee, Irreducible Brillouin conditions and contracted Schrödinger equations for nelectron systems. IV. Perturbative analysis. J. Chem. Phys. (2004) 120 7350–7368.
 P.O. Löwdin, Quantum theory of manyparticle systems. 1. Physical interpretations by means of density matrices, natural spinorbitals, and convergence problems in the method of configuration interaction. Phys. Rev. 97 (1955) 1474–1489. [CrossRef] [MathSciNet]
 J.E. Mayer, Electron correlation. Phys. Rev. 100 (1955) 1579–1586. [CrossRef]
 D.A. Mazziotti, Contracted Schrödinger equation: Determining quantum energies and twoparticle density matrices without wave functions. Phys. Rev. A 57 (1998) 4219–4234. [CrossRef]
 D.A. Mazziotti, Approximate solution for electron correlation through the use of Schwinger probes. Chem. Phys. Lett. 289 (1998) 419–427. [CrossRef]
 D.A. Mazziotti, Pursuit of Nrepresentability for the contracted Schrödinger equation through densitymatrix reconstruction. Phys. Rev. A 60 (1999) 3618–3626. [CrossRef]
 D.A. Mazziotti, Comparison of contracted Schrödinger and coupledcluster theories. Phys. Rev. A 60 (1999) 4396–4408. [CrossRef]
 D.A. Mazziotti, Correlated purification of reduced density matrices. Phys. Rev. E 65 (2002) 026704. [CrossRef]
 D.A. Mazziotti, A variational method for solving the contracted Schrödinger equation through a projection of the Nparticle power method onto the twoparticle space. J. Chem. Phys. 116 (2002) 1239–1249. [CrossRef]
 D.A. Mazziotti, Variational minimization of atomic and molecular groundstate energies via the twoparticle reduced density matrix. Phys. Rev. A 65 (2002) 062511. [CrossRef]
 D.A. Mazziotti, Solution of the 1,3contracted Schrödinger equation through positivity conditions on the 2particle reduced density matrix. Phys. Rev. A 66 (2002) 062503. [CrossRef]
 D.A. Mazziotti, Realization of quantum chemistry without wavefunctions through firstorder semidefinite programming. Phys. Rev. Lett. 93 (2004) 213001. [CrossRef] [PubMed]
 D.A. Mazziotti, Firstorder semidefinite programming for the direct determination of twoelectron reduced density matrices with application to manyelectron atoms and molecules. J. Chem. Phys. 121 (2004) 10957–10966. [CrossRef] [PubMed]
 D.A. Mazziotti, Variational twoelectron reduceddensitymatrix theory for manyelectron atoms and molecules: Implementation of the spin and symmetryadapted T_{2} condition through firstorder semidefinite programming. Phys. Rev. A 72 (2005) 032510. [CrossRef]
 D.A. Mazziotti, Variational reduceddensitymatrix method using threeparticle Nrepresentability conditions with application to manyelectron molecules. Phys. Rev. A 74 (2006) 032501. [CrossRef]
 D.A. Mazziotti, ReducedDensityMatrix with Application to Manyelectron Atoms and Molecules, Advances in Chemical Physics 134, D.A. Mazziotti Ed., John Wiley and Sons, New York (2007).
 D.A. Mazziotti and R.M. Erdahl, Uncertainty relations and reduced density matrices: Mapping manybody quantum mechanics onto four particles. Phys. Rev. A 63 (2001) 042113. [CrossRef]
 M.V. Mihailović and M. Rosina, Excitations as groundstate variational parameters. Nucl. Phys. A130 (1969) 386.
 M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata and K. Fujisawa, Variational calculations of fermion secondorder reduced density matrices by semidefinite programming algorithm. J. Chem. Phys. 114 (2001) 8282–8292. [CrossRef]
 M. Nakata, M. Ehara and H. Nakatsuji, Density matrix variational theory: Application to the potential energy surfaces and strongly correlated systems. J. Chem. Phys. 116 (2002) 5432–5439. [CrossRef]
 H. Nakatsuji, Equation for the direct determination of the density matrix. Phys. Rev. A 14 (1976) 41–50. [CrossRef]
 H. Nakatsuji and K. Yasuda, Direct determination of the quantummechanical density matrix using the density equation. Phys. Rev. Lett. 76 (1996) 1039–1042. [CrossRef] [PubMed]
 M. Nayakkankuppam, Solving largescale semidefinite programs in parallel. Math. Program., Ser. B 109 (2007) 477–504.
 Y. Nesterov and A.S. Nemirovskii, Interior Point Polynomial Method in Convex Programming: Theory and Applications. SIAM: Philadelphia (1993).
 E. Polak, Optimization: Algorithms and Consistent Approximations. SpringerVerlag, New York (1997).
 J.H. Sebold and J.K. Percus, Model derived reduced density matrix restrictions for correlated fermions. J. Chem. Phys. 104 (1996) 6606–6612. [CrossRef]
 R.H. Tredgold, Density matrix and the manybody problem. Phys. Rev. 105 (1957) 1421–1423. [CrossRef] [MathSciNet]
 L. Vandenberghe and S. Boyd, Semidefinite programming. SIAM Rev. 38 (1996) 49–95. [CrossRef] [MathSciNet]
 S. Wright, PrimalDual InteriorPoint Methods. SIAM, Philadelphia (1997).
 K. Yasuda, and H. Nakatsuji, Direct determination of the quantummechanical density matrix using the density equation II. Phys. Rev. A 56 (1997) 2648–2657. [CrossRef]
 Z. Zhao, B.J. Braams, H. Fukuda, M.L. Overton and J.K. Percus, The reduced density matrix method for electronic structure calculations and the role of threeindex representability conditions. J. Chem. Phys. 120 (2004) 2095–2104. [CrossRef] [PubMed]
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