Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group.

We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10 microE(h) precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.

[1]  Josef Paldus,et al.  Coupled-cluster approach to electron correlation in one dimension. II. Cyclic polyene model in localized basis , 1984 .

[2]  Jhinhwan Lee,et al.  Real space imaging of one-dimensional standing waves: direct evidence for a Luttinger liquid. , 2004, Physical review letters.

[3]  Leon Balents,et al.  Luttinger-liquid behaviour in carbon nanotubes , 1998, Nature.

[4]  Garnet Kin-Lic Chan,et al.  An algorithm for large scale density matrix renormalization group calculations. , 2004, The Journal of chemical physics.

[5]  Markus Reiher,et al.  Construction of environment states in quantum-chemical density-matrix renormalization group calculations. , 2006, The Journal of chemical physics.

[6]  U. Schollwoeck.  The density-matrix renormalization group , 2004, cond-mat/0409292.

[7]  Yuansheng Jiang,et al.  Spin distribution in neutral polyene radicals: Pariser-Parr-Pople model studied with the density matrix renormalization group method. , 2005, The Journal of chemical physics.

[8]  Gregory J O Beran,et al.  Second-order correction to perfect pairing: an inexpensive electronic structure method for the treatment of strong electron-electron correlations. , 2006, The Journal of chemical physics.

[9]  Y Hieida,et al.  Universal asymptotic eigenvalue distribution of density matrices and corner transfer matrices in the thermodynamic limit. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Hans-Joachim Werner,et al.  Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD) , 2001 .

[11]  Joseph G. Hoffman,et al.  Quantum Theory of Atoms, Molecules and the Solid State: A Tribute to John C. Slater , 1967 .

[12]  Hans-Joachim Werner,et al.  Local perturbative triples correction (T) with linear cost scaling , 2000 .

[13]  Garnet Kin-Lic Chan,et al.  Exact solution (within a triple-zeta, double polarization basis set) of the electronic Schrödinger equation for water , 2003 .

[14]  B. A. Hess,et al.  QC-DMRG study of the ionic-neutral curve crossing of LiF , 2002 .

[15]  G. Fano,et al.  The density matrix renormalization group method. Application to the PPP model of a cyclic polyene chain. , 1998, cond-mat/9803071.

[16]  Martin Head-Gordon,et al.  Connections between coupled cluster and generalized valence bond theories , 2001 .

[17]  Robert J. Cave,et al.  On the Vertical and Adiabatic Excitation Energies of the 21Ag State of trans-1,3-Butadiene , 2000 .

[18]  Jürgen Gauss,et al.  State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve. , 2004, The Journal of chemical physics.

[19]  Garnet Kin-Lic Chan,et al.  Canonical transformation theory for multireference problems. , 2006, The Journal of chemical physics.

[20]  Richard L. Martin,et al.  Ab initio quantum chemistry using the density matrix renormalization group , 1998 .

[21]  Legeza,et al.  Accuracy of the density-matrix renormalization-group method. , 1996, Physical review. B, Condensed matter.

[22]  C. Daul,et al.  Full‐CI quantum chemistry using the density matrix renormalization group , 1999 .

[23]  Guido Fano,et al.  Quantum chemistry using the density matrix renormalization group II , 2003 .

[24]  E. Davidson.  The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .

[25]  Markus Reiher,et al.  Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings. , 2005, The Journal of chemical physics.

[26]  Martin Head-Gordon,et al.  The imperfect pairing approximation , 2000 .

[27]  Richard A. Friesner,et al.  Application and development of multiconfigurational localized perturbation theory , 2001 .

[28]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals , 1969 .

[29]  Paweł Sałek,et al.  Dalton, a molecular electronic structure program , 2005 .

[30]  Jean-Luc Bredas,et al.  Quantum confinement effects on the ordering of the lowest-lying excited states in conjugated polymers , 1997, Optics & Photonics.

[31]  Markus Reiher,et al.  Relativistic DMRG calculations on the curve crossing of cesium hydride. , 2005, The Journal of chemical physics.

[32]  Emily A. Carter,et al.  Multi-reference weak pairs local configuration interaction: efficient calculations of bond breaking , 2001 .

[33]  M. Head‐Gordon,et al.  Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group , 2002 .

[34]  David Yaron,et al.  COMPARISON OF DENSITY MATRIX RENORMALIZATION GROUP CALCULATIONS WITH ELECTRON-HOLE MODELS OF EXCITON BINDING IN CONJUGATED POLYMERS , 1998 .

[35]  Yuansheng Jiang,et al.  "Triplet-excited region" in polyene oligomers revisited: Pariser-Parr-Pople model studied with the density matrix renormalization group method. , 2004, The Journal of chemical physics.

[36]  S. Evangelisti,et al.  Density matrix renormalization group study of dimerization of the Pariser–Parr–Pople model of polyacetilene , 1999 .

[37]  Martin Head-Gordon,et al.  A nonorthogonal approach to perfect pairing , 2000 .

[38]  Josef Paldus,et al.  Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory , 1984 .

[39]  Philippe Y. Ayala,et al.  Linear scaling coupled cluster and perturbation theories in the atomic orbital basis , 1999 .

[40]  F Kun,et al.  Structure of magnetic noise in dynamic fracture. , 2004, Physical review letters.

[41]  B. Roos.  The Complete Active Space Self‐Consistent Field Method and its Applications in Electronic Structure Calculations , 2007 .

[42]  Guido Fano,et al.  Quantum chemistry using the density matrix renormalization group , 2001 .

[43]  P Onorato,et al.  Crossover from the Luttinger-liquid to Coulomb-blockade regime in carbon nanotubes. , 2005, Physical review letters.

[44]  Paul W. Ayers,et al.  On the Distribution of Eigenvalues of Grand Canonical Density Matrices , 2002 .

[45]  B. A. Hess,et al.  Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach , 2002, cond-mat/0204602.

[46]  Kimihiko Hirao,et al.  Theoretical study of the π→π* excited states of linear polyenes: The energy gap between 11Bu+ and 21Ag− states and their character , 1998 .

[47]  S. Rommer,et al.  CLASS OF ANSATZ WAVE FUNCTIONS FOR ONE-DIMENSIONAL SPIN SYSTEMS AND THEIR RELATION TO THE DENSITY MATRIX RENORMALIZATION GROUP , 1997 .

[48]  Yuansheng Jiang,et al.  Theoretical study of the lowest π →π* excitation energies for neutral and doped polyenes , 2005 .

[49]  Emily A. Carter,et al.  Local correlation in the virtual space in multireference singles and doubles configuration interaction , 2003 .

[50]  P. Tavan,et al.  Electronic excitations in finite and infinite polyenes. , 1987, Physical review. B, Condensed matter.

[51]  Martin Schütz,et al.  Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction (T) , 2000 .

[52]  Garnet Kin-Lic Chan,et al.  Density-matrix renormalization-group algorithms with nonorthogonal orbitals and non-Hermitian operators, and applications to polyenes. , 2005, The Journal of chemical physics.

[53]  Martin Head-Gordon,et al.  A local correlation model that yields intrinsically smooth potential-energy surfaces. , 2005, The Journal of chemical physics.

[54]  E. Carter,et al.  Size extensive modification of local multireference configuration interaction. , 2004, The Journal of chemical physics.

[55]  Östlund,et al.  Thermodynamic limit of density matrix renormalization. , 1995, Physical review letters.

[56]  J. Catalán,et al.  On the ordering of the first two excited electronic states in all-trans linear polyenes. , 2004, The Journal of chemical physics.