QC-DMRG study of the ionic-neutral curve crossing of LiF

Legeza, Örs; Röder, Johannes; Heß, Bernd A.

doi:10.1080/0026897031000155625

Cited by 135 publications

(154 citation statements)

References 24 publications

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“…[6][7][8][9][10][11] After early attempts to use the DMRG as a full configuration interaction (FCI) method for small molecules, 7,10,[12][13][14] it was recognised that DMRG is best used to describe non-dynamical correlation in active spaces. The DMRG algorithm exhibits a cost scaling of O(k 3 …”

Section: Introductionmentioning

confidence: 99%

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

Sharma¹,

Chan²

2012

The Journal of Chemical Physics

277

392

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We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett. 57, 852 (2002)] to quantum chemical Hamiltonians. This involves using a quasi-density matrix, to ensure that the renormalized DMRG states are eigenfunctions ofŜ 2 , and the Wigner-Eckart theorem, to reduce overall storage and computational costs. We argue that the spin-adapted DMRG algorithm is most advantageous for low spin states. Consequently, we also implement a singlet-embedding strategy due to Tatsuaki [Phys. Rev. E 61, 3199 (2000)] where we target high spin states as a component of a larger fictitious singlet system. Finally, we present an efficient algorithm to calculate one-and two-body reduced density matrices from the spin-adapted wavefunctions. We evaluate our developments with benchmark calculations on transition metal system active space models. These include the Fe 2 S 2 , [Fe 2 S 2 (SCH 3 ) 4 ] 2− , and Cr 2 systems. In the case of Fe 2 S 2 , the spin-ladder spacing is on the microHartree scale, and here we show that we can target such very closely spaced states. In [Fe 2 S 2 (SCH 3 ) 4 ] 2− , we calculate particle and spin correlation functions, to examine the role of sulfur bridging orbitals in the electronic structure. In Cr 2 we demonstrate that spin-adaptation with the Wigner-Eckart theorem and using singlet embedding can yield up to an order of magnitude increase in computational efficiency. Overall, these calculations demonstrate the potential of using spin-adaptation to extend the range of DMRG calculations in complex transition metal problems.

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Section: Introductionmentioning

confidence: 99%

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

Sharma¹,

Chan²

2012

The Journal of Chemical Physics

277

392

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“…Different attempts to avoid the length of configurational expansions are the density matrix renormalization group method, [72][73][74][75] the variational density matrix method, 76,77 and the iterative configuration interaction method. 78 In order to make contact with physical reality, all orbitalconfiguration-based wavefunctions and/or energies must be extrapolated to the "complete basis set ͑CBS͒ limit."…”

Section: Introductionmentioning

confidence: 99%

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

Bytautas

Nagata

Gordon

et al. 2007

The Journal of Chemical Physics

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The recently introduced method of correlationenergy extrapolation by intrinsic scaling (CEEIS) is used to calculate the nonrelativistic electron correlations in the valence shell of the F2 molecule at 13 internuclear distances along the ground state potential energy curve from 1.14Åto8Å, the equilibrium distance being 1.412Å. Using Dunning's correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlationenergies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail. The recently introduced method of correlation energy extrapolation by intrinsic scaling ͑CEEIS͒ is used to calculate the nonrelativistic electron correlations in the valence shell of the F 2 molecule at 13 internuclear distances along the ground state potential energy curve from 1.14 Å to 8 Å, the equilibrium distance being 1.412 Å. Using Dunning's correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail.

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“…[163] the symmetric reverse Cuthill-Mckee reordering, which attempts to make t i j as band-diagonal as possible, was shown to lead to faster convergence in m and the number of finite-system sweeps as compared to Hartree-Fock ordering. Improvement was also obtained by optimizing the ordering using the Fock term which contains contributions from both t i j and parts of the interaction V i jkl [164]. Ideas from Quantum Information Theory also seem to be important: Legeza and Sólyom [109] have shown that the profile along the chain of the entanglement entropy between single sites and the rest of the system is important.…”

Section: Dynamicsmentioning

confidence: 99%

Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

Noack¹,

Manmana²

2005

AIP Conference Proceedings

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Abstract. In these lecture notes, we present a pedagogical review of a number of related numerically exact approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson's Numerical Renormalization Group (NRG) and White's Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low-dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.

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QC-DMRG study of the ionic-neutral curve crossing of LiF

Cited by 135 publications

References 24 publications

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

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