Quantum chemistry using the density matrix renormalization group II

200

288

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 E h precision͒ 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.

Section: Sweep and Error Convergencesupporting

confidence: 74%

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

Hachmann¹,

Cardoen²,

Chan³

2006

200

288

“…[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

277

392

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.

“…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 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.