Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene

We present two efficient and intruder-free methods for treating dynamic correlation on top of general multi-configuration reference wave functions-including such as obtained by the density matrix renormalization group (DMRG) with large active spaces. The new methods are the second order variant of the recently proposed multi-reference linearized coupled cluster method (MRLCC) [S. Sharma, A. Alavi, J. Chem. Phys. 143, 102815 (2015)], and of N-electron valence perturbation theory (NEVPT2), with expected accuracies similar to MRCI+Q and (at least) CASPT2, respectively. Great efficiency gains are realized by representing the first-order wave function with a combination of internal contraction (IC) and matrix product state perturbation theory (MPSPT). With this combination, only third order reduced density matrices (RDMs) are required. Thus, we obviate the need for calculating (or estimating) RDMs of fourth or higher order; these had so far posed a severe bottleneck for dynamic correlation treatments involving the large active spaces accessible to DMRG. Using several benchmark systems, including first and second row containing small molecules, Cr2, pentacene and oxo-Mn(Salen), we shown that active spaces containing at least 30 orbitals can be treated using this method. On a single node, MRLCC2 and NEVPT2 calculations can be performed with over 550 and 1100 virtual orbitals, respectively. We also critically examine the errors incurred due to the three sources of errors introduced in the present implementation -calculating second order instead of third order energy corrections, use of internal contraction and approximations made in the reference wavefunction due to DMRG.

Section: Oxo-mn(salen)mentioning

confidence: 99%

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

Sharma

Knizia

Guo

et al. 2017

“…In combination with a self-consistent-field orbital optimization ansatz (DMRG-SCF) [25][26][27] , active orbital spaces of about five to six times the CASSCF limit are accessible. The selection of a suitable active orbital space is a tedious procedure, but may be automatized 28,29 .…”

Section: Introductionmentioning

confidence: 99%

“…This ansatz was first exploited for DMRG-SCF in the [augmented Hessian (AH)] Newton-Raphson-like (NR) implementation by Ghosh and co-workers 26 and Wouters et al 36,37 . Its implementation was also described by Ma and Ma 38 who, in addition, presented a pilot DMRG-SCF implementation of the Werner-Meyer (WM) MCSCF algorithm 39 .…”

Section: Introductionmentioning

confidence: 99%

Second-Order Self-Consistent-Field Density-Matrix Renormalization Group

Knecht

Keller

et al. 2017

We present a matrix-product state (MPS)-based quadratically convergent densitymatrix renormalization group self-consistent-field (DMRG-SCF) approach. Following a proposal by Werner and Knowles (J. Chem. Phys. 82, 5053, (1985)), our DMRG-SCF algorithm is based on a direct minimization of an energy expression which is correct to second-order with respect to changes in the molecular orbital basis. We exploit a simultaneous optimization of the MPS wave function and molecular orbitals in order to achieve quadratic convergence. In contrast to previously reported (augmented Hessian) Newton-Raphson and super-configuration-interaction algorithms for DMRG-SCF, energy convergence beyond a quadratic scaling is possible in our ansatz.Discarding the set of redundant active-active orbital rotations, the DMRG-SCF energy converges typically within two to four cycles of the self-consistent procedure.

“…CASSCFbased methods are among the most robust available and have the advantage of systematic convergence via expansions of the active space, but they suffer from the need * Electronic mail: eneuscamman@berkeley.edu for state-averaging and combinatorially growing costs. More recent methods offering systematic convergence include full configuration interaction quantum Monte Carlo (FCI-QMC) [6,7] and the density matrix renormalization group [8,9], although these also have combinatorially growing costs in general.…”

Section: Introductionmentioning

confidence: 99%

Equation of Motion Theory for Excited States in Variational Monte Carlo and the Jastrow Antisymmetric Geminal Power in Hilbert Space

Zhao

Neuscamman

2016

An equation of motion formalism for excited states in variational Monte Carlo is derived and a pilot implementation for the Jastrow-modified antisymmetric geminal power is tested. In single excitations across a range of small molecules, this combination is shown to be intermediate in accuracy between configuration interaction singles and equation of motion coupled cluster with singles and doubles. For double excitations, energy errors are found to be similar to those for coupled cluster.