The density matrix renormalization group self-consistent field method: Orbital optimization with the density matrix renormalization group method in the active space

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%

“…The first approach 23,25 exploits the generalized Brillouin theorem 30 where orbital changes are obtained from the coefficients of a so-called 'Super-CI' procedure 2,31,32 consisting of the DMRG-SCF wave function and all Brillouin singly excited configurations. Such an orbital-optimization scheme is implemented in many popular quantum chemical packages, for example, in Molcas 7 and Orca 33 .…”

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.

“…Since the computational cost of traditional CASSCF scales exponentially with the number of active orbitals and electrons, tractable active orbital spaces are presently limited to about 18 electrons in 18 orbitals 29 . These limitations can be overcome by resorting to the density matrix renormalization group (DMRG) approach [30][31][32][33] in quantum chemistry [34][35][36][37][38][39][40][41][42][43][44] which, in combination with a self-consistent-field orbital optimization ansatz (DMRG-SCF) 45,46 , is capable of approximating CASSCF wave functions to chemical accuracy with merely a polynomial scaling.…”

Section: Introductionmentioning

confidence: 99%

A Nonorthogonal State-Interaction Approach for Matrix Product State Wave Functions

Knecht

Keller

Autschbach

et al. 2016

We present a state-interaction approach for matrix product state (MPS) wave functions in a nonorthogonal molecular orbital basis. Our approach allows us to calculate for example transition and spin-orbit coupling matrix elements between arbitrary electronic states provided that they share the same one-electron basis functions and active orbital space, respectively. The key element is the transformation of the MPS wave functions of different states from a nonorthogonal to a biorthonormal molecular orbital basis representation exploiting a sequence of non-unitary transformations following a proposal by Malmqvist (Int. J. Quantum Chem. 30, 479 (1986)). This is well-known for traditional wave-function parametrizations but has not yet been exploited for MPS wave functions.