Accelerated One-Step Density Matrix Renormalization Group Self-Consistent Field Method

Tsubasa Iino

Dominika Zgid, Marcel Nooijen

We present the density matrix renormalization group self-consistent field (DMRG-SCF) approach that is analogous to the complete active space self-consisted field (CASSCF) method but instead of using for the description of the active space the full configuration interaction (FCI) method, the DMRG-SCF uses the density matrix renormalization group (DMRG) method. The DMRG-SCF approach, similarly to CASSCF, properly describes the multiconfigurational character of the wave function but avoids the exponential scaling of the FCI method and replaces it with a polynomial scaling. Hence, calculations for a larger number of orbitals and electrons in the active space are possible since the DMRG method provides an efficient tool to automatically select from the full Hilbert space the many-body contracted basis states that are the most important for the description of the wave function.

Haibo Ma, Ulrich Schollwöck, Zhigang Shuai

Im Fachbereich Physik

Dominika Zgid

Despite the success of modern quantum chemistry in predicting properties of organic molecules, the treatment of inorganic systems, which have many close lying states, remains out of quantitative reach for current methods. To treat non-dynamic correlation, we take advantage of the density matrix renormalization group (DMRG) method that has become very successful in the field of solid state physics. We present a detailed study of the DMRG method, and we pay special attention to the evolution of the understanding behind the mathematical structure of the DMRG wave function. Our primary goal is to develop a density matrix renormalization group self--consistent--field (DMRG-SCF) approach, analogous to the complete active space self--consistent field (CASSCF) method, but dealing with large active spaces that are too demanding for the full configuration interaction (FCI) method. \nAs a first step towards such a DMRG-SCF procedure, we present a spin-adapted DMRG algorithm designed to target spin- and spatial-symmetry states that are hard to obtain while using an unrestricted algorithm. \nOur next step is a modification of the DMRG algorithm to obtain decreasing energy at every step during the sweep. This monotonically convergent DMRG scheme lets us obtain the two-body density matrix as a by--product of the existing procedure without any additional cost in storage. Additionally, the two-body density matrix produced at convergence using this scheme is free from the N-representability problem that is present when the two--body density matrix is produced with the two-site DMRG scheme without additional storage cost. Finally, taking advantage of the modifications developed herein, we present results obtained from our DMRG-SCF method. Lastly, we discuss possible ways of incorporating dynamical correlation into the DMRG scheme, in order to obtain a modern multireference approach.

Jiaao Su, Wei Huang, Yinxuan Song +1 more

Accurate prediction of nuclear magnetic resonance (NMR) shielding constants for strongly correlated systems remains challenging. In this context, we present a density matrix renormalization group self-consistent-field (DMRG-SCF) implementation for NMR shielding calculations with large active spaces. Within a gauge-including atomic orbital DMRG-SCF (GIAO-DMRG-SCF) framework, we formulate and solve the coupled-perturbed DMRG-SCF (CP-DMRG-SCF) equations using local-site effective Hamiltonians. This approach enables the direct evaluation of the wave function's response to an external magnetic field. In the limit of small active spaces, the computed NMR shieldings are in agreement with conventional complete active space self-consistent-field (CASSCF) results, while the present approach naturally extends to larger active spaces inaccessible to standard multiconfigurational methods. Applications to a series of molecular systems, particularly strongly correlated transition metal complexes, demonstrate that the proposed implementation can be both reliable and accurate.