Toward Large-Scale Restricted Active Space Calculations Inspired by the Schmidt Decomposition

Abstract

We present an alternative, memory-efficient, Schmidt decomposition-based description of the inherently bipartite restricted active space (RAS) scheme, which can be implemented effortlessly within the density matrix renormalization group (DMRG) method via the dynamically extended active space procedure. Benchmark calculations are compared against state-of-the-art results of C2 and Cr2, which are notorious for their multireference character. Our results for ground and excited states together with spectroscopic constants demonstrate that the proposed novel approach, dubbed as DMRG-RAS, which is variational and free of uncontrolled method errors, has the potential to outperfom conventional methods for strongly correlated molecules.

Predicting the FCI Energy of Large Systems to Chemical Accuracy from Restricted Active Space Density Matrix Renormalization Group Calculations

“…Next, using the predicted full-CI energy, E RAS-X = −2086.891, we show in Figure 7c that the linear scaling on double logarithmic axes for different values is recovered, as expected. Comparing our result to multireference configuration interaction (MRCI), coupled cluster singles, doubles, and perturbative triples (CCSD(T)), coupled cluster singles, doubles and triples (CCSDT), and coupled cluster singles, doubles, triples and quadruples (CCSDTQ) 27 (E = −2086.7401, −2086.8785, −2086.8675, −2086.8689, respectively), we conclude that our data point E 0 (17, 2) = −2086.8769 is already below the CCSDTQ by 8 × 10 −3 . The extrapolated energy is E RAS-X = 2086.891 (p RAS-X = 1.88) using all 14 data points in the figure.…”

“…We remark here that the -dependence hinges on a good choice of the CAS space and on the chosen basis. 27,62 Since the orbitals lying close to the Fermi surface possess the largest one-orbital entropies, 25 a selection based on orbital entropy together with keeping the almost fully occupied orbitals in the CAS space is an efficient protocol. 25,46,63 Let us also note that a very accurate extrapolation procedure requires to perform CAS and DMRG-RAS calculations for various χ values for each in order to perform an extrapolation to the DMRG truncation-free limit, i.e, to obtain = E ( lim E ( )…”

“…Therefore, the main question to be answered is the error dependence on . We remark here that the -dependence hinges on a good choice of the CAS space and on the chosen basis. , Since the orbitals lying close to the Fermi surface possess the largest one-orbital entropies, a selection based on orbital entropy together with keeping the almost fully occupied orbitals in the CAS space is an efficient protocol. ,, …”

“…Although the main features of the electronic states are often characterized by the static correlations, the contributions of an intractable number of high-energy excited configurations with small weights, i.e., dynamical effects, can be crucial for an accurate theoretical description in light of experimental data. 16,17 Quite recently, a cross-fertilization of the conventional restricted active space (RAS) scheme 18−22 with the density matrix renormalization group (DMRG) method 23,24 via the dynamically extended active space procedure 25,26 has emerged as a new powerful method 27 to capture both static and dynamic correlations, and numerical benchmarks on molecules with notorious multireference characters have revealed various advantages of the new method compared to conventional approaches. 21,28−31 Furthermore, mapping of quantum lattice models to an ab initio framework paves the road to attack challenging problems that are untractable by conventional approaches.…”

“…Quite recently, a cross-fertilization of the conventional restricted active space (RAS) scheme − with the density matrix renormalization group (DMRG) method , via the dynamically extended active space procedure , has emerged as a new powerful method to capture both static and dynamic correlations, and numerical benchmarks on molecules with notorious multireference characters have revealed various advantages of the new method compared to conventional approaches. ,− Furthermore, mapping of quantum lattice models to an ab initio framework paves the road to attack challenging problems that are untractable by conventional approaches. − The dramatic reduction of entanglement for higher-dimensional lattice models via Fermionic mode transformation , also makes the resulting ab intio problems excellent candidates for the DMRG-RAS method.…”