We introduce a new database SC1MC-2020 of artificial mono transition metal complexes involving reference data (HF energy, orbitals, and integrals), and one- and two-site entropies obtained from corresponding DMRG calculations. The purpose of this database is to include all important metal - ligand interactions of strongly correlated systems and obtain as much as possible information about the electronic correlation structure, which could be exploited by machine learning models to estimate these important information almost immediately for any similar systems with high degree of transferability.
We introduce a new database SC1MC-2020 of artificial mono transition metal complexes involving reference data (HF energy, orbitals, and integrals), and one- and two-site entropies obtained from corresponding DMRG calculations. The purpose of this database is to include all important metal - ligand interactions of strongly correlated systems and obtain as much as possible information about the electronic correlation structure, which could be exploited by machine learning models to estimate these important information almost immediately for any similar systems with high degree of transferability.
We introduce a new version of the database SC1MC (SC1MC-2022), obtained by extension of the recent SC1MC-2020, which includes artificial mono transition metal complexes. The database involves reference data used as inputs for training of machine learning models, one- and two-site entropies, and mutual information obtained at the DMRG level for canonical and split-localised orbitals. The purpose of this database is to obtain as much as possible information about the electronic correlation structure, which could be exploited by machine learning models to estimate these important information without a significant computational cost for any similar type of systems with some degree of transferability.
Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe(II)-porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.
The active-space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial, but a non-trivial task. In this article, we present the neural network (NN) based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed from one transition metal and various ligands, on which we have performed DMRG and calculated single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our ML models could correctly predict the importance of orbitals with the high accuracy. Also, the ML models show a high degree of transferability on systems much larger than any complex used in training procedures.
Strong electron correlation in transition-metal chemistry motivates both advanced classical solvers, such as the density matrix renormalization group (DMRG), and quantum algorithms, but a claim of quantum utility requires a converged classical baseline. This baseline is established for a concrete problem, the C–O stretching signature of CO on small Mn clusters (M = Cu, Ag, Au, Pd, Pt; n = 2–5). Shifts and adsorption energies of 35 complexes from PBE0/def2-TZVPP full numerical Hessians, corrected with CCSD(T) and tested against six further functionals, are organized by site coordination: top-site CO shifts by +6 to −108 cm −1 , bridgesite CO by −202 to −387 cm −1 , and hollow-site CO by −339 to −508 cm −1 , separated by at least 94 cm −1 , more than the estimated uncertainty of 15–20 cm −1 . Multireference diagnostics test the classical hierarchy. CASSCF with 8 and 12 active orbitals gives linear minima for CuCO and AuCO, which contradicts the bent minima of PBE0. DMRG for eight cluster complexes with up to 36 active orbitals and 61 electrons changes by 0.5 m E h or less between bond dimensions 500 and 1000 and takes 0.3–2.8 h per complex. Seven complexes are weakly entangled (largest single-orbital entropy 0.21–0.26), whereas top-site Pt5CO is moderately multiconfigurational (0.62). A noiseless UCCSD variational quantum eigensolver (VQE) reproduces CASSCF in 16-qubit active spaces only to within 2.0–4.3 m E h , above chemical accuracy. For these systems classical methods suffice, and entanglement screening with DMRG is proposed as the test that a candidate system must pass before quantum advantage is sought.
The acceleration of exact continuous time quantum Monte Carlo (CTQMC) approaches in multi-site or multi-orbital systems is extremely interesting work, because these approaches are very time-consuming in terms of numerical computation and might account for the nature of exotic behaviors such as high-temperature superconductivity and Mott insulator behavior observed in the strongly correlated materials. We extend the recently developed interaction-expansion CTQMC method in combination with a machine learning (CTQMC+ML) approach for the single-site and single-orbital systems to multi-site and multi-orbital ones. This method can be applied to explore the nonlocal correlation effects in lattice models and to study the electronic structure of real materials via an ab-initio density functional theory plus dynamical mean field theory approach. We find that our CTQMC+ML method for multi-site (and multi-orbital) systems accurately predicts the impurity Green’s function with less computational time than the CTQMC approaches, as in the case of the single-site and single-orbital version.
This article presents an efficient and parallelized implementation of the density matrix renormalization group (DMRG) algorithm for quantum chemistry calculations. The DMRG method as a large-scale multireference electronic structure model is by nature particularly efficient for one-dimensionally correlated systems, while the present development is oriented toward applications for polynuclear transition metal compounds, in which the macroscopic one-dimensional structure of electron correlation is absent. A straightforward extension of the DMRG algorithm is proposed with further improvements and aggressive optimizations to allow its application with large multireference active space, which is often demanded for metal compound calculations. Special efficiency is achieved by making better use of sparsity and symmetry in the operator and wave function representations. By accomplishing computationally intensive DMRG calculations, the authors have found that a large number of renormalized basis states are required to represent high entanglement of the electron correlation for metal compound applications, and it is crucial to adopt auxiliary perturbative correction to the projected density matrix during the DMRG sweep optimization in order to attain proper convergence to the solution. Potential energy curve calculations for the Cr(2) molecule near the known equilibrium precisely predicted the full configuration interaction energies with a correlation space of 24 electrons in 30 orbitals [denoted by (24e,30o)]. The energies are demonstrated to be accurate to 0.6mE(h) (the error from the extrapolated best value) when as many as 10,000 renormalized basis states are employed for the left and right DMRG block representations. The relative energy curves for [Cu(2)O(2)](2+) along the isomerization coordinate were obtained from DMRG and other correlated calculations, for which a fairly large orbital space (32e,62o) is modeled as a full correlation space. The DMRG prediction nearly overlaps with the energy curve from the coupled cluster with singles, doubles, and perturbative triple [CCSD(T)] calculations, while the multireference complete active space self-consistent field (CASSCF) calculations with the small reference configuration (8e,8o) are found to overestimate the biradical character of the electronic state of [Cu(2)O(2)](2+) according to the one-electron density matrix analysis.