Abstract The accurate evaluation of electron correlations is highly necessary for the proper descriptions of the electronic structures in strongly correlated molecules, ranging from bond‐dissociating molecules, polyradicals, to large conjugated molecules and transition metal complexes. For this purpose, in this paper, a new ab‐initio quantum chemistry program Kylin 1.0 for electron correlation calculations at various quantum many‐body levels, including configuration interaction (CI), perturbation theory (PT), and density matrix renormalization group (DMRG), is presented. Furthermore, fundamental quantum chemistry methods such as Hartree‐Fock self‐consistent field (HF‐SCF) and the complete active space SCF (CASSCF) are also implemented. The Kylin 1.0 program possesses the following features: (1) a matrix product operator (MPO) formulation‐based efficient DMRG implementation for describing static electron correlation within a large active space composed of more than 100 orbitals, supporting both and symmetries; (2) an efficient second‐order DMRG‐self‐consistent field (SCF) implementation; (3) an externally contracted multi‐reference CI (MRCI) and Epstein‐Nesbet PT with DMRG reference wave functions for including the remaining dynamic electron correlation outside the large active spaces. In this paper, we introduce the capabilities and numerical benchmark examples of the Kylin 1.0 program.
Abstract The accurate evaluation of electron correlations is highly necessary for the proper descriptions of the electronic structures in strongly correlated molecules, ranging from bond‐dissociating molecules, polyradicals, to large conjugated molecules and transition metal complexes. For this purpose, in this paper, a new ab‐initio quantum chemistry program Kylin 1.0 for electron correlation calculations at various quantum many‐body levels, including configuration interaction (CI), perturbation theory (PT), and density matrix renormalization group (DMRG), is presented. Furthermore, fundamental quantum chemistry methods such as Hartree‐Fock self‐consistent field (HF‐SCF) and the complete active space SCF (CASSCF) are also implemented. The Kylin 1.0 program possesses the following features: (1) a matrix product operator (MPO) formulation‐based efficient DMRG implementation for describing static electron correlation within a large active space composed of more than 100 orbitals, supporting both and symmetries; (2) an efficient second‐order DMRG‐self‐consistent field (SCF) implementation; (3) an externally contracted multi‐reference CI (MRCI) and Epstein‐Nesbet PT with DMRG reference wave functions for including the remaining dynamic electron correlation outside the large active spaces. In this paper, we introduce the capabilities and numerical benchmark examples of the Kylin 1.0 program.
Accurate evaluation of electron correlations is essential for the reliable quantitative description of electronic structures in strongly correlated systems, including bond-dissociating molecules, polyradicals, large conjugated molecules, and transition metal complexes. To provide a user-friendly tool for studying such challenging systems, our team developed Kylin 1.0 [J. Comput. Chem. 44, 1316 (2023)], an ab initio quantum chemistry program designed for efficient density matrix renormalization group (DMRG) and post-DMRG methods, enabling high-accuracy calculations with large active spaces. We have now further advanced the software with the release of Kylin 1.3, featuring optimized DMRG algorithms and an improved tensor contraction scheme in the diagonalization step. Benchmark calculations on the Mn4CaO5 cluster demonstrate a remarkable speed-up of up to 16 fater than Kylin 1.0. Moreover, a more user-friendly and efficient algorithm [J. Chem. Theory Comput. 17, 3414 (2021)] for sampling configurations from DMRG wavefunction is implemented as well. Additionally, we have also implemented a spin-adapted version of the externally contracted multi-reference configuration interaction (EC-MRCI) method [J. Phys. Chem. A 128, 958 (2024)], further enhancing the program’s efficiency and accuracy for electron correlation calculations.
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.
Abstract The accurate electronic structure calculation for strongly correlated chemical systems requires an adequate description for both static and dynamic electron correlation, and is a persistent challenge for quantum chemistry. In order to account for static and dynamic electron correlations accurately and efficiently, in this work we propose a new method by integrating the density matrix renormalization group (DMRG) method and multi-reference second-order Epstein–Nesbet perturbation theory (ENPT2) with a selected configuration interaction (SCI) approximation. Compared with previous DMRG-based dynamic correlation methods, the DMRG-ENPT2 method extends the range of applicability, allowing us to efficiently calculate systems with very large active space beyond 30 orbitals. We demonstrate this by performing calculations on H 2 S with an active space of (16e, 15o), hexacene with an active space of (26e, 26o) and 2D H 64 square lattice with an active space of (42e, 42o).
Thanks to the high compression of the matrix product state (MPS) form of the wave function and the efficient site-by-site iterative sweeping optimization algorithm, the density matrix normalization group (DMRG) and its time-dependent variant (TD-DMRG) have been established as powerful computational tools in accurately simulating the electronic structure and quantum dynamics of strongly correlated molecules with a large number (10 1–2 ) of quantum degrees of freedom (active orbitals or vibrational modes). However, the quantitative characterization of the quantum many-body behaviors of realistic strongly correlated systems requires a further consideration of the interaction between the embedded active subsystem and the remaining correlated environment, e.g., a larger number (10 2–3 ) of external orbitals in electronic structure or infinite condensed-phase phononic modes in nucleus dynamics. To this end, we introduced three new post-DMRG and TD-DMRG approaches, namely (1) DMRG2sCI-MRCI and DMRG2sCI-ENPT by the reconstruction of selected configuration interaction (sCI) type of compact reference function from DMRG coefficients and the use of externally contracted MRCI (multireference configuration interaction) and Epstein–Nesbet perturbation theory (ENPT), without recourse to the expensive high order n -electron reduced density matrices ( n -RDMs). (2) DMRG combined with RR-MRCI (renormalized residue-based MRCI), which improves the computational accuracy and efficiency of internally contracted (ic) MRCI by renormalizing the contracted bases with small-sized buffer environment(s) of a few external orbitals as probes based on quantum information theory. (3) HM (hierarchical mapping)-TD-DMRG in which a large environment is reduced to a small number of renormalized environmental modes (which accounts for the most vital system–environment interactions) through stepwise mapping transformation. These advances extend the efficacy of highly accurate DMRG/TD-DMRG computations to the quantitative characterization of the electronic structure and quantum dynamics in realistic strongly correlated systems coupled with large environments and are reviewed in this paper.
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.
The ab initio density matrix renormalization group (DMRG) method has been well-established and has become one of the most accurate numerical methods for the precise electronic structure solution of large active spaces. In the past few years, to capture the missing dynamic correlation, various post-DMRG approaches have been proposed through the combination of DMRG and multireference quantum chemical methods or density functional theory. With this in mind, this work provides a brief overview of ab initio DMRG principles and the new developments within post-DMRG methods. For clarity, post-DMRG methods are classified into two main categories depending on whether high-order n -electron reduced density matrices are used, and their merits and disadvantages are properly discussed. Finally, we conclude by discussing unsolved bottlenecks and giving development perspectives of post-DMRG approaches, which are expected to yield quantitative descriptions of complex electronic structures in large strongly correlated molecules and materials.