We describe in detail our high-performance density matrix renormalization group (DMRG) algorithm for solving the electronic Schrodinger equation. We illustrate the linear scalability of our algorithm with calculations on up to 64 processors. The use of massively parallel machines in conjunction with our algorithm considerably extends the range of applicability of the DMRG in quantum chemistry.
We describe in detail our high-performance density matrix renormalization group (DMRG) algorithm for solving the electronic Schrodinger equation. We illustrate the linear scalability of our algorithm with calculations on up to 64 processors. The use of massively parallel machines in conjunction with our algorithm considerably extends the range of applicability of the DMRG in quantum chemistry.
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.
We present, to the best of our knowledge, the first attempt to exploit the super-computer platform for quantum chemical density matrix renormalization group (QC-DMRG) calculations. We have developed the parallel scheme based on the in-house MPI global memory library, which combines operator and symmetry sector parallelisms, and tested its performance on three different molecules, all typical candidates for QC-DMRG calculations. In case of the largest calculation, which is the nitrogenase FeMo cofactor cluster with the active space comprising 113 electrons in 76 orbitals and bond dimension equal to 6000, our parallel approach scales up to approximately 2000 CPU cores.
There has been recent interest in the deployment of ab initio density matrix renormalization group (DMRG) computations on high performance computing platforms. Here, we introduce a reformulation of the conventional distributed memory ab initio DMRG algorithm that connects it to the conceptually simpler and advantageous sum of the sub-Hamiltonian approach. Starting from this framework, we further explore a hierarchy of parallelism strategies that includes (i) parallelism over the sum of sub-Hamiltonians, (ii) parallelism over sites, (iii) parallelism over normal and complementary operators, (iv) parallelism over symmetry sectors, and (v) parallelism within dense matrix multiplications. We describe how to reduce processor load imbalance and the communication cost of the algorithm to achieve higher efficiencies. We illustrate the performance of our new open-source implementation on a recent benchmark ground-state calculation of benzene in an orbital space of 108 orbitals and 30 electrons, with a bond dimension of up to 6000, and a model of the FeMo cofactor with 76 orbitals and 113 electrons. The observed parallel scaling from 448 to 2800 central processing unit cores is nearly ideal.
In the past two decades, the density matrix renormalization group (DMRG) has emerged as an innovative new method in quantum chemistry relying on a theoretical framework very different from that of traditional electronic structure approaches. The development of the quantum chemical DMRG has been remarkably fast: it has already become one of the reference approaches for large-scale multiconfigurational calculations. This perspective discusses the major features of DMRG, highlighting its strengths and weaknesses also in comparison with other novel approaches. The method is presented following its historical development, starting from its original formulation up to its most recent applications. Possible routes to recover dynamical correlation are discussed in detail. Emerging new fields of applications of DMRG are explored, such as its time-dependent formulation and the application to vibrational spectroscopy.
We study the recently developed Density Matrix Renormalization Group (DMRG) algorithm in the context of quantum chemistry. In contrast to traditional approaches, this algorithm is believed to yield arbitrarily high accuracy in the energy with only polynomial computational effort. We describe in some detail how this is achieved. We begin by introducing the principles of the renormalization procedure, and how one formulates an algorithm for use in quantum chemistry. The renormalization group algorithm is then interpreted in terms of familiar quantum chemical concepts, and its numerical behavior, including its convergence and computational cost, are studied using both model and real systems. The asymptotic convergence of the algorithm is derived. Finally, we examine the performance of the DMRG on widely studied chemical problems, such as the water molecule, the twisting barrier of ethene, and the dissociation of nitrogen. In all cases, the results compare favorably with the best existing quantum chemical methods, and particularly so when the nondynamical correlation is strong. Some perspectives for future development are given.
Abstract: In the last decades, many algorithms have been developed to use high-performance computing (HPC) techniques to accelerate the density matrix renormalization group (DMRG) method, an effective method for solving large active space strong correlation problems. In this article, the previous DMRG parallelization algorithms at different levels of the parallelism are introduced. The heterogeneous computing acceleration methods and the mixed-precision implementation are also presented and discussed. This mini-review concludes with some summary and prospects for future works.