Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

Abstract

Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674−5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantummechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.

Analytic Gradient for Time-Dependent Density Functional Theory Combined with the Fragment Molecular Orbital Method

“…Quantum-mechanical (QM) methods provide a general framework for computing molecular properties. Large-scale QM calculations are time-consuming, and a variety of approaches have been proposed to reduce the cost, including various fragment-based methods. − …”

Cluster-in-Molecule Local Correlation Method for Dispersion Interactions in Large Systems and Periodic Systems

“…Nakai and co-workers have developed a divide-and-conquer (DC) electron correlation method based on AO-based partial summation of correlation energies in subsystems. 30 Some direct and cluster-based local correlation methods have also been extended to condensed-phase systems with periodic boundary conditions (PBCs), 31 such as the LMP2 method, 32−34 the DEC method, 35 and our own CIM method. 3,4 Compared to the canonical electron correlation methods based on Bloch orbitals (with either atomic basis sets 36,37 or plane wave basis sets 38−40 In this Account, we will review the developments of the CIM local correlation approach and its applications in describing structures, relative stability, and binding (or absorption) energies of a wide range of large molecules and periodic systems, in which the dispersion interaction plays an essential role.…”

“…A series of different approaches have been developed for large molecules or clusters, which include, for example, the generalized energy-based fragmentation (GEBF) approach, the systematic molecular fragmentation approach, the fragment molecular orbital approach, the molecular tailoring approach, etc. Nakai and co-workers have developed a divide-and-conquer (DC) electron correlation method based on AO-based partial summation of correlation energies in subsystems . Some direct and cluster-based local correlation methods have also been extended to condensed-phase systems with periodic boundary conditions (PBCs), such as the LMP2 method, − the DEC method, and our own CIM method. , Compared to the canonical electron correlation methods based on Bloch orbitals (with either atomic basis sets , or plane wave basis sets − ), local correlation methods have much lower scaling with respect to the unit cell size and k points and thus can treat systems with quite large cells unavailable to canonical methods.…”

Local Second-Order Møller–Plesset Theory with a Single Threshold Using Orthogonal Virtual Orbitals: Theory, Implementation, and Assessment

“…65−67 Implementation has been extended to include GPUs, 68 as well as massively parallel computing. 52,69 Novel ideas continue to be put forward, including an algorithm for the opposite spin MP2 energy 70,71 that avoids two-electron integrals 72 and another that employs Slater orbitals. 73 This diversity of approaches reflects the fact that the problem of developing an optimal fast MP2 framework cannot be viewed as fully solved despite all of the progress we have briefly reviewed.…”

“…Other highly effective local MP2 methods have also been reported. As an alternative to the iterative solution of linear equations for the first-order correlation amplitudes, the Laplace transform approach replaces the solver with a fixed number of quadrature points. , With use of localized orbitals, this becomes a basis for competitive fast local MP2 methods. ,− Another family of fast methods is the divide and conquer paradigm − as well as the divide–expand–consolidate approach. , Other fragmentation ideas have also led to highly efficient fast local MP2 methods. − Tensor hypercontraction ideas have also been applied to MP2 to lower the formal scaling. − Combinations of these ideas have also proven effective. − Implementation has been extended to include GPUs, as well as massively parallel computing. , Novel ideas continue to be put forward, including an algorithm for the opposite spin MP2 energy , that avoids two-electron integrals and another that employs Slater orbitals . This diversity of approaches reflects the fact that the problem of developing an optimal fast MP2 framework cannot be viewed as fully solved despite all of the progress we have briefly reviewed.…”