Linear-scaling divide-and-conquer second-order Møller–Plesset perturbation calculation for open-shell systems: implementation and application

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

It has long been clear that electron correlation methods exhibit unphysical compute scalings with molecular size, which has motivated the development of local correlation methods to discard effectively zero contributions in a controlled way to yield an approximate correlation energy. The ideal local correlation method should have a single numerical threshold that controls the dropping of terms with the ability to have that threshold set small enough so that the correlation energy is reproduced to enough significant figures such that the result is chemically identical. This work reports such a method for the second-order Møller-Plesset (MP2) theory. The theory, implementation, and testing of this local MP2 theory are reported. Thresholds ranging from 10-5 to 10-8 and basis sets ranging from split valence plus polarization through to quadruple-ζ are assessed for local MP2 calculations on a range of molecules, including linear chains and molecules with two- and three-dimensional character. The implementation is shared memory parallel via OpenMP and yields roughly 50% parallel efficiency with 16 cores for a large job. Considerable efforts were made to minimize memory demands, which increased as thresholds were tightened. A variety of relative energy calculations are presented as a function of threshold to provide some guidance to users on how to obtain adequate precision at a low compute cost. It is particularly clear that derivative properties require tighter thresholds in order to achieve an adequate precision.

A double exponential coupled cluster theory in the fragment molecular orbital framework

Fragmentation-based methods enable electronic structure calculations for large chemical systems through partitioning them into smaller fragments. Here, we have developed and benchmarked a dual exponential operator-based coupled cluster theory to account for high-rank electronic correlation of large chemical systems within the fragment molecular orbital (FMO) framework. Upon partitioning the molecular system into several fragments, the zeroth order reference determinants for each fragment and fragment pair are constructed in a self-consistent manner with two-body FMO expansion. The dynamical correlation is induced through a dual exponential ansatz with a set of fragment-specific rank-one and rank-two operators that act on the individual reference determinants. While the single and double excitations for each fragment are included through the conventional rank-one and rank-two cluster operators, the triple excitation space is spanned via the contraction between the cluster operators and a set of rank-two scattering operators over a few optimized fragment-specific occupied and virtual orbitals. Thus, the high-rank dynamical correlation effects within the FMO framework are computed with rank-one and rank-two parametrization of the wave operator, leading to significant reduction in the number of variables and associated computational scaling over the conventional methods. Through a series of pilot numerical applications on various covalent and non-covalently bonded systems, we have shown the quantitative accuracy of the proposed methodology compared to canonical, as well as FMO-based coupled-cluster single double triple. The accuracy of the proposed method is shown to be systematically improvable upon increasing the number of contractible occupied and virtual molecular orbitals employed to simulate triple excitations.

GPU-Accelerated Large-Scale Excited-State Simulation Based on Divide-and-Conquer Time-Dependent Density-Functional Tight-Binding

The present study implemented the divide-and-conquer time-dependent density-functional tight-binding (DC-TDDFTB) code on a graphical processing unit (GPU). The DC method, which is a linear-scaling scheme, divides a total system into several fragments. By separately solving local equations in individual fragments, the DC method could reduce slow central processing unit (CPU)-GPU memory access, as well as computational cost, and avoid shortfalls of GPU memory. Numerical applications confirmed that the present code on GPU significantly accelerated the TDDFTB calculations, while maintaining accuracy. Furthermore, the DC-TDDFTB simulation of 2-acetylindan-1,3-dione displays excited-state intramolecular proton transfer and provides reasonable absorption and fluorescence energies with the corresponding experimental values. © 2019 Wiley Periodicals, Inc.

RAQET: Large-scale two-component relativistic quantum chemistry program package

The Relativistic And Quantum Electronic Theory (RAQET) program is a new software package, which is designed for large-scale two-component relativistic quantum chemical (QC) calculations. The package includes several efficient schemes and algorithms for calculations involving large molecules which contain heavy elements in accurate relativistic formalisms. These calculations can be carried out in terms of the two-component relativistic Hamiltonian, wavefunction theory, density functional theory, core potential scheme, and evaluation of electron repulsion integrals. Furthermore, several techniques, which have frequently been used in non-relativistic QC calculations, have been customized for relativistic calculations. This article introduces the brief theories and capabilities of RAQET with several calculation examples. © 2018 Wiley Periodicals, Inc.

Computerized implementation of higher-order electron-correlation methods and their linear-scaling divide-and-conquer extensions

We have implemented a linear-scaling divide-and-conquer (DC)-based higher-order coupled-cluster (CC) and Møller-Plesset perturbation theories (MPPT) as well as their combinations automatically by means of the tensor contraction engine, which is a computerized symbolic algebra system. The DC-based energy expressions of the standard CC and MPPT methods and the CC methods augmented with a perturbation correction were proposed for up to high excitation orders [e.g., CCSDTQ, MP4, and CCSD(2)_TQ ]. The numerical assessment for hydrogen halide chains, polyene chains, and first coordination sphere (C1) model of photoactive yellow protein has revealed that the DC-based correlation methods provide reliable correlation energies with significantly less computational cost than that of the conventional implementations. © 2017 Wiley Periodicals, Inc.

The divide-and-conquer second-order proton propagator method based on nuclear orbital plus molecular orbital theory for the efficient computation of proton binding energies

An efficient computational method to evaluate the binding energies of many protons in large systems was developed.

Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems

Recent developments in the fragment molecular orbital (FMO) method for theoretical formulation, implementation, and application to nano and biomolecular systems are reviewed. The FMO method has enabled ab initio quantum-mechanical calculations for large molecular systems such as protein-ligand complexes at a reasonable computational cost in a parallelized way. There have been a wealth of application outcomes from the FMO method in the fields of biochemistry, medicinal chemistry and nanotechnology, in which the electron correlation effects play vital roles. With the aid of the advances in high-performance computing, the FMO method promises larger, faster, and more accurate simulations of biomolecular and related systems, including the descriptions of dynamical behaviors in solvent environments. The current status and future prospects of the FMO scheme are addressed in these contexts.