Energy-based automatic determination of buffer region in the divide-and-conquer second-order Møller-Plesset perturbation theory

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.

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

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, quantum-mechanical 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.

Energy-based automatic determination of buffer region in the divide-and-conquer second-order Møller-Plesset perturbation theory

In the linear‐scaling divide‐and‐conquer (DC) electronic structure method, each subsystem is calculated together with the neighboring buffer region, the size of which affects the energy error introduced by the fragmentation in the DC method. The DC self‐consistent field calculation utilizes a scheme to automatically determine the appropriate buffer region that is as compact as possible for reducing the computational time while maintaining acceptable accuracy (J. Comput. Chem. 2018, 39, 909). To extend the automatic determination scheme of the buffer region to the DC second‐order Møller–Plesset perturbation (MP2) calculation, a scheme for estimating the subsystem MP2 correlation energy contribution from each atom in the buffer region is proposed. The estimation is based on the atomic orbital Laplace MP2 formalism. Based on this, an automatic buffer determination scheme for the DC‐MP2 calculation is constructed and its performance for several types of systems is assessed.