Multilayer Divide-Expand-Consolidate Coupled-Cluster Method: Demonstrative Calculations of the Adsorption Energy of Carbon Dioxide in the Mg-MOF-74 Metal–Organic Framework

Abstract

The implementation and evaluation of a multilayer extension of the divide-expand-consolidate (DEC) scheme within the LSDalton program is presented. The DEC scheme is a linear-scaling, fragmentation-based local coupled-cluster (CC) method that provides a means of overcoming the scaling wall associated with canonical CC electronic structure calculations on large molecular systems. Taking advantage of the local nature of correlation effects, the correlation energy for the full molecule is calculated from a set of independent fragments using localized molecular orbitals. However, when only a small subsystem of a larger system is of interest, for example, adsorption sites or catalytically active sites, the majority of the computational time may be spent evaluating the correlation energy of fragments which have little effect on the properties in the area of interest (AOI). The multilayer DEC (ML-DEC) scheme addresses this by taking advantage of the independent nature of the fragments in order to evaluate the correlation energy of various regions of the system at different levels of theory. Regions far from the AOI are evaluated at lower (cheaper) levels of theory such as Hartree−Fock (HF) or Møller−Plesset second-order perturbation theory (MP2), while the area immediately surrounding the AOI is treated with a higher level CC model. Through the ML-DEC scheme, the computational cost of CC calculations on these types of systems can be significantly reduced while maintaining the accuracy of higher-level calculations. Results from HF/RI-MP2 and RI-MP2/CCSD ML-DEC calculations of the binding energy of a fatty acid dimer are presented. We find that the ML-DEC scheme is capable of reproducing DEC energy differences at a target level of theory, provided that the region treated at the target level of theory is chosen to be sufficiently large. Time-tosolution is found to be significantly reduced, particularly in the RI-MP2/CCSD calculations. Finally, the ML-DEC scheme is applied to the calculation of CO 2 adsorption in a Mg-MOF-74 channel.

Coupled cluster theory on modern heterogeneous supercomputers

“…In the second phase, each fragment’s contribution would be added to obtain the complete description and total electronic energy of the entire molecule. This straightforward yet effective subdividing technique for computing the total energy of large systems embodies the core concept behind the Divide-Expand-Consolidate (DEC) scheme for correlated electron methods ( Eriksen et al, 2015a ; Ettenhuber et al, 2016 ; Kjærgaard et al, 2017a ; Kjærgaard et al, 2017b ; Barnes et al, 2019 ).…”

Analytical Gradient Using Cluster-in-Molecule RI-MP2 Method for the Geometry Optimizations of Large Systems

“…These methods can be classified into two categories. The first, often referred to as direct local correlation methods, treats the entire molecule at once by omitting insignificant contributions. − The second category is the cluster-based methods, obtaining the total correlation energy as the sum of contributions from smaller clusters containing a subset of occupied LMOs and their virtual orbitals. − Although both direct and cluster-based methods can achieve a linear scaling computational cost with the system size, the cluster-based methods require much less storage and thus are applicable to much larger systems. Resolution-of-the-identity (RI) − approximation, a technique employed to accelerate electronic structure calculations by approximating the four-index two-electron integrals with two- and three-index integrals, can be combined with local correlation methods to further reduce the computational costs.…”

Parametrization of Nonbonded Force Field Terms for Metal–Organic Frameworks Using Machine Learning Approach

“…The accuracy–efficiency dilemma is especially acute for MOFs due to their hybrid organic–inorganic nature and the relatively large sizes of the unit cells (the typical number of atoms is hundreds or even thousands). The level of theory used to describe host–guest interactions depends on the specific task faced by researchers; a broad set of approximations, differing in electronic coarse graining, have been applied. , Ab initio methods based on Møller–Plesset second-order perturbation theory and coupled cluster approaches provide accurate binding energies. − Due to the high computational demands, MOF–adsorbate systems are represented as cluster models that contain adsorption sites and gas molecules, resulting in a loss of a reliable description of the dispersion interactions. The hybrid quantum mechanics/molecular mechanics approach has been successfully adopted to solve this issue .…”